Technical Report Documentation Page 

1. Report No. 

FHWA-SA-02-054 

2. Government Accession No. 3. Recipient’s Catalog No. 

5. Report Date 

September 2002 

4. Title and Subtitle 

GEOTECHNICAL ENGINEERING CIRCULAR NO. 6 

Shallow Foundations 6. Performing Organization Code 

7. Author(s) 

Robert E. Kimmerling 

8. Performing Organization Report No. 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) 

PanGEO, Inc. 

3414 N.E. 55th Street 

Seattle, Washington 98105 

11. Contract or Grant No. 

DTFH61-00-C-00031 

13. Type of Report and Period Covered 

Technical Manual 

12. Sponsoring Agency Name and Address 

Office of Bridge Technology 

Federal Highway Administration 

HIBT, Room 3203 

400 Seventh Street, S.W. 

Washington, D.C. 20590 

14. Sponsoring Agency Code 

15. Supplementary Notes 

Contracting Officer’s Technical Representative: Chien-Tan Chang (HIBT) 

FHWA Technical Consultant: Jerry DiMaggio (HIBT) 

16. Abstract 

This document is FHWA’s primary reference of recommended design and procurement 

procedures for shallow foundations. The Circular presents state-of-the-practice guidance on the 

design of shallow foundation support of highway bridges. The information is intended to be 

practical in nature, and to especially encourage the cost-effective use of shallow foundations 

bearing on structural fills. To the greatest extent possible, the document coalesces the research, 

development and application of shallow foundation support for transportation structures over the 

last several decades. 

Detailed design examples are provided for shallow foundations in several bridge support 

applications according to both Service Load Design (Appendix B) and Load and Resistance Factor 

Design (Appendix C) methodologies. Guidance is also provided for shallow foundation 

applications for minor structures and buildings associated with transportation projects. 

17. Key Words 

Shallow foundation, spread footing, 

abutment, mat foundation, bearing capacity, 

settlement, eccentricity, overturning, sliding, 

global stability, LRFD 

18. Distribution Statement 

No Restrictions. This document is available to the 

public from the National Technical Information 

Service, Springfield, Virginia 22161 

19. Security Classification (of this report) 20. Security Classification (of this page) 21. No. of Pages 

310 

22. Price 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
NOTICE

The information in this document has been funded wholly or in part by the U.S. Department of 

Transportation, Federal Highway Administration (FHWA), under Contract No. DTFH61-00-C00031 to PanGEO, Inc. The document has been subjected to peer and administrative review by 

FHWA and has been approved for publication as a FHWA document. 

The contents of this report reflect the views of the author, who is responsible for the facts and 

accuracy of the data presented herein. The contents do not necessarily reflect the policy of the 

Department of Transportation. This report does not constitute a standard, specification or 

regulation. The United States Government does not endorse products or manufacturers. 

Mention of trade names or commercial products does not constitute endorsement or 

recommendation for use by either the author or FHWA.
GEOTECHNICAL ENGINEERING CIRCULAR NO. 6 

SHALLOW FOUNDATIONS 

PREFACE

This document is the sixth in a series of Geotechnical Engineering Circulars (GEC) developed by 

the Federal Highway Administration (FHWA). This Circular focuses on the design, procurement 

and construction of shallow foundations for highway structures. The intended users are 

practicing geotechnical, foundation and structural engineers involved with the design and 

construction of transportation facilities. 

Other circulars in this series include the following: 

- GEC No. 1 – Dynamic Compaction (FHWA-SA-95-037) 

- GEC No. 2 – Earth Retaining Systems (FHWA-SA-96-038) 

- GEC No. 3 – Design Guidance: Geotechnical Earthquake Engineering for 

Highways, Volume I – Design Principles (FHWA-SA-97-076) 

Volume II – Design Examples (FHWA-SA-97-077) 

- GEC No. 4 – Ground Anchors and Anchored Systems (FHWA-SA-99-015) 

- GEC No. 5 – Evaluation of Soil and Rock Properties (FHWA-IF-02-034) 

- GEC No. 7 – Soil Nailing (under development)

This Circular is intended to be a stand-alone document geared toward providing the practicing 

engineer with a thorough understanding of the analysis and design procedures for shallow 

foundations on soil and rock, with particular emphasis on bridges supported on spread footings. 

Accordingly, the manual is organized as follows: 

• Chapters 1 and 2 present background information regarding the applications of shallow 

foundations for transportation structures. 

• Chapters 3 and 4 present methods used to perform foundation type selection, including 

the minimum level of subsurface investigation and laboratory testing needed to support 

design of shallow foundations. 

• Chapter 5 presents the soil mechanics theory and methods that form the basis of shallow 

foundation design. 

• Chapter 6 describes the shallow foundation design process for bridge foundation support 

on spread footings. Chapters 5 and 6, together with the detailed bridge foundation 

design examples presented in Appendix B, provide the practical information 

necessary to complete shallow foundation design for a highway bridge. 

i 
• Chapters 7 and 8 discuss the application and special spread footing design considerations 

for minor transportation structures and buildings. 

• Chapters 9 and 10 provide guidelines for procurement and construction monitoring of 

shallow foundations. 

• Appendix A provides recommended materials specifications for embankments 

constructed to support shallow foundations. The appendix also includes example 

material specifications used by state highway agencies that design and construct spread

footings in compacted structural embankments. 

• Appendix B includes five worked design examples of shallow foundations for highway 

bridges based on Service Load Design methodology. 

• Appendix C includes practical guidance on the use of Load and Resistance Factor Design 

(LRFD) methodology for shallow foundation design and reworks two of the design 

examples from Appendix B using LRFD. 

This Circular was developed for use as a desktop reference that presents FHWA 

recommended practice on the design and construction of shallow foundations for 

transportation structures. To the maximum extent possible, this document incorporates the 

latest research in the subject matter area of shallow foundations and their transportation 

applications. Attention was given throughout the document to ensure the compatibility of its 

content with that of reference materials prepared for the other FHWA publications and training 

modules. Special efforts were made to ensure that the included material is practical in 

nature and represents the latest developments in the field.

ii 
ACKNOWLEDGMENTS

Special thanks are given to the state highway agency personnel who contributed to the collection 

of data regarding the state of the practice in using shallow foundations for support of highway 

bridges. The Nevada, Michigan and Washington State Departments of Transportation are 

especially acknowledged for providing the case history data included in this Circular. 

Notable and much appreciated contributions to the design examples included in this Circular 

were provided by Messrs. George Machan, Will Shallenberger and Kenji Yamasaki of Cornforth 

Consultants, Inc., Portland, Oregon, and by Ms. Tiffany Adams and Mr. Siew Tan of PanGEO, 

Inc., Seattle, Washington. 

Particular gratitude is extended to Mr. Ronald G. Chassie, formerly with FHWA, Mr. Monte J. 

Smith of Sargent Engineers, Inc., Olympia, Washington, and Mr. James L. Withiam of 

D’Appolonia, Monroeville, Pennsylvania for their extremely helpful technical review, input and 

commentary provided on the document. 

For her superior technical editing and outstanding positive attitude during the final production of

this document, the author extends heartfelt thanks to Ms. Toni Reineke of Author’s Advantage, 

Seattle, Washington. 

Last but not least, the author wishes to acknowledge the members of the Technical Working 

Group, Mr. Mike Adams; Mr. James Brennan; Mr. Myint Lwin; Mr. Mohammed Mulla; Dr. 

Sastry Putcha; Mr. Benjamin S. Rivers; Mr. Jésus M. Rohena; Ms. Sarah Skeen; Mr. Chien-Tan 

Chang, Contracting Officers Technical Representative; and Mr. Jerry DiMaggio for their review 

of the Circular and provision of many constructive and helpful comments. 

iii 
ENGLISH TO METRIC (SI) CONVERSION FACTORS 

The primary metric (SI) units used in civil and structural engineering are: 

• meter (m) 

• kilogram (kg) 

• second (s) 

• newton (N) 

• Pascal (Pa = N/m

2

) 

The following are conversion factors for units presented in this manual: 

Quantity 

From English 

Units 

To Metric (SI) 

Units Multiply by:

For Aid to Quick 

Mental Calculations 

Mass lb kg 0.453592 1 lb (mass) = 0.5 kg 

Force lb 

kip 

N 

kN 

4.44822 

4.44822 

1 lb (force) = 4.5 N 

1 kip (force) = 4.5 kN 

Force/unit 

length 

plf 

klf 

N/m

kN/m

14.5939 

14.5939 

1 plf = 14.5 N/m

1 klf = 14.5 kN/m

Pressure, 

stress, modulus 

of elasticity

psf 

ksf 

psi 

ksi 

Pa 

kPa 

kPa 

Mpa 

47.8803 

47.8803 

6.89476 

6.89476 

1 psf = 48 Pa 

1 ksf = 48 kPa 

1 psi = 6.9 kPa 

1 ksi = 6.9 MPa 

Length 

inch 

foot 

foot 

mm 

m 

mm 

25.4 

0.3048 

304.8 

1 in = 25 mm 

1 ft = 0.3 m 

1 ft = 300 mm 

Area 

square inch 

square foot 

square yard 

mm2

m2

m2

645.16 

0.09290304

0.83612736

1 sq in = 650 mm2

1 sq ft = 0.09 m2

1 sq yd = 0.84 m2

Volume

cubic inch 

cubic foot 

cubic yard 

mm3

m3

m3

16386.064 

0.0283168 

0.764555 

1 cu in = 16,400 mm3

1 cu ft = 0.03 m3

1 cu yd = 0.76 m3

A few points to remember: 

1. In a “soft” conversion, an English measurement is mathematically converted to its exact

metric equivalent. 

2. In a “hard” conversion, a new rounded, metric number is created that is convenient to 

work with and easy to remember. 

3. Only the meter and millimeter are used for length (avoid centimeter) 

4. The Pascal (Pa) is the unit for pressure and stress (Pa and N/m2

) 

5. Structural calculations should be shown in MPa or kPa 

6. A few basic comparisons worth remembering to help visualize metric dimensions are: 

• One mm is about 1/25 inch or slightly less than the thickness of a dime

• One m is the length of a yardstick plus about 3 inches 

• One inch is just a fraction (1/64 in) longer than 25 mm (1 in = 25.4 mm)

• Four inches are about 1/16 inch longer than 100 mm (4 in = 101.6 mm) 

• One foot is about 3/16 inch longer than 300 mm (12 in = 304.8 mm)

iv 
CHAPTER 1 

INTRODUCTION 

1.1 PURPOSE AND SCOPE

This Geotechnical Engineering Circular (GEC) coalesces more than four decades of research, 

development and practical experience in the application of shallow foundations for support of 

transportation structures. The document is intended to be a definitive desk reference for the 

transportation professional responsible for design, procurement and construction of shallow 

foundations for bridges and other transportation-related structures. 

This GEC draws heavily from previous published work by the Federal Highway Administration 

(FHWA), State (and Local) Highway Agencies (SHAs) and other authors of practical guidance 

related to shallow foundations. As such, this document generally does not represent “new” 

research but is intended to provide a single reference source for state-of-the-practice information 

on the design and construction of shallow foundations. 

The one exception to the foregoing statement is in the area of bridge support on shallow 

foundations bearing on compacted structural fills. Special attention has been given to case 

histories and design examples on the use of shallow foundations to support abutments in 

compacted approach embankments. 

1.2 BACKGROUND

Shallow foundations represent the simplest form of load transfer from a structure to the ground 

beneath. They are typically constructed with generally small excavations into the ground, do not 

require specialized construction equipment or tools, and are relatively inexpensive. In most 

cases, shallow foundations are the most cost-effective choice for support of a structure. Your 

house is most likely supported on shallow spread footings, and you probably supported that deck 

you constructed last year on pre-cast concrete pier blocks because they were inexpensive and 

easy to place. 

Bridges, however, are frequently supported on deep foundations such as driven piling. This may 

be as much a result of the continued use of past practice than for any other reason and has its 

roots not in highway construction, but railroads. The need to maintain constant and reliable 

grades over vastly differing ground conditions and topography made the choice to support 

virtually all railroad bridges on piles rather obvious. At the time of rapid rail expansion in North 

America, and all over the world, the concepts of soil mechanics and geotechnical engineering 

had not even been conceived. Railroad engineers needed a reliable way to support bridges and 

trestles, and the available technology directed them to driven piles. 

1 
As the pace of highway construction increased and eventually passed that of rail construction, 

the knowledge base for construction of bridges passed from the rail engineers to the highway 

engineers. It is likely that most of the early highway engineers were, in fact, ex-rail engineers, so 

it is not surprising that piling would be chosen to support highway bridges. 

In many cases, and for very good reasons, pile support of transportation structures is wise, if not 

essential. Waterway crossings demand protection from the potentially disastrous effects of scour 

and other water-related hazards. Poor ground conditions and transient load conditions, such as 

vessel impact or seismicity, also may dictate the use of deep foundations such as piles. In more 

recent times, congested urban and suburban environments restrict the available construction 

space. The use of deep foundations, such as shafts, that can be constructed in a smaller footprint 

may be preferable to the costs associated with shoring, subterranean utility relocation, and rightof-way acquisition that would be necessary to construct a shallow foundation. 

However, many transportation bridges are associated with upland development and interchanges. 

These locations are frequently removed from waterway hazards and are in areas with competent 

ground conditions. The engineers responsible for these structures, both geotechnical and 

structural, should be constantly on the lookout for the potential prudent and cost-effective use of 

shallow foundations. 

The fortuitous combination of good, competent ground conditions and an available source of 

good-quality, granular fill material should always be seen as an opportunity to save bridge 

construction costs. By supporting the bridge abutments within the compacted approach fills, cost

savings will be realized from the following: 

• A shortened construction schedule 

• Deletion of piles placed or driven through a good-quality, compacted fill to competent 

foundation materials 

• Reduction in concrete and steel materials costs in the case where a spread footing was 

detailed, but bearing below the approach fill 

Various studies on the use of shallow foundations yielded the following information, which 

underscores the potential cost savings that can result from the judicious use of shallow 

foundations: 

• There are currently approximately 600,000 highway bridges in the United States. The 

average replacement cost is about $500,000 per bridge. About 50 percent of the 

replacement cost is associated with the substructure. Shallow foundations can generally 

be constructed for 50 to 65 percent of the cost for deep foundations (Briaud & Gibbens, 

1995). 

• The Washington State Department of Transportation (WSDOT) constructed more than 

500 highway bridges between 1965 and 1980 with one or more abutments or piers 

supported on spread footings (DiMillio, 1982). WSDOT continues using shallow 

foundations supported in structural fills on a regular basis. 

2 
• In 1986, FHWA conducted research to evaluate the settlement performance of 21 bridge 

foundations supported on shallow foundations on cohesionless soil. This research 

demonstrated that 70 percent of the settlement of the shallow foundations occurred prior 

to placement of the bridge deck. The average post-deck settlement of the structures 

monitored was less than 6 mm (1⁄4 inch), (Gifford et al., 1987). 

The following important conclusions were drawn from this research: 

1) There is sufficient financial incentive to promote the use of shallow foundations, where 

feasible (Briaud & Gibbens, 1995); 

2) The use of shallow foundation support of bridges has a proven track record on literally 

hundreds of bridge projects (DiMillio, 1982); and 

3) Sufficient performance data exist to alleviate concerns over settlement performance of 

shallow foundations in most bridge support applications where good ground conditions 

exist (Gifford et al., 1987). 

1.3 RELEVANT PUBLICATIONS

Although the Shallow Foundations GEC is intended to be a stand-alone reference document, 

additional detail and background on the methods and procedures collectively included can be 

found in the following publications: 

• AASHTO Standard Specifications for Highway Bridges, 16th Edition, with 1997, 1998, 

1999 and 2000 Interim Revisions (AASHTO, 1996) 

• AASHTO LRFD Bridge Design Specifications, 2nd Edition, with 1999, 2000 and 2001 

Interim Revisions (AASHTO, 1998)

• NHI 13212 Soils and Foundations Workshop Reference Manual (Cheney & Chassie, 

2000) 

• NHI 132037 Shallow Foundations Workshop Reference Manual (Munfakh et al., 2000) 

• NHI 132031 Subsurface Investigation Workshop Reference Manual (Arman et al., 1997) 

• NHI 132035 Module 5 – Rock Slopes: Design, Excavation and Stabilization (Wyllie & 

Mah, 1998) 

• Foundation Engineering Handbook (Fang, 1991) 

• Soil Mechanics (Lambe & Whitman, 1969) 

• Rock Slope Engineering (Hoek & Bray, 1981) 

3 
4 

1.4 SHALLOW FOUNDATION SYSTEMS APPLICATIONS

Shallow foundations principally distribute structural loads over large areas of near-surface soil or 

rock to lower the intensity of the applied loads to levels tolerable for the foundation soils. 

Shallow foundations are used in many applications in highway projects when the subsurface 

conditions are appropriate. Such applications include bridge abutments on soil slopes or 

embankments, bridge intermediate piers, retaining walls, culverts, sign posts, noise barriers, and 

rest stop or maintenance building foundations. Footings or mats may support column loads 

under buildings. Bridge piers are often supported on shallow foundations using various 

structural configurations. 

The next chapter describes common applications for transportation structure support on shallow 

foundations. 
CHAPTER 2 

TYPES OF SHALLOW FOUNDATIONS

2.1 INTRODUCTION

The definition of a “shallow foundation” varies from author to author but generally is thought of 

as a foundation that bears at a depth less than about two times the foundation width. The 

definition is less important than understanding the theoretical assumptions behind the various 

design procedures. Stated another way, it is important to recognize the theoretical limitations of 

a design procedure that may vary as a function of depth, such as a bearing capacity equation. 

Common types of shallow foundations are shown in Figures 2-1 through 2-5. 

2.2 ISOLATED SPREAD FOOTINGS

Isolated spread footings (Figure 2-1) are designed to distribute the concentrated loads delivered 

by a single column to prevent shear failure of the bearing material beneath the footing and to 

minimize settlement by reducing the applied bearing stress. The forces, strength and plan 

dimensions of the column may govern the minimum size of an isolated spread footing. For 

bridge columns, isolated spread footings are typically greater than 3 m by 3 m (10 feet by 10 

feet). These dimensions will increase when eccentric loads are distributed to the footing. The 

size of the footing is a function of the loads distributed by the supported column and the strength 

and compressibility characteristics of the bearing materials beneath the footing. Structural 

design of the footing includes consideration for moment resistance at the face of the column and 

in the short direction of the footing, as well as shear and punching around the column. 

Figure 2-1: Isolated Spread Footing 

5 
2.3 CONTINUOUS STRIP SPREAD FOOTINGS

The most commonly used type of foundation for buildings is the continuous strip spread footing 

(Figure 2-2). Continuous or strip footings generally have a minimum length to width ratio of at 

least 5 (i.e., length > 5 x width). They support a single row of columns or a bearing wall to 

reduce the pressure on the bearing materials. These footings may tie columns together in one 

direction. Sizing and structural design considerations are similar to isolated spread footings with 

the exception that plane strain conditions are assumed to exist in the direction parallel to the long 

axis of the footing. The structural design of these footings is generally governed by beam shear 

and bending moments. 

Figure 2-2: Continuous Strip Spread Footing 

2.4 SPREAD FOOTINGS WITH CANTILEVER STEMWALLS

When a spread footing with a bearing wall is used to resist lateral loads applied by backfill, the 

foundation and the wall must perform both vertical load distribution and retaining wall functions. 

The foundation is designed to resist the resulting eccentric load, and the lateral earth pressures 

are resisted by cantilever action of the stemwall and overturning resistance provided by the 

footing. 

2.4.1 Bridge Abutments 

Bridge abutments are required to perform numerous functions, including the following: 

• Retain the earthen backfill behind the abutment 

• Support the superstructure and distribute the loads to the bearing materials below the 

spread footing 

• Provide a transition to the approach fill 

6 
• Depending on the structure type, accommodate shrinkage and temperature movements 

within the superstructure

Spread footings with cantilever stemwalls are well suited to performing these multiple functions. 

The general arrangement of a bridge abutment with spread footing and cantilever stemwall is 

shown in Figure 2-3. 

Figure 2-3: Spread Footing with Cantilever Stemwall 

at Bridge Abutment 

2.4.2 Retaining Structures 

The bases of semi-gravity concrete cantilever retaining walls (inverted “T” walls) are essentially 

shallow spread footings. The wall derives its ability to resist loads from a combination of the 

dead weight of the backfill on the heel of the wall footing and the structural cantilever of the 

stem (Figure 2-4). 

2.4.3 Building Foundations 

When a building stemwall is buried, partially buried or acts as a basement wall, the stemwall 

resists the lateral earth pressures of the backfill. Unlike bridge abutments and semi-gravity 

cantilever walls, the tops or the ends of the stemwalls are frequently restrained by other structural 

members (e.g., beams, floors, transverse interior walls, etc.) to provide additional structural 

resistance. 

7 
Figure 2-4: Semi-Gravity Cantilever Retaining Wall 

2.5 COMBINATION FOOTINGS

Combination, or combined, footings are similar to isolated spread footings except that they 

support two or more columns and are rectangular or trapezoidal in shape (Figure 2-5). They are 

primarily used when the column spacing is non-uniform (Bowles, 1996) or when isolated spread 

footings become so closely spaced that a combination footing is simpler to form and construct. 

In the case of bridge abutments, an example of a combination footing is the so-called “spillthrough” type abutment (Figure 2-6). This configuration was used during some of the initial 

construction of the Interstate freeways on new alignments where spread footings could be 

founded on competent native soils. Spill-through abutments are also used at stream crossings to 

make sure foundations are below the scour level of the stream. 

Due to the frame action that develops with combination footings, they can be used to resist large 

overturning or rotational moments in the longitudinal direction of the column row. 

There are a number of approaches for designing and constructing combined footings. The choice 

depends on the available space, load distribution among the columns supported by the footing, 

variations of soil properties supporting the footing and economics. 

8 
Figure 2-5: Combined Footing 

2

1

Original Ground

Abutment Fill

Toe of Side Slope

Toe of End Slope

Figure 2-6: Spill-Through Abutment on Combination Strip Footing 

9 
2.6 MAT FOUNDATIONS

A mat foundation consists of a single heavily reinforced concrete slab, which underlies the entire 

structure or a major portion of the structure. Mat foundations are often economical when spread 

footings would cover more than about 50 percent of the footprint of the plan area of a structure 

(Peck et al. 1974). A mat (Figure 2-7) typically supports a number of columns and/or walls in 

either direction or a uniformly distributed load (i.e., tank). The principal advantage of a mat 

foundation is its ability to bridge over soft spots and reduce differential movement. 

Structures founded on relatively weak soils or lightweight structures may be economically 

supported on mat foundations. Column and wall loads are transferred to the foundation materials 

through the mat foundation. Mat foundations distribute the loads over a large area, thus reducing 

the intensity of contact pressures. Mat foundations are designed with sufficient reinforcement 

and thickness to be rigid enough to distribute column and wall loads, minimizing differential 

settlements and tolerating larger uniform settlements. Often the mat also serves as the base floor 

level of building structures. 

Mat foundations have limited applicability for bridge support, except where large bridge piers, 

such as bascules or other movable bridge supports, have the opportunity to bear at relatively 

shallow depth without deep foundation support. This type of application may arguably be a deep 

foundation, but the design of such a pier may include consideration of the base of the bascule 

pier as a mat. Discussion of large mat foundation design is included in Section 8.6. 

A more common application of mat foundations to transportation structures might include lightly 

loaded rest or maintenance facilities such as small masonry block structures or sand storage bins 

or sheds, or box culverts constructed as a continuous structure. 

10 

REINFORCED CONCRETE MAT

Figure 2-7: Typical Mat Foundation 
2.7 SHALLOW FOUNDATIONS IN PERFORMANCE APPLICATIONS 

High quality case histories regarding shallow foundations in transportation applications are 

difficult to obtain, largely because settlement data following construction are often not recorded. 

This makes it difficult to evaluate the performance of the foundation with respect to the 

settlement predictions made during design. Several relevant case histories are documented in 

“Performance of Highway Bridge Abutments on Spread Footings” (DiMillio, 1982). These case 

histories are not reproduced here. However, three new case histories are included to highlight 

design and construction practices in use by various state highway agencies that take advantage of 

the cost savings available by constructing spread footings in compacted engineered fills and in 

competent natural ground. 

2.7.1 Case History No. 1: I-5 Kalama Interchange, Washington 

Project Background 

During Interstate construction in the 1960s and 1970s, the Washington State Highway 

Commission, later to become the Washington State Department of Transportation (WSDOT), 

constructed numerous bridges with foundation support by shallow spread footings, many of 

which were built on structural fills (DiMillio, 1982). This case history demonstrates the 

significant cost savings achievable through the process of thorough site investigation, laboratory 

testing, application of sound geotechnical engineering and follow-through during construction 

with the observational method (Peck, 1969). The observational method in this application 

included measuring settlement as a function of time during a settlement delay period following 

construction of the approach embankment. These data were used to evaluate the feasibility of

using shallow foundations at the abutments and to predict long-term settlement potential for the 

abutment footings. 

The project included design and construction of a 71-m (233-ft) long by 8.5-m (28-ft) wide, fourspan, prestressed concrete structure that provides east-west traffic access across Interstate 5 in 

Kalama, a town in southwestern Washington State. The foundation elements are numbered as 

Piers 1 through 5. Note that WSDOT calls out abutments as piers, so Piers 1 and 5 are the 

abutments. The bridge layout and the location of subsurface exploration borings are shown in 

Figure 2-8. The bridge was constructed in 1968 and 1969. 

Subsurface Conditions 

The bridge alignment is underlain by approximately 30 m (100 ft) of alluvial sediments, 

consisting of interbedded loose to medium dense sand, soft to medium stiff silt and occasional 

peat layers. Bedrock was encountered directly below the alluvium. Summary logs of three 

exploratory borings drilled along the bridge alignment are shown in Figure 2-9. Standard 

Penetration Test (SPT) N-values and moisture content test results are also indicated on the 

profile. 

11 
Note: Dimensions in feet (1 ft = 0.305 m)

Figure 2-8: Bridge Layout and Exploration Plan, I-5 Kalama Interchange 

Results of three one-dimensional consolidation tests were available and are summarized in Table 

2-1. 

Foundation Design Approach 

In light of the excessive depth of compressible soil and the high costs associated with a deep 

foundation system, the Washington State Highway Commission decided to support the bridge on 

conventional spread footings. To reduce the potential for post-construction settlement of the site 

soils and to improve the level of performance for the footings, ground improvement by means of 

preloading was performed prior to construction of the footings. During the design and planning 

phase of the project, a preload period of one year was allowed in the construction schedule. 

At least 3 m (10 ft) of compacted granular fill was maintained below the footings at the interior

piers. Up to 14 m (45 ft) of compacted granular fill was placed at the abutments (Figure 2-9). 

12 
Note: Dimensions in feet (1 ft = 0.305 m)

Figure 2-9: Subsurface Profile, I-5 Kalama Interchange 

TABLE 2-1: RESULTS OF ONE-DIMENSIONAL CONSOLIDATION TESTS, 

I-5 KALAMA INTERCHANGE 

Sample Soil Type Test Results

Test Hole 24U @ 2.9 m 

(Pier 1/West Abutment) 

Gray sandy 

silt 

Moisture = 46%; Moist unit weight = 16.5 

kN/m3

; Compression Index Cc = 0.19 

Test Hole 28U @ 5.2 m 

(Pier 5/East Abutment) 

Gray claysilt Moisture = 50%; Moist unit weight = 17.1 

kN/m3

; Compression Index Cc = 0.22 

Test Hole 28U @ 16.8 m 

(Pier 5/East Abutment) 

Gray claysilt Moisture = 49%; Moist unit weight = 16.8 

kN/m3

; Compression Index Cc = 0.24 

13 
The specification for Gravel Borrow included in Appendix A is currently used by WSDOT for 

granular fills beneath footings. This specification has not changed significantly since the time

this bridge was built. A maximum allowable bearing pressure of 3 tsf was used for sizing the 

footings. This is the presumptive value used by WSDOT for fills constructed using Gravel 

Borrow. The actual design bearing pressures were 280 kPa (2.9 tsf) for Piers 1 through 4, and 

244 kPa (2.55 tsf) for Pier 5. 

Construction Sequencing and Performance 

The preload fill was placed in two stages such that the foundation soils would gain strength 

during the Stage 1 preload operation and to reduce the potential for embankment instability. In 

mid-October 1967, Stage 1 preload fill was completed, and as much as 7.6 m (25 ft) of fill was 

placed. Stage 2 preload fill was placed about 6 months after completion of Stage 1. The total 

preload fill thickness was about 13 m (43 ft) and 14.6 m (48 ft) thick at abutment Piers 1 and 5, 

respectively. At the interior piers, the preload fill was about 7.6 m (25 ft) thick. Available data 

indicated that, in late June 1968, 0.34 m (1.1 ft) and 0.9 m (3.0 ft) of settlement had occurred 

under the preload fill at Piers 1 and 5, respectively. Settlement data for the interior piers preload 

fill are not available. 

Subsequent to the preloading, footings and columns at Piers 3 through 5 were completed in 

August 1968. Construction at Piers 1 and 2 was delayed until November 1968 because 3 months 

earlier, when Piers 3 through 5 were constructed, settlement data indicated that the rate of 

settlement of the approach fills was still excessive. 

The bridge deck was completed in December 1968. Settlement monitoring of the bridge deck 

was performed on a monthly basis for the following 4 months. At the end of the monitoring 

period in April 1969, 37 to 49 mm (0.12 to 0.16 ft) of settlement was measured at the abutments 

and 21 to 34 mm (0.07 to 0.11 ft) at the interior piers. Detailed settlement data are shown in 

Table 2-2 and are plotted in Figure 2-10. The settlement data show that vertical deflections at 

each pier are relatively uniform and differential settlement is small. Based on this data, the 

maximum angular distortion (δ′/l) between adjacent piers is less than 0.002. 

The project was completed in June 1969, and the bridge has performed well since its completion 

more than 30 years ago. The bridge as it appears today is shown in Figure 2-11. 

Costs 

Using an inflation-adjusted cost of $20 per square foot for a prestressed girder bridge in a nonwater crossing situation (source: WSDOT price records, 1975 data), the estimated contract 

amount for the EB-line under crossing was about $130,000. According to a project 

memorandum, the use of the spread footings instead of timber piles represented savings of 

approximately $25,000. The estimated savings were based on the assumption that a total of 124 

timber piles 15 to 18 m (50 to 60 ft) in length would be adequate for supporting the bridge. The 

cost savings of deleting the piling therefore represented about 20 percent of the total cost of the 

structure. 

14 
TABLE 2-2: SETTLEMENT DATA – AFTER COMPLETION OF BRIDGE 

DECK, I-5 KALAMA INTERCHANGE 

12/20/68 1/7/69 2/5/69 3/11/69 4/29/69

SE Corner of S Wing Wall 53.16 53.14 53.10 53.05 53.02 Pier 1 

SE Corner of N Wing Wall 53.13 53.10 53.05 52.97 52.97 

S Side of Deck 52.75 52.74 52.69 52.68 52.67 Pier 2 

N Side of Deck 52.77 52.75 52.70 52.68 52.66 

S Side of Deck 52.02 52.01 51.96 51.96 51.95 Pier 3 

N Side of Deck 52.01 52.00 51.95 51.95 51.93 

S Side of Deck 51.29 51.28 51.22 51.22 51.20 Pier 4 

N Side of Deck 51.26 51.25 51.19 51.18 51.15 

SE Corner of S Wing Wall 50.60 50.59 50.55 50.52 50.48 Pier 5 

SE Corner of N Wing Wall 50.59 50.57 50.52 50.49 50.45 

Note: Survey data in feet (1 ft = 0.305 m)

50.00

50.50

51.00

51.50

52.00

52.50

53.00

53.50

28-Nov-68 28-Dec-68 27-Jan-69 26-Feb-69 28-Mar-69 27-Apr-69 27-May-69

Note: Data in feet (1 ft = 0.305 m)

Figure 2-10: Settlement Following Completion of Bridge Deck, I-5 Kalama Interchange 

Acknowledgment: Al Kilian, formerly of WSDOT, collected and compiled the information for 

this case history, and Dave Jenkins of WSDOT Geotechnical Branch made this information 

available. Mike Bauer of the WSDOT Bridge and Structures Office provided the historical cost 

data. 

15 
Figure 2-11: I-5 Kalama Interchange 

2.7.2 Case History No. 2: I-580 Mt. Rose Highway Interchange, Nevada 

Project Background 

This case history is of a bridge at the Mt. Rose Highway Interchange on Interstate Highway 580, 

in Washoe County, Nevada. The bridge is the northbound I-580 overpass over Mt. Rose 

Highway and was constructed in 1994. The bridge is 107.6 m (353 ft) long and 25.8 m (84.5 ft) 

wide, and is a two-span concrete structure supported by two end abutments and an intermediate 

pier (Figure 2-12). The abutments and pier are supported by spread footings. 

Subsurface Conditions 

According to the geotechnical investigation (SHB AGRA, 1993), the site lies within a 

combination of Donner Lake Glacial Outwash and Mt. Rose Alluvial Fan Deposits. A total of 10 

borings were drilled, from which the following information was obtained. 

North Abutment Area: The predominant soil type in this area is a dense, fine- to mediumgrained silty sand to sand with varying amounts of fine to coarse gravels and cobbles. Blow 

counts (SPT N-values) generally ranged from 25 to 75, with 50 as the average. 

16 
Figure 2-12: Mt. Rose Interchange: I-580 Overcrossing at Mt. Rose Highway, Nevada 

Center Pier Area: From approximately 0.6 to 7.6 m (2 to 25 ft) below the existing surface grade, 

a medium dense to very dense, fine- to medium-grained silty sand to sand was encountered. This 

horizon contained varying amounts of fine to coarse gravels and occasional cobbles. This layer 

was underlain by 1.5 to 3.0 m (5 to 10 ft) thick, low to medium plasticity, hard clayey sand to 

clayey gravel with varying amounts of fine to coarse gravels, which graded into a very dense 

sandy gravel with depth. 

South Abutment Area: The predominant soil type in this area is a dense to very dense, fine- to 

medium-grained silty sand to sand with varying amounts of fine to coarse gravels. 

Ground water was not encountered during the field exploration and is believed to lie at depths 

greater than 30 m (100 ft) below the site. 

Foundation Design Approach 

As indicated above, the foundation soils consist primarily of dense, silty sand to sand. The 

estimated settlements of spread footings were 32 mm for the abutments and 44 to 57 mm for the 

center pier. These settlements were associated with a design bearing pressure of 190 kPa (2 tons 

17 
per square foot) and were considered to be within tolerable limits. Thus, spread footings were 

selected for the abutments and pier. Due to the sloping terrain at the abutments, the abutment 

footings were founded on both cuts and structural fills. The maximum height of the structural 

fill is about 2.5 m (8 ft). The center pier is founded on natural ground. The elevation of the 

bridge is shown in Figure 2-13. 

Figure 2-13: Elevation of Mt. Rose Interchange Bridge, I-580, Nevada 

Construction Sequencing and Performance 

The structural fills on which the footings were founded were compacted aggregate base (Nevada 

DOT designation is Type 1 Class B Aggregate Base), which consisted of crushed rock, 100 

percent passing the 37.5 mm (11⁄2 in) sieve and 1 to 12 percent passing the 75 μm (No. 200) sieve 

(other materials requirements are included in specifications in Appendix A). Construction 

specifications called for this material to be placed in lifts not exceeding 200 mm (8 in) in 

thickness, and compacted to 95 percent of the maximum density as determined by Test Method 

No. Nev. T101. (Note: T101 is based on the use of the Harvard Miniature Compaction Device.) 

Figure 2-14 shows the footing of the south abutment. 

Settlement of the bridge structure was not monitored. According to the Nevada DOT, the 

structure has performed without problems since construction. 

18 
Figure 2-14: Footing at South Abutment, I-580, Nevada 

Costs 

This bridge was part of a project that involved about 7.2 km (4.5 mi) of new Interstate highway 

with numerous structures. The total construction cost of the entire project was about $52.9 

million. The contract items were measured and paid on a unit-cost basis for the entire project, so 

direct comparison of individual bridge costs is not possible. However, the unit contract price to 

drive piles elsewhere on the project was $1,000 per pile, and the price for furnishing pipe piles 

was $65 per 0.3 m (1 ft). Assuming approximately 20 piles about 7.5 m (25 ft) in length had 

been driven at each abutment (and if the spread footings were not founded on structural fill), the 

cost savings based on deletion of the piles alone is estimated at $105,000. Assuming an average 

estimated cost for the entire structure of about $1,000 per square meter, the total estimated 

structure cost was about $2.8 million. The costs savings of using spread footings at the 

abutments bearing in compacted structural fills are therefore estimated to be at least 4 percent of 

the overall cost of the structure. 

Acknowledgment: Parviz Noori, Todd Stefonowicz, and Jeff Palmer of Nevada DOT provided 

the information for this case history. 

19 
2.7.3 Case History No. 3: Cadillac Bypass Structure S01, Michigan 

Project Background 

The Cadillac Bypass project involves extending the limited-access US-131 around Cadillac to 

Manton, Michigan. The project includes 24 structures, 10 of which are or will be supported on 

spread footings. The entire project is scheduled for completion in 2004. 

Structure S01, one of the structures supported on spread footings, is the northbound US-131 

relocation (overpass) over S–43 Road and is 77.8 m (255.4 ft) long and 14.7 m (48.3 ft) wide. It 

is a three-span concrete structure with two abutments and two piers. Figure 2-15 shows an 

elevation of the bridge. 

Figure 2-15: Elevation of Cadillac Bypass Structure S01, Michigan 

Subsurface Conditions 

Four borings were drilled at the site, one at each at abutment and pier location. Subsurface 

conditions at the site consist of a loose sand layer, up to about 6 m (20 ft) thick, underlain by 

medium dense to very dense sand with trace fine gravel. Three borings were dry at the time of 

completion, and the fourth had a water level 2.4 m (8 ft) below the ground surface. 

Foundation Design Approach 

The abutment and pier footings were placed on structural fill (Michigan DOT designation is 

Structure Embankment). Structure Embankment was placed on the existing ground after topsoil 

removal. Abutment footings were placed on the Structure Embankment. The thickness of the 

Structure Embankment under the abutment footings was about 7.6 m (25 ft) at the centerline. 

20 
Loose soils were removed from under the pier locations and backfilled with Structure

Embankment. Pier footings were placed on Structure Embankment with a total thickness of over 

4.6 m (15 ft). Figure 2-16 shows the structural fill under and above the footings of the bridge. 

Figure 2-16: Profile Along Centerline Showing the Limits of Structural Fill, 

Cadillac Bypass Structure S01, Michigan 

Construction Sequencing and Performance 

Structure Embankment consisted of granular material with 100 percent passing the 150 mm (6 

in) sieve, 95 to 100 percent passing the 75 mm (3 in) sieve, and 0 to 15 percent passing the 75 

μm (No. 200) sieve. It was placed in lifts with a thickness of 230 mm (9 in) to 380 mm (15 in) 

and compacted to 100 percent of the Maximum Unit Weight. The Maximum Unit Weight is 

determined by a method that is equivalent to the Modified Proctor Method. The specifications 

for the embankment material are included in Appendix A. Settlement of the structure has not 

been monitored. 

Costs 

The estimated cost for the entire project is $117 million. The cost for Structure S01 alone was 

about $2.3 million. Comparative costs of pile foundations were not available, but based on a 

rule-of-thumb cost for an in-place pile of about $2,500 and an assumption that about 18 piles per 

pier would be required if spread footings were not used, the cost savings is estimated at about 

$180,000, or about 8 percent of the total structure cost. 

Acknowledgment: Richard Endres, Greg Perry and Al Rhodes of the Michigan DOT provided 

the information for this case history. 

21 
22 

2.8 PRE-CAST FOUNDATION ELEMENTS, MUDSILLS AND TEMPORARY FOOTINGS

Many bridges require temporary support, or falsework, in order to complete the permanent 

structure. Falsework is, in turn, supported on temporary foundations. Because they are 

temporary, these foundations do not need the same design considerations as permanent 

structures. For instance, frost protection is usually not required, so the temporary footings can 

bear at shallow depth or directly on the ground surface. 

However, the temporary footing still must be designed to limit the stress applied to the 

supporting soil such that a shear failure does not develop (see Section 5.2), and to limit the 

settlement to a tolerable amount (Section 5.3). The analytical procedures for checking the 

performance of a temporary footing are the same as for permanent structures (Chapters 5 and 6). 

Many transportation agencies include a requirement to perform a field plate load test (ASTM 

Test Method 1194 and AASHTO test method 235 are identical) to confirm the load-carrying 

capacity and settlement of falsework foundations. Plate load test data should be used with 

caution when a stiff, near surface crust overlies softer, saturated soils, since the depth of 

influence (see Section 3.1.5) will be less for the plate than the actual falsework foundations. In 

this case, site-specific settlement analyses should be required. 
CHAPTER 3 

SHALLOW FOUNDATION TYPE SELECTION 

3.1 GENERAL CONSIDERATIONS

In most cases, spread footings represent the most economical foundation type if they do not have 

to be installed deeply into the ground. At some limiting depth, a “shallow” foundation begins to 

behave like and have the associated construction needs of a “deep” foundation. This limiting 

depth is somewhat arbitrary but generally can be taken as about two times the least-plan

dimension of the foundation. 

The decision to use a shallow foundation for support of a structure includes checking that an 

adequate margin of safety is provided against failure of the ground below the bearing depth 

(bearing capacity failure), and checking that deformations (settlement) under expected loading 

conditions will be acceptable. Design checks will also be performed to make sure the footing 

will not slide and that it is stable (e.g., will not overturn). 

If the foundation can meet these fundamental design requirements, it also must be constructible. 

Constructability considerations are discussed in Section 3.3. 

3.1.1 Footings on Cohesionless Soils 

Granular, or cohesionless, soils are generally more suited to support of shallow foundations than 

cohesive soils, particularly when a foundation is supported on a structural fill. Cohesionless soils 

tend to be less prone to settlement under applied loads. Settlement of cohesionless soils 

generally occurs rapidly, as loads are applied. 

Special consideration should be given to situations in which the following conditions may occur 

or be present: 

• Water table close to or above the foundation bearing elevation. Saturated ground 

conditions will result in reduced effective stresses in the soils supporting the footing and 

in an associated reduction in the bearing capacity of the soil. See Section 4.4 for 

discussion of effective stress theory and computation and Chapter 5 for specific 

foundation design criteria and considerations. 

• Steep slopes near the bearing elevation of a footing. An adequate factor of safety with 

respect to global stability must be maintained over the life of the structure. 

• Presence of collapsible soils. Collapsible soils are generally stable when dry, but upon 

wetting or saturation, rapid settlement (collapse) can occur that could exceed the 

performance (settlement) criteria for the structure. Collapsible soils are regional in their

23 
occurrence. The potential for the presence of collapsible soils should be evaluated based 

on site-specific subsurface data and on local knowledge and experience. 

• Presence of seismic hazards. Seismic hazards, including liquefaction potential under 

seismic conditions, should be evaluated. If liquefaction is possible, the dynamic stability 

of the footing should be checked and the potential for dynamic settlement assessed. 

3.1.2 Footings on Cohesive Soils 

Normally consolidated cohesive soils (clays) will experience consolidation settlement when 

subjected to an increase in stress such as that applied by a shallow foundation. The consolidation 

process and the procedure for calculating consolidation settlement are described in Section 5.3. 

Normally consolidated cohesive soils may also exhibit relatively low shear strength when loaded 

rapidly. This is an undrained loading condition. Therefore, both the bearing capacity of such 

soils and the potential for short- and long-term settlement must be evaluated as part of the 

preliminary design process when considering support of a shallow foundation on cohesive soils. 

Because cohesive soils can experience large increases and decreases in volume as a result of 

changes in water content, bridge foundations should not be supported on embankments 

constructed of such materials. Expansive clays in natural conditions can also experience large 

volume changes. If clay soils are encountered at a site, the expansive potential should be 

evaluated as part of the site investigation and laboratory testing program before confirming the 

suitability of spread footings supported on the natural clay soils. Additional information on the 

identification of expansive soils can be found in the Subsurface Investigation Workshop 

Reference Manual (Arman et al., 1997). 

Lightly overconsolidated cohesive soils (e.g., materials with over-consolidation ratios (OCR) of 

about 1 to 2) may also experience consolidation settlement in primary (virgin) compression 

under the range of stresses applied by a spread footing. Serviceability must be checked during 

the foundation type selection process to make sure total and differential settlements are within 

the acceptable performance range for the structure. 

Heavily overconsolidated cohesive soils with OCRs greater than about 3 or 4 represent the most 

suitable cohesive soil conditions for consideration of support of shallow foundations. Heavily 

overconsolidated clays possess relatively high strength and low compressibility characteristics. 

3.1.3 Footings on Intermediate Geomaterials (IGMs) and Rock 

Intermediate geomaterial (IGM) is a term for ground conditions that are dense and stiff enough 

to no longer be characterized as a “soil” but are not considered intact “rock” (O’Neill et al., 

1996). Even so, the term is convenient for discussions of ground conditions that differ in a 

geologic sense, but that behave similarly from an engineering perspective. IGMs include 

materials such as glacial till, completely weathered rock, poorly to moderately indurated 

sediments and chemically cemented materials. These materials may occur as the transition from

overburden soil to intact rock. The term IGM is therefore rather broad in its definition and may 

carry regional connotations that are not consistent from location to location. For example, what 

24 
may be considered “soft” sedimentary rock in one part of the world may be considered elsewhere 

to be so weak that it should be treated, for engineering purposes, as a soil. 

For the purpose of shallow foundation discussions here, IGMs are considered to be sufficiently 

strong and stiff such that design considerations other than the strength of the material (e.g., 

overturning potential) will typically govern the design of a shallow foundation supported on such 

a material. Note that by their nature, IGMs may demand consideration of rock-like 

characteristics, such as mass structure and discontinuities. 

Where an IGM or rock material is at or near the ground surface, the most economical foundation 

system to support highway structures will usually be a shallow foundation bearing in or on the 

IGM or rock. Three basic types of shallow foundations on IGMs or rock are shown in Figure 

3-1. 

IGM or Intact Rock

Backfill Backfill

Potential Plane of

Weakness

Backfill

 (a) (b) (c) 

Figure 3-1: Typical Shallow Foundations on IGM or Rock for 

Highway and Bridge Structures 

Figure 3-1(a) illustrates a shallow footing founded directly on a relatively horizontal or mildly 

sloping, stable IGM or rock surface. 

Figure 3-1(b) shows a shallow foundation near the crest of an IGM or rock slope. The 

geotechnical design of foundations near the crest of a slope should include detailed consideration 

of global stability, including planar, wedge, sliding and toppling failure mechanisms of the 

supporting slope. The potential for slope instability in IGMs and rock may be a function of the 

intact mass strength properties, orientation and condition of unfavorable structure or 

discontinuities (e.g., bedding, joints, foliations, etc.) or both. The stability analysis of IGM and 

rock slopes is not presented in detail here. The reader is referred to NHI Module 5, “Rock 

Slopes” (Wyllie & Mah, 1998) and Rock Slope Engineering (Hoek & Bray, 1981) for detailed 

discussions of rock slope stability analysis and design. 

When supporting structures with large horizontal or uplift loads, shallow foundations may need 

to be tied into the IGM or rock to provide sufficient resistance to uplift and lateral forces and 

overturning moments, as portrayed in Figure 3-1(c). When considering design of a foundation in 

25 
IGM or rock conditions that will be required to resist large uplift or lateral loads, consideration 

should be given to the use, economics and constructability of a deep foundation socketed into the 

foundation material, as discussed in Drilled Shafts: Construction Procedures and Design 

Methods (O’Neill & Reese, 1999). Other options for resistance of uplift or lateral loads include 

micropiles and ground anchors. Refer to Micropile Design and Construction Guidelines 

Implementation Manual (Armour et al., 2000) and GEC No. 4: Ground Anchors and Anchored 

Systems (Sabatini et al., 1999) for guidance regarding these options. 

Rock and IGMs can perform as competent and reliable foundation materials. However, the 

condition of the rock or IGM must be evaluated for degree of weathering, rock strength, 

durability, and the orientation and condition of discontinuities (e.g., joints, bedding or faults). 

An IGM or rock mass can also be shattered by blasting and/or undermined by cavities that can 

compromise the capability of the material to provide reliable support for a shallow foundation. 

Heavily overconsolidated IGMs, such as glacially overridden lakebed sediments and some

residual weathered rock materials, may possess high intact strength but, if subjected to adverse 

stress changes or minimal shearing, will experience a drastic reduction in shear strength. 

Therefore, the stress history of an IGM should be considered during the foundation type 

selection process. 

The selection of a shallow foundation supported on IGM or rock should therefore include early 

assessment of global stability (including structurally controlled failure mechanisms) and the 

potential for loss of stability due to sinkhole or subterranean cavern collapse. As with shallow 

foundations bearing on soils, the design of a footing on IGM or rock should also include 

checking bearing capacity, sliding, overturning and settlement. 

3.1.4 Scour Potential 

Scour is a hydraulic erosion process that lowers the grade of a water channel or river bed. This 

erosion is caused by flowing water. Excessive removal of the material around a shallow 

foundation or undermining of a footing can cause excessive deformation or structure collapse. 

Foundations for bridges and structures located near rivers, channels and in floodplains should be 

located below the limits of scour. If the scour depth is too deep for a shallow foundation to be 

constructed using normal methods, consideration should be given to selection of a deep 

foundation system for support of the structure. Additional details regarding scour potential 

evaluation and protection are presented in Section 6.2.2. 

3.1.5 Depth of Influence and Frost Protection 

Because spread footings have plan dimensions of limited areal extent, the stress induced in the 

ground mass below the footing will diminish with depth. In general, the ground conditions at a 

depth greater than about four times the lesser plan dimension of a continuous spread footing will 

be affected by less than about ten percent of the stresses induced under the footing (2 times the 

lesser plan dimension for square or nearly square footings). Closely spaced footings can have 

overlapping zones of influence that can combine to produce a zone of influence that extends 

deeper than these rules of thumb. The procedures in Section 5.3 can be used to calculate the 

stress at a given depth and location below a spread footing. These stress distributions are used in 

Chapter 5 for evaluation of bearing capacity and settlement. 

26 
Spread footings should be designed to bear below the frost depth for local conditions, or on 

materials that are not frost susceptible. Section 6.2.3 contains additional discussion on frost 

protection. 

As can be seen from the stress bulbs in Figures 5-9 and 5-10, the depth of stress influence is a 

function of the width of the footing. The dimensions of the footing therefore play a role in the 

assessment of settlement and bearing capacity. Note that presumptive bearing capacities for 

footings on soils that can be found in the literature are typically not a function of width. This is 

one reason why presumptive values for footings on soils are not presented in this manual, and 

also why they should be used with caution, or for preliminary design purposes only. 

3.2 GEOTECHNICAL CRITERIA IN PRELIMINARY DESIGN

The geotechnical engineer should provide input to the preliminary design process. At this time

there is usually insufficient information about pier locations and bridge length to warrant detailed 

subsurface information with borings. If no existing subsurface information is available in the 

area, preliminary borings may be appropriate to gain a general understanding of the subsurface 

conditions at the site. An assessment of ground conditions based on geologic and site 

reconnaissance, supplemented with subsurface information (either from existing information or 

preliminary explorations), is critical to structure layout and configuration. Some key 

considerations may include the following. 

• Potential soft or weak ground conditions can be identified that will limit the steepness of 

embankment slopes. For bridges, this may dictate pier locations and overall structure 

length. 

• Geologic hazards, such as earthquakes, volcanic eruption, flood, tsunami, avalanche, 

landslides, collapsible ground conditions, expansive soils, liquefaction potential, etc., 

should be identified. The presence of any of these conditions at a structure site can have 

significant impact not only on foundation type selection, but also on design, cost and/or 

construction schedules. 

• Feasible foundations types should be evaluated. There may be sufficient existing 

information to conclude that shallow foundations are feasible at a site. 

Early consultation with the geotechnical engineer can help avoid costly redesign, either late in 

the project development process or during construction. 

3.3 SHORING AND CONSTRUCTION EXCAVATION REQUIREMENTS

The design of a spread footing should be both efficient and constructible. Sometimes temporary 

shoring has to be installed before a spread footing can be constructed. The designer should 

consider whether shoring will be necessary and how it can be constructed. Some of the 

questions a designer should ask prior to selection of a shallow foundation include: 

• Will normal excavation equipment be capable of constructing the footing, or will rock or

difficult ground conditions in the excavation require special equipment? The 

geotechnical engineer should consider the type of equipment that will be necessary for 

27 
28 

the excavation, based on the results of the geotechnical investigation, and provide 

sufficient commentary in the geotechnical report for the structural designer and estimator 

to adequately specify the construction requirements. 

• Will the excavation be stable under the temporary conditions, or will shoring be required 

to stabilize excavation sidewalls? The geotechnical engineer should consider the 

maximum slope angles at which the excavation slopes will stand without external 

support, and evaluate the potential for instability due to zones of weak ground and the 

location of the ground water table. 

• Will obstructions be encountered? Buried structures, utilities, old pile foundations or 

boulders can result in contractor claims for additional compensation if provisions are not 

made for relocation or removal of obstructions in the footing excavation. The 

geotechnical investigation may or may not disclose the presence of obstructions, but the 

geotechnical engineer may provide commentary in the geotechnical report when geologic 

conditions or knowledge of prior site activities indicates that obstructions may be 

encountered. Existing utility location, including physical confirmation by potholing, is 

an activity that should be completed early in design to adequately assess construction 

costs. 

• Will water be encountered in the foundation excavation? Water can pose a problem in 

the construction of shallow foundations. If there is a high water table, then consideration 

should be given to the stability of the bottom of the foundation soils just before the 

footing is placed. Softening or heaving of the bottom should be prevented. In some 

cases, dewatering and seals may be required. The geotechnical investigation should 

identify the presence and elevation of the water table below a site. The ground water 

conditions should be assessed at all times of the year, particularly when there is potential 

for seasonal variation of the water level. 
CHAPTER 4 

GEOTECHNICAL INVESTIGATION 

4.1 PRELIMINARY DESIGN

Once a bridge layout or preliminary plan of the proposed structure is available, the geotechnical 

engineer can proceed with preliminary design activities. This process and its application are 

described in the Soils and Foundations Workshop Reference Manual (Cheney & Chassie, 2000) 

and are reiterated below. Preliminary design activities should include a terrain reconnaissance, 

which is predominantly an office study that includes collecting and reviewing existing

information relevant to the project area. Sources of information include the following: 

• Topographic maps available from the U.S. Geologic Survey (USGS) or the U.S. Coast 

and Geodetic Survey 

• Geologic maps or bulletins available from the USGS or state geology agency 

• Soil survey maps available from the U.S. Department of Agriculture National 

Conservation and Resource Survey (formerly Soil Conservation Survey) 

• Well logs available from local or state water resource or protection agencies 

• Air photos available from the USGS or state or private geographic services 

• Construction records from nearby structures available from local building or highway 

jurisdictions

The last item is becoming increasingly valuable, as highway projects are frequently located in 

congested urban and suburban environments where numerous nearby existing structures, 

especially bridges, may be located. The geotechnical and subsurface information from the 

design and construction of these structures should be reviewed with judgment as to the reliability 

of the data, considering the methods available at the time of subsurface exploration. In 

particular, drilling methods may have been used that disturbed the soils, thus rendering Standard 

Penetration Test (SPT) test data unreliable. Refer to Section 4.3.1 for additional discussion on 

the performance and potential errors in the SPT test. 

The terrain reconnaissance should focus on gaining an understanding of the geologic and 

geomorphic features (landforms) likely to be present at the project site. This information should 

be used to plan the subsurface exploration program for the site. Once this information is 

reviewed and understood, a field reconnaissance should be scheduled with the bridge engineer 

and other members of the design team to discuss foundation type alternatives and to plan a 

29 
subsurface exploration accordingly. Other disciplines, such as hydraulics, environmental and 

general civil engineers can also benefit from, and provide valuable input during, the site 

reconnaissance on issues that may affect foundation type selection and location (e.g, stream

stability, environmentally sensitive areas, utility location, etc.). 

4.2 FIELD RECONNAISSANCE

The area concept of site exploration allows the geotechnical engineer to extend the results from

a limited number of explorations in a particular landform to the entire geologic deposit. The area 

concept is a powerful tool in reducing subsurface exploration costs. The application of the area 

concept is described within the context of an entire transportation project in the Soils and 

Foundations Workshop and Reference Manual (Cheney & Chassie, 2000) 

Application of the area concept requires the use of proper subsurface exploration equipment and 

techniques. An adequate site investigation can be accomplished only under the direction of a 

geotechnical engineer who knows the general limitations of the exploration equipment, as well as 

the general demands of the project. A site reconnaissance, preferably with the bridge engineer 

and other members of the design team, is recommended to assess foundation conditions, 

particularly for the purpose of foundation type selection. 

The field reconnaissance for structures should include the following: 

• Visually assess any nearby structures to determine their performance with the particular 

foundation type used. If settlement is suspected, and the original structure plans are 

available, arrange to have the structure surveyed using the original benchmark, if 

possible, to determine the magnitude of settlement experienced. If the structure is a 

bridge, review the bridge inspection reports and files to assess the performance history of 

the structure. 

• Visually assess the surface geology and geomorphology, including looking for evidence 

of slope instability, rock or boulder outcrops, erosion or debris deposits, pre-existing fills, 

performance of existing cut and fill slopes and ground water seepage or springs. 

• For water crossings, inspect any existing structure footings and the stream banks up- and 

downstream for evidence of scour. Take careful note of the streambed material. Often, 

large boulders exposed in the stream but not encountered in the borings are an indication 

of obstructions that could impact foundation construction, including shoring or 

cofferdams that may be required to construct a shallow foundation. 

• Note the location, type and depth of any existing structures or abandoned foundations that 

may infringe on the foundation for the new structure. 

• Locate subsurface and overhead utilities prior to subsurface exploration and show the 

utility locations on the bridge plans.

• Relate site conditions to proposed site exploration operations. Assess access for site 

exploration equipment, including the potential for problems with utilities (overhead and 

30 
underground), site access (temporary clearing or grading, and site restoration), private 

property (right-of-entry) or obstructions (natural or man-made).

A field reconnaissance report form should be used to record observations and notes and to serve 

as a checklist of important items to note during the reconnaissance. Figure 1 of the Soils and 

Foundations Workshop Reference Manual (Cheney & Chassie, 2000) is an example of a field 

reconnaissance form that may be used to record data pertinent to the site. 

Upon completion of the site reconnaissance, the geotechnical engineer should prepare a 

subsurface exploration plan or terrain reconnaissance report outlining the following: 

• General suitability of the site for the proposed construction, specifically, addressing the 

potentially stable end-slope configuration (affects bridge length) and likely foundation 

types. 

• Proposed exploration locations, equipment, required sampling intervals and standard test 

methods. 

• Potential problems that may impact construction and cost. 

• Beneficial shifts in alignment or pier location. 

• Expected subsurface conditions so that the field exploration crew can communicate early 

if the encountered conditions are different. 

• An estimate of subsurface exploration quantities, costs and time required for completion. 

This information will be used by a variety of people to help the geotechnical engineer obtain the 

minimum level of subsurface investigation needed for design. The plan or report should be 

distributed to anyone who needs this information to proceed with their job responsibilities and 

may include the following persons or offices: 

Bridge Engineer – The findings of the terrain reconnaissance may affect the bridge layout, 

including pier location and span length, which may, in turn, affect structure type and hence 

the performance expectations of shallow foundations. 

Project Office – The design office may be requested to assist in obtaining right-of-entry 

permission and any necessary permits. A well-prepared exploration plan that documents the 

desired access requirements and the equipment and methods proposed can aid in obtaining 

work permits or approvals for access to sensitive areas or over water. The project office will 

also be advised of any potential impacts to construction cost or schedule that may result from

ground conditions at the site. This helps avert the proverbial “search for the guilty” at later 

stages of project development and construction. 

Field Exploration Crew – The exploration plan forms the basis for future communication 

between the drill crew and the geotechnical engineer. If conditions are encountered during 

subsurface exploration that are different from those expected and described in the plan, the 

drill crew should ask the geotechnical engineer if any changes should be made to the plan. 

31 
4.3 SUBSURFACE EXPLORATIONS AND IN SITU TESTING

The procedures employed in any subsurface exploration program are dependent on a variety of 

factors that vary from site to site. However, the project design objectives and the expected site 

soil conditions have a major influence on the subsurface explorations. Further, for shallow 

foundation consideration, the extent, location and sampling of subsurface materials will be 

different than if a deep foundation is anticipated. The minimum level of subsurface exploration 

and sampling is discussed in detail in the Soils and Foundations Workshop Reference Manual

(Cheney & Chassie, 2000), in Geotechnical and Foundation Engineering, Module 1 – 

Subsurface Investigations (Arman et al., 1997), and in the Manual on Subsurface Investigations

(AASHTO, 1988) 

4.3.1 Standard Penetration Test 

Probably the most widely used field test in the United States is the Standard Penetration Test 

(SPT). Both AASHTO T-206 and ASTM D-1586 have standardized this test. Despite the 

numerous drawbacks to the test that have been noted by various authors (see Cheney & Chassie, 

2000), an extensive number of correlations have been developed based on this enormous quantity 

of data. Many of the design procedures in this Circular are based on the SPT. 

SPT testing is therefore recommended for all transportation projects due to the simplicity and 

economy of the test and the usefulness of the data obtained. The SPT may be supplemented with 

other in situ tests as discussed in Section 4.3.3. In the SPT test, a relative measure of soil density 

and a soil sample are obtained. The test consists of driving the split-spoon sampler 0.46 m (18 

in) with the 63-kg (140-lb) hammer falling through a drop of 0.76 m (30 in). The first 150-mm 

(6-in) increment is referred to as the seating load. The sum of the next two 150 mm (6-in) 

increments is known as the Standard Penetration Value (N). The soil sample obtained is 

disturbed but can be used for visual description and laboratory classification. The detailed 

procedures for conducting the test, as well as for limiting the potential errors frequently

associated with the test, are well-documented in the Soils and Foundations Workshop Reference 

Manual (Cheney & Chassie, 2000) and in Geotechnical and Foundation Engineering, Module 1 

– Subsurface Investigations (Arman et al., 1997). 

The N-values of the SPT are an indication of the relative density of cohesionless soils and the 

consistency of cohesive soil. General N-value ranges are correlated with relative density and 

consistency in Table 4-1. It is emphasized that for gravels and clays the correlations to relative 

density and consistency are rather unreliable and should serve only as general estimates. 

The SPT N-values are also frequently used to estimate strength and compressibility 

characteristics of granular soils, especially sands. The correlations shown in Figures 4-1 and 4-2 

can be used to estimate the friction angle of granular soils, which then can be used to calculate 

bearing capacity, as described in Chapter 5. Note that Figure 4-1 is a function of both the Nvalue and the effective overburden stress, σ′vo (see Section 4.4.2). Therefore, the N-value used 

to enter the chart should not be corrected for overburden stress. However, the chart assumes a 

rope and cathead operated hammer, with an assumed efficiency of about 60 percent for a 

hammer operated with two wraps of rope on the cathead. 

32 
TABLE 4-1: SOIL PROPERTIES CORRELATED WITH 

STANDARD PENETRATION TEST VALUES* 

Sands 

(reliable) 

Clays 

(relatively unreliable) 

Number of 

Blows per 0.3 

m (1 ft), N 

Relative 

Density 

Number of 

Blows per 0.3 

m ( 1 ft), N Consistency 

0 – 4 Very loose Below 2 Very soft 

4 – 10 Loose 2 – 4 Soft 

10 – 30 Medium 4 – 8 Medium

30 – 50 Dense 8 – 15 Stiff 

Over 50 Very dense 15 – 30 Very stiff 

Over 30 Hard

*Measured with 9.5 mm (3/8 in) I.D., 51 mm (2 in) O.D. sampler driven 0.3 m

(1 ft) by a 63-kg (140 lb) hammer falling 0.76 m (30 in) 

If a hammer system other than a rope and cathead is used, the N-value should be corrected to an 

efficiency of 60 percent. The correction is as follows: 

(N ) 60%

ER N60 = FIELD (4-1) 

where: N60 = SPT N-value corrected for hammer efficiency 

ER = “Energy Ratio,” the efficiency or percent of theoretical free fall energy 

delivered by the hammer system actually used 

 NFIELD = Blowcount recorded in field 

The use of automatic drop sampling hammers is increasing. Physical measurements of the 

efficiency of these hammer systems indicate ER values in the range of 70 to 90 percent, with 80 

percent commonly assumed for correction of the N-values for automatic hammers. 

For example, if an automatic hammer with an Energy Ratio (ER) of 80 percent is used to obtain 

a field SPT blowcount (NFIELD) of 30 blows per 0.3 m (1 ft), the blowcount corrected for hammer 

efficiency is: 

(30) 40

60%

80% (N ) 60%ER N60 = FIELD = =

33 
1 k/ft2

 = 1 ksf = 47.88 kPa 

1 ft. = 0.3 m 

Figure 4-1: Correlation Between Relative Density and SPT 

Resistance (NAVFAC, 1986a, after Gibbs & Holtz) 

34 
Note: Use caution in the shaded portion of the chart due to 

the potential for unreliable SPT N-values in gravels 

Figure 4-2: Correlation Between Relative Density, Material Classification and Angle of 

Internal Friction for Coarse-Grained Soils (NAVFAC, 1986a) 

4.3.2 Subsurface Exploration Program 

With regard to the scope of the subsurface program for a structure, one must carefully consider 

the small cost of a boring in relation to the foundation cost. A 65-mm (21⁄2-in) diameter drill hole 

will cost less than one 0.3-m (12-in) diameter pile. Yet the knowledge gained from that boring 

will permit the use of proper design techniques that may allow the cost-effective use of shallow 

foundations and elimination of all piles for that structure. 

The number, depth, spacing and character of tests to be made in any individual exploration 

program are so dependent upon site conditions and the type of structure and its requirements that 

no rigid rules may be established. Conceptually, the exploration program must provide sufficient 

information to allow the geotechnical engineer to assess the strength and compressibility of the 

soils within the zone of influence of the foundation. To evaluate these design considerations, the 

geotechnical engineer will need site-specific data at each pier, abutment and retaining wall, as to 

the material type, the density or consistency of the material, and the location and depth of ground 

water. 

35 
The scale of the exploration and testing program usually depends on the importance and 

criticality of the structure, the magnitude of the loading, the availability of the budget and 

funding and the limitations of project schedule. The exploration and testing programs for 

foundations supporting less critical structures will be less extensive than those for critical 

structures such as bridges, elevated highways or official buildings, etc. 

The following program will produce the minimum foundation data for a typical structure site. 

Soft ground conditions may require undisturbed sample explorations or in situ testing. 

1. As a minimum, advance one drill hole at each pier or abutment that measures over 9 

m (30 ft) in length. The drill hole pattern should be staggered at the opposite ends of 

adjacent footings. Piers or abutments over 9 m (100 ft) in length require one drill 

hole at the extremities of each element. The drill holes should be advanced using 

techniques that will allow in situ tests to be conducted in accordance with the test 

standards and that produce a hole that is stable. Appropriate drill techniques may 

include mud rotary with or without casing and continuous flight augers. Cone 

penetration tests (CPT) may be substituted for drilled test holes but should not be 

relied on solely as a method of obtaining subsurface data at a given bridge site. The 

CPT is not appropriate for all ground conditions, such as very dense soils or soil 

profiles with cobbles and boulders. Also, the CPT recovers no samples, so soil 

descriptions are based on empirical correlations, and no soil classification is possible. 

However, the readout of data is essentially continuous, so definition of soil layers is 

better than drilling and split-spoon sampling alone. 

2. Estimate the boring depth from existing data obtained during the terrain 

reconnaissance phases in conjunction with minimum requirements that are 

established to help ensure that the borings are not terminated too soon or in a soft soil 

layer. The borings should also extend past the estimated depth of influence (Section 

3.1.5), unless rock is encountered first. Minimum requirements may include criteria 

such as these: 

• The borings for structure foundations shall be terminated when a minimum 

SPT resistance of 20 blows per 0.3 m (1 foot) on the sample spoon has been 

achieved for 6 continuous meters (20 feet) of drilling, or 

• The boring shall extend 3 m (10 feet) into rock having an average recovery of 

50 percent or greater. 

Such minimum criteria should be developed based on the design requirements of the

local area and the expected subsurface conditions. More stringent criteria, such as 

higher blows for longer depths of penetration, should be specified where high lateral 

load conditions may be present (e.g., impact or seismic loads). 

3. Obtain standard split-spoon samples at 1.5-m (5-ft) intervals or at changes in material. 

Split-spoon samples at 0.75-m (21⁄2-ft) intervals are recommended for a minimum 4.5-

m (15-ft) zone beneath the elevation where spread footings may be placed on natural 

soil. These spoon samples are “disturbed” samples generally not suited for laboratory 

36 
determination of strength or consolidation parameters, but they can be used for 

general index tests (e.g., moisture content, Atterberg limits and grain-size analysis). 

Undisturbed (e.g. thin-walled or Shelby tube) samples should be obtained at 1.5-m (5-

ft) intervals in at least one boring in cohesive soils. For cohesive deposits greater 

than 9 m (30 ft) in depth, the tube sample interval can be increased to 3 m (10 ft). In 

soft clay deposits, in situ vane shear strength tests are recommended at 1.5- to 3-m (5- 

to 10-ft) intervals for measurement of intact shearing resistance. 

4. Record the Standard Penetration Test data on each drill hole in accordance with 

ASTM D-1586. This is the most economical method presently available for 

procuring useful data, regardless of the frequently cited drawbacks of the test. 

5. Instruct the drilling crew to perform a rough visual analysis of the soil samples and 

record all pertinent data on a standard drill log form. The disturbed split-spoon 

samples must be carefully sealed in plastic bags, placed in jars and sent to the soil 

mechanics laboratory for analysis. Undisturbed tube samples must be sealed and 

stored upright in a shockproof, insulated container normally constructed from

plywood and filled with cushioning material. 

6. Observe the water level in each boring, then record the depth below the top of the 

hole and the date of the reading on the drill log for the following: 

a. Water seepage or artesian pressure encountered during drilling. Artesian 

pressure may be measured by extending drill casing above the ground until 

flow stops. Report the pressure as the number of meters (feet) of head above 

ground. 

b. Water level at the end of each day and at completion of boring. 

c. Water level 24 hours (minimum) after hole completion. Long-term readings 

may require installation of a perforated plastic tube before abandoning the 

hole. 

A false indication of water level may be obtained when water is used during drilling 

and adequate time is not permitted after hole completion for the water level to 

stabilize. In low-permeability soils, such as clays, more than 1 week may be required 

to obtain accurate readings. In this case, the boring should be completed as a 

piezometer so that water levels can be measured over time. 

The reasons for obtaining this minimum data are clear; the engineer must have adequate data to 

determine the soil type and relative density or consistency, as well as the position of the static 

water level. Methods such as driving open-end rod without obtaining soil samples or taking 

water-level readings after the last soil sample was removed must be discouraged. Good

communication between the driller and the foundation engineer is essential during all phases of 

the subsurface investigation program. 

37 
4.3.3 In Situ Testing 

The SPT test is considered the minimum level of in situ testing needed to complete a foundation 

design. Other in situ tests are available that can be employed when specific site data are desired, 

or to support the implementation of a particular type of engineering analysis. In the design of 

shallow foundations, this may include attempts to measure compressibility characteristics of the 

soils below the footing directly. 

After the SPT, the cone penetration test (CPT) is probably the next most common in situ test

performed to support foundation design activities. The CPT has the advantage of collecting 

nearly continuous data as the probe is pushed into the ground. The definition of the soil layering 

is therefore more discrete and accurate than that obtained from split-spoon sampling at 1.5-m (5-

ft) intervals. Correlations to SPT N-values are available for interpretation of the CPT data. 

Drawbacks of the CPT include the limitation of material types that can be penetrated by the cone 

and the fact that no samples are recovered for material description or classification. Refer to

ASTM 3441 and “The Cone Penetrometer Test” (Riaund & Miran, 1992) for details in 

performance of the CPT and for reduction and interpretation of the data. 

Other in situ tests such as the pressuremeter test (PMT) and the flat dilatometer test can be used 

to measure the stress-strain properties of soils in situ, and have been used to predict the 

performance of shallow foundations. Refer to “The Pressuremeter Test for Highway 

Applications” (Briaud, 1989), “The Flat Dilatometer Test” (Riaund & Miran, 1992) and 

Geotechnical and Foundation Engineering, Module 1 – Subsurface Investigations (Arman et al., 

1997) for guidance on the performance and interpretation of these tests and their results. 

Recent research by Briaud and colleagues (Briaud & Gibbens, 1994, Briaud & Gibbens, 1995, 

and Briaud et al., 2000) has resulted in development of a new method of predicting shallow 

foundation settlement as a function of applied load based on in situ data obtained directly from

the PMT. This procedure has potential for improving the geotechnical engineer’s ability to 

predict settlement of a spread footing, not only under ordinary working loads, but also for higher 

loads that may be transient, such as earthquake or ice loads. The procedure and considerations 

regarding its use are presented in Section 5.3.4.3. 

4.3.4 Rock and IGM Mass Characterization 

A natural rock or intermediate geomaterial (IGM) mass is rarely a continuous, isotropic, 

homogeneous material. It can be highly variable and may be very difficult to characterize in a 

generalized manner. A rock mass is generally composed of intact or weathered blocks of rock 

separated by discontinuities (e.g., joints, bedding planes, sheared zones and faults). An IGM can 

exhibit variable zones of weathering or texture. The first step in a successful design of a footing 

on rock or IGM is to properly establish the material and discontinuity and weathering 

characteristics. The following are important characteristics for a shallow foundation design: 

• Rock lithology (such as granite, gneiss, schist, limestone, sandstone) 

• IGM genesis (e.g., weathered in place, glacially overridden, cemented) 

• Strength properties (e.g., unconfined compressive strength, cohesion intercept, frictional 

angle) 

38 
• Deformation properties (e.g., Young’s modulus, Poisson’s ratio) 

• Frequency of discontinuities (e.g., RQD) 

• Spacing (S) of discontinuities (especially with respect to foundation width) 

• Orientation of discontinuities (e.g. strike and dip, or dip and dip direction) 

• Aperture, filling, and condition (open or closed) of discontinuities 

• Degrees of weathering 

• Ground water condition 

To establish the above rock or IGM mass characteristics, the following exploration and testing 

methods as described in detail in various chapters of Geotechnical and Foundation Engineering, 

Module 1 – Subsurface Investigations (Arman et al., 1997) should be employed with proper 

planning: 

• Field reconnaissance 

• Geological mapping 

• Drilling/coring 

• Test excavation/test trench, if feasible 

• In situ testing (see Table 4-2) 

• Geophysical methods (see Table 4-2) 

• Field load testing (see Table 4-2) 

• Laboratory testing (see Table 4-2) 

In addition, Module 5, “Rock Slopes” (Wyllie & Mah, 1998) includes detailed descriptions of 

geological mapping. In this Circular, Table 4-2 summarizes the characteristics of interest and 

available in situ and laboratory tests (after Corps of Engineer Manual EM 1110-1-2908). Note 

that not all of these tests will be applicable or feasible for all rock and IGM types. Some are 

applicable for stronger and stiffer materials (e.g., borehole jacking, unconfined compression), 

while others can yield useful design information for weaker and softer IGMs (e.g., 

pressuremeter, dilatometer). 

It is common for a geotechnical engineer to provide design recommendations for a footing on 

rock or IGM based on limited data including rock type, core description, percentage of core 

recovery, Rock Quality Designation (RQD) values, and unconfined compressive strength. This 

information should be combined with the local geological knowledge, experience and judgment 

of the geotechnical engineer to develop the foundation recommendations. 

4.4 LABORATORY TESTING

To develop a laboratory testing program that will provide data useful in design, it is important to 

test the sample under conditions that either exist currently in the ground or that will occur as a 

result of shallow foundation construction and loading. This means that the stress conditions, 

moisture states and load paths imposed on the representative soil sample in the laboratory should 

match the conditions that will be experienced by the material in the field. A detailed discussion 

of laboratory testing procedures is not presented here. However, the basic concepts of laboratory 

testing of soils to determine strength and deformation characteristics are reviewed, beginning 

with a discussion of the phase relationships of the constituents of soil, continuing with an 

39 
TABLE 4-2: SUMMARY OF COMMONLY USED IN SITU AND LABORATORY 

TESTING FOR FOOTINGS ON ROCK OR IGMS (AFTER ARMAN ET AL., 1997) 

Purposes Types of In Situ/Field Tests Types of Laboratory Tests 

Shear Strength Pressuremeter 

Borehole shear test 

Torsional shear test 

Uniaxial compression 

Triaxial compression 

Direct shear 

Point load 

Tensile Strength Direct tensile strength 

Split strength (Brazilian 

tensile strength tests) 

Bearing Capacity Plate bearing load test (Same as shear strength) 

Deformability Pressuremeter 

Dilatometer

Borehole jacking 

Seismic refraction survey 

• Cross-hole 

• Down-hole 

Plate bearing load test 

Deformation moduli from: 

• Uniaxial compression 

• Triaxial compression 

Swell 

Creep 

Discontinuity Study Geologic mapping 

Geophysical methods 

• Seismic refraction 

• Ground penetrating radar 

• Electrical resistivity 

Visual observation 

Durability Slake durability

Freezing and thawing 

Void/Sinkhole Detection Ground penetrating radar 

Electrical resistivity imaging 

Microgravity 

Rock Anchor (Uplift 

Resistance) 

Anchor pull test 

Note: See Module 1, “Subsurface Investigation” (Arman et al., 1997), for detailed descriptions of each testing 

procedure. 

explanation of the principle of effective stress (which is used throughout this Circular), and 

finishing with a discussion of common laboratory tests used to determine the strength and 

deformation characteristics of soil. 

4.4.1 Phase and Volume Relationships 

Soil particles are irregularly shaped solids that are in contact with adjacent soil particles. The 

weight and volume of a soil sample depends on the specific gravity (ratio of the density of the 

soil particles to the density of water) of the soil particles (solids), the size of the space between 

40 
soil particles (void or pore space), and the amount of the void space filled with water (pore 

water). 

Soil is therefore usually a three-phase material (solid, water and gas), as shown in Figure 4-3. 

The proportion of the various phases, in terms of both weight and volume, can be represented 

schematically with the aid of the block diagram shown in Figure 4-3. 

Air

Water

Solid

Volume Weight

V

VV

VW

VS

VA 0

WW

WS

W

Note: Subscript s stands for solids, w for water, a for air and v for 

voids (the space between soil solids or alternatively, the air 

and water volumes combined). No subscripts are used

relative to weight W and volume V of the entire soil mass. 

Figure 4-3: Phase Relation Block Diagram

Relative to the block diagram, there are a number of weight-volume or phase relationships (i.e., 

ratios) that are useful in geotechnical engineering and are essential values or parameters used in 

laboratory testing. 

These relationships are summarized in Table 4-3. 

Of particular note is the void ratio, e, which is a general indicator of the relative strength and 

compressibility of a soil sample. Low void ratios generally indicate strong, incompressible soils,

and high void ratios may indicate weak, compressible soils. 

When a load is applied to a soil sample, the deformation that occurs will depend on the forces 

between the soil particles that are in contact with each other (intergranular forces) and the 

amount of water in the void space (pore water). Dry soils with no pore water in the void space 

will deform by a combination of sliding between the soil particles and deformation or crushing 

of the particles themselves. Intergranular sliding accounts for most of the deformation that 

occurs as the particles move to increase the contact area between the particles to support the 

increase in load. 

41 
TABLE 4-3: WEIGHT-VOLUME RELATIONSHIPS, DIMENSIONLESS 

RATIOS AND FUNCTIONAL RELATIONSHIPS 

Unit weight 

General definition 

V

W

γ = (4-2) 

where: γ = unit weight (F/L3

) 

W = weight, units of force, F 

V = Volume, units of length cubed, L3

Unit weight of saturated soil is also: 

V

W

γsat = (4-3)

Unit weight of soil solids

S

S

S V

W

γ = (4-4)

Unit weight of water

W

W w V

W

γ = (4-5) 

= 9.8 kN/m3

 (62.4 pcf) 

Dry unit weight

V

WS γd = (4-6)

the ratio of the weight of soil solids (only), 

WS, to the total volume V 

Buoyant (or submerged) unit weight

V

W' γ '= (4-7) 

γ '= γsat − γw (4-8) 

where W' is the buoyant weight of the soil 

mass upon complete submergence in water, 

i.e., W' = W- wγ V 

Dimensionless ratios 

Specific gravity of soil solids

W

S

S

γ

G γ = (4-9)

Void ratio (a ratio of volumes, void vs. solid) 

S

V

V

V

e = (4-10) 

Porosity (a ratio of volumes, void vs. total) 

V

V

n V = (4-11) 

Water content (a ratio of weights, water vs. 

solid) 

S

W

W

W

w = (4-12) 

Degree of saturation 

V

W

V

V S = (4-13) 

Functional relationships

Se = wGS (4-14) 

1 e

e

n

+ = ; 1 n

n

e − = (4-15) 

( )

1 e

GS Se W

+

+ γ γ = (4-16) 

1 e

S W

d +

γ = G γ (4-17) 

1 w

d +

γ γ = (4-18) 

1 w

W WS + = (4-19) 

( )

1 e

G 1 ' S W

+

− γ γ = (4-20) 

42 
Because water is essentially incompressible, the water contained in the pore space of soils that 

are saturated (i.e., pore spaces completely filled with water) is also a function of the ability for 

water to be expelled from the pore space. The permeability of a soil is a measure of the speed 

with which water molecules can pass through the pore space. The lower the permeability of a 

soil sample, the longer it takes for water to be expelled from the pore space. If a load is applied 

quickly to a soil sample with low permeability, the pore water will initially carry the load until 

the water drains from the pore space and the soil particles begin to slide and accept the load. 

While the load is still carried by the pore water, the water will experience increased, or excess, 

pore-water pressure. As the excess pore-water pressure dissipates, the soil sample will deform

into a smaller volume and a denser configuration. This process is termed “consolidation.” 

The consolidation of soil may be explained by the spring analogy shown in Figure 4-4. The 

ability of the intergranular contact areas to carry load is represented by the spring. The valve 

represents the permeability of the soil. The water inside the piston chamber and surrounding the 

spring is analogous to the pore water filling the pore space of the soil sample. 

Figure 4-4: Spring Analogy as Applied to Consolidation (Holtz and Kovacs, 1981) 

A load is applied to the piston with the valve closed (Figure 4-4a). With the valve closed, the 

incompressible water cannot be expelled, and the spring is unable to compress to accept an 

increase in load. Essentially the entire applied load is resisted by an increase in fluid pressure 

within the chamber (i.e., excess pore-water pressure). 

When the valve is opened, water will begin to escape through the valve (Figure 4-4b). As water 

escapes, the spring shortens and begins to carry an increasing proportion of the applied load. 

There is a corresponding decrease in the fluid pressure within the fluid chamber. Eventually, a 

condition is reached (Figure 4-4c) in which the entire applied load is carried by the spring, and 

the pressure in the water has returned to its initial state, termed the “hydrostatic condition.” 

Once this stage is reached, there is no further flow of water, the spring no longer continues to 

compress and there is no more reduction in the volume of the chamber. 

43 
4.4.2 Principle of Effective Stress 

The consolidation process demonstrates the important principle of effective stress. Under an 

applied load, the total stress in a saturated soil sample is composed of two parts. One part acts in 

the water and the soil in all directions with equal intensity. This part is termed the “pore-water 

pressure” (or neutral stress). The other part acts solely between the areas of soil particle contact 

and is termed the “intergranular stress.” Because the pore water has no shear strength and is 

essentially incompressible, only the intergranular stress is effective in resisting shearing or 

limiting compression of the soil. The intergranular stress is therefore called the “effective 

stress.” The effective stress is the portion of the total stress over and above the pore-water 

pressure and can therefore be represented mathematically by Equation 4-21. 

σ′ = σ – u (4-21) 

Where σ is the total stress, u is the pore water pressure, and σ′ is the effective stress. 

Changes in the effective stress control the volumetric strain that develops in a soil. For instance, 

consider the load applied to a soil specimen by a laboratory oedometer as shown in Figure 4-5. 

The saturated specimen of clay can be compressed when sufficient pressure is applied to the soil 

skeleton to develop vertical deformations. However, essentially zero volume change occurs if 

the soil is loaded quickly – zero change in the volume of the voids (VV = VW). The water 

pressure increases by approximately the same amount as the total stress increases, while the 

effective stress does not initially change. If the load is maintained for a sufficient period of time, 

water will be squeezed out of the soil through the porous stones, and the increase in pore-water 

pressure will slowly dissipate until it is zero. After the excess pore water pressure has dissipated, 

the effective stress in the soil sample will be equal to the new total stress (note that in the 

oedometer the hydrostatic water pressure is negligible). 

Soil Specimen

Porous Stone

Loading Plate

Base

Porous Stone

Floating

Ring

Load

Figure 4-5: Conceptual Arrangement of Laboratory Oedometer Test 

44 
4.4.3 Overburden Stress 

As mentioned in the introduction to this section, the laboratory testing required to solve soilrelated problems involves simulating the conditions that exist naturally in the ground. Soils 

existing at a distance below the ground surface are influenced by the weight of the soil above 

that depth. The weight of the overlying soil exerts a pressure on the soil at that depth. This 

pressure is called the “overburden stress” and is a function of the unit weight of the overlying 

soil and the depth to the point under consideration. When a soil sample is removed from depth, 

the state of stress is relieved as all weight confining the sample is removed. When conducting a 

test on the sample, it is important to reestablish the state of stress in the soil sample that existed 

prior to removal of the sample from the ground. Changing the state of stress on the sample and 

observing the resulting strain can then provide information useful in design. The changes in 

stress that are applied to the sample should be representative of the changes in stress that are 

expected to occur as a result of constructing the shallow foundation upon the soil. As discussed, 

the effective stress resulting from intergranular contact is the controlling factor in evaluating the 

shearing resistance and compression characteristics of the soil sample. 

Before requesting laboratory testing of soil samples, the engineer must estimate the total and 

effective stress resulting from overburden at the depth of sampling. The total or effective stress 

overburden stress is specified to the lab as the beginning stress state for a particular test. 

The total overburden stress is computed by summing the product of the total unit weight of the 

soil times the layer thickness. The soil can be broken into stratigraphic layers if the unit weight

varies with depth. Unit weight may be determined from undisturbed samples or estimated from

SPT N-values, soil descriptions and moisture-content data. A plot of total stress and effective 

stress with depth is extremely useful and should be plotted for each foundation location under 

consideration. The plot can be constructed as follows: 

1. Divide the subsurface profile into layers based on the soil stratigraphy. Layers should be 

selected based on material description or classification, the location of the ground water 

table, changes in soil unit weight and increments of about one-half the estimated footing 

width for a distance of about twice the footing width below the estimated bearing depth. 

2. Determine the total vertical stress at the mid-point and bottom of each layer or sub-layer 

by multiplying the total unit weight by the thickness of each respective soil layer above 

the depth of calculation. 

3. Determine the pore water pressures below the water table by multiplying the depth below 

the water table to the point of calculation by the unit weight of water ( = 9.81 kN/m

wγ 3

= 62.4 pcf). 

4. Calculate the effective vertical stress by subtracting the pore water pressure from the total 

stress at each point below the water table. 

5. Plot the calculated total and effective vertical stresses versus depth or elevation. 

45 
46 

The initial stress for laboratory tests can be read easily from this plot, which also will be used 

throughout the design of a shallow foundation. 

Laboratory testing to determine the shearing resistance and compression characteristics of soils is 

relatively expensive and time consuming. The engineer should consider the cost and time 

required to perform such tests relative to the benefit achieved in terms of reduced foundation cost 

that results from an optimized design. In many cases, footings on cohesionless soils can be 

designed safely and effectively using shear strength and compressibility correlations based on the 

SPT N-values, as described in Chapter 5. 

Cohesive soils, however, can exhibit both low-strength and high-compressibility characteristics 

that are not reliably reflected in the SPT N-values. Consolidation testing is usually essential to 

predict the settlement of a shallow footing founded on cohesive soils. Shear-strength testing of 

cohesive soils should also be considered if a bearing failure mechanism could develop under the 

footing. 
CHAPTER 5 

GEOTECHNICAL DESIGN 

The design of shallow foundations involves calculating an allowable bearing pressure that will 

(a) maintain an adequate factor of safety relative to shear failure of the bearing soil, and (b) limit 

the settlement of the foundation to meet serviceability requirements. The allowable bearing 

capacity of a shallow foundation is defined as the lesser of: 

• The pressure that will result in a shear failure divided by a suitable factor of safety (FS), 

or 

• The pressure that results in a specified limiting amount of settlement. 

This chapter presents and discusses the theory behind calculation of allowable bearing capacities, 

considering both of these important design requirements. 

This chapter also presents the geotechnical procedures for computing the resistance to sliding for 

a shallow foundation, and the geotechnical considerations needed to ensure the foundation is 

stable from a global, or slope stability, perspective. 

5.1 ALLOWABLE BEARING CAPACITY

The allowable bearing capacity of a spread footing historically has combined the design 

considerations of minimizing the potential for shear failure of the soil and limiting vertical 

deflection (settlement). Both of these design considerations are a function of the least footing 

dimension, typically called the “footing width,” and designated as the variable, B or Bf. In 

general, for a footing bearing on essentially an isotropic, homogenous material, with no 

embedment (i.e., founded at the surface), the factor of safety against a shear failure developing 

beneath the footing will increase as the footing width, B, increases. However, as a footing’s 

dimension increases, the depth of influence also increases. Stated another way, as the footing 

dimension, B, increases, the stress increase “felt” by the soil extends more deeply below the 

bearing elevation. 

The effect of footing width on bearing capacity and settlement is shown conceptually in Figure 

5-1. Note that the allowable bearing capacity of a footing is controlled by shear-failure 

considerations for narrow footing widths. But as the footing width increases, the allowable 

bearing capacity is limited by the settlement potential of the soils supporting the footing. 

47 
0

100

200

300

400

500

600

700

800

900

0.0 1.0 2.0 3.0 4.0 5.0

Footing Width, B (m)

Bearing Pressure (kPa) 

Allowable Bearing Capacity (FS = 3.0)

Bearing Pressure for 25-mm (1 in) Settlement

Shear failure

controls

Settlement

controls

Figure 5-1: Allowable Bearing Capacity Controlled by Shear Failure 

Considerations versus Settlement Considerations

5.2 BEARING CAPACITY THEORY

This section discusses bearing capacity theory and its application toward computing allowable 

bearing capacities for shallow foundations. Methods of calculating settlement displacements are 

presented in Section 5.3. 

When a load is transferred through a footing to the foundation soil/rock, the subsurface materials 

experience settlement due to elastic (immediate) strains and long-term consolidation (elastic 

and/or plastic deformation) of the ground. The footing will penetrate into the foundation 

soil/rock when the intensity of applied loads is such that the load-carrying capacity of the 

foundation material is exceeded. A foundation failure will occur when the footing penetrates 

excessively into the ground or experiences excessive rotation (Figure 5-2). Excessive foundation 

movements such as penetration and rotation of the foundation may cause structural damage or 

collapse. A failure caused by the vertical and lateral displacement of foundation soils due 

to lack of sufficient strength is called a “bearing capacity failure.” The load that develops 

this type of subsurface collapse is called the “ultimate bearing capacity” of the soil. 

48 
Figure 5-2: Bearing Capacity Failure of Silo Foundation 

(Vesic, 1975, from Tschebotarioff, 1951) 

5.2.1 Failure Mechanisms 

5.2.1.1 General Shear 

The kinematic conditions (strain states) that develop when a uniform, rigid-plastic, weightless 

soil (possessing cohesion c' and friction φ') reaches the ultimate bearing capacity were 

determined theoretically by Prandtl (1920) and Reissner (1924). When a footing is loaded to the 

ultimate bearing capacity, the condition of plastic flow of foundation soils develops.

Terzaghi and Peck (1948) further defined the zones of plastic equilibrium after failure of soil 

beneath continuous footing (Figure 5-3). As shown in Figure 5-3, a triangular wedge beneath the 

footing, designated as Zone I, remains in an elastic state and moves down into the soil with the 

footing. Radial shear develops in Zone II such that radial lines extending from the footing 

change length based on a logarithmic spiral until the failure plane reaches Zone III. A passive 

state develops in Zone III at an angle of 45o

 – (φ′/2) from the horizontal. This configuration of 

the ultimate bearing capacity failure, with well-defined shear planes developing and extending to 

the surface, with footing rotation, and bulging of the soil on both sides of the footing, is called 

“general shear.” General shear-type ultimate bearing capacity failures (Figure 5-4a) are believed 

to be the prevailing mode of failure for soils that are relatively incompressible and reasonably 

strong, or saturated, normally consolidated clays that are loaded rapidly so that undrained 

conditions and therefore undrained soil strength governs (Coduto, 1994). 

49 
II

I III

D C

A B E

Q

L = ∞ q

ψ

Figure 5-3: Boundaries of Zone of Plastic Equilibrium after Failure of 

Soil Beneath Continuous Footing 

(a) GENERAL SHEAR

(b) LOCAL SHEAR

(c) PUNCHING SHEAR

LOAD

SETTLEMENT

LOAD

SETTLEMENT

LOAD

SETTLEMENT

SURFACE TEST

TEST AT

GREATER

DEPTH

Figure 5-4: Modes of Bearing Capacity Failure (After Vesic, 1975) 

(a) General Shear (b) Local Shear (c) Punching Shear 

50 
5.2.1.2 Local Shear 

In some cases, the bearing capacity shear planes are not well developed, and the failure planes do 

not extend all the way to the ground surface. This mode of ultimate bearing capacity failure 

(Figure 5-4b) is called “local shear.” The deformation patterns in local shear involve vertical 

compression (Vesic, 1975) beneath the footing, bulging of the soil at the ground surface and 

essentially no rotation or tilting of the footing. Local shear failures may occur in soils that are 

relatively loose or soft when compared to soils susceptible to general shear failure. 

5.2.1.3 Punching Shear 

Another type of failure observed under ultimate bearing-capacity conditions involves vertical 

compression of the soils beneath the footing without bulging of the soil. As shown in Figure 

5-4c, the bearing load continuously increases when the footing is loaded under strain-controlled 

conditions (‘test at greater depth’). This kinematic mode of ultimate bearing capacity failure is 

called “punching shear.” Punching shear is considered a potential failure mode for shallow 

foundations when loose or compressible soils are loaded slowly under drained conditions. For 

instance, footings placed at great depth on dense sand or on dense sand underlain by soft, 

compressible soil can fail under punching-shear modes. A footing on soft clay can also fail 

under punching shear if it is loaded slowly. 

Note that from a perspective of bridge foundation design, soils so obviously weak as to 

experience local or punching shear failure modes should be avoided for supporting shallow 

foundations. Additional guidance on dealing with soils that fall in the intermediate, or local 

shear range of behavior is provided in Section 5.2.3.6. 

5.2.2 Bearing Capacity Equation Formulations 

The gross ultimate bearing pressure is equivalent to the stress applied to the soil by the footing at 

ultimate (failure) conditions at the bearing elevation. In theoretical formulations, Prandtl (1920) 

and Reissner (1924) developed an expression for the gross ultimate bearing capacity that 

considered both frictional and cohesion components of soil shear strength and a uniform 

surcharge pressure at the base of the footing due to the depth of embedment of the footing, Df. 

The gross ultimate bearing pressure (qult gross) for this case is: 

qult gross = c(N ) q ( N ) (5-1) c + q

where: c = cohesion of the soil 

 q = γDf

 = surcharge at the base of the footing 

γ = Unit weight of the overburden material causing the surcharge pressure 

 Df = Depth of embedment (Figure 5-5) 

 Nq = bearing capacity factor for the surcharge term: 

= )

2

 tan (45 tan 2 e φ ° + π φ (5-2)

51 
Lf

Df

Bf

Figure 5-5: Design Terminology for Spread Footing Foundation 

Nc = bearing capacity factor for the cohesion term: 

= 1)cotφ for φ > 0° q (N - (5-3)

 = 2 + π = 5.14 for φ = 0° (5-4)

The net ultimate bearing pressure is the difference between the gross ultimate bearing pressure 

and the pressure that existed due to the surcharge at the bearing depth before the footing was 

constructed, q (= γDf

). The net ultimate bearing pressure can thus be computed by subtracting 

the surcharge (q) from Equation 5-1: 

qult net = qult gross – q (5-5) 

qult net = c N q ( N -1) (5-6) c + q

By inspection of Equation 5-6, the actual difference between qult net and qult gross is generally small 

for cohesionless soils (i.e., φ > 0o

). 

52 
Further, the structural designer will typically include the self-weight of the concrete footing and 

the backfill over the footing (approximately equal to γ Df

) in the loads that contribute to the 

applied bearing stress. Therefore, if the geotechnical engineer computes and reports a net 

ultimate bearing pressure, the effect of the surcharge directly over the footing area is counted 

twice. This is conservative, but generally not recommended, provided that a suitable factor of 

safety is maintained against bearing capacity failure. If the geotechnical engineer chooses to 

report an allowable bearing capacity computed from a net ultimate bearing pressure, this fact 

should be clearly stated in the foundation report. 

Therefore, it is recommended that qult gross be used in determination of the allowable 

bearing capacity of a soil (e.g., qult ≈ qult gross). 

There are no analytical solutions available to extend the bearing capacity equations to include the 

effects of unit weight of the foundation material. Numerous investigators have proposed 

relationships for the inclusion of the unit weight. They involve adding an independent term (Nγ) 

to the ultimate gross bearing capacity equation. Analyses were developed by assuming the 

shapes of the failure surfaces and performing trial analyses until a solution was obtained. The 

revised ultimate gross bearing capacity equation for a centrically loaded strip footing on a 

foundation material with unit weight now becomes: 

qult = c (N ) q (N ) 0.5 ( )(B )(N ) c q f γ + + γ (5-7) 

where: c = cohesion of the soil 

 Nc = bearing capacity factor for the cohesion term

q = surcharge at the base of the footing 

 Nq = bearing capacity factor for the surcharge term

 Bf = footing width 

γ = unit weight of soil beneath the footing 

 Nγ = bearing capacity factor for soil unit weight 

Note that a range of values has been proposed by various authors for Nγ. The differences 

reported by various researchers range from about one-half to double the values presented below, 

depending on the friction angle selected for design (Chen & McCarron, 1991). Caquot and 

Kerisel’s (1948) equation for Nγ is currently used by FHWA and AASHTO: 

Nγ = 2 (Nq + 1) tan( φ ) (5-8)

The values of Nc, Nq, and Nγ as functions of the friction angle are included in Table 5-1 and in 

Figure 5-6. 

Note from Equation 5-7 that the ultimate bearing capacity of a soil is a function of the cohesive 

and frictional strength of the soil (c and φ ), the effective weight of the soil above and below the 

footing (γ or γ′), and the depth and width of the footing (Df and Bf). Consider now the effect 

each of these variables has on the computed ultimate bearing capacity. For cohesive soils (i.e., 

φ = 0, undrained loading), the last term is zero and the first term is a constant. Therefore the 

53 
ultimate bearing capacity will only be a function of the cohesion and the depth of embedment of

the footing. 

Cohesionless soils, on the other hand, will experience large changes in ultimate bearing capacity 

when properties and/or dimensions are changed. The embedment effect is particularly important. 

Removal of soil from over an embedded footing, either by excavation or scour, can substantially 

reduce bearing capacity and cause footing subsidence. Similarly, a rise in the ground water level 

to the ground surface will reduce the effective (buoyant) unit weight of the soil, thus reducing 

those terms that are a function of unit weight by essentially one-half. 

TABLE 5-1: BEARING CAPACITY FACTORS (AASHTO, 1996) 

φ Nc Nq Nγ φ Nc Nq Nγ

0 5.14 1.0 0.0 23 18.1 8.7 8.2

1 5.4 1.1 0.1 24 19.3 9.6 9.4

2 5.6 1.2 0.2 25 20.7 10.7 10.9

3 5.9 1.3 0.2 26 22.3 11.9 12.5

4 6.2 1.4 0.3 27 23.9 13.2 14.5

5 6.5 1.6 0.5 28 25.8 14.7 16.7

6 6.8 1.7 0.6 29 27.9 16.4 19.3

7 7.2 1.9 0.7 30 30.1 18.4 22.4

8 7.5 2.1 0.9 31 32.7 20.6 26.0

9 7.9 2.3 1.0 32 35.5 23.2 30.2

10 8.4 2.5 1.2 33 38.6 26.1 35.2

11 8.8 2.7 1.4 34 42.2 29.4 41.1

12 9.3 3.0 1.7 35 46.1 33.3 48.0

13 9.8 3.3 2.0 36 50.6 37.8 56.3

14 10.4 3.6 2.3 37 55.6 42.9 66.2

15 11.0 3.9 2.7 38 61.4 48.9 78.0

16 11.6 4.3 3.1 39 67.9 56.0 92.3

17 12.3 4.8 3.5 40 75.3 64.2 109.4

18 13.1 5.3 4.1 41 83.9 73.9 130.2

19 13.9 5.8 4.7 42 93.7 85.4 155.6

20 14.8 6.4 5.4 43 105.1 99.0 186.5

21 15.8 7.1 6.2 44 118.4 115.3 224.6

22 16.9 7.8 7.1 45 133.9 134.9 271.8

54 
1

10

100

1000

0 10 20 30 40 50

Friction Angle, degrees

Bearing Capacity Factor

60

s

Nc

N Nγ q

Figure 5-6: Bearing Capacity Factors versus Friction 

Angle (AASHTO, 1996)

5.2.3 Bearing Capacity Correction Factors 

A number of factors influence the ultimate bearing capacity of shallow foundations that were not 

included in the derivations discussed earlier. Note that Equation 5-7 assumes a rigid strip 

(continuous) footing that is loaded through its centroid bearing on a level surface of 

homogeneous soil. Various correction factors have been proposed by numerous investigators to 

account for footing shape, location of the ground water table, embedment depth, sloping ground 

surface, an inclined base, the mode of shear (local or punching shear), inclined loading and soil 

compressibility. The general philosophy of correcting the ultimate bearing capacity involves 

using semi-empirical factors that are multiplied by each of the three terms in the bearing capacity 

equation to account for the particular effect. Each correction factor includes a subscript denoting 

the term to which the factor should be applied: “c” for the cohesion term, “γ” for the unit weight

(footing width) term and “q” for the surcharge (embedment) term. Each of these factors and 

suggestions for their application are discussed separately below. In some, but not all, cases these 

factors should be used in combination. The following sections provide guidance on the use of 

the factors, and whether or not certain factors should be used in combination. 

5.2.3.1 Footing Shape 

AASHTO guidelines distinguish a strip footing as one whose length (Lf) exceeds five times the 

footing width (Bf). Corrections of the ultimate bearing capacity should be made for rectangular 

footings with Lf/Bf ratios less than 5. The shape (eccentricity) correction factors are summarized 

in Table 5-2. Note that for eccentrically loaded footings, AASHTO (1996) recommends using 

the effective footing dimensions, B′f and L′f, to compute the shape correction factors (refer to 

Section 6.4.1 for discussion of eccentricity and effective footing dimensions). However, in 

55 
routine foundation design, this is not practical, since the effective dimensions will change for 

various load cases, and the difference in the computed shape correction factors will generally be 

small. Therefore the geotechnical engineer should make reasonable assumptions about the 

footing shape and dimensions and compute the correction factors using Table 5-2. 

TABLE 5-2: SHAPE CORRECTION FACTORS (AASHTO 1996) 

Factor 

Friction 

Angle Cohesion Term (sc) Unit Weight Term (sγ) Surcharge Term (sq) 

φ = 0 















+

f

f

5L

B 1 1.0 1.0 Shape 

Factors, 

sc, sγ, sq φ > 0 































+

c

q

f

f

N

N

L

B 1 













 −

f

f

L

B 1 0.4 















+ tan φ L

B 1

f

f

Note: Shape (eccentricity) factors, s, should not be applied simultaneously with inclined loading 

factors, i. See Section 5.2.3.7.

5.2.3.2 Location of the Ground Water Table 

If the ground water table is located within the potential zone of shear below or above a footing, 

effective stresses will control the magnitude of overburden stress and thus the shearing resistance 

along that portion of the shearing surface that lies below the water table.

A simplified method for accounting for the reduction in shearing resistance is to apply factors to 

the two terms in the bearing capacity equation that include a unit weight term. Recall that the 

cohesion term is neither a function of soil unit weight nor effective stress. The factors may be 

computed using the following equations, or by interpolating values between those provided in 

Table 5-3. 

1.0

1.5B D

D C 0.5 0.5

f f

W

W ≤















+ = +

γ (5-9) 

1.0

D

D C 0.5 0.5

f

W

Wq

≤













 = + (5-10)

56 
TABLE 5-3: CORRECTION FACTOR FOR LOCATION 

OF GROUND WATER TABLE (AASHTO, 1998) 

Depth of Ground Water 

Table, DW CWγ CWq

0 0.5 0.5

Df 0.5 1.0

> 1.5Bf + Df 1.0 1.0

Note: For intermediate positions of the ground water table, interpolate 

between the values shown above or use Equations 5-9 and 5-10. 

5.2.3.3 Embedment Depth 

Because the surcharge term, q, was developed considering the effect on bearing capacity as a 

vertical pressure applied at the footing bearing elevation, the effect of the shearing resistance as 

the failure surface passes through the footing embedment cover was neglected in the theory. If 

the backfill or cover over the footing is known to be of high-quality, compacted granular material 

that can be reliably assumed to remain in place over the life of the footing, this additional 

shearing resistance can be included by addition of the embedment depth factor, dq, shown in 

Table 5-4. Otherwise, the depth correction factor can be conservatively omitted. 

TABLE 5-4: DEPTH CORRECTION FACTOR 

(BRINCH HANSEN, 1970) 

Friction Angle, φ

(degrees) Df/Bf dq

32

1 

2 

4 

8 

1.20 

1.30 

1.35 

1.40 

37 

1 

2 

4 

8 

1.20 

1.25 

1.30 

1.35 

42 

1 

2 

4 

8 

1.15 

1.20 

1.25 

1.30 

Note: The depth correction factor should be used only when

the soils above the footing bearing elevation are as competent 

as the soils beneath the footing level; otherwise, the depth 

correction factor should be taken as 1.0. 

57 
5.2.3.4 Sloping Ground Surface 

Placement of footings on or adjacent to slopes requires that the designer perform calculations to 

ensure that both the bearing capacity and the overall slope stability are acceptable. The bearing 

capacity equation should include corrections recommended by AASHTO as adapted from

NAVFAC (1986b) to design the footings. Calculation of overall, or global, stability is discussed 

in Section 5.5. 

The ultimate bearing capacity equation (Equation 5-7) is therefore modified to include terms Ncq

and Nγq that replace the Nc and Nγ terms (Equation 5-11). 

q c (N ) 0.5 ( )(B )(N ) ult cq f γq = + γ (5-11)

Charts are provided (Figure 5-7) to determine these terms for cohesive (φ = 0o

) and cohesionless 

(c = 0) soils. Note in Figure 5-7d that beyond a distance, ‘b,’ of two to six times the foundation 

width, the bearing capacity is independent of the slope angle (identical to the horizontal ground 

surface). Also note that the depth of embedment term goes to zero because the surcharge effect 

on the slope side of the footing should be ignored. 

Other forms of the equation are available for cohesive soils (φ = 0o

). However, because footings 

located on both cohesive soils and near slopes are likely to have design limitations due to either 

settlement or slope stability, or both, the presentation of these equations is omitted here. The 

reader is referred to the NHI Shallow Foundations Workshop Reference Manual (Munfahk et al., 

2000) or the NAVFAC DM-7 (1986a, 1986b) manuals for discussion of these equations and their 

applications and limitations. 

The form of the equation that includes the width term on cohesionless soils is useful in designing 

footings constructed within bridge approach fills. The calculation procedure is as follows: 

• Obtain Nγq from Figure 5-7(c) or 5-7(f) and compute the ultimate bearing capacity using 

Equation 5-11, or the general form of the bearing capacity expression, Equation 5-14, with 

the Nγ term replaced by Nγq. 

5.2.3.5 Inclined Base 

In general, inclined footings for bridges should be avoided, or limited to shallow inclinations, α, 

of less than about 8 to 10 degrees from horizontal. Steeper inclinations may require keys, dowels 

or anchors to provide sufficient resistance to sliding. If the footing is inclined to the horizontal, 

the bearing capacity equation should be modified using the factors as determined from Table 5-5. 

58 
Figure 5-7: Modified Bearing Capacity Factors for Footing on Sloping Ground, 

(after Meyerhof, 1957, from AASHTO, 1996) 

59 
TABLE 5-5: INCLINED BASE CORRECTION FACTOR (BRINCH HANSEN, 1970) 

Factor 

Friction 

Angle Cohesion Term (c) Unit Weight Term (γ) Surcharge Term (q) 

bc bγ bq

φ = 0 



 



 α − 147.3

1 1.0 1.0

Base 

Inclination 

Factors, 

bc, bγ, bq φ > 0 















φ

− − N tan1 b

b

c

q

q (1-0.017α tanφ)

2 (1-0.017α tanφ)2

Definitions: φ = friction angle, degrees; α = footing inclination from horizontal, upward +, degrees 

5.2.3.6 Local or Punching Shear 

Several references, including AASHTO, recommend reducing the soil strength parameters if 

local or punching shear failure modes can develop. Figure 5-8 shows conditions when these 

modes can develop. The recommended reductions are shown in Equations 5-12 and 5-13. 

c* = 0.67c (5-12)

* tan (0.67tan ) 1 φ = φ − (5-13)

Note: This chart was developed for normally consolidated native soil deposits.

Figure 5-8: Modes of Failure of Model Footings in Sand (after Vesic, 1975) 

60 
Soil types that can develop local or punching shear failure modes include loose sands, very 

sensitive clays [St > 8, sensitivity is defined as the ratio of the unconfined compressive strengths 

of an undisturbed sample to the unconfined compressive strength of a remolded sample 

(Terzaghi & Peck, 1967)], metastable (collapsible, see Section 3.1.1) sands and silts and brittle 

clays (OCR > 4 to 8; see Section 5.3.3 for discussion of OCR). These are all “problem” soil 

conditions that should be identified with a thorough geotechnical investigation, as described in 

Chapter 4. In general, these problem soils will have other characteristics that make them 

unsuitable for support of shallow foundations for bridges, including large settlement potential for 

loose sands, sensitive clays and metastable soils. Brittle clays exhibit relatively high strength at 

small strains, but significant reduction in strength at larger strains (strain-softening). This 

behavior should be identified and quantified through the field and laboratory testing program and 

compared to the anticipated stress changes resulting from the shallow foundation and ground 

slope configuration under consideration. 

Although local or punching shear failure modes can develop in loose sands or when very narrow 

footings are used, this local condition seldom applies to bridge foundations because spread 

footings are not used on obviously weak soils and relatively large footing sizes are needed for 

structural stability (Cheney & Chassie, 2000). 

The geotechnical engineer may encounter the following two situations where application of the 

one-third reduction according to Equation 5-13 can result in an unnecessarily over-conservative 

design. 

The first is when considering a footing bearing on cohesionless soils that fall in the local shear 

portion of Figure 5-8. Note that a one-third reduction in the tangent of a friction angle of 38 

degrees (a common value for good-quality, compacted, granular fill) results in a 73 percent 

reduction in bearing capacity factor Nq, and an 81 percent reduction in Nγ! Also note that Figure 

5-8 does not consider the effect of large footing widths, such as used for support of bridges. 

Therefore, provided that settlement potential is checked independently (Section 5.3.4) and 

found to be acceptable, spread footings on normally consolidated cohesionless soils falling 

within the local shear portion Figure 5-8 should not be designed using the one-third 

reduction according to Equation 5-13. 

The second situation is when considering a spread footing bearing on a compacted structural fill. 

Note that Figure 5-8 is for normally consolidated, natural soil deposits. The relative density of

compacted structural fills as compared to compactive effort (percent relative compaction) 

indicates that for fills compacted to a minimum of 95 percent of maximum density (as 

determined by AASHTO T-180) the relative density should be at or above 75 percent (Lee & 

Singh, 1971). This is consistent with the excellent performance history of spread footings in 

structural fills (DiMillio, 1982). The use of the one-third reduction therefore should not be 

used in the design of footings on compacted structural fills constructed with good quality, 

granular material. Appendix A includes materials specifications used by State highway 

agencies that routinely construct bridge abutments and pier footings supported within compacted 

structural fills. 

61 
5.2.3.7 Inclined Loading 

The inclined load case is the resultant formed by both axial and shear load components applied to 

the footing by the column or wall stem. If the components of this resultant (i.e., axial and shear 

forces) are checked against the available resistance in the respective direction (i.e., bearing 

capacity and sliding, respectively), the inclusion of the inclined loading factor in the bearing 

capacity equation can generally be omitted. The bearing capacity should, however, be evaluated 

using effective footing dimensions, as discussed in Section 6.4.1 and in the footnote to Table 5-2, 

since large moments can frequently be transmitted to bridge foundations by the columns or pier 

walls. The simultaneous application of shape and load inclination factors can result in an 

overly conservative design. Henceforth, the inclination factor will be omitted in calculation of

bearing capacity. A check for sliding stability should be made for all footings with inclined 

loads. 

Unusual column geometry or loading configurations should be evaluated on a case-by-case basis 

relative to the foregoing recommendation to omit the load inclination factors. An example might 

be a strut column that is not aligned normal to the footing bearing surface. In this case, it may be 

prudent to consider an inclined footing base for improved bearing efficiency. Keep in mind that 

bearing surfaces that are not level may be difficult to both construct and inspect. 

5.2.3.8 Soil Compressibility 

Vesic (1975) included correction factors for soil compressibility for footings on sands and 

gravels, cq and cγ. These factors were developed to effectively limit the allowable bearing 

capacity accounting for compression settlement of granular materials. The factors are a function 

of soil density and applied load, and the factors do not account for soil layering or the reduction 

in stress with depth below a footing (see Section 5.3). The procedures recommended in this 

chapter directly compute the estimated compression settlement of footings on sands and granular 

materials. Therefore, the soil compressibility factors should not be used in calculation of 

ultimate bearing capacity of footings on granular soils when a separate settlement

calculation is performed. 

5.2.4 Additional Considerations Regarding Bearing Capacity Correction Factors 

The inherent or implied factor of safety of a settlement-limited allowable bearing capacity 

relative to the computed ultimate bearing capacity is usually large enough to render the 

magnitude of the application of the individual correction factors small. Consider the following 

observations: 

• AASHTO (1996) guidelines recommend calculating the shape, s, factor using the 

effective footing dimensions, B′f and L′f. However, the original references (e.g., Vesic, 

1975) do not specifically recommend using the effective dimensions to calculate the 

shape factor. Since the geotechnical engineer typically does not have knowledge of the 

loads causing eccentricity, it is recommended that the full footing dimensions be used to 

calculate the shape factor (Table 5-2) for use in computation of ultimate bearing capacity. 

• Bowles (1982) also recommends that the shape and load inclination factors (s and i) 

should not be combined. 

62 
• In certain loading configurations, the simultaneous application of the shape factor 

correction, the load inclination factor correction, local shear potential, the soil 

compressibility factors and a suitable factor of safety can result in a computed allowable 

bearing capacity that is only 5 percent or less of the uncorrected ultimate bearing 

capacity. This emphasizes the over-conservatism resulting from the simultaneous 

application of all the factors that have been proposed by various researchers. 

The form of the bearing capacity equation in Equation 5-14 is therefore recommended for 

routine design applications. 

Further, the bearing capacity correction factors were developed assuming that each correction for 

each of the terms involving Nc, Nγ and Nq can be found independently. The bearing capacity 

theory is an idealization of the response of a foundation that attempts to account for the soil 

properties and boundary conditions. Bearing capacity analysis of foundations is frequently 

limited by the geotechnical engineer’s ability to accurately determine material properties as 

opposed to inadequacies in the theory used to develop the bearing capacity equations. Consider 

Table 5-1 and note that a one degree change in friction angle can result in a 10 to 15 percent 

change in the factors Nc, Nγ and Nq. Also note that the value of Nγ more than doubles when the 

friction angle increases from 35o

 to 40o. Clearly, the uncertainties in the material properties will 

control the uncertainty of a bearing capacity computation to a large extent. The importance of 

application of the correction factors is therefore secondary to adequate assessment through 

field exploration and laboratory testing of the inherent strength characteristics of the 

foundation soils. 

It should also be noted that very few spread footings of the size used for bridge support have 

been load tested to failure. The evaluation of bearing capacity is based primarily on theory and 

laboratory testing of small-scale footings, with modification of the theoretical based on

observation. 

5.2.5 Bearing Capacity Calculation 

The general form of the resulting ultimate bearing capacity equation, including correction terms, 

is thus: 

γ γ γ γ q = cN s b + qN C sqbqdq + 0.5γBf N CW s b Wq ult c c c q (5-14)

where: sc, sγ and sq are shape correction factors 

bc, bγ and bq are correction factors for the inclination of the base 

dq is a correction factor to account for the shearing resistance along the failure surface 

passing through cohesionless material above the bearing elevation (recall that the 

embedment is modeled as a surcharge pressure only, applied at the bearing elevation) 

CWγ and CWq are correction factors considering the location of the ground water table 

Nc, Nγ and Nq are obtained from Table 5-1 or Figure 5-6 

Nc and Nγ are replaced with Ncq and Nγq for the sloping ground or footing near slope case 

63 
The friction angle of the soil is needed to obtain Nc, Nq and Nγ from either Table 5-1 or Figure 5-

6. Figures 4-1 and 4-2 can be used to correlate friction angles from SPT data in cohesionless 

soil, or measured directly by laboratory tests or in situ testing. 

5.2.6 Bearing Capacity Factors of Safety 

The minimum factor of safety applied to the calculated ultimate bearing capacity will be a 

function of: 

• The confidence in the design soil strength parameters (c and φ), 

• The importance of the structure, and

• The consequence of failure. 

Typical minimum factors of safety for shallow foundations are in the range of 2.5 to 3.5. For 

most bridge foundation applications, a minimum factor of safety against bearing capacity failure 

of 3.0 is recommended (Cheney & Chassie, 2000). 

This factor of safety was selected through a combination of applied theory, experience and 

consensus for comparison to unfactored load combinations [allowable stress, or Service Load 

Design (SLD)]. As such, the uncertainty in both the magnitude of the loads and the available 

soil bearing strength were combined into this single factor of safety. The general factor of safety 

equation in allowable stress, or SLD, is as follows: 

FS

R Q n ∑ i ≤ (5-15)

where: Qi = applied stress (by the spread footing) 

Rn = yield stress of the member (or ultimate bearing capacity of the soil) 

FS = the applied factor of safety 

Load Factor Design (LFD) was first recommended by AASHTO in the late 1970s. At that time, 

uncertainty in the loads was captured in the load factors. However, it was not until the 

implementation of the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design 

Specifications (AASHTO, 1994) that an attempt was made to incorporate the uncertainty of the 

foundation soil resistances in performance, or resistance (φ), factors. 

A performance or resistance factor is not strictly the reciprocal of the factor of safety. It is more 

properly a partial factor of safety that incorporates the potential for variation in the computed 

capacity or resistance. It must be emphasized that performance (resistance) factors for 

geotechnical design of shallow foundations were developed using a combination of 

reliability-based calibrations, calibration with SLD (fitting) and engineering judgment. 

The performance (LFD – AASHTO, 1996) and resistance (LRFD – AASHTO, 1998) factors 

were therefore selected to match existing practice and to mimic the factors of safety used in 

allowable stress design. The general LFD equation is: 

βiQi ≤ φRn γ∑ (5-16)

64 
where: γ = load factor for load combination, 

βi = load factor for particular load, Qi 

Qi = particular service load or stress 

φ = resistance factor 

Rn = nominal strength of member (e.g., yield strength for steel) 

In the years between adoption of LFD for calculating factored loads and the development of 

resistance factors for soils, agencies that elected to implement LFD found it necessary to make 

interim provisions to increase the allowable bearing capacities for spread footings provided by 

the geotechnical engineers. If this was not done, they found that their LFD designs were 

noticeably more conservative than they had been using SLD (allowable stress) design. 

One approach used to reduce this added conservatism was to multiply the allowable bearing 

capacities by some factor, say 1.5 to 2. Although this procedure may result in foundation 

designs that are generally similar to those developed using allowable stress methods, the 

approach should generally be avoided, because the settlement computations used to develop the 

allowable bearing capacity were based on unfactored loads, not factored (increased) loads. 

It was not until the adoption of the Load and Resistance Factor Design method (AASHTO, 1994)

that these inconsistencies were at least partially resolved. Appendix C contains two of the 

example problems presented in Appendix B that are solved using the LRFD method. Notice that 

the designs are not radically different. This is to be expected, since the LRFD resistance factors 

in AASHTO were selected such that designs would be similar to past practice. 

Clearly, the structural designer and the geotechnical engineer must be consistent in 

communication of their design criteria and methodologies. A mixed approach of SLD for 

foundation capacities and LFD or LRFD for load calculation can result in very conservative 

designs. The importance of good communication between the structural and geotechnical 

engineers has never been more important. Miscommunication about the SLD factors of 

safety used to develop allowable bearing capacities can result in overconservative designs 

when LFD or LRFD load factors are used to increase the design loads that are then used to 

size a foundation. This is especially true for AASHTO SLD Load Groups VII through XI 

(AASHTO, 1996, see Section 6.3 for a discussion of load groups and their definitions), which 

are the rare, or extreme event, loading conditions resulting from earthquake, ice loading and ice 

plus wind, respectively. If the allowable bearing capacity provided by the geotechnical engineer 

is used to size a shallow foundation when one of these load conditions controls, the designer will 

frequently conclude that a shallow foundation must be enormous and therefore impractical. 

Expensive deep foundations such as piles or shafts are often unnecessarily selected when this 

miscommunication occurs. 

5.2.7 Presumptive Bearing Capacities 

5.2.7.1 Soil 

The use of presumptive bearing capacities for footings bearing in soils is not recommended 

for final design of shallow foundations for transportation structures, especially bridges. 

Guesses about the geology and nature of a site and application of a presumptive value from

generalizations in the literature are not a substitute for an adequate site-specific subsurface 

65 
exploration and laboratory testing program. An exception is preliminary evaluation of shallow 

foundation feasibility and estimation of footing dimensions for preliminary constructability or 

cost evaluation. 

Local sources of suggested presumptive values, available in engineering geology or geotechnical 

literature, are generally more realistic than capacities generalized to soil classification or found in 

design codes such as AASHTO (1996, 1998) or the NAVFAC manuals (NAVFAC, 1986a and 

1986b). 

5.2.7.2 Rock 

For conditions of intact sound rock that is stronger and less compressible than concrete, footings 

on rock with small applied loads are generally stable and thus do not require extensive study of 

the strength and compressibility characteristics of rock behavior. However, site investigation is 

still required to confirm the consistency and extent of rock formations beneath a shallow 

foundation. 

Allowable bearing capacities for footings on relatively uniform and sound rock surfaces are 

documented in applicable building codes and engineering manuals. Many different definitions

for sound rock are available. In simple terms, however, “sound rock” can generally be defined 

as rock mass that does not disintegrate after exposure to air or water, and with discontinuities 

that are unweathered, closed or tight (less than about 3 mm wide) and spaced no closer than 1 m

apart. Table 5-6 presents allowable bearing pressures recommended in selected local building 

codes (Goodman, 1989). These values were developed based on experience in sound rock 

formations, with an intention of satisfying both bearing capacity and settlement criteria in order 

to provide a satisfactory factor of safety. In most cases, it is prudent to follow the codes since 

these code-recommended values tend to be more conservative based on local experience. 

However, for supporting heavy structures, use of presumptive values may lead to overly 

conservative and costly foundations. In such cases, most codes do allow for variance if the 

request is supported by an engineering report. 

In areas where building codes are not available or applicable, other recommended presumptive 

bearing values, such as those listed in Table 5-7, may be used to determine the allowable bearing 

pressure for sound rock. For footings designed using these published values, the elastic 

settlements are generally less than 13 mm. Where rock is reasonably sound, but fractured, the 

presumptive values listed in Tables 5-6 and 5-7 should be reduced to prevent potential excessive 

settlement. Most building codes also provide reduced recommended bearing pressures to 

account for the degree of fracturing. For example, Table 5-8 presents the allowable rock bearing 

pressures in accordance with the New York City Building Code (2001). 

66 
TABLE 5-6: ALLOWABLE BEARING PRESSURES FOR FRESH ROCK OF 

VARIOUS TYPES1,2,3,4

 (GOODMAN, 1989) 

Rock Type Age Location 

Allowable Bearing 

Pressure (MPa) 

Massively bedded limestone5 U.K.

6 3.8 

Dolomite L. Paleoz. Chicago 4.8

Dolomite L. Paleoz. Detroit 1.0 – 9.6 

Limestone U. Paleoz. Kansas City 0.5 – 5.8 

Limestone U. Paleoz. St. Louis 2.4 – 4.8 

Mica schist Pre-Camb. Washington 0.5 – 1.9 

Mica schist Pre-Camb. Philadelphia 2.9 – 3.8 

Manhattan schist Pre-Camb. New York 5.8 

Fordham gneisse Pre-Camb. New York 5.8 

Schist and slate - U.K.6 0.5 – 1.2 

Argillite Pre-Camb. Cambridge,

MA 

0.5 – 1.2 

Newark shale Triassic Philadelphia 0.5 – 1.2 

Hard, cemented shale - U.K.6 1.9

Eagleford shale Cretaceous Dallas 0.6 – 1.9 

Clay shale - U.K.6 1.0

Pierre shale Cretaceous Denver 1.0 – 2.9 

Fox Hills sandstone Tertiary Denver 1.0 – 2.9 

Solid chalk Cretaceous U.K.6 0.6

Austin chalk Cretaceous Dallas 1.4 – 4.8 

Friable sandstone and 

claystone 

Tertiary Oakland 0.4 – 1.0 

Friable sandstone 

(Pico formation) 

Quaternary Los Angeles 0.5 – 1.0 

Notes: 

1

 According to typical building codes; reduce values accordingly to account for weathering or

unrepresentative fracturing 2

 Values from Thornburn (1966) and Woodward, Gardner and Greer (1972). 3 When a range is given, it relates to usual range in rock conditions. 4 Sound rock that rings when struck and does not disintegrate. Cracks are unweathered and open

less than 10 mm. 5 Thickness of beds greater than 1 m, joint spacing greater than 2 mm; unconfined compressive

strength greater than 7.7 MPa (for a 100-mm cube). 6 Institution of Civil Engineers Code of Practice 4.

67 
TABLE 5-7: PRESUMPTIVE VALUES OF ALLOWABLE BEARING PRESSURES 

FOR SPREAD FOUNDATIONS ON ROCK (MODIFIED AFTER NAVFAC, 1986b) 

Allowable Bearing Pressure 

(MPa) 

Type of Bearing Material 

Consistency In 

Place Range 

Recommended

Value for Use 

Massive crystalline igneous and 

metamorphic rock: granite, diorite, basalt, 

gneiss, thoroughly cemented 

conglomerate (sound condition allows

minor cracks) 

Hard, sound 

rock 

5.8 to 9.6 7.7 

Foliated metamorphic rock: Slate, schist 

(sound condition allows minor cracks) 

Medium-hard, 

sound rock 

2.9 to 3.8 3.4 

Sedimentary rock; hard cemented shales, 

siltstone, sandstone, limestone without 

cavities 

Medium-hard, 

sound rock 

1.4 to 2.4 1.9 

Weathered or broken bedrock of any kind 

except highly argillaceous rock (shale). 

RQD less than 25 

Soft rock 0.8 to 1.2 1 

Compaction shale or other highly 

argillaceous rock in sound condition 

Soft rock 0.8 to 1.2 1 

Notes: 

1. For preliminary analysis or in the absence of strength tests, design and proportion shallow foundations to

distribute their loads using presumptive values of allowable bearing pressure given in this table. Modify the 

nominal value of allowable bearing pressure for special conditions described in notes 2 through 8.

2. The maximum bearing pressure beneath the footing produced by eccentric loads that include dead plus 

normal live load plus permanent lateral loads shall not exceed the above nominal bearing pressure. 

3. Bearing pressures up to one-third in excess of the nominal bearing values are permitted for transient live 

load from wind or earthquake. If overload from wind or earthquake exceeds one-third of nominal bearing 

pressures, increase allowable bearing pressures by one-third of nominal value. 

4. Extend footings on soft rock to a minimum depth of 40 mm below adjacent ground surface or surface of 

adjacent floor, whichever elevation is the lowest. 

5. For footings on soft rock, increase allowable bearing pressures by 5 percent of the nominal values for each 

0.3 m of depth below the minimum depth specified in note 4.

6. Apply the nominal bearing pressures of the three categories of hard or medium hard rock shown above 

where the base of the foundation lies on rock surface. Where the foundation extends below the rock

surface, increase the allowable bearing pressure by 10 percent of the nominal values for each additional 0.3 

m of depth extending below the surface. 

7. For footings smaller than 1 m in the least lateral dimension, the allowable bearing pressure shall be the 

nominal bearing pressure multiplied by the least lateral dimension (in meters). 

8. If the above-recommended nominal bearing pressure exceeds the unconfined compressive strength of intact

specimen, the allowable pressure equals the unconfined compressive strength. 

68 
TABLE 5-8: ALLOWABLE BEARING PRESSURES FOR SPREAD 

FOUNDATIONS ON ROCK IN NEW YORK CITY 

(NEW YORK CITY BUILDING CODE, 2001) 

Description Classifications q allowable (MPa)

Hard sound 

rock 

Crystalline rocks such as Fordham Gneiss, Ravenswood Gneiss, 

Palisades Diabase and Manhattan Schist. Characteristics: the 

rock rings when struck with pick or bar; does not disintegrate 

after exposure to air or water; breaks with sharp fresh fracture; 

cracks are unweathered and less than 3 mm (1/8 in) wide, 

generally no closer than 0.9 m (3 ft) apart; core recovery with a 

double tube, diamond core barrel is generally 85 percent or 

greater for each 1.5-m (5-ft) run 

5.8 

Medium

sound rock 

Includes the above crystalline rocks, plus Inwood marble and 

serpentine. Characteristics include above hard rock 

characteristics, except that cracks may be 6 mm (1⁄4 inch) wide

and slightly weathered, generally spaced no closer than 0.6 m (2 

ft) apart; core recovery with a double tube, diamond core barrel 

is generally 50 percent or greater for each 1.5-m (5-ft) run 

3.8 

Intermediate

sound rock 

Includes the all of the above rock types plus cemented shale and 

sandstone of the Newark formation. Characteristics: the rock 

gives dull sound when struck with pick or bar; does not 

disintegrate after exposure to air or water; broken pieces may 

show weathered surfaces; may contain fracture and weathered 

zones up to 25-mm (1-in) wide spaced as close as 0.3 m (1 ft); 

core recovery with a double tube, diamond core barrel is 

generally 35 percent or greater for each 1.5-m (5-ft) run 

1.9 

Soft rock Includes all of the above rocks in partially weathered condition, 

plus cemented shale and sandstones. Characteristics: rock may 

soften on exposure to air or water; may contain thoroughly 

weathered zones up to 75 mm (3 in) wide but filled with stiff

soil; core recovery with a double tube, diamond core barrel is 

less than 35 percent for each 1.5-m (5-ft) run, but standard 

penetration resistance in soil sampling is more than 50 blows 

per 0.3 m (1 ft) 

0.8 

Peck et al. (1974) presented an empirical correlation of presumptive allowable bearing pressure 

with Rock Quality Designation (RQD), as shown in Table 5-9. AASHTO recommends using 

presumptive values proposed by Peck et al. for selecting the allowable bearing pressures; but if 

the recommended value of allowable bearing pressure exceeds the unconfined compressive 

strength of the rock or allowable stress of concrete the allowable bearing pressure should be 

taken as the lower of the two values. Although the suggested bearing values of Peck et al. (1974) 

are substantially greater than most of the other published values and ignore the effects of rock 

types and conditions of discontinuities, they provide a useful guide for an upper-bound 

69 
estimation as well as an empirical relationship between allowable bearing values and intensity of 

fracturing and jointing (Table 5-9). Note that with a slight increase of the degree of fracturing of 

the rock mass, when the RQD value drops from, say, 100 percent to 90 percent, the 

recommended bearing capacity value is reduced drastically from 29 to 19 MPa. 

Rock Quality Designation (RQD) is defined as the total sum of pieces of rock core greater than 

100 mm (4 in) in length. [Example: Rock core run sample is 1.5 m (60 inches). Summation of 

pieces of rock core greater than 100 mm (4 in) is 0.5 m (18 in). Therefore, the RQD = 0.5/1.5 = 

0.33 or 33 percent.] 

In no instance should the allowable bearing capacity exceed the allowable stress of the concrete. 

Furthermore, Peck et al. (1974) also suggested that the average RQD for the bearing rock within 

a depth of footing width (Bf) below the base of the footing should be used if the RQD values 

within the depth are relatively uniform. If rock within a depth of 0.5Bf is of poorer quality, the 

RQD of the poorer quality rock should be used to determine the allowable bearing capacity. 

TABLE 5-9: SUGGESTED VALUES OF ALLOWABLE BEARING 

CAPACITY (PECK ET AL., 1974) 

RQD (%) Rock Mass Quality 

Allowable Pressure

(MPa) 

100 Excellent 29

90 Good 19

75 Fair 12

50 Poor 6

25 Very Poor 3

0 Soil-like 1

Note: Rock Quality Designation (RQD) is defined as the total sum of

pieces of rock core greater than 100 mm (4 in) in length. See example 

calculation in text. 

5.2.8 Allowable Bearing Capacities on Soil 

An acceptable and safe design can be achieved by first calculating the ultimate bearing capacity 

of a spread footing using the procedure in Section 5.2.5 and applying an adequate factor of safety 

(Section 5.2.6), then performing a settlement analysis to ensure that the foundation will function 

within performance limits under the applied stress (Sections 5.3.3, 5.3.4 and 5.3.5). If the 

settlement at the allowable bearing stress is excessive, the allowable bearing capacity must be 

reduced until the calculated settlement is within tolerable limits. Note that the soils within a 

zone about 1.5 times the footing width below the footing are the most significant when 

considering shear failure and settlement. It is therefore beneficial to obtain good data about the 

subsurface soils in this zone. SPT tests and soil sampling on 0.75-m (2.5-ft) spacing should be 

considered the minimum level of subsurface data obtained through this zone. Sampling intervals 

can be reduced to the usual 1.5 m (5-foot) spacing below this level. Borings still must be 

70 
extended at least through the zone of influence for settlement considerations (two to four times 

the estimated least footing width), as described in Section 4.3.2. 

Remember that allowable bearing capacity also includes consideration for limiting the potential 

for the footing to settle. The design of shallow foundations for bridges is frequently governed by 

settlement rather than shear failure considerations, due to the large footing widths. However, an 

adequate margin of safety should be maintained for all expected loading conditions relative to 

the potential for shear failure to develop below the footing. 

5.2.9 Allowable Bearing Capacities on IGMs and Rock 

The geotechnical engineer should use site investigation, in situ testing and lab testing to confirm

material properties of IGMs and rock. Judgment must then be applied to the theoretically 

computed bearing capacities combined with local experience (presumptive bearing values) when 

selecting an allowable bearing capacity for design. To preserve stability, the geotechnical 

engineer must evaluate the potential for global stability or rock mass discontinuities to limit the 

allowable bearing capacity. Recall that the bearing capacity of some sedimentary rock can 

dramatically decrease when exposed to weathering and moisture. 

5.2.10 Allowable Bearing Capacities on Compacted Structural Fills 

Allowable bearing capacities for spread footings constructed on compacted structural fills will be

a function of the quality of the fill (e.g., gradation, durability, drainage), the degree of

compaction achieved in the field, and the strength and compressibility of the embankment 

foundation materials. For fill materials such as sands, the design allowable bearing capacity can 

be determined rationally through laboratory testing such as the direct shear test, conducted at the 

proper level of compaction and applied stress. The friction angle yielded from such a testing 

program can be used to directly calculate an allowable bearing capacity. 

It is typically desirable and recommended that the compacted structural fills supporting spread 

footings be a select and specified material that includes sand- and gravel-sized particles. Direct 

shear testing of such materials requires large test equipment and is therefore not practical on a 

project-by-project basis. The design of spread footings on compacted sand and gravel materials 

is therefore a combination of experience and infrequent lab testing on specified gradations of 

select fill materials. Materials specifications are then developed based on the specified

gradations that ensure good quality control during construction. This procedure helps ensure that 

the conclusions from the lab tests are valid for the construction practices used to place the fills. 

Table 5-10 lists the presumptive allowable bearing capacities used by some state highway 

agencies for design of spread footings supported on compacted structural fills. The material and 

construction specifications associated with these bearing capacities are included in Appendix A. 

71 
TABLE 5-10: PRESUMPTIVE BEARING CAPACITY VALUES FOR FOOTINGS

CONSTRUCTED ON COMPACTED STRUCTURAL FILLS 

Agency 

Allowable Bearing 

Capacity 

Associated Anticipated 

Settlement 

Fill Material

Specified1,2

Washington State 

DOT 

290 kPa (3 tsf) < 40 mm (11⁄2 in) Gravel Borrow 

Nevada DOT 190 kPa (2 tsf) < 32 mm (11⁄4 in) Type 1A Aggregate 

Base 

Michigan DOT 170 kPa (13⁄4 tsf) Not available Granular Material 

Class III 

1

 Specifications included in Appendix A. 2

 Specifications must state levels of control quality for fill material (e.g., gradation, durability), lift thickness and

compactive effort.

5.2.11 Overstress Allowances for Bearing Stresses 

Under Service Load Design (AASHTO, 1996), certain load groups (e.g., seismic) are permitted 

to exceed the allowable bearing stress of a member (in this case the foundation bearing material) 

by a specified percentage that ranges from 25 to 50 percent. These overstress allowances are 

permitted for short-duration, infrequently occurring loads and may also be applied to calculated 

allowable bearing capacities. 

5.3 SETTLEMENT ESTIMATION

The two primary considerations that affect the selection and design of shallow foundations are 

bearing capacity (discussed in the previous section) and the settlement potential of ground within 

the zone of influence below the foundation. This section discusses the parameters and methods 

of analysis used to estimate the magnitude and time-rate of settlement for shallow foundations. 

Total settlement of a shallow foundation will result from one, or more likely, a combination of 

the following: 

a) Immediate Compression: This settlement may result from elastic compression of the 

material supporting the foundation, or from reduction in the pore space in nonsaturated 

soils due to expulsion of air from the void space. In cohesionless soils, nearly all the 

settlement that results from an increase in stress is associated with immediate, or elastic, 

compression. 

b) Primary Consolidation: Consolidation settlement occurs when saturated, fine-grained

soils experience an increase in stress. The water in the pore spaces initially carries the 

load. Then, as the water is expelled from the pore space, the soil experiences a reduction 

in volume and a decrease in the pore space between soil particles. The process can be

slow to rapid and is strongly a function of the permeability of the soil in the direction of

drainage. The process slows and eventually stops once all the excess pore water pressure 

72 
induced by the stress increase is dissipated. Primary consolidation is principally a 

concern for fine-grained, or cohesive soils, since coarser grained soils are typically 

permeable enough that any volume change that occurs as a result of expulsion of water 

from void space occurs as rapidly as the loads are applied. 

c) Secondary Compression: Some soils, after first experiencing primary consolidation 

settlement, continue to strain after excess pore-water pressures are dissipated. This 

process is termed secondary compression, or “creep.” Organic soils and some inorganic 

silts are soil types that can exhibit both primary consolidation and secondary 

compression, or creep, settlement. 

Initial compression accounts for the major portion of consolidation in granular soils. Primary 

compression accounts for the major portion of consolidation in cohesive soils. Primary and 

secondary compression both contribute significantly to consolidation settlement in organic soils. 

Differential settlement occurs when one load-bearing member of a structure experiences total 

settlement of a different magnitude than an adjacent load-bearing member. Because differential 

settlement will introduce load and stress in the structure above the foundations, limiting

differential settlement may frequently be of more interest in the design of a structure than total 

settlement. If total settlements are limited, of course, differential settlements will be limited to 

an even greater extent. 

Transportation structures, especially bridges, are not exceptionally tolerant of differential 

settlement. Deformation limitations will therefore frequently form the upper bound of allowable 

soil bearing capacities used to design shallow foundations. 

5.3.1 Serviceability Criteria 

The tolerable movements a structure can withstand depend on the type of structure, the expected 

service life and the consequences of excessive movements. Tolerable movements are frequently 

described in terms of angular distortion between members. “Angular distortion” is defined as the 

ratio of the differential settlement (δ') between footings to the span length (l), or δ'/l. The 

maximum angular distortion should be limited to some acceptable value to minimize structural 

strength and serviceability problems. Excessive differential displacements can induce significant 

structural cracking. 

Empirical studies of the performance of bridges subjected to various maximum angular 

distortions between adjacent foundations concluded that the serviceability criteria would be met 

if the angular distortion for simple span bridges is less than 0.005 and, for continuous span 

bridges, less than 0.004 (Moulton et al., 1982, 1985). Using these criteria, a continuous span 

bridge having a span length of 30 m (100 ft) can tolerate a differential settlement of about 130 

mm (5 in) between supports. In practice, bridges are typically designed for tolerable settlements 

much smaller than this. It is not uncommon for continuous span structures to be designed for 

differential settlements between adjacent piers of about 25 mm (1 in) or less, and for simply 

supported spans of about 38 to 50 mm (11⁄2 to 2 in). 

DiMillio (1982) reports in the FHWA research report “Performance of Highway Abutments on 

Spread Footings” that moderate differential movements of 25 to 75 mm (1 to 3 in) caused very 

73 
little distress in any of the structures studied. Of the 148 bridges with spread footings studied, 

the foundation movements observed were small, and the movements did not cause significant 

distress. 

For large footings on non-uniform soil profiles, or footings subjected to large eccentric loads, 

footing rotation may be a concern. In these cases the magnitude of the rotation can be computed 

by considering the potential differential settlement due to the difference in the applied loads or 

the non-uniformity of the soil profile. 

It should be noted that tolerable differential movement between adjacent columns within a single 

pier or bent may be significantly smaller than between adjacent piers on the same structure due 

to the rigidity and relatively short length of the superstructure cross beam. The geotechnical and 

structural engineers should confer when there is potential for adjacent individual spread footings 

supporting columns within the same pier to experience differential settlements. 

In some situations, the total movements may be the criteria that are critical in ensuring that 

serviceability issues are met. An example might be a simply supported, single-span structure 

with predicted settlements of several tenths of a meter at both abutments. While the structure 

itself is not at structural or performance risk due to the total, but relatively uniform movements, 

the resulting sag in the roadway profile may be unacceptable for vehicle ride, safety or aesthetic 

issues. 

5.3.2 Vertical Stress Distribution 

This section discusses methods to determine changes in total vertical stress (∆σv) due to 

foundation loading from a spread footing. The following methods for calculating total vertical 

stress change assume uniformly loaded foundations. Other references (Poulos & Davis, 1974) 

may be consulted for other load distributions. 

Methods based on the theory of elasticity are the easiest and most commonly used methods to 

determine the changes in total stress due to applied foundation pressures. Most closed-form

solutions based on the theory of elasticity involve the assumptions that the soil is homogeneous, 

isotropic and elastic. Lambe and Whitman (1969) report that the stresses predicted under these 

assumptions agree remarkably well with the relatively few comparisons that have been made to 

actual measured stresses, but the authors go on to point out that the computed stresses may be in 

error by as much as 25 percent or more. The charts in Figures 5-9 to 5-11 can be used to 

estimate the stress increases beneath circular, strip and rectangular loaded areas. The loadings 

are assumed to be uniform, an assumption that has been found to yield reasonable results for 

settlement prediction purposes. 

Note that the principle of superposition may be used with Figure 5-11 to evaluate stresses 

resulting from irregular or multiple loaded areas. The FHWA EMBANK program (Urzua, 1993) 

uses these procedures to compute stress increases beneath embankments, which can be used for 

settlement analysis of approach embankments. 

74 
Note: In the above Figures, and ∆σv ∆σh are analogous to, may be substituted for, ∆ and , 

respectively. 

1 σ 3

∆σ

Figure 5-9: Stresses Under Uniform Load on Circular Area (Lambe & Whitman, 1969) 

75 
Figure 5-10: Stresses Under Uniform Strip Load (Lambe & Whitman, 1969) 

76 
Figure 5-11: (a) Chart for Use in Determining Vertical Stresses Below Corners of 

Loaded Rectangular Surface Areas on Elastic, Isotropic Material 

(b) At Point A, ∆σv = ∆qs × f (m,n) (From Newmark, 1942) 

77 
Alternatively, stress distributions can also be obtained by assuming a 2-to-1 distribution of stress 

below the footing, as shown in Figure 5-12. This is much simpler to compute and is a reasonably

accurate approximation of the decrease in stress with depth due to an applied surficial load of 

limited areal extent. 

A comparison of the simplified 2-to-1 distribution with the actual distributed stress according to

elastic theory is shown in Figure 5-13. This distribution can be computed as a function of 

applied stress according to: 

q

∆σv = 

(B Z)(L Z)

B L

f f

f f

+ +

(5-17)

where: ∆σV = Change in vertical stress at depth Z below the footing bearing elevation 

q = Stress applied by the footing at the bearing elevation 

Z = Depth below footing bearing elevation to point of interest, usually the center 

or midpoint of a soil layer or sublayer where a settlement computation is to 

be made 

 Bf = Width of footing 

 Lf = Length of footing 

5.3.3 Footings on Cohesive Soils 

Primary and secondary consolidation of clays or clayey deposits may result in substantial 

settlements when the structure is founded on saturated cohesive soils. Settlement resulting from

primary consolidation may take weeks to years to be completed. Furthermore, because soil 

properties may vary beneath the foundation, the duration of the primary consolidation and the 

amount of settlement may also vary with the location of the footing, resulting in differential 

settlement between footing locations. If such settlements are not within tolerable limits, the 

structure may not perform as expected or intended. 

When a foundation is wide compared to the compressible layer thickness beneath it, a large 

portion of the soil will settle vertically (one-dimensionally) with very little lateral displacement 

because of the constraining forces exerted by the neighboring soil elements. Based on

measurements of lateral displacements beneath embankments and tanks, it is usually reasonable 

to assume that the settlements beneath a foundation will be one-dimensional even for narrow 

foundations, provided an adequate factor of safety is applied to bearing capacity (Terzaghi & 

Peck, 1967). Desiccated crust or overburden above the base of the footing will tend to minimize 

the amount of lateral displacements. Experience suggests that reasonably good estimates of 

settlement can be predicted assuming one-dimensional compression as long as the factor of 

safety is at least three (3) against bearing capacity failure. One-dimensional consolidation theory 

is presented in this section and is used to calculate settlement estimates for shallow foundations 

on cohesive soils. 

78 
Figure 5-12: Distribution of Vertical Stress by the 2:1 Method 

(Chen and McCarron, 1991) 

79 
Figure 5-13: Comparison of Vertical Stress Increase Below a Uniformly 

Loaded Square Area as Computed by Elastic Theory and 

Approximated by the 2:1 Method (Perloff, 1975) 

One-dimensional consolidation testing (ASTM D-2435) on undisturbed soil samples is 

recommended for determining the compressibility of clays. The procedure for obtaining 

undisturbed samples and specifying the appropriate load increments for conducting the test is 

described in detail in the Soils and Foundations Workshop Reference Manual (Cheney & 

Chassie, 2000). 

Some natural deposits of cohesive soils have undergone heavy compression in their geologic 

history due to the weight of glaciers, the weight of overlying soil that was subsequently eroded 

away or dessication (drying) of the soils. These soils are called “preconsolidated” or 

“overconsolidated” and have been subjected to larger stresses in the past than at present. 

Preconsolidated soils can exhibit compressibility that is up to an order of magnitude less than 

normally consolidated soils. Preconsolidated soils can therefore be reloaded to a stress level 

lower than the preconsolidation pressure without experiencing large settlements. Identification 

of preconsolidated soils through consolidation testing can allow the cost-effective use of 

shallow foundations on such soils.

Settlement due to consolidation can be estimated from the slope of the one-dimensional 

consolidation test void ratio (e = volume of void/volume of solids) versus the logarithm of the 

vertical effective stress (σ′v) curve. Figure 5-14 shows a typical consolidation curve from a onedimensional consolidation test and the recommended procedure to obtain the preconsolidation 

pressure (σ′p) developed by Casagrande (1936). The following definitions apply to the variables 

in the drawing. 

80 
Figure 5-14: Void Ratio versus Log Effective Vertical Stress Curve from a Consolidation 

Test on Clay and the Casagrande Procedure for Determining the 

Preconsolidation Pressure (after Holtz & Kovacs, 1981) 

Preconsolidation pressure, σ′p – The maximum pressure to which a soil has been loaded in the 

past. It is useful to carefully establish a maximum and minimum value of σ′p and plot the range 

as a function of depth on the effective stress versus depth chart for the foundation location under 

consideration. 

Compression Index, CC – The slope of virgin compression in the e-log(σ′vc) curve. Virgin 

compression is the soil response to stresses higher than the preconsolidation pressure. 

Recompression Index, CR – The slope of the e-log(σ′vc) curve at pressures less than the 

preconsolidation pressure. In general, the recompression index is approximately one-tenth the 

magnitude of the compression index in virgin compression. 

Initial Void Ratio, eo – The void ratio at the initial overburden stress, σ′Vo. 

The overconsolidation ratio (OCR) is used to distinguish overconsolidated soils from normally 

consolidated soils and is defined as the ratio of the preconsolidation pressure (σ′p) at depth z to 

the existing vertical normal effective pressure (σ′vo) at the same depth, z. 

OCR= σ′p/σ′vo (5-18)

81 
Soils with an OCR=1 are normally consolidated, while those with an OCR>1 are 

preconsolidated. The magnitude of expected settlement depends on the magnitude of loading of 

the subsurface soils relative to the magnitude of σ'p. The magnitude of σ'p is determined from the 

corrected one-dimensional consolidation test results. 

Sampling disturbance can mask whether a soil is normally consolidated or overconsolidated, 

resulting in quantitatively poor estimates of settlements. Therefore, the highest quality samples 

should be obtained to measure the soil shear strength, compressibility and degree of 

preconsolidation in laboratory tests. The principal error in computing settlement for 

homogeneous clays is in the estimating of the degree of overconsolidation (Peck et al., 1974). 

The designer should use all available evidence to estimate the degree of preconsolidation. The 

undrained shear strength (cu) and plasticity index (PI) can be used as a check (Peck et al., 1974) 

to estimate if a soil deposit is overconsolidated. The ratio of the undrained shear strength (cu) 

and the vertical effective stress for normally consolidated clays has been correlated to plasticity 

index (Skempton, 1948; Bjerrum & Simons, 1960) and can be computed according to Equation 

5-19.

0.10 0.004 (PI) c

v

u = +

σ′ (5-19)

If the cu/σ'v values in the field are significantly higher than Equation 5-19, the soil is probably 

overconsolidated. Furthermore, if the deposit is known to be normally consolidated (i.e., 

OCR=1), the undrained shear strength determined from in situ or laboratory tests can be checked 

with this relationship. 

The settlement induced by a shallow foundation can be kept to a minimum if the combined effect 

of the initial effective stress and the stress increase transmitted by the footing is lower than the 

preconsolidation pressure, σ′p. When site and economic conditions permit, the foundations may 

be designed to distribute structure loads such that they remain below preconsolidation stresses. 

Numerous correlations have been made between the compression index, Cc, and common index 

tests for normally consolidated soils and several are included in Table 5-11. Note that the 

values of Cc can vary by as much as a factor of 5 (using the average trend line) in these 

empirical correlations for cohesive soils. They should not be used for final design of 

footings on cohesive soils. 

The primary consolidation settlement, Sc, of a foundation resting on layers of normally 

consolidated soils (σ′p=σ′vo) can be computed from: 

vo

vf o 10

i o

c c '

' H log 1 e

C S

σ

σ ∑

+ = n

 (5-20)

82 
TABLE 5-11: CORRELATIONS FOR COMPRESSION INDEX, CC

Correlation Soil Source

Cc = 0.009 (LL-10) (1) Clay of medium to low 

sensitivity (St

<4) (2)

Terzaghi & Peck (1967) 

Cc = 0.0115 wn

(3) Organic soils, peat ASCE (1994) 

Cc = 0.04 to 0.006 (4) Uniform silts Hough (1959) 

Cc = 0.015 to 0.02 (4) Uniform sand, loose Hough (1959) 

Cc = 0.004 to 0.008 (4) Uniform sand, dense Hough (1959) 

1

 LL=liquid limit 2

 St=sensitivity=Undisturbed undrained shear strength/Remolded undrained shear strength 3

 wn= natural water content 4

 Cc = 1/C′ where C′ is the bearing capacity index (Figure 5-19). Note: These are for cohesionless 

soils, but are included here for comparison purposes.

where: Sc = primary consolidation due to the change in void ratio of the soil 

Cc = compression index of the normally consolidated portion of the e–log 

σ′v curve 

 eo = initial void ratio 

 Ho = thickness of layer n

σ′vo = initial effective vertical stress at the center of layer n

σ′vf = final effective vertical stress at the center of layer n

The final effective vertical stress is computed by adding the stress change due to the foundation 

load to the initial vertical effective stress. The change in the vertical effective stress is computed 

using the methods discussed in Section 5.3.2. The total settlement will be the sum of the 

compression in each of the n layers of soil. 

Normally, the slope, Cc, of the virgin portion of the e-log σ′v curve is determined from the 

corrected one-dimensional consolidation curve measured on specimens taken from each relevant 

soil in the stratigraphic column. 

Sometimes the consolidation data are presented in terms of vertical strain (εv) instead of void 

ratio (Figure 5-15). In this case, the slope of the virgin portion of the εv versus log σv curve is

denoted as Ccε, and the settlement is computed using Equation 5-21 for normally consolidated 

soils. 

S H C log ( ' / ' ) o c 10 vf' vo

n

1 c = ∑ ε σ σ (5-21)

83 
 (a) (b) 

Figure 5-15: Typical Consolidation Curve for Normally Consolidated Soil 

(a) Void Ratio and (b) Vertical Strain versus Vertical Effective Stress 

If the water content of a clay layer below the water table is closer to the plastic limit than the 

liquid limit, or if the ratio of cu/σ'

v exceeds the value from Equation 5-19, then the soil is likely 

overconsolidated. As a result, the field state of stress (before footing loads are applied) will 

reside on the recompression portion of the e versus log σ'

v curve. When a footing applies a load 

to the overconsolidated layer, the state of stress will first follow the recompression portion of the

curve, until the preconsolidation pressure is reached. For stress states larger than the 

preconsolidation pressure, the virgin portion of the curve is followed. The settlements for the 

case of n layers of over-consolidated soils (OCR>1) are computed from Equation 5-22 (Figure 5-

16a) or Equation 5-23 (Figure 5-16b). 

) '

' C log '

' ( C log 1 e

H S

p

vf

c 10

vo

p

r 10

o

o

n

1

c

σ

σ

+

σ

σ

+ = ∑ (5-22)

) '

' C log '

' S H ( C log

p

vf

c 10

vo

p

o r 10

n

1

c

σ

σ

+

σ

σ = ∑ ε ε (5-23) 

The total settlement is computed by subdividing each compressible layer within the zone of 

influence, ZI, into a sufficient number of sublayers, n, such that the initial and final stress 

calculated at the center of each layer is representative of the average stress for the layer, and the 

material properties are reasonably constant within the layer. The layers are typically 1.5 to 3 m

thick in highway bridge applications. In cases where the various stratigraphic layers represent 

combinations of both normally and preconsolidated soils, the settlement is computed using the 

appropriate combinations of Equations 5-20 through 5-23. 

84 
 (a) (b) 

Figure 5-16: Typical Consolidation Curve for Overconsolidated Soil 

(a) Void Ratio and (b) Vertical Strain versus Vertical Effective Stress 

5.3.3.1 Time Rate of Consolidation 

Consolidation occurs when a saturated compressible layer of soil is loaded and water is squeezed 

out of the layer. The time required for the (primary) consolidation process to end will depend on 

both the compressibility and the permeability of the soil. 

The rate of consolidation is usually of lesser concern for foundations because superstructure 

damage will occur once the differential settlements become excessive. Shallow foundations are 

designed to withstand the settlement that will ultimately occur during the life of the structure, 

regardless of the time it takes for the settlement to occur. It is generally much more important to 

predict the time rate of the settlement of an approach embankment on soft clay, particularly if the 

embankment is surcharged in order to allow use of a spread footing. The procedure for 

computing the time-rate of settlement is beyond the scope of this document. However, design of 

approach embankments and surcharges for dealing with settlement of approach embankments is 

included in the Soils and Foundations Workshop Reference Manual (Cheney & Chassie, 2000). 

These procedures can be used to manage the potential for approach embankment settlement to 

allow the use of a spread footing supported in the approach fill. Example 3 in Appendix B 

shows the elements of this procedure. 

5.3.3.2 Secondary Compression 

Soils susceptible to secondary compression (creep) are generally too poor to consider supporting 

a shallow foundation on them. Even if the primary consolidation can be managed with 

surcharging, the uncertainty associated with predicting the magnitude of secondary compression 

settlements is generally too great to reliably found a spread footing on or over creep-susceptible 

soils. 

85 
5.3.4 Footings on Cohesionless Soils 

The design of shallow foundations on cohesionless soils (sand, gravel and non-plastic silt), either 

as found in situ or as engineered fill, is often controlled by settlement potential, rather than 

bearing capacity limitations. The method used to estimate settlement of footings on cohesionless 

soils should therefore be reliable so that the predicted settlement is rarely less than the observed 

settlement, yet still reasonably accurate so that designs are not inefficient. Most settlement 

estimation methods are based on either elasticity theory or semi-empirical correlation to large 

databases of soil test data. 

Settlement estimation methods based on elastic theory can be unreliable due to the difficulty of 

measuring the elastic modulus of granular soils. Modulus estimation is difficult because true 

undisturbed sampling of cohesionless soils is neither simple nor practical for routine foundation 

design. The modulus of granular soils can be estimated from in situ tests but, again, the 

reliability can be variable. 

Semi-empirical methods are therefore the predominant techniques used to estimate settlements of 

shallow foundations on cohesionless soils. These methods have been correlated to large 

databases of simple and inexpensive tests such as the Standard Penetration Test (SPT) and the 

Cone Penetrometer Test (CPT). 

Two major studies (Burland & Burbidge, 1984; and Gifford et al., 1987) on shallow foundations 

in sands included 76 independent case histories that are relevant to highway bridge shallow 

foundations. The Gifford et al. study compiled data from 21 case histories to compare the 

predictive capabilities of 11 methods of computing settlements of shallow foundations on sands. 

Gifford et al. conducted a monitoring program to evaluate the actual time-settlement behavior of 

typical spread footing foundations on cohesionless soil. Over a period of 3 years, they monitored 

21 bridge foundations on shallow spread footings from initial construction through completion of 

the structures. The data from this instrumentation program then were used to evaluate the 

accuracy of several settlement calculation methods. The methods that Gifford et al. evaluated in 

their final study were Burland & Burbidge (1984), D’Appolonia et al. (1968), Hough (1959), 

Peck & Bazaraa (1969), Schmertmann (1970), and Oweis (1979). For each of the five settlement 

prediction methods, Gifford et al. plotted measured settlement versus calculated settlement for 

each bridge foundation as shown in Figure 5-17. 

In the 1990s, FHWA funded a study to examine the load-settlement behavior of large footings on 

cohesionless soils (Briaud & Gibbens, 1994, Briaud & Gibbens, 1995, and Briaud et al., 2000). 

The study included measuring settlement as vertical loads were applied to five square test 

footings ranging in size from 1 m by 1 m to 3 m by 3 m. The subsurface conditions at the 

National Geotechnical Experimental Site on the Riverside Campus of Texas A&M University 

were extensively evaluated using a wide range of exploration and testing procedures, including 

SPT, CPT, PMT, dilatometer tests, triaxial tests, borehole shear tests, and other measurements. 

As part of a prediction symposium, thirty-one authors submitted papers with alpha predictions of 

the load that would induce 25 mm (1 in) of settlement. Although an effort was made to compare 

predicted versus measured settlements for the numerous settlement computation methods used 

by the authors, it was concluded that there was too much variability in the way the various 

86 
0 

1 

Calculated Settlement 

Measured Settleme

nt

0 1 2

 + Burland & Burbidge 

● D’Appolonia 

 * Hough 

 o Peck & Bazaraa 

 x Schmertmann 

Figure 5-17: Calculated versus Measured Settlements (Gifford et al., 1987) 

authors applied the methods to draw valid conclusions about the reliability and accuracy of the 

various methods. The most promising development resulting from this research is a method for

computing settlement versus applied load using pressuremeter data. The method is presented in 

summary form in Section 5.3.4.3. This method is of particular interest in deformation-based 

analysis (as opposed to force-based analysis) and holds promise for evaluation of extreme load 

cases such as earthquake. The method may also be of notable value in the implementation of

Load and Resistance Factor Design (LRFD), as discussed in Appendix C. 

Considering the performance expectation of any settlement estimation method, the following 

criteria are important: 

• The method should be reliable. That is, it should predict settlement with reasonable 

accuracy over a relatively wide range of soil conditions. 

• The method should not exhibit a large standard deviation when comparing predicted 

settlement to actual settlement. A method that exhibits a large standard deviation in this 

regard has the potential for underpredicting settlement to a large extent, a condition that 

may result in poor structure performance. 

• The method should be easy to implement and be based on site-specific data that are 

readily available and inexpensive to obtain. 

• The method should have a substantial history of use with satisfactory results. 

Unfortunately, no method for estimating settlement on granular soils does an outstanding job of 

meeting all these criteria. However, the studies discussed above do conclude that at least some

of the methods meet most of these criteria reasonably well. Using these criteria, two methods 

were selected as currently preferred and recommended procedures for estimating settlement of 

foundations on granular soils: the Hough method and the D’Appolonia method. The load87 
settlement curve method recently developed by Briaud is also presented as a promising new 

method for computing deflections of spread footings on cohesionless soils (specifically sands) 

over a range of applied loads when pressuremeter test data are available. 

The data from the Gifford study indicate that the Hough method, on average, overpredicts 

settlement by a factor of about 2, and is thus less than desirable with respect to accuracy. 

However, the Hough method is relatively reliable in that it is conservative and consistent. The 

Gifford study found that the method has a relatively low standard deviation of calculated versus 

predicted measurements (so = 0.82). The Hough method is based on the SPT test and is easy and 

inexpensive to implement. Most notably, it is already currently used by many highway agencies, 

so it has a vast history of satisfactory application in the design of shallow bridge foundations 

across the United States. It also has the desirable attributes of rationally accounting for both the 

increase in stress induced below a footing and the layering of soil deposits. 

The Gifford study found the D’Appolonia method to be the most statistically accurate method 

evaluated. The standard deviation of calculated versus predicted measurements was also the 

lowest of the methods studied (so = 0.51). It computes settlement based on the modulus of 

compressibility of sand as correlated to the SPT test; therefore it is easy and inexpensive to 

implement. The method has the additional advantage of explicitly accounting for the effect of 

soil preloading, although the database to which preloaded modulus values were correlated was 

limited. Potential current drawbacks of the D’Appolonia method include the following: 

• It has limited application history for highway bridges, especially as compared to the 

Hough method. 

• It does not expressly account for soil layering. 

• The distribution of stress below the loaded area is accounted for with an empirical 

correction factor that does not suggest a limiting depth of stress influence.

• The population of the database used to develop the method’s modulus correlation as a 

function of SPT N-values is limited. 

• Because it is statistically more “accurate,” it is also potentially unconservative in 

practical application. That is, about half the normally distributed data will fall on the 

unconservative side of predicted versus measured settlement. 

The data from the five full-scale load tests (Briaud & Gibbens, 1995) were used by the author to 

compare the performance of both the Hough and D’Appolonia methods of predicting the load 

that would result in 25 mm (1 in) of settlement. Note that this was not a true alpha prediction. 

Nevertheless, the field performance data from the five load tests is excellent, and the two 

methods were applied as strictly as possible according to the procedures described below. The 

comparison yielded the following conclusions: 

• The Hough method was found to over-predict settlement by an average factor of about 

1.8 for the five footings (the standard deviation, so, was 0.53). In no case, however, did 

the Hough method under-predict the observed settlement. 

88 
• The D’Appolonia method under-predicted the settlement by an average factor of about 

0.77 for the five footings, but the accuracy was generally better than Hough, and the 

scatter in the predicted settlement values was also less (standard deviation, so = 0.22). 

The data from the five load tests therefore generally corroborate the conclusions from the Gifford 

et al. and Burland & Burbidge studies. 

Therefore, it is currently recommended that the Hough method be used as a primary 

design and analysis tool. The D’Appolonia or load-settlement methods could be employed as 

alternates, or when a more accurate estimate of settlement is desired, recognizing that these 

alternate methods have less history of use in the design of highway bridges. Naturally, if another 

method is locally or regionally known to provide more reliable estimates of settlement on 

granular soils, and the method meets the criteria noted above, the geotechnical engineer should 

exercise judgment and use the best method available. 

5.3.4.1 Hough Method 

Hough (1959) developed an empirical method for predicting settlements of shallow foundations 

on cohesionless soils that follows the same approach as that used for calculating consolidation 

settlement of clay layers. Note that the method is applicable only for normally consolidated 

cohesionless soils. Cheney and Chassie (2000) recommend that the SPT blowcounts be 

corrected for overburden pressure before correlating the N-values to the bearing capacity index, 

C′. An overburden correction by Bazaraa (1967) was recommended by Cheney and Chassie 

(2000). Since that time, many researchers have studied the effect of overburden stress on the 

SPT N-value, largely in support of liquefaction hazard assessment procedures. Recent consensus 

by the 1996 and 1998 National Center for Earthquake Engineering Research (NCEER) (Youd et 

al., 2001) concluded that the correction proposed by Liao & Whitman (1986) (shown in Figure 

5-18) could be used for routine engineering applications. Therefore, the correction by Liao & 

Whitman is included here as part of the Hough procedure, in particular because it is easy to 

calculate and can be used without charts in simple computation spreadsheets. The soil is divided 

into layers, and the change in effective vertical stress at the mid-height of the layer as a result of 

the applied load is estimated using elastic theory.

The total settlement by the Hough method is calculated as follows: 

1. Correct SPT blowcounts for overburden stress using Figure 5-18. 

2. Determine bearing capacity index (C′) from Figure 5-19 using corrected SPT blowcounts, 

N′, determined in Step 1.

3. Subdivide subsurface soil profile into approximately 3-m (10-ft) layers based on 

stratigraphy to a depth of about three times the footing width. 

4. Calculate the effective vertical stress, σ′vo, at the midpoint of each layer and the average 

bearing capacity index for that layer. 

5. Calculate the increase in stress at the midpoint of each layer, ∆σv, using either Figure 5-9, 

5-10 or 5-11, or the 2:1 method (Figure 5-12). 

89 
Correction Factor for SPT (N) Blow Counts

0.1

1.0

10.0

0 100 200 300

σ'Vo (kPa)

N'/N

N'/N = 1/(σ'Vo/95.76)

0.5 

σ'Vo in kPa

2.0 max.

Figure 5-18: Corrected SPT (N) versus Overburden Pressure (after Liao & Whitman, 1986) 

6. Calculate the settlement in each layer, ∆H, under the applied load using the following 

formula:

















σ′

σ′ + ∆σ

′ ∆ =

vo

vo v

o

f log C

1 H H (5-24)

7. Sum the incremental settlements to determine the total settlement. 

5.3.4.2 D’Appolonia Method 

The D’Appolonia method calculates settlement using the following basic equation: 

o 1

V f

M

B H μ μ 

 



 ∆σ ∆ = (5-25)

where: ∆H = settlement in sand or sand and gravel 

∆σv = applied stress beneath footing 

 Bf = footing width 

 μO = correction factor for embedment – see Figure 5-20 (dimensionless) 

 μ1 = correction factor for thickness of sand layer – see Figure 5-20 (dimensionless) 

M = modulus of compressibility of sand – see Figure 5-21 

Any consistent set of units can be used for ∆H, ∆σv, Bf and M. 

90 
Figure 5-19: Bearing Capacity Index versus Corrected SPT 

(Cheney & Chassie, 2000, modified from Hough, 1959) 

91 
Figure 5-20: Correction Factors for Embedment and Layer Thickness 

(Christian & Carrier, 1978) 

Note: In the above Figure, “Table” refers to a tabulation of load versus settlement data from seven case

histories, including six bridge footings, by D’Appolonia et al., (1970), and “Site” refers to the load versus 

settlement data obtained by D’Appolonia at al., (1968) at a large steel mill site in northern Indiana. 

Figure 5-21: Modulus of Compressibility (D’Appolonia, 1968, 1970) 

92 
Further discussion of the application and use of other methods to calculate settlement can be 

found in the NHI Shallow Foundations Reference Manual (Munfakh et al., 2000). Methods 

covered in the Reference Manual include Schmertmann (1970), Peck & Bazaraa (1969), and 

Terzaghi & Peck (1967). 

5.3.4.3 Load-Settlement Curve Method 

In recent research, Briaud and colleagues (Briaud & Gibbens, 1994, Briaud & Gibbens, 1995, 

and Briaud et al., 2000) developed a procedure to estimate settlements of spread footings on sand 

using pressuremeter test (PMT) data. They developed the procedure because they had observed 

that the movement of the soil below a footing during large scale load tests showed an analogy to 

the movement of soil around an expanding pressuremeter probe during a pressuremeter test. The 

procedure is as follows: 

1. Perform pre-bored pressuremeter tests within the depth of influence of the footing, 

typically at depths of 0.5B, 1B and 2B below the bearing elevation of the footing. Refer 

to The Pressuremeter Test for Highway Applications (Briaud, 1989) or The 

Pressuremeter (Briaud, 1992) for details regarding performance of the test and reduction 

of the test data. 

2. Reduce the data and average the pressuremeter curves into a single pressuremeter curve. 

3. Transform the average pressuremeter curve point-by-point into the load-settlement curve 

for the footing using Equations 5-26 through 5-35. Equation 5-26 aims at ensuring strain 

compatibility. The footing limit pressure is defined as the footing pressure corresponding 

to a settlement equal to 10 percent of the footing width (ρ/B = 0.1). Correspondingly, the 

pressuremeter limit pressure is defined as the pressure reached when the relative increase 

in cavity radius is equal to 0.42. Equation 5-26 ensures that when ρ/B is equal to 0.1,

∆R/R0 is equal to 0.42, and therefore the two limit pressures are corresponding. 















 ∆ = ρ

R0

R

4.2

1

B (5-26)

where: ρ = Vertical settlement of the footing 

B = Footing width 

∆R/R0 = Ratio of the increase in cavity radius to the original radius from average 

pressuremeter test

Once Equation 5-26 is satisfied, Equation 5-27 is used to transform the pressuremeter pressure, 

pp, into the footing pressure, pf, through the gamma function, Γ. 

pf = fL/B fe fδ fβ,d Γ (pp) (5-27)

where: pf = Transformed footing pressure 

pp = Pressuremeter pressure 

Γ = Gamma function computed according to Equation 5-28 

fL/B = Influence factor for footing shape, Equation 5-29 

fe = Influence factor for load eccentricity, Equations 5-30 & 5-31

93 
fδ = Influence factor for load inclination, Equations 5-32 & 5-33 

fβ,d = Influence factor for influence of slope, Equations 5-34 & 5-35 

The gamma function, Γ, transforms the pressuremeter pressure, pp, into the footing pressure, pf, 

for a square footing loaded vertically at its center on a flat ground surface. This function was 

developed using data from 22 footing load tests from 9 different sand and silt sites. The gamma 

function recommended for design was chosen as the mean function through the data points 

minus one standard deviation to be on the safe side (conservative). The gamma function is 

computed according to Equation 5-28. 

Γ = 0.8

0.5

B

100

0.9

+

 +



 



 ρ (5-28)

where: ρ = Vertical settlement of the footing 

 B = Footing width 

The influence factors, f, for more complex loading conditions were developed from numerical 

simulations because there are insufficient load tests available for these load cases to correlate the 

factors directly to performance data. The influence factors were compared with the few existing 

applicable load tests and with other existing recommendations for influence factors. 

The influence factor for footing shape can be computed using Equation 5-29. 

fL/B = 



 



 +

L

B 0.8 0.2 (5-29)

where: L = Footing length 

 B = Footing width 

The influence factor for eccentric loading can be computed using Equations 5-30 and 5-31, 

depending on the settlement location of interest. 

fe = 



 



 − B

e 1 0.33 at the center of the footing (5-30) 

 = 

0.5

B

e 



 



 1− at the edge of the footing (5-31) 

where: B = Footing width 

 e = Eccentric distance due to applied moment in the direction of B 

The influence factor for inclined loading can be computed using Equations 5-32 and 5-33, 

depending on the settlement location of interest. 

fδ = 

2

90

1 



 



 δ − at the center of the footing (5-32) 

94 
fδ = 

0.5

360

1 



 



 δ − at the edge of the footing (5-33) 

where: δ = Inclination of load from the vertical, in degrees. 

The influence factor for a footing located adjacent to a slope can be computer using Equations 5-

34 and 5-35, depending on the slope inclination and the proximity of the footing to the slope. 

fβ,d = 

0.1

B

d 0.8 1 



 



 + β = 18.4 degrees (3:1 slope) (5-34) 

 = 

0.15

B

d .7 1 



 



 0 + β = 26.6 degrees (2:1 slope) (5-35) 

where: β = Slope inclination from the horizontal 

d = Horizontal distance from top of slope to closest edge of footing 

 B = Footing width 

Based on the comparison data studied to date, the load settlement curve method shows 

significant promise for accurately predicting the settlement of a spread footing on cohesionless 

soils over a fairly large range of applied loads. The method may therefore prove uniquely useful 

in deformation-based design. Deformation-based design is not covered here, but holds promise 

for analysis of structures under extreme loading conditions, such as earthquake. 

Important considerations regarding use of the load-settlement curve method: 

1. The researchers that developed this method acknowledge that it is new and that use in 

parallel with existing design approaches on full scale bridge projects, with performance 

measurements, is needed before the method can be implemented as a validated, everyday 

design tool. 

2. Pressuremeter tests are still used infrequently, as compared to the SPT, hence the skills 

needed to perform and interpret the test results may be locally limited. 

3. The method develops load settlement relationships in normalized displacement (i.e., ρ/B). 

This form should be reduced to displacement versus footing width for a tolerable 

magnitude of settlement (as defined by the performance requirements of the structure) in 

order to be used in the recommended design procedures in this GEC (see Chapter 6 and 

the design examples in Appendices B and C). 

5.3.5 Footings on Structural Fills 

Calculation of settlement within the structural fill due to a spread footing supported in the fill 

requires an assumption about the compressibility of the constructed fill material. Because 

structural fills should be constructed using good-quality granular materials, the estimation of 

settlement lends itself to application of the methods discussed in the previous section. To do so, 

an assumption must be made about the representative SPT N-value of the compacted fill. 

95 
The Gifford et al., (1987) study used a corrected (for overburden pressure) SPT N-value of 32 

blows per foot as a representative value for estimating settlement in structural fills. This would 

correspond to a relative density, DR, of about 85 percent at an overburden stress of about 100 kPa 

(1 tsf) (Figure 4-1). Correlations of relative density to percent relative compaction suggest that 

this value of DR is at or above 95 percent relative compaction (Lee & Singh, 1971) and therefore 

approximates the compaction criteria for structural fill used by most highway agencies. 

Although Lee & Singh (1971) do not specifically state the relative compaction criteria (i.e., 

standard or modified Proctor), the comparisons were for granular soils and the modified Proctor 

method is mentioned. It is therefore assumed that the comparisons were based on the modified 

Proctor test. In the absence of other SPT data in structural fills, the settlement of a footing 

supported on structural fill can be estimated using an assumed corrected N-value (N′) of 32 

and the Hough method for computing settlement. 

5.3.6 Footings on IGMs and Rock 

As discussed in Section 3.1.3, the assumption is made in this GEC that intermediate geomaterials 

(IGMs) are stiff and strong enough that bearing capacity and settlement considerations will 

generally not govern design of a spread footing supported on such material. If a settlement 

estimate is necessary for shallow foundations supported on IGM or rock, a method based on 

elasticity theory will generally be the best approach. As with any of the methods for estimating 

settlement that use elasticity theory, a major limitation is the engineer’s ability to accurately 

estimate the modulus parameter(s) required by the method. 

Equation 5-36 may be used to compute settlement on rock based on Young’s modulus of the 

intact rock. In this equation, the stress applied at the top of the rock surface can be calculated 

using the stress distribution methods shown in Figures 5-9 through 5-12. 

E IR

2

d V f v E

C B (1 )

α

∆σ − ν δ = (5-36)

where: δv = Vertical settlement at surface 

 Cd = Shape and rigidity factors (Table 5-12) 

∆σv = Change in stress at top of rock surface due to applied footing load 

 Bf = Footing width or diameter 

ν = Poisson’s ratio (Table 5-13) 

 EIR = Young’s modulus of intact rock (Table 5-14) 

αE = Modulus reduction factor based on RQD (Equation 5-37) 

0.0231(RQD) 1.32 0.15 αE = − ≥ (5-37)

where: RQD = Rock Quality Designation, in percent. 

96 
TABLE 5-12: SHAPE AND RIGIDITY FACTORS, Cd, FOR CALCULATING 

SETTLEMENTS OF POINTS ON LOADED AREAS AT THE SURFACE 

OF AN ELASTIC HALF SPACE WITH INFINITE DEPTH 

(AFTER WINTERKORN & FANG, 1975) 

Shape Center Corner

Middle of 

Short Side 

Middle of 

Long Side Average 

Circle 1.00 0.64 0.64 0.64 0.85

Circle (rigid) 0.79 0.79 0.79 0.79 0.79

Square 1.12 0.56 0.76 0.76 0.95

Square (rigid) 0.99 0.99 0.99 0.99 0.99

Rectangle (length/width):

1.5 1.36 0.67 0.89 0.97 1.15

2 1.52 0.76 0.98 1.12 1.30

3 1.78 0.88 1.11 1.35 1.52

5 2.10 1.05 1.27 1.68 1.83

10 2.53 1.26 1.49 2.12 2.25

100 4.00 2.00 2.20 3.60 3.70

1000 5.47 2.75 2.94 5.03 5.15

10000 6.90 3.50 3.70 6.50 6.60

TABLE 5-13: SUMMARY OF POISSON’S RATIO FOR INTACT ROCK 

(AASHTO, MODIFIED AFTER KULHAWY, 1978) 

Poisson’s Ratio, v 

Rock Type 

No. of 

Values 

No. of 

Rock 

Types Maximum Minimum Mean

Standard 

Deviation 

Granite 22 22 0.39 0.09 0.20 0.08

Gabbro 3 3 0.20 0.16 0.18 0.02

Diabase 6 6 0.38 0.20 0.29 0.06

Basalt 11 11 0.32 0.16 0.23 0.05

Quartzite 6 6 0.22 0.08 0.14 0.05

Marble 5 5 0.40 0.17 0.28 0.08

Gneiss 11 11 0.40 0.09 0.22 0.09

Schist 12 11 0.31 0.02 0.12 0.08

Sandstone 12 9 0.46 0.08 0.20 0.11

Siltstone 3 3 0.23 0.09 0.18 0.06

Shale 3 3 0.18 0.03 0.09 0.06

Limestone 19 19 0.33 0.12 0.23 0.06

Dolostone 5 5 0.35 0.14 0.29 0.08

97 
TABLE 5-14: SUMMARY OF YOUNG’S MODULUS FOR INTACT 

ROCK (MODIFIED AFTER KULHAWY, 1978) 

Elastic Modulus, EIR 

(kPa x 106)

Rock Type 

No. of 

Values 

No. of 

Rock 

Types Maximum Minimum Mean

Standard 

Deviation 

Granite 26 26 99.97 6.41 52.67 24.48

Diorite 3 3 111.69 17.10 51.36 42.68

Gabbro 3 3 84.11 67.57 75.84 6.69

Diabase 7 7 104.11 68.95 88.25 12.27

Basalt 12 12 84.11 28.96 56.12 17.93

Quartzite 7 7 88.25 36.47 66.12 16.00

Marble 14 13 73.77 4.00 42.61 17.17

Gneiss 13 13 82.05 28.47 61.09 15.93

Slate 11 2 26.13 2.41 9.58 6.62

Schist 13 12 68.95 5.93 34.27 21.92

Phyllite 3 3 17.31 8.62 11.79 3.93

Sandstone 27 19 39.16 0.62 14.69 8.20

Siltstone 5 5 32.82 2.62 16.48 11.38

Shale 30 14 38.61 0.01 9.79 10.00

Limestone 30 30 89.63 4.48 39.30 25.72

Dolostone 17 16 78.60 5.72 29.10 23.72

Additional corrections can be made for complex geologic conditions. The NHI Shallow 

Foundations Workshop Reference Manual (Munfakh et al., 2000) includes discussion of layered 

and anisotropic rock conditions and methods for correcting the deformation calculation. 

The elastic modulus of IGMs and some rocks may be measurable by in situ testing with 

equipment such as the pressuremeter, the flat dilatometer, plate load tests or flat jacks. The 

reader is referred to FHWA publications, including The Pressuremeter Test for Highway 

Applications (FHWA-IP-89-008) and The Flat Dilatometer Test (FHWA-SA-91-044), or the 

relevant ASTM test method for details regarding performance and interpretation of the in situ 

test data. 

Alternatively, some modulus values are available from various researchers based on the rock 

type. Sources include Bieniawski (1984, 1989), Kulhawy (1975) and Lama and Vutukuri 

(1978). Tables 5-13 and 5-14 summarize suggested values for Poisson’s ratio and elastic 

modulus as presented in AASHTO (1996) and modified after Kulhawy (1978). 

98 
5.4 SLIDING AND LATERAL STABILITY

A shallow foundation will resist lateral loads by a combination of the shear resistance along the 

base of the footing and the lateral earth pressure that develops in front of the footing in the 

direction of loading. The shear resistance along the base will develop its full capacity at very 

small deflections. The lateral earth pressure is termed “passive resistance” and requires much 

larger deflections to develop the full passive capacity. By the time the passive resistance is fully 

developed, the shearing resistance is fully mobilized and may even by reduced to some residual 

value less than the peak shearing resistance. For this reason, the design of most shallow 

foundations conservatively ignores passive resistance. 

Sliding resistance between the base of a shallow foundation and a granular soil will be governed 

by the coefficient of friction (tan δ) that develops between the foundation soil and the footing. 

The value of the coefficient of friction is a function of the soil type and the roughness of the 

footing. For concrete cast against cohesionless or granular material, the coefficient of friction, 

tan δ, will be equal to the tangent of the friction angle (tan φ) for the soil supporting the footing. 

If the bottom of the footing consists of something other than concrete cast against the ground, 

then the coefficient of friction (tan δ) is not solely a property of the soil but is also a function of

the footing material type and roughness. In the absence of specific data, Table 5-15 may be used 

to estimate the coefficient of friction between soil and various footing material types.

TABLE 5-15: ULTIMATE FRICTION FACTORS FOR 

DISSIMILAR MATERIALS (NAVFAC, 1986B) 

Interface Materials 

Coefficient of 

Friction, tan δ

Friction 

Angle, δ

(degrees) 

Mass concrete on the following materials: 

Clean sound rock 0.70 35 

Clean gravel, gravel sand mixtures, coarse sand 0.55 to 0.60 29 to 31 

Clean fine to medium sand, silty medium to 

coarse sand, silty or clayey gravel

0.45 to 0.55 24 to 29 

Clean fine sand, silty or clayey fine to medium

sand 

0.35 to 0.45 19 to 24 

Fine sandy silt, nonplastic silt 0.30 to 0.35 17 to 19 

Very stiff and hard residual or preconsolidated 

clay 

0.40 to 0.50 22 to 26 

Medium stiff and stiff clay and silty clay 

(masonry on foundation materials has same

friction factor) 

0.30 to 0.35 17 to 19 

99 
If the base of the footing rests on clay, the sliding resistance will be limited by the adhesion that 

develops between the bearing surface of the footing and the cohesive bearing material, ca. In 

practice, ca is typically taken as equal to the undrained shear strength (cohesion, cu) of the clay. 

The general equation for sliding resistance for footings with planar bearing surfaces on frictional 

(drained) materials is: 

FR = (W + Pv) tan δ (5-38)

where: FR = ultimate sliding resistance

W = weight of the footing and soil backfill over the footing 

 Pv = loads applied to the top of the footing 

δ = friction angle between the base of the footing and frictional bearing material 

The general equation for sliding resistance for footings with planar bearing surfaces on cohesive 

(undrained) materials is: 

FR = caBf (5-39)

where: FR = ultimate sliding resistance

 ca = adhesion between the base of the footing and cohesive bearing material 

 Bf = footing width 

Because drained and undrained conditions will not occur simultaneously, Equations 5-38 and 5-

39 should not be combined for use at the same time. 

A minimum factor of safety (FS) of 1.5 against sliding should be used for design of bridge 

foundations: 

FSsliding = 1.5

F

F

sliding

R ≥ (5-40)

where: FSsliding = factor of safety with respect to sliding 

 FR = ultimate sliding resistance

 Fsliding = sum of horizontal loads acting to cause footing to slide 

Equations 5-38 and 5-39 assume the bottom surface of the footing is planar. If sliding resistance 

as determined by Equation 5-39 for a footing on clay soils is insufficient, the footing width 

should be increased to provide additional sliding resistance. If the footing width becomes 

impractical in terms of economic or constructability factors, consideration may be given to 

including a key constructed under the bearing surface of the footing. A typical configuration of a 

key is shown in Figure 5-22. Keys are typically difficult to construct while maintaining the 

intact shearing resistance of the soil adjacent to the key. 

In reality, keys constructed in granular soils are not very efficient in developing passive 

pressures in front of the key. Due to the deflections required to develop passive pressures 

described above, the frictional shearing resistance will already be fully mobilized. The effect of

100 
a key in granular soils is more properly considered as increasing the effective length of the 

shearing surface. 

In stiff, overconsolidated clays and soft rock, the additional resistance provided by a key can be 

computed using Figure 5-22 and Equation 5-41. 

Pa

Bf

Figure 5-22: Resistance Against Sliding from Keyed Foundation 

in Cohesive Soils and Soft Rock 

The general equation for sliding resistance of footings on cohesive soils provided with a key is: 

FR = a f 1 u 1 Pp c (B − a b) + c (a b) + (5-41)

where: FR = ultimate sliding resistance

 ca = adhesion between the base of the footing and cohesive bearing material 

 Bf = footing width 

a1b = distance from point a1 to point b 

 cu = undrained shear strength of cohesive soil 

 Pp = passive resistance force 

5.5 GLOBAL STABILITY

Global stability of shallow foundations should be evaluated when the geometry of the ground 

surface in any direction away from the footing suggests that the assumptions associated with the 

bearing capacity theory used to calculate the bearing capacity of the footing are not valid, and the 

stress applied by the footing loads is acting to destabilize the slope geometry. Figure 5-23 

depicts slope configurations and footing locations that act to either improve or degrade the global 

stability of the slope. 

101 
 (a) (b) 

Figure 5-23: Global Slope Stability with Respect to Shallow Foundation Locations 

(a) Footing Acting to Stabilize Slope, (b) Footing Acting to Destabilize Slope 

In cases where the stress applied by the footing acts to destabilize the slope, the global stability 

of the footing should be checked using limit equilibrium methods such as the method of slices 

(Bishop, 1955; or Spencer, 1967). 

Detailed guidance for the evaluation of slope stability is not included in this Circular. The Soils 

and Foundation Workshop Reference Manual (Cheney & Chassie, 2000) includes fundamental 

discussion of slope stability analysis methods considering the presence of a loaded footing within 

the slope. The reference work TRB Special Report 247: Landslides, Investigation and 

Mitigation (TRB, 1996) includes more detailed discussion on the analysis of global slope 

stability. 

102 
CHAPTER 6 

SHALLOW FOUNDATION DESIGN FOR BRIDGES 

This chapter presents the practical application of shallow foundation design for bridge structures. 

A design process is presented in a step-by-step format that will result in a satisfactory solution 

for most applications of shallow foundation bridge support. The design process involves 

multiple engineering disciplines. The discipline generally responsible for each design step is 

identified, whether it be geotechnical, structural, hydraulic, environmental or general civil. 

Worked foundation design examples that follow this process are included in Appendix B for 

spread footing support of bridge piers in the following applications: 

• Interior bridge pier supported on a spread footing founded in native soil 

• Integral stub abutment supported on compacted structural fill 

• Stub seat-type abutment footing supported in compacted structural fill 

• Full-height seat abutment founded in native soil 

• Interior bridge pier supported on a spread footing on native rock 

A discussion of the application of Load and Resistance Factor Design (LRFD) to the design of 

spread footings is included in Appendix C. The first and third examples in Appendix B are reworked in Appendix C using LRFD methodology. 

It should be noted that these examples are intended to convey one approach and process 

that can lead to a satisfactory design of bridge support on a shallow foundation. The 

examples should not be construed as representations of the only approach that can lead to a 

satisfactory design. Also note that the examples only check one or, at most, a few specific 

load cases. In practice, every complete design should consider all applicable load cases. 

6.1 DESIGN PROCESS AND FLOW CHART

The design process of a bridge supported on shallow foundations includes the steps shown in 

Table 6-1 and also in the design process flow chart, Figure 6-1. 

6.2 GENERAL CONSIDERATIONS

The depth and size of a shallow foundation for support of a bridge need to be selected to ensure 

that the bearing materials are able to support the loads imparted without shear failure or 

excessive settlement. This includes verifying that the bearing materials are nonliquefiable during 

earthquakes. The base of the footing also needs to be below the frost depth for frost susceptible 

soils, and below the probable scour during a design high water extreme event. 

103 
TABLE 6-1: STEPS IN DESIGN PROCESS FOR BRIDGE 

SUPPORTED ON SHALLOW FOUNDATIONS 

Step Design Activity Responsible Discipline(s) 

1. Develop preliminary bridge layout. Establish the desired 

bridge type, size and location. Define span lengths and pier 

locations, considering geometrical and environmental constraints. 

Structural, in coordination

with general civil and 

environmental considerations 

and geotechnical for approach 

stability

2. Determine the shallow foundation feasibility based on review of 

existing geologic and subsurface data. Competent bearing 

material must be present within a reasonable distance from the 

ground surface. A preliminary assessment of approach 

embankment stability should be conducted to evaluate potential 

impacts to abutment locations and span lengths (Section 4.1). 

Geotechnical, in coordination 

with structural, general civil 

and environmental 

3. A site reconnaissance with the structural and general civil 

engineer should be completed at this stage to evaluate 

constructability of foundation types (Section 4.2). 

Geotechnical, in coordination 

with structural, general civil 

and environmental 

4. Determine the depth of the footing so that it will not be 

susceptible to scour potential or frost (Section 6.2). 

Hydraulic, with geologic 

input from geotechnical 

5. Determine the loads applied to the footing and tolerable total 

and differential settlement for each pier (Section 6.3). 

Structural 

6. Determine the design soil properties from the subsurface 

exploration and laboratory testing program (Sections 4.3 and

4.4). 

Geotechnical 

7. Calculate the allowable bearing capacity, considering both the 

potential for bearing capacity failure (Section 5.1) and settlement 

(Section 5.2)

Geotechnical 

8. Calculate the allowable sliding and passive soil resistance

(Section 5.4) for evaluating lateral stability of the footing. 

Geotechnical 

9. In cases where overall stability of the footing may govern the 

design (e.g., footings on or near slopes), perform a global 

stability analysis of the footing using service (unfactored) loads 

(Section 5.5). 

Geotechnical 

10. Size the footing dimensions using service (unfactored) loads and 

the effective footing dimensions (Section 6.4.1). 

Structural 

11. Check the stability of the footing for sliding and overturning

using service loads (Sections 5.4 and 6.4). 

Structural 

12. Complete the structural design of the footing using factored 

loads per Load Factor Design requirements and assuming a 

trapezoidal distribution of contact pressure beneath the footing 

(Section 6.5). The design should consider the moment at the face 

of the column, one-way shear and two-way shear. 

Structural 

104 
1. Develop preliminary bridge

layout (ST)

2. Review existing geologic and

subsurface data (GT)

3. Site reconnaissance (GT)

4. Determine depth of footing for

scour and frost protection

(Hydraulic, GT) 

6. Subsurface exploration and

laboratory testing (GT)

7. & 8. Calculate allowable bearing

capacity, sliding and passive soil 

resistance (GT)

9. Check overall (global) stability 

using service (unfactored) loads

(GT)

11. Check stability of footing for

overturning and sliding (ST)

5. Determine loads applied to the

footing (ST)

10. Size the footing using service

(unfactored) loads (ST)

12. Complete structural design of

the footing using factored loads (ST)

ST – Structural

GT – Geotechnical

Figure 6-1: Design Process Flow Chart – Bridge Shallow Foundation 

105 
6.2.1 Scour Potential and Depth 

Scour is localized erosion of the channel bed that occurs around flow obstructions such as piers 

and bridge abutments, at channel contractions such as bridges, and on the outside of channel 

bends. It can also be the result of long-term erosion of the channel bed that can occur during a 

structure’s life. 

Scour is a site-specific process that is a function of the flow velocity and duration, the geometry 

of the structural elements exposed to the flow of water, the geomorphology of the channel and 

the properties of the foundation and channel bed materials. The process of scour is complex. A 

multidisciplinary team of hydraulic, geotechnical and structural engineers should evaluate the 

risk of scour-induced failure at each structure site.

This section describes the assessment of scour susceptibility for spread footing foundations. 

Basic scour concepts and techniques for scour protection are presented. The discussion focuses 

on scour at bridges, but concepts presented also apply to culverts, retaining walls and other 

transportation structures built near channels and rivers. Information presented here is consistent 

with FHWA publications on stream stability and scour, and the reader is encouraged to read the 

following for a detailed discussion of scour analysis and scour countermeasure design: 

• HEC 20 – Stream Stability at Highway Structures (Lagasse et al., 2001a) 

• HEC 23 – Bridge Scour and Stream Instability Countermeasures (Lagasse et al., 2001b) 

Scour assessment requires a determination of the cumulative effects of the three main 

components of scour: aggradation/degradation, contraction scour and local scour. It also requires 

an evaluation of potential changes in channel geometry and location that may occur during a 

structure’s design life. 

Aggradation and degradation are long-term changes in the channel bed elevation. They can be 

caused by human activities within the watershed or naturally occurring changes in basin 

hydrology and geology. “Aggradation” is an increase in channel bed elevation caused by an 

increase in sediment load or decrease in sediment transport in the watercourse. It is common 

upstream of dams and reservoirs where flow velocities are reduced and sediment deposition 

tends to occur. “Degradation” is a lowering of the channel bed that can be caused by reductions 

in sediment load or increases in a stream’s sediment transport. Degradation is common in 

urbanizing basins due to increases in flood magnitude and flow duration. It can also occur 

downstream of dams and in channels subject to aggregate mining, where sediment loads are 

reduced. 

Contraction scour is the lowering of the channel bed due to localized narrowing of a channel as 

caused by a bridge or culvert constriction or an encroachment, such as a bridge approach 

embankment, into the channel. A channel contraction will cause a reduced flow area, an increase 

in velocity at the constriction and increased erosive power of the flow. An increase in discharge 

in the main channel, as overbank flows return at the bridge opening, also increases contraction 

scour magnitude. 

106 
Local scour occurs at bridge piers and abutments due to complex flow patterns that occur in the 

vicinity of these obstructions. Pier scour is caused by strong turbulence that occurs at the base of 

a pier as flows are deflected down toward the channel bed and accelerated around the pier. Pier 

scour magnitude is related to pier width, pier shape and alignment to flow. It is also related to 

the depth and velocity of the flow upstream of the structure. Effective pier width is the most 

influential parameter and is a factor in most pier scour equations. Greater effective pier widths 

result in deeper scour depth potential. Abutment scour is caused by the turbulent mixing of 

flows in the channel with flows obstructed by the abutment. 

Natural channels continuously change shape and location within a floodplain. In addition to the 

vertical components of scour described above, the potential for changes in channel geometry and 

location must be assessed. Channel migration can expose structures to flows not anticipated at 

the time of design. It can also increase scour potential due to changes in flow direction or 

increase velocities at a structure. A foundation located in a floodplain should be designed for the 

worst scour condition that can occur during its life. If lateral stream migration could expose a 

shallow foundation or abutment, it should be designed for the same scour condition as 

foundations in the main channel. 

Scour can undermine shallow foundations or remove sufficient overburden to redistribute 

foundation forces causing foundation displacement and detrimental stresses to structural 

elements. Table 6-1 provides general guidelines for design of shallow foundations. One of the 

hazards of placing a structure in a river or channel is the potential for scour around the 

foundations. For new structures the foundation should be designed deep enough such that scour 

protection is not required (Richardson & Davis, 1995). Deep foundation systems may be 

preferable from both constructability and/or cost perspectives. 

6.2.2 Scour Design Considerations for Shallow Foundations 

Richardson & Davis (1995) provides the following guidance on scour design considerations for 

shallow foundation support of bridges at stream crossings. 

a. Spread Footings on Soil

• Ensure that the top of the footing is below the sum of the long-term degradation, 

contraction scour and lateral migration (excluding local scour). 

• Place the bottom of the footing below the total scour line. 

• The top of the footing can act as a local scour arrestor. 

b. Spread Footings on Rock Highly Resistant to Scour

Place the bottom of the footing directly on the cleaned rock surface for massive rock 

formations (such as granite) that are highly resistant to scour. Avoid small embedment 

(keying) since blasting to achieve keying frequently damages the rock structure beneath 

the footing and makes it more susceptible to scour. Keys into softer rock or IGMs may 

be feasible using pneumatic and hydraulic excavation tools without detriment to the 

quality of the underlying bearing materials. If footings on massive hard rock surfaces 

107 
require lateral constraint, steel dowels should be drilled and grouted into the rock below 

the footing level. 

c. Spread Footings on Erodible Rock or IGMs

Weathered or other potentially erodible rock formations need to be carefully assessed for 

scour. An engineering geologist familiar with the area geology should be consulted to 

determine if rock, soil or other criteria should be used to calculate the support for the 

spread footing foundation. The decision should be based on an analysis of intact rock 

cores, including rock quality designations and local geology, as well as hydraulic data 

and anticipated structure life. An important consideration may be the existence of a high 

quality rock formation below a thin, weathered zone. For deep deposits of weathered 

rock, the potential scour depth should be estimated and the footing base placed below 

that depth. Excavation into weathered rock should be made with care. If blasting is 

required, light, closely spaced charges should be used to minimize overbreak beneath the 

footing level. Loose rock pieces should be removed and the zone filled with clean 

concrete. In any event, the final footing should be poured in contact with the sides of 

the excavation for the full designed footing thickness to minimize water intrusion below 

footing level. Guidance on scourability of rock formations is given in FHWA 

memorandum “Scourability of Rock Formations,” dated July 19, 1991.

AASHTO specification requires footings for stream piers and each abutment to be founded at 

least 1.8 m (6 ft) below the streambed. For existing structures identified as scour susceptible, 

scour countermeasures are often required to protect foundations from scour conditions not 

identified at the time of design. 

There are four general types of scour protection: 

• Localized armoring 

• River training 

• Modifications to the foundations 

• Monitoring 

Localized armoring techniques include the following: 

• Rock riprap

• Gabions and slope mattress 

• Pre-cast concrete blocks 

• Grouted riprap 

Discussion of other armoring systems, including concrete slope pavement, grouted fabric, 

sand/cement bags and soil cement, and a thorough treatise on current technology for stream

instability and bridge scour countermeasures, are provided in HEC 23 (Lagasse et al., 2001b). 

108 
6.2.3 Frost Depth 

Footings founded in seasonal and permanently frozen grounds must be embedded below the 

depth of frost penetration (frost depth) to provide adequate frost protection. This is required to 

prevent heaving of the footings due to volumetric expansions of the subgrade soils from freezing 

and/or to prevent settling due to loss of shear strength and stiffness from thawing. 

In general, for frost action to occur, the following conditions must apply: 

• Presence of frost-susceptible soil 

• Availability of water 

• Freezing conditions 

Fine-grained soils with low cohesion tend to be more frost susceptible. Silty soil containing a 

high percentage of particles smaller than the No. 200 U.S. Standard sieve tends to have a 

network of pores and fissures that promote frost penetration. Common frost-susceptible soils 

include silts (ML, MH), silty sands (SM) and low-plasticity clays (CL-CL/ML). In regions 

where freezing of the ground occurs during the winter months, lenses of clear ice will form

within the fine-grained soils and result in a sequence of frozen soil and ice. If there is a source of 

water in liquid phase, such as a water table available under the frost depth, the water will be 

drawn toward these ice lenses by capillary and suction actions, further expanding the lenses, and 

consequently producing surface heave. In addition, the degree of air temperature and duration of 

below-freezing temperatures also influence the depth of penetration. The U.S. Army Corps of 

Engineers proposed a relationship between frost penetration depth and the freezing index. The 

“freezing index” is a product of the number of days below freezing and the average number of 

degrees below freezing during the freezing season. Refer to Corps of Engineers’ Technical 

Manual TM 5-852-6 (U.S. Army Corps of Engineers, 1988) for calculation methods to determine 

frost depths in soils. 

Footings should be located below the maximum depth of frost penetration to minimize the 

potential for freeze/thaw movements. The maximum depth of frost penetration generally is 

established by local experience or from published maps. The use of generalized maps showing 

large regions is discouraged. Local building codes, agency design policy and experience should 

be consulted for appropriate design values. 

Discussion about special considerations for foundations in permanently frozen regions 

(permafrost regions) is beyond the scope of this document. Readers are referred to Canadian 

Foundation Engineering Manual (1985) for special principles and practices needed for 

successful design and construction in cold environments. 

6.2.4 Expansive and Collapsible Soils 

Both expansive and collapsible soils are regional in occurrence. Neither soil type is well suited 

for shallow foundation support without some sort of mitigation for the potential for large volume 

changes in these soils due to changes in moisture content. Because deep foundations are 

frequently used for bridge support in both soil types, detailed guidance for ground treatment to 

permit use of shallow foundations for bridge support is not included here. 

109 
Expansive clays experience increases in volume due to increases in moisture content. The 

magnitude of the volume change can cause severe damage to structures. In general, deep 

foundations are preferred for bridge support in expansive soil terrain, unless the potential for the 

volume change can be mitigated. The most common and effective strategy for mitigating 

expansion potential is to excavate and replace the expansive soil with sufficient nonexpansive 

material to counteract the swell potential. This is generally practical only if a ready source of 

nonexpansive material is located nearby. For approach embankment and abutment design, the 

expansion potential should be evaluated considering the construction and loads of both. The 

Shallow Foundations Workshop Reference Manual (Munfakh et al., 2000) provides the 

procedures for laboratory testing for expansion potential and analysis of the results. 

Collapsible soils, when dry, can provide adequate support for relatively high loads. However, 

upon wetting after the load has been applied, the soils can experience dramatic decreases in 

volume. It is most important to identify collapse potential of foundation soils at a bridge site. 

Due to the difficulties in obtaining undisturbed samples of these materials, exploration and 

testing alone may not identify the collapse potential. Local experience and review of geologic 

mapping are therefore essential to identification of collapsible soil deposits. 

6.2.5 Drainage Considerations 

When a shallow foundation supports a stemwall, and there is a difference in elevation of the 

backfill on either side of the stemwall so that unbalanced lateral earth pressures will act on the 

stemwall, the footing and the stemwall combine to function as a retaining structure. This is a 

typical configuration for bridge abutments. As with most retaining structures, the material 

retained by the structure should be drained such that hydrostatic pressures do not also act against 

the abutment. 

Abutments are important structures that perform multiple functions. Drainage details, including 

weep holes and perforated drainage pipes, are an essential inclusion in the plans and 

specifications. Most highway agencies use standard details and specifications to ensure adequate 

drainage behind abutments. 

Additional discussion of abutment and retaining wall drainage requirements and construction 

details are provided in Chapter 9. 

6.2.6 Seismic Considerations and Dynamic Stability 

Seismic hazards should be assessed as part of the foundation type selection process. Shallow 

foundations are susceptible to excessive movements or damage if the bearing soils are subject to 

liquefaction or lateral spreading due to an earthquake. GEC No. 3, Geotechnical Earthquake 

Engineering for Highways (Kavazanjian et al., 1997), presents guidance on assessing seismic 

hazards at a site, including evaluation of liquefaction and lateral spreading potential. In general, 

shallow foundations will not be an appropriate choice for support of bridge piers when there is 

potential for liquefaction to develop under the design seismic event unless the liquefaction 

potential is mitigated by ground improvement. Refer to Munfakh et al., (2000) for discussion of 

design and construction techniques to improve poor ground conditions and allow use of spread 

footings. 

110 
If liquefaction and lateral spreading are not expected at a site, shallow foundations may be a 

suitable and cost-effective choice for support of a bridge, provided the foundation is designed to 

adequately resist the seismic loading conditions appropriate for the design event. Seismic design 

checks should, at a minimum, include the following (others may also apply): 

• Design for seismic loads that act through the column or stemwall to the footing. A 

minimum factor of safety of about 1.0 to 1.15 should be maintained against bearing 

capacity or sliding failure of the footing. 

• AASHTO (1996) permits eccentricity due to seismic loading to fall within the middle 

two-thirds (2/3) of the footing, based on a trapezoidal distribution of earth pressure (see 

Section 6.4). However, equivalent rectangular soil pressure distribution is recommended 

for sizing footings in this GEC; therefore, when using the rectangular pressure 

distribution, the seismic eccentricity should be kept within the middle one-half of the 

footing. 

• Recall that seismic loads act in opposite directions at different times during the 

earthquake. Be sure to check for stability (overturning and sliding) as well as bearing 

capacity using loads applied in the direction that results in the most critical condition. 

Check to see if the foundation experiences uplift. A deep foundation may be needed to 

resist uplift forces. 

• Design for seismic lateral earth pressures that can act on the footing. This is typically 

done using the Mononobe–Okabe equations as described in AASHTO (1996, 1998). 

• Check global stability of any slope that supports the footing, or is supported by the 

footing, by including a seismic coefficient in the slip circle or other method of calculating 

a factor of safety of a slope. In general, the calculated factor of safety should be greater 

than 1.0 when the applied horizontal seismic coefficient is one-half the peak ground 

acceleration (Hynes-Griffin & Franklin, 1984). 

6.3 LOADS

Calculation of loads applied to shallow foundations is presented in AASHTO (1996, 1998). 

Numerous load groups provide for a variety of possible loading conditions and also consider the 

special loading requirements of non-routine structures, such as long span bridges. A summary of 

load cases and the conditions they are intended to check is included in Table 6-2. 

The designer should be aware of the possibility that a non-codified loading condition may 

actually control the design of a foundation. For instance, the construction sequence and methods 

should be considered when evaluating the critical load case for a shallow foundation. If an 

abutment may be fully backfilled prior to application of the superstructure loads, the overturning 

load of the backfill may be the most critical loading condition the foundation must ever resist. 

111 
TABLE 6-2: SERVICE LOAD DESIGN LOAD GROUPS 

Load Group Description 

Groups I though III check the structure without consideration for long term creep, shrinkage, 

shortening, or thermal movements. 

I Load combination with normal vehicles using the bridge without wind. 

IA Load combination for vehicles smaller than an H 20 using the bridge without 

wind. 

IB Load combination with permit vehicles using the bridge without wind. 

II Load combination with maximum wind, without vehicles. 

III Load combination with normal vehicles using the bridge with wind. 

Groups IV to VI check the structure with consideration for long term movements. 

IV Load combination with normal vehicles using the bridge without wind, and with 

consideration of long term shrinkage, shortening, and thermal movements. 

V Load combination with maximum wind without vehicles, and with consideration 

of long term shrinkage, shortening, and thermal movements. 

VI Load combination with normal vehicles using the bridge with wind, and with 

consideration of long term shrinkage, shortening, and thermal movements. 

Group VII is for seismic loading. 

VII Load combination for seismic loading. 

Groups VIII and IX check the structure for ice loads on the piers. 

VIII Load combination with normal vehicles using the bridge without wind and ice 

acting on the bridge. 

IX Load combination with maximum wind and ice, and without vehicles. 

Group X is for culvert design, the other load groups do not apply to culverts. 

X Load combination for culverts with normal vehicles using the culvert. 

112 
6.3.1 Vertical Loads and Pressures 

Vertical loads should be calculated in accordance with the design specification selected as the 

design criteria for the project. Calculation of infrequent loads, such as seismic, should consider 

the potential range of soil and ground water conditions that may exist under and around the 

footing over the life span of the structure. It is important to ensure that the structure will perform 

well over the range of expected conditions that may occur, considering the potential for the 

following: 

• Seasonal variations in ground water level 

• Variation in the depth of cover over a footing due to scour or excavation 

• Increased loads due to changes in permitted loads or the addition of overlays 

• Intermediate construction conditions or equipment loading that may exceed design live 

loads 

Section 5.2.2 discusses the concepts of gross and net bearing pressures. An additional 

consideration that is related to the concept of net bearing pressure is the calculation of loads due 

to the self-weight of the footing and the backfill over the footing. 

Consider a footing constructed in an excavation below existing grade and then subsequently 

backfilled. The increase in stress experienced by the soil below the bearing elevation will be the

net increase due to a change in the unit weight of material that is replaced over the top. This is 

usually only due to the concrete in the footing itself, unless a specified select backfill material 

replaces the soil excavated to construct the footing. Because the concrete has a higher unit 

weight than the soil it replaces, there is slight increase in bearing stress below the footing. For 

most applications, including bridge foundations, this effect is usually less than one or two 

percent of the loads applied by the column and is therefore commonly ignored. 

Alternatively, consider the effect of a mat foundation constructed well below the existing grade. 

In this case, the soil removed during construction is replaced largely by air, so there is potentially 

a net decrease in the stress due solely to the self-weight of the shallow foundation and the lack of 

backfill. 

The decision to include or ignore the effect of the footing self-weight and backfill should be 

evaluated on a case-by-case basis considering the following effects that the increase in stress will 

have on the design conditions checked while sizing the footing:

• The bearing stress increases, so the factor of safety with respect to bearing capacity will 

decrease, and the settlement will also potentially increase. These are undesirable effects. 

If the effect of self-weight is more than one or two percent of the applied column or 

structure loads, the weight should be included when sizing the footing. 

• The effect of a net stress increase on eccentricity (overturning) or sliding of a footing will 

be to stabilize the foundation. It is therefore conservative to ignore the increase when 

computing the factor of safety against overturning (eccentricity), or sliding. 

Mat foundations below grade with no backfill will experience the opposite effects. 

113 
6.3.2 Lateral Loads and Pressures 

The transfer of shear applied by the column may apply lateral loads on a shallow foundation. 

The computation of these loads should be done in accordance with the appropriate section of 

AASHTO or the selected design criteria. For the case of abutments that retain fill, the lateral 

earth pressures and associated design loads must also be computed to size and design the footing. 

Lateral earth pressures are determined based on the characteristics of the fill material behind the 

abutment. The different states of stress that should be considered include active, at-rest, passive 

and seismic. Computation of seismic earth pressures is not included here. The reader is referred

to GEC No. 3, Geotechnical Earthquake Engineering for Highways (Kavazanjian et al., 1997) 

for design guidance on calculating lateral earth pressures due to seismic loads. In addition, a soil 

pressure distribution has to be determined for traffic surcharge. For the active, passive and atrest states, the pressure distribution can be assumed to be triangular, with the resultant applied at 

H/3 from the bottom of the footing. The general equation for computing lateral loads due to 

lateral earth pressures is: 

2 K H

2

1 P = γ′ (6-1)

where: P = Lateral load, typically computed per unit length of wall or abutment 

K = Lateral earth pressure coefficient 

γ′ = Effective unit weight of soil acting against the wall or abutment 

H = Height of retained backfill behind the wall or abutment 

The lateral load will be computed based on the earth pressure condition expected to develop 

behind the wall or abutment, active, at-rest or passive. The loads and the lateral earth pressure

coefficients are typically written with a subscript of ‘a,’ ‘o’ or ‘p,’ for active, at-rest, or passive

earth pressure, respectively, to denote the earth pressure computed. 

6.3.2.1 Active Pressure Distribution 

The pressure distribution is determined using calculations based on Coulomb theory. The active 

pressure coefficient, Ka, is computed from Equation 6-2. This is the general case for Coulomb 

lateral earth pressure theory. It does not account for surcharge or seismic loads. 

2

2

2

a

cos( ) cos( )

sin( ' )sin( ' ) cos cos( ) 1

cos ( ' ) K





 





θ + δ θ − β

φ +δ φ −β θ θ + δ +

φ −θ = (6-2)

where: Ka = Active earth pressure coefficient 

δ = Wall/backfill interface friction angle

β = Angle of backfill slope behind the wall to the horizontal (β = 0o

 for horizontal 

backfill surface 

θ = Angle of back wall face inclination (θ = 0o

 for vertical wall face) 

φ′ = Effective angle of internal friction for the soil 

114 
Figure 6-2 shows these terms. 

For the case of a vertical wall (no batter) and where the ground surfaces above and below the 

wall are level, the active pressure coefficient may be calculated using the simpler Rankine 

equation: 

Ka = 



 



 φ ° − 2

' tan 45 2 (6-3)

where: Ka = Active earth pressure coefficient 

φ′ = Effective angle of internal friction for the soil 

The Rankine equation assumes no friction between the wall and the soil backfill. Note that 

Equation 6-3 does not include consideration for surcharge or seismic loads. 

H/3

H

θ

Pa

δ

β

γ, φ'

Figure 6-2: Coulomb Lateral Earth Pressure Definitions 

6.3.2.2 At-Rest Pressure Distribution 

The at-rest coefficient can be determined from the following equation developed by Mayne and 

Kulhawy (1982): 

Ko = ( (6-4) sin( ) 1 sin )(OCR) φ′ − φ′

where: Ko = At-rest pressure coefficient 

φ′ = Effective angle of internal friction for the soil 

 OCR = Overconsolidation (preconsolidation) ratio (see Section 5.3.3) 

Some agencies design abutment walls for at-rest earth pressures. However, if the wall is free to 

rotate such that the displacement at the top of the abutment is about 0.2 percent of the height of 

the wall (i.e., 0.002H), then active earth pressures can be assumed to develop. 

115 
6.3.2.3 Passive Pressure Distribution 

The passive pressure distribution should be determined for special abutment cases. The passive 

pressure is generally ignored in front of the abutment due to the large lateral displacements 

required to fully mobilize passive lateral earth pressures and the potential for poor compaction or 

subsequent removal of the backfill. The passive earth pressure coefficient may be computed 

using Coulomb earth pressure theory or estimated from charts such as Figures 5.5.2C and 5.5.2D 

in the AASHTO “Standard Specifications” (1996). 

6.3.2.4 Equivalent Fluid Methods 

The AASHTO “Standard Specifications” (1996) state that structures that resist loads due to 

lateral earth pressures should not be designed for less than an equivalent fluid weight of 4.8 

kN/m3

 (30 pounds per cubic foot). If the above methods yield pressures lower than this 

equivalent fluid weight, the equivalent fluid pressure should be used as a minimum. Note that 

these earth pressures only apply to gravity and semi-gravity cantilever walls. 

6.3.2.5 Live Load Surcharge 

If live loads (traffic) can occur within a horizontal distance behind the top of a wall or abutment 

wall equal to one-half of the wall height (measured from the heel of the footing), the lateral load 

for design should be increased to account for the additional lateral earth pressure that will act on 

the wall. 

The live load surcharge is estimated as an equivalent soil surcharge behind the wall or abutment. 

However, if there is an approach slab, the live loads are applied to the corbel on the abutment 

backwall. The equivalent height of soil to use in calculating the live load surcharge is 0.6 m (2 

ft). The unit weight for this imaginary surcharge is typically taken as 19.6 kN/m3

 (125 pcf). The 

pressure distribution from this equivalent soil height is uniform along the back of the wall, and 

the resultant is halfway up from the base of the wall. The lateral load due to live load surcharge 

is then calculated as: 

PLS = K γ′heqH (6-5)

where PLS = Lateral load due to live load surcharge, in units of force per unit length of wall 

K = Lateral earth pressure coefficient, either at-rest, Ko, or active, Ka

γ′ = Effective unit weight of soil acting against the wall or abutment 

 heq = Equivalent height of soil surcharge representing live load (0.6 m)

H = Height of retained backfill behind the wall or abutment 

The general loading configuration for lateral earth pressures acting on walls or abutments is 

shown in Figure 6-3. 

116 
H/3

0.5 H

Active Earth

Pressure, pa

Traffic

Surcharge, pLS

PA

PLS

Figure 6-3: Lateral Earth Pressures on Abutments 

6.4 SIZING THE FOOTING

Once all the loads acting on the footing have been calculated, the footing should be sized such 

that: 

• The footing is stable under eccentrically applied loads (i.e., the footing will not overturn) 

and such that negative contact stress does not develop beneath the footing (soil cannot 

transfer tensile stress). This is determined by computing the effective footing dimensions 

(Section 6.4.1). 

• The maximum applied bearing stress is less than the allowable bearing capacity, 

considering the potential for both shear failure and settlement. This is determined using 

the effective footing area computed per Section 6.4.1 and comparing it with the 

calculated allowable bearing capacity (Section 6.4.2). 

• The footing will not slide due to lateral loads (Section 6.4.3).

6.4.1 Effective Footing Dimensions and Overturning Stability 

Eccentric loading occurs when a footing is subjected to a combination of vertical loads and 

moments, or moments induced by shear loads transferred to the footing. Abutments and 

retaining wall footings are examples of footings subjected to this type of load condition. 

Moments can also be applied to interior column footings due to skewed superstructures, impact 

117 
loads from vessels or ice, seismic loads or loading in any sort of continuous frame. The effect of 

the eccentric load is to distribute the load over a smaller area than the entire footing area. The 

eccentricity correction is usually applied by reducing the width (Bf) and length (Lf) such that: 

B′

f

 = Bf – 2eB (6-6)

L′

f

 = Lf – 2eL (6-7)

In these equations, eB and eL are the eccentric distances (Figure 6-4) in the Bf

 and Lf directions, 

respectively, and are computed by dividing the applied moment by the applied vertical load. 

Recall that it is important to maintain consistent sign conventions and coordinate directions. The 

reduced footing dimensions B′f and L′f are termed the effective footing dimensions. When 

eccentric load occurs in both directions, the bearing pressure is assumed to act over a fictitious 

area (A') of the footing (AASHTO, 1998): 

A′= B′

f

 L′

f (6-8)

Figure 6-4: Notations for Footings Subjected to Eccentric, 

Inclined Loads (after Kulhawy, 1983) 

Note that the concept of effective footing dimensions and area is an approximation made to 

account for eccentric loading and is not representative of the actual stress distribution under a 

footing subjected to eccentric loads. Structural design of the footing is performed using 

trapezoidal or triangular stress distributions that more conservatively model the stress 

distribution under an eccentrically loaded footing as described in Section 6.6. A comparison of 

the two loading distributions is shown in Figure 6-5. 

118 
 (a) (b) 

Figure 6-5: Eccentrically Loaded Footing with (a) Linear Pressure Distribution (Structural 

Design) and (b) Equivalent Uniform Pressure Distribution (Sizing the Footing) 

Footings on soil should be designed such that the eccentricity in any direction (eB or eL) is less 

than one-sixth (1/6) of the (actual) footing dimension in the same direction to ensure that zero 

contact pressure does not exist beneath the footing (AASHTO, 1996). For footings on rock, the 

eccentricity should be less than one-fourth (1/4) of the (actual) footing dimension. If the 

eccentricity does not exceed these limits, separate calculation for stability with respect to 

overturning need not be performed. 

6.4.2 Allowable Bearing Stress 

Using the procedures in Sections 5.2 and 5.3, an allowable bearing capacity should be computed 

that provides a minimum factor or safety of 3.0 against bearing failure in shear and limits the 

settlement of the footing to a tolerable amount. It is typically convenient to present the allowable 

bearing capacity as a range of bearing stresses plotted as a function of (effective) footing widths. 

Alternatively, settlements could be computed and tabulated for a variety of applied stresses and 

footing widths. 

An acceptable footing design may be obtained by sizing the footing such that the applied bearing 

stress over the effective footing area, A′, assuming a rectangular pressure distribution, is less 

than the allowable bearing pressure computed using the procedures in Chapter 5. Because the 

pressure distribution is assumed to be uniform, Bf in Equation 5-14 may be replaced by B′f. 

6.4.3 Sliding 

The loads that act laterally on the footing should be compared to the allowable sliding resistance 

computed according to the procedures in Section 5.4. If the computed factor of safety is less 

than 1.5, the footing width should be increased. Addition of a key may also be considered, 

keeping in mind the limitations of key construction and effectiveness described in Section 5.4. 

119 
6.5 DESIGN OF SHALLOW FOUNDATIONS FOR INFREQUENT TRANSIENT LOADS

Bridge design may need to include consideration of loading conditions that rarely, if ever, occur 

during the life of the structure. Some of these load conditions can impose large loads on the 

structure and the foundations. Examples of loads that may impact bridge design include ice load, 

wind load, vessel impact and, notably, earthquake or seismic loads. These large loads can 

control the design and size of a foundation. 

The performance objective of the structure, and therefore the foundations, should be selected 

before establishing the design criteria for the structure. It may be considered that structural

collapse is not acceptable, but that some structural damage is tolerable if one of these transient 

loads is applied to the structure. 

The concept of allowable bearing capacity that includes consideration of limiting both bearing 

failure in shear and settlement does not lend itself to design for infrequent transient loads. If 

some structural damage, but no collapse, is considered an acceptable result from the application 

of such a load, it is not reasonable to design the foundations for total settlement (i.e., settlement 

due to “normal” loads plus any additional settlement due to the transient load) that is limited to, 

say, 25 mm (1 in). 

When considering infrequent transient loads Service Load Design provisions include an 

allowance for overstress above the allowable capacity of a member. For soils, however, the 125 

to 150 percent overstress allowance means that there is still a factor of safety against a collapse 

(bearing failure in shear) of at least 2.0. Compared to other construction materials, such as 

concrete and steel, this is still a large margin of safety under this type of load. The design codes 

have evolved, and will continue to evolve, with regard to achieving consistent levels of

performance and safety. One step in this process is AASHTO’s adoption of the Load and 

Resistance Factor Design (LRFD) methodology (AASHTO, 1998), which includes provisions for 

considering the performance of a structure under typical, or service loads, that are generally 

controlled by deflection (e.g., settlement), and strength or extreme event loads that may be 

controlled by the ultimate strength of a material (e.g., ultimate bearing capacity). Further 

discussion of the LRFD method as applied to shallow foundations is included in Appendix C. 

6.5.1 Soil–Structure Interaction Analyses and Shallow Foundation Stiffness 

An additional consideration for shallow foundations designed to resist large, transient loads is the 

effect of soil–structure interaction. The loads calculated for a structure subjected to a large 

transient load will depend on how the structure responds to the application of the load. The 

structure response is, in turn, dependent on the stiffness of the foundation and the foundation 

soils. An accurate prediction of the loads will depend on an accurate prediction of the 

foundation stiffness. 

Of particular interest to designers is the response of foundations to transient lateral loads, such as 

those applied by seismic loads or vessel impact. For shallow foundations, the foundation 

stiffness will therefore be a function of the shear modulus and Poisson’s ratio of the soil. A 

detailed description of evaluating soil and foundation stiffnesses is not included here. The reader 

is referred to GEC No. 3: Geotechnical Earthquake Engineering for Highways (Kavazanjian et 

120 
al., 1997) and the course materials and design examples developed for National Highway 

Institute’s Seismic Design of Bridges (Mast et al., 1996) for guidance on calculating foundation 

loads due to transient lateral forces. 

6.6 STRUCTURAL DESIGN OF THE FOOTING

The contact pressure beneath a spread footing is, in reality, a function of the stiffness of the 

footing and the compressibility and strength of the soil. However, the most common practical 

approach is to assume that the footing is rigid with a linear distribution of contact pressure. This 

results in either a trapezoidal or triangular shaped contact pressure distribution, as shown in 

Figure 6-6. The maximum and minimum pressures beneath the footing can be computed using 

Equations 6-9 through 6-13. 

 (a) (b) 

Figure 6-6: Contact Pressure for Footing Loaded Eccentrically About One Axis: 

(a) for eL ≤ Lf/6, and (b) for Lf/6 < eL < Lf/2 (AASHTO, 1996) 

For eL < Lf

/6: 

max L f fLf q = Q[1 + 6(e /L )]/B (6-9)

min L f fLf q = Q[1 − 6(e /L )]/B (6-10)

121 
For Lf /6 < eL < Lf /2: 

q 2Q /(3B [(L / 2) e ]) max = f f − L (6-11)

q min = 0 (6-12)

L 3[(L /2) - e ] 1 = f L (6-13)

where: L1 = the length of the triangular-shaped contact pressure distribution 

Note: When the eccentricity is in the Bf

 direction, the minimum and maximum contact pressures 

are computed with Equations 6-9 through 6-13 by replacing eL with eB, Lf

 with Bf, and Bf with 

Lf

. 

The structural design of the footing should then be performed in accordance with Section 8 of the 

AASHTO Standard Specifications (1996). The soil pressures used for this design are the 

customary trapezoidal or triangular pressures shown in Figure 6-6 and calculated using 

Equations 6-9 through 6-13, not the equivalent uniform rectangular pressures used to size the 

footing dimensions. The following failure modes should be considered during structural design 

of the footing: 

• Consider the moment in the footing as a function of the column connection (i.e., pinned, 

fixed or sliding, an equivalent rectangular column is used). 

• Increase moment (flexural) steel in the short direction as specified in the AASHTO 

Standard Specifications (1996). 

• When compression is induced at the face of the column, investigate shear at “d” away

from the column face in compression (where “d” is the full depth of the footing). If 

tension is induced at the face of the column, investigate shear at the face of the column. 

• Consider punching or two-way shear around the column. 

For abutments, each of the structural elements is designed similar to spread footings. In addition, 

the backwall and stem wall are designed for the design soil pressures that can be applied. 

Wingwalls, if included, are designed for the maximum soil pressures that can be applied. The 

connection of the wingwall to the stem wall is critical so that it will not fracture. 

122 
CHAPTER 7 

MINOR STRUCTURE SUPPORT ON SHALLOW 

FOUNDATIONS 

Transportation projects frequently include minor structures such as signs, signals and 

illumination. Because these structures are both relatively tall and lightweight, the controlling 

load for design of their foundations is nearly always overturning due to wind loading or 

cantilever arms. As a result, the moments applied at the foundation connection tend to be large 

as compared to the axial load due to the dead weight of the structure. 

Spread footings must resist these moments by transferring the moment to an effective bearing 

area that is small due to the large eccentricity; therefore, spread footings tend to be large for 

support of signs, signals and illumination. Most agencies have developed standard plans for 

supporting minor structures on small, shaft-type foundations that are more efficient at resisting 

the applied lateral shears and moments than spread footings because they spread the load over a 

large, lateral surface area. 

However, there are some ground conditions, such as very soft soils, that may lend themselves to 

minor structure support on a spread footing. Because the axial loads are not very large for minor 

structures, settlement considerations may not govern the allowable bearing capacity. An 

example might be a deep soft clay or organic silt deposit that provides poor near-surface lateral 

resistance against a shaft or pile foundation. In this situation a large spread footing could be a 

cost-effective alternate to a pile group. 

7.1 GEOTECHNICAL INVESTIGATION

The geotechnical investigation for minor structures should include the same considerations as 

presented in Chapter 4, but the depth and frequency of explorations may be reduced according to 

identified similar geologic conditions for groups of structures. 

7.2 ALLOWABLE BEARING STRESSES

Allowable bearing stresses for minor structure support on shallow foundations follow the same

principles and procedures presented in Chapter 5. 

7.2.1 Settlement Limitations 

Settlement considerations for minor structures should include determining how much the 

foundation might tilt when supporting a tall, slender structure. Visually perceptible tilt of signals

and illumination towers, while not necessarily a problem for the function of the structure, will 

certainly be noticeable, and reported, by the public. As mentioned above, however, the 

123
controlling design load may be wind, which is transient and therefore not likely to be of 

sufficient duration to induce consolidation settlement of cohesive soils. If the structure includes 

a cantilever arm, however, consolidation settlement should be computed and kept within 

tolerable limits. 

The potential for differential settlement of sign bridge supports should be checked if the applied 

bearing stresses are sufficient to induce consolidation settlement. 

7.2.2 Bearing Capacity Limitations 

As mentioned in the introduction to this section, shallow foundations for minor structures may be 

cost-effective when deep, soft soils are present. Punching shear mechanisms can develop in 

these types of soils. This is a situation in which the one-third reduction in the soil strength 

parameters discussed in Section 5.2.3.6 should be included when computing the ultimate bearing 

capacity. 

7.3 OVERTURNING

As mentioned in Section 6.4.1, the factor of safety against overturning does not need to be 

calculated if the eccentricity is within certain prescribed limits that ensure negative bearing stress

does not occur. For lightweight structures that have large overturning moments, these design 

criteria may be overly conservative. Recall that the assumption of the actual distribution of 

stress beneath a spread footing is that the footing is perfectly rigid with respect to the soil. For 

wide spread footings that would be needed to withstand the overturning moment applied by, say, 

a signal mast arm, the assumption of perfect rigidity is not valid. Both the footing and the 

supporting soil will deform under the applied load, and the stresses will redistribute accordingly. 

If the eccentricity is allowed to exceed the limits stated in Section 6.4.1 for a minor structure 

foundation, then a separate computation for overturning should be performed. A minimum 

factor of safety against overturning (i.e., the resisting moments divided by the moments acting to 

overturn the structure) should be greater than about 2.0 for permanent dead loads and greater 

than about 1.5 for infrequent transient loads such as the maximum wind force. 

7.4 SLIDING

The design of shallow foundations supporting minor structures should be checked, following the 

procedures in Sections 5.4 and 6.4, so that sliding will not occur. 

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CHAPTER 8 

SHALLOW FOUNDATION DESIGN FOR BUILDINGS

Foundation design for buildings is typically performed in accordance with the current version of 

the Uniform Building Code (UBC) or the International Building Code (IBC). These codes 

provide minimum criteria for design of building foundations, including considerations for frost 

protection; maximum presumptive bearing stresses; and dead, live, wind, seismic and other 

loads. 

8.1 GEOTECHNICAL INVESTIGATION

The field and laboratory procedures for geotechnical investigation of a building site are the same

as described in Chapter 4. The extent of sampling and testing should be commensurate with the 

performance expectation and importance of the structure. A maintenance facility, for instance, 

may include several one- and two-story structures, including an equipment bay, that are 

constructed as slabs-on-grade with spread footing support of lightweight column and wall loads. 

The subsurface investigation for this type of facility should be sufficient to describe the vertical 

and lateral extent and variability of foundation bearing soils beneath the structures. A 1,500 to 

2,000 m2

 facility will typically require a minimum of three to five borings or test pits that extend

at least 3 to 9 m (10 to 30 ft). The required quantity of subsurface information will depend on 

the geotechnical engineer’s confidence that the subsurface conditions are adequately defined to 

proceed with confidence in designing a shallow foundation system. 

8.2 SHALLOW FOUNDATION TYPES

The types of shallow foundations used to support buildings are similar to those described in 

Chapter 2, with the notable difference being generally much smaller dimensions. 

8.2.1 Isolated Spread Footings 

Isolated spread footings are frequently used to support individual or occasionally multiple 

column loads for buildings. Depending on the anticipated potential for differential movements 

or the potential for high floor loads, the footings may or may not be constructed integral with 

slabs-on-grade. It may be preferable for slabs to bear on the subgrade soils independently from

footings. For lightly loaded structures on compressible soil, it can be economical to partially 

overexcavate the poor foundation soils and replace them with compacted granular backfill to 

limit the potential for settlement or bearing capacity problems. 

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8.2.2 Continuous Strip Footings 

Continuous strip footings are frequently used to support perimeter and load-bearing walls. 

Where designed and constructed continuous with slabs-on-grade, the footings can be built as 

thickened edges to achieve the minimum depth requirements for bearing capacity and frost 

protection. 

8.2.3 Mat Foundations 

Mats are heavily reinforced concrete foundations that usually cover the entire plan area of a 

building. Mat foundations may be designed to minimize differential settlements. Mats are 

usually more economical and preferable when column loads are so large that more than 50 

percent of the plan area would be covered by spread footings (Peck et al., 1974). Mats can be 

used to create deep basements, distribute column loads more uniformly and provide basement 

slabs (water barrier). Mats may be used when the foundation soil has a low bearing capacity or 

large differential settlements are anticipated. 

Mats, by design, are rigid elements that distribute column and wall loads over a larger area, thus 

reducing the magnitude of the vertical stress on the foundation soil. This not only decreases the 

stress but also produces a more uniform settlement profile and subsequently reduces differential 

settlement. Figures 8-1(a) and (b) present the pressure distribution profiles versus depths for 

footing and mat foundations, respectively, assuming that the total load from the superstructure is 

the same for both a and b. As shown in Figure 8-1, the applied stress on the subgrade soil 

directly below the spread footings is higher than directly below the mat; however, this condition 

reverses with depth. Additionally, a mat foundation is preferred for a subsurface soil profile 

containing erratic changes in strength and/or stiffness (Figure 8-2) because the mat tends to 

bridge over these erratic loose zones better than isolated footings and is expected to undergo 

smaller differential displacements (about 50 percent less). 

PRESSURE

DISTRIBUTION

Figure 8-1: Distribution of Pressure in Soil Beneath Buildings Supported by 

(a) Widely Spaced Footings and (b) Concrete Mat 

126
POCKETS OF LOOSE SAND

WITHIN DENSE SAND PRESSURE INFLUENCE

Figure 8-2: Mat Foundation on a Dense Sand Stratum with Erratic 

Distribution of Pockets of Loose Sand 

8.3 ALLOWABLE BEARING STRESSES

8.3.1 Settlement Limitations 

Tolerable total and differential movements for buildings, like bridges, are strongly a function of 

the materials and methods used to construct the building. Steel frame buildings are capable of 

withstanding surprisingly large differential movements without experiencing structural distress 

or damage. However, such movement may result in objectionable appearances of wall facings 

and coverings. Masonry structures, on the other hand, are relatively settlement intolerant and 

may experience structural distress (cracking) if angular distortions exceed 1/300. 

In practice, bearing stresses are typically limited so that total settlements are on the order of 25 

mm (1 in) and differential settlements about half the total settlement. 

In designing building foundations, considerable benefits can be derived by permanently 

excavating a portion of the soil by including a basement. This reduces the net increase in 

stresses on the subgrade, which in turn reduces or eliminates consolidation even in normally 

consolidated soils. 

8.3.2 Bearing Capacity Limitations 

Due to the relatively small width of spread footings for buildings, the potential for bearing 

capacity failure may control the design of footings, especially foundations on clay. Knowing 

that most building foundations for lightweight one- and two-story frame construction have 

widths of about 0.5 to 1.0 m, and referring to Figure 5-1, it can be seen that these values fall to 

the left, in the bearing capacity limited portion of the chart. 

127
8.4 OVERTURNING AND ECCENTRICITY

Spread footings for buildings are designed to maintain a minimum factor of safety against 

overturning of at least 1.5. Eccentricity may also be checked using the procedures in Chapter 6, 

although this is generally not part of the code requirements for design of buildings. 

8.5 SLIDING AND PASSIVE RESISTANCE

The procedures for calculating sliding and passive resistance for building spread footings are 

described in Chapter 5. A minimum factor of safety of 1.5 should be provided for sliding 

stability. Due to the generally small width of spread footings used for buildings, inclusion of the 

passive resistance may be necessary. Because of the differences in strains required to develop 

sliding and passive resistance, as described in Section 5.4, a practical approach is to include only 

one-half of the computed passive resistance when combining both sliding and passive 

components. For narrow footing widths, simply deepening the footing to increase passive 

resistance may be more practical than attempting construction of a key. 

8.6 DESIGN OF MAT FOUNDATIONS AND FLOOR SLABS

The design of mat foundations should account for bearing capacity, as well as immediate and 

long-term settlements. The bearing capacity and settlement of a mat foundation may be 

determined using the methods presented in Chapter 5. Due to the large size of mat foundations, 

bearing capacity will generally not govern design. Controlling deflections will usually be the 

most critical aspect of design. Mat settlements can be controlled to some degree with the lower 

applied soil pressures as compared to isolated or strip spread footings. Also, the volume of soil 

displaced by the foundation will result in a lower net applied stress that will limit settlement. 

Mat foundations on cohesive soils (clays) may be controlled by deep-seated bearing capacity. 

The subsurface explorations must be carried to sufficient depth to assess both deep-seated 

bearing capacity and the zone of stress influence (Section 5.3) for settlement computation. Due 

to the large dimensions of a mat, the zone of influence will be deeper than for isolated or strip 

spread footings. 

A common design approach for mat foundations uses beam on elastic foundation theory to 

compute the soil-structure interaction and deflections. The reinforcement of the mat can then be 

designed based on the deflections computed within the mat. The beam on elastic foundation 

approach models the support of foundation soils as a bed of discrete elastic springs (Winkler 

foundation). The soil reaction at any particular point beneath a mat is: 

qapplied = Kvy (8-1)

where: qapplied = Applied stress 

 Kv = Modulus of subgrade reaction (force/length3) 

 y = Vertical displacement 

128
The modulus of subgrade reaction can be obtained from Figure 8-3. Note that the notation for 

the modulus is KV1 in Figure 8-3. The modulus of subgrade reaction can also be obtained from

plate load tests but should be corrected for size and shape effects according to Figure 8-4. 

The validity of the beam on elastic foundation approach has been called into question due to the 

fundamental assumption regarding the relative rigidity of the mat as compared to the soil. Also, 

the modulus of subgrade reaction is not an intrinsic soil property, and is a function not only of 

the stiffness of the soil, but the stiffness, shape and depth of the mat. Despite these limitations, 

the method is still a practical and commonly used way of computing displacements to design the 

structural reinforcement of the mat. 

129
Figure 8-3: Modulus of Subgrade Reaction (NAVFAC, 1986a) 

130
Figure 8-4: Analysis of Plate Load Test Results (NAVFAC, 1986a) 

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132
CHAPTER 9 

CONSTRUCTION DOCUMENTS 

9.1 DESIGN-BID-BUILD PROCUREMENT

9.1.1 Plans, Specifications and Estimates 

Plans are typically developed to show footing locations, dimensions and details for steel 

reinforcement, required footing elevations, and the embedment and backfill dimensions. A 

foundation data sheet is usually provided to show summary subsurface data in spatial relation to 

the foundations. Material descriptions, ground water levels, SPT data and other subsurface 

investigation information are particularly valuable to the contractor for evaluation of excavation, 

shoring, dewatering and other construction details that are usually left up to the contractor to 

design or select. The geotechnical report should be made available to contractors. 

The plans should detail the drainage and backfill requirements for abutments and retaining walls. 

For bridges, the abutment area is critical because it performs many functions. To prevent the 

notorious “bump at the end of the bridge,” the abutment backfill must be properly compacted and

not prone to material loss due to migration of fine-grained material. Refer to the Soils and 

Foundations Workshop Reference Manual (Cheney & Chassie, 2000) for specific details 

regarding materials that can be specified to promote good compaction of the backfill. 

Underdrain filter material or prefabricated geocomposite drains can be specified to prevent the 

fine-grained soil migration problem. Drainage details should be provided to prevent build up of 

pore water pressures behind the stemwall. 

Specifications typically include requirements for concrete, steel reinforcement and construction 

procedures. The FHWA Standard Specifications (FHWA, 1996) include Section 208, “Structure 

Excavation and Backfill for Selected Major Structures,” Section 209, “Structure Excavation and 

Backfill,” Section 552, “Structural Concrete” and Section 554 “Reinforcing Steel.” Items 

covered by these specifications include material requirements, preparation and compaction of a 

suitable bearing level in soil or rock, temporary cut slopes and shoring, requirements for shop 

drawings, protection of foundation conditions during construction, concrete delivery and 

placement, curing requirements and acceptance requirements.

The specifications should reference the availability of the geotechnical report. Special 

provisions might be necessary where special foundation soil/rock treatment or ground water 

control is required. Soft or liquefiable foundation soils may need special treatment to develop 

firm foundation conditions. When constructing in tight and sensitive areas, such as next to 

existing structure foundations, special shoring requirements might be necessary. 

133
Pay items may include Structure Excavation, Foundation Fill, Structural Backfill, Shoring and 

Bracing and Cofferdams. The actual footings may be considered incidental to structure 

construction. Alternatively, concrete and steel would be measured and paid for according to unit 

quantities and prices. 

9.1.2 Structural Fills 

Special details and specifications are necessary when constructing a compacted structural fill to 

support a bridge foundation such as an abutment. Figure 9-1, adapted from Cheney and Chassie 

(2000) shows recommended details for construction of a structural approach embankment. Note 

the zones of specified materials and compaction requirements. The materials specifications are 

chosen to provide a material that is capable of being compacted to a firm, non-yielding condition 

that will be suitable for support of a bridge abutment spread footing. The specification for select 

material recommended in the Soils and Foundations Workshop Reference Manual (Cheney & 

Chassie, 2000) is included in Appendix A. The specifications used by the Washington, Nevada 

and Michigan state transportation departments for structural fills beneath spread footing 

abutments are also included in Appendix A. 

Select structural fill and highway embankment material should not include unsuitable material. 

The specifications for these materials should prohibit unsuitable or deleterious material such as 

peat, muck, wood, organic waste, coal, charcoal or any other material that would perform poorly 

in an embankment. 

9.2 DESIGN-BUILD PROCUREMENT

The design-build procurement approach should include owner-provided geotechnical data, to the 

extent sufficient for normal foundation design. A Geotechnical Data Report (GDR) is 

recommended. Geotechnical Interpretive Reports and Geotechnical Baseline Reports may also 

be prepared to document the expected surface and subsurface conditions. These documents will 

help to reduce uncertainty during bidding and reduce the potential for risk contingencies. The 

GDR should identify any special conditions that might affect structural fill and shallow 

foundation design/construction and should provide the test results for necessary geotechnical 

properties. Sometimes the alignment and structure locations are not fixed at the time of the 

Design-Build procurement; therefore, the contractor may need to provide supplemental 

explorations and testing. 

Special Provision specifications should include the requirements the contracting agency wants to 

impose on the contractor to achieve the desired foundation performance – for example, codified 

design criteria, tolerable settlement criteria, estimated scour depths, seismic criteria and 

adherence to standard specifications. A submittal and review process should be prescribed, 

along with a minimum quality control and assurance plan. 

134
15 m (50') min

1

1

3 min

1

1.5 m (5')

Select Structural Fill

(Minimum 100% compaction, T99)

Highway Embankment Material, 150 mm (6") Max. Topsize

(Minimum 95% compaction, T180)

Highway Embankment Material

(Minimum 90% compaction, T180)

Place embankment to this line

prior to abutment construction

or pile driving

Working lines drawn perpendicular to projected

centerline of bearing to determine end limit for

placement of Select Material and Highway

Embankment Material

Backfill abutment to a point 1.5 m

(5') behind the wingwall with

Material per Note 1 to subgrade

1.5 m (5') Pad of Select

Material placed beneath

abutments on spread

footings

Minimum breakpoint of berm

and end slope may be located

0.6 m (2') above the top of the

footing and 1.2 m (4') out from

the front edge

See Note 1

Projection of abutment wingwall

Note 1: Highway embankment material and select material shall be placed simultaneously of the

 vertical payment line

Figure 9-1: Structural Approach Fill Details (after Cheney & Chassie, 2000) 

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136
CHAPTER 10 

INSPECTION AND CONSTRUCTION MONITORING 

Because of the limitations of geotechnical explorations and geologic interpretations, there is 

always the possibility that significant deviations from anticipated subsurface conditions might be 

encountered. In addition, construction operations can change the behavior of in-place soils, as 

well as the foundation support and stability of nearby facilities. Therefore, observations by an 

experienced geotechnical engineer during construction are recommended to identify additional 

concerns in the field and to provide adjustments to the design when necessary. 

The contracting agency’s construction personnel normally provide inspection and monitoring. 

The geotechnical report should discuss the anticipated ground conditions at the footing bearing 

level. In addition, the geotechnical engineer should explain how to identify the expected ground 

conditions to the inspection staff and be sure the inspectors know how to contact the designers if 

any questionable conditions are observed. Geotechnical staff may need to make site visits to 

observe questionable subsurface conditions and to oversee specialized instrumentation. 

Additional discussion and guidance regarding inspection and monitoring can be found in the 

Guide to Earthwork Construction (TRB, 1990). 

10.1 INSPECTION

Inspection of foundation construction is only as good as the qualifications and experience of the 

inspector. Most problems can be avoided by having, in addition to a qualified and cooperative 

contractor, a competent inspector who follows systematic inspection and documentation 

procedures and communicates issues with the foundation designer. The inspector should be 

aware of conditions that could affect the intended performance of the foundation and structure. 

This can be accomplished by reviewing the plans and specifications, along with the geotechnical 

report, and consulting with the geotechnical engineer. Foundations are usually designed to: 

• Perform within settlement tolerances, 

• Maintain an adequate safety margin with respect to bearing capacity failure, 

• Provide frictional resistance against sliding, 

• Provide resistance against lateral earth pressures, and 

• Provide sufficient support to prevent slope instability. 

Accepting materials or procedures different from those specified could compromise the design 

intent and potentially lead to distress or failure. Exceeding a criterion can sometimes lead to 

problems such as over-compaction behind an abutment wall, which could lead to increased 

stresses on the foundation element. 

137
Ground water impacts can be serious, possibly contributing to the disturbance of in-place soils. 

When dewatering operations may be necessary, they should be mentioned in the construction 

considerations section of the geotechnical report. Ground water control using sumps will have 

different effects on foundation soils and slopes than the use of dewatering wells. For instance, 

the stability of temporary sloped excavations may be compromised if water is allowed to seep 

directly from the sidewalls of the excavation for removal from a sump. In this case dewatering 

wells would locally lower the ground water level and improve the stability of the slopes. 

Conversely, dewatering in a clay soil profile can induce consolidation settlement by the resulting 

increase in vertical effective stress, a condition the geotechnical engineer may not have allowed 

for or considered in the settlement computations. 

Improper construction methods and procedures can potentially lead to foundation and slope 

failures. The inspector should regularly (e.g., daily) observe foundation and slope conditions for 

potential weaknesses that may need to be observed and addressed by the geotechnical engineer. 

Surface water and precipitation can deteriorate the condition of foundation bearing materials. If

the ground conditions expected at the bearing elevation are considered moisture sensitive, the 

geotechnical report should identify this potential and make a recommendation that the bearing 

materials be protected from the effects of surface moisture. Some rocks and IGMs can also be 

adversely affected by moisture, seepage and relaxation due to excavation. 

The bottoms of footing excavations can be probed with small diameter rods to confirm bearing 

resistance. More quantitative information can be obtained using cone penetration tests and 

nuclear densometers. Test pit excavation into and below the bearing stratum should be avoided 

due to the difficulty in compacting the backfill. 

Routine inspection should include checking that procedural requirements are followed, materials 

are provided that meet performance criteria and satisfactory compaction/density test results are 

obtained. The inspector should review the geotechnical report for special issues that should be 

observed during construction. 

10.2 MATERIALS

10.2.1 Line, Grade and Bearing Elevation 

The agency inspector should confirm that surveyed locations and elevations of the footing 

elements conform to the plans and shop drawings. Where foundation elevations and location 

vary from those specified, the actual dimensions should be documented and then checked with 

the designer for concurrence. 

10.2.2 Bearing Stratum 

The in-place bearing stratum of soil or rock should be checked to verify the in situ condition and 

the degree of improvement achieved by the contractor’s preparation approach. Some soil types 

can become remolded and weakened from disturbance. If the conditions deviate from those 

anticipated in the geotechnical report and/or the plans and specifications, the geotechnical 

engineer should be consulted to determine if additional measures are necessary. 

138
10.2.3 Structural Fill Materials 

The fill requirements should be strictly adhered to because the fill must perform within expected 

limits with respect to strength (bearing capacity) and, more importantly, within tolerance for 

differential settlement. Sometimes the area for construction of the fill is small, such as abutment 

and wingwall backfill, which may necessitate the use of smaller compaction equipment. 

10.3 MONITORING

When monitoring the construction of structural fills that will support shallow foundations, 

particular attention should be paid to the following: 

• The material should be tested for gradation and durability at sufficient frequency to 

ensure the material placed meets the specification.

• The specified level of compaction must be obtained in the fill. Testing, if applicable, 

should be performed in accordance with standard operating procedures and at the 

recommended intervals or number of tests. 

• If a surcharge fill is required for pre-loading, it should be verified that the unit weight of 

the surcharge fill meets the value assumed in design. 

The elevation of constructed foundations should be checked before and after the structural load is 

applied. This will serve as a baseline for long-term bridge monitoring. Subsequently, additional 

survey measurements could be made to confirm satisfactory performance or to identify whether 

potentially harmful settlements are occurring. It may be important to check the completion of fill 

settlements before foundation construction if soft compressible soils exist below (e.g., settlement 

plates, horizontal inclinometers, etc.). The lateral displacement potential can be greater than the 

vertical movements; therefore, if conditions warrant, monitoring may also include complete 

survey coordinates and possibly more accurate instrumentation. 

Monitoring may also be necessary to evaluate the impact on neighboring ground and facilities. 

Such concerns could be monitored with simple survey tag lines (with benchmark and monitoring 

hubs) and telltales to measure lateral deviations and vertical subsidence/heave. Higher reliability 

expectations may require more sophisticated instrumentation, such as inclinometers, strain gages, 

extensometers and tiltmeters. Pre-existing condition surveys of neighboring structures could be 

valuable, particularly in congested urban areas. 

The instrumentation program should be developed considering the anticipated performance, risks 

and potential consequences. Parameters should be identified that are critical to project success 

and appropriate instrumentation selected. A key to successful use of instrumentation is to 

measure, plot and interpret the data in a timely manner to be able to take corrective measures, if

needed. 

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140

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147
148

(This page intentionally blank) 
APPENDIX A 

STRUCTURAL FILL MATERIALS AND SPECIFICATIONS 

FHWA SOILS AND FOUNDATIONS REFERENCE MANUAL

The following specification for select material is recommended in the Soils and Foundations 

Workshop Reference Manual (Cheney & Chassie, 2000). This specification should be used in 

conjunction with the suggested plan detail, Figure 9-1. 

SELECT MATERIAL 

Description This work shall consist of excavation, disposal, placement and compaction of all 

materials that are not provided for under another section of these specifications and shall be 

executed in conformance with payment lines, grades, thicknesses and typical sections specific in 

the contract documents. 

Materials – Tests and Control Methods Materials tests and control methods pertaining to the item 

requirements and work of this section will be performed in conformance with the procedures 

used by the Department. 

Materials furnished under these items shall conform to the following requirements: 

1. Gradation. The material shall have the following gradation: 

Sieve Size Percent Passing (by weight)

100 mm 100 

No. 40 0 to 70 

No. 200 0 to 15 

2. Soundness. The material shall be substantially free of shale or other soft, poor-durability 

particles. Where the State elects to test for this requirement, a material with a magnesium

sulfate soundness loss exceeding 30 percent shall be rejected.

Construction The type of material to be used in filling and backfill at the structures, and payment 

lines, therefore, shall be in conformance with the details shown on the appropriate Standard 

Sheet or as noted on the plans or as ordered by the engineer. 

Fill or backfill material at structures, culverts and pipes shall be deposited in horizontal layers 

not exceeding 150 mm in thickness prior to compaction. Compaction of each layer shall be as 

specified. A minimum of 100 percent of standard proctor maximum density will be required. 

When filling behind abutments and similar structures, all material shall be placed and compacted 

in front of the walls prior to placing fill behind the walls to a higher elevation. The limits to 

A - 1 
which this subsection will apply shall be in accordance with the Standard Sheets or as modified 

by the plans. 

Measurement Quantities for this work shall be computed in cubic meters in the final compacted 

position. A deduction shall be made for pipes (based on nominal diameters) and other payment 

items when the combined cross-sectional area exceeds one 0.1 m2

 unless shown otherwise on the 

plans. No deduction will be made for the cross-sectional area of an existing facility. 

Basis of Payment The unit price bid for all pay items of work encompassed by this section shall 

include the costs of furnishing all equipment, labor, and materials as necessary to complete the 

work of the item, except where specific costs are designated or included in another pay item of 

work. All incidental costs, such as acquisition of borrow pits or material outside of the right-ofway, rock drilling and blasting, compaction and special test requirements, stockpiling and rehandling of materials – precautionary measures to protect private property and utilities and to 

form and trim graded surfaces – shall be included in the unit price of the pay item where such 

costs are incurred. 

WASHINGTON STATE DOT GRAVEL BORROW SPECIFICATION

The Washington State DOT uses the following materials specifications for embankments that 

will support bridge foundations: 

Gravel Borrow

Aggregate for gravel borrow shall consist of granular material, either naturally occurring or 

processed, and shall meet the following requirements for grading and quality: 

Sieve Size Percent Passing

100 mm (4′′) 100

50 mm (2′′) 75 – 100 

4.75 mm (#4) 50 – 80 

0.425 mm (#40) 30 max. 

0.075 mm (#200) 7.0 max. 

Sand equivalent 42 min. 

Method “C” compaction required (minimum of 95 percent maximum density according to 

AASHTO T-99 or WSDOT Test Method 606). Lift thickness limited to 200 mm (100 mm in top 

0.6 m). 

Note: WSDOT usually specifies Gravel Borrow for the entire embankment below the footing. 

A - 2 
NEVADA DOT STRUCTURAL FILL SPECIFICATION

The following specification was used for the Mt. Rose Highway Interchange Project (Nevada

DOT) described in Section 2.7.2: 

Materials for the Structural Fill Under the Footings 

Type 1 Class B Aggregate Base

Sieve Analysis: 

Sieve Size Percent Passing

37.5 mm 100 

25 mm 80 – 100 

4.75 mm 30 – 65 

1.18 mm 15 – 40 

75 μm 2 – 12 

R-value: 70 Min. 

Percentage of Wear (500 Rev.): 45% Max. 

Liquid Limit: 35 Max. 

Plasticity Index: 

Percent Finer than 75 μm PI

0.1 – 3.0 15 max 

3.1 – 4.0 12 max 

4.1 – 5.0 9 max 

5.1 – 8.0 6 max 

8.1 – 11.0 4 max 

11.1 – 15.0 3 max 

Fractured Faces: 15% Min. 

Placement

Place in layers not exceeding 200 mm in thickness before compaction. 

Compaction

Compact to not less than 95% of the maximum density as determined by Test Method No. Nev. 

T101. (Note: T101 is based on the use of the Harvard Miniature Compaction Device.)

A - 3 
A - 4 

MICHIGAN DOT STRUCTURAL FILL SPECIFICATION

The following specification was used for the Cadillac Bypass Project, Structure S01 

(Michigan DOT) described in Section 2.7.3: 

Materials for the Structural Fill Under the Footings

The material under the footings is specified as Structure Embankment. The structure 

embankment shall be constructed of Granular Material Class III. 

Granular Material Class III 

Sieve Analysis: 

Sieve Size Percent Passing 

150 mm 100 

75 mm 95 – 100 

Loss by Washing: 0 – 15 percent 

Placement

Granular materials, for backfill, shall be deposited and spread in layers not more than 250 mm in 

thickness. 

Compaction

The compaction required will be 100 percent of its Maximum Unit Weight. (Note: According to 

Greg Perry of MDOT, the Maximum Unit Weight is determined by the Modified Proctor 

Method.)
APPENDIX B 

DESIGN EXAMPLES 

INTRODUCTION

This appendix provides worked design examples for bridge foundation support on shallow 

foundations in several applications using Service Load Design (SLD) methodology. The 

applications and design considerations for each are discussed briefly below. The examples 

follow the design process outlined in Table 6-1 and shown in the flow chart in Figure 6-1. 

It should be noted that these examples are intended to convey one approach and process 

that can lead to a satisfactory design of bridge support on a shallow foundation. The 

examples should not be construed as representations of the only approach that can lead to a 

satisfactory design. Also note that the examples only check one or, at most, a few specific 

load cases. In practice, every complete design should consider all applicable load cases. 

EXAMPLE 1: INTERIOR BRIDGE PIER ON A SPREAD FOOTING FOUNDED IN NATIVE SOIL

This example uses SLD Group I loads from service load design of an interior bridge column. 

The purpose of the example is to show how bearing capacity and settlement are considered 

together to calculate an allowable bearing capacity that controls the design of the footing. 

EXAMPLE 2: INTEGRAL STUB ABUTMENT ON COMPACTED STRUCTURAL FILL

This example shows the successful and cost-effective application of a spread footing at a 

structurally integral abutment supported in a compacted structural fill over good foundation 

conditions. Since integral abutments are most frequently supported on pile foundations, this 

example was developed to illustrate the feasibility of using a spread footing in lieu of piles in 

order to realize the cost savings potential of shallow foundations. The load case is SLD Group I. 

EXAMPLE 3: STUB SEAT-TYPE ABUTMENT FOOTING IN COMPACTED STRUCTURAL FILL

This example uses SLD Group IV loads to show the effect of shear loads transmitted through the 

bearing pads due to temperature and shrinkage, etc., at a seat-type abutment with a joint. The 

example also shows the effective use of engineered embankment design and stage construction 

to permit the use of a spread footing supported in an approach fill over embankment foundation 

conditions that are less than excellent. 

B - 1 
EXAMPLE 4: FULL-HEIGHT SEAT ABUTMENT FOUNDED IN NATIVE SOIL

This example shows the design of a tall abutment founded on a spread footing in good ground 

conditions. The load case is SLD Group I. The example also shows design of a concrete 

cantilever retaining wall, since the intermediate construction stage of a backfilled stem without 

superstructure loads is also checked.

EXAMPLE 5: INTERIOR BRIDGE PIER ON A SPREAD FOOTING ON NATIVE ROCK

This example uses excellent foundation conditions and Group VII seismic loads to show an 

example of foundation design governed by considerations other than bearing capacity or 

settlement. 

Note: Unless cited with a specific reference (e.g., AASHTO, 1996), the equation numbers in the 

examples refer to those in the main body of this Circular.

B - 2 
EXAMPLE 1: INTERIOR BRIDGE PIER ON SPREAD FOOTING

Given: 

• Subsurface profile at the interior bridge pier is shown in Figure B1-1. 

• There is no scour potential at this site. 

• Frost penetration depth is 0.6 m (2 ft). 

• Tolerable settlement is 38 mm (1.5 in). 

• The sign conventions and loading directions are shown in Figure B1-2. 

Find: 

• Size the footing based on AASHTO Service Load Design, Group I loads (allowable stress 

design method) considering both the settlement and bearing capacity. Check for 

overturning and sliding. 

Boring B-1

?

Unit 1:

Lean Clay

Unit 2:

Silty Sand

Unit 3a:

Well-graded Sand

Unit 3b:

Well-graded Sand

(saturated)

Unit 4:

Clean, uniform Sand

6

7

18

20

22

42

38

47

33

45

42

37

49

Column Diameter,

D = 0.6 m

SPT N-value

g =19.6 kN/m3

2.3 m

2.1 m

4.7 m

3.0 m

3.0 m

g =19.6 kN/m3

g =19.6 kN/m3

g =19.6 kN/m3

Figure B1-1: Subsurface Profile 

B - 3 
Area of Column, Acol

Lf

Bf

Df

Z - Transverse

Direction of Bridge

Y - Longitudinal

Direction of Bridge

P

Mz - Moment About

Z-Axis due to

Longitudinal Loading

My - Moment About

Y-Axis due to

Transverse Loading

Soil

Footing

Figure B1-2: Sign Conventions and Loading Directions 

Solution:

The solution can be obtained by following the step-by-step process shown in Figure 6-1, Design 

Process Flow Chart. 

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulics and geotechnical engineers completed these steps. The required 

design information is provided in the problem-given statement. 

Step 5 – Determine the loads applied to the footing: 

The structural engineer has calculated and provided the values shown in Table B1-1. 

B - 4 
TABLE B1-1: LOADS AT COLUMN BASE 

Load 

Axial, P 

(kN) 

Shear, V 

(kN) 

Moment, MZ 

(kN-m)

Moment, MY 

(kN-m)

Dead load (D) 6400 167 211 748

Live load (L) 1670 42 409 196.5

Impact (I) 315 8 77 37

Wind on structure 

(W) 

884 49 89 226

Wind on live load 

(WL) 

18 4 7 26

Earthquake (EQ) 1671 804 1675 5546

Service Load Design Loads for Group I: 

The general equation is: 

P = γ [βD(D) + βL (L + I) + βC(CF) + βE (E) + βB (B) I (AASHTO, 1996, 

(SF) W (W) WL(WL) L (LF) R (R S T) + βS +β +β + β +β + + Eqn. 3-10) 

(EQ) (ICE)] +βEQ +βICE

where: γ = Load factor (always equal to 1.0 for SLD) 

= Coefficient for particular load, i, as found in Table 3.22.1A of AASHTO (1996). βi

Recall from Table 6-2, that SLD Group I is the load combination for normal vehicles using the 

bridge without wind, and that earthquake loads are only considered in Load Group VII. 

Therefore the coefficients for W, WL and EQ are all zero and the general load equation reduces 

to the following for this example: 

P = γ [βD (D) + βL (L + I) ] I

The AASHTO provisions permit neglecting the impact load, I, for foundations and buried 

structures. Also, since the footing is relatively shallow, assume that the effect of footing selfweight is negligible. The factored loads are as follows: 

Axial Loads:

kN

kN kN

I D L

8070

6400 1670

P D L

=

=1.0 [1.0 ( ) +1.0 ( ) ]

= γ [β ( ) + β ( ) ]

B - 5 
Shear: 

kN

kN kN

D L

209

1.0[1.0 (167 ) 1.0 (42 ) ]

V [ (D) (L)]

=

= +

= γ β + β

Moment in the Z direction: 

kN-m

kN-m kN-m

Z D L

620

1.0[1.0 (211 ) 1.0 (409 ) ]

M [ (D) (L)]

=

= +

= γ β + β

Moment in the Y direction: 

kN-m

kN-m kN-m

Y D L

944.5

1.0[1.0 (748 ) 1.0 (196.5 ) ]

M [ (D) (L I)]

=

= +

= γ β + β +

Step 6 – Subsurface Exploration and Laboratory Testing: 

This step is complete, and the subsurface data are shown in Figure B1-1. Laboratory testing was 

limited to soil classifications and moisture content due to the granular nature of the soils 

encountered in the boring. The foundation design will be based largely on design parameters 

correlated to the soil classifications and the field SPT N-values. Apply judgment and recognize 

that it is minimal excavation to remove all of the medium stiff Unit 1 lean clay to avoid any 

associated low strength or compressibility problems in this material. Therefore, select depth of 

footing, Df, of 2.3 m to bear below Unit 1. Compute the initial vertical effective stresses at the 

midpoint of each soil layer below the footing: 

Layer 2: 

' 3.35m(19.6 ) 65.7 kPa 3 m

kN

2 σ vo = =

Layer 3a: 

' 6.75m(19.6 ) 132 kPa 3 m

kN

vo3a σ = =

Layer 3b: 

' 10.6m(19.6 ) 1.5m(9.8 ) 193kPa 3 m

kN

3 m

kN

3b σ vo = − =

B - 6 
Layer 4: 

' 13.6m(19.6 ) 4.5m(9.8 ) 222 kPa 3 m

kN

3 m

kN

4 σ vo = − =

The effective stress diagram for the profile at the pier location is plotted in Figure B1-3. 

2

4

6

8

10

12

14

16

0

D

epth (

m)

0 3 100 200 00 400

u

Vertical Stress (kPa)

132

65.7

267

193 208

222

Unit 1

Unit 2

Unit 3a

Unit 4

Unit 3b

σ Voσ'

Vo

Figure B1-3: Effective Stress Diagram

Step 7 – Calculate allowable bearing capacity: 

The geotechnical engineer will calculate the allowable bearing capacity, considering both the 

potential for bearing capacity failure (Section 5.1) and settlement (Section 5.2). 

Calculate ultimate bearing capacity: 

The general equation for bearing capacity is: 

qult cNcscbc qNqCW sqbqdq 0.5 Bf N CW s b

q γ γ γ γ = + + γ (Eqn. 5-14) 

B - 7 
The first term goes to zero since the foundation materials are granular and cohesionless, so the 

cohesion term, c, is zero. 

For the interior pier, we will assume that the footing is essentially rectangular (L/B < 5). Recall 

that the shape and inclination factors should not be applied together (see discussion in Section 

5.2). Since the effect of the shape factors is significant for rectangular footings, and the 

inclination resulting from the relatively small shear load component (V) is small, we will only 

apply the shape factors as follows: 

s 0.6

L

B

s 1 0.4

f

f

=

= −

γ

γ

Assume the effect of eccentricity is small for 

now, so Bf ≅ Lf

(Table 5-2) 

A design friction angle associated with Layer 2 is needed to calculate sq. The geotechnical 

engineer has recommended that the footing be cast against the firm, undisturbed soil of Unit 2. 

Unit 2 is 2.1-m thick and overlies denser material at depth, so the properties of Unit 2 will 

govern the footing design. From Figure B1-1, the average uncorrected field SPT N-value for this 

layer is 20. From Figure B1-3, the average vertical effective stress in Layer 2 is 65.7 kPa (about 

1.4 ksf). Entering Figure 4-1 with a blowcount of 20 and a vertical effective stress of 1.4 ksf, a 

relative density, DR, of about 75 percent is read. Entering Figure 4-2 with this relative density 

for silty sand (Unified Soil Classification ‘SM’), a friction angle of 35 is selected for computing 

bearing capacity. 

s 1.7

tan(35 ) 1

1

s 1

tan

L

B

s 1

q

o

q

f

f

q

=

= +

= + φ (Table 5-2)

Since the overburden materials above the footing are cohesive soils, the correction factor to 

account for shearing resistance of the material above the bearing elevation, dq, should be set 

equal to 1.0: 

d 1.0 q = (Table 5-4)

Since this footing will be level, there is no effect of inclination of the base, so: 

b b 1.0 γ = q = (Table 5-5)

Calculate the effect of the footing embedment, q. Apply judgment and recognize that it is 

minimal excavation to remove all of the Unit 1 medium stiff lean clay and avoid any associated 

low strength or compressibility characteristics in this material. Therefore select Df = 2.3 m to 

bear below Unit 1: 

B - 8 
In this case q is only a function of the depth of bearing. 

f vo q = σ' = γ'D where: 3 m '= 19.6 kN

γ γ bulk =

q (19.6 )( ) 2.3m 3 m

kN =

q = 45.1kPa

Check ground water effect: 

Depth of ground water table below the bearing depth: 

Df = Depth of footing = 2.3 m Assumes a 0.9-m thick footing and 1.4-m cover 

Dw = Depth of ground water below the ground surface (Df ) = 9.1 m

Conservatively estimate the footing width with an upper bound value of Bf = 6 m.

Calculate ground water correction factors, CWγ and CWq: 

1.0

1.5B D

D C 0.5 0.5

f f

W

W ≤















+ = +

γ (Eqn. 5-10) 

0.9

1.5(6) 2.3

9.1 CW 0.5 0.5 =















+ = +

γ 

1.0

D

D C 0.5 0.5

f

W

Wq

≤













 = + (Eqn. 5-11) 

2.48

2.3

9.1 C 0.5 0.5 Wq  =



 



 = + ; Use CWq = 1.0 

From Table 5-1, the bearing capacity factors, Nγ and Nq, are 48.0 and 33.3, respectively, for a 

friction angle of 35 degrees in Layer 2. 

So the equation for bearing capacity is: 

ult f

ult f

ult q W q q q f W

q 2553kPa 254B

q = 45.1kPa (33.3)(1.0)(1.7)(1.0)(1.0) 0.5 (19.6 )(B )(48.0)(0.9)(0.6)(1.0)

q qN C s b d 0.5 B N C s b

3 m

kN

q

= +

+

= + γ γ γ γ γ

B - 9 
Incorporating a factor of safety of 3.0: 

q 851 85B kPa

q (2553kPa 254B ) 3.0

q q 3.0

all f

all f

all ult

= +

= + ÷

= ÷

Estimate Footing Settlement

Calculate stress increase at the midpoint of each soil layer using the 2-on-1 stress distribution 

method for various footing widths – say, Bf = 3, 4.6 and 6.1 m:

(B Z)(L Z)

(B )(L )

q f f

V f f

+ + = ∆σ

(Figure 5-12)

2

f

2

f

V

f f

B /(B Z)

q

butB L , so :

= +

∆σ

≅

Layer 2 with midpoint of layer @ Z = 1.05 m below base of footing: 

3 /(3 1.05) 0.55

q

V2 2 2 = + = ∆σ

Layer 3a with midpoint of layer @ Z = 4.45 m below base of footing: 

3 /(3 4.45) 0.16

q

V3a 2 2 = + = ∆σ

Layer 3b with midpoint of layer @ Z = 8.3 m below base of footing: 

3 /(3 8.3) 0.07

q

V3b 2 2 = + = ∆σ

Layer 4 with midpoint of layer @ Z = 11.3 m below base of footing: 

3 /(3 11.3) 0.04

q

V4 2 2 = + = ∆σ

Perform similar calculations for Bf = 4.6 m and Bf = 6.1 m and tabulate: 

B - 10 
TABLE B1-2: STRESS INCREASE WITH DEPTH 

AS FUNCTION OF FOOTING WIDTH 

Stress Increase, ∆σv

Soil Layer 

Depth 

Range (m) Bf = 3 m Bf = 4.6 m Bf = 6.1 m

2 2.3 – 4.4 0.55q 0.66q 0.73q 

3a 4.4 – 9.1 0.16q 0.26q 0.33q 

3b 9.1 – 12.1 0.07q 0.13q 0.18q 

4 12.1 – 15.1 0.04q 0.08q 0.12q 

Determine stress applied by footing to generate 38 mm of settlement for same range of footing 

widths, Bf = 3, 4.6 and 6.1 m, using the Hough method: 

General equation:

















σ′

σ′ + ∆σ

′ ∆ =

vo

vo v

o

f log C

1 H H (Eqn. 5-24)

Correct SPT blowcounts to account for overburden pressure, N′, for each layer, and enter Figure 

5-19 to obtain bearing capacity factor, C′: 

Layer 2: 

Navg = 20 

N′/N = 1.2 (from Figure 5-18) 

N′ = 24 

C′ = 65 (from Figure 5-19 for silty Sand) 

Layer 3a: 

Navg = 40 

N′/N = 0.9 (from Figure 5-18) 

N′ = 36 

C′ = 120 (from Figure 5-19 for well-graded Sand and Gravel) 

Layer 3b: 

Navg = 43 

N′/N = 0.7 (from Figure 5-18) 

N′ = 30 

C′ = 102 (from Figure 5-19 for well-graded Sand and Gravel) 

Layer 4: 

Navg = 40 

N′/N = 0.66 (from Figure 5-18) 

N′ = 26 

C′ =110 (from Figure 5-19 for clean, uniform Sand) 

B - 11 
Calculate settlement in each layer and sum the settlements to obtain the total settlement for a 

range of applied stresses and footing widths. Select applied stresses of q = 240 kPa, 290 kPa, 

335 kPa and 380 kPa (corresponding to about 3, 4, 5 and 6 ksf) and nominal footing widths of 3, 

4.6 and 6.1 m:

Layer 2 (Bf = 3 m): 

H 0.015m 15mm

H 2.1m(1/ 65)log[(65.7kPa 0.55(240kPa))/ 65.7kPa)]

H H (1/C')log[( ' )/ ' ]

2

2

2 2 v v v o o

∆ = =

∆ = +

∆ = σ +∆σ σ

H 0.004m 4mm

H 4.7m(1/120)log[(132 kPa 0.16(240 kPa))/132 kPa)]

H H (1/ C')log[( ' )/ ' ]

3a

3a

3a 3a vo v vo

∆ = =

∆ = +

∆ = σ +∆σ σ

H 0.001m 1mm

H 3.0m(1/102)log[(193kPa 0.07(240kPa))/193kPa)]

H H (1/C')log[( ' )/ ' ]

3b

3b

3b 3 v v v o o

∆ = =

∆ = +

∆ = σ +∆σ σ

H 0.0005m 1mm

H 3m(1/110)log[(222kPa 0.04(240kPa))/ 222kPa)]

H H (1/C')log[( ' )/ ' ]

4

4

4 4 v v v o o

∆ = ≅

∆ = +

∆ = σ +∆σ σ

∑∆Hi =15mm + 4mm +1mm +1mm = 21mm

Repeat and tabulate for various footing widths and applied stresses (a spreadsheet or computer 

tool can make these calculations rapidly): 

TABLE B1-3: SETTLEMENT AS A FUNCTION OF 

APPLIED STRESS AND FOOTING WIDTH 

Applied Stress Settlement (mm)

(kPa) Bf = 3 m Bf = 4.6 m Bf = 6.1 m

240 21 28 31

290 25 31 35

335 28 34 38

380 30 37 41

B - 12 
Compare to allowable bearing capacities at same footing widths relative to shear failure, 

remembering that the maximum tolerable settlement is 38 mm:

For Bf = 3 m:

q 851 85(3m)kPa 1106kPa all = + = >> 380 kPa (with 30 mm settlement) 

For Bf = 4.6 m:

q 851 85(4.6m)kPa 1242kPa all = + = >> 335 kPa (with 34 mm settlement) 

For Bf = 6.1 m:

q 851 85(6.1m)kPa 1369kPa all = + = >> 290 kPa (with 35 mm settlement) 

Settlement will therefore limit the allowable bearing capacity for the design of this footing. 

Interpolating the values in Table B1-3, find ranges of footing widths that will limit settlement to 

38 mm or less at allowable bearing capacities of 335 kPa and 380 kPa as shown in Table B1-4. 

TABLE B1-4: SETTLEMENT-LIMITED ALLOWABLE 

BEARING CAPACITIES 

Allowable Bearing Capacity 

(kPa) 

Range of Footing Widths That Will 

Limit Settlement to < 38 mm

380 < 5.0 m

335 5.0 to 6.1 m 

The geotechnical engineer should provide this table to the structural designer for sizing of the 

footing. 

Step 8 – Calculate sliding and passive soil resistance: 

The footing will bear in the Unit 2 soils. The friction angle, φ, of 35 degrees selected in Step 7 

will be used to compute sliding resistance. 

The general equation for sliding resistance on cohesionless soils is: 

FR = (W + Pv) tan δ (Eqn. 5-38)

The second term goes to zero since we are founding the footing on a cohesionless soil unit. For a 

concrete footing cast against the ground, δ = φ, so the ultimate sliding resistance is: 

F (W P )tan 35 0.7(W P ) R v = + v = + °

B - 13 
Since the sliding resistance will develop at strain levels much lower than those needed to develop 

passive pressures against the side of the footing, passive pressure will be ignored unless it is 

found that sliding resistance governs the design of the footing. The geotechnical engineer should 

provide this equation and the assumptions regarding use of passive pressures to the structural 

engineer for checking the footing’s resistance to sliding. 

Step 9 – Check global stability of the footing: 

The geotechnical engineer has determined that since this is an interior pier with level ground 

conditions, global stability is not a concern. 

Step 10 – Size the footing: 

The structural designer should make a preliminary estimate of the size of the footing by dividing 

the Group I axial load by the largest allowable bearing pressure from Table B1-4: 

B L A 4.6m

A 8070 380 kPa 21.2m

A P q

f f

kN 2

I all

= = ≅

= ÷ =

= ÷

Then calculate eccentricity and effective footing dimensions: 

f f y B′ = B − 2e (Eqn. 6-6)

B 4.6m 2(0.077m) 4.45m

e 620 8070 0.077m

e M P

f

kN m kN

y

y Z

′ = − =

= ÷ =

= ÷

−

f f z L′ = L − 2e (Eqn. 6-7)

L 4.6m 2(0.117m) 4.37m

e 944.5 8070 0.117m

e M P

f

kN m k z

z Y

′ = − =

= ÷ =

= ÷

−

2 A′ = B′

f ⋅ L′f = (4.45m)(4.37m) = 19.4m

Check allowable bearing stress for effective footing area: 

q P A 8070 19.4m 416 kPa kN 2

applied = ÷ ′ = ÷ =

This is greater than qall = 380 kPa for footings less than 5.0 m wide, according to Table B1-4, in 

order to limit settlement to less than 38 mm. Therefore the footing should be sized larger. 

B - 14 
Try a 4.9 m-by-4.9 m footing. Calculate eccentricity and effective footing dimensions: 

f f y B′ = B − 2e (Eqn. 6-6)

B 4.9m 2(0.077m) 4.75m

e 620 8070 0.077m

e M P

f

kN m kN

y

y Z

′ = − =

= ÷ =

= ÷

−

f f z L′ = L − 2e (Eqn. 6-7)

L 4.9m 2(0.117m) 4.67m

e 944.5 8070 0.117m

e M P

f

kN m k z

z Y

′ = − =

= ÷ =

= ÷

−

2 A′ = B′

f ⋅ L′f = (4.75m)(4.67m) = 22.2m

Check allowable bearing stress for effective footing area: 

q P A 8070 22.2m 364 kPa kN 2

applied = ÷ ′ = ÷ =

This is less than qall = 380 kPa for footings less than 5.0 m wide, according to Table B1-4, in 

order to limit settlement to less than 38 mm. 

The design is acceptable for bearing capacity and settlement considerations. 

Step 11 – Check overturning (eccentricity) and sliding: 

Overturning will be acceptable if eccentricity in any direction is less than one-sixth the footing 

dimension in that direction. 

(4.9m) 0.82m e e 0.077

6

1 L

6

1 B

6

1

f = f = = > z > y = (OK) 

A minimum factor of safety of 1.5 should be provided against sliding: 

V

0.7(W P )

F

F FS V

sliding

R + = = (FR from Step 8) 

V

0.7(W P ) FS + V =

Calculate the weight of cover over the footing and the weight of footing: 

The footing is bearing 2.3 m below grade. The footing can be assumed to be 0.9 m thick. 

B - 15 
The area of the column is: 

2 2

col (0.6m) 0.28m

4

A = π =

The weight of the footing and the soil cover is then (assume unit weight of concrete, γconc, 

of 23.5 kN/m3): 

kN

cover col

kN

ftg

W [(1.4m)(4.9m)(4.9m) A (1.4m)](19.6 ) 651

W (0.9m)(4.9m)(4.9m)(23.5 ) 508

3 m

kN

3 m

kN

= − =

= =

kN kN kN W = Wftg + Wcover = 508 + 651 = 1159

So: 

31 1.5

209

0.7(1159 8070 ) FS kN

kN kN

= >

+ = (OK) 

Step 12 – Complete structural design of footing: 

The structural engineer completes this step. 

B - 16 
EXAMPLE 2: INTEGRAL BRIDGE ABUTMENT ON STRUCTURAL FILL

Given: 

• An integral abutment on a spread footing is proposed for a bridge. 

• There is no scour potential at this site. 

• The footing length is L = 25.0 m (82 ft); other abutment dimensions are shown in Figure 

B2-1. 

• The approach embankment and the foundation soils are shown in Figure B2-1. 

• The SPT hammer energy ratio is assumed to be ER = 60%. 

• Frost penetration depth is 0.6 m (2 ft). 

• Tolerable settlement is 25 mm (1 in). 

• Abutment symbols are shown in Figure B2-2. 

Find: 

• Size the footing based on Service Load Design, Group I loads (allowable stress design 

method), considering both the settlement and bearing capacity. Check for overturning 

and sliding. 

Hard BASALT

Well-graded clean SAND

6.0 m

SPT N-v alue

19

24

27

25

33

37

37

41

RQD =80%

5.24 m

2

1

0.46 m 0.91 m

1.22 m

2.0 m

0.51 m

B 1.5 B

Structural f ill (Well-graded silty SAND & GRAVEL)

N = Uncorrected SPTBlowcount

4.57 m Existing Ground

Surf ace

Key

Boring B-1 φ = 38 deg (assumed, N' = 32)

γ = 20.5 kN/m 3

φ = friction angle

N' = Corrected SPT Blowcount

γ = 18.6 kN/m 3

γ sat = 19.6 kN/m 3

Figure B2-1: Approach Embankment and Foundation Soils 

B - 17 
Pg

H/3

0.5 H

Wh

Wf

Wtoe

Vg

At-rest

Earth Pressure, po

Live Load

Surcharge, pLS

PO

PLS

Toe

M toe

Wstem

M

g

Footing

Habut

Bf

Tf

Dtoe

Tstem

Superstructure

Backfill

Heel Toe

Tg

Figure B2-2: Integral Abutment Symbols 

B - 18 
Solution:

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulic and geotechnical engineers completed these steps. The required design 

information is provided in the problem-given statement. 

Step 5 – Determine the loads applied to the footing: 

The superstructure loads are transmitted to the abutment at the girder-stem connection as shown 

in Figure B2-2. The sense of the shear force is positive if it is in the direction from the toe to the 

heel (right to left) and negative if opposite. The sense of the moment of the couple is positive for 

resisting moments (counterclockwise) and negative for overturning moments (clockwise). 

Moments of these loads are taken about the toe of the footing. Their sense is determined in the 

same manner as for the couple Mg. Application of the superstructure loads is assumed at the top 

of the effective abutment stem, or one-half the girder height. 

Loads from the superstructure (per m length of abutment wall): 

The structural engineer has determined the following. 

TABLE B2-1: LOADS FROM SUPERSTRUCTURE 

Load 

Vertical, Pg 

(kN/m)

Shear, Vg 

(kN/m)

Couple, Mg 

(kN•m/m)

Moment, Mtoe

(kN•m/m)

Dead load of components 

(DC) 

169.22 42.61 -158.00 272.27

Dead load of wearing 

surfaces (DW)

19.99 16.64 -57.43 42.61

Vehicular live load (LL) 48.60 22.91 -65.65 103.17 

Vehicular braking force (BR) 0.58 3.65 -10.02 6.31 

Dead loads of the footing and earth fill (per m length of abutment wall): 

Weight of the stem, Wstem: 

45.30 kN / m

(23.5kN / m )(0.51m)(5.24m 0.460 0.5(2.0m))

W T (H T 0.5T )

3

stem conc stem abut f g

=

= − −

= γ − −

1.48m

1.22m 0.51m/ 2

arm D T / 2 stem toe stem

=

= +

= +

B - 19 
67.04kN m/m

(45.30kN/m)(1.48m)

M W (arm ) toe stem stem

= ⋅

=

=

Weight of the footing, Wf (Bf in m): 

10.81B kN / m

(23.5kN / m )(0.46m)B

W T B

f

f

3

f conc f f

=

=

= γ

armf = Bf / 2m

5.41B kN m / m

M W (arm )

2

f

toe f f

= ⋅

=

Weight of the soil over the toe, Wtoe: 

Assume granular backfill for toe and heel . Calculate the 

weight of the soil over the toe for the minimum cover. 

( 19.6kN/m , 36 ) 3 γ = φ′ = °

21.76kN /m

(19.6kN / m )(1.22m)(0.91m)

W (D )(D T )

3

toe soil toe f f

=

=

= γ −

0.61m

1.22m / 2

arm D / 2 toe toe

=

=

=

13.27kN m/ m

(21.76kN / m)(0.61m)

M W (arm ) toe toe toe

= ⋅

=

=

Weight of the soil over the heel, Wh: Bf in m

(93.69)(B 1.73)kN/m

(19.6kN/m )(B 1.22m 0.51m)(5.24m 0.46m)

W (B D T )(H T )

f

f

3

h soil f toe stem abut f

= −

= − − −

= γ − − −

B - 20 
0.865 0.5B m

2

(B 1.22m 0.51m) 1.22m 0.51m

2

(B D T ) arm D T

f

f

f toe stem

h toe stem

= +

− − = + +

− − = + +

(93.69)(B 1.73)(0.865 0.5B ) kN m/ m

M W (arm )

f f

toe h h

= − + ⋅

=

Loads from the approach fill: 

Earth Pressure Load: It is assumed that at-rest earth pressures will exist behind the wall because

the wall is restrained from rotating sufficiently to prevent active earth pressures from developing. 

Assume granular backfill( behind the wall. The coefficient of earth 

pressure at rest is 

19.6kN/m , 36 ) 3 γ = φ′ = °

0.41

1 sin 36

K 1 sin ' o

=

= − °

= − φ

110.32 kN / m

(0.5)(0.41)(19.6 kN / m )(5.24m)

P (0.5)K H

3 2

2

o o abut

= −

= −

= − γ

1.75m

5.24m/ 3

armP Habut / 3 o

=

=

=

193.06kN m/ m

( 110.32kN / m)(1.75m)

M P (arm ) o Po toe

= − ⋅

= −

=

Horizontal earth pressure from live load surcharge: Use HLS = 0.60 m.

25.27kN / m

(0.41)(19.6kN / m )(0.60m)(5.24m)

P (K H )H

3

LS o LS abut

= −

= −

= − γ

B - 21 
2.62m

(0.5)(5.24m)

armLS (0.5)Habut

=

=

=

66.21kN m/ m

( 25.27 kN / m)(2.62m)

M PLS(armLS) toe

= − ⋅

= −

=

The above are summarized in Table B2-2. 

TABLE B2-2: LOADS OF ABUTMENT COMPONENTS AND 

HORIZONTAL EARTH PRESSURES 

Load 

Vertical 

(kN/m)

Horizontal 

(kN/m)

Moment, Mtoe

(kN•m/m)

Weight of stem (Wstem) 45.30 - 67.04

Weight of footing (Wf) 10.81Bf - 5.41Bf

2

Weight of soil over toe (Wtoe) 21.76 - 13.27

Weight of soil over heel (Wh) (93.69)(Bf –1.73) - (93.69)(Bf –1.73)

*(0.865+0.5Bf) 

At-rest earth pressure load (Po) - -110.32 -193.06

Horizontal earth load from live 

load surcharge (PLS) 

- -25.27 -66.21

Note: Bf = width of footing in m

Step 6 – Field exploration and laboratory testing: 

This step is complete, and the subsurface data are shown in Figure B2-1. It was conservatively 

assumed that N′ (SPT blowcount corrected for overburden pressure) would not change after the 

construction of the approach embankment. For this example, the subsurface data includes the 

structural fill under the footing. 

The initial vertical stresses are calculated using the layers shown in Figure B2-3. The initial 

effective vertical stresses are defined as the stresses that exist after the approach embankment is 

constructed up to the bearing elevation (bottom of the footing). Thus the initial vertical stresses 

at the midpoint of each layer are calculated as follows. It is assumed that the approach 

embankment is constructed to its full height concurrently with the abutment and superstructure 

construction. 

B - 22 
Hard BASALT

Well-graded clean SAND

Lay er 3 (geologically pre-loaded)

3.0 m

SPT N-v alue

19

24

27

25

33

37

37

41

RQD =80%

5.24 m

2

1

0.46 m 0.91 m

1.22 m

2.0 m

0.51 m

B 1.5 B

Structural f ill (Well-graded silty SAND & GRAVEL)

N = Uncorrected SPTBlowcount

Lay er 1

2.0 m Existing Ground

Surf ace

Key

Boring B-1

φ = 38 deg (assumed, N' = 32)

γ = 20.5 kN/m 3

φ = friction angle

N' = Corrected SPTBlowcount

γ = 18.6 kN/m3 ; N' = 44

γ sat = 19.6 kN/m 3 ; N' = 43

Lay er 4

3.0m

Well-graded clean SAND

(geologically pre-loaded)

Lay er 2

2.57 m

Figure B2-3: Layers Used in the Analysis 

Compute the initial vertical effective stresses at the midpoints of each layer below the footing: 

Layer 1: Structural fill (H1 = 2.0 m)

20.5kPa

(20.5kN /m )(2.0m/ 2)

(H / 2)

3

vo 1 1 1

=

=

σ′ = γ

Layer 2: Structural fill (H2 = 2.57 m) 

67.3kPa

(20.5kN / m )(2.0m) (20.5kN / m )(2.57m/ 2)

(H ) (H / 2)

3 3

vo 1 1 2 2 2

=

= +

σ′ = γ + γ

Layer 3: Well-graded clean sand (H3 = 3.0 m)

( )

121.6kPa

(20.5kN / m )(2.0m) (20.5kN /m )(2.57m) (18.6kN / m )(3.0m/ 2)

(H ) (H ) H / 2

3 3 3

vo 1 1 2 2 3 3 3

=

= + +

σ′ = γ + γ + γ

B - 23 
Layer 4: Saturated, well-graded clean sand (H4 = 3.0 m)

( )

164.1kPa

(18.6 kN / m )(3.0m) (19.6 kN / m 9.81kN / m )(3.0m / 2)

(20.5kN / m )(2.0m) (20.5kN / m )(2.57m)

(H ) (H ) (H ) H / 2

3 3 3

3 3

vo 1 1 2 2 3 3 4 4 4

=

+ −

= + +

σ′ = γ + γ + γ + γ′

Step 7 – Calculate allowable bearing capacity: 

Calculate the allowable bearing capacity, considering both the bearing capacity failure and 

settlement. 

Calculate qall Based on Bearing Capacity Failure:

Use Equation 5-14. 

γ γ γ γ q = cN s b + qN C s b d + 0.5γB N CW s b ult c c c q Wq q q q f (Eqn. 5-14) 

In our example, the soils are all cohesionless, and c = 0. So the first term becomes zero. Assume

no cover on the footing, so the second term also becomes zero. Replace with from 

Figure 5-7 to account for slope effects.

Nγ Nγq

Look at footing widths of Bf = 2, 3, and 4 m.

Bf = 2 m:

12.5 5

2.0m

25.0m

B

L

f

f = = >

This is greater than five, so the shape factor is 

s = 1 γ (Table 5-2)

The base of the footing is horizontal, so the base factor is 

b = 1 γ (Table 5-5)

The water table is 4.57 m + 3.0 m = 7.57 m below the base of the footing and is greater than 1.5 

Bf = (1.5)(2.0 m) = 3.0 m. Therefore the ground water correction factor is 

CW = 1 γ

A slope inclination angle of i = 26.6o (for 2H : 1V slope) will be used to obtain the bearing 

capacity factor, . Although the upper portion of the slope is flatter, this will be more 

conservative. 

Nγq

D / B 1.37m / 2.0m 0.69 f f = =

B - 24 
The drained friction angle of the structural fill is assumed to be φ′= 38°. Using Figure 5-7c, for 

i = 26.6o and φ′= 38°, the following are obtained: 

For D / B 0, N 17. f f = γq ≅

For D / B 1, N 80. f f = γq ≅

By interpolation, for D / B 0.69, f f =

N 17 (0.69)(80 17) 60 γq = + − ≅

Thus 

1230kPa

(0.5)(20.5kN/m )(2.0m)(60)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

Using a factor of safety of 3, the allowable bearing capacity is 

410 kPa

1230 kPa / 3

q q / 3 all ult

=

=

=

Bf = 3 m:

Proceeding in a similar manner, we obtain the following. 

8.33 5

3.0m

25.0m

B

L

f

f = = >

s = 1 γ , b = 1, and C . γ W = 1 γ

D / B 1.37m / 3m 0.46 f f = =

By interpolation, for D / B 0.46, f f =

N 17 (0.46)(80 17) 46 γq = + − ≅

Thus 

1414kPa

(0.5)(20.5kN/m )(3.0m)(46)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

B - 25 
Using a factor of safety of 3, the allowable bearing capacity is 

471kPa

1414 kPa / 3

q q / 3 all ult

=

=

=

Bf = 4 m:

Proceeding in a similar manner, we obtain the following. 

6.25 5

4.0m

25.0m

B

L

f

f = = >

s = 1 γ , b = 1, and C . γ W = 1 γ

D / B 1.37m / 4m 0.34 f f = =

When Bf = 4 m, the potential failure surface can extend into Layer 3 (well-graded sand). Check 

to determine if the design friction angle needs to be modified for the purpose of calculating 

bearing capacity. From Figure B2-3, the average uncorrected SPT N-value for Layer 3 is about 

24. The effective vertical stress at the midpoint of Layer 3 at the time of drilling was: 

(H / 2) (18.6kN /m )(3m/ 2) 27.9kPa ( 0.58kips/ft ) 3 2

vo 3 3 drilling σ′ = γ = = ≅

Entering Figure 4-1 with a blowcount of 24 and a vertical effective stress of 0.58 ksf, a relative 

density, DR, of about 95 percent is read. Entering Figure 4-2 with this relative density for a wellgraded sand (Unified Soil Classification ‘SW’), a friction angle of 39 degrees is obtained. It is 

therefore conservative and acceptable to use φ′ of 38° to obtain . Nγq

By interpolation, for D / B 0.34, f f =

N 17 (0.34)(80 17) 38 γq = + − ≅

Also use a weighted average of the soil unit weights in Layers 2 and 3: 

3

3 3

ave 19.6kN / m

2

20.5kN / m 18.6kN / m = +

γ =

The bearing capacity is therefore: 

1490kPa

(0.5)(19.6kN / m )(4.0m)(38)(1)(1)(1)

q 0.5 B N C s b

3

ult ave f q W

=

=

= γ γ γ γ γ

B - 26 
Using a factor of safety of 3, the allowable bearing capacity is 

497 kPa

1490 kPa / 3

q q / 3 all ult

=

=

=

Calculate qall based on allowable settlement: 

To estimate the bridge loading to generate 25 mm of settlement, use both the Hough method and 

D’Appolonia’s method. Use the Hough method to estimate the settlement in the structural fill 

Layers 1 and 2. However, because the native sand of Layers 3 and 4 is known to be geologically

preloaded, use D’Appolonia’s method to avoid overestimating the settlement in these layers. 

The total settlement can be calculated by summing the settlements in each layer. 

The Hough method estimates settlements based on average changes in stress for the layer. 

D’Appolonia’s method estimates settlements based on the applied stress at the top of the layer. 

Therefore, calculate the stress increase at the midpoint of Layers 1 and 2, and at the top of Layer 

3 using the 2-on-1 stress distribution method for footing widths of Bf = 2, 3, 4 m.

(B Z)(L Z)

B L

q f f

v f f

+ + = ∆σ (Eqn. 5-17)

where q = bridge loading per unit area at the base of the footing 

Z = depth to the midpoint of a layer 

Using this equation, /q, the stress increases due to bridge footing loads are summarized in 

Table B2-3. 

∆σV

TABLE B2-3: STRESS INCREASE DUE TO BRIDGE LOADING 

Stress Increase, /q ∆σV Soil Layer Effective Level 

of Loading 

Depth to 

Effective Level (m) Bf = 2 m Bf = 3 m Bf = 4 m

1 Middle of Layer 1.0 0.64 0.72 0.77 

2 Middle of Layer 3.28 0.33 0.42 0.49 

3,4 Top of Layer 4.57 0.26 0.34 0.39 

Use the Hough method to estimate the settlement in Layers 1 and 2. The general equation is: 

















σ′

σ′ + ∆σ

′ ∆ =

vo

vo v

o

f log C

1 H H (Eqn. 5-24)

Bearing capacity index (C′) for the structural fill of layers 1 and 2 is obtained from Figure 5-19. 

For structural fill consisting of well-graded silty sand & gravel, use the recommended corrected 

B - 27 
SPT N-value for compacted structural fill of 32. Entering Figure 5-19 with N′ = 32 for wellgraded silty sand and gravel, a C′ of 110 is read. 

For a footing pressure, q, of 100 kPa and a footing width of Bf = 2 m, the settlement in Layers 1 

and 2 are calculated as follows. 

Layer 1: 

0.0112m 11.2mm

20.5kPa

20.5kPa (0.64)(100kPa) log 1101 (2m)

(q)

q log C '

1 H H

1

1

1

vo

v

vo

1

1 1

= =















 + =





























σ′

∆σ

σ′ +

∆ =

Layer 2: 

0.004m 4mm

67.3kPa

67.3kPa (0.33)(100kPa) log 1101 (2.57m)

(q)

q log C '

1 H H

2

2

2

vo

v

vo

2

2 2

= =















 + =





























σ′

∆σ

σ′ +

∆ =

Use D’Appolonia’s method to estimate the settlement in Layers 3 and 4. General equation is: 

o 1

V f

M

B

H μ μ 

 



 ∆σ ∆ = (Eqn. 5-25)

The modulus of compressibility of sand and gravel (M) for Layers 3 and 4 is obtained from

Figure 5-21, and the correction factors (μo and μ1) are obtained from Figure 5-20. Combining 

Layers 3 and 4 into one layer, the average uncorrected SPT N-value for the layer is 30. Entering 

Figure 5-21 with an average uncorrected blowcount of 30 and an M of 750 tsf, or 71820 kPa, is 

read for preloaded sand. Entering the upper chart of Figure 5-20 for D = 4.57 m and B = 6.57 to 

8.57 m (based on the 2-on-1 stress distribution method and Bf = 2, 3, and 4 m), a μ of 0.74 is 

read. Entering the lower chart of Figure 5-20 for H = 6 m and B = 6.57 to 8.57 m, a μ of 0.25 is 

read. 

o

1

B - 28 
For a footing pressure of 100 kPa and a footing width of Bf = 2 m, the settlement in layers 3 and 

4 are calculated as follows. 

0.0004m 0.4mm

(0.74)(0.25) 71820kPa

0.26(100kPa)(6.57m)

M

(q)(B )

q H o 1

3,4

f

v

3,4

3,4

= =





 



 =

μ μ



























 ∆σ

∆ =

The total settlement is therefore: 

∑∆Hi = 11.2 + 4.0 + 0.4 = 16mm

In a similar manner, the settlements for different widths and bridge loadings are obtained and are 

summarized as follows. 

TABLE B2-4: SETTLEMENTS DUE TO VARIOUS 

FOOTING PRESSURES AND WIDTHS 

Footing Pressure Settlement (mm) 

(kPa) Bf = 2 m Bf = 3 m Bf = 4 m

100 16 17 19

150 20 22 24

200 23 26 28

250 26 29 31

Table B2-4 shows that the maximum allowable footing pressure to limit the settlement to 25 mm

decreases from about 233 kPa for Bf = 2 m to about 163 kPa for Bf = 4 m. These values are 

smaller than the qall values based on bearing capacity failure that were calculated earlier. 

Settlement will therefore limit the allowable bearing capacity for the design of this footing. 

Interpolating the values in Table B2-4, find ranges of footing widths that will limit settlement to 

25 mm or less at nominal allowable bearing capacities of 150 kPa, 190 kPa and 230 kPa. These 

are summarized in Table B2-5. 

B - 29 
TABLE B2-5: SETTLEMENT-LIMITED 

ALLOWABLE BEARING CAPACITIES 

Allowable Bearing Capacity 

(kPa) 

Range of Footing Widths That Will 

Limit Settlement to 25 mm 

230 ≤ 2.0 m

190 2.0 to 3.0 m 

150 3.0 to 4.0 m 

The geotechnical engineer should provide this table to the structural designer for sizing of the 

footing. 

Step 8 – Calculate sliding and passive soil resistance: 

The footing concrete will be poured on compacted structural fill. Therefore, the friction angle, 

δ , to be used in the sliding analysis of the footing will be δ = φ′ = 38°. 

The passive resistance of the soil in front of the footing will be ignored. The ultimate sliding 

resistance is therefore: 

F = (W + P )tan δ R v (Eqn. 5-38)

0.78(W P )

(W P )tan(38 )

v

v

= +

= + °

Step 9 – Check global stability of the footing: 

The geotechnical engineer has checked an abutment and approach embankment with the same

dimensions and similar loading conditions but with a weaker foundation soil (silt with N′ = 10) 

and found that the minimum factor of safety was about 1.6 and satisfactory (see Example 3). 

Thus, with stronger foundation soils, the factor of safety should be greater than 1.6 and 

satisfactory. 

Step 10 – Size the footing under full loading: 

From Table B2-1, the total vertical load from the superstructure is 

238.39kN / m

169.22kN / m 19.99kN / m 48.60kN / m 0.58kN / m

Pv structure DC DW LL BR

=

= + + +

= + + +

Referring to Table B2-2, the additional load from the abutment components per 1-m length of the 

abutment wall for Bf = 3 m is 

B - 30 
P 45.30 32.43 21.76 118.99 218.48kN / m

W (93.69)(B 1.73) (93.69)(3 1.73) 118.99 kN / m

W 21.76 kN / m

W 10.81B (10.81)(3) 32.43kN / m

W 45.30 kN / m

v abut

h f

toe

f f

stem

= + + + =

= − = − =

=

= = =

=

Thus 

457 kN / m

238.39kN / m 218.48kN / m

Pv Pv structure Pv abut

=

= +

= +

From Table B2-5, an allowable bearing pressure of 190 kPa may be applied by the footing if Bf = 

2 to 3 m. Using a footing pressure of 190 kPa, the required footing width Bf is 

2.40m

(457 kN / m)/(190 kPa)

B P /(190 kPa) f v

=

=

=

This satisfies Bf = 2 to 3 m but appears to be too small to meet overturning requirements for Habut

= 5.24 m. A preliminary dimension for a footing width can be estimated as one-half the 

abutment height, or Habut = (0.5)(5.24 m) = 2.62 m. Therefore, try Bf = 2.7 m.

Step 11 – Check overturning and sliding under full loading: 

Check overturning for Bf = 2.7 m:

Analyze for 1 m of abutment wall length. 

From Step 10 and Table B2-1, the loads and moments due to the superstructure are 

Pv structure = 238.39 kN / m

424.36 kN m / m

Mtoe structure 272.27 kN m / m 42.61kN m / m 103.17 kN m / m 6.31kN m / m

= ⋅

= ⋅ + ⋅ + ⋅ + ⋅

Referring to Table B2-2, the loads and moments due to abutment components are 

187.13kN / m

45.30 (10.81)(2.7) 21.76 (93.69)(2.7 1.73)

P 45.30 10.81B 21.76 (93.69)(B 1.73) v abut f f

=

= + + + −

= + + + −

B - 31 
61.78kN m / m

193.06 66.21

67.04 (5.41)(2.7) 13.27 (93.69)(2.7 1.73)(0.865 (0.5)(2.7))

193.06 66.21

M 67.04 5.41B 13.27 (93.69)(B 1.73)(0.865 0.5B )

2

f f

2

abut f toe

= ⋅

− −

= + + + − +

− −

= + + + − +

The total loads and moments are: 

425.52 kN / m

238.39 kN / m 187.13kN / m

Pv Pv structure Pv abut

=

= +

= +

486.14kN m / m

424.36kN m / m 61.78kN m / m

Mtoe Mtoe structure Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is 

1.14m

425.52 kN / m

486.14 kN m / m

armR Mtoe / Pv

=

⋅ =

=

The eccentricity, ey, is 

0.21m

1.35m 1.14m

2.7m / 2 1.14m

ey Bf / 2 armR

=

= −

= −

= −

For stability, the eccentricity should be less than one-sixth the footing width: 

ey = 0.21m < Bf / 6 = 2.7m/ 6 = 0.45m (OK) 

Check bearing stress for effective footing area:

2.28m

2.7m (2)(0.21m)

B B 2e f f y

=

= −

′ = −

B - 32 
186.6kPa

(425.52 kN / m)(2.28m)

qfooting Pv / Bf

=

=

= ′

From Table B2-5, the allowable bearing pressure for B′f = 2 to 3 m is 190 kPa. Therefore, 

 and the bearing stress is smaller than the allowable value. (OK) qfooting < qall

Check sliding:

In Table B2-1, the vehicular live load (LL) and the vehicular braking force (BR) act to resist

sliding. To be conservative, these two loads will be ignored in the sliding analysis. The forces 

that tend to induce sliding are the sum of the following: 

Shear from the dead load of components, DC (Table B2-1) 

Shear from the dead load of wearing surfaces, DW (Table B2-1) 

At-rest earth pressure load, Po (Table B2-2) 

Horizontal earth load from live load surcharge, PLS (Table B2-2) 

Analyzing per m length of the abutment wall, Fsliding is 

76.34kN /m

42.61 16.64 110.32 25.27

Fsliding DC DW Po PLS

= −

= + − −

= + + +

The force FR available to resist sliding (from Step 8) is 

( ) R 78 W Pv F = 0. +

Neglecting the vehicular live load (LL) and vehicular breaking force (BR): 

169.22 19.99 kN / m 189.21kN / m

Pv structure DC DW

= + =

= +

W = Pv abut = 187.13kN / m

B - 33 
The factor of safety FS against sliding is 

( )

3.8

76.34 kN / m

293.54 kN / m

76.34 kN / m

0.78 189.21kN / m 187.13kN / m

F

F FS

sliding

R

=

=

+ =

=

FS >1.5 (OK) 

Step 12 – Complete structural design of the footing: 

The structural engineer completes this step. 

B - 34 
EXAMPLE 3: STUB SEAT-TYPE BRIDGE ABUTMENT ON STRUCTURAL FILL

Given: 

• A seat-type abutment on a spread footing is proposed for a bridge. 

• There is no scour potential at this site. 

• The footing length is L = 25.0 m (82 ft); other dimensions are shown in Figure B3-1. 

• The approach embankment and the foundation conditions are shown in Figure B3-1.

• The SPT hammer energy ratio is assumed to be ER = 60%. 

• Frost penetration depth is 0.6 m (2 ft). 

• Tolerable settlement is 38 mm (1.5 in). 

• Abutment loading symbols are shown in Figure B3-2. 

Find: 

• Size the footing based on Service Load Design, Group IV loads (allowable stress design 

method), considering both settlement and bearing capacity. Check overturning and 

sliding. 

5.24 m

2

1

0.46 m 0.91 m

1.22 m

2.0 m

0.51 m

B 1.5 B

Dense GRAVEL

Structural f ill(Well-graded silty SAND & GRAVEL)

SILT

Well-graded f ineto medium silty SAND

N = Uncorrected SPT Blowcount

4.57 m

6.0m

6.0m

Existing Ground

Surf ace

Key

Boring B-1

SPT N-v alue

5

4

6

6

7

11

8

10

15

19

22

28

> 50

> 50

φ = 38 deg (assumed, N' = 32)

γ = 20.5 kN/m3

γ = 17.3 kN/m 3

φ = f riction angle

γ sat = 19.6kN/m 3

N' = Corrected SPT Blowcount

Figure B3-1: Approach Embankment and Foundation Soils 

B - 35 
P

H/3

0.5 H

Wh

Wstem

Wf

Wtoe

V

Active Earth

Pressure,pa

Live Load

Surcharge,p LS

PA

PLS

Footing

Habut

Bf

Tf

Dtoe

Tstem

Superstructure

Backfill

TGS

Toe

Mtoe

Stem and

Girder Seat

Figure B3-2: Abutment Loading Symbols 

B - 36 
Solution:

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulic and geotechnical engineers completed these steps. The required design 

information is provided in the problem-given statement. 

Step 5 – Determine the loads applied to the footing: 

Moments are taken about the front toe of the footing. The direction of the moment is positive for 

resisting moments (counterclockwise) and negative for overturning moments (clockwise). 

Loads from the girders: 

The structural engineer has provided Group IV loads as summarized in Table B3-1. Recall that 

Group IV is the SLD load combination with normal vehicles using the bridge without wind, and 

with consideration of long term shrinkage, shortening, and thermal movements. 

TABLE B3-1: LOADS FROM GIRDERS 

Load 

Vertical, P 

(kN) 

Shear, V 

(kN) 

Moment, Mtoe

(kN•m)

Dead load of components 

(DC) 

5233 - 7274

Dead load of wearing 

surfaces (DW)

446 - 620

Vehicular live load (LL) 1538 - 2138 

Shear loads from bearing 

pads (V) 

- 1047 -3392

Dead loads of the abutment components (per m of abutment wall, assume γconcrete = 23.5 kN/m3

)

Weight of the stem, Wstem (for simplicity, this computation does not subtract out the weight of 

the seat):

57.29kN / m

(23.5kN / m )(0.51m)(5.24m 0.46m)

W T (H T )

3

stem conc stem abut f

=

= −

= γ −

1.48m

1.22m 0.51m / 2

arm D T / 2 stem toe stem

=

= +

= +

B - 37 
84.79kN m/ m

(57.29kN / m)(1.48m)

M W (arm ) toe stem stem

= ⋅

=

=

Weight of the footing, Wf (Bf in m): 

10.81B kN / m

(23.5kN / m )(0.46m)B

W T B

f

f

3

f conc f f

=

=

= γ

armf = Bf / 2m

5.41B kN m / m

M W (arm )

2

f

toe f f

= ⋅

=

In this example, the weight of the soil over the toe, Wtoe, is ignored for design purposes because

the soil may not get placed until after the bridge superstructure is constructed. Assume granular 

backfill for toe and heel ( 19.6kN/m , 36 ) . 3 γ = φ′ = °

Weight of the soil over the heel, Wh (Bf in m): 

(93.69)(B 1.73)kN/m

(19.6kN/m )(B 1.22m 0.51m)(5.24m 0.46m)

W (B D T )(H T )

f

f

3

h soil f toe stem abut f

= −

= − − −

= γ − − −

0.865 0.5B m

2

(B 1.22m 0.51m) 1.22m 0.51m

2

(B D T ) arm D T

f

f

f toe stem

h toe stem

= +

− − = + +

− − = + +

(93.69)(B 1.73)(0.865 0.5B ) kN m/ m

M W (arm )

f f

toe h h

= − + ⋅

=

Loads from Approach Fill:

Active earth pressure: Assume that the stem wall will rotate sufficiently to develop active earth 

pressures behind the wall. Use Rankine’s active earth pressure coefficient. Assume granular 

backfill( 19.6kN/m , 36 ) behind the wall. 3 γ = φ′ = °

B - 38 




 



 φ = ° − 2

' K tan 45 2

a (Eqn. 6-3)

0.26

2

36

tan 45 2

=





 



 ° = ° −

69.96 kN / m

(0.5)(0.26)(19.6 kN / m )(5.24)

P (0.5)K H

3 2

2

A a abut

=

=

= γ

1.75m

5.24m / 3

arm H / 3 PA abut

=

=

=

122.43kN m/ m

(69.96kN / m)(1.75m)

M P (arm ) toe A PA

= − ⋅

= −

= −

Horizontal earth pressure from live load surcharge (use HLS = 0.60 m): 

16.02kN / m

(0.26)(19.6kN / m )(0.60m)(5.24m)

P (K H )H

3

LS a LS abut

=

=

= γ

2.62m

(0.5)(5.24m)

armLS (0.5)Habut

=

=

=

41.97 kN m/ m

(16.02kN / m)(2.62m)

M PLS(armLS) toe

= − ⋅

= −

= −

These loads are summarized in Table B3-2. 

B - 39 
TABLE B3-2: LOADS OF ABUTMENT COMPONENTS 

AND HORIZONTAL EARTH PRESSURES 

Load 

Vertical 

(kN/m)

Horizontal 

(kN/m)

Moment, Mtoe

(kN•m/m)

Weight of stem (Wstem) 57.29 - 84.79

Weight of footing (Wf) 10.81Bf - 5.41Bf

2

Weight of soil over toe (Wtoe) - - -

Weight of soil over heel (Wh) (93.69)(Bf –1.73) - (93.69)(Bf –1.73)

*(0.865+0.5Bf) 

Active earth pressure load (PA) - 69.96 -122.43

Horizontal earth load from live 

load surcharge (PLS) 

- 16.02 -41.97

Note: Bf = width of footing in m

Step 6 – Conduct subsurface exploration and laboratory testing: 

This step is complete, and the subsurface data are shown in Figure B3-1. It was conservatively 

assumed that N′ (SPT blowcount corrected for overburden pressure) would not change after the 

construction of the approach embankment. For this example, the subsurface data include the 

structural fill under the footing. 

The initial vertical stresses are calculated using the layers shown in Figure B3-3. The initial 

vertical stresses were calculated as the stresses that exist after the approach embankment is 

constructed to its full height. These are estimated by using the depth from the estimated ground 

surface of the approach embankment after its construction, as shown in Figure B3-3. The initial 

vertical stresses at the midpoint of each layer are calculated as follows. 

Layer 1: Structural fill (H1 = 2.0 m); note that the height of backfill is taken as the average 

height of the surcharge at the stem: 

89.1kPa

(19.6kN / m )(3.5m) (20.5kN / m )(2.0m/ 2)

(3.5m) (H / 2)

3 3

vo backfill 1 1 1

=

= +

σ′ = γ + γ

Layer 2: Structural fill (H2 = 2.57 m) 

135.9kPa

(19.6kN / m )(3.5m) (20.5kN / m )(2.0m) (20.5kN / m )(2.57m/ 2)

(3.5m) H (H / 2)

3 3 3

vo backfill 1 1 2 2 2

=

= + +

σ′ = γ + γ + γ

B - 40 
3.5m

2

1

0.46 m 0.91 m

1.22 m

2.0m

0.51 m

B 1.5 B

Dense GRAVEL

Structural f ill(Well-graded silty SAND &GRAVEL)

SILT

Well-graded f ine to medium

silty SAND

N = Uncorrected SPT Blowcount

 Lay er 1

2.0m Existing Ground

Surf ace

Key

Boring B-1

SPT N-v alue

5

4

6

6

7

11

8

10

15

19

22

28

> 50

> 50

φ = 38 deg (assumed, N' = 32)

γ = 20.5 kN/m 3

γ = 17.3 kN/m 3

φ = friction angle

γ sat = 19.6kN/m 3

N' = Corrected SPT Blowcount

Lay er 2

2.57 m

Lay er 3

3.0m

Lay er 4

3.0m

Lay er 5

3.0m

Lay er 6

3.0m

N' =10

N' =10

N' =15

N' =20

Estimated surf ace of

approach embankment

to calculate σVo

γ backfill = 19.6 kN/m3

Figure B3-3: Layers Used in the Analysis 

Layer 3: Silt (H3 = 3.0 m)

188.2kPa

(17.3kN / m )(3.0m/ 2)

(19.6kN / m )(3.5m) (20.5kN / m )(2.0m) (20.5kN / m )(2.57m)

(3.5m) H H (H / 2)

3

3 3 3

vo backfill 1 1 2 2 3 3 3

=

+

= + +

σ′ = γ + γ + γ + γ

B - 41 
Layer 4: Silt (H4 = 3.0 m) 

240.1kPa

(17.3kN / m )(3.0m) (17.3kN /m )(3.0m/ 2)

(19.6kN / m )(3.5m) (20.5kN / m )(2.0m) (20.5kN / m )(2.57m)

(3.5m) H H (H ) (H / 2)

3 3

3 3 3

vo backfill 1 1 2 2 3 3 4 4 4

=

+ +

= + +

σ′ = γ + γ + γ + γ + γ

Layer 5: Saturated silty sand (H5 = 3.0 m)

280.7kPa

(19.6 9.81kN / m )(3.0m/ 2)

(17.3kN / m )(3.0m) (17.3kN /m )(3.0m)

(19.6kN / m )(3.5m) (20.5kN / m )(2.0m) (20.5kN / m )(2.57m)

(3.5m) H H (H ) (H ) (H / 2)

3

3 3

3 3 3

vo5 backfill 1 1 2 2 3 3 4 4 5 5

=

+ −

+ +

= + +

σ′ = γ + γ + γ + γ + γ + γ

Layer 6: Saturated silty sand (H6 = 3.0 m)

310.1kPa

(19.6 9.81kN / m )(3.0m) (19.6 9.81kN / m )(3.0m/ 2)

(17.3kN / m )(3.0m) (17.3kN / m )(3.0m)

(19.6kN / m )(3.5m) (20.5kN / m )(2.0m) (20.5kN / m )(2.57m)

(3.5m) H H (H ) (H ) (H ) (H / 2)

3 3

3 3

3 3 3

vo6 backfill 1 1 2 2 3 3 4 4 5 5 6 6

=

+ − + −

+ +

= + +

σ′ = γ + γ + γ + γ + γ + γ + γ

Step 7 – Calculate allowable bearing capacity:

Calculate the allowable bearing capacity, considering both bearing capacity failure and 

settlement. 

First calculate qall using bearing capacity theory: 

γ γ γ γ q = cN s b + qN C s b d + 0.5γB N CW s b ult c c c q Wq q q q f (Eqn. 5-14) 

In this example, the soils are all cohesionless, and c = 0. So the first term becomes zero. 

Assume no cover on the footing, so the second term also becomes zero. Replace with 

from Figure 5-7 to account for slope effects.

Nγ

Nγq

Look at footing widths of Bf = 3, 4 and 5 m.

B - 42 
Bf = 3 m:

8.33 5

3.0m

25.0m

B

L

f

f = = >

This ratio is greater than five, so the shape factor is 

s =1 γ (Table 5-2)

The base of the footing is horizontal, therefore the base factor is 

b =1 γ (Table 5-5)

The water table is 4.57 m + 6.0 m = 10.57 m below the base of the footing and is greater than 1.5 

Bf = (1.5)(3.0 m) = 4.5 m. Therefore, the ground water correction factor is 

CW =1 γ (Table 5-3)

A slope inclination angle of i= 26.6o (for 2H : 1V slope) will be used to obtain the bearing 

capacity factor This will be conservative, even though the upper portion of the slope is 

flatter. 

N . γq

D / B 1.37m / 3.0m 0.46 f f = =

The drained friction angle of the structural fill is assumed to be φ′ = 38°. Using Figure 5-7f, for 

i = 26.6o and φ′ = 38°, the following are obtained: 

For D /B 0, N 17. f f = γq ≅

For D /B 1, N 80. f f = γq ≅

By interpolation, for D / B 0.46, f f =

N 17 (0.46)(80 17) 46 γq = + − ≅

The ultimate bearing capacity is 

1414kPa

(0.5)(20.5kN/m )(3.0m)(46)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

B - 43 
Using a factor of safety of 3, the allowable bearing capacity is 

471kPa

1414 kPa / 3

q q / 3 all ult

=

=

=

Bf = 4 m: 

Proceeding in a similar manner, 

6.25 5

4.0m

25.0m

B

L

f

f = = >

s = 1 γ , bγ = 1, and CW = 1 γ

D / B 1.37m / 4m 0.34 f f = =

By interpolation, for D / B 0.34, f f =

When Bf = 4 m, the potential failure surface can extend into Unit 3 (silt). To determine how 

much of the failure surface will engage Unit 3, use the rule of thumb that the failure surface will 

extend to a maximum depth of about 1.5 times the footing width, or in this case 1.5(4 m) = 6 m. 

This extends about 1.5 m into Unit 3, which corresponds to about one-half of the failure surface 

passing through Unit 3 (visually estimated from Figure B3-1). Therefore, use a weighted 

average friction angle to obtain . A design friction angle associated with Layer 3 is needed. 

From Figure B3-3, the average uncorrected SPT N-value for this layer is about 5.2. The 

effective vertical stress at the midpoint at the time of drilling was: 

Nγq

3 2

v 3 3 (H / 2) (17.3kN / m )(3m/ 2) 25.95kPa 0.54kips/ft drilling σ′ = γ = = ≅

Entering Figure 4-1 with a blowcount of 5.2 and a vertical effective stress of 0.54 ksf, a relative 

density, DR, of about 50 percent is read. Entering Figure 4-2 with this relative density for lean 

silt (Unified Soil Classification ‘ML’), a friction angle of 32o is obtained. Use a reduced φ′ from

38° to 34° to obtain . Using Figure 5-7, for i = 26.6o and Nγq φ′= 34°, the following is 

obtained: 

N 12 ( ) 0.34 (43 12) 23 γq = + − ≅

Use a weighted average of the soil unit weights in Units 2 and 3: 

3

3

average 18.9kN / m

2

20.5kN / m 17.3kN / m = +

γ =

B - 44 
The ultimate bearing capacity is 

869kPa

(0.5)(18.9kN / m )(4.0m)(23)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

Using a factor of safety of 3, the allowable bearing capacity is 

290kPa

869kPa /3

q q /3 all ult

=

=

=

Bf = 5 m: 

Proceeding in a similar manner, 

5

5.0m

25.0m

B

L

f

f = =

s = 1 γ , b = 1, and C . γ W = 1 γ

D / B 1.37m / 5m 0.27 f f = =

When Bf = 5 m, the potential failure surface can extend deeply into Unit 3 (silt). Therefore, 

conservatively use Unit 3 soil properties (γ = 17.3 kN/m3

, φ = 32 degrees) to compute bearing 

capacity: 

For D /B 0, N 7. f f = γq ≅

For D /B 1, N 32. f f = γq ≅

By interpolation, for D / B 0.27, f f =

N 7 (0.27)(32 7) 14 γq = + − ≅

Thus 

605kPa

(0.5)(17.3kN / m )(5.0m)(14)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

B - 45 
Using a factor of safety of 3, the allowable bearing capacity is 

202kPa

605kPa /3

q q /3 all ult

=

=

=

Calculate qall based on allowable settlement: 

Since the embankment weight is so large, settlement due to approach embankment construction 

is, in general, much greater than the settlement due to bridge loading alone. Due to the presence 

of the compressible silt, the settlement due to the approach embankment alone was computed 

using the FHWA program EMBANK. The input parameters for soil unit weight and 

compression index shown below were estimated from the subsurface exploration SPT N-values 

per the Hough method. The EMBANK output is shown in Figure B3-4. 

┌───── ONE DIMENSIONAL SETTLEMENT ANALYSIS/Federal Highway Administration ─────┐

│ INCREMENT OF STRESSES BENEATH THE END OF FILL CONDITION │

│ │

│ Project Name : Example 3 Client : Shallow Fnd GEC │

│ File Name : Ex3.dat Project Manager : │

│ Date : 12/20/01 Computed by : rek │

│ │

│ │

│ Settlement for X = 106.00 (ft) Y = 64.00 (ft) │

│ │

│ Embank. slope, x direc. = 64.00 (ft) Height of fill H = 32.00 (ft) │

│ y direc. = 64.00 (ft) Unit weight of fill = 130.00 (pcf) │

│ Embankment top width = 82.00 (ft) p load/unit area = 4160.00 (psf) │

│ Embankment bottom width = 210.00 (ft) Foundation Elev. = 100.00 (ft) │

│ Ground Surface Elev. = 100.00 (ft) │

│ Water table Elev. = 80.00 (ft) Unit weight of Wat. = 62.40 (pcf) │

│ │

│ │

│ LAYER COMP. RECOMP. SWELL. UNIT Settlement │

│ No. TYPE THICK. (1/C’) RATIO WEIGHT │

│ (ft) (pcf) (in.) │

│ │

│ 1 COMP. 20.0 0.033 0.003 0.000 110.00 5.73 │

│ 2 COMP. 10.0 0.020 0.002 0.000 125.00 0.93 │

│ 3 COMP. 10.0 0.017 0.002 0.000 125.00 0.65 │

│ │

│ Total Settlement = 7.31 │

│ │

│ │

│ SUBLAYER SOIL STRESSES │

│ Nد. THICK. ELEV. INITIAL INCREMENT MAX.PAST PRESS. SETTLEMENT │

│ (ft) (ft) (psf) (psf) (psf) (in.) │

│ │

│ 1 10.00 95.00 550.00 4073.24 550.00 3.66 │

│ 2 10.00 85.00 1650.00 3846.32 1650.00 2.07 │

│ 3 10.00 75.00 2513.00 3614.73 2513.00 0.93 │

│ 4 10.00 65.00 3139.00 3373.09 3139.00 0.65 │

│ │

│ Total Settlement = 7.31 (in.) │

│ = 186 mm │

└───── Hit arrow keys to display next screen. <F8> Print. <F10> Main Menu ─────┘

Figure B3-4: Summary Output of EMBANK Settlement Analysis 

B - 46 
The settlement was computed to be 186 mm. This is excessive for the bridge. It will therefore 

be necessary to mitigate the settlement by surcharging the site prior to construction of the 

abutment foundation. The contract will specify that the embankment must be built full height 

and to full dimensions and settlement monitored until complete, before excavating back down to 

the bearing elevation and constructing the footing. Since the settlement potential is mostly due 

to the inelastic silt layer, the settlement should occur relatively quickly, and the potential for 

post-construction settlement due to secondary consolidation (creep) will be low. Therefore, a 

spread footing is still a cost-effective foundation choice for this site. 

The design of the abutment footing will therefore need to consider only the potential settlement 

due to the structure loads, as follows: 

Calculate the stress increase at the midpoint of each soil layer using the 2-on-1 stress distribution 

method for footing widths of Bf = 3, 4, 5 m.

(B Z)(L Z)

B L

q f f

v f f

+ + = ∆σ (Eqn. 5-17)

Using this equation, /q ratios are tabulated in Table B3-3. ∆σV

TABLE B3-3: STRESS INCREASE DUE TO BRIDGE LOADING 

Stress Increase, ∆σV /q 

Soil Layer 

Depth to 

Midpoint (m) Bf = 3 m Bf = 4 m Bf = 5 m

1 1.0 0.72 0.77 0.80

2 3.28 0.42 0.49 0.53

3 6.07 0.27 0.32 0.36

4 9.07 0.18 0.22 0.26

5 12.07 0.13 0.17 0.20

6 15.07 0.10 0.13 0.16

Use the Hough method to estimate the bridge loading to generate 38 mm of settlement. 

General equation is: 

















σ′

σ +∆σ

′ ∆ =

vo

vo v

o

' log C

1 H H (Eqn. 5-24)

Bearing capacity index (C′) of the layers are obtained from Figure 5-19 as follows. This assumes 

N, and therefore N′ is unchanged after pre-loading, which is conservative. 

Layers 1 and 2: Structural fill consisting of well-graded silty sand & gravel 

B - 47 
Use the recommended assumed corrected SPT N-value for compacted structural fill: 

N' = 32

From Figure 5-19, C′1,2 = 110. 

Layer 3: Alluvium consisting of inorganic silt 

Nave = 5.2 (Figure B3-3) 

The effective vertical pressure at the time of drilling was 

(H / 2) (17.3kN / m )(3m/ 2) 25.9kPa 3

vo 3 3 drilling3 σ′ = γ = =

Thus N′/N = 1.92 (Figure 5-18). 

N′ = 10 

C′3 = 30 (Figure 5-19) 

Layer 4: Alluvium consisting of inorganic silt 

Nave = 9.0 (Figure B3-3) 

77.8kPa

25.95kPa 25.95kPa 25.95kPa

25.95kPa (17.3kN / m )(3m/ 2) (17.3kN / m )(3m/ 2)

(H / 2) (H / 2)

3 3

vo vo 3 3 4 4 drilling4 drilling3

=

= + +

= + +

σ′ = σ′ + γ + γ

N′/N = 1.11 (Figure 5-18) 

N′ = 10 

C′4 = 30 (Figure 5-19) 

Layer 5: Alluvium consisting of well-graded fine to medium sand 

Nave = 17.0 (Figure B3-3) 

118.5kPa

77.85kPa 25.95kPa 14.69kPa

77.85kPa (17.3kN / m )(3m/ 2) (19.6 9.81kN / m (3m/ 2)

(H / 2) (H / 2)

3 3

vo vo 4 4 5 5 drilling5 drilling4

=

= + +

= + + −

σ′ = σ′ + γ + γ′

B - 48 
N′/N = 0.9 (Figure 5-18) 

N′ = 15 

C′5 = 50 (Figure 5-19) 

Layer 6: Alluvium consisting of well-graded fine to medium sand 

Nave = 25.0 (Figure B3-3) 

147.9kPa

118.49kPa 14.69kPa 14.69kPa

118.49kPa (19.6 9.81kN / m (3m/ 2) (19.6 9.81kN / m (3m/ 2)

(H / 2) (H / 2)

3 3

vo vo 5 5 6 6 drilling6 drilling5

=

= + +

= + − + −

σ′ = σ′ + γ′ + γ′

N′/N = 0.805 (Figure 5-18) 

N′ = 20 

C′6 = 58 (Figure 5-19) 

The total settlement can be calculated by summing the settlements in each layer. For a range of 

bridge loadings from, say, q = 100 kPa to 300 kPa and footing widths of Bf = 3 m to 5 m, the 

settlements are calculated as follows: 

Layer 1: 

0.0047m 5mm

89.1kPa

89.1kPa (0.72)(100kPa) log 110

1 2m

log C

1 H H

1

1 1

vo

vo v

1

1 1

= ≅















 + 



 



 =

















σ′

σ′ + ∆σ

′ ∆ =

Layer 2: 

0.0027m 3mm

135.9kPa

135.9kPa (0.42)(100kPa) log 110

1 2.57m

log C

1 H H

2

2 2

vo

vo v

2

2 2

= ≅















 + 



 



 =

















σ′

σ′ + ∆σ

′ ∆ =

B - 49 
Layer 3: 

0.0058m 6mm

188.2kPa

188.2kPa (0.27)(100kPa) log 30

1 3.0m

log C

1 H H

3

3 3

vo

vo v

3

3 3

= ≅















 + 



 



 =

















σ′

σ′ + ∆σ

′ ∆ =

Layer 4: 

0.0031m 3mm

240.1kPa

240.1kPa (0.18)(100kPa) log 30

1 3.0m

log C

1 H H

4

4 4

vo

vo v

4

4 4

= ≅















 + 



 



 =

















σ′

σ′ + ∆σ

′ ∆ =

Layer 5: 

0.0012m 1mm

280.7 kPa

280.7 kPa (0.13)(100kPa) log 50

1 3.0m

log C

1 H H

5

5 5

vo

vo v

5

5 5

= ≅















 + 



 



 =

















σ′

σ′ + ∆σ

′ ∆ =

Layer 6: 

0.0007m 1mm

310.1kPa

310.1kPa (0.10)(100kPa) log 58

1 3.0m

log C

1 H H

6

6 6

vo

vo v

6

6 6

= ≅















 + 



 



 =

















σ′

σ′ + ∆σ

′ ∆ =

The total settlement is: 

∑∆Hi = 5 + 3 + 6 + 3 +1+1 = 19mm

In a similar manner, the settlements for different footing widths and bridge loadings are 

calculated and summarized in Table B3-4. 

B - 50 
TABLE B3-4: SETTLEMENTS DUE TO BRIDGE LOADING 

Bridge Loading Settlement (mm)

q (kPa) Bf = 3 m Bf = 4 m Bf = 5 m

100 19 21 24

200 33 38 42

300 46 53 59

Table B3-4 shows that the maximum allowable q to limit the settlement to 38 mm decreases 

from about 238 kPa for Bf = 3 m to about 178 kPa for Bf = 5 m. These values are smaller than 

the qall values based on bearing capacity failure that were calculated earlier. Therefore, the 

settlement will limit the allowable bearing capacity of the footings. 

The allowable bearing pressure is summarized in Figure B3-5. 

100

200

300

400

2 3 4 5 6

Footing width, Bf (m)

Allowable bearing pressure (kPa)

Figure B3-5: Allowable Bearing Pressure as a Function of Footing Width 

Step 8 – Calculate sliding and passive soil resistance: 

The footing concrete will be poured on compacted structural fill. Thus the friction angle, δ , to 

be used in the sliding analysis of the footing will be δ = φ′ = 38°. 

The passive resistance of the soil in front of the footing will be ignored. The ultimate sliding 

resistance is therefore: 

F = (W + P )tan δ R v (Eqn. 5-38)

0.78(W P )

(W P )tan(38 )

v

o

v

= +

= +

B - 51 
Step 9 – Check global stability of the footing: 

The slope stability program XSTABLTM was used to evaluate the global stability of the approach 

embankment with the abutment and the bridge loading applied. The program uses Bishop’s 

method of slices to compute a global stability factor of safety for the slope. A footing width of 

Bf = 3.5 m was assumed. The footing loads and the abutment backfill were modeled as applied 

vertical surcharge loads at the footing bearing elevation. The applied footing stress corresponded 

to the allowable bearing pressure for this footing width (e.g., 240 kPa from Figure B3-4). At this 

stress, the critical failure surface was just behind the heel of the footing. The minimum factor of 

safety was about 1.6 and satisfactory. The potential failure arc is shown in Figure B3-6. 

2

1

Dense GRAVEL

Structural fill

(Well-graded silty

SAND & GRAVEL)

SILT

Well-graded fine to

medium silty SAND

FS = 1.6

Live load surcharge

Figure B3-6: Global Stability 

Step 10 – Size the footing under full loading: 

From Table B3-1, the total vertical load from the bridge girders is 

7217 kN

5233kN 446kN 1538kN

P DC DW LL

=

= + +

= + +

Using Lf = 25 m,

B - 52 
288.7 kN / m

25m

7217 kN

L

P P

f

v girders

=

=

=

 

The additional load from the abutment components per 1-m length of the abutment wall is 

calculated as follows for Bf = 3 m.

P 57.29 32.43 118.99 208.71kN / m

118.99 kN / m

(93.69)(3 1.73)

W (93.69)(B 1.73)

W 10.81B (10.81)(3) 32.43kN / m

W 57.29 kN / m

v abut

h f

f f

stem

= + + =

=

= −

= −

= = =

=

Thus 

497 kN / m

288.7 kN / m 208.7 kN / m

Pv Pv girders Pv abut

≅

= +

= +

From Figure B3-4, a bearing pressure of up to 230 kPa may be applied by the footing. Using q = 

230 kPa, the required footing width Bf is 

2.16m

(497 kN / m)/(230 kPa)

B P / q f v

=

=

=

This appears to be too small for Habut = 5.24 m. A preliminary dimension for a footing width can 

be estimated as one-half the abutment height, or Habut = (0.5)(5.24 m) = 2.62 m. Therefore, try 

Bf = 2.7 m.

Step 11a – Check overturning (eccentricity), bearing pressure and sliding under full 

loading without PDW and PLL: 

Check overturning for Bf = 2.7 m: 

Analyze for 1 m of abutment length. 

From Table B3-1, the loads and moments due to girders are 

B - 53 
209.3kN / m

25m

5233kN

L

5233kN P

f

v girders

=

=

=

155.3kN m / m

25m

3882kN m

L

(7274 3392) kN m M

f

toe girders

= ⋅

⋅ =

− ⋅ =

From Table B3-2, the loads and moments due to abutment components are 

177.4kN / m

57.29 (10.81)(2.7) (93.69)(2.7 1.73) kN / m

Pv abut 57.29 10.81Bf (93.69)(Bf 1.73) kN / m

=

= + + −

= + + −

161.1kN m / m

122.43 41.97

84.79 (5.41)(2.7) (93.69)(2.7m 1.73)(0.865 (0.5)(2.7m))

M 84.79 5.41B (93.69)(B 1.73)(0.865 0.5B ) 122.43 41.97

2

f f

2

toe abut f

= ⋅

− −

= + + − +

= + + − + − −

The total loads are 

386.7 kN / m

209.3kN / m 177.4kN / m

Pv Pv girders Pv abut

=

= +

= +

316.4kN m / m

155.3kN m / m 161.1kN m / m

Mtoe Mtoe girders Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is 

0.82m

(316.4 kN m / m)/(386.7 kN / m)

armR Mtoe / Pv

=

= ⋅

=

B - 54 
The eccentricity, ey, is 

0.53m

1.35m 0.82m

2.7m/ 2 0.82m

ey Bf / 2 armR

=

= −

= −

= −

For stability, the eccentricity should be less than one-sixth the footing width: 

ey = 0.53m < Bf / 6 = 2.7m/ 6 = 0.45m (No Good) 

Try increasing Bf to 3.2 m. 

Check overturning for Bf = 3.2 m:

Analyze for 1 m of abutment length. 

From the previous calculations, the loads and moments due to girders are 

Pv girders = 209.3kN / m

Mtoe girders = 155.3kN ⋅m / m

From Table B3-2, the loads and moments due to abutment components are 

229.6kN / m

57.29 (10.81)(3.2) (93.69)(3.2 1.73) kN / m

Pv abut 57.29 10.81Bf (93.69)(Bf 1.73) kN / m

=

= + + −

= + + −

315.3kN m / m

122.43 41.97

84.79 (5.41)(3.2) (93.69)(3.2m 1.73)(0.865 (0.5)(3.2m))

M 84.79 5.41B (93.69)(B 1.73)(0.865 0.5B ) 122.43 41.97

2

f f

2

abut f toe

= ⋅

− −

= + + − +

= + + − + − −

The total loads are 

438.9kN / m

209.3kN / m 229.6kN / m

Pv Pv griders Pv abut

=

= +

= +

B - 55 
470.6kN m / m

155.3kN m / m 315.3kN m / m

Mtoe Mtoe girders Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is 

1.07m

(470.6 kN m / m)/(438.9 kN / m)

armR Mtoe / Pv

=

= ⋅

=

The eccentricity, ey, is 

0.527m

1.6m 1.07m

3.2m/ 2 1.07m

ey Bf / 2 armR

=

= −

= −

= −

For stability, the eccentricity should be less than one-sixth the footing width: 

ey = 0.527m < Bf / 6 = 3.2m/ 6 = 0.533m (OK) 

Check bearing stress for effective footing area: 

f y B B 2e f

′ = − (Eqn. 6-6)

2.14m

3.2m (2)(0.53m)

=

= −

205.1kPa

(438.9 kN / m)/(2.14m)

q Pv / Bf

=

=

= ′

By extrapolating the values in Figure B3-4, the allowable bearing pressure for B′f = 2.14 m to 

limit settlement to less than 38 mm is about 

q 275kPa all =

Under Group IV loads, the 25 percent overstress allowance can be applied to this allowable 

bearing pressure. By inspection, however, this computation is not necessary since , and 

the bearing stress is smaller than the allowable value. (OK) 

q < qall

Check sliding: 

The forces, Fsliding, that tend to induce sliding are the sum of the following: 

B - 56 
Shear loads from bearing pads, V (Table B3-1) 

Active earth pressure load, PA (Table B3-2) 

Horizontal earth load from live load surcharge, PLS (Table B3-2) 

Analyzing per m of the abutment wall, Fsliding is 

127.9kN / m

1047kN / 25m 69.96kN / m 16.02kN / m

Fsliding V / Lf PA PLS

=

= + +

= + +

The force, FR, available to resist sliding (from Step 8) is 

F 0.78(W P ) R = + v

The vertical force, Pv computed above includes the self-weight of the footing, W. The live load 

and weight of the wearing surface should not be included in this calculation. Thus the factor of 

safety FS against sliding is 

FSsliding = 1.5

F

F

sliding

R ≥ (Eqn. 5-40)

2.7

127.9kN / m

342.3kN / m

127.9kN / m

0.78(438.9kN / m)

=

=

=

Step 11b – Check overturning, bearing pressure and sliding under full loading: 

Check overturning for Bf = 3.2 m: 

Analyze for 1 m of abutment length. 

From Table B3-1, the loads and moments due to girders are 

288.7 kN / m

25m

7217 kN

L

(5233 446 1538) kN P

f

v girders

=

=

+ + =

B - 57 
265.6kN m / m

25m

6640kN m

L

(7274 620 2138 3392) kN m M

f

toe girders

= ⋅

⋅ =

+ + − ⋅ =

From Step 11a, the loads and moments due to abutment components are 

Pv abut = 229.6 kN / m

Mtoe abut = 315.3kN ⋅m / m

The total loads are 

518.3kN / m

288.7 kN / m 229.6kN / m

Pv Pv girders Pv abut

=

= +

= +

580.9kN m / m

265.6kN m / m 315.3kN m / m

Mtoe Mtoe girders Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is 

1.12m

(580.9 kN m / m)/(518.3kN / m)

armR Mtoe / Pv

=

= ⋅

=

The eccentricity, ey, is 

0.48m

1.6m 1.12m

3.2m/ 2 1.12m

ey Bf / 2 armR

=

= −

= −

= −

For stability, the eccentricity should be less than one-sixth the footing width: 

ey = 0.48m < Bf / 6 = 3.2m/ 6 = 0.53m (OK) 

B - 58 
Check bearing stress for effective footing area: 

f y B B 2e f

′ = − (Eqn. 6-6)

2.24m

3.2m (2)(0.48m)

=

= −

231.4 kPa

(518.3kN / m)/(2.24m)

q Pv / Bf

=

=

= ′

By extrapolating the values in Figure B3-4, the allowable bearing pressure for B′f = 2.24 m to 

limit settlement to less than 38 mm is about 

q 270kPa all =

Under Group IV loads, the 25 percent overstress allowance can be applied to this allowable 

bearing pressure. By inspection, however, this computation is not necessary since , and 

the bearing stress is smaller than the allowable value. (OK) 

q < qall

Check sliding: 

The forces, Fsliding, that tend to induce sliding are the sum of the following: 

Shear loads from bearing pads, V (Table B3-1) 

Active earth pressure load, PA (Table B3-2) 

Horizontal earth load from live load surcharge, PLS (Table B3-2) 

Analyzing per m of the abutment wall, Fsliding is 

127.9kN / m

1047kN / 25m 69.96kN / m 16.02kN / m

Fsliding V / Lf PA PLS

=

= + +

= + +

The force, FR, available to resist sliding (from Step 8) is 

F 0.78(W P ) R = + v

The vertical force, Pv, computed above includes the self-weight of the footing, W. The live load 

should not be included in this calculation. Thus the factor of safety FS against sliding is 

FSsliding = 1.5

F

F

sliding

R ≥ (Eqn. 5-40)

B - 59 
2.8

127.9kN / m

356.3kN / m

127.9kN / m

0.78(518.3kN / m 1538kN / 25m)

=

=

− =

Again, the 25 percent overstress allowance could be applied, but since FS > 1.5, this is not 

necessary. (OK) 

Step 11c – Check overturning, bearing pressure, and sliding without the bridge loading 

from the girders: 

Consider the loads of abutment components only, without the horizontal earth load from live 

load surcharge, PLS. Note that this condition would not occur in the consideration of Group IV 

loads because the superstructure must be in place for the temputerature and shrinkage loads to 

be applied to the footing. This check is normally done when considering Group I loads but is 

included here for completeness. 

Check overturning (eccentricity) for Bf = 3.2 m: 

Referring to Step 11b above and Table B3-2, the following are obtained without the contribution 

from PLS. 

M 315.3kN m / m 41.97 kN m / m 357.3kN m / m

P 229.6kN / m

toe abut

v abut

= ⋅ + ⋅ = ⋅

=

The arm of the resultant is 

1.56m

(357.3kN m / m)/(229.6kN / m)

armR Mtoe abut / Pv abut

=

= ⋅

=

The eccentricity, ey, is 

0.04m

1.6m 1.56m

3.2m/ 2 1.56m

ey Bf / 2 armR

=

= −

= −

= −

For stability, the eccentricity should be less than one-sixth the footing width: 

ey = 0.04m < Bf / 6 = 3.2m/ 6 = 0.53m (OK) 

B - 60 
Check bearing stress for effective footing area:

3.12m

3.2m (2)(0.04m)

B B 2e f f y

=

= −

′ = −

73.6kPa

(229.6kN / m)/(3.12m)

q Pv abut / Bf

=

=

= ′

From Figure B3-4, the allowable bearing pressure for B′f = 3.12 m to limit settlement to less than 

35 mm is about 

q 235kPa all =

The applied bearing stress is smaller than the allowable value. (OK) 

Check sliding: 

The force, Fsliding, that tends to induce sliding consists only of the active earth pressure load, PA 

(Table B3-2): 

Fsliding = PA = 69.96 kN / m

The force FR available to resist sliding (from Step 8) is 

F 0.78(W P ) R = + v

The factor of safety FS against sliding is: 

FSsliding = 1.5

F

F

sliding

R ≥ (Eqn. 5-40)

2.6

69.96kN / m

179.4kN / m

69.96kN / m

0.78(229.6kN / m)

=

=

=

This should be > 1.5. (OK) 

Step 12 – Complete structural design of the footing: 

The structural engineer completes this step. 

B - 61 
(This page intentionally blank)

B - 62 
EXAMPLE 4: FULL-HEIGHT BRIDGE ABUTMENT WITH LATERAL EARTH PRESSURE

Given: 

• Subsurface profile at the abutment is shown in Figure B4-1. 

• Geometry of the abutment is shown in Figure B4-2. 

• Abutment stem is located Bf/3 from the footing toe. 

• Tstem = 1.0 m, TGS = 0.5 m, and Tf = 0.9 m.

• The height of the abutment, Habut, is 8.5 m, and the length is 25 m.

• There is no scour potential at this site. 

• Frost penetration depth is 0.6 m (2 ft). 

• Tolerable settlement is 25 mm (1.0 in). 

Find: 

• Size the footing based on Service Load Design, Group I loads (allowable stress design 

method), considering both the settlement and bearing capacity. Check for overturning 

and sliding. 

Boring B-1

Unit 1a:

Well-graded sand

Unit 2:

Shale

14

18

25

28

25

37

>50

>50

SPT N-value

g =19.6 kN/m3

1.5 m

1.5 m

g =23.5 kN/m3

RQD = 80%

33 g =19.6 kN/m3

4.5 m

Unit 1b:

Well-graded sand

(saturated)

Footing

Habut

Bf

Backfill

Tf

Stem

and

Girder

Seat

Tstem

TGS Superstructure

Dtoe

Figure B4-1: Subsurface Profile Figure B4-2: Abutment Geometry 

B - 63 
Solution:

The solution can be obtained by following the step-by-step process shown in Figure 6-1, Design 

Process Flow Chart. 

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulics and geotechnical engineers completed these steps. The required 

design information is provided in the problem-given statement. 

Step 5 – Determine the loads applied to the footing: 

The structural engineer has calculated the following values for loading along the abutment wall: 

Loads at base of the superstructure (applied through the bearings at the girder seat) are 

summarized on Table B4-1. 

TABLE B4-1: LOADS AT SUPERSTRUCTURE BASE 

Load 

Axial, P 

(kN/m)

Shear, V 

(kN/m)

Dead load (D) 227 41.9 

Live load (L) 61.6 0 

The shear load shown in Table B4-1 is the shear transferred through the bearings due to 

temperature, shrinkage and rib shortening. Under Group I loads, the load factor for this shear 

component is zero and will therefore not be included in the design loads for this example. 

Final Service Load Design Loads for Group I: 

The general equation is (refer to Example B-1 for discussion of variables): 

(EQ) (ICE)]

(SF) (W) (WL) (LF) (R S T)

P D L I (CF) (E) B

EQ ICE

S W WL L R

I D L C E B

+ β + β

+ β + β + β + β + β + +

= γ [β ( ) + β ( + ) + β + β + β ( ) (AASHTO, 1996, 

Eqn. 3-10)

This reduces to the following for the loads under consideration for Load Group I in this example: 

P = γ [β (D) + β (L)] I D L

B - 64 
So the factored loads are as follows: 

Axial Loads:

kN/m

kN/m kN/m

I D L

289

227 61.6

P D L

=

=1.0[1.0 ( ) +1.0 ( )]

= γ [β ( ) + β ( )]

Shear: 

kN/m

kN/m

D

41.9

1.0[1.0 (41.9 )]

V [ (D)]

=

=

= γ β

Step 6 – Conduct field exploration and laboratory testing: 

This step is complete, and the subsurface data are shown in drawing at pier location, Figure B4-

1. Laboratory testing was limited to soil classifications and moisture content due to the granular 

nature of the soils encountered in the boring. The foundation design will be based largely on 

design parameters correlated to the soil classifications and the SPT N-values. Compute the 

initial vertical effective stresses at the midpoint of each layer: 

Layer 1a: 

' 2.25m(19.6 ) 44.1kPa 3 m

kN

v1a σ = =

Layer 1b: 

' 5.25m(19.6 ) 0.75m(9.8 ) 95.6kPa 3 m

kN

3 m

kN

v1b σ = − =

The effective stress diagram for the profile at the abutment is plotted in Figure B4-3. 

Step 7 – Calculate allowable bearing capacity: 

The geotechnical engineer will calculate the limiting allowable bearing capacity, considering 

both the potential for bearing capacity failure (Section 5.2) and settlement (Section 5.3). 

Calculate Ultimate Bearing Capacity: 

The general equation for bearing capacity is: 

γ γ γ γ q = cN s b + qN C sqbqdq + 0.5γBf N CW s b Wq ult c c c q (Eqn. 5-14)

B - 65 
1

2

3

4

5

6

7

0

Depth (m)

0 7 25 50 5

u

Vertical Stress (kPa)

44.1

95.6 103

Unit 1a

Unit 1b

Unit 2 σVo σ'

Vo

100 125 150

Figure B4-3: Effective Stress Diagram

The first term goes to zero since the foundation materials are granular and cohesionless, so the 

cohesion term, c, is zero. 

The footing length (Lf) is 25 m. For footing widths (Bf) less than 5 m, the ratio of footing length, 

Lf, to width is greater than 5. This footing classifies as a strip footing, and the shape factors 

should be set equal to 1.0: 

s γ = sq = 1.0 (Table 5-2)

Since this footing will be level, there is no effect of inclination of the base, so: 

bγ = bq =1.0 (Table 5-5)

Calculate the effect of the footing embedment, q. Assuming a 0.9-m-thick footing and 0.6-m

cover, Df = 1.5 m:

In this case, q is only a function of the depth of bearing. 

f ov q = σ' = γ'D where: 3 m

'= bulk 19.6 kNγ γ =

q (19.6 3 )( ) 1.5m m

kN =

q = 29.4kPa

B - 66 
Since the ratio of the footing depth, Df, to the footing width, Bf, will be less than one, the 

correction factor to account for shearing resistance of the material above the bearing elevation, 

dq, should be set equal to 1.0: 

dq = 1.0 (Table 5-4)

Check ground water effect: 

Depth of ground water table below the bearing depth: 

Df = Depth of footing = 1.5 m Assumes a 0.9-m-thick footing and 0.6-m

cover 

Dw = Depth of ground water below the ground surface = 4.5 m 

Conservatively estimate the footing width for ground water correction factors 

with an upper bound value of Bf = 6 m. 

Calculate ground water correction factors, CWγ and CWq: 

1.0

1.5B D

D C 0.5 0.5

f f

W

W ≤















+ = +

γ (Eqn. 5-9) 

0.7

1.5(6) 1.5

4.5 CW 0.5 0.5 =















+ = +

γ 

1.0

D

D

C 0.5 0.5

f

W

Wq

≤













 = + (Eqn. 5-10) 

2.0

1.5

4.5 C 0.5 0.5 Wq  =



 



 = + ; Use CWq = 1.0 

A design friction angle associated with Unit 1a is needed to calculate the bearing capacity 

factors. From Figure B4-1, the average uncorrected SPT N-value for this unit is 22. From

Figure B4-3, the average vertical effective stress in Unit 1 is 44.1 kPa (about 0.9 ksf). Entering 

Figure 4-1 with a blowcount of 22 and a vertical effective stress of 0.9 ksf, a relative density, DR, 

of about 85 percent is read. Entering Figure 4-2 with this relative density for well-graded sand 

(Unified Soil Classification ‘SW’), a friction angle of 38 degrees is selected for computing 

bearing capacity. 

From Table 5-1, the bearing capacity factors, Nγ and Nq, are 78.0 and 48.9, respectively, for a 

friction angle of 38 degrees. So the equation for bearing capacity is: 

B - 67 
ult f

f

ult

q 1438kPa 535B

0.5 (19.6 )(B )(78.0)(0.7)(1.0)(1.0)

q = 29.4 kPa (48.9)(1.0)(1.0)(1.0)(1.0)

3 m

kN

= +

+

Incorporating a factor of safety of 3.0: 

q 479 178B kPa

q (1438 535B kPa) 3.0

q q 3.0

all f

all f

all ult

= +

= + ÷

= ÷

Estimate Footing Settlement: 

First, estimate the settlement in the sand layers, 1a and 1b, assuming that settlement in the shale, 

Layer 2, will be negligible. Calculate stress increase at the midpoint of each soil layer using the 

2-on-1 stress distribution method for various footing widths – say, Bf = 3.0, 4.3, 5.5 and 6.7 m:

B /(B Z)

q

f f

V = +

∆σ (for strip footing) (Figure 5-12) 

Layer 1a with midpoint of layer @ Z = 1.5 m below base of footing: 

3.0 /(3.0 1.5) 0.67

q

V1a = + = ∆σ

Layer 1b with midpoint of layer @ Z = 3.75 m below base of footing: 

3.0 /(3.0 3.75) 0.44

q

V1b = + = ∆σ

Perform similar calculations for Bf = 3.0, 4.3, 5.5 and 6.7 m, then tabulate as shown in Table 

B4-2. 

TABLE B4-2: STRESS INCREASE WITH DEPTH 

AS FUNCTION OF FOOTING WIDTH 

Stress Increase, ∆σv

Soil Layer 

Depth 

Range (m) Bf = 3.0 m Bf = 4.3 m Bf = 5.5 m Bf = 6.7 m

1a 1.5 – 4.5 0.67q 0.74q 0.79q 0.82q 

1b 4.5 – 6.0 0.44q 0.53q 0.59q 0.64q 

B - 68 
Determine stress applied by footing to generate 25 mm of settlement for the same range of 

footing widths, Bf = 3.0, 4.3, 5.5 and 6.7 m, using the Hough method: 

General equation:

H H (1/C')log[( ' )/ ' ] o vo v vo ∆ = σ +∆σ σ (Eqn. 5-24)

Correct SPT blowcounts to account for overburden pressure, N′, for each layer, and enter Figure 

5-19 to obtain bearing capacity factor, C′: 

Layer 1a: 

Navg = 22 

N′/N = 1.47 (from Figure 5-18) 

N′ = 32 

C′ = 108 (from Figure 5-19 for well-graded sand and gravel) 

Layer 1b: 

Navg = 35 

N′/N = 1.0 (from Figure 5-18) 

N′ = 35 

C′ = 115 (from Figure 5-19 for well-graded sand and gravel) 

Calculate settlement in each layer and sum the settlements to obtain the total settlement under a 

range of applied stresses of q = 240, 290 and 335 kPa and a range of footing widths from 3.0 to 

6.7 m:

Layer 1a: 

H 0.0160m 16mm

H 3m(1/108)log[(58.8kPa 0.67(240 kPa))/ 58.8kPa)]

H H (1/C')log[( ' )/ ' ]

1a

1a

1a 1a vo v vo

∆ = =

∆ = +

∆ = σ +∆σ σ

Layer 1b: 

H 0.004m 4mm

H 1.5m(1/115)log[(95.6 kPa 0.44(240 kPa))/ 95.6 kPa)]

H H (1/C')log[( ' )/ ' ]

1b

1b

1b 1b vo v vo

∆ = =

∆ = +

∆ = σ +∆σ σ

∑ ∆Hi = 16mm + 4mm = 20mm

Repeat and tabulate for various footing widths and applied stresses (a spreadsheet or other 

computer tool can make these calculations rapidly): 

B - 69 
TABLE B4-3: SETTLEMENT AS A FUNCTION OF 

APPLIED STRESS AND FOOTING WIDTH 

Settlement (mm)

Applied Stress (kPa) Bf = 3.0 m Bf = 4.3 m Bf = 5.5 m Bf = 6.7 m

240 20 22 23 23

290 22 24 25 26

335 24 26 27 28

Check the estimated settlement in the shale, Layer 2, to verify that this settlement is negligible. 

For settlement analysis, the shale can be modeled as elastic half-space. From elastic theory: 

E IR

2

d V f v E

C B (1 )

α

∆σ − ν δ = (Eqn. 5-36) 

0.0231(RQD) 1.32 0.15 αE = − ≥ (Eqn. 5-37) 

From Table 5-12 for a rectangle with L/B ratio of 5, Cd = 1.83. For a shale with RQD = 80%, ν

= 0.14 and EIR = 9.8 x 106

 kPa, from Tables 5-13 and 5-14. For a conservative footing width of 

5.5 m and a bearing pressure of 290 kPa: 

B = Bf + Z− Df = 5.5m+ 6.0m−1.5m =10m

q(B /B) 290kPa(5.5m/10m) 159kPa ∆σV = f = =

0.0231(80) 1.32 0.53 αE = − =

0.0005m 0.5mm

(0.53)(9800000 kPa)

(1.83)(159 kPa)(10 m)(1 0.14 ) 2

v = = − δ =

This settlement is negligible. 

Compare the values in Table B4-3 to allowable bearing capacities at the same footing widths 

relative to shear failure. Recall that the water table correction factor was conservatively 

computed near the upper bound of footing widths at Bf = 6 m. This would be revisited only if 

bearing capacity failure is found to limit the allowable bearing capacity. 

For Bf = 3.0 m:

q 479 178(3.0m)kPa 1013kPa all = + = >> 335 kPa (with 24 mm settlement) 

B - 70 
For Bf = 4.3 m:

q 479 178(4.3m)kPa 1244kPa all = + = >> 290 kPa (with 24 mm settlement) 

For Bf = 5.5 m:

q 479 178(5.5m)kPa 1458kPa all = + = >> 290 kPa (with 25 mm settlement) 

For Bf = 6.7 m:

q 479 178(6.7m)kPa 1672kPa all = + = >> 240 kPa (with 23 mm settlement) 

Settlement will therefore limit the allowable bearing capacity for the design of this footing. 

Interpolating the values in Table B4-3, find ranges of footing widths that will limit settlement to 

25 mm or less at allowable bearing capacities of 240, 290 and 335 kPa: 

TABLE B4-4: SETTLEMENT-LIMITED 

ALLOWABLE BEARING CAPACITIES 

Allowable Bearing Capacity 

(kPa) 

Range of Footing Widths That Will 

Limit Settlement to ≤ 25 mm

335 ≤ 3.0 m

290 3.0 to 5.5 m 

240 5.5 to 6.7 m 

The geotechnical engineer should provide this table to the structural designer for sizing of the 

footing. 

Step 8 – Calculate sliding and passive soil resistance: 

The geotechnical engineer has recommended that the footing be cast against the firm, 

undisturbed soil of Unit 1a. The friction angle of 38 degrees selected in Step 7 will be used to 

compute sliding resistance. 

The general equation for sliding resistance is: 

FR = (W + Pv) tan δ (Eqn. 5-38)

The second term goes to zero since we are founding the footing on a cohesionless soil unit. For a 

concrete footing cast against the ground, δ = φ, so the ultimate sliding resistance is: 

F (W P )tan 38 0.78(W P ) R v = + v = + °

Since the sliding resistance will develop at strain levels much lower than those needed to develop 

passive pressures against the side of the footing, passive pressure will be ignored unless it is 

B - 71 
found that sliding resistance governs the design of the footing. The geotechnical engineer should 

provide this equation and the assumptions regarding use of passive pressures to the structural 

engineer for checking the footing’s resistance to sliding. 

Step 9 – Check global stability of the footing: 

The global stability of the abutment was checked using Bishop’s simplified method of slices 

using the slope stability computer program XSTABLTM. For this analysis, the actual footing was 

modeled as a very strong material, thus forcing the critical failure surface behind the heel of the 

footing (i.e., failure surfaces that passed through the footing were not permitted). The output is 

shown in Figure B4-4. 

The calculated factor of safety for the specified surface was 2.6, which is larger than 1.5. (OK) 

Step 10a – Size the footing: 

The footing should be designed based on three loading conditions: (1) Intermediate Construction 

Step 1, after construction and backfill of the abutment and before erection of the superstructure 

(Figure B4-5); (2) Intermediate Construction Step 2, after erection of the superstructure and 

before live loads are applied (Figure B4-6); and (3) Final Loading Conditions (Figure B4-7). 

Structural fill

(Well-graded silty

SAND & GRAVEL)

FS=2.6

Well-graded

SAND

SHALE

Live load surcharge

Figure B4-4: Global Stability Analysis Results 

B - 72 
H / 3

Active Earth

Pressure, pa

PA

Wf

Wtoe

Wh Wstem

Figure B4-5: Intermediate Construction Step 1 Loading Conditions 

Perform Steps 10 and 11 for the first intermediate construction step loading conditions: 

Try a 5.2-m footing width: 

Given that the superstructure will be erected before the girder seat is constructed, assume that the 

top of the backfill is at the base of the girder seat. The height of the girder seat is approximately 

1.8 m.

Calculate earth pressures and weights: 

2 PA = (1/ 2)Ka γ H (Eqn. 6-1)

K tan (45 '/ 2) 2

a = − φ (Eqn. 6-3) 

K tan (45 38/ 2) 0.24 2

a = − =

2 kN

3 m

kN PA = (1/ 2)(0.24)(19.6 )(8.5m −1.8m) =106

B - 73 
AASHTO recommends using a minimum Ka of 0.3. However, because this material will be a 

specified compacted select granular material, we will use the calculated Ka value of 0.24 for 

design. 

kN

3 m

kN Wstem = (1.0m)(8.5m −1.8m − 0.9m)(23.5 ) =136 assume 3 m

kN

γ concrete = 23.5

kN

3 m

kN Wf = (5.2m)(0.9m)(23.5 ) =110

kN

h 0.5m)(8.5m 1.8m 0.9m)(19.6 ) 338

3

2 W (5.2m 3 m

kN  − − − = 

 



 =

kN

toe 0.5m)(0.6m)(19.6 ) 14.5

3

1 W (5.2m 3 m

kN  − = 

 



 =

Calculate moment arms about toe:

armstem = 5.2m/ 3 =1.73m

armf = 5.2m/ 2 = 2.6m

armh = 0.5(5.2m +[(5.2m/ 3) + 0.5m] = 3.72m

armtoe = 0.5(5.2m/3− 0.5m) = 0.62m

arm (8.5m 1.8m)/ 3 2.23m PA = − =

Calculate eccentricity: 

e (B / 2) (M / PR ) = f − toe

kN kN kN kN kN

R

R v stem f h toe

P 136 110 338 14.5 599

P W P W W W W

= + + + =

= + = + + +

kN m kN m kN m toe

kN

kN kN kN kN

toe

toe stem stem f f h h toe toe A PA

M 1787 236 1551

(106 )(2.23m)

M (136 )(1.73m) (110 )(2.6m) (338 )(3.72m) (14.5 )(0.62m)

M W (arm ) W (arm ) W (arm ) W (arm ) P (arm )

− − − = − =

−

= + + +

= + + + −

e (5.2m / 2) (1551 / 599 ) 0.01m kN m kN = − = −

B - 74 
Calculate effective footing dimensions: 

B B 2e ′

f = f − (Eqn. 6-6)

B′

f = 5.2m − 2(0.01m) = 5.18m

Check allowable bearing stress for effective footing area: 

q P B 599 5.18 116kPa kN

applied = ÷ ′f = ÷ =

This is less than qall = 290 kPa for footings between 3.0 and 5.5 m wide, according to Table B4-

4, to limit settlement to less than 25 mm. (OK) 

Step 11a – Check overturning and sliding: 

Overturning will be acceptable if eccentricity in any direction is less than one-sixth the footing 

dimension in that direction. 

(5.2m) 0.87m e 0.01

6

1 B

6

1

f = = > = (OK) 

The loads resisting sliding are: 

kN W + Pv = PR = 599

The force, Fsliding, that tends to induce sliding consists only of the active earth pressure load, PA: 

106kN

Fsliding PA

=

=

The force, FR, available to resist sliding (from Step 8) is 

F 0.78(W P ) R = + v

The factor of safety FS against sliding is 

FSsliding = 1.5

F

F

sliding

R ≥ (Eqn. 5-40)

4.4

106kN

467kN

106kN

0.78(599kN)

=

=

=

B - 75 
The factor of safety should be > 1.5. (OK) 

Repeat Steps 10 and 11 for the second intermediate construction step loading conditions as 

shown in Figure B4-6: 

H / 3

Active Earth

Pressure, pa

PA

Wf

Wtoe

Wh

PV

V

Wstem

Figure B4-6: Intermediate Construction Step 2 Loading Conditions 

Step 10b – Size the footing: 

For a 5.2-m footing width: 

Calculate earth pressures and weights: 

2

A Ka H

2

1 P = γ (Eqn. 6-1)

K tan (45 '/ 2) 2

a = − φ (Eqn. 6-3)

B - 76 
K tan (45 38/ 2) 0.24 2

a = − =

2 kN

A (0.24)(19.6 )(8.5m) 170

2

1 P 3 m

kN = =

kN

3 m

kN Wstem = [(1.0m)(8.5m − 0.9m) − (0.5m)(1.8m)](23.5 ) =157 

kN

3 m

kN Wf = (5.2m)(0.9m)(23.5 ) =110

kN

h 0.5m)(8.5m 0.9m)(19.6 ) 442

3

2 W (5.2m 3 m

kN  − − = 

 



 =

kN

toe 0.5m)(0.6m)(19.6 ) 14.5

3

1 W (5.2m 3 m

kN  − = 

 



 =

Calculate moment arms about toe: 

1.77m

(8.5m 0.9m)(1m) (1.8m)(0.5m)

(5.2m/ 3)(8.5m 0.9m 1.8m)(1m) [(5.2m/ 3) 0.25m](1.8m)(0.5m) armstem

=

− −

− − + + =

armf = 5.2m/ 2 = 2.6m

armh = 0.5(5.2m +[(5.2m/ 3) + 0.5m] = 3.72m

armtoe = 0.5(5.2m/ 3 − 0.5m) = 0.62m

arm (5.2m/ 3 0.25m) 1.48m Pv = − =

arm 8.5m / 3 2.83m PA = =

armv = 8.5m −1.8m = 6.7m

Calculate eccentricity: 

e (B / 2) (M / PR ) = f − toe

kN kN kN kN kN kN

R

R v stem f h toe v

P 157 110 442 14.5 227 951

P W P W W W W P

= + + + + =

= + = + + + +

B - 77 
kN m kN m kN m toe

kN kN kN

kN kN kN kN

toe

A PA V

toe stem stem f f h h toe toe v Pv

M 2553 762 1791

(227 )(1.48m) (170 )(2.83m) (41.9 )(6.7m)

M (157 )(1.77m) (110 )(2.6m) (442 )(3.72m) (14.5 )(0.62m)

P (arm ) V(arm )

M W (arm ) W (arm ) W (arm ) W (arm ) P (arm )

− − − = − =

+ − −

= + + +

− −

= + + + +

e (5.2m / 2) (1791 / 951 ) 0.72m kN m kN = − = −

Calculate effective footing dimensions: 

B B 2e ′

f = f − (Eqn. 6-6)

B′

f = 5.2m − 2(0.72m) = 3.76m

Check allowable bearing stress for effective footing area: 

q P B 951 3.76m 253kPa kN

applied = ÷ ′f = ÷ =

This is less than qall = 290 kPa for footings between 3.0 and 5.5 m wide, according to 

Table B4-4, to limit settlement to less than 25 mm. (OK)

Step 11b – Check overturning and sliding: 

Overturning will be acceptable if eccentricity in any direction is less than 1/6 the footing 

dimension in that direction. 

(5.2m) 0.87m e 0.72

6

1 B

6

1

f = = > = (OK)

The loads resisting sliding are: 

kN W + Pv = PR = 951

The force, Fsliding, that tends to induce sliding consists of the active earth pressure load, PA and 

the shear load, V (Table B4-1): 

212kN

170kN 41.9kN

Fsliding PA V

=

= +

= +

B - 78 
The force, FR, available to resist sliding (from Step 8) is 

F 0.78(W P ) R = + v

The factor of safety FS against sliding is 

FSsliding = 1.5

F

F

sliding

R ≥ (Eqn. 5-40)

3.5

212kN / m

742kN / m

212kN / m

0.78(951kN / m)

=

=

=

The factor of safety should be > 1.5. (OK) 

Repeat Steps 10 and 11 for the final loading conditions: 

H / 3

H / 2

Active Earth

Pressure, pa

Traffic

Surcharge, pLS

PA

Wf

Wh

PV

V

Wstem

Figure B4-7: Final Loading Conditions 

B - 79 
Step 10c – Size the footing: 

For a 5.2-m footing width: 

From Step 10b: 

kN

LS

LS a LS abut

P (0.24)(19.6 )(0.6m)(8.5m) 24.0

P K H H

3 m

kN = =

= γ

arm 8.5m/ 2 4.25m PLS = =

Calculate eccentricity: 

e (B / 2) (M / PR ) = f − toe

kN kN kN kN kN kN kN

R

R v stem f h toe v

P 157 110 442 14.5 227 61.6 1013

P W P W W W W P

= + + + + + =

= + = + + + +

kN m kN m kN m

toe

kN kN kN kN kN

kN kN kN kN

toe

A P LS LS V

toe stem stem f f h h toe toe v P

M 2645 864 1781

(227 61.6 )(1.48m) (170 )(2.83m) (24.0 )(4.25m) (41.9 )(6.7m)

M (157 )(1.77m) (110 )(2.6m) (442 )(3.72m) (14.5 )(0.62m)

P (arm ) P (arm ) V(arm )

M W (arm ) W (arm ) W (arm ) W (arm ) P (arm )

A

v

− − − = − =

+ + − − −

= + + +

− − −

= + + + +

e (5.2m / 2) (1781 /1013 ) 0.84m kN m kN = − = −

Calculate effective footing dimensions: 

B B 2e ′

f = f − (Eqn. 6-6)

B′

f = 5.2m − 2(0.84m) = 3.52m

Check allowable bearing stress for effective footing area: 

q P B 1013 3.52m 288Pa kN

applied = ÷ ′f = ÷ =

This is less than qall = 290 kPa for footings between 3.0 and 5.5 m wide, according to Table B4-

4, to limit settlement to less than 25 mm. (OK)

B - 80 
Step 11c – Check overturning and sliding: 

Overturning will be acceptable if eccentricity in any direction is less than one-sixth the footing 

dimension in that direction. 

(5.2m) 0.87m e 0.84 OK

6

1 B

6

1

f = = > =

The loads resisting sliding are: 

kN W + Pv = PR = 1013

The force, Fsliding, that tends to induce sliding consists of the active earth pressure load, PA and 

the shear load, V (Table B3-2): 

212kN

170kN 41.9kN

Fsliding PA V

=

= +

= +

The force FR available to resist sliding (from Step 8) is 

F 0.78(W P ) R = + v

The factor of safety FS against sliding is 

FSsliding = 1.5

F

F

sliding

R ≥ (Eqn. 5-40)

3.7

212kN / m

790kN / m

212kN / m

0.78(1013kN / m)

=

=

=

This should be > 1.5. (OK) 

Step 12 – Complete structural design of footing: 

The structural engineer completes this step. 

B - 81 
(This page intentionally blank)

B - 82 
EXAMPLE 5: INTERIOR BRIDGE PIER ON IN-SITU ROCK

Given: 

• Subsurface profile at the interior bridge pier is shown in Figure B5-1. 

• There is no scour potential at this site. 

• Tolerable settlement is 38 mm (1.5 in). 

• The direction conventions are shown in Figure B5-2. 

Find: 

• Size the footing based on Service Load Design, Group VII (seismic) loads (allowable 

stress design method), considering both the settlement and bearing capacity. Check for 

overturning and sliding. 

Boring B-1

?

Unit 1:

Silty Sand

Unit 2:

Granite Bedrock

6

7

18

Column Diameter,

D = 0.6 m

SPT N-value

g =19.6 kN/m3

1.2 m

RQD =100%

Figure B5-1: Subsurface Profile 

B - 83 
Area of Column, Acol

Lf

Bf

Df

Z - Transverse

Direction of Bridge

Y - Longitudinal

Direction of Bridge

P

Mz - Moment About

Z-Axis due to

Longitudinal Loading

My - Moment About

Y-Axis due to

Transverse Loading

Soil

Footing

Figure B5-2: Sign Conventions and Loading Directions 

Solution:

The solution can be obtained by following the step-by-step process shown in Figure 6-1, Design 

Process Flow Chart. 

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulics and geotechnical engineers completed these steps. The required 

design information is provided in the problem given statement. 

Step 5 – Determine the loads applied to the footing: 

The structural engineer has provided the loads applied at the base of the column as shown in 

Table B5-1. 

B - 84 
TABLE B5-1: LOADS AT COLUMN BASE 

Load 

Axial, P 

(kN)

Shear, V 

(kN)

Moment, MZ

(kN-m)

Moment, MY

(kN-m)

Deadload (D) 6400 167 211 748 

Live load (L) 1670 42 409 196.5 

Impact (I) 315 8 77 37 

Wind on 

Structure (W) 

884 49 89 226

Wind on Live 

Load (WL) 

18 4 7 26

Earthquake (EQ) 1671 804 1675 5546 

Service Load Design Loads for Group VII: 

The general equation is (refer to Example B-1 for discussion of variables): 

(EQ) (ICE)]

(SF) (W) (WL) (LF) (R S T)

P D L I (CF) (E) B

EQ ICE

S W WL L R

I D L C E B

+ β + β

+ β + β + β + β + β + +

= γ [β ( ) + β ( + ) + β + β + β ( ) (AASHTO, 1996, 

Eqn. 3-10)

Because the coefficients, β , for live load (L), impact (I), wind (W) and wind on live load (WL) 

are all zero for Load Group VII, this reduces to the following: 

P = γ [β (D) + β (E) + β (B) + β (SF) + βEQ (EQ)] VII D E B S

Also, because there are no earth (E), buoyancy (B) or stream force (SF) loads in Table B5-1, the 

equation further reduces to: 

PVII = γ [βD (D) + βEQ (EQ)]

The axial load due to earthquake can act in either the positive or negative direction. For 

checking bearing stress, the load will be considered to act downward. For checking overturning 

(eccentricity), the load will be considered to act upward. So the factored loads are as follows: 

Axial loads for checking bearing stress: 

kN

kN kN

v D EQ

8071

1 0 1 0 6400 1.0 1671

P γ β D β (EQ) bearing

=

= . [ . ( ) + ( )]

= [ ( ) + ]

B - 85 
Axial loads for checking overturning: 

kN

kN kN

v D EQ

4729

1 0 1 0 6400 1.0 1671

P γ β D β (EQ) OT

=

= . [ . ( ) + (− )]

= [ ( ) + ]

Shear: 

kN

kN kN

D EQ

971

1 0 1 0 167 1.0 804

V γ β D β (EQ)

=

= . [ . ( ) + ( )]

= [ ( ) + ]

Moment about the Z-axis: 

kN-m

kN-m kN-m

Z D EQ

1886

1.0[1.0 (211 ) 1.0 (1675 )]

M γ β D β (EQ)

=

= +

= [ ( ) + ]

Moment about the Y-axis: 

kN-m

kN-m kN-m

Y D EQ

6294

1.0[1.0 (748 ) 1.0 (5546 )]

M γ β D β (EQ)

=

= +

= [ ( ) + ]

Step 6 – Conduct field exploration and laboratory testing: 

This step is complete, and the subsurface data are shown in Figure B5-1. The information 

indicates that the granite bedrock is hard, sound rock with discontinuities less than 2 mm wide, 

spaced more than 6 m apart. Granite RQD = 100 percent. 

Step 7 – Calculate allowable bearing capacity: 

Allowable bearing capacities for footings on competent rock can be determined using 

presumptive bearing pressures. From Table 5-7, the recommended allowable bearing capacity 

for sound granite is 7.7 MPa. According to AASHTO (1996) Table 3.22.1A for earthquake 

loadings, the allowable bearing capacity can be increased by one-third, resulting in an overstress 

allowable bearing capacity under earthquake loads of 10.2 MPa; therefore, use qall = 10,200 kPa. 

In general practice, settlement is not checked for Group VII loads because seismic loads are 

transient and temporary in nature. However, for completeness, we will check settlement in Step 

10 based on elastic theory for the actual footing dimensions and bearing stress. 

B - 86 
Step 8 – Calculate sliding and passive soil resistance: 

The geotechnical engineer has recommended that the footing be cast against unweathered granite 

rock in Unit 2. 

The general equation for sliding resistance is: 

FR = (W + Pv) tan δ (Eqn. 5-38)

The second term goes to zero since we are not founding the footing on a cohesive soil unit. For a 

concrete footing cast against the ground, assume an interface friction angle of δ = 35 degrees 

(Table 5-15, after NAVFAC (1986b)). In reality, this is a very conservative assumption for mass 

concrete poured on a rough, monolithic rock surface. However, sliding is not usually the 

controlling condition for interior bridge foundations, so we will use this conservative assumption 

unless it is found to control the design of the footing. The ultimate sliding resistance is therefore: 

F (W P )tan35 0.7(W P ) sliding v = + v = + °

Since the sliding resistance will develop at strain levels much lower than those needed to develop 

passive pressures against the side of the footing, passive pressure will be ignored unless it is 

found that sliding resistance governs the design of the footing. The geotechnical engineer should 

provide this equation and the assumptions regarding use of passive pressures to the structural 

engineer for checking the footing’s resistance to sliding. 

Step 9 – Check global stability of the footing: 

The geotechnical engineer has determined that since this is an interior pier with level ground 

conditions global stability is not a concern. 

Step 10 – Size the footing: 

The moments applied to the footing will create large eccentric loadings. First determine the 

minimum effective footing area necessary to provide sufficient bearing capacity. Then size the 

footing to account for the eccentric loading applied by the moment. 

The minimum effective footing area is calculated as follows using the maximum axial load: 

kN 2

v all

A 8071 10,200 kPa 0.79m

A P q bearing

′ = ÷ =

′ = ÷

Due to the large differences in applied moments, make the footing rectangular to optimize the 

size. The relative dimensions of the footing should be the same as the relative magnitudes of the 

moments. 

0.3(L ) 6294

1886 (L ) M

M B (L ) f f

Y

Z

f f ′ = ′ = ′ = ′

B - 87 
Determine the effective footing dimensions: 

B 0.3(L ) 0.3(1.62m) 0.49m

1.62m

0.3

0.79m

0.3

A L

A 0.3L L

A B L

f f

2

f

f f

f f

′ = ′ = =

= = ′ ′ =

′ = ′ × ′

′ = ′ × ′

The actual footing dimensions are influenced by the eccentricity. Calculate the eccentricity 

using the minimum axial load. 

e 1886 4729 0.399m

e M P

kN m kN

y

y Z vOT

= ÷ =

= ÷

−

e 6294 4729 1.33m

e M P

kN m k z

z Y vOT

= ÷ =

= ÷

−

Determine the footing dimensions necessary to resist the moments by rearranging Equations 6-6 

and 6-7: 

Lf = L′

f + 2ez =1.62m + 2(1.33m) = 4.28m

Bf = B′

f + 2ey = 0.49m + 2(0.399m) =1.29m

Perform a quick check to ensure that overturning is also acceptable. Overturning will be 

acceptable if eccentricity in any direction is less than one-fourth the footing dimension in that 

direction for footings on rock, as discussed in Section 6.4.1. 

(1.3m) 0.33m e 0.399m

4

1 B

4

1

f = = < y = (not OK)

(4.3m) 1.01m e 1.33m

4

1 L

4

1

f = = < z = (not OK)

Therefore, use a minimum footing width and length of 4 times ey and ez, respectively.

Bf = 4ey = 4(0.399m) =1.6m

Lf = 4ez = 4(1.33m) = 5.32m

Therefore, a footing with dimensions Lf = 5.4 m by Bf = 1.6 m will be stable and adequate for 

bearing capacity. Typically, the minimum footing width should be at least 3 column diameters 

B - 88 
[i.e., 3(0.6 m) = 1.8 m] to provide the required development length for the reinforcement of the 

column-footing connection. The final dimensions of the footing will be controlled by the 

structural design of the footing, but the footing dimension should be no smaller than Lf = 5.4 m

and Bf = 1.8 m.

Check the assumption regarding settlement: 

Using elastic theory: 

E IR

2

d V f v E

C B (1 )

α

∆σ − ν δ = (Eqn. 5-36) 

0.0231(RQD) 1.32 0.15 αE = − ≥ (Eqn. 5-37) 

From Table 5-12 for a rectangle with L/B ratio of 3, Cd = 1.78. For a granite with RQD = 100%, 

ν = 0.2 and EIR = 52 x 106

 kPa, from Tables 5-13 and 5-14. The applied stress will be equal to 

the allowable bearing stress since the footing bears directly on the rock. 

0.0231(100) 1.32 0.99 αE = − =

So: 

0.0003m 0.3mm

(0.99)(52000000kPa)

(1.78)(10200kPa)(1m)(1 0.20 ) 2

v = = − δ =

This settlement is negligible. 

The design is acceptable for bearing capacity and settlement considerations. 

Step 11 – Check overturning and sliding: 

Overturning was already checked during the sizing of the footing in Step 10. 

The footing will be stable against sliding if: 

1.5

F

F FS

sliding

R = ≥

From Step 8: 

F 0.7(W P ) R = + v

Calculate the weight of cover over the footing and the weight of the footing: 

The footing is bearing 1.2 m below grade and can be assumed to be 1 m thick. 

B - 89 
The area of the column is: 

2 2

col (0.6m) 0.28m

4

A = π =

The weight of the footing and the soil cover is then: 

2 kN

cover

kN

ftg

W [(0.2m)(1.8m)(5.4m) (0.2m)(0.28m )](19.6 ) 37.0

W (1.0m)(1.8m)(5.4m)(23.5 ) 228.4

3 m

kN

3 m

kN

= − =

= =

So, resistance to sliding is: 

F 0.7(W P ) R vOT = +

kN kN kN kN

R ftg cover v

0.7(228.4 37 4729 ) 3496

F 0.7(W W P ) OT

= + + =

= + +

The forces acting to cause the footing to slide are only due to the shear force, V, so 

Fsliding = V = 971kN

Then: 

3.6

971

3496

F

F FS

sliding

R = = =

This should be greater than about 1.0 to 1.15 for seismic loads. (OK) 

Step 12 – Complete structural design of footing 

The structural engineer completes this step. 

B - 90 
APPENDIX C 

LOAD AND RESISTANCE FACTOR DESIGN 

This appendix provides a discussion of the design of shallow foundations for bridges using Load 

and Resistance Factor Design (LRFD) methodology, and is based on the AASHTO LRFD 

Bridge Design Specifications (1998). Design examples B-1 and B-3 are re-worked using LRFD 

methods and principles. The purpose of these examples is to show that designs completed using 

LRFD methodology are not radically different from those completed by SLD. 

It should be noted that these examples are intended to convey one approach and process 

that can lead to a satisfactory design of bridge support on a shallow foundation. The 

examples should not be construed as representations of the only approach that can lead to a 

satisfactory design. Also note that the examples only check one or, at most, a few specific 

load cases. In practice, every complete design should consider all applicable load cases. 

EXAMPLE C-1: INTERIOR BRIDGE PIER ON A SPREAD FOOTING FOUNDED IN NATIVE SOIL

This example sizes the footing for an interior pier considering the LRFD Service I, Strength I 

and Extreme I limit states. The loads and ground conditions are the same as used in Example B1. 

EXAMPLE C-2: STUB SEAT-TYPE ABUTMENT FOOTING IN COMPACTED STRUCTURAL FILL

This example sizes an abutment footing considering the LRFD Service I and Strength I limit 

states. The loads and ground conditions are the same as used in Example B-3. 

Note: Unless cited with a specific reference (e.g., AASHTO, 1996), the equation numbers in the 

examples refer to those in the main body of this Circular. 

C.1 INTRODUCTION

This section compares and contrasts the differences and similarities of Load and Resistance 

Factor Design (LRFD) methodology with Service Load Design (SLD) and explains how the 

geotechnical engineer must modify the design recommendations to make them usable for the 

structural engineer. It is not intended to provide comprehensive coverage on the background and 

application of LRFD to bridge design. 

The reader should keep in mind that the fundamental theories and procedures used to calculate 

bearing capacity and settlement for shallow foundations are not different between LRFD and 

SLD. The differences come in the way the geotechnical engineer presents the design

C - 1 
recommendations and the way the structural engineer compares them to the factored load 

combinations. 

Recall that the “Standard Specifications” (AASHTO, 1996) were based on Service Level Design 

(SLD). In this design method, the stresses caused in members by design loads are compared to 

an allowable stress for the member. The allowable stress is determined by taking the nominal 

strength of the material (e.g., yield stress for steel) and applying a factor of safety. The 

allowable stress is also limited for serviceability considerations such as settlement. The 

following equation demonstrates the basic principle of the SLD method: 

∑ = FS

R Q n

i (Eqn. C-1)

where: Qi is an applied load or stress 

 Rn is the resistance (e.g., strength or yield stress) of the member or material 

FS is the applied factor of safety 

The allowable stress includes considerations for strength, fatigue, serviceability and settlement. 

The factors of safety used in the allowable stress method are derived from industry code writing 

groups such as ACI and AISC. Factors of safety for geotechnical engineering are derived from

industry practice and performance observation. Typically, the factors of safety for structural 

materials are in the range of 1.7, while the geotechnical factors of safety for foundations are from

2 to 3. These factors of safety are not derived based on probability theory. They are based on 

observation, full-scale tests, theory and judgment. Factors of safety adopted in the design codes 

are then agreed upon by committee consensus. 

The allowable stress method has some limitations in that the variability in the strengths of the 

materials and the variability in the different loads are all combined into a single safety factor. 

For example, truck live loads have a much greater variability than the dead load of the structure, 

but a single factor of safety implies that the variability of all loads are similar. 

The goal of LRFD methodology is to statistically account for the variability of the individual 

loads and resistances computed for design. Most of the AASHTO specification was calibrated 

based on the data available through NCHRP Project 12-33 (Nowak, 1992). Because not much 

data existed for calibrating the foundation (geotechnical) portion of the specification, some of the 

resistance factors for foundations and most of the resistance factors for walls were back-fit to 

match the existing SLD levels of reliability. The basic equation for the LRFD method is: 

∑ηiγiQi ≤ φRn = Rr (Eqn. C-2)

where: ηi is a factor that includes the effects of ductility, redundancy and importance 

γi is the load factor for a particular load 

 Qi is a service level load

φ is the resistance factor

 Rn is the nominal resistance 

 Rr is the factored resistance 

C - 2 
Note that the load and resistance factors in the AASHTO (1998) LRFD Specification were 

calibrated with ηi equal to 1.0. The use of ηi other than 1.0 will therefore result in factored loads 

that are not consistent with the calibration, and should be done with caution or in accordance 

with the policies and procedures of the owner agency. 

C.2 LIMIT STATES

A “limit state,” as defined by the AASHTO 1998 specification, is a condition beyond which the 

bridge or component ceases to satisfy the provisions for which it was designed. To meet the 

limit states applied to a design, the above equation must be satisfied for each limit state. The 

limit states are described in Table C-1. The descriptions of these limit states and the design 

conditions they consider can be compared with the load groups used in SLD (see Table 6-2 in the 

main text). 

TABLE C-1: LRFD LIMIT STATES 

Limit State Description

Strength The structure is checked for enough strength and stability to resist the 

loads imparted on it. 

Strength I Load combination with normal vehicles using the bridge without wind 

Strength II Load combination with permit vehicles using the bridge without wind 

Strength III Load combination with maximum winds and no vehicles 

Strength IV In this load case, large spans create large dead-to-live load effects. This 

load case need be used only where the dead-to-live load ratio is above 

about 7.0. 

Strength V Load combination with normal vehicles using the bridge with wind 

Extreme Event Load combinations relating to ice load, collision by vessels and vehicles, 

and to certain hydraulic events and earthquakes, whose recurrence 

interval exceeds the design life of the structure. The structure needs to 

survive these events. Some of these events need to be checked in the 

scoured condition. 

Extreme Event I Load combination for seismic loading 

Extreme Event II Load combination relating to ice load, collision by vessels and vehicles, 

and certain hydraulic events 

Service This is a check so that crack widths, deflections and other conditions do 

not jeopardize the life of the structure. 

Service I Load combination with normal vehicles and wind

Service II Load combination for slip-critical steel connections 

Service III Load combination to control cracks in prestressed concrete structures 

Fatigue Fatigue and fracture load combination using a special fatigue vehicle 

C - 3 
The AASHTO (1998) LRFD specification is very explicit regarding the different limit states that 

have to be considered in design. The LRFD strength limit states are similar to the AASHTO 

(1996) “Standard Specifications” for factored Load Groups I through VI, and the extreme limit 

states are similar to the factored Load Groups VII through IX. However, the “Standard 

Specifications” (AASHTO, 1996) do not include the explicit service (deformation) checks for all 

design elements that are included throughout the LRFD specifications (AASHTO, 1998). 

SLD

Deformations 

Capacity

LRFD

Service 

Strength 

C.3 LOADS AND LOAD COMBINATIONS

The AASHTO LRFD specifications prescribe the procedures used to compute loads and detail 

how to factor and combine the loads for comparing to the factored resistance. The load 

combinations and load factors per Table 3.4.1-1 (AASHTO, 1998) are shown in Table C-2. 

TABLE C-2: LRFD LOAD COMBINATIONS AND LOAD FACTORS (AASHTO, 1998) 

Load

Combination

DC 

DD 

DW

LL 

IM

CE 

WA WS WL FR TU 

CR 

SH 

TG SE Use One of These at a Time

Limit State 

EH 

EV 

ES 

BR 

PL 

LS 

EL 

EQ IC CT CV

Strength I 

(unless noted)

γP 1.75 1.00 - - 1.00 0.50/1.20 γTG γSE - - - -

Strength II γP 1.35 1.00 - - 1.00 0.50/1.20 γTG γSE - - - -

Strength III γP - 1.00 1.40 - 1.00 0.50/1.20 γTG γSE - - - -

Strength IV 

EH, EV, ES, DW 

DC only

γP 

1.50 

- 1.00 - - 1.00 0.50/1.20 - - - - - -

Strength V γP 1.35 1.00 0.40 1.0 1.00 0.50/1.20 γTG γSE - - - -

Extreme Event I γP γEQ 1.00 - - 1.00 - - - 1.00 - - -

Extreme Event II γP 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00

Service I 1.00 1.00 1.00 0.30 1.0 1.00 1.00/1.20 γTG γSE - - - -

Service II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - - -

Service III 1.00 0.80 1.00 - - 1.00 1.00/1.20 γTG γSE - - - -

Fatigue LL, IM

& CE only

- 0.75 - - - - - - - - - - -

C - 4 
For permanent loads: 

DD = downdrag 

DC = dead load of structural components and 

nonstructural attachments 

DW = dead load of wearing surfaces and utilities 

EH = horizontal earth pressure load 

EL = accumulated locked-in effects resulting from

the construction process (not usually

important for foundation design) 

ES = earth surcharge load 

EV = vertical pressure from dead load of earth fill 

For transient loads: 

BR = vehicular braking force 

CE = vehicular centrifugal force 

CR = creep 

CT = vehicular collision force (not usually 

important for foundation design) 

CV = vessel collision force (only important over 

navigable waterways) 

EQ = earthquake 

FR = friction (usually applies only with respect to

forces from bearing assemblies) 

IC = ice load 

IM = vehicular dynamic load allowance (This is

zero for the buried portions of structures. So

for most foundations, this is zero.) 

LL = vehicular live load

LS = live load surcharge 

PL = pedestrian live load 

SE = settlement

SH = shrinkage 

TG = temperature gradient (not usually a factor for 

foundations) 

TU = uniform temperature 

WA = water load and stream pressure 

WL = wind on live load

WS = wind load on structure 

Per the specification, the larger of the two load factor values for TU, SH and CR should be used 

for deformations, and the smaller values for all other effects. 

Table C-3 shows the load factors for permanent loads (γP) per Table 3.4.1-2 (AASHTO, 1998). 

TABLE C-3: LOAD FACTORS FOR PERMANENT LOADS 

Load Factor - γP

Type of Load Maximum Minimum

DC: Component and Attachment 1.25 0.90 

DD: Downdrag 1.80 0.45 

DW: Wearing Surfaces and Utilities 1.50 0.65 

EH: Horizontal Earth Pressure 

• Active 

• At-Rest 

1.50 

1.35 

0.90 

0.90 

EL: Locked-in Erection Stresses 1.00 1.00 

EV: Vertical Earth Pressure 

• Retaining Walls and Abutments 

• Rigid Buried Structure 

• Rigid Frames 

• Flexible Buried Structures other 

than Metal Box Culverts 

• Flexible Metal Box Culverts 

1.35 

1.30 

1.35 

1.95 

1.50 

1.00 

0.90 

0.90 

0.90 

0.90 

ES: Earth Surcharge 1.50 0.75 

C - 5 
γTG and γSE are to be determined on a project-by-project basis. Traditionally, they are usually 

taken as zero for the design of open girders and multiple steel box girders. However, the 

specification proposes to use 0.0 at the strength and extreme limit states, 1.0 at the service limit 

state without live load, and 0.5 at the service limit state when live load is considered. 

γEQ is a load factor applied to live load effects when considering earthquake loads and is 

supposed to be determined on a project specific basis. Traditionally this has been taken as zero. 

However, commentary to the specification suggests that 0.5 may be more appropriate when 

considering the possibility of a partial live load combined with seismic loads. 

For foundation design not all of the above load cases will apply. The following load cases will 

generally apply to the design of foundations: 

• Strength I 

• Strength II (although with the new live loading being applied, this load case may not be 

necessary) 

• Strength III 

• Strength IV (this will only control for long-span structures where creep, shrinkage and 

temperature effects become significant) 

• Strength V 

• Extreme I 

• Service I 

Note that maximum and minimum load factors can be applied for any given foundation. 

Usually, the maximum load factors will be used to find the maximum soil pressures, while the 

minimum load factors will be used to check stability of a foundation. 

Individual loads also have numerous different maximum and minimum effects. A good example 

of this is live load (LL). Live load effects on a foundation will include a loading case with 

maximum vertical load and two loading cases with maximum moments in the orthogonal 

directions. These all need to be checked when sizing and designing a shallow foundation. There 

are also configurations for which minimum live load effects can cause uplift at foundations. 

These also need to be included in the design of the foundation. 

C.3.1 Live Load Surcharge 

The live load surcharge under the LRFD methodology is also modeled as an equivalent soil 

surcharge behind the wall or abutment. However, the equivalent height of soil to use in

calculating the live load surcharge varies as a function of the height of the wall and can be 

computed according Table C-4. The lateral load due to live load surcharge is then calculated and 

applied according to Section 6.3. 

C - 6 
TABLE C-4: LIVE LOAD SURCHARGE 

Wall Height (m) heq (m) 

1.5 1.2

3.0 0.9

6 or higher 0.6 

C.4.1 Active Lateral Earth Pressures 

Under LRFD methodology, the application of active lateral earth pressures on abutments and 

retaining walls is at four-tenths the height of the abutment (0.4 x Habut) to account for backfill 

compaction effects. 

C.4 GEOTECHNICAL DESIGN

Computations of bearing capacity and settlement of shallow foundations under LRFD 

methodology use the same procedures and equations as used in SLD. These are described in 

Chapter 5. 

C.4.1 Service Limit State Bearing Stress 

The service limit state checks in LRFD ensure that deflections and movements under normal 

bridge loads are within tolerable limits. For shallow foundations, service limit state 

considerations will be controlled by settlement computations. The procedures in Section 5.3 

should be used to estimate settlement of footings as a function of the effective footing width, B′f. 

This information can be plotted as the nominal bearing resistance for the service limit state on a 

graph, or tabulated, for use by the structural engineer in sizing the footing. 

C.4.2 Strength and Extreme Limit State Bearing Resistance 

For shallow foundations, the nominal bearing resistance at the strength and extreme limit states 

is usually taken as the ultimate bearing capacity computed using the procedures in Section 5.2. It 

is generally convenient to plot or tabulate the computed values as a function of effective footing 

width, B′f. The geotechnical engineer should also recommend the resistance factor to apply to 

the nominal bearing resistance for performing the strength limit state checks. 

It is not unusual for geotechnical engineers to initially feel uncomfortable with the magnitude of

the ultimate bearing capacity that is computed. These bearing capacities are generally much 

larger than the allowable bearing capacities associated with Service Load Design. The 

geotechnical engineer should be aware that applying too much conservative judgment at this 

point could result in overconservative designs. Good communication with the structural 

engineer will help prevent designs being unnecessarily controlled by the strength limit state due 

to an overly conservative nominal bearing resistance. The geotechnical engineer should keep in 

mind that the load combinations in the strength limit state are multiplied by load factors that are 

larger than 1.0. 

C - 7 
Note that presumptive bearing capacities include combined consideration of settlement and 

bearing capacity. For normally consolidated soils (e.g., not IGMs or rock), use of presumptive 

values for strength and extreme limit state checks will frequently result in grossly overconservative designs, since they are generally controlled by settlement, which is a service limit 

state consideration. There is no rational approach to obtaining service and extreme limit state 

nominal bearing resistance. Increasing the presumptive values with arbitrary factors for use in 

strength and extreme limit state design checks is unwise and could be unsafe. 

C.4.3 Resistance Factors 

Resistance factors for the service and extreme limit states are nearly always taken as 1.0. 

Resistance factors for the strength limit state are less than 1.0 and are a function of the method 

used to compute the nominal (ultimate) bearing capacity. 

Table C-5 presents the strength limit state resistance factors recommended by AASHTO for 

shallow foundations. 

C.4.5 Global Stability 

When the location of a shallow foundation can contribute to the instability of a slope, such as an 

abutment constructed in an approach fill, the overall, or global, stability of the slope should be 

checked. It is important to note that limit equilibrium methods are by far the most expedient 

method for evaluating slope stability. An important prerequisite of limit equilibrium methods is 

that the solutions are based on failure, or ultimate, stresses. It is recommended that this be done 

at the Service I limit state using unfactored loads and resistances. That is, the loads applied by 

the footing that are acting to destabilize the slope should be unfactored working loads. Classic 

limit equilibrium methods, as described in Section 5.5, should be used to calculate the factor of 

safety of the slope. All slopes supporting footings should have a global factor of safety of at 

least 1.5. 

C.5 SHALLOW FOUNDATION DESIGN

The structural engineer will use the nominal bearing resistances provided by the geotechnical 

engineer to size the footing and perform all the necessary limit state checks.

C.5.1 Sizing the Footing 

Since settlement considerations frequently control the size and design of shallow foundations, it 

is generally expedient to size the footing at the service limit state and then check to see that the 

nominal bearing resistances are below the factored resistance at the strength and extreme limit 

state. 

C.5.2 Bearing Stresses 

Once an initial sizing of the footing is made, all applicable limit states should be checked to 

ensure that the applied bearing stress is below the factored resistance at that limit state. 

C - 8 
TABLE C-5: RESISTANCE FACTORS FOR STRENGTH LIMIT 

STATE FOR SHALLOW FOUNDATIONS (MODIFIED 

AFTER TABLE 10.5.5-1, AASHTO, 1998) 

Method/Soil/Condition 

Resistance 

Factor 

Sand 

- Semiempirical procedure using SPT data 

- Semiempirical procedure using CPT data 

- Rational Method: 

--using φf estimated from SPT data 

--using φf estimated from CPT data 

0.45 

0.55 

0.35 

0.45 

Clay 

- Semiempirical procedure using CPT Data 

- Rational Method: 

--using shear resistance measured in lab 

tests 

--using shear resistance measured in field 

vane tests 

--using shear resistance estimated from CPT 

data 

0.50 

0.60 

0.60 

0.50 

Rock 

Semiempirical procedure, Carter and 

Kulhawy (1988) 

0.60 

Bearing Capacity 

Plate Load Test 0.55 

Precast concrete placed on sand 

--using φf estimated from SPT data 

--using φf estimated from CPT data 

0.90 

0.90 

Sliding

Concrete cast-in-place on sand 

--using φf estimated from SPT data 

--using φf estimated from CPT data 

0.80 

0.80 

φT

Clay (where shear resistance is less than 0.5 

times normal pressure) 

--using shear resistance measured in lab 

tests 

--using shear resistance measured in field 

tests 

--using shear resistance estimated form CPT 

data 

Clay (where the resistance is greater than 0.5 

times normal pressure) 

Soil on soil 

0.85 

0.85 

0.80 

0.85 

1.0 

Passive Pressure φep

Passive earth pressure component of sliding 

resistance

0.50 

C - 9 
C.5.3 Eccentricity 

The check for overturning potential is also performed by determining the eccentricity of the 

resultant load under maximum overturning conditions. This usually occurs using the minimum 

load factors for resisting loads. The maximum eccentricity of the loads determined with the 

minimum load factors should be less than one-fourth of the corresponding footing dimension, B 

or L, on soil and less than three-eights of the corresponding footing dimension, B or L, on rock. 

Note that these permissible ranges differ from those used in Service Load Design. 

Eccentricity is computed using the procedure and equations in Section 6.4. 

C.5.4 Sliding 

Sliding of the footing is checked to make sure that lateral loads do not make the footing move. 

The lateral capacity of the footing due to lateral loads is: 

QR = φTQT+φepQep (Eqn. C-3, after AASHTO 1998 Eqn. 10.6.3.3-1) 

where: QR is the factored resistance 

φT is the resistance factor for shear resistance between the footing base and the soil 

 QT is the nominal shear resistance between soil and foundation 

φep is the resistance factor for passive soil resistance 

 Qep is the nominal passive resistance 

As in Service Load Design, it is customary to neglect or reduce the passive resistance for the 

same reasons discussed in Section 5.4. 

For cohesionless soils in which the concrete is cast against the soil: 

QT = Pv tan φ (Eqn. C-4, after AASHTO 1998 Eqn. 10.6.3.3-2) 

For cohesionless soils where the concrete is precast use: 

QT = Pv(0.8)tan φ (Eqn. C-5, after AASHTO 1998 Eqn. 10.6.3.3-2) 

where: QT = Nominal sliding resistance 

φ = Internal friction angle of soil 

 Pv = Applied vertical force 

Note that these equations inherently account for the lower sliding resistance resulting from

precast (formed) concrete. The associated resistance factors in Table C-5 must therefore be used 

with these equations. For a footing bearing directly on cohesive soils the sliding resistance is 

equal to the undrained shear strength of the soil or one-half the vertical stress, whichever is less. 

C.6 DESIGN PROCESS FLOW CHART

The LRFD design process for a bridge supported on shallow foundations includes the steps 

shown in Table C-6 and in the LRFD design process flow chart, Figure C-1.

C - 10 
TABLE C-6: STEPS IN LRFD DESIGN PROCESS FOR BRIDGE 

SUPPORTED ON SHALLOW FOUNDATIONS 

Step LRFD Design Activity Responsible Disciplines 

1. Develop preliminary bridge layout. The desired bridge type, 

size and location will be established. Span lengths and pier 

locations will be defined, considering geometrical and

environmental constraints. 

Structural, in coordination with 

general civil and environmental 

considerations and geotechnical 

for approach stability

2. Determine the shallow foundation feasibility based on review 

of existing geologic and subsurface data. Competent bearing 

material must be present within a reasonable distance from the 

ground surface. A preliminary assessment of approach 

embankment stability should be conducted to evaluate potential 

impacts to abutment locations and span lengths. (Section 4.1). 

Geotechnical, in coordination 

with structural, general and 

environmental 

3. A site reconnaissance with the structural and general civil 

engineer should be completed at this stage to evaluate 

constructability of foundation types (Section 4.2). 

Geotechnical, in coordination 

with structural, general and 

environmental 

4. Determine the depth of the footing so that it will not be 

susceptible to scour potential or frost (Section 6.2). 

Hydraulic, with geologic input 

from geotechnical 

5. Determine the loads applied to the footing (Section 6.3). Structural 

6. Determine the design soil properties from the subsurface 

exploration and laboratory testing program (Sections 4.3 and

4.4). 

Geotechnical 

7. Calculate the nominal bearing resistance, based on effective 

footing width, B′f (Section 5.2) at the strength and extreme

limit states. 

Geotechnical 

8. Calculate the nominal bearing resistance based on effective 

footing dimensions at the service limit state (Section 5.3). 

Geotechnical 

9. Calculate the sliding and passive soil resistance at the 

strength and extreme limit state (Section 5.4). 

Geotechnical 

10. When overall stability of the footing may govern the design 

(e.g., footings on or near slopes), perform a global stability 

analysis of the footing using service (unfactored) loads 

(Section 5.4). 

Geotechnical 

11. Size the footing dimensions at the service limit state (Section 

6.4.1). 

Structural 

12. Check the bearing pressure, maximum eccentricity and 

sliding at the strength limit state (Sections 6.4.3 and 6.4.4). 

Structural 

13. Check the bearing pressure, maximum eccentricity and 

sliding at the extreme limit state (Sections 6.4.3 and 6.4.4). 

Structural 

14. Complete the structural design of the footing using factored 

loads according to the concrete section of the specification 

(AASHTO, 1998). 

Structural 

C - 11 
1. Develop Preliminary Bridge

Layout (ST) 

2. Review existing geologic and

subsurface data (GT) 

3. Site Reconnaissance (GT)

4. Determine depth of footing for

scour and frost protection

(Hydraulic, GT) 

6. Subsurface exploration and 

laboratory testing (GT)

7. Calculate nominal bearing

resistance at the strength and 

extreme limit states (GT)

10. Check overall (global) stability

using service (unfactored) loads

(GT) 

13. Check the bearing pressure, 

eccentricity and sliding at the 

extreme limit state (ST) 

5. Determine loads applied to the

footing (ST)

11. Size the footing at the service 

limit state (ST)

14. Complete structural design of 

the footing using factored loads (ST)

8. Calculate nominal bearing

resistance at the service limit state 

(GT) 

9. Calculate sliding and passive soil

resistance at the strength and 

extreme limit states (GT)

12. Check the bearing pressure, 

eccentricity, and sliding at the

strength limit states (ST)

ST = Structural 

GT = Geotechnical

Figure C-1: LRFD Design Process Flow Chart – Bridge 

Shallow Foundations 

C - 12 
LRFD EXAMPLE C1: INTERIOR BRIDGE PIER ON SPREAD FOOTING

(Note: This example uses the same given geometry, loading and subsurface conditions as 

Example 1 in Appendix B, which was worked using Service Load Design criteria.) 

Given: 

• Subsurface profile at the interior bridge pier is shown in Figure C1-1. 

• There is no scour potential at this site. 

• Frost penetration depth is 0.6 m (2 ft). 

• Tolerable settlement is 38 mm (1.5 in). 

• The direction conventions are shown in Figure C1-2. 

Find: 

• Size the footing based on Load and Resistance Factor Design at the Service I, Strength I 

and Extreme I limit states (Table C-2). Assume factor, η, = 1.0. 

Boring B-1

?

Unit 1:

Lean Clay

Unit 2:

Silty Sand

Unit 3a:

Well graded Sand

Unit 3b:

Well graded Sand

(saturated)

Unit 4:

Clean, uniform Sand

6

7

18

20

22

42

38

47

33

45

42

37

49

Column Diameter,

D = 0.6 m

SPT N-value

g =19.6 kN/m3

2.3 m

2.1 m

4.7 m

3.0 m

3.0 m

g =19.6 kN/m3

g =19.6 kN/m3

g =19.6 kN/m3

Figure C1-1: Subsurface Profile 

C - 13 
Area of Column, Acol

Lf

Bf

Df

Z - Transverse

Direction of Bridge

Y - Longitudinal

Direction of Bridge

P

Mz - Moment About

Z-Axis due to

Longitudinal Loading

My - Moment About

Y-Axis due to

Transverse Loading

Soil

Footing

Figure C1-2: Sign Conventions and Loading Directions 

Solution:

The solution can be obtained by following the step-by-step process shown in Figure C-1, Design 

Process Flow Chart. 

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulics and geotechnical engineers completed these steps. The required 

design information is provided in the problem given statement. 

Step 5 – Determine the loads applied to the footing: 

The structural engineer has calculated and provided the values shown in Table C1-1. 

C - 14 
TABLE C1-1: LOADS AT COLUMN BASE 

Axial, P Shear, V Moment, MZ Moment, MY

Load kN kN kN-m kN-m

Dead load 

components (DW)

6400 167 211 748

Live load (LL) 1670 42 409 196.5 

Vehicular dynamic 

load allowance 

(IM) 

315 8 77 37

Wind on structure 

(WS) 

884 49 89 226

Wind on live load 

(WL) 

18 4 7 26

Earthquake (EQ) 1671 804 1675 5546 

Loads for Service I Limit State:

The general equation for this set of loads and limit state is: 

Q [ DC LL (IM) ∑ηiγi i = η γP ( ) + γLL ( ) + γIM (after Eqn. 3.4.1-1, 

+γWS(WS) + γWL (WL) + γEQ (EQ)] AASHTO, 1998) 

At the Service I limit state, all load factors are 1.0 except for wind on the structure (WS), which 

is taken as 0.3, and earthquake, which is an extreme limit state load and is not included in service 

limit state checks (Table 3.4.1-1, AASHTO, 1998). Also note that the AASHTO specifications 

provide for taking the vehicular dynamic load allowance (impact) as zero for design of 

substructures. We will also take the factor, η, to be 1.0. Assume the effect of footing self-weight 

is negligible. So the Service I limit state loads are as follows: 

 Axial loads: 

kN

kN kN kN kN kN kN

P LL IM WS WL EQ

P 8353

P 1.0[1.0 (6400 1.0 (1670 1.0(0 ) 0.3(884 ) 1.0 18 0(1671 )]

P [ DC LL (IM) (WS) WL (EQ)]

=

= ) + ) + + + ( ) +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

 Shear: 

kN

kN kN kN kN kN kN

P LL IM WS WL EQ

V 228

V 1.0[1.0 167 1.0 42 1.0(0 ) 0.3(49 ) 1.0 4 0(804 )]

V [ DC LL (IM) (WS) WL (EQ)]

=

= ( ) + ( ) + + + ( ) +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

C - 15 
Moment in the Z direction: 

kN m

Z

kN m kN m

kN m kN m kN m kN m

Z

Z P LL IM WS WL EQ

M 654

1.0 7 0(1675 )]

M 1.0[1.0 211 1.0 409 1.0(0 ) 0.3(89 )

M [ DC LL (IM) (WS) WL (EQ)]

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

Moment in the Y direction: 

kN m

Y

kN m kN m

kN m kN m kN m kN m

Y

Y P LL IM WS WL EQ

M 1038

1.0 26 0(5546 )]

M 1.0[1.0 748 1.0 196.5 1.0(0 ) 0.3(226 )

M [ DC LL (IM) (WS) WL (EQ)]

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

Loads for Strength I Limit State:

At the strength limit state, all load factors for the dead load components will be taken as 

minimums or maximums, depending on whether the load acts to stabilize or destabilize the 

footing. For this set of loads, the following load factors, γP, will be applied for the various design 

checks: 

For checking bearing resistance: γP = γmax = 1.25 

For checking sliding: γP = γmin = 0.9 

For checking eccentricity: γP = γmin = 0.9 

Note that the AASHTO specifications provide for taking the vehicular dynamic load allowance 

(impact) as zero for design of substructures. Also assume that the effect of footing self-weight is 

negligible. The minimum load cases will conservatively ignore live load. So the Strength I limit 

state loads are as follows: 

 Axial loads: 

kN

max

kN

kN kN kN kN kN

max

max P LL IM WS WL EQ

P 10923

0(1671 )]

P 1.0[1.25 6400 1.75 1670 1.0(0 ) 0(884 ) 0 18

P [ DC LL (IM) (WS) WL (EQ)]

=

+

= ( ) + ( ) + + + ( )

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

C - 16 
kN

min

kN kN kN kN kN kN

min

P 5760

P 1.0[0.9 6400 1.75 0 1.0(0 ) 0(884 ) 0 18 0(1671 )]

=

= ( ) + ( ) + + + ( ) +

 Shear: 

kN

max

kN kN kN kN kN kN

max

max P LL IM WS WL EQ

V 282

V 1.0[1.25 167 1.75 42 1.0(0 ) 0(49 ) 0 4 0(804 )]

V [ DC LL (IM) (WS) WL (EQ)]

=

= ( ) + ( ) + + + ( ) +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

kN

min

kN kN kN kN kN kN

min

V 150

V 1.0[0.9 167 1.75 0 1.0(0 ) 0(49 ) 0 4 0(804 )]

=

= ( ) + ( ) + + + ( ) +

Moment in the Z direction: 

kN m

Zmax

kN m kN m

kN m kN m kN m kN m

Zmax

Zmax P LL IM WS WL EQ

M 980

0 7 0(1675 )]

M 1.0[1.25 211 1.75 409 1.0(0 ) 0(89 )

M [ DC LL (IM) (WS) WL (EQ)]

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

kN m

Zmin

kN m kN m

kN m kN m kN m kN m

Zmin

M 190

0 7 0(1675 )]

M 1.0[0.9 (211 1.75 0 1.0(0 ) 0(89 )

−

− −

− − − −

=

+ ( ) +

= ) + ( ) + +

Moment in the Y direction: 

kN m

Y max

kN m kN m

kN m kN m kN m kN m

Y max

Y max P LL IM WS WL EQ

M 1279

0 26 0(5546 )]

M 1.0[1.25 748 1.75 196.5 1.0(0 ) 0(226 )

M [ DC LL (IM) (WS) WL (EQ)]

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

kN m

Y min

kN m kN m

kN m kN m kN m kN m

Y min

M 673

0 26 0(5546 )]

M 1.0[0.9 748 1.75 0 1.0(0 ) 0(226 )

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

C - 17 
Loads for Extreme I Limit State:

At the extreme limit state, all load factors for the dead load components will be taken as 

maximums, since the dynamic model used maximum factored loads to compute the earthquake 

forces. The designer should be consistent with respect to application of load factors. A separate 

check using earthquake loads computed using minimum load factors should also be performed. 

For the set of loads in this example, the following load factors, γP, will be applied for the various 

design checks: 

For checking bearing resistance: γP = γmax = 1.25 

For checking sliding: γP = γmax = 1.25 

For checking eccentricity: γP = γmax = 1.25 

The AASHTO commentary suggests that the load factor for live load at the extreme limit state, 

γEQ, should be taken as 0.5. This does not reflect current practice; therefore, γEQ for live load will 

be taken as zero. 

Note that the AASHTO specifications provide for taking the vehicular dynamic load allowance 

(impact) as zero for design of substructures. Also assume that the effect of footing self-weight is 

negligible. So the Extreme I limit state loads are as follows: 

Axial loads for evaluating bearing stress (seismic force acting downward): 

kN

E

kN kN kN kN kN kN

E

E P LL IM WS WL EQ

P 9671

P 1.0[1.25 6400 0 1670 1.0(0 ) 0(884 ) 0 18 1.0(1671 )]

P [ DC LL (IM) (WS) WL (EQ)]

max

max

max

=

= ( ) + ( ) + + + ( ) +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

Axial loads for evaluating eccentricity and sliding (seismic force acting upward): 

kN

E

kN kN kN kN kN kN

E

P 6329

P 1.0[1.25 6400 0 1670 1.0(0 ) 0(884 ) 0 18 1.0(1671 )]

min

min

=

= ( ) + ( ) + + + ( ) −

 Shear: 

kN

E

kN kN kN kN kN kN

E

E P LL IM WS WL EQ

V 1013

V 1.0[1.25 167 0 42 1.0(0 ) 0(49 ) 0 4 1.0(804 )]

V [ DC LL (IM) (WS) WL (EQ)]

=

= ( ) + ( ) + + + ( ) +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

 

C - 18 
Moment in the Z direction: 

kN m

Z

kN m kN m

kN m kN m kN m kN m

Z

Z P LL IM WS WL EQ

M 1939

0 7 1.0(1675 )]

M 1.0[1.25 211 0 409 1.0(0 ) 0(89 )

M [ DC LL (IM) (WS) WL (EQ)]

E

E

E

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

= η γ ( ) + γ ( ) + γ + γ + γ ( ) + γ

Moment in the Y direction: 

kN m

Y

kN m kN m

kN m kN m kN m kN m

Y

M 6481

0 26 1.0(5546 )]

M 1.0[1.25 748 0 196.5 1.0(0 ) 0(226 )

E

E

−

− −

− − − −

=

+ ( ) +

= ( ) + ( ) + +

Step 6 – Conduct Field Exploration and Laboratory Testing: 

This step is complete, and the subsurface data are shown in a drawing at the pier location, Figure 

C1-1. Because of the granular nature of the soils encountered in the boring, laboratory testing 

was limited to soil classifications and moisture content. The foundation design will be based 

largely on design parameters correlated to the soil classifications and the SPT N-values. 

Compute the initial vertical effective stresses at the midpoint of each layer: 

Layer 2: 

' 3.35m(19.6 ) 65.7 kPa 3 m

kN

2 σ vo = =

Layer 3a: 

' 6.75m(19.6 ) 132 kPa 3 m

kN

vo3a σ = =

Layer 3b: 

' 10.6 m(19.6 ) 1.5m(9.8 ) 193 kPa 3 m

kN

3 m

kN

vo3b σ = − =

Layer 4: 

' 13.6m(19.6 ) 4.5m(9.8 ) 222 kPa 3 m

kN

3 m

kN

vo4 σ = − =

The effective stress diagram for the profile at the pier location is plotted in Figure C1-3. 

C - 19 
2

4

6

8

10

12

14

16

0

Depth (

m)

0 100 200 300 400

u

Vertical Stress (kPa)

132

65.7

267

193 208

222

Unit 1

Unit 2

Unit 3a

Unit 4

Unit 3b

σVo σ'

Vo

Figure C1-3: Effective Stress Diagram 

Step 7 – Calculate nominal bearing resistance at the strength and extreme limit state: 

The general equation for bearing capacity is: 

qult cNcscbc qNqCW sqbqdq 0.5 Bf N CW s b

q γ γ γ γ = + + γ (Eqn. 5-14) 

The first term goes to zero since the foundation materials are granular and noncohesive, so the 

cohesion term, c, is zero. 

For the interior pier, we will assume that the footing is essentially rectangular (L/B < 5). Recall 

that the shape and inclination factors should not be applied together (see discussion in Section 

5.2). Since the effect of the shape factors is significant for rectangular footings, and considering 

the inclination resulting from the relatively small shear load component (V), we will only apply 

the shape factors as follows: 

f

f

L

B

sγ =1− 0.4 (Table 5-2)

sγ = 0.6 Assume the effect of eccentricity is small for now, so Bf ≅ Lf

A design friction angle associated with Layer 2 is needed to calculate sq. The geotechnical 

engineer has recommended that the footing be cast against the firm, undisturbed soil of Unit 2. 

Unit 2 is 2.1 m thick and overlies denser material at depth, so the properties of Unit 2 will govern 

C - 20 
the footing design. From Figure C1-1, the average uncorrected SPT N-value for this layer is 20. 

From Figure C1-3, the average vertical effective stress in Layer 2 is 65.7 kPa (about 1.4 ksf). 

Entering Figure 4-1 with a blowcount of 20 and a vertical effective stress of 1.4 ksf, a relative 

density, DR, of about 75 percent is read. Entering Figure 4-2 with this relative density for silty 

sand (Unified Soil Classification ‘SM’), a friction angle of 35 degrees is selected for computing 

bearing capacity. 

= + tanφ L

B

s 1

f

f

q (Table 5-2)

s 1.7

tan(35 ) 1

1

s 1

q

q

=

= + °

Since this footing will be level, there is no effect of inclination of the base, so: 

bγ = bq = 1.0 (Table 5-5)

Since the overburden materials above the footing are cohesive soils, the correction factor to 

account for shearing resistance of the material above the bearing elevation, dq, should be set 

equal to 1.0: 

dq = 1.0 (Table 5-4)

Calculate the effect of the footing embedment, q. Apply judgment; recognize that minimal 

excavation is necessary to remove all of the medium stiff, lean clay; thus avoiding any low 

strength or compressibility characteristics associated with this material. Therefore, select Df = 

2.3 m to bear below Unit 1: 

In this case, q is only a function of the depth of bearing. 

f vo q = σ' = γ'D where: 3 m

kN

γ'= γ bulk =19.6

q (19.6 )(2.3m) 3 m

kN =

q = 45.1 kPa

Check ground water effect: 

Depth of ground water table below the bearing depth: 

Df = Depth of footing = 2.3 m Assumes a 0.9-m-thick footing and 1.4-m

cover 

Dw = Depth of ground water below the ground surface (Df ) = 9.1 m

C - 21 
Conservatively estimate the footing width with an upper bound value of Bf = 6 m.

Calculate ground water correction factors, CWγ and CWq: 

1.0

1.5B D

D C 0.5 0.5

f f

W

W ≤















+ = +

γ (Eqn. 5-9) 

0.9

1.5(6) 2.3

9.1 CW 0.5 0.5 =















+ = +

γ 

1.0

D

D C 0.5 0.5

f

W

Wq

≤













 = + (Eqn. 5-10) 

2.0

2.3

6.8 C 0.5 0.5 Wq  =



 



 = + ; Use CWq = 1.0 

From Table 5-1, the bearing capacity factors, Nγ and Nq, are 48.0 and 33.3, respectively, for a 

friction angle of 35 degrees in Layer 2. 

So the equation for nominal bearing resistance at the strength and extreme limit states is: 

q 254B 2553kPa

q = 0.5 (19.6 )(B )(48.0)(0.9)(0.6)(1.0) + 45.1kPa (33.3)(1.0)(1.7)(1.0)(1.0)

q 0.5 B N C s b qN C s b d

ult f

ult f

ult f W q W q q q

3 m

kN

q

= +

= γ γ γ γ +

γ

Since the nominal bearing resistance was computed using a soil friction angle correlated to SPT 

N-values, a resistance factor of φ = 0.35 should be applied to resistances computed using this 

equation when checking strength limit states per Table C-5 (from AASHTO (1998) Table 

10.5.5-1). 

Step 8 – Calculate the nominal bearing resistance at the service limit state: 

Calculate stress increase at the midpoint of each soil layer using the 2-on-1 stress distribution 

method for various footing widths; say Bf = 3, 4.6 and 6.1 m, as a function of the stress applied 

by the footing, q: 

B L /(B Z)(L Z)

q

f f f f

V = ⋅ + +

∆σ (Figure 5-12)

2

f

2

f

V

f f

B /(B Z)

q

butB L ,so :

= +

∆σ

≅

 

C - 22 
Layer 2 with midpoint of layer @ Z = 1.05 m below base of footing: 

3 /(3 1.05) 0.55

q

V2 2 2 = + = ∆σ

Layer 3a with midpoint of layer @ Z = 4.45 m below base of footing: 

3 /(3 4.45) 0.16

q

V3a 2 2 = + = ∆σ

Layer 3b with midpoint of layer @ Z = 8.3 m below base of footing: 

3 /(3 8.3) 0.07

q

V3b 2 2 = + = ∆σ

Layer 4 with midpoint of layer @ Z = 11.3 m below base of footing: 

3 /(3 11.3) 0.04

q

V4 2 2 = + = ∆σ

Perform similar calculations for Bf = 4.6 m and Bf = 6.1 m and tabulate: 

TABLE C1-2: STRESS INCREASE WITH DEPTH AS FUNCTION 

OF FOOTING WIDTH AND STRESS APPLIED BY THE FOOTING (q) 

Stress Increase, ∆σv

Soil Layer 

Depth 

Range (m) Bf = 3 m Bf = 4.6 m Bf = 6.1 m

2 2.3 – 4.4 0.55q 0.66q 0.73q 

3a 4.4 – 9.1 0.16q 0.26q 0.33q 

3b 9.1 – 12.1 0.07q 0.13q 0.18q 

4 12.1 – 15.1 0.04q 0.08q 0.12q 

For these footing widths, determine the stress that would need to be applied by footing in order 

to generate 38 mm of settlement using the Hough method. These stresses will be plotted as a 

function of footing width to generate the nominal bearing resistance at the service limit state for 

a deformation (settlement) criterion of 38 mm. 

General equation:

H H(1/C')log[( ' )/ ' ] vo v vo∆ = σ +∆σ σ (Eqn. 5-24)

Correct SPT blowcounts to account for overburden pressure, N′, for each layer, and enter Figure 

5-19 to obtain bearing capacity factor, C′: 

C - 23 
Layer 2: 

Navg = 20 

N′/N = 1.2 (from Figure 5-18) 

N′ = 24 

C′ = 65 (from Figure 5-19 for silty Sand) 

Layer 3a: 

Navg = 40 

N′/N = 0.9 (from Figure 5-18) 

N′ = 36 

C′ = 120 (from Figure 5-19 for well-graded Sand) 

Layer 3b: 

Navg = 43 

N′/N = 0.7 (from Figure 5-18) 

N′ = 30 

C′ = 102 (from Figure 5-19 for well-graded Sand) 

Layer 4: 

Navg = 40 

N′/N = 0.66 (from Figure 5-18) 

N′ = 26 

C′ =110 (from Figure 5-19 for clean, uniform Sand) 

Calculate settlement in each layer and sum the settlements to find the applied stress required to 

yield a total settlement of 38 mm at a footing width of 3 m. This is an iterative process. 

Layer 2: 

H 0.025m 25mm

H 2.1m(1/ 65)log[(65.7 kPa 0.55(600kPa))/ 65.7 kPa)]

H H (1/C')log[( ' )/ ' ]

2

2

2 2 v v v o o

∆ = =

∆ = +

∆ = σ +∆σ σ

Layer 3a: 

H 0.009m 9mm

H 4.7m(1/120)log[(132kPa 0.16(600kPa))/132kPa)]

H H (1/C')log[( ' )/ ' ]

3a

3a

3a 3a v v v o o

∆ = =

∆ = +

∆ = σ +∆σ σ

Layer 3b: 

H 0.003m 3mm

H 3.0m(1/102)log[(193kPa 0.07(600kPa))/193kPa)]

H H (1/C')log[( ' )/ ' ]

3b

3b

3b 3 v v v o o

∆ = =

∆ = +

∆ = σ +∆σ σ

C - 24 
Layer 4: 

H 0.001m 1mm

H 3m(1/110)log[(222kPa 0.04(600kPa))/ 222kPa)]

H H (1/C')log[( ' )/ ' ]

4

4

4 4 v v v o o

∆ = =

∆ = +

∆ = σ +∆σ σ

∑∆Hi = 25mm + 9mm + 3mm +1mm = 38mm

Repeat this process for several footing widths over the expected range of footing dimensions – 

say, 1.5 to 7 m (a spreadsheet or computer tool can make these iterative calculations rapidly). 

Plot the results as a function of effective footing width as shown in Figure C1-4. 

LRFD Service Limit State Nominal Bearing Resistance vs.

Effective Footing Width for 38 mm of Settlement

0

200

400

600

800

1000

1200

024 6

Effective Footing Width, B' (m)

N

o

minal B

earing Stress (kP

a)

8

Figure C1-4: Nominal Bearing Resistance vs. Effective Footing 

Width at Service-I Limit State 

The geotechnical engineer should provide this chart and the equation for computing nominal 

resistances at the strength limit state, with the corresponding resistance factor (Step 7), to the 

structural designer for sizing of the footing. Note that the nominal resistance shown in Figure 

C1-4 is only applicable for service limit state design checks because it was developed with a 

serviceability limitation (e.g., maximum permissible settlement of 38 mm). The resistance factor 

associated with nominal resistances obtained from Figure C1-4 is 1.0. 

C - 25 
Step 9 – Calculate nominal sliding and passive soil resistance at the strength and extreme 

limit state:

The footing will bear in the Unit 2 soils. The friction angle of 35 degrees selected in Step 7 will 

be used to compute sliding resistance. 

The equation for calculating sliding resistance of concrete footings cast against the soil is: 

QT = Pv tanφ (Eqn. C-4)

The ultimate, or nominal, sliding resistance is: 

Q P tan35 0.7(P ) T v = v = °

The resistance factor associated with strength limit state checks is φ = 0.8 (Table 10.5.5-1, 

AASHTO, 1998). 

Since the sliding resistance will develop at strain levels much lower than that needed to develop 

passive pressures against the side of the footing, passive pressure will be ignored unless it is 

found that sliding resistance governs the design of the footing. The geotechnical engineer should 

provide this equation and the assumptions regarding use of passive pressures to the structural 

engineer for checking the footing’s sliding resistance at the strength and extreme limit states. 

Step 10 – Check global stability of the footing: 

The geotechnical engineer has determined that since this is an interior pier with level ground 

conditions, global stability is not a concern. 

Step 11 – Size the footing at the service limit state: 

First determine the eccentricity of the loads applied to the footing in both directions. This will be

used to find the effective footing dimensions, B′f and L′f. 

e 654 8353 0.078m

e M P

kN m kN

y

y Z

= ÷ =

= ÷

−

e 1038 8353 0.124m

e M P

kN m k z

z Y

= ÷ =

= ÷

−

Estimate trial footing dimensions. Try 5-m-by-5-m footing and calculate effective footing 

dimensions. The smaller will be used to enter Figure C1-4 to determine the nominal bearing 

resistance at the service limit state. 

B 5m 2(0.078m) 4.844m

B B 2e

f

f f y

′ = − =

′ = − (Eqn. 6-6)

C - 26 
L 5m 2(0.124m) 4.752m

L L 2e

f

f f z

′ = − =

′ = − (Eqn. 6-7)

Since L′f is less than B′f, use L′f = 4.752 m to check nominal bearing resistance at the service 

limit state. From Figure C1-4, the nominal bearing resistance for this effective footing 

dimension is about 390 kPa. Compute applied bearing stress over effective footing area, A′: 

2 A′ = B′

f ⋅L′f = (4.844m)(4.752m) = 23.0m

q P A 8353 23.0 m 363 kPa kN 2

applied = ÷ ′ = ÷ =

This is less than 390 kPa from Figure C1-4 for settlement less than 38 mm. Use 5-m-by-5-m

footing to perform the rest of the design checks. 

Check assumption to neglect self-weight of footing, assuming a footing thickness of 1 m:

kN / m kN / m kN

ftg

ftg ftg concrete soil

W (5m)(5m)(1m)(23.5 19.6 ) 98

W V ( )

3 3

= − =

= γ − γ

This should be less than about 1 to 2 percent of the axial load applied to the footing, or: 

kN kN 2%P = 0.02(8353 ) = 167 (OK) 

Step 12 – Check the bearing pressure, maximum eccentricity and sliding at the strength 

limit state:

Bearing Pressure:

Compute effective footing dimensions and bearing area using maximum load factors applied to 

the dead load components: 

e 980 10923 0.089m

e M P

kN m kN

y

y Zmax max

= ÷ =

= ÷

−

e 1279 10923 0.117m

e M P

kN m k z

z Y max max

= ÷ =

= ÷

−

B 5m 2(0.089m) 4.82m

B B 2e

f

f f y

′ = − =

′ = − (Eqn. 6-6)

L 5m 2(0.117m) 4.766m

L L 2e

f

f f z

′ = − =

′ = − (Eqn. 6-7)

C - 27 
2 A′ = B′

f ⋅L′f = (4.82m)(4.766m) = 23.0m

q P A 10923 23.0m 475 kPa kN 2

applied = ÷ ′ = ÷ =

Nominal bearing resistance at this effective footing width (use L′f as minimum value):

q 254(4.766m) 2553kPa 3764kPa

q 254B 2553kPa

ult

ult f

= + =

= ′ +

The factored resistance at the strength limit state is then: 

Q 1317kPa

Q (q ) 0.35(3764kPa)

R

R ult

=

= φ =

This is greater than qapplied = 475 kPa (OK) 

Maximum eccentricity:

The maximum eccentricity in any direction should be less than one-fourth of the actual footing 

dimension (AASHTO, 1998). The maximum eccentricity is evaluated using the minimum load 

factor combination:

e 190 5760 0.033m

e M P

kN m kN

y

y Zmin min

= ÷ =

= ÷

−

e 673 5760 0.117m

e M P

kN m k z

z Y min min

= ÷ =

= ÷

−

(5m) 1.25m

4

1 L

4

1 B

4

1

f = f = =

ey < ez <1.25m (OK) 

Sliding:

The factored horizontal shear force must be less than the factored nominal sliding resistance. 

This is evaluated using minimum load factors. The equation for QT is provided in Step 9. 

Passive resistance is ignored, so Qep is zero. 

QR = φTQT+φepQep (Eqn. C-3)

kN kN QR = 0.8(0.7(5760 )) = 3226

C - 28 
kN kN Vmin = 224 < 3226 (OK) 

Step 13 – Check the bearing pressure, maximum eccentricity and sliding at the extreme 

limit state:

Bearing Pressure:

Compute effective footing dimensions and bearing area using maximum load factors applied to 

the dead load components: 

e 1939 9671 0.200m

e M P

kN m kN

y

y ZE Emax

= ÷ =

= ÷

−

e 6481 9671 0.670m

e M P

kN m k z

z YE Emax

= ÷ =

= ÷

−

B 5m 2(0.200m) 4.60m

B B 2e

f

f f y

′ = − =

′ = − (Eqn. 6-6)

L 5m 2(0.670m) 3.66m

L L 2e

f

f f z

′ = − =

′ = − (Eqn. 6-7)

2 A′ = B′

f ⋅L′f = (4.60m)(3.66m) =16.8m

q P A 9671 16.8m 576 kPa kN 2

applied Emax = ÷ ′ = ÷ =

Nominal bearing resistance at this effective footing width (use either B′f or L′f as minimum 

value): 

q 254(3.66m) 2553kPa 3483kPa

q 254B 2553kPa

ult

ult f

= + =

= ′ +

The factored resistance at the extreme limit state is then: 

Q 3483kPa

Q (q ) 1.0(3483kPa)

R

R ult

=

= φ =

This is greater than qapplied = 576 kPa (OK) 

C - 29 
Maximum eccentricity:

The maximum eccentricity in any direction should be less than one-fourth of the actual footing 

dimension. The maximum eccentricity is evaluated using the minimum load factor combination: 

e 1939 6329 0.306m

e M P

kN m kN

y

y ZE Emin

= ÷ =

= ÷

−

e 6481 6329 1.024m

e M P

kN m k z

z YE Emin

= ÷ =

= ÷

−

(5m) 1.25m

4

1 L

4

1 B

4

1

f = f = =

ey < ez <1.25m (OK) 

Sliding:

The factored horizontal shear force must be less than the factored nominal sliding resistance. 

This is evaluated using minimum load factors: 

QR = φTQT+φepQep (Eqn. C-3)

kN kN QR =1.0(0.7(6329 )) = 4430

kN kN VE =1013 < 4430 (OK) 

Step 14 – Complete structural design of footing: 

The structural engineer completes this step. 

C - 30 
LRFD EXAMPLE 2: STUB SEAT-TYPE BRIDGE ABUTMENT ON STRUCTURAL FILL

(Note: This example uses the same given geometry, loading and subsurface conditions as 

Example 3 in Appendix B, which was solved using Service Load Design criteria.) 

Given: 

• A seat-type abutment on a spread footing is proposed for a bridge. 

• The footing length is L = 25.0 m (82 ft). 

• The foundation soils and abutment dimensions are shown in Figure C2-1. 

• Frost penetration depth is 0.6 m (2 ft). 

• Tolerable settlement is 38 mm (1.5 in). 

• Abutment loading symbols are shown in Figure C2-2. 

Find: 

• Size the footing based on Load and Resistance Factor Design at the Service I and 

Strength I states. Assume that the importance factor, η, = 1.0. Check for overturning and 

sliding. 

5.24 m

2

1

0.46 m 0.91 m

1.22 m

2.0m

0.51 m

B 1.5 B

Dense GRAVEL

Structural f ill (Well-graded silty SAND & GRAVEL)

SILT

Well-graded f ine to medium

siltySAND

N = Uncorrected SPT Blowcount

 Lay er 1

2.0m Existing Ground

Surf ace

Key

Boring B-1

SPT N-v alue

5

4

6

6

7

11

8

10

15

19

22

28

> 50

> 50

φ = 38 deg (assumed, N' = 32)

γ = 20.5 kN/m 3

γ = 17.3 kN/m 3

φ = friction angle

γ sat = 19.6kN/m 3

N' = Corrected SPT Blowcount

Lay er 2

2.57 m

Lay er 3

3.0m

Lay er 4

3.0m

Lay er 5

3.0m

Lay er 6

3.0m

N' =10

N' =10

N' =15

N' =20

Figure C2-1: Approach Embankment and Foundation

C - 31 
0.4 H

0.5 H

Active Earth

Pressure, pa

Traffic

Surcharge, pLS

PA

PLS

Stem and

Girder Seat

Footing

Habut

Bf

Tf

Dtoe

Tstem

Superstructure

Backfill

TGS

Toe

Mtoe

+

Figure C2-2: Direction and Load Conventions per LRFD Methodology 

C - 32 
Solution:

Steps 1 through 4 – Preliminary bridge layout, review of existing geologic and subsurface 

data, site reconnaissance, scour and frost potential: 

The structural, hydraulic and geotechnical engineers completed these steps. The required design 

information is provided in the problem-given statement. 

Step 5 – Determine the loads: 

Moments are taken about the toe of the footing. The sense of the moment is positive if 

counterclockwise (resisting moments) and negative if clockwise (overturning moments). 

Loads from the girders: 

The structural engineer has calculated and provided the values shown in Table C2-1. 

TABLE C2-1: LOADS FROM GIRDERS 

Load 

Axial, P 

(kN) 

Shear, V 

(kN) 

Moment, MZ

(kN•m)

Dead load of components, P (DC) 5233 - 7274 

Dead load of wearing surfaces, P (DW) 446 - 620 

Vehicular live load, P (LL) 1538 - 2138 

Shear loads from bearing pads, V 

(TU+CR+SH) 

- 1047 -3392

The shear load is computed as the force transmitted through the bearings due to rib shortening, 

shrinkage and temperature and is considered in both Strength I and Service I states. The 

moments calculated are due to the vertical and shear loads and are taken about the toe of the 

footing. 

Dead loads of the abutment components (per m of abutment wall):

Dead loads of the abutment components, and the moments caused by these loads about the toe of 

the footing, were calculated as part of Service Load Design Example 3 (Appendix B). These 

values are valid for the unfactored loads of the LRFD design and are listed in Table C2-2. 

Loads from approach fill: 

Loads from the approach fill, and the moments caused by these loads about the toe of the 

footing, were calculated as part of Service Load Design Example 3 (Appendix B). These values 

remain valid for the LRFD solution, with the exception of the horizontal earth pressure for the 

live load surcharge, PLS, and the moment due to active lateral earth pressure (Mtoe due to EH). 

Horizontal earth pressure from live load surcharge: 

C - 33 
From Table C-4, heq = 0.7 m for a wall height of 5.24 m, and: 

18.69kN / m

(0.26)(19.6kN / m )(0.70m)(5.24m)

P (K h )H

3

LS a eq abut

=

=

= γ

2.62m

(0.5)(5.24m)

armLS (0.5)Habut

=

=

=

48.97 kN m/ m

(18.69kN / m)(2.62m)

Mz PLS armLS

= − ⋅

= −

= − ⋅

Moment due to active lateral earth pressure: 

The code (AASHTO, 1998) specifies application of the resultant due to lateral earth 

pressure at 0.4 times the height of the abutment, Habut, due to the effects of backfill 

compaction. Therefore: 

146.6 kN m / m

0.4( 69.96kN / m)(5.24 m)

M 0.4(P )(H ) toe A abut

= − ⋅

= −

=

The loads and moments computed above are summarized in Table C2-2, along with values that 

are unchanged from Service Load Design Example 3 (Appendix B). 

TABLE C2-2: LOADS OF ABUTMENT COMPONENTS AND 

HORIZONTAL EARTH PRESSURES 

Load Vertical

(kN/m)

Horizontal 

(kN/m)

Moment, Mtoe

(kN•m/m)

Weight of stem, Wstem (DC) 57.29 - 84.79 

Weight of footing, Wf (DC) 10.81Bf - 5.41Bf

2

Weight of soil over toe, Wtoe (EV) - - - 

Weight of soil over heel, Wh (EV) (93.69)(Bf –1.73) - (93.69)(Bf –1.73) 

*(0.865+0.5Bf) 

Active earth pressure load, PA (EH) - 69.96 -146.6 

Horizontal earth load from live load 

surcharge, PLS (LS) 

- 18.69 -48.97

Note: Bf = width of footing in meters

C - 34 
Loads for Service I Limit State:

The general equation for this set of loads and limit states is: 

(LL LS (TU) (CR) (SH)]

Q [ DC DW EV EH

LL LL TU CR SH

P P P P i i i

+ γ ) + γ ( ) + γ + γ + γ

∑η γ = η γ ( ) + γ ( ) + γ ( ) + γ ( )

At the service limit state, all load factors except those for uniform temperature, creep and 

shrinkage are 1.0. At the service limit state, the load factors γTU, γCR and γSH for force effects are 

all equal to 1.0. 

Loads for Strength I Limit State:

At the strength limit state, all load factors for the dead load components will be taken as 

minimums or maximums, depending on whether the load acts to stabilize or destabilize the 

footing. At the strength limit state, the load factors γTU, γCR and γSH for force effects are all equal 

to 0.5. 

For this set of loads, the following load factors, γP, will be applied for the various design checks:

For checking bearing resistance: γP for DC = γmax = 1.25 

 γP for DW = γmax = 1.50 

 γP for EV = γmax = 1.35 

 γLL = 1.75 

 γLS = 1.75 

For checking sliding: γP for DC = γmin = 0.90 

 γP for DW = γmin = 0 

 γP for EV = γmin = 1.00 

 γP for EH = γmax = 1.50 

 γLL = 0 

 γLS = 1.75 

 γTU,CR,SH = γmax = 0.5 

For checking eccentricity: γP for DC = γmin = 0.90 

 γP for DW = γmin = 0 

 γP for EV = γmin = 1.00 

 γP for EH = γmax = 1.50 

 γLL = 0 

 γLS = 1.75 

 γTU,CR,SH = γmax = 0.5 

C - 35 
Step 6 – Conduct field exploration and laboratory testing: 

This step is complete and the subsurface data are shown in Figure C2-1. The initial vertical 

effective stresses are the same as computed for Service Load Design Example 3 (Appendix B) 

and are not repeated here. 

Step 7 – Calculate nominal bearing resistance at the strength limit state:

The ultimate bearing capacity was calculated for this abutment in Service Load Design Example 

3 (Appendix B). The ultimate bearing capacity for effective footing widths of 3, 4, and 5 m were 

1414 kPa, 869 kPa, and 605 kPa. Due to the eccentric load effects, it will be useful to plot a few 

more values for smaller effective footing widths. Using the same methods used in the Service 

Load Design Example 3 (Appendix B) for effective footing widths of 2 and 2.5 meters: 

12.5 5

2.0m

25.0m

B

L

f

f = = >

s =1 γ , bγ =1, and CW =1 γ

D /B 1.37m/ 2m 0.685 f f = =

By interpolation, for D /B 0.685, f f =

N 17 (0.685)(80 17) 60 γq = + − ≅

And: 

1230kPa

(0.5)(20.5kN / m )(2.0)(60)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

Similarly, for 2.5 m:

D /B 1.37m/ 2.5m 0.548 f f = =

By interpolation, for D /B 0.548, f f =

N 17 (0.548)(80 17) 51.5 γq = + − ≅

And: 

C - 36 
1320kPa

(0.5)(20.5kN /m )(2.5)(51.5)(1)(1)(1)

q 0.5 B N C s b

3

ult f q W

=

=

= γ γ γ γ γ

The results are plotted in Figure C2-3. As discussed in Example 3, the pressure bulb for 

effective footing widths greater than about 3 m begins to extend into the upper foundation silt 

layer, reducing the bearing capacity, and producing the shape of curve shown in Figure C2-3.

LRFD Strength Limit State Nominal Bearing 

Resistance vs. Effective Footing Width

500

700

900

1100

1300

1500

1.5 2.5 3.5 4.5 5.5

Effective Footing Width, B'

f

 (m)

Nominal Bearing Stress (k

Pa)

Figure C2-3: Nominal Stress versus Effective Footing 

Width at Strength 1 Limit State 

Since the nominal bearing resistance was computed using a soil friction angle correlated to SPT 

N-values, a resistance factor of φ = 0.35 should be applied to resistances from Figure C2-3 when 

checking strength limit states. 

Step 8 – Calculate the nominal bearing resistance at the service limit state: 

Settlement estimates were made for effective footing widths of 3 m, 4 m, and 5 m, as part of the 

Service Load Design Example 3. The estimated settlement for various combinations of footing 

widths and applied load were used to estimate the bearing pressure resulting in 38 mm of 

settlement for each footing width. The process was repeated for several footing widths over the 

expected range of footing dimensions (a spreadsheet or other computer tool can make these 

calculations rapidly). The results are plotted as a function of effective footing width, as shown in 

Figure C2-4. 

C - 37 
LRFD Service Limit State Nominal Bearing Resistance vs.

Effective Footing Width for 38 mm of Settlement

0

50

100

150

200

250

300

350

400

0123 45678

Effective Footing Width, B'f (m)

N

o

minal Bearing Stre

s

s (

k

P

a)

Figure C2-4: Nominal Bearing Resistance versus Effective Footing 

Width at Service-1 Limit State 

The geotechnical engineer should provide both charts of nominal resistances at the strength and 

service limit states (e.g. Figures C2-3 and C2-4) to the structural designer for sizing of the 

footing. 

Step 9 – Calculate nominal sliding and passive soil resistance at the strength limit state: 

The footing concrete will be poured on compacted structural fill. Thus the friction angle δ to be 

used in the sliding analysis of the footing will be: 

δ = φ′ = 38°

The equation for calculating sliding resistance of concrete footings cast against the soil is: 

QT = Pv tanφ

The ultimate, or nominal, sliding resistance is: 

Q 0.78(P ) T = v

The resistance factor associated with strength limit state checks is φ = 0.8 (Table 10.5.5-1, 

AASHTO, 1998). 

C - 38 
The passive resistance of the soil in front of the footing will be ignored. 

Step 10 – Check global stability of the footing: 

The geotechnical engineer has determined that the global stability is satisfactory (see Service 

Load Design Example 3). 

Step 11 – Size the footing at the service limit state under full loading: 

Select a trial footing width, say Bf = 3.2 m.

Check bearing resistance for Bf = 3.2 m:

Analyze for 1 m of abutment width. Under the service limit state the load factors are taken as 

1.0. 

From Table C2-1, the loads and moments due to the loads of the superstructure are:

288.7 kN/m

25m

(5233 446 1538)kN

DC DW LL

1.0[1.0 DC 1.0 DW 1.0 LL ]

P [ (DC DW LL LL ] v girders P P

=

+ + =

= + +

= ( ) + ( ) + ( )

= η γ ) + γ ( ) + γ ( )

265.6 kN m/m

25m

(7274 620 2138)kN m 1.0( 3392)kN m

1.0[1.0(DC) 1.0(DW) 1.0(LL) 1.0(TU CR SH)]

M [ (DC) (DW) LL (LL) 1.0(TU) 1.0(CR) 1.0(SH)] toe girders P P

= ⋅

+ + ⋅ + − ⋅ =

= + + + + +

= η γ + γ + γ + + +

From Table C2-2, the loads and moments due to abutment components are: 

229.6 kN /m

57.29 (10.81)(3.2) (93.69)(3.2 1.73)

57.29 10.81B (93.69)(B 1.73)

1.0[1.0 DC 1.0 EV ]

P [ (DC EV ]

f f

v abut P P

=

= + + −

= + + −

= ( ) + ( )

= η γ ) + γ ( )

C - 39 
M [ DC EV EH LS(LS)] toe abut P P P = η γ ( ) + γ ( ) + γ ( ) + γ

284.1kN m/ m

84.79 (5.41)(3.2) (93.69)(3.2 1.73)(0.865 (0.5)(3.2)) 146.6 48.97

84.79 5.41B (93.69)(B 1.73)(0.865 0.5B ) 146.6 48.97

1.0[1.0 DC 1.0 EV 1.0 EH 1.0 LS ]

2

f f

2

f

= ⋅

= + + − + − −

= + + − + − −

= ( ) + ( ) + ( ) + ( )

The total loads and moments are: 

518.3kN m/ m

288.7kN / m 229.6kN / m

Pv Pv girders Pv abut

= ⋅

= +

= +

549.7kN m/m

265.6kN m/m 284.1kN m/m

Mtoe Mtoe girders Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is: 

1.06m

(549.7 kN m/ m)/(518.3kN / m)

armR Mtoe / Pv

=

= ⋅

=

The eccentricity, ey, is 

0.54m

1.6m 1.06m

3.2m/ 2 1.06m

ey Bf / 2 armR

=

= −

= −

= −

Check bearing stress for effective footing area:

2.12m

3.2m (2)(0.54m)

B B 2e f f y

=

= −

′ = −

C - 40 
246.8kPa

(518.3kN / m)/(2.12m)

qapplied Pv /Bf

=

=

= ′

This is less than 295 kPa from Figure C2-4 for settlement less than 38 mm and B′f = 2.12 m. Use 

3.2 m footing to perform the rest of the design checks. 

Step 12a – Check the bearing pressure, maximum eccentricity and sliding at the Strength I 

limit state under full loading: 

Check maximum eccentricity for Bf = 3.2 m:

From Table C2-1, resisting loads are multiplied by minimum factors and driving loads are 

multiplied by maximum factors. At the strength limit state, the load factors γTU, γCR and γSH for 

force effects are all equal to 0.5. 

The loads and moments due to the superstructure are: 

188.4 kN/m

25m

0.9(5233) 0(446) 0(1538)kN

0.9(DC) 0(DW) 0(LL)

1.0[0.9 DC 0 DW 0(LL ]

P [ (DC) min (DW LL LL ] v girders P min P

=

+ + =

= + +

= ( ) + ( ) + )

= η γ + γ ) + γ ( )

194.0kN m/m

25m

0.9(7274) 0(620) 0(2138) 0.5( 3392)kN m

1.0[0.9(DC) 0(DW) 0(LL) 0.5(TU CR SH)]

M [ (DC) min (DW) LL (LL) 0.5(TU) 0.5(CR) 0.5(SH)] toe girders P min P

= ⋅

+ + + − ⋅ =

= + + + + +

= η γ + γ + γ + + +

From Table C2-2, the loads and moments due to abutment components are: 

220.4kN/m

0.9(57.29) 0.9(10.81)(3.2) (93.69)(3.2 1.73)

0.9(57.29 10.81B ) (93.69)(B 1.73)

1.0[0.9(DC) 1.00(EV)]

P [ (DC) (EV)]

f f

v abut P min P min

=

= + + −

= + + −

= +

= η γ + γ

C - 41 
160.1 kN m/ m

1.5(146.6) 1.75(48.97)

0.9(84.79) 0.9(5.41)(3.2) (93.69)(3.2 1.73)(0.865 (0.5)(3.2))

1.5(146.6) 1.75(48.97)

0.9(84.79 5.41B ) 1.0[(93.69)(B 1.73)(0.865 (0.5)(B ))]

1.0[0.9 DC 1.0 EV 1.5 EH 1.75 LS ]

M [ (DC) (EV) (EH) (LS)]

2

f f

2

f

toe abut P min P min P max LS

= ⋅

− −

= + + − +

− −

= + + − +

= ( ) + ( ) + ( ) + ( )

= η γ + γ + γ + γ

The total loads and moments are: 

408.8 kN m/ m

188.4 kN / m 220.4 kN / m

Pv Pv girders Pv abut

= ⋅

= +

= +

354.1 kN m/m

194.0 kN m/m 160.1 kN m/m

Mtoe Mtoe girders Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is: 

0.866 m

(354.1 kN m/ m)/(408.8 kN / m)

armR Mtoe / Pv

=

= ⋅

=

And the eccentricity, ey, is: 

0.73m

1.6m 0.866m

3.2m/ 2 0.866m

ey Bf / 2 armR

=

= −

= −

= −

The eccentricity should be in the middle half of the footing, or: 

Bf / 4 = (3.2m)/ 4 = 0.8m

Since ey < Bf / 4 , Bf = 3.2 m satisfies the eccentricity (overturning) requirement. 

C - 42 
Check bearing stress for effective footing area:

Compute B′f using maximum load factors. At the strength limit state, the load factors γTU, γCR

and γSH for force effects are all equal to 0.5. 

396.1 kN/m

25m

1.25(5233) 1.5(446) 1.75(1538)kN

1.0[1.25 DC 1.5 DW 1.75 LL ]

P [ DC max DW LL LL ] v girders P max P

=

+ + =

= ( ) + ( ) + ( )

= η γ ( ) + γ ( ) + γ ( )

482.7 kN m/ m

25m

1.25(7274) 1.5(620) 1.75(2138) 0.5( 3392)kN m

1.0[1.25(DC) 1.5(DW) 1.75(LL) 0.5(TU CR SH)]

M [ (DC) max (DW) LL (LL) 0.5(TU) 0.5(CR) 0.5(SH)] toe girders P max P

= ⋅

+ + + − ⋅ =

= + + + + +

= η γ + γ + γ + + +

300.8kN /m

1.25(57.29) 1.25(10.81)(3.2) 1.35(93.69)(3.2 1.73)

1.25(57.29 10.81B ) 1.35(93.69)(B 1.73)

1.0[1.25(DC) 1.35(EV)]

P [ (DC) (EV)]

f f

v abut P max P max

=

= + + −

= + + −

= +

= η γ + γ

328.0 kN m/ m

1.75(48.97)

1.35[(93.69)(3.2 1.73)(0.865 (0.5)(3.2))] 1.5(146.6)

1.25(84.79) 1.25(5.41)(3.2)

1.5(146.6) 1.75(48.97)

1.25(84.79 5.41B ) 1.35[(93.69)(B 1.73)(0.865 (0.5)(B ))]

1.0[1.25 DC 1.35 EV 1.5 EH 1.75 LS ]

M [ (DC) (EV) (EH) (LS)]

2

f f

2

f

toe abut P min P min P max LS

= ⋅

−

+ − + −

= +

− −

= + + − +

= ( ) + ( ) + ( ) + ( )

= η γ + γ + γ + γ

C - 43 
The total loads and moments are: 

696.9 kN m/ m

396.1 kN / m 300.8 kN / m

Pv Pv girders Pv abut

= ⋅

= +

= +

810.7 kN m/ m

482.7 kN m/ m 328.0 kN m/ m

Mtoe Mtoe girders Mtoe abut

= ⋅

= ⋅ + ⋅

= +

The arm of the resultant is: 

1.163 m

(810.7 kN m/ m)/(696.9 kN / m)

armR Mtoe / Pv

=

= ⋅

=

The eccentricity, ey, is: 

0.44m

1.6m 1.163m

3.2m/ 2 1.163m

ey Bf / 2 armR

=

= −

= −

= −

And the effective footing width is: 

2.32m

3.2m 0.88m

3.2m 2(0.44m)

B B 2e f f y

=

= −

= −

′ = −

So the applied stress is: 

300kPa

696.9kN / 2.32m

qapplied Pv /Bf

=

=

= ′

From Figure C2-3, the nominal bearing resistance at the strength limit state for an effective 

footing width of 2.32 m is about 1300 kPa. Applying a resistance factor of 0.35, the factored 

resistance at the strength limit state is: 

C - 44 
R ult applied Q = φ(q ) = 0.35(1300 kPa) = 455 kPa ≥ q (OK) 

Check sliding:

The factored horizontal shear force must be less than the factored nominal sliding resistance. 

This is evaluated using minimum load factors: 

QR = φTQT+φepQep (Eqn. C-3)

QR = 0.8(0.78(408.8kN)) = 255.1kN

Vmax =1.5(EH) +1.75(LS) + 0.5(TU + SH + CR)

=1.5(69.96) +1.75(18.69) + 0.5(1047 / 25) =158.6kN < 255.1kN (OK) 

Step 12b – Check the bearing pressure, maximum eccentricity and sliding at the Strength I limit 

state without the bridge loading from the girders: 

Check maximum eccentricity for Bf = 3.2 m:

From Table C2-2, considering that resisting loads are multiplied by minimum factors and driving 

loads are multiplied by maximum factors, the loads and moments due to abutment components 

are: 

220.4kN/m

0.9(57.29) 0.9(10.81)(3.2) (93.69)(3.2 1.73)

0.9(57.29 10.81B ) (93.69)(B 1.73)

1.0[0.9(DC) 1.00(EV)]

P [ (DC) (EV)]

f f

v abut P min Pmin

=

= + + −

= + + −

= +

= η γ + γ

M [ (DC) (EV) max (EH)] toe abut Pmin Pmin P = η γ + γ + γ

245.8 kN m/ m

0.9(84.79) 0.9(5.41)(3.2) (93.69)(3.2 1.73)(0.865 0.5(3.2)) 1.5(146.6)

0.9(84.79 5.41B ) 1.0(93.69)(B 1.73)(0.865 0.5B ) 1.5(146.6)

1.0[0.9(DC) 1.0(EV) 1.5(EH)]

2

f f

2

f

= ⋅

= + + − + −

= + + − + −

= + +

C - 45 
The arm of the resultant is: 

1.12m

(245.8kN m/ m)/(220.4kN / m)

armR Mtoe abut / Pv abut

=

= ⋅

=

The eccentricity, ey, is: 

0.48m

1.6m 1.12m

3.2m/ 2 1.12m

ey Bf / 2 armR

=

= −

= −

= −

The eccentricity should be in the middle half of the footing, or: 

Bf / 4 = (3.2m)/ 4 = 0.8m

Since ey < Bf / 4 , Bf = 3.2 m satisfies the eccentricity (overturning) requirement. 

Check bearing stress for effective footing area:

300.8kN /m

1.25(57.29) 1.25(10.81)(3.2) 1.35(93.69)(3.2 1.73)

1.25(57.29 10.81B ) 1.35(93.69)(B 1.73)

1.0[1.25(DC) 1.35(EV)]

P [ (DC) (EV)]

f f

v abut P max P max

=

= + + −

= + + −

= +

= η γ + γ

328.0 kN m/ m

1.5(146.6) 1.75(48.97)

1.25(84.79) 1.25(5.41)(3.2) 1.35[(93.69)(3.2 1.73)(0.865 (0.5)(3.2))]

1.5(146.6) 1.75(48.97)

1.25(84.79 5.41B ) 1.35[(93.69)(B 1.73)(0.865 (0.5)(B ))]

1.0[1.25 DC 1.35 EV 1.5 EH 1.75 LS ]

M [ (DC) (EV) (EH) (LS)]

2

f f

2

f

toe abut P min P min P max LS

= ⋅

− −

= + + − +

− −

= + + − +

= ( ) + ( ) + ( ) + ( )

= η γ + γ + γ + γ

C - 46 
The arm of the resultant is: 

1.090 m

(328.0 kN m/ m)/(300.8 kN / m)

armR Mtoe abut / Pv abut

=

= ⋅

=

The eccentricity, ey, is: 

0.51m

1.6m 1.09m

3.2m/ 2 1.09m

ey Bf / 2 armR

=

= −

= −

= −

And the effective footing width is: 

2.18m

3.2m 1.02m

3.2m 2(0.51m)

B B 2e f f y

=

= −

= −

′ = −

So the applied stress is: 

138kPa

300.8kN / 2.18m

qapplied Pv /Bf

=

=

= ′

From Figure C2-3, the nominal bearing resistance at the strength limit state for an effective 

footing width of 2.18 m is about 1260 kPa. Applying a resistance factor of 0.35, the factored 

resistance at the strength limit state is: 

R ult applied Q = φ(q ) = 0.35(1260 kPa) = 441 kPa ≥ q (OK) 

Check sliding:

The factored horizontal shear force must be less than the factored nominal sliding resistance. 

This is evaluated using minimum load factors: 

QR = φTQT + φepQep (Eqn. C-3)

C - 47 
QR = 0.8(0.78(220.4kN)) =137.5kN

Vmax =1.5(EH)

=1.5(69.96) =104.9kN <137.5kN (OK) 

Step 13 Check the bearing pressure, eccentricity and sliding at the extreme limit state: 

This step is skipped in this example. See Example C-1 for an extreme limit state design check. 

Step 14 Perform the structural design of the footing: 

The structural engineer performs this step. 

C - 48