Federal Guidelines 

for Dam Safety 

Earthquake Analyses and Design of Dams

May 2005
Cover Photo 

Lower Van Norman Dam showing concrete dropping into the lake. 

A considerable amount of water had been emptied from the lake 

at the time. San Fernando, California, Earthquake, February 1971. 

Photo Credit: USGS. 
i

PREFACE

In April 1977, President Carter issued a memorandum directing the review of federal dam safety 

activities by an ad hoc panel of recognized experts. In June 1979, the ad hoc interagency 

committee on dam safety (ICODS) issued its report, which contained the first guidelines for 

federal agency dam owners. The Federal Guidelines for Dam Safety (Guidelines) encourage 

strict safety standards in the practices and procedures employed by the federal agencies or 

required of dam owners regulated by the federal agencies. The Guidelines address management 

practices and procedures but do not attempt to establish technical standards. They provide the 

most complete and authoritative statement available of the desired management practices for 

promoting dam safety and the welfare of the public. 

To supplement the Guidelines, ICODS prepared and approved federal guidelines in the areas of 

emergency action planning; earthquake analysis and design of dams; selecting and 

accommodating inflow design floods for dams; and glossary of terms. These publications, based 

on the most current knowledge and experience available, provided authoritative statements on 

the state of the art for these important technical areas involving dam safety. In 1994, the ICODS 

Subcommittee to Review/Update Federal Guidelines began an update to these guidelines to meet 

the new dam safety challenges and to ensure consistency across agencies and users. In addition, 

the ICODS Subcommittee on Federal/Non-Federal Coordination developed a new guideline on 

hazard potential classification systems for dams. 

With the passage of the National Dam Safety Program Act of 1996, Public Law 104-303, ICODS 

and its Subcommittees were reorganized to reflect the objectives and requirements of Public Law 

104-303. In 1998, the newly convened Guidelines Development Subcommittee completed work 

on the update of the following guidelines: 

• Federal Guidelines for Dam Safety: Emergency Action Planning for Dam Owners, FEMA 

64, October 1998, reprinted April 2004 

• Federal Guidelines for Dam Safety: Selecting and Accommodating Inflow Design Floods 

for Dams, FEMA 94, October 1998, reprinted April 2004 

• Federal Guidelines for Dam Safety: Hazard Potential Classification Systems for Dams, 

FEMA 333, October 1998, reprinted April 2004 

With the amendment of the Act into the National Dam Safety and Security Act of 2002, Public 

Law 107-310, former ICODS Subcommittees were reorganized under the National Dam Safety 

Review Board (NDSRB). In 2004, two task groups finalized the ongoing work of the previous 

Subcommittee on the update of the following guidelines: 

• Federal Guidelines for Dam Safety: Glossary of Terms, FEMA 148, printed April 2004 

• Federal Guidelines for Dam Safety: Earthquake Analyses and Design of Dams, FEMA 65, 

printed May 2005 
ii

The publication of these guidelines marks the final step in the review and update process. In 

recognition of the continuing need to enhance dam safety through coordination and information 

exchange amongst federal and state agencies, the NDSRB will assume responsibility for 

maintaining these documents and establishing additional guidelines that will help achieve the 

objectives of the National Dam Safety Program. The NDSRB has established a task group and 

work is currently underway to prepare an update to the ground motions portion of this document 

with new research and methodologies. 

The members of all of the task groups and others responsible for the update of this guideline 

(listed on the next two pages) are to be commended for their diligent and highly professional 

efforts. 
 iii 

Earthquake Analyses and Design of Dams 

The original document was developed by the following task group and published in 

March 1985. 

Thomas J. Abraham Tennessee Valley Authority Chair 

Earl L. Spearman Tennessee Valley Authority Interim Chair 

James M. Fargo Federal Energy Regulatory Commission 

Lucian G. Guthrie U. S. Army Corps of Engineers 

Dinesh Gupta Nuclear Regulatory Commission 

R. Joe Hunt Tennessee Valley Authority 

Richard W. Kramer Dept of Interior, Bureau of Reclamation 

Tej Mathur Dept of Agriculture, Forest Service 

Peter V. Patterson Dept of Agriculture, Soil Conservation Service 

Owen Thompson Nuclear Regulatory Commission 

Jeff Kimball Nuclear Regulatory Commission 

Ralphine Major Tennessee Valley Authority 

H. Kenneth McLean Tennessee Valley Authority 

Several iterations of revisions were developed by the following task group between 

1993-1996. 

James R. Talbot Dept of Agriculture, Soil Conservation Service Initial Chair 

Charles Wagner Tennessee Valley Authority 

William H. Allerton Federal Energy Regulatory Commission Interim Chair 

Richard Davidson U. S. Army Corps of Engineers 

Lucian Guthrie U. S. Army Corps of Engineers Interim Chair 

J. Lawrence Von Thun Dept of Interior, Bureau of Reclamation 

A revised document was peer reviewed and edited by the following USCOLD 

members in 1998. 

Gilles J. Bureau Dames & Moore, Oakland, CA 

Joseph L. Ehasz Raytheon Engineers & Constructors, NY 

John A. Barneich Woodward-Clyde, Santa Ana, CA 

Donald H. Babbit Dept of Water Resources, Division of Dam Safety, CA 

This final document was reviewed, updated, and finalized by the following group in 

2003. 

William Allerton Federal Energy Regulatory Commission Chair 

Gus Tjoumas Federal Energy Regulatory Commission 

Eugene Zeizel Federal Emergency Management Agency 

Dave Gillette Dept of Interior, Bureau of Reclamation 

John Ake Dept of Interior, Bureau of Reclamation 

Dave Gutierrez Dept of Water Resources, Division of Dam Safety, CA 

George H. Gardner Dept of Labor, Mine Safety and Health Administration 

John W. Fredland Dept of Labor, Mine Safety and Health Administration 

David A. Pezza U. S. Army Corps of Engineers 
Anjana K. Chudgar U. S. Army Corps of Engineers 

Bill Irwin Dept of Agriculture, Natural Resource Conservation Service 

Steve Reinsch Dept of Agriculture, Natural Resource Conservation Service 

Tom Brown Dept of Agriculture, Natural Resource Conservation Service

 iv 
TABLE OF CONTENTS 

I. INTRODUCTION 1 

A. Purpose 1 

B. Scope 1 

C. References and Glossary 1 

D. Scope of Earthquake Design or Evaluation Required 1 

1. General 1 

2. Evaluations Using Risk-Based Analyses 2 

E. Overview of Design and Evaluation Processes 2 

1. Basic Seismic Studies 2 

2. Detailed Seismic Studies 2 

II. DESIGN AND SAFETY EVALUATION EARTHQUAKES 5 

A. Terminology 5 

1. Maximum Credible Earthquake (MCE) 5 

2. Maximum Design Earthquake (MDE) 

or Safety Evaluation Earthquake (SEE) 5 

3. Operating Basis Earthquake (OBE) 5 

B. Conducting Seismotectonic Studies 5 

1. Seismotectonic Studies 5 

2. Factors to Consider 6 

C. Selecting Maximum Design and Safety Evaluation Earthquakes 9 

1. General 9 

2. Determining Maximum Credible Earthquakes 10 

3. Selecting Maximum Design Earthquakes or 

Safety Evaluation Earthquakes 10 

4. Selecting Operating Basis Earthquakes 11 

III. CHARACTERIZING SITE GROUND MOTIONS 13

A. General 13 

B. Ground Motion Parameters 13 

1. General 13 

2. Attenuation Relationships 13 

3. Components 13 

4. Duration 13 

C. Elastic Response Spectra 14 

1. Standard or Normalized Response Spectra 14 

2. Response Spectra from U.S. Geological Survey 

Probabilistic Maps 14 

3. Site-Specific Response Spectra 14 

D. Time Histories of Ground Motions 15 

1. General 15 

2. Approaches to Developing Time Histories 16 

3. Application 17 

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IV. SEISMIC ANALYSES 19

A. Type and Extent of Analyses 19 

1. Consistency 19 

2. Progressive Analyses 19 

B. Concrete Dams 19 

1. Safety Concerns 19 

2. Defensive Design Measures 20 

3. Structural Modeling 20 

4. Methods of Analysis 21 

C. Embankment Dams 28 

1. Safety Concerns 28 

2. Defensive Design Measures 29 

3. Methods of Analysis 30 

V. EVALUATION OF STRUCTURAL ADEQUACY FOR 

EARTHQUAKE LOADING 37 

A. Performance Criteria 37 

B. Evaluating Analysis Results for Concrete Dams 37 

1. Dynamic Analyses 37 

2. Sliding and Overturning Stability 38 

C. Evaluating Analysis Results for Embankment Dams 38 

1. General 38 

2. Stability Analyses 38 

3. Deformation Analysis 39 

D. Past Experience of Dams Shaken by Earthquakes 39 

1. Concrete Dams 39 

2. Embankment Dams 42 

E. Evaluating Existing Dams 44 

F. Seismic Remediation of Earth Dams Subject to Liquefaction 44 

1. Excavate and Replace 44 

2. In-Site Densification or Cementing 44 

3. Berms/buttresses 45 

4. Drains 45 

5. Additional Freeboard 45 

Appendix A References A-1 

Appendix B-1 Bibliography B-1 

Appendix B-2 Bibliography B-3 

Appendix B-3 Bibliography B-7 

Appendix C Glossary C-1

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1

I. INTRODUCTION

A. Purpose 

These guidelines provide a basic framework for the earthquake design and evaluation of dams. 

The general philosophy and principles for each part of the framework are described in sufficient 

detail to achieve a reasonable degree of uniformity in application among the Federal agencies 

involved in the planning, design, construction, operation, maintenance, and regulation of dams. 

The guidelines deal only with the general concepts and leave the decisions on specific criteria 

and procedures for accomplishing this work up to each agency. Because these guidelines 

generally reflect current practices, it will be necessary to make periodic revisions, additions, and 

deletions to incorporate state-of-the-practice earthquake engineering. 

B. Scope 

This document contains general guidelines for specifying design earthquake loadings (for design 

or safety evaluation) and performing seismic analyses for the design of new dams (for evaluating 

the safety of existing dams or modifying existing dams). The guidelines are presented in four 

parts: 

• Selection of design or safety evaluation earthquakes 

• Characterization of ground motions 

• Seismic analyses of the dams and foundations 

• Evaluation of structural adequacy for earthquake loading 

C. References and Glossary 

Appendix A includes the references used in the text. Appendix B is a bibliography of selected 

publications (arranged by subject) that should assist in the use of earthquake engineering 

applications. Appendix C is the glossary of terms used in the guidelines. 

D. Scope of Earthquake Design or Evaluation Required 

1. General. The scope of the seismic hazard study at a site depends on the seismicity of a 

region or site-specific considerations, the types of structures involved, and the consequences of 

failure. The design and evaluation of dams for earthquake loading should be based on a 

comparable level of study and analysis for each phase of the study (seismotectonic, geological, 

site, geotechnical and structural investigations) and that level of study should reflect both the 

criticality of the structure and the complexity of the analysis procedures. Dams in zones of low 

seismicity generally should not require extensive seismic investigations and analyses unless 

failure would result in an unacceptable threat to life, property, or environment. Previous studies, 

as well as the performance of and experience with existing dams, suggest that concrete dams in 

regions of low to moderate seismicity, when adequately designed to withstand the appropriate 

static forces, have been competent to also withstand historic earthquakes. The same is true of 

well-constructed fill-type dams of conventional geometry placed on sound foundations, such as 

well-compacted rolled fill dams on rock foundations. Extensive investigations and design 
2

analysis may be required if the consequences of failure are unacceptable where the seismic 

hazard is high. 

2. Evaluations Using Risk-Based Analyses. Risk management and risk analysis can be used 

in making seismic evaluations of dams. These methods may be applied to help accomplish the 

following: prioritize safety evaluations when considering a large number of dams; evaluate the 

benefits of alternative remedial measures; select load levels; and evaluate the structural response. 

Risk management and risk analysis tools may also be applied as a framework for the overall 

seismic evaluation leading to the final decisions. The application of risk assessment procedures 

in a comprehensive and quantitative manner is used as a tool by various agencies to improve the 

quality and consistency of decisions on the seismic safety of structures. It is recognized that risk 

is considered in the application of engineering judgment even when more formal risk analysis 

procedures are not employed. 

E. Overview of Design and Evaluation Processes 

The first requirement of this process is to establish the design earthquakes and associated ground 

motions to be used by giving due consideration to the hazard potential classification of the 

structure (FEMA 1998), regional and site-specific seismic hazard considerations, and the 

designated operational function of the dam (Reclamation 1993, USACE 1995). The second 

requirement is to calculate the response of the structure, taking into account a realistic 

idealization of the structure and its foundation and the interaction of the structure with the 

foundation and the impounded water. The calculated response should be evaluated by 

recognizing the limitations, assumptions, and the uncertainties associated with the seismic input 

and the method of analysis. 

1. Basic Seismic Studies. These studies generally rely on existing seismological studies, 

available site data and information, and simplified methods of design or evaluation developed for 

similar projects or structures. In general, these studies use preliminary values of the ground 

motions obtained from existing studies or published seismic ground motion maps, a simplified 

structural analysis, and a simplified assessment of soil liquefaction and deformation to determine 

if seismic loadings control the design and to set the scope of any proposed site-specific studies. 

Basic studies are useful for preliminary evaluation and screening investigations in all seismic 

zones, and may be satisfactory for final design or evaluation for dams in zones of low seismicity 

and for dams with low consequences of failure. Detailed studies may be warranted if the seismic 

loading condition is the critical loading condition for the structure or if the failure consequences 

are significant. 

2. Detailed Seismic Studies. These studies involve the use of site-specific studies in 

evaluating the earthquake hazard and more refined dynamic analyses for determining the 

response of project features to seismic loading. Geologic studies describe the seismotectonic 

province, characterize the site, and investigate all faults that may be the source of significant 

ground shaking at the site. Extensive field exploration and testing programs are usually required. 

Seismologic investigations describe the earthquake history, earthquake recurrence relationship, 

and the strong motion records to be used in design or evaluation. Special emphasis should be 

placed on identifying all geological, seismological, and geotechnical parameters necessary to 
3

encompass the design and response of foundations and structures. Structural investigations 

should accurately account for all relevant factors that affect the seismic hazard at the specific site 

and the actual dynamic performance of the structure, including damping and nonlinear behavior 

of the structural systems. Geotechnical investigations should determine (a) the types and spatial 

distribution of foundation and embankment materials and the engineering properties of soil and 

rock; (b) the propagation of the ground motion through the foundation and embankment; 

liquefaction potential of the foundation and embankment soils; stability of natural and artificial 

slopes; and estimates of deformations, as well as the potential for piping due to deformation 

cracking. The final results of these studies are used as a basis for making design or evaluation 

decisions and for designing any remedial measures. These more complex studies should be 

conducted for projects having a high- or significant-hazard potential classification (FEMA 1998), 

projects which are located in zones of high seismicity, and for those projects in zones of 

moderate and low seismicity for which earthquake loadings could control the design. 
5

II. DESIGN AND SAFETY EVALUATION EARTHQUAKES

A. Terminology 

The earthquake or earthquakes used for the design or safety evaluation analysis of a dam have 

been specified by a variety of terms such as the maximum credible earthquake (MCE), the 

maximum design earthquake (MDE), or the Safety Evaluation Earthquake (SEE). An operating 

basis earthquake (OBE) is often used in addition to the MCE, MDE, or SEE. 

1. Maximum Credible Earthquake (MCE). The MCE is the largest earthquake magnitude 

that could occur along a recognized fault or within a particular seismotectonic province or source 

area under the current tectonic framework. The loading resulting from the MCE can and often is 

exceeded for Probabilistic Methods for high return period faults close in, such as the San 

Andreas Fault in California. 

2. Maximum Design Earthquake (MDE) or Safety Evaluation Earthquake (SEE). This is 

the earthquake that produces the maximum level of ground motion for which a structure is to be 

designed or evaluated. The MDE or SEE may be set equal to the MCE or to a design earthquake 

less than the MCE, depending on the circumstances. Factors to consider in establishing the size 

of MDE or SEE are the hazard potential classification of the dam (FEMA 1998), criticality of the 

project function (water supply, recreation, flood control, etc.), and the turnaround time to restore 

the facility to operability. Guidance on selecting the MDE and SEE is contained in paragraph 

C.3. In general, the associated performance requirement for the MDE or SEE is that the project 

perform without catastrophic failure, such as uncontrolled release of a reservoir, although 

significant damage or economic loss may be tolerated. If the dam contains a critical water 

supply reservoir, the expected damage should be limited to allow the project to be restored to 

operation in an acceptable time frame. 

3. Operating Basis Earthquake (OBE). The OBE is an earthquake that produces ground 

motions at the site that can reasonably be expected to occur within the service life of the project. 

The associated performance requirement is that the project function with little or no damage, and 

without interruption of function. The purpose of the OBE is to protect against economic losses 

from damage or loss of service. Therefore, the return period for the OBE may be based on 

economic considerations. 

B. Conducting Seismotectonic Studies 

1. Seismotectonic Studies. A seismotectonic study evaluates the geologic and seismologic 

history for the site. It defines the earthquake source or sources, determines the maximum 

earthquake potential for each source, develops magnitude-recurrence relationships, and provides 

information for use in the seismic attenuation studies. A seismotectonic study includes the 

identification and characterization of faults and other geologic structures that may be the sources 

of the earthquakes that could affect the site. This effort typically starts with literature searches in 

the fields of tectonics, seismology, and geology, and may include analyses of remote sensing 

imagery, geophysical data, and field mapping and exploration programs to verify and further 
6

evaluate documented or suspected tectonically active structures. Activities in seismotectonic 

studies typically include the following: 

• Documenting and evaluating the type, location, areal extent, displacement, and age of 

displacement of faults in the area of interest. Evaluating the age of Quaternary surfaces 

and deposits may also be required in areas where active, concealed faults may be present. 

• Characterizing located faults by sense of movement, degree and age of activity, 

recurrence, and slip rate (Page 1997). Potential for surface faulting in the immediate 

vicinity of the dam should also be addressed and may require detailed evaluation. 

• Characterizing other seismotectonic structures that are not correlative with surface 

features using geophysical techniques, regional geologic data, and historical seismicity 

characteristics. 

• Analyzing recent earthquakes or data from micro-earthquake monitoring to gain 

information on current stress orientations. 

• Establishing relationships between identified faults and other seismotectonic features and 

the historical seismicity by (1) integrating the data for identified faults and other 

structures with the seismicity data to develop event/source correlations; and (2) 

developing and evaluating conceptual models to explain significant earthquake events 

that do not correlate with identified faults or other seismic sources or geologic structures. 

• Establishing earthquake magnitude and distance pairs that would be expected to produce 

the largest ground motions at the site. 

• Developing magnitude-recurrence relationships. 

2. Factors to Consider. The factors enumerated below, ranging from regional to site-specific, 

should be considered in conducting a seismotectonic study. Bureau of Reclamation 

(Reclamation 1993), U.S. Committee on Large Dams (USCOLD 1999), and U.S. Geological 

Survey (Hays 1980) are recommended as source documents for additional information on this 

subject. Locating the project area in published information of source zones and seismic hazard 

areas (FEMA 1997) may indicate the level of anticipated seismicity as well as provide a starting 

point for a more comprehensive evaluation of seismic activity. 

a. Regional Tectonic Setting. The regional geology and late Cenozoic tectonic history study 

area should cover, at a minimum, a 100 km radius around the site, but may be extended to 

include any major fault or structure that could affect the ground motions at the site. This study 

should include such items as the following: 

• Identification of the physiographic and seismotectonic province(s) relevant to the project. 
7

• Geologic history of the project area. 

• Description of the regional geologic formations, rock types, and soil deposits to evaluate 

seismic energy transmission, effects, and duration of ground motions. 

• Location of major regional geological structural features, including folds and fracture or 

joint patterns. 

• Interpretation of the regional tectonic mechanism(s) and associated type(s) of faulting. 

• Location and description of faults and shear zones and assessment of the capability of 

faults to generate earthquakes or to be displaced by earthquakes. 

• Estimation of the relative degrees of fault activity for each of the faults of concern to the 

study area. 

b. Historic Seismicity. Compilation of historical earthquake data helps to identify the 

seismicity patterns of an area and provides a basis for estimating a lower bound of the severity of 

possible future earthquake motion at the site considered. The lack of historic earthquakes, 

however, does not necessarily imply that the area considered is aseismic. Historical 

seismological information exists primarily within governmental and academic references and the 

media record. The National Earthquake Information Center of the U.S. Geological Survey, 

California Division of Mines & Geology, and the Engineering Research and Development 

Center of the U.S. Army Corps of Engineers compile source and magnitude information for 

earthquake events. The collection and evaluation of historic seismicity data involves the 

following activities: 

• Defining the limits of the historical data search area (considering boundaries of 

seismotectonic sources and provinces with potential significance to the site). 

• Conducting a search of the historic seismological records to determine the location, date, 

and characteristics (e.g., earthquake source parameters and wave propagation effects) of 

seismic events within the area of interest. The completeness of the historic record, the 

location accuracy, and the independence of events are considered in a thorough 

evaluation. 

• Developing frequency, magnitude, and recurrence relationships considering the 

relationships between regional province-wide recurrence and recurrence for individual 

faults or sources. A probabilistic estimate of the peak acceleration and, if required, the 

peak velocity ground motion and/or spectral accelerations expected to occur at the site 

within a given time period may be based on the historic record of seismicity and 

appropriate attenuation relationships. 
8

• Displaying the seismic history information using tabulations, graphs, and maps. 

Historical records of any surface effects of past earthquake events are included in the 

Seismotectonic study. 

c. Local or Site Geology. Site-specific geologic information is required to determine the 

potential for surface rupture and to evaluate local site response effects on earthquake ground 

motions. This information may be obtained through the evaluation of published geologic 

reports, field observations, and detailed site-specific investigations that may include geologic 

mapping, trenching, shear wave velocity measurements, drilling, material sampling, and 

laboratory testing. The site geology investigation could cover the following items: 

• The geotechnical character, depositional history, orientation, lateral extent, and thickness 

of soil units beneath the site and on adjacent slopes. 

• The character, lateral extent, and thickness of rock units at the site area. 

• The structural geology of the site to include rock unit attitudes, faults and joint systems, 

folding, and intrusive bodies. 

• The age and activity level of faults in the dam and reservoir area. 

• The geohydrology of the site area to include water table conditions, soil and rock 

transmissivity coefficients, and recharge areas. 

• The existing and potential ground failure and subsidence, including rock and soil 

stability, dispersive soil conditions, and soil units exhibiting characteristics for potential 

liquefaction. 

• The potential for seiche action by examination of fault location, reservoir shape, 

topography, and slope stability conditions. 

d. Seismic Attenuation. The seismotectonic study can provide support to determine ground 

motions at the site and the attenuation of seismic ground motion with distance. Because of the 

inhomogeneity of areal and cross-sectional geology, the assessment of local or regional 

attenuation is difficult, and to a large extent is based upon historical, empirical, or theoretical 

data. The advancements in attenuation assessment take place through the development and 

testing of better mathematical models and the incorporation of new data. The seismotectonic 

study may require the following information for use in seismic attenuation studies: 

• Instances where ground motion data are available, to develop site-specific attenuation 

relationships or scattering functions. 

• Isoseismal maps constructed from historical earthquake data provide an indirect measure 

of ground motion attenuation. 
9

The most common approach is to use published attenuation relationships applicable to the 

general site conditions and type of expected faulting. Recent attenuation relationships are 

summarized in a series of papers published by the Seismological Society of America (SSA 

1997). Attenuation relationships are frequently modified and refined. As a result, the most 

recent published research should be consulted to determine the appropriate attenuation models. 

e. Reservoir-Induced Seismicity. USCOLD published a report (USCOLD 1997) examining 

the topic of reservoir-triggered seismicity. From a worldwide standpoint, only a small number of 

reservoirs impounded by large dams have triggered known seismic activity. It is generally 

accepted that reservoir filling will not cause damaging earthquakes where they would not 

otherwise occur; however, reservoir filling can cause earthquakes to occur more frequently than 

they would otherwise occur. Thus, the MCE is considered to be the same, with or without 

reservoir filling, but reservoir filling can alter the magnitude-recurrence relationship, at least 

temporarily. Seismic activity associated with reservoir filling has been reported at more than 40 

reservoirs. Included in the USCOLD report is a list of the more frequently cited cases. 

C. Selecting Maximum Design and Safety Evaluation Earthquakes 

1. General. There are two general approaches for conducting site-specific analyses for 

determining site ground motions (Reiter 1991). Either or both of these approaches may be used 

for a given site. The selection would be based upon the framework of the engineering 

assessments being conducted. It is also important to understand that in some cases different 

sources will control the design for different structural elements depending on the structures 

response. For example, the piers on a spillway structure may be controlled by nearby smaller 

events whereas a more massive structure, such as a high embankment dam subject to 

liquefaction, may be controlled by larger more distant sources. The two approaches are 

discussed below. 

a. Deterministic Seismic Hazard Analysis (DSHA). The DSHA approach uses the known 

seismic sources near the site and available historical seismic and geological data to generate 

discrete single-valued events or models of ground motion at the site. Typically, one or more 

earthquakes that will produce the greatest ground motion at the site are specified by magnitude 

and location with respect to the site. Usually, the earthquakes are assumed to occur on the 

portion of the source closest to the site. The site ground motion parameters (peak ground 

acceleration/velocity, spectrum intensities, duration of strong shaking, etc.) are estimated 

deterministically for each source, given the magnitude, source-to-site distance, and site 

conditions, using an attenuation relationship and/or theoretical models. 

b. Probabilistic Seismic Hazard Analysis (PSHA). The PSHA approach uses the elements of 

the DSHA and adds an assessment of the likelihood that ground motions of a given magnitude 

would occur. The probability or frequency of occurrence of different magnitude earthquakes on 

each significant seismic source and inherent uncertainties are directly accounted for in the 

analysis. The possible occurrence of each magnitude earthquake at any part of a source 

(including the closest location to the site) is directly incorporated in a PSHA. The results of a 

PSHA are used to select the design earthquake ground motion parameters based on the 
10

probability of exceeding a given parameter level during the service life of the structure or for a 

given return period. Results from the PSHA approach can also be used to identify which 

combinations of magnitudes and distance (or specific seismic sources) are the largest contributor 

to hazard. Identification of these controlling earthquakes can then be used in scenario or DSHA 

analyses. Several of the Federal agencies are currently developing guidelines on procedures to 

follow when performing a PSHA study. 

2. Determining Maximum Credible Earthquakes. The MCE for each potential earthquake 

source, judged to have a significant influence on the site, is established by a DSHA based on the 

results of a seismotectonic study (site-specific investigations and/or literature review). The MCE 

for each seismotectonic structure or source area within the region examined is defined preferably 

by magnitude, but in some cases in terms of epicentral Modified Mercalli Intensity, distance, and 

focal depth. Earthquake recurrence relationships (i.e., the frequency of occurrence of 

earthquakes of different sizes if appropriate for the fault) should also be established for the 

significant seismic sources. For source zones consisting of random seismicity, an MCE can be 

determined by finding the magnitude and distance that best matches the equal hazard response 

spectrum from a PSHA in the design earthquake frequency range appropriate for the structure. 

Judgments on activity of each potential fault source are generally based on recency of the last 

movement. For high-hazard potential dams, movement of faults within the range of 35,000 to 

100,000 years BP is considered recent enough to warrant an "active" or "capable" classification. 

All of the above MCE assessments for the various earthquake sources are candidates for one or 

more controlling MCEs at the site. It is also important to look at earthquakes that have a long 

duration but not necessarily the highest peak acceleration at the dam site. For embankment dams 

and foundations subject to liquefaction, this longer duration earthquake may be the controlling 

event if it triggers liquefaction of the embankment/foundation materials. Other appurtenant 

structures should be evaluated to determine if a higher magnitude distant earthquake is critical to 

the overall stability of the structure. 

3. Selecting Maximum Design Earthquakes or Safety Evaluation Earthquakes 

a. Criteria. The final selection of the MDE considers whether or not the dam must be capable 

of resisting the controlling MCE without catastrophic failure, such as uncontrolled release of a 

reservoir, although severe damage or economic loss may occur. For high-hazard potential dams, 

the MDE usually is equated with the controlling MCE. However, for low or significant-hazard 

dams, the MDE may be determined based on faults active in Holocene time, or according to 

other agency specified criteria. 

b. Combining Seismic Hazard Analyses. The combined application of deterministic and 

probabilistic seismic hazard analyses is an effective approach for determining the MDE ground 

motions. The probabilistic analysis allows the probabilities or return periods for exceeding 

different levels of site ground motion to be evaluated. This information can then be used to 

complement the deterministic analysis. For example, the probabilistic results can aid in deciding 

whether mean, or mean-plus-one standard-deviation, or greater estimates of ground motion 

would be justified for the MDE from the deterministic ground motion analysis to achieve an 

acceptably low probability of exceedance or long expected return period for the ground motion. 
11

4. Selecting Operating Basis Earthquakes. The second level of design earthquake, the OBE, 

represents the maximum level of ground shaking that corresponds to the desired level of 

protection for the project from an operations standpoint. Factors to be considered are 

earthquake-induced structural and mechanical damage and loss of service during the project's 

service life or remaining service life for existing dams. The OBE is generally determined from a 

PSHA. 
13

III. CHARACTERIZING SITE GROUND MOTIONS

A. General 

The next requirement for the seismic evaluation or design of structures is to establish an 

adequate representation of the earthquake ground motions to which the structure might be 

subjected. Earthquake ground motions are characterized for design, analysis, or evaluation in 

one or more of the following ways: by a set of ground motion parameters (e.g., peak ground 

acceleration, peak ground velocity, peak ground displacement, and duration of ground shaking); 

by response spectral values; or by one or more accelerograms. The spectral characteristics of the 

ground motion are normally presented in the form of response spectra. The response spectrum is 

very useful for the design and analysis of structures because it directly provides the structure 

dependent response to the design earthquake excitation. In practice, time-history representation 

of the seismic input is generally presented in terms of the ground accelerations (accelerograms), 

although velocity and displacement records may also be developed. Time-history records are 

used to perform linear or nonlinear time-history analyses. 

B. Ground Motion Parameters

1. General. Peak ground acceleration, velocity, and displacement are estimated using seismic 

history data, site-specific observations, and/or magnitude-distance attenuation relations if 

specific earthquake sources have been identified. 

2. Attenuation Relationships. Values of peak ground acceleration, velocity, displacement, 

spectral acceleration, and duration at various distances from an earthquake source have been 

compiled from past earthquakes. These values are used to develop relationships between 

distance from the source of energy release and earthquake magnitude or MM intensity for 

various subsurface conditions (bedrock, stiff soil, and soft sites). 

3. Components. Previous practice commonly assumed that accelerations in the two horizontal 

directions are equal or used the acceleration pairs from actual records with common scaling. The 

maximum vertical value has generally been taken as one-half to two-thirds or more of the 

maximum horizontal value. Current practice is to use attenuation relations for vertical 

acceleration which are now available. Ratios of vertical to horizontal ground motions are 

strongly dependent on earthquake source-to-site distance, local site conditions, and on the 

particular period range of interest. Detailed fault specific ground motion studies take into 

account directional aspects of the rupture and thus provide different motions for each of the 

horizontal components. Near-fault ground motions require special considerations. Rupture 

directivity on near-fault ground motions can significantly alter the amplitude and duration of the 

ground motion. The component of ground motion normal to the fault plane is often more severe 

than the component parallel to the fault plane. Peak vertical acceleration may also equal or 

exceed the peak horizontal acceleration. The effects of directivity in near fault ground motions 

are discussed in detail by Somerville (et al 1997 & 1998). 

4. Duration. Duration of shaking has been identified as one of the most important parameters 

of ground motion that causes damage to a structure. Some earthquakes have produced short, 
14

high-frequency accelerograms, but did not cause structural damage, even though the peak ground 

accelerations were very large. Other earthquakes where damage occurred had lower peak ground 

accelerations but had a long duration of ground shaking. Duration plays an important role in 

determining if liquefaction is triggered, determining deformations, and in conducting nonlinear 

dynamic analyses. Specific definitions of duration are discussed in the glossary. 

C. Elastic Response Spectra 

Elastic response spectra can be defined by using standard or site-specific procedures. Elastic 

response spectra represent maximum responses of a series of single-degree-of-freedom systems 

of different natural periods to a given ground-motion excitation (Newmark and 

Rosenblueth1971). The response spectrum amplifications vary with the value of damping. 

Typically, they are plotted at a damping ratio of 5 to 10 percent. Damping ratios of up to 10 

percent should generally only be allowed in dams showing energy dissipation through joint 

opening and tension cracking. Response spectra are significantly influenced by earthquake time 

history, source-to-site distance, and site conditions. These factors must be considered in 

developing site-specific design response spectra. 

1. Standard or Normalized Response Spectra. The standard response spectra commonly 

used is Newmark-Hall Spectrum (Newmark and Hall 1982). The spectra is developed using the 

peak or effective ground motion parameters in conjunction with a standard spectral shape that 

ignores the influence of earthquake magnitude and distance and site-type on the shape of the 

spectra. For critical structures located in regions with moderate or high seismic activity, or at 

sites close to the epicentral region or founded on soft soils, the site-specific spectra described in

Paragraph 3 below are used in lieu of standard response spectra.

2. Response Spectra from U.S. Geological Survey (USGS) Probabilistic Maps. USGS 

probabilistic maps of the United States are now available to construct preliminary design 

response spectra. These maps give ground acceleration and spectral response acceleration with 

10 percent, 5 percent, and 2 percent probabilities of exceedance in 50 years. These probabilities 

of exceedance correspond to return periods of approximately 500, 1000, and 2500 years, 

respectively. The use of spectral ordinates to construct design response spectra directly is a 

marked improvement to using peak ground accelerations and standard scaled spectral shapes, as 

discussed in paragraph 1 above. 

3. Site-Specific Response Spectra. Site-specific procedures are used to produce response 

spectra that correspond closely with those expected on the basis of the seismological and 

geological conditions at the site. These procedures use either the deterministic or probabilistic 

method to develop site-specific spectra. 

a. Deterministic Approach. Deterministic estimates of response spectra can be obtained 

either by 1) establishing the accelerograms to be used for the site and directly computing their 

response spectra; 2) estimating the response spectrum directly; or 3) anchoring a response 

spectral shape to the estimated peak ground acceleration. If approach 2 is used, estimating the 

response spectrum directly, this involves one or more of the following procedures: using 

response spectral attenuation relationships; performing statistical analyses of response spectra of 
15

a suite of ground motion records; and/or applying theoretical (numerical) ground motion 

modeling (USACE 1999). Approach 3, anchoring a response spectral shape to the estimated 

peak ground acceleration, is the least desirable approach for high consequences dams. 

Response spectra developed from a deterministic seismic hazard analysis are normally 

provided as median and median-plus-one standard deviation (84th percentile) spectra. The 

decision on the spectrum to use for design should be based on site-specific and agency criteria. 

In particular, for sites with either high rates of nearby seismicity or nearby high slip rate fault(s), 

using mean-plus-one standard deviation spectra may be prudent. 

b. Probabilistic Approach. Site ground motions are estimated for selected values of the 

probability of ground motion exceedance in a design time period. These values can also be 

represented by values of the annual frequency or return period of ground motion exceedance. A 

probabilistic ground motion assessment incorporates the probability or frequency of occurrence 

of earthquakes of different magnitudes from the various seismic sources, the uncertainty of the 

earthquake locations of the sources, and the ground motion attenuation including its uncertainty. 

In a probabilistic approach, response spectral attenuation relationships for each of several periods 

of vibration are used. By drawing a curve that connects the response spectral values to the same 

probability of exceedance, a response spectrum having an equal probability of exceedance at 

each period of vibration (termed equal or uniform hazard spectrum) is obtained. The resulting 

spectrum is preferred because of the direct incorporation into the analysis of the influence of 

different earthquake magnitudes and distances and source-site geometry on the results for each 

period of vibration. 

Response spectra developed from a probabilistic seismic hazard analysis are provided, 

generally, as mean equal hazard spectra. A comprehensive PSHA incorporates not only the 

inherent randomness, or variability, of earthquake generation and seismic wave propagation, but 

also the uncertainty associated with the choice of particular models and model parameters for 

characterizing seismic sources and estimating ground motions. Accordingly, no additional 

conservatism is normally added to mean equal hazard spectra from a comprehensive PSHA. The 

degree of conservatism is explicitly defined by the choice of annual exceedance probability. 

c. Site-Specific Characteristics. The site-specific characteristics to be considered in 

developing response spectra are the foundation conditions (soil or rock, deep or shallow soil, 

rock type, basin configuration, and impedence contrast), magnitude of the design earthquake, 

distance of the site from the earthquake, attenuation characteristics of the earthquake to the site, 

and the source mechanisms of the earthquake, including identifying if the site fault is on the 

hanging wall versus footwall (Sommerville et al 1997, Abrahamson and Silva 1997), depth of 

faulting, and other factors. 

D. Time Histories of Ground Motions

1. General. When acceleration time histories (also referred to as accelerograms) of ground 

motions are required for the dynamic analysis of a structure, they should be developed to be 

consistent with the design response spectrum, as well as have an appropriate strong motion 
16

duration for the particular design earthquake. In addition, whenever possible, the acceleration 

time histories should be representative of the design or safety evaluation earthquake in all the 

following aspects: earthquake magnitude, distance from source-to-site, fault rupture mechanisms 

(fault type, focal depth), transmission path properties, and regional and geological conditions. 

Since it is not always possible to find empirical records that satisfy all of the above criteria, it is 

often necessary to modify existing records or develop synthetic records that meet most of these 

requirements. 

2. Approaches to Developing Time Histories. There are two general approaches to 

developing acceleration time histories: selecting a suite of recorded motions and synthetically 

developing or modifying one or more motions. These approaches are discussed below. For 

either approach, when modeling near-source earthquake ground motions (i.e., minimum sourcesite distance less than 10 km), it is desirable that the motions include a strong intermediate- to 

long-period pulse to model this particular characteristic of ground motion often observed in the 

near field and generally accepted to be responsible for significant damage. Of specific 

importance at distances less than 10 km are the effects of directivity in developing fault normal 

and fault parallel components (Somerville et al 1997). 

a. Selecting Recorded Motions 

(1) Typically, in selecting recorded motions, it is necessary to select a suite of time histories 

(typically 3 or more) such that, in aggregate, valleys of individual spectra that fall below the 

design (or “target”) response spectrum are compensated by peaks of other spectra and the 

exceedance of the design response spectrum by individual spectral peaks is not excessive 

(preferably at least within the bandwidth of interest for structures specific analysis). For 

nonlinear analyses, it is desirable to have additional time histories because of the importance of 

phasing (pulse sequencing) to nonlinear response. In the past, when using selected recorded 

motions, simple scaling of acceleration time histories was frequently performed to enhance 

spectral fit. However, scaling should be done with caution. The ramifications of significant 

scaling of acceleration time-histories on velocity, displacement, and energy can be profound. 

(2) The advantage of selecting recorded motions is that each accelerogram is an actual 

recording; thus, the structure is analyzed for motions that are presumably most representative of 

what the structure could experience. The disadvantages are: multiple dynamic analyses are 

needed for the suite of accelerograms selected; although a suite of accelerograms is selected, 

there will typically be some exceedances of the smooth design spectrum by individual spectrum 

peaks; and although a reasonably good spectral fit may be achieved for one horizontal 

component, when the same simple scaling factors are applied to the other horizontal components 

and the vertical components for the records selected, the spectral fit is usually not as good for the 

other components. 

b. Synthetically Developing or Modifying Motions 

(1) Techniques. A number of techniques and computer programs have been developed to 

either completely synthesize an accelerogram or modify a recorded accelerogram so that the 
17

response spectrum of the resultant waveform closely matches the design or target spectrum. 

Recent advances have used either (a) frequency-domain techniques with an amplitude spectrum 

based upon band-limited white noise and a simple, idealized source spectrum combined with the 

phase spectra of an existing record; or (b) kinematic models that produce three components of 

motion using complex source and propagation characteristics. Such motions have the character 

of recorded motions since the modeling procedures are intended to simulate the earthquake 

rupture and wave propagation process. Recent research suggests dynamic and three-dimensional 

models may be important in estimating engineering ground motions in the future. 

(2) Comments. The natural appearance and duration of strong motion can be maintained using 

these techniques. A good fit to the target spectrum may or may not be possible with a single 

component of motion. However, for non-linear applications, it is particularly desirable to have 

multiple accelerograms because different accelerograms may have different phasing (pulse 

sequencing) characteristics of importance to nonlinear response yet have essentially identical 

response spectra. For near-field situations, the characteristics of the motions should reproduce 

the coherent velocity pulses (“fling”) commonly observed in near-field recordings. 

(3) Advantages and Disadvantages. The advantages of synthetic techniques for developing 

time-histories are: the natural appearance and strong motion duration can be maintained in the 

accelerograms; three component motions (two horizontal and one vertical) each providing a good 

spectral match can be developed; and the process is relatively efficient. The disadvantage is that 

the motions are not “real” motions. Real motions generally do not exhibit smooth spectra. 

Although a good fit to a design spectrum can be attained with a single accelerogram, it may be 

desirable to fit the spectrum using more than one accelerogram. Such motions have the 

character of recorded motions since the modeling procedures are intended to simulate the 

earthquake rupture and wave propagation process. 

3. Application. Ground motion parameters should be specified in a manner that is consistent 

with the analyses to be performed. Where ground motions are specified at one location (e.g., a 

rock outcrop) and are used in the analysis at a different location (e.g., at the base of a soil layer), 

the motions need to be adjusted accordingly. Where magnitude and distance are used in 

empirical procedures, it is important to verify that distance-attenuation definitions in the 

procedure are consistent with those inferred for the site of interest. 
19

IV. SEISMIC ANALYSES 

A. Type and Extent of Analyses 

1. Consistency. The extent and type of analysis required for the seismic design or evaluation 

of a dam depends on the hazard potential classification (FEMA 1998), criticality of project 

function, level of seismic loading, the site conditions, type and height of dam, construction 

methods, as-built as well as current material properties, and engineering judgment. Consistency 

should be maintained between the level of analysis and the level of effort given to the 

development of seismotectonic data, the ground motion parameters, and the site investigation. 

For example, a highly refined structural analysis based on an assumed earthquake loading is not 

reasonable in most cases. Likewise, a highly refined structural analysis should use site-specific 

tested material properties and not assumed values.

2. Progressive Analyses. In general, it is the most cost-effective for seismic analyses to begin 

with the simplest conservative method appropriate to the problem. If the structure is judged able 

to resist the earthquake loading within certain safety margins from the initial analysis, then 

further analysis should not be necessary. If further studies are needed, they would be 

progressively more detailed and the structure designed or evaluated accordingly. Regardless of 

the method of analysis, the final evaluation of the seismic safety of the dam should be based on 

engineering judgment and past experience, not just on the numerical results of the analyses.

B. Concrete Dams 

1. Safety Concerns 

a. Instability. The most important safety concern of concrete dams subjected to earthquakes is 

excessive cracking, which can lead to potential instability from sliding or overturning. Sliding 

can be on an existing plane of weakness in the dam or foundation or along planes of weakness 

formed by excessive cracking of the concrete above or at the foundation-dam interface. Although 

no concrete dam has failed as a result of earthquake loadings, failure modes can be postulated 

and tested on shake tables (Payne 2002). For concrete dams, sliding instability is possible due to 

an earthquake-induced vibratory motion on a plane of weakness at, above, or below the 

foundation-dam interface. For an arch dam, sliding instability is more likely to occur by failure 

of the abutment support because the arching (shell) effect provides additional resistance to 

sliding within the dam. In general, instability of gravity and arch dams caused by excessive 

cracking of the concrete is most likely to occur in the upper half of the dam. Buttress dams also 

are particularly vulnerable to cross-valley shear motions that can result in tipping of the 

buttresses and loss of support for the reinforced concrete slab. 

b. Importance of Foundation. Of the two possible types of instability discussed above, 

historical experience shows that foundation (abutment) induced failure is the chief source of 

concern for concrete dams. In contrast to the dam itself, the supporting medium consists of 

natural materials of varying composition, irregular joints, and planes of weakness. The strength 
20

of this medium is generally estimated from exploratory borings and tests on only a small fraction 

of the material present. Key zones of weakness are critical and often difficult to detect. 

c. Field Performance. No major concrete dam is known to have failed due to 

earthquake-induced ground motion, although some have experienced strong ground motion and 

some damage. The field performance of concrete dams during earthquakes is further discussed 

in Section V. 

2. Defensive Design Measures. The application of defensive design measures when designing 

new dams is the most dependable approach to alleviate safety concerns. Defensive design 

measures for concrete dams include the following: 

a. Sufficient foundation and abutment exploration, material testing, and strengthening to assure 

foundation and abutment integrity. The importance of foundation and abutment integrity cannot 

be overemphasized. Adequate drainage is usually the first line of defense against foundation 

instability, in part because it is the most economical. 

b. Use of the best geometric design and structural detailing appropriate to the structure. The 

structural configuration should have minimum geometric irregularities and gradual variations in 

structural stiffness. Examples of good geometric designs are curved transitions, minimal mass at 

the crest, gradual changes in arch and cantilever stiffness at the top half of arch dams, and a 

downstream face slab for buttress dams. Continuous load paths, load path redundancy, and 

ductile behavior are important safeguards to ensure that structures loaded past their elastic limit 

will continue to perform adequately and will function after extensive cracking. Any necessary 

structural irregularities should be properly detailed to account for the localized effects of stress 

concentrations. 

c. Effective quality control during construction to ensure adequate foundation preparation, 

strength of the concrete and appropriate cleaning and preparation of lift joints, and placement of 

the reinforcement when used. For existing dams where the seismic loading has substantially 

increased and engineering analysis demonstrates poor performance of the structure, remediation 

schemes will depend on site-specific conditions. However, general types of seismic remediation 

of existing concrete structures where the dam or foundation has been determined to be 

inadequate are post-tensioned anchors, additional mass concrete, buttressing, and drainage. 

3. Structural Modeling

a. General. Structural modeling should be undertaken by an engineer (seismic structural 

analyst) knowledgeable in the basic theory of structural dynamics, materials, seismology, and 

finite-element structural analysis. The structural engineer, materials engineer, geologist, 

geotechnical engineer, and seismologist should all work closely together to understand the level 

of study and the level of certainty required from each discipline. The team should develop 

failure modes and describe the level of certainty for each failure mode. Concrete dams are very 

complex structures. The dynamic interactions among various components of the structure must 

be considered when developing the failure modes and the analysis models. In particular, 
21

interaction effects of the structure with its foundation and the impounded, surrounding, or 

contained water should be included in the analysis. However, the structural model selected 

should be consistent with the level of refinement used in specifying the earthquake ground 

motion, and should begin with the simplest model that can provide the required information and 

level of certainty for evaluation. Information required for modeling the rock foundation and any 

backfill soils or soil foundation should be provided by the project team's geotechnical engineer 

and/or engineering geologist. The geotechnical engineer must know how the information will be 

used in the structural analysis. For example, if the analysis uses an approach that incorporates 

mass in the foundation, the dam response can be highly sensitive to the modulus values being 

used. The material engineer needs to know where in the dam the concrete properties are most 

critical for the structural engineer and what properties are desired. If lift line strength is critical, 

a core extraction and testing program should be devised to try and obtain the best possible in situ 

values possible. For dynamic stability, the dynamic tensile strength may have to be measured 

along with the static tensile strength. The direct tensile strength may be desired along with the 

splitting tensile strength. 

b. Types of Models. The development of an appropriate structural model requires 

consideration of the geometry, stiffness, damping, and mass distributions of the structure, all of 

which affect its dynamic characteristics. Engineering judgment and knowledge of dynamics of 

structures are required to develop a satisfactory model that is both simple and representative of 

the most important dynamic behavior of the structure. Depending on its nature and the level of 

complexity, a hydraulic structure may be represented by a planar or two-dimensional model 

whose deformations are restricted in a plane, or by a more extensive three-dimensional model to 

account for three-dimensional behavior. 

4. Methods of Analysis

a. General. For a concrete dam on a rock foundation with no major known structural 

deficiencies, such as significant cracks in the structure, major weak joints, or adversely oriented 

discontinuities in the foundation, stability during an earthquake loading based on previous case 

histories and/or analyses should be satisfactory if all the following conditions are satisfied: 

• The dam is well-constructed (quality concrete and lift joints) and is in good condition. 

• Peak bedrock accelerations are 0.2g or less. 

• The resultant location for a gravity dam under static conditions is within the middle 1/3 

of the base and the factor of safety against sliding is acceptable for static conditions. 

If these conditions are not satisfied, the methods of dynamic analysis currently being applied 

for various levels of studies and types of dams, in the order of complexity, are linear-elastic 

response spectrum, linear-elastic time-history, and non-linear time-history methods. 
22

b. Dynamic Analysis Methods. Dynamic analysis methods are those that determine the 

structural response based on the dynamic characteristics of the structure and the earthquake 

ground motions established for the site. The dynamic method most commonly used is the linearelastic modal superposition analysis method. This method is based on the fact that, for certain 

forms of damping that are reasonable models for many structures, the response in each natural 

mode of vibration can be computed independently of the others and the modal responses can be 

combined to determine the total response. Either a response spectrum or an acceleration-time 

record can be used with the analysis technique. Time-history responses can also be calculated 

using step-by-step direct integration. 

(1) Response Spectrum Method 

(a) Description. In this method, the maximum response in each mode of vibration is directly 

computed from the design response spectrum and the dynamic characteristics of the structure. 

These modal responses are then combined to obtain estimates (but not the exact value) of the 

maximum modal response. Adding the absolute values of each mode gives an upper limit for the 

total response, while using the square root of the sum of the squares yields a more probable total 

response. Either a simple beam analysis (P/A +/- Mc/I) or finite element analysis can be used to 

compute the stresses. Dynamic stresses are combined with the static stress to obtain the total 

stress. The response spectrum method does not account for stress variation with time. See U. S. 

Army Corps of Engineers (USACE 1999) for guidance on the use of the response spectrum 

method for concrete dams. 

(b) Evaluation of Response. In most cases, when the dynamic response of the structure is 

entirely within the linear elastic range, the response spectrum analysis will suffice. However, in 

the case of earthquakes for which the calculated stresses for mass concrete structures may 

approach or exceed the tensile strength of the concrete, a time-history linear dynamic analysis 

provides valuable information for the approximation of the potential damage, or the expected 

inelastic response behavior that may occur and the potential need for a nonlinear analysis. 

(2) Time-History Method 

(a) Linear-elastic Analysis. In this method, the response of the dam is calculated for the entire 

duration of an acceleration time-history, starting with initial static conditions and computing the 

response at the end of each time interval. The stresses and/or deflections of each mode are added 

together for each time interval to yield the total time-history response. The dynamic responses 

are added algebraically to the static responses. Stress histories are developed to show the 

maximums, the number and duration of excursions beyond the tension or compression limits, 

and the areal distribution of stresses in the dam at particular times during the earthquake. 

(b) Evaluation of Response. For major earthquakes occurring close to some concrete dams, it 

is probable that the elastic capacity of the mass concrete would be exceeded, and some damage 

or yielding could occur. For these cases, the prediction of the actual response and estimation of 

the expected damage and inelastic behavior of the dam can only be judged in a linear analysis. 

Evaluating actual damage and failure requires a more involved nonlinear analysis. However, 
23

linear analysis can still be very valuable for a preliminary assessment of the damage and the level 

of post-elastic response, and can aid in the decision of whether a nonlinear analysis should be 

performed. As part of this evaluation, the results of a linear analysis for hydraulic structures 

should be examined in a systematic manner to identify the extent of over-stressed regions at any 

particular point in time. This will aid in the production of plots to show time-histories of stresses 

and other response quantities of interest, and to establish statistics on the number of stress cycles 

exceeding the allowable values and the corresponding excursions of these stress cycles beyond 

the specified limits. Minor, local damages, indicated from an elastic analysis, would have little 

effect on the overall integrity of the structure and can still be evaluated by proper interpretation 

of the results of linear analyses. An alternative evaluation technique that has been used by some 

agencies to evaluate a structure indicating distress using a linear elastic analysis is to assume 

cracking along the total width of the plane being investigated and evaluate structural stability in 

the post earthquake (static) condition. Stability during the earthquake would also have to be 

checked or assured if cracking took place prior to the conclusion of the event. 

(c) Nonlinear Analysis. A complete nonlinear analysis should take into account all sources of 

nonlinearity that contribute significantly to the nonlinear behavior. The damage caused by 

earthquake shaking is normally associated with significant loss in the structural stiffness, a result 

of concrete cracking, yielding of steel, opening of contraction joints, slippage across the 

construction joints or cracking planes, and nonlinear material behavior. Additional sources of 

nonlinearity arise from the nonlinear response of the foundation supporting the structure, as well 

as the separation of the structure and the foundation at the contact surface. A complete and 

reliable nonlinear dynamic analysis that includes tensile cracking of concrete, yielding of 

reinforcements, opening of joints, and foundation/abutment displacements is becoming more 

practical. Having a complete and reliable nonlinear analysis for the seismic safety evaluation of 

dams depends on continuing developments in the following areas: 

• Definition of spatially varying seismic input. 

• Energy absorption factors for reservoir sides and bottom and at infinite boundaries at the 

reservoir and foundation extents of the models. 

• Boundary identification and specification of significant nonlinear mechanisms (joint 

opening, tensile cracking, steel yielding, nonlinear material behavior under dynamic 

loads, etc.). 

• Development of idealized models representing the nonlinear behavior (contact surfaces 

for modeling contraction joints and sliding along discontinuities, and validated 

constitutive models for concrete cracking) 

• Development of efficient and numerical sound techniques and solution strategies for 

computing the nonlinear response. 

• Development of criteria for acceptable performance. 
24

• Identification of possible modes of failure. 

(d) See Canadian Electrical Association (CEA 1990a) for additional guidance on using linear 

and nonlinear dynamic methods of analysis for concrete dams. 

(3) Foundation Stability Dynamic Analysis 

(a) General. A dynamic stability analysis should generally be performed on the same 

foundation blocks and wedges that were identified and used in the static stability analysis. The 

same methods of foundation analysis used for static stability calculations are used for dynamic 

evaluations with the following additions, modifications, and exceptions: 

• The analysis must include dynamic loads from both the dam acting on the foundation 

blocks and the inertial loads from the blocks themselves. 

• The inertial load from the mass of the foundation block is included. If a time-history 

analysis is being performed, the load is equal to the mass multiplied by the acceleration at 

any instant of time. If a response spectrum analysis is being performed, appropriate 

effective peak acceleration is used. 

• If the analysis indicates that the sliding resistance on the potential sliding plane (frictional 

resistance plus intact rock cohesion) is exceeded at some point during the earthquake 

loading, a strength reduction (typically reduction or elimination of cohesion) is necessary. 

Dynamic strengths of the intact rock and/or concrete must also be accounted for in 

making the analysis. 

• Deformations can be computed for the foundation blocks by a Newmark-type rigid-block 

sliding analysis, and the dam’s performance can be evaluated by comparison with 

acceptable-deformation criteria. This approach is especially valuable for cases where 

blocks can be assumed to be formed by continuous joints, faults, and shear zones. For 

atypical dams, commonly-used criteria may not be applicable, and there can be separate 

issues for appurtenant features. 

• Research has shown that dynamic loading can affect water pressures in joints and shear 

zones. At this time, however, water pressure adjustments to account for that are not 

routine in practice. 

(b) Seismic Stability Criteria. Seismic stability criteria for foundations depend on the method 

of analysis and the basic assumptions made for the geologic discontinuities. The three general 

cases are: 

• A specified minimum factor of safety in a pseudo-static analysis at the time of critical 

dynamic loading from the dam, in which the rock is considered to be intact. 
25

• A specified minimum factor in pseudo-static analysis of blocks assumed to be bounded 

by fully continuous joints, shears, or faults. 

• Acceptable deformations calculated by time-history analysis with or without 

consideration of the strength of intact rock, in which sliding during excursions are 

evaluated below a factor of safety less than 1.0 (if any). 

(c) For guidance on the use of two- and three-dimensional rigid block and finite element 

methods of dynamic analysis for rock foundations see Canadian Electrical Association (CEA 

1990b). 

(d) Coupled dam and foundation analysis. Typically, the foundation stability analysis is 

performed separately from the dam analysis, as discussed above. A more realistic approach is to 

analyze the dam and foundation together in a coupled analysis. This way, the interaction 

between the dam and the rock wedges in question can be modeled. Because a coupled analysis 

can model non-linearity caused by changes in geometry, explicit coupled methods can be very 

effective. 

(4) Material Properties for Dynamic Analysis. The ability to analyze a dam often exceeds 

the ability to define material properties. This is particularly true for nonlinear analysis where 

many times the material models in the finite element codes have theoretical inputs that can only 

be estimated and not tested. Concrete and rock are not homogeneous materials. The material 

properties can be quite variable and possess a degree of uncertainty. This should be kept in mind 

when performing investigations. Sensitivity studies using variations on material properties 

should be performed where appropriate. 

(a) Concrete Properties for Analysis. The concrete properties required for input into a linear 

dynamic analysis are the unit weight, Young's modulus of elasticity, damping, and Poisson's 

ratio. The concrete properties used should account for, as nearly as practicable, the effects of 

aging and existing cracks and the expected rate of loading. 

(b) Concrete Strengths for Evaluation of Results. The concrete properties needed to perform 

dynamic analysis are the compressive, tensile, and shear strengths. The standard unconfined 

uniaxial compression test, excluding creep effects, is generally acceptable as a first test for the 

compressive strength. Usually, this test suffices, even though it does not account for the rate of 

loading, since compressive generally does not control the outcome of the analysis. The tensile 

strength of concrete generally governs because it is a small fraction of the compressive strength. 

(c) Concrete Tensile Strength. Tensile strengths of the lift joints and the parent concrete are 

determined from tests on cores taken from test fill placements for new dams and the actual 

concrete in existing dams. The modulus-of-rupture test and the splitting tensile test are 

commonly used for the parent concrete. Direct tensile tests are preferred, but less-expensive 

splitting tensile tests can be used, with the results adjusted to reflect the results of a smaller 

number of direct tensile tests. The direct tensile test is also used to measure the strength of the 
26

lift lines. From these tests, allowable design tensile stresses can be established for both lift joints 

and parent concrete can be adjusted using factors to account for the high strain rate associated 

with dynamic loading. However, the best approach is to actually test the strength of the parent 

concrete and lift lines under rapid loading. Tensile and bond strengths of concrete dams are as 

much related to mix consistency, placement methods, and compaction procedures as they are to 

mix proportions. Maximum aggregate size, consistency, and mortar bedding also influence 

tensile strength of the joints. The effects of pre-existing cracks, lift joints, and construction joints 

on the tensile strength must also be accounted for, whether assessing the results of linear-elastic 

analysis or performing nonlinear analysis. If dynamic analyses indicate high tensile stresses, the 

effects of cracks and weakened joints can be modeled conservatively by assuming that cracking 

occurs, and reanalyzing the dam to determine whether the remaining capacity of the dam in the 

cracked state is sufficient. 

(d) Rock Properties for Analysis. When the foundation is included in the seismic analysis, 

elastic moduli and Poisson's ratios for the foundation materials are required. If the foundation is 

not considered as massless, rock densities and damping characteristics are also required. 

Determining the elastic moduli for a rock foundation may be accomplished using one of several 

approaches that account for the effects of rock inhomogeneity and discontinuities on foundation 

behavior. The determination of foundation compressibility should consider both elastic and 

inelastic (plastic) deformations. The resulting "modulus of deformation" is lower than the elastic 

modulus of intact rock. The effects of the rate of loading on the foundation moduli is considered 

insignificant relative to the other uncertainties involved in determining rock foundation 

properties; rate effects are generally not measured. To account for the uncertainties, lower and 

upper limits for the foundation moduli should be used in the structural analysis to determine the 

sensitivity of the results to variation in moduli. For dynamic loading, the upper limit is generally 

the most realistic estimate because the inelastic "set" has already occurred. However, the shear 

strength used for static analysis is usually used for dynamic analysis without adjustment. The 

shear strength of discontinuities is generally a critical element in the stability analysis. 

(e) Damping Ratio. For concrete gravity dams built on competent rock, where cracking of the 

concrete does not occur, the viscous damping ratio is usually assumed to be 5 percent of critical. 

If calculated stresses indicate that cracking would occur, a value from 7 to 10 percent of critical 

can be used (depending on the severity of cracking expected). Some analysis codes use 

hysteretic damping and Rayleigh damping, which require different values specific to the form of 

damping. It may also be necessary to account for radiation damping and the effects of reservoirbottom reflection (Nuss et al 2003, Ghanaat 1995). 

c. Sliding Stability 

(1) Methods of Analysis. The sliding stability evaluation of hydraulic structures under 

earthquake loading can be made according to the traditional pseudostatic (seismic coefficient) 

and permanent displacement approaches (Ebeling and Morrison 1992). In the traditional 

approach, the sliding stability is expressed in terms of a prescribed factor of safety against 

sliding, whereas in the permanent displacement approach, the structure is permitted to slide 

along its base but the accumulated displacement during the ground shaking is limited to a 
27

specified allowable value. Some federal agencies have encouraged the use of conducting a post 

earthquake stability analysis to demonstrate seismic stability. Under this type of analysis, 

conservative assumptions are used to reduce the amount of information needed of the ground 

motions, and the exploration and testing required of the dam/foundation material properties. For 

example, a typical analysis would assume the seismic event has created a crack that extends 

entirely through the base of the dam. Sliding along deep seated failure surface in the foundation 

should also be considered or ruled out. An analysis is then conducted, assuming no cohesion and 

a reduced friction angle, to determine if the dam has an adequate post earthquake factor of safety 

or if remediation or additional analysis is warranted. 

(2) Pseudostatic (Seismic Coefficient) Method. In this method, seismic inertia forces due to 

weight of the structure and to hydrodynamic pressures are included as part of the driving force, 

and a static analysis of sliding is performed (Ebeling and Morrison 1992). Treating the system 

above the failure surface as a rigid block, the inertia force associated with the mass of the 

structure is computed as the product of the assumed earthquake acceleration (seismic coefficient 

x g) and the mass of the block. Similarly, the product of the earthquake acceleration and the 

added-mass of water that is moving with the structure, according to the theory of Westergaard 

(1933), produce inertia force due to the hydrodynamic pressures. The motion of the structure 

relative to the failure surface is resisted by the shear strength mobilized between the structure 

and failure surface by the friction and cohesion. When the earthquake forces are included in the 

sliding stability analysis, the calculated factor of safety against sliding (i.e., ratio of the resisting 

to driving shear forces) may become less than one. When this occurs, the sliding is assumed to 

occur for as long as the ground acceleration is greater than the critical value required for the 

driving force to exceed the resistance. However, due to oscillatory nature of the earthquake 

ground motion, the sliding displacement is limited and can be estimated by the permanent 

displacement approach described below. 

(3) Permanent Displacement Method. The factor of safety against sliding required by the 

pseudostatic method (e.g., >1.0-1.5 at all times) may not be attainable for larger seismic forces 

representative of moderate to high intensity earthquake ground motions. Where the sliding 

factor of safety drops below 1.0, sliding can occur during periods of time when the acceleration 

cycles exceed a critical acceleration period of time associated with the acceleration cycles 

exceeding a critical acceleration, ac, and the relative velocity between the structure and the base 

is greater than zero (Chopra and Zhang 1991). Knowing the critical acceleration ac, the 

permanent sliding displacements can be estimated using Newmark's rigid block model 

(Newmark 1965). Newmark's model provides an easy means for approximate estimation of the 

upper bounds for permanent sliding displacements, but is based on certain assumptions that 

ignore the true dynamic response behavior of the sliding. More accurate estimates of the sliding 

displacements can be made from the response history analysis proposed by Chopra and Zhang as 

referenced above. 

d. Rotational Stability. Hydraulic structures subjected to large lateral forces produced by 

major earthquakes may tip and start rocking when the resulting driving moment becomes so 

large that the structure breaks contact with the foundation or cracks all the way through at an 

upper elevation. However, under earthquake excitation large driving moments occur for only a 
28

fraction of a second in each cycle, with intermediate unloading. Stability studies of structures 

(Housner 1963, Scholl 1984) infer that dynamic rotational stability for rigid structures with 

height to base width ratios typical of gravity dams is not a problem. In addition, the study by 

Chopra and Zhang (1991) indicate that a concrete dam under earthquake loading will slide 

downstream before tipping will occur. U. S. Army Corps of Engineers (USACE 1999) discusses 

each of the above references. However, if the dynamic analysis indicates that extensive 

cracking, block rocking, or translational displacement is expected, the dam in its post-earthquake 

condition should be checked for sliding stability to assess if it is capable of containing the 

reservoir for a sufficient period of time to allow for strengthening of the dam, if necessary, to 

restore the dam to acceptable factors of safety for the various credible loading conditions. The 

post-earthquake analysis should use residual shear strength parameters. 

C. Embankment Dams 

1. Safety Concerns. The first step in the design or evaluation of any dam is the development 

of an understanding of the way the dam can fail. Several earthquake-induced conditions that can 

cause failure of an embankment dam are described below. 

a. Overtopping of the Embankment. The evaluation of the seismic safety of embankment 

dams often depends on determining, directly or indirectly, the magnitude of expected 

deformations. If the embankment crest falls below the elevation of the reservoir surface, erosion 

from overtopping can cause the dam to fail. Direct methods of assessing deformation model the 

design earthquake, the dam, and foundation to calculate the expected deformation. There are 

also indirect methods to predict the response of the embankment and foundation based on 

empirical observations. Post-earthquake stability analysis can, in a sense, also be considered an 

indirect prediction of deformation – if the post-earthquake factor of safety is high, the 

deformations should be limited to a few feet except under very severe loading. Deformation 

analyses are discussed further below. 

The magnitude of deformations is very dependent on the strengths of the materials involved. 

During strong shaking, permanent deformations (usually small) may occur simply because the 

dynamic stresses temporarily exceed the available strength. In saturated soils, there is frequently 

some loss of shearing resistance due to an increase in pore water pressure when shaken. This 

increases the dynamic deformations over what they would be with no strength loss. In very 

loose, contractive soils, the strength may become a small fraction of its static, drained value due 

to excess pore-water pressure, a process called "liquefaction." If the strength drops below that 

required for static stability, very large deformations can result, driven by gravity even after the 

shaking ends. These can be anywhere from a few feet to hundreds of feet, depending on the 

driving forces, geometry, and post-earthquake strength. Liquefaction evaluations are described 

in 3.b. of this section. There is an intermediate condition known as "cyclic mobility," in which 

the shearing resistance is initially very low due to excess pore pressure, but increases with larger 

shear strains, helping to prevent gross instability but still permitting significant deformation. 

Overtopping leading to failure of the dam can also result from the following: 
29

• Movement on a fault through the reservoir or through the embankment foundation, 

causing the reservoir elevation to rise above the crest of the dam (or the dam crest to fall 

below the reservoir surface). 

• An earthquake-induced landslide that displaces a significant volume of water. 

• A large seiche wave generated by an earthquake. 

b. Cracking and Internal Erosion. If a dam is deformed by earthquake excitation or fault 

displacement, the deformations can cause cracks in the dam and/or disrupt internal filters, either 

of which could lead to failure of the dam by erosion. Cracks are most likely to occur at 

interfaces with concrete structures (e.g., spillway walls) or at abrupt changes in the 

embankment’s cross section. There is also evidence that shaking could precipitate piping even 

without formation of a crack if the dam is already on the verge of piping. The amount of 

deformation a dam can withstand without risk of failure by erosion through cracks depends on 

the materials in the dam and foundation, the details of internal zoning (filters, drains, and cutoff), 

the reservoir elevation at the time of the earthquake, and the nature and location of appurtenant 

structures. Should there be conduits through the embankment, deformation of the dam can 

rupture them or cause joints to separate, leading to erosive failure by either creating an unfiltered 

exit for seepage or exposing the embankment or foundation to full reservoir head where not 

intended. Erosion along intact conduits has also caused dam failures. 

2. Defensive Design Measures. Many situations that could develop into a dam safety 

emergency or failure of the dam if not properly designed do not always require extensive 

analytical evaluation. The simple application of defensive measures will sometimes give the 

evaluator assurance that the structure will perform satisfactorily, assuming even the worse 

scenario. Conversely, poorly designed defensive measures may invalidate the beneficial effects 

of the defensive measures. Such defensive measures include the following: 

• Remove foundation materials that may present problems. 

• Use wide core zones of plastic materials resistant to erosion. 

• Use well-graded wide filter zones upstream of the core to help choke-off any cracks that 

may open and downstream of it to prevent movement of particles eroded from the core. 

• Construct chimney drains downstream of the embankment core to lessen saturation. 

• Use crest details and downstream slope protection that will prevent or greatly inhibit 

erosion in the event of moderate overtopping. 

• Flare the embankment core at abutment contacts. 

• Locate the core to attain the lowest practicable phreatic line within the embankment. 
30

• Stabilize slopes around the reservoir rim to prevent slides into the reservoir. 

• Provide special details for treating the embankment-foundation interface if the potential 

for fault movement in the foundation exists. 

• Provide high quality, free draining rockfill shells. 

• Provide ample freeboard to allow for settlement, slumping, or fault movements. 

• Shape foundation contacts to avoid abrupt changes in profile, overhangs, or large 

"stairsteps." 

• Compact embankment fill materials adequately to prevent or minimize generation of 

excess pore pressures. 

• Provide filters or other measures to prevent erosion along the outside of conduits or other 

structures within the embankment. 

3. Methods of Analysis 

a. General. For a dam and foundation not subject to liquefaction, minor deformation may take 

place but should not lead to failure if all of the following conditions are satisfied: 

• Dam and foundation materials are not subject to liquefaction and do not include loose 

soils or sensitive clays. 

• The dam is well built and compacted to at least 95% of the laboratory maximum dry 

density, or to a relative density greater than 80%. 

• The slopes of the dam are 3:1 (H:V) or flatter, and/or the phreatic line is well below the 

downstream slope of the embankment.

• The peak horizontal acceleration at the base of the embankment is no more than 0.2 g. 

• The static factors of safety for all potential failure surfaces (other than shallow surficial 

slides) are greater than 1.5 under loading and pore-pressure conditions expected 

immediately prior to the earthquake. 

• The freeboard at the time of the earthquake is at least 3% to 5% of the embankment 

height and not less than 3 feet (0.9 m). (Freeboard requirements to accommodate 

reservoir seiche waves or coseismic movement of faults at the dam site or in the reservoir 

must be considered as a separate issue.) 
31

• There are no critical appurtenant features that would be harmed by small movements of 

the embankment, or that have the potential to cause cracks that would allow internal 

erosion. 

If these conditions are not satisfied, more detailed study is required. This may include 

assessment of liquefaction potential, post-earthquake stability analysis, and/or deformation 

analysis. If there are no potentially liquefiable materials present, this can usually be done by the 

simple Newmark sliding-block approach, discussed in c. below. In situations where excess pore 

pressure could develop, it may be necessary to conduct more rigorous (but more timeconsuming) finite-element or finite-difference analyses. The objective of deformation analysis is 

to determine whether plausible movements would be sufficient to allow overtopping by the 

reservoir, or if cracking at critical locations could result in failure by internal erosion. From 

these results and historic performance of embankment dams subjected to earthquake loading, one 

must make an overall assessment of whether the dam and foundation can be expected to safely 

withstand the loading. 

b. Liquefaction Evaluation 

(1) General. For existing dams/foundations, as well as for the foundations for proposed new 

dams, the most important part of a liquefaction investigation is adequate subsurface 

investigations (mapping, drilling, sampling, geophysical) so that the extent of any weak material 

is identified. In general, sands, gravels, and fine-grained nonplastic soils should be evaluated for 

susceptibility to liquefaction. The basic steps for the procedure are described below. It is 

important to determine whether a continuous weak layer could exist over some large area of the 

foundation or embankment. If the investigation is unable to rule this out, the analysis should be 

made, assuming that the layer is continuous. 

Before beginning an evaluation of liquefaction potential, appropriate ground motions must be 

established. 

Evaluations of liquefaction potential are usually made by indirect reference to the considerable 

body of case histories of earthquake-induced liquefaction and absence of liquefaction under 

earthquake loading. The most widely used procedures are based on correlations between results 

of standard penetration tests (SPTs) or cone penetration tests (CPTs), and field performance 

under various levels of loading. Note, however, that to verify the material types predicted by 

CPT test data, samples must be obtained, preferably by SPTs, which would also provide 

corroboration for the indications of the CPT regarding liquefaction potential. Soils that contain 

gravels can be tested using the Becker Hammer penetration test, with appropriate correlations to 

estimate equivalent SPT values from the Becker blowcounts (Harder and Seed 1986, Sy and 

Campanella 1994, Youd and Idriss 1997). As with the CPT, separate sampling holes are 

required because the BPT does not retrieve a sample. Down-hole or cross-hole measurements of 

shear-wave velocity (SWV) can also be used for gravelly soils (Andrus and Stokoe 1997). 

(2) Analysis for Static Factor of Safety Immediately After Shaking. If liquefaction would 

be triggered by the evaluation earthquake, a conventional slope stability evaluation using post-
32

earthquake properties and conditions should be made to determine whether instability would 

result. The critical slide masses typically consist of active and passive wedges with a neutral 

block in between (sliding on a thin horizontal layer of liquefied soil), but they can also be 

defined by circular slip surfaces. The strength of the liquefied material is generally estimated 

from correlations between SPT blowcount and strengths back-calculated from historic failures 

(Seed and Harder 1990), or by other in-situ or laboratory strength testing. If the factor of safety 

against sliding is greater than 1.0 for expected conditions following the earthquake, gross 

instability will presumably not occur. However, because of the great uncertainty in such 

calculations, post-liquefaction factors of safety are generally required to be a minimum of 1.2 to 

1.3, along with some limit being placed on the expected deformation. If the factor of safety is 

below 1.0, the only conclusion that can be drawn is that large deformations would occur; it is not 

possible to predict where the slide would stop without sophisticated deformation analysis by 

nonlinear finite-element or finite-difference codes. Section 3 below discusses methods for 

calculating the expected deformation. 

(3) Post-Earthquake Deformation Analysis

(a) General. If the post-earthquake stability analyses indicate factors of safety against sliding 

above 1.0, the expected amount of deformation can be estimated using several methods. The 

most rigorous method is to use finite element or finite difference programs such as TARA (Finn 

et al 1986), FLAC (Itasca Group 2002), or PLAXIS (PlaxisBV 2002) in which dynamic 

response, pore-pressure development, and deformations can be fully coupled. Simpler, more 

common methods for estimating deformation are the Newmark method (Newmark 1965) and the 

Makdisi-Seed simplified method based on the Newmark method (Makdisi and Seed 1977). 

These two are applicable only to slopes with post-earthquake factors of safety significantly 

above 1.0. Simpler still are deformation estimates based on historic performance with 

procedures (Byrne 1991, Swaisgood 1993). Included below is a step-by-step procedure to 

determine embankment/foundation liquefaction resistance. 

(b) Practical Approach. A practical engineering approach to analyzing an 

embankment/foundation for liquefaction resistance and resulting seismic stability using the 

techniques developed by the late Professor H. B. Seed and other researchers (Seed and Harder 

1990) is summarized in the following steps: 

• Conduct SPTs and/or CPTs at close spacing, as continuously as practical. In addition, 

obtain samples for laboratory index tests (grain size and Atterberg limits), and to confirm 

predictions of soil type from the CPT. 

• Establish the effective stresses existing in the embankment and foundation before the 

earthquake, preferably using a two-dimensional finite element program such as 

FEADAM (Duncan et al 1985). Well below the foundation contact, the one-dimensional 

approximation may be reasonable. 

• Select ground motions (acceleration vs. time) to be used in analysis. 
33

• Establish dynamic shear moduli of the soils in the embankment and foundation. These 

can be determined by in-situ geophysical measurements (down-hole and cross hole 

testing) and by comparison with published values for similar materials. Other needed 

dynamic properties, such as modulus degradation and damping ratio as a function of 

shear strain, have been investigated by Seed (et al 1984) and others. Available "generic" 

curves for damping and modulus degradation can often be used. 

• Calculate the earthquake-induced stresses in the embankment and its foundation. This 

can be performed in a one-dimensional columnar analysis using the computer program 

SHAKE (Schnabel et al 1972) if the suspected liquefiable material is in the foundation or 

near the lower part of the embankment. For high embankments or other site conditions 

where a two-dimensional dynamic analysis is warranted, a two-dimensional FEM 

program such as QUAD4M (Hudson et al 1994) may be needed. 

• Evaluate the liquefaction resistance of the embankment and foundation using the adjusted 

SPT, CPT, and/or SWV data using available correlations. 

• If the factor of safety against triggering liquefaction from the previous two steps is near 

or below 1, residual strength values should be assigned. This is done using (Seed and 

Harder 1990) correlation with SPT data or laboratory testing. It may also be necessary to 

reduce the strength of other zones below their drained strength due to excess pore 

pressure from cyclic loading or simply from undrained shearing, as in the case of 

normally consolidated clays. 

• Perform a static post-earthquake slope-stability analysis using the lower bound residual 

strength values for the liquefied zones. If this shows the factor of safety against sliding is 

below 1.0, the only conclusion that can be made is that instability could occur. If the 

embankment has a factor of safety against sliding above 1.0, a Newmark analysis, or 

preferably a large-strain finite-element or finite-difference analysis, can be used to 

evaluate the dynamic performance of the embankment, as described below. 

c. Deformation Analysis for Non-Liquefying or Non-Sliding Conditions. If instability is not 

expected or no liquefaction is anticipated, deformations should be estimated by one or both of 

the following methods, depending on the nature of the materials at the site. 

 

(1) Newmark Deformation Analysis

(a) General. The Newmark deformation analysis (Newmark 1965) is the most common 

method for evaluating the dynamic performance of an embankment dam. The method assumes 

that the mode of deformation in response to earthquake shaking will be the sliding of rigid blocks 

(masses) of dam and foundation material. Sliding is assumed to occur whenever the base 

acceleration exceeds the yield acceleration, which is the horizontal seismic acceleration that 

results in a factor of safety of exactly 1.0 using conventional slope stability analysis. Through 
34

the course of the earthquake ground motion, sliding stops and starts as the factor of safety rises 

above and falls below 1.0. 

(b) Input Motion. To perform this analysis, a time-history representation of the motions along 

the potential sliding surface is required. This motion is obtained based on a dynamic response 

analysis of the dam. 

(c) Makdisi-Seed Simplified Method. A simplified method, based on application of the 

Newmark method to several dams using several different earthquakes, was developed by Dr. 

Faiz I. Makdisi and Dr. H. Bolton Seed (Makdisi and Seed 1977). The resulting nomograph 

procedure is commonly referred to as the Makdisi-Seed Method. This approach provides an 

estimate of expected net displacement as a function of (1) pseudostatic horizontal yield 

coefficient for a potential slide mass; (2) peak effective horizontal acceleration within the slide 

mass; and (3) duration of strong shaking, approximated by an empirical correlation with 

earthquake magnitude. Makdisi and Seed also developed a simplified response analysis to find 

the peak acceleration of the slide mass that treats the dam embankment as a triangular prism of 

elastic material and approximates its response by a Bessel series. 

(d) Other "Newmark-Type" Methods. Several other methods based on the Newmark 

procedure have been developed. The most basic of these is the Sarma analysis, which represents 

the earthquake by a horizontal acceleration and computes the horizontal movement of the mass. 

Subsequent computation of loss of crest elevation, based on the shape of the potential sliding 

surface, is required. More rigorous analyses include both horizontal and vertical accelerations, 

as well as variations of pore pressures and shear strength with time during the earthquake (Von 

Thun and Harris 1981). A detailed case study on the deformation analysis for Eastside Reservoir 

Project, Riverside County, California is available (USCOLD 1996). Another study (Hynes and 

Franklin 1984) concluded from a series of Newmark analyses that deformations of an 

embankment dam would be fairly minor as long as the peak horizontal ground acceleration is 

less than 3 times the yield acceleration (provided that there would be no excess pore pressures 

from shaking and that undrained shear strengths are properly accounted for). This is consistent 

with observed performance of dams in earthquakes. 

(e) Analysis Results. Once one has obtained an estimate of deformation from the Newmark 

(or other) method, the expected performance of the dam under seismic loading is judged 

considering the severity of deformation (loss of available freeboard and potential for cracking 

leading to failure of the embankment or foundation by internal erosion). Limiting the amount of 

allowable deformations along critical failure surfaces to two feet has been used as a criterion by 

some agencies. 

(2) Generalized Settlement. In addition to deformation of the embankment from slipping in 

response to earthquake shaking, the dam may settle in response to the stresses developed in each 

soil element. This generalized settlement can be estimated by using soil mechanics 

consolidation, empirical, and/or finite element procedures. An empirical relationship has been 

developed (Jansen 1988) for estimating settlement of an embankment dam under seismic loading 

if the dam and foundation are not susceptible to liquefaction. 
35

d. Pseudostatic Analysis. A pseudostatic analysis (sometimes called seismic coefficient 

analysis) should only be considered as an index of the seismic resistance available in a structure 

not subject to build-up of pore pressure from shaking. It is not possible to predict failure by 

pseudostatic analysis, and other types of analysis are generally required to provide a more 

reliable basis for evaluating field performance. However, if there are no soils present that would 

develop excess pore pressure from shaking, and undrained shear strengths are properly 

incorporated where needed, a pseudo-static factor of safety greater than 1.0 is very strong 

evidence that there would be little or no damage to the dam from an earthquake. 
37

V. EVALUATION OF STRUCTURAL ADEQUACY FOR EARTHQUAKE LOADING 

A. Performance Criteria

Dams should be capable of withstanding the MDE without failure resulting in a catastrophic loss 

of the reservoir, or should present an acceptably low risk of failure if that is how the relevant 

agency approaches decision making. Damage without catastrophic release of the reservoir may 

be acceptable in some cases, provided the risk of release is suitably low. However, the extent of 

damage allowed should not impair the ability to quickly and safely draw down the reservoir to 

alleviate any potential threat to downstream life and property. Even if there is no potential for 

sudden loss of the reservoir, determining the acceptable level of damage to a project may be 

linked to the ability to quickly undertake repairs and return the project to full operation. If 

drawing down the reservoir to undertake repairs cannot be done easily, then significant damage 

may not be acceptable. In addition, agencies typically require that dams should be capable of 

resisting an OBE without sustaining serious damage (or present a suitably low risk of damage), 

so that they remain operational and do not require extensive repair work. All systems and 

components necessary to maintain the project should be designed to remain operable during and 

after the OBE (or have sufficiently low risk of becoming inoperable). Other factors that may 

play a role in determining the acceptability of the performance of the dam following an 

earthquake are (1) the use of the reservoir; and (2) the ability or lack thereof to quickly repair a 

damaged structure. A primary water supply facility damaged from an earthquake may cause 

severe economic and health consequences while projects with lost freeboard and cracking may 

be vulnerable to further damage from after shocks or the next significant flood. 

B. Evaluating Analysis Results for Concrete Dams 

 1. Dynamic Analyses. Results of dynamic analyses are generally evaluated in terms of 

compressive and tensile strengths of the concrete. The compressive stresses resulting from the 

combination of static and earthquake loads usually remain below the dynamic strength of the 

concrete. However, since the mere occurrence of tensile stresses does not necessarily lead to 

failure, the significance of predicted tensile stresses is not evaluated as easily. The number and 

amplitudes of stress cycles that exceed the dynamic tensile strength are taken into account for 

this purpose in linear analysis. To evaluate the effects of stresses that exceed the tensile strength, 

sound engineering judgment is required and should be based on the expected effects of nonlinear 

behavior and the past performance of dams under similar earthquake loadings. To estimate the 

extent of cracking, one must consider nonlinear behavior resulting in stiffness degradation and 

energy absorption. Nonlinear behavior from cracking reduces the stiffness of the dam and shifts 

the dam’s response into other frequency contents of the ground motion. The energy level of the 

earthquake corresponding to the frequency of the cracked structure may or may not be more 

severe than when uncracked. As a result, the peak values of tensile stress and the extent of 

tensile zones may increase or decrease, and large tensile stresses given by linear elastic analysis 

may or may not necessarily indicate an unsafe condition. They may, in fact, be “artifacts” of the 

analysis rather than real behavior. The past performance of concrete dams under large 

earthquake loading is discussed later in this section. A nonlinear analysis should be performed if 

the response of the dam would be influenced significantly by nonlinearity from material behavior 

or changes in geometry. For an arch dam, this might include 1) cantilever tensile stresses larger 
38

than the tensile strength of the concrete over significant areas of the dam; 2) a long duration 

earthquake; 3) opening and closing of contraction joints indicated by simultaneous arch tensions 

on the upstream and downstream faces; and 4) large displacements or distortions of the arch. 

 2. Sliding and Overturning Stability. Pseudostatic methods are generally discouraged and 

should only be used for screening from further consideration those dams where a seismic 

stability failure is highly improbable. Structures that fail to meet the prescribed pseudostatic 

stability requirements (i.e., sliding safety factors and resultant location) should be subjected to 

in-depth study, but should not be considered unsafe until the in-depth analysis is performed. A 

better screening devise used by some federal agencies, discussed above under section c. Sliding 

Stability (1) Methods of Analysis, is to conduct a post earthquake stability analysis to 

demonstrate seismic stability. Under this type of analysis, conservative assumptions are used to 

reduce the amount of information needed of the ground motions and the exploration and testing 

required of the dam/foundation material properties. The failure to meet these requirements 

should only suggest the need for dynamic analyses that fairly assess the demands placed on the 

dam and foundation during a major earthquake. 

Dynamic time-history analyses are used to determine the displacements and stresses experienced 

by the dam and foundation. Evaluation of the results is used to determine if there is a risk of a 

stability failure. Physical model studies of the Koyna Dam conducted at the University of 

California at Berkeley (Niwa and Clough 1980) demonstrated the inherent capability of a 

cracked dam to withstand severe earthquake shaking without a sliding or overturning failure 

even though extreme rocking of the cracked upper section of the model occurred. However, this 

is not to say that all gravity dams are stable during an earthquake. Concrete dams (gravity, arch, 

or buttress dam) and sites are very unique and should all be evaluated for stability. Consequences 

from a dam failure can be too large for anything less to be acceptable. 

C. Evaluating Analysis Results for Embankment Dams 

1. General. In some cases, the analyses may indicate that the dam is either clearly safe or 

clearly unsafe. Frequently, however, judgments concerning the safety of the dam must take 

into account not only the results of the analyses but also the level of confidence that can be put 

in those analyses and underlying assumptions and, to some extent, the consequences of 

misjudging the level of uncertainty. 

2. Stability Analyses. If the results of post-earthquake sliding stability analyses for critical 

failure surfaces indicate a safety factor well above 1.0 (e.g., 1.25 or greater) using the strengths 

expected after the earthquake, experience from past earthquakes suggests that deformations 

will be small and the dam will perform satisfactorily. Confidence in the safety of the dam 

decreases when the factor of safety against triggering of liquefaction is 1.0 or less and a postearthquake sliding factor of safety less than or approaching 1.0 is calculated using residual 

shear strengths for materials assumed to be liquefied. In general, many analyses have shown 

that when a wedge or circular sliding surface has a low post-earthquake sliding factor of safety, 

the deformations on these sliding planes will be excessive. If these failure planes are critical to 
39

the overall integrity of the dam, deformations may lead to failure of the dam by overtopping or 

internal erosion. 

3. Deformation Analysis. Predicted deformations, whether from a Newmark analysis or 

nonlinear finite-element or finite-difference analysis, should not be greater than what the dam 

can safely withstand without catastrophic release of the reservoir. Important factors to consider 

in making this determination are discussed below. Deformation analyses can be made for three 

conditions: 1) liquefaction would not occur; 2) liquefaction may occur but instability would not; 

and 3) liquefaction may occur, resulting in instability. In the first two conditions, judgment is 

required to determine whether the predicted deformations along the critical failure surfaces are 

small enough that cracking of the embankment/foundation materials does not occur that could 

eventually cause a piping failure of the dam. A determination also must be made whether the 

post-earthquake sliding factors of safety and available freeboard are adequate to ensure the dam 

would not be overtopped and would be able to safely retain the reservoir. The predicted 

deformations are very sensitive to the post-earthquake strength that is used in the analysis. The 

critical question is often will liquefaction be triggered and, if it is, what is the appropriate 

residual shear strength parameter to use in the analysis. Confidence, or lack thereof, in the 

strengths that are used, and hence confidence in the predicted deformations, are important factors 

to consider in evaluating the results of a deformation analysis. In the case where large 

deformations or relatively low post-earthquake sliding factors of safety are predicted, the 

question is generally whether a lowered reservoir level can be safely maintained without the 

potential loss of the reservoir. A comprehensive review of the factors to be considered in the 

earthquake resistance design of dams, as well as a review and commentary on the field 

performance of dams during earthquakes, can be found in Seed (1979). A compilation of 

relevant papers can also be found in Duncan (1990). 

D. Past Experience of Dams Shaken by Earthquakes 

USCOLD published a report (USCOLD 1992) listing the observed performance of various types 

of dams during earthquakes. Some of these case studies are listed in the following sections. In 

addition to these case studies, a summary of the performance of embankment dams was 

documented by Swaisgood (1993). This information was updated by for the Eastside Reservoir 

Project (Ebasco et al 1994). 

1. Concrete Dams. No major concrete dam is known to have failed due to earthquake-induced 

ground motion, although several are known to have experienced strong ground motion. The 

following is a review of some of these experiences. 

a. Gravity Dams 

(1) The Crystal Springs Dam, a 154-foot-high gravity-arch dam located only one-fourth of a 

mile from the San Andreas Fault, survived the 8.3 magnitude (estimated) 1906 San Francisco 

earthquake with no apparent damage. 
40

(2) Several 200-foot-high gravity dams in Japan experienced earthquakes producing an MM 

intensity of VIII in the area of the dams and were not damaged. However, some examples exist 

of partial earthquake damage to concrete dams in Japan. In 1923, the piers of spillway gates at 

the top of a hydroelectric intake dam cracked at their bases. These piers were of plain concrete, 

indicating that reinforcing steel should be used in piers of dams built in areas where large 

earthquakes are anticipated. In 1943, a gravity dam for deposition of muck from a mine was 

sheared at a horizontal section at the elevation of approximately two-thirds up the dam height. 

However, the cross section of this dam was smaller than that of a water storage dam, probably 

because the pressure exerted by deposited muck was less than the water pressure. 

(3) In 1967, the Koyna Dam, a 340-foot-high gravity dam in India, survived a near-field 

magnitude 6.4 earthquake, with an MM intensity of VIII or IX at the site. A peak horizontal 

acceleration of 0.51g perpendicular to the dam axis and a peak vertical acceleration of 0.36g, 

were measured at the dam. The dam experienced major cracking on both upstream and 

downstream faces of the non-overflow monoliths. The overflow monoliths were not damaged. 

A dynamic analysis of the Koyna Dam was performed using two-dimensional finite element 

methods that incorporated hydrodynamic interaction and assumed linear elastic behavior in the 

concrete and foundation. The analysis indicated tensile stresses in the upper part of the nonoverflow monoliths exceeded the tensile strength of the concrete up to three times. Analysis of 

the overflow monolith indicated maximum tensile stresses approximately equal to the concrete 

tensile strength. 

(4) Hoover Dam, a 726-foot-high curved gravity dam, has been suspected of being the cause of 

moderate reservoir-triggered seismicity of Richter Magnitude M5 or less (USCOLD 1992). No 

damage to the dam has occurred due to these earthquakes. 

(5) In 1995, the concrete dams of Sengari and Aono, located 15 km and 30 km north of the 

earthquake source in Kobe, Japan, were shaken by the Great Hanshin earthquake of Richter 

magnitude M7.2, but suffered no damage (Krinitzsky et al 1995). These concrete dams were 

founded on rock and received relatively low levels of ground motion. The level of ground 

motion is based on the fact that there was little damage to residences with tile roofs and unstable 

grave markers in a cemetery nearer the closest dam were not overturned. Overturning of grave 

marker stones approximately 4-feet high with a 4-inch-square base indicated horizontal ground 

motion of approximately 0.2g. Peak rock acceleration within the source area in Kobe registered 

an equivalent 0.45g. 

b. Arch Dams 

(1) In 1971, the Pacoima Dam, a 372 foot high arch dam, survived the magnitude 6.6 San 

Fernando earthquake, the epicenter of which was only four miles north of the dam. Despite the 

estimated 0.6 to 0.8g foundation acceleration, there was no evidence of distress within the dam. 

However, a separation of the arch dam proper and the left abutment thrust block occurred in the 

upper part of the dam; the thrust block and upper abutment moved away from the dam. A threedimensional linear finite element analysis of this arch dam was performed using the 

accelerograms (modified) recorded on the rock above the left abutment of the dam during the 
41

San Fernando event. The analysis indicated tensile stresses in the dam that should have caused 

cracking due to the earthquake; however, on-site visual examination of the dam did not reveal 

cracking of the concrete. Similar studies of the Big Tujunga concrete arch dam, which was also 

shaken by the San Fernando event, have been conducted using three-dimensional finite element 

procedures. The analysis results showed peak tensile stresses that should have caused cracking, 

but again there was no physical evidence of any structural damage to the dam from that 

earthquake. 

(2) In 1976, several Italian arch dams (Ambiesta, Maina di Sauris, and Barcis) were subjected 

to a series of earthquakes with reported intensities as high as MM IX in the vicinity of the dams. 

At Ambiesta Dam, a 194 foot high arch dam, the peak ground acceleration was recorded to be 

0.33g at the right abutment (USCOLD 1992). No structural damage was reported at any of these 

dams during inspection after the earthquakes. 

(3) In 1994, the Pacoima Dam was again severely shaken by the Northridge/San Fernando 

Earthquake, a Moment Magnitude of M6.7 with its epicenter approximately 11 miles southwest 

of the site (Morrison Knudsen 1994). Peak horizontal acceleration values of up to 0.5g 

horizontal and 0.4g vertical were measured near the base of the dam. Cross-canyon accelerations 

on the abutments were measured at 2.0g horizontal and 1.3g vertical. There were three 

significant consequences of the earthquake on the dam: (1) cracking in the left block of the arch 

which extends from the upstream to the downstream face; (2) permanent upstream deflection of 

the crest of the dam (on the order of 1.8 inches); and (3) opening of the contraction joint between 

the dam and the left thrust block. Two rock masses, one critical to the stability of the left 

abutment of the dam, permanently displaced away from the dam (on the order of inches) during 

the earthquake. The spillway tunnel and covered downstream chute suffered considerable 

damage as a result of rockslides. The Pacoima Reservoir, which is maintained low to provide 

storage for floodwater, was at about 65 percent of the height of the dam (at station 0+00) at the 

time of the earthquake. 

(4) In 1992, Bear Valley Dam survived the M6.7, Big Bear Lake Earthquake, located 

approximately 8 miles from the epicenter. The Bear Valley Dam was originally constructed as a 

multiple arch dam. However, in 1989 the multiple arch bays were filled with mass concrete. No 

damage was reported to the dam. 

(5) Some of the observed ability of arch dams to resist large earthquakes, even though 

calculations show large tensile stress, may be due to the ability of arch dams to transfer load. 

When cracking occurs as a result of large tensile cantilever stresses, the decrease in flexibility of 

the section will cause loads to transfer to adjacent arches and cantilevers, thereby reducing the 

areas that are over-stressed. Vertical cracking may be pre-empted by additional damping, due to 

nonlinearity of material properties or the computed, but nonexistent, formation of horizontal 

tensile stresses across contraction joints. The implementation of good defensive design 

mechanisms in the construction of arch dams may have contributed to their sound performance. 

These factors were discussed at the beginning of this chapter and include adequate abutment and 

foundation investigations, good design practices that alleviate local stress concentrations, and an 

effective quality control program to assure the dam is constructed as designed. 
42

c. Buttress Dams 

(1) In 1962, the Hsingfengkiang Dam, a 345 foot high buttress dam in China, survived a nearfield magnitude 6.1 earthquake, but developed horizontal cracks at a change of section in the 

non-overflow blocks on each side of the spillway, although no leakage occurred (USCOLD 

1992, Clough and Ghanaat 1993). No instrumentation was installed at the time of the main 

shock, but strong motion seismographs were brought in to record the aftershocks and a 

magnitude 4.5 aftershock produced a peak acceleration of 0.54g at the dam crest. 

(2) In 1990, the Sefid Rud Dam, a 106-meter-high buttress dam in northern Iran, was damaged 

by an earthquake of Richter Magnitude of M7.3 at a distance of 5 km (Ahmadi et al 1992, 

Clough and Ghanaat 1993). The principal damage to the central monoliths were cracks at lift 

joints extending from the dam face through the buttress face and web. These occurred adjacent 

to a change of slope near the crest of the dam and were accompanied by a 20 mm sheardisplacement toward downstream. Offsets between buttresses indicated about 50 mm of 

distortion of the whole valley (USCOLD 2000). There was minor damage and displacement on 

all of the gates. This event was approximately equivalent to the MCE for the site. By 

extrapolation from the 15 accelerograms from nearby sites, the peak horizontal ground 

acceleration at the dam was estimated as 0.71g, greatly exceeding the design earthquake for the 

dam. 

2. Embankment Dams. The behavior of earth and rock-fill dams when subjected to 

earthquake shaking depends strongly on the design of internal drainage features and the method 

of construction used. A comprehensive review of past experience with numerous embankment 

dams shaken by six earthquakes produced the following conclusions (Seed et al 1978, Seed 

1979). 

a. Hydraulic fill dams have been found to be vulnerable to failures under unfavorable 

conditions, in particular shaking produced by strong earthquakes. The near failure of the Lower 

Van Norman Dam during the 1971 San Fernando earthquake is the most famous case history in 

that it triggered the development of modern methods for the dynamic analysis of embankment 

dams (USCOLD 1992). This earthquake, with a Richter Magnitude of M6.5, was centered 

approximately 11.2 km from the dam. 

b. Virtually any well-built compacted embankment dam can withstand moderate earthquake 

shaking, with peak accelerations of 0.2g and more, with no detrimental effects. 

c. Dams constructed of clay soil on clay or rock foundations have withstood extremely strong 

shaking, ranging from 0.35 to 0.8g, from a magnitude 8.25 earthquake with no apparent damage. 

This conclusion is based on the results of the performance of 33 embankment dams that were 

shaken during the 1906 San Francisco earthquake. These dams range in height from 15 to 140 

feet, and are located within 37 miles (60km) of the San Andreas Fault. Almost one-half (16) 

were located within 5 miles (8km) of the causative fault. Explorations performed in the 1980's 

and observations of piezometers indicate that puddled cores in some of the higher dams may 

have kept the downstream slopes from being saturated. Performance of embankment dams in 
43

earthquakes subsequent to the Seed publication (Seed et al 1978) has also been good, except 

when liquefaction or unusual circumstances have been involved. See Matahina Dam below. 

d. Two rockfill dams have withstood moderately strong shaking with no significant damage. If 

the rockfill dam is kept dry by means of an impervious facing, they should be able to withstand 

extremely strong shaking with only small deformations. The strongest shaking to which a 

concrete face rockfill (CFR) dam has been subjected to is around 0.2g. In areas of moderate 

seismic shaking, CFR dams have been built with slopes of the order of 1H:1.3V. Analysis of the 

dams under these conditions show the dam should have an acceptable level of seismic 

performance. When the design earthquake is as high as Magnitude 7.5 and capable of producing 

a peak ground acceleration of 0.5g, the desirable slope is on the order of 1H:1.65V (Seed et al 

1985). However site-specific analysis should always be performed for critical structures. 

e. The performance of modern compacted embankment dams was further demonstrated in 1994 

when the Los Angeles Reservoir, a modern reservoir constructed in 1979 comprising two rolled 

fill embankments, was severely shaken by the Northridge Earthquake, a magnitude ML of 6.8 

with its epicenter approximately 7 miles south of the site (Davis and Sakado 1994). The Los 

Angeles Dam (LAD), on the south side of the reservoir, is 155 feet high. The North Dike (ND), 

on the northern side of the reservoir, is 117 feet high. Both dams are founded on Saugus 

Formation bedrock, are zoned with shell material on the upstream and downstream slopes, and 

contain a chimney drain at the center section. The LAD also has a clay zone upstream of the 

chimney drain. The degree of compaction of fill, clay zone, and blended sand and gravel was 

specified to be compacted to 93 percent modified Proctor (ASTM D1557 2002) and was 

carefully controlled during construction. Peak horizontal acceleration values of up to 0.43g were 

measured on the right abutment and 0.56g on the crest of the LAD. A survey of the reservoir 

following the earthquake showed 3-1/2 in. of crest settlement and lateral downstream movement 

of over 1 in. on the crest of LAD. The ND showed no more than 1-1/4 in. of crest settlement and 

lateral downstream movement of less than 1/3 in. on the crest. The reservoir was within nearly 

80 percent of its capacity, as defined by the high water elevation, at the time of the earthquake. 

f. A few recent case histories have provided opportunities to verify analysis procedures for 

estimating earthquake-induced deformations. In each of these cases, instrumental measurements 

have been made of accelerations and displacements during and after strong ground shaking, 

allowing comparison with numerical model predictions of the same quantities. 

(1) Elgamal (et al 1990) describe the dynamic response and permanent deformations recorded 

at La Villita Dam in Mexico consequent to five earthquakes, most recently the September 19, 

1985 Michoacan Earthquake. Yielding was confirmed to have occurred within the embankment 

by asymmetry of acceleration records recorded at various points on the dam, i.e., some of the 

peaks in the acceleration history were truncated as material slipped in the vicinity of the 

accelerograph. The authors used simplified displacement estimation techniques involving a 

“sliding rock” analogy (Newmark 1965) to successfully predict stick-slip type deformations and 

to evaluate the accumulation of displacement over several earthquake events. 
44

(2) Matahina Dam, New Zealand was shaken and deformed by the 1987 Edgecumbe 

Earthquake (M6.7)and the dynamic response and displacements were recorded by extensive 

instrumentation (Finn et al 1994). A nonlinear finite element computer code, TARA-3 (Finn et 

al 1986), was employed to simulate the performance of the Matahina Dam, using engineering 

properties carefully determined by laboratory and field-testing. Deformations were generally 

small (less than 0.5m), but the results of this study boosted the confidence of geotechnical 

engineers to analytically estimate earthquake behavior of embankment dams for stronger events. 

About 10 months later, a sinkhole appeared near one abutment, and fairly extensive erosion 

damage was found in the low-plasticity core (Gillon and Newton 1991). The earthquake was 

thought to have accelerated or reactivated the erosion damage that was discovered and repaired 

shortly after first filling. 

g. To summarize, experience has shown that well-compacted, impervious rolled-fill dams are 

resistant to earthquake forces, provided they are constructed on rock or overburden foundations 

resistant to liquefaction. The same is true of well-drained, compacted rockfill dams or dumped 

rockfill dams with impervious cores, although some surface deformation can be expected on 

steep slopes. Rockfill dams with membrane facing (e.g., concrete) have performed well under 

strong shaking; however, permanent displacement or cracking of the facing can be expected 

which may require remediation following the seismic event. Low-density embankments built of 

low plasticity granular soils, especially hydraulic or semihydraulic fills, are highly susceptible to 

earthquake damage due to the potential for liquefaction. Existing dams that have been 

constructed on foundations of low density cohesionless materials formed in continuous layers 

also may be subject to excessive deformations during the seismic event due to liquefaction. 

E. Evaluating Existing Dams 

The criteria and analysis methods cited in these guidelines may differ significantly from those in 

use when many older dams were designed. Therefore, some existing structures may be found 

deficient using the procedures outlined. If the analyses indicate the dam is over-stressed or 

unstable under the earthquake conditions examined, the consequences of failure should be 

determined and assessed. A decision analysis, scoped to the magnitude of potential 

consequences, should be used as guidance for further action. If the safety evaluation indicates 

that failure of the dam does not pose a hazard to downstream life or property, remedial action 

may not be necessary. However, this position should be fully documented. 

F. Seismic Remediation of Earth Dams Subject to Liquefaction 

Present methods available for engineering remediation of seismic deficient earth dams are listed 

below. 

1. Excavate and Replace. This method provides positive assurance that what is designed is 

actually constructed in the field. This approach is viable when the suspect material is near the 

surface and it can be removed down to a firm foundation. 

2. In Situ Densification or Cementing. Stone columns, vibrocompaction, compaction 

grouting, and other methods of soil mixing and densification. Compaction grouting requires 

extreme caution because of the possibility of hydraulic fracturing in the embankment/foundation. 
45

Verification of the amount of improvement should be required when using these methods. 

3. Berms/buttresses. These are used to increase the effective overburden pressures and thus 

decrease the potential for liquefaction. It also increases the factor of safety by lengthening the 

potential failure surface. 

4. Drains. Use of drains to lower the phreatic surface in the embankment can be an effective 

way to treat potentially liquefiable material. However, dependence on drains to reduce the 

buildup of excess pore pressure in potentially liquefiable soils during an earthquake creates many 

uncertainties and is generally not a recommended practice. One unknown that is a major factor 

in the effectiveness of the drains is the permeability of the problem material. 

5. Additional Freeboard. Additional freeboard can be obtained by either raising the 

embankment crest or restricting the reservoir surface. This would lower the potential for loss of 

the reservoir if large deformation of the dam were to occur during the seismic event. It should be 

recognized, however, that a crest raise to increase the freeboard adds weight to the crest, 

increasing the driving force for instability or deformation. 
APPENDIX A 

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Earthquakes, Volume II” 

Von Thun and Harris 1981

Von Thun, J. L., Harris, C.W., 1981. “Estimated Displacements of Rockfill Dams Due to 

Seismic Shaking”, Proceedings of the International Conference on Recent Advances in 

Geotechnical Earthquake Engineering and Soil Dynamics, Vol. 1, St. Louis, MO, April 26-May 

3, 1981, pp. 417-423 

Westergaard 1933

Westergaard, H. M., 1933. “Water Pressure on Dams during Earthquakes”, Transactions of 

ASCE 

Youd and Idriss 1997

Youd, T. L., Idriss, I. M., Editors, 1997. “NCEER Workshop on Evaluation of Liquefaction 

Resistance of Soils, January 5-6, 1996, Salt Lake City, UT”, National Center for Earthquake 

Engineering Research, NCEER 97-0022 

 A-7 
APPENDIX B-1 

BIBLIOGRAPHY 

SEISMOLOGY, DETERMINISTIC SEISMIC HAZARD ANALYSIS, PROBABILISTIC 

SEISMIC HAZARD ANALYSIS, & GROUND MOTIONS 

Algermissen 1983 

Algermissen, S. T. 1983. An Introduction to the Seismicity of the United States. Engineering 

Monograph (MNO-7), Earthquake Engineering Research Institute, Oakland, CA 

Ambraseys 1988 

Ambraseys, N. N. 1988, "Engineering Seismology," Earthquake Engineering and Structural 

Dynamics, Vol. 17, No. 1, pp. 1-105 

Bolt 1988 

Bolt, B.A., 1988, Earthquakes: W. H. Freeman and Co., New York 

Department of the Army 1995 

Department of the Army. 1995. Engineering Manual-Response Spectra and Seismic Analysis for 

Concrete Hydraulic Structures, EC l110-2-6050, Office, Chief of Engineers, Washington, D.C. 

Green 1992

Green, R. 1992. Selection of Ground Motions for the Seismic Evaluation of Embankments, ASCE 

Specialty Conference on Stability and Performance of Slopes and Embankments 11, A 25-Year 

Perspective, Geotechnical Special Publication No. 31, Vol. 1, pp. 593-607 

Hudson 1979 

Hudson, D. E. 1979. Reading and Interpreting Strong Motion Accelerograms, Earthquake 

Engineering Research Institute, 499 14th Street, Oakland, CA, p. 112 

Idriss 1993 

Idriss, I. M. 1993 (Mar). Procedures for Selecting Earthquake Ground Motions at Rock Sites, A 

Report to the National Institute of Standards and Technology, U.S. Dept. of Commerce, 

Gaithersburg, MD 

Joyner and Boore 1988 

Joyner, W. B. and Boore, D. M. 1988. Measurement, Characterization and Prediction of Strong 

Ground Motion, Earthquake Engineering and Soil Dynamics 11 -Recent Advances in Ground 

Motion Evaluation, ASCE Geotechnical Special Publication No. 20, pp. 43-102 

Krinitzsky and Chang 1987 

Krinitzsky, E. L. and Chang, F. K. 1987. "State-of-the-Art for Assessing Earthquake Hazards in 

the United States, Report 25 Parameters for Specifying Intensity-Related Earthquake Ground 

Motions," MP S-73-1, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, 

MS 

 B-1 
Krinitzsky and Others 1987 

Krinitzsky, E. L., Chang, F. K., and Nuttli, 0. W. 1987. "State-of-the-Art for Assessing Earthquake

Hazards in the United States, Report 26-Parameters for Specifying Magnitude-Related Earthquake 

Ground Motions," MP S-73-1, U.S. Army Corps of Engineers, Waterways Experiment Station, 

Vicksburg, MS 

Krinitzsky and Others 1993 

Krinitzsky, E. L., Gould, J. P., and Edinger, P. H. 1993. Fundamentals of Earthquake Resistant 

Construction, John Wiley and Sons, Inc. New York, NY 

Leeds 1992 

Leeds, D. L. 1992. "State-of-the-Art for Assessing Earthquake Hazards in the United States, 

Report 28 Recommended Accelerograms for Earthquake Ground Motions," MP S-73-1, U.S. Army 

Corps of Engineers, Waterways Experiment Station, Vicksburg, MS 

National Research Council 1988 

National Research Council. 1988. Probabilistic Seismic Hazard Analysis: National Academy 

Press, Washington, D.C., p. 97 

Newmark and Hall 1983 

Newmark, N.N., and Hall, W.J. 1983. Earthquake Spectra and Design, Earthquake Engineering 

Research Institute, 499 14th Street, Oakland, CA, p. 103 

Nuttli 1981 

Nuttli, O.W., “Similarities and Differences Between Western and Eastern United States 

Earthquakes and their Consequences for Earthquake Engineering,” Earthquakes and Earthquake 

Engineering: Earthquakes in the Eastern United States, Vol. 1, ed. J. E. Beavers, 1981, pp. 25-52 

Reiter 1991 

Reiter, L. 1991. Earthquake Hazard Analysis -Issues and Insights. Columbia University Press. 

New York, NY 

Schneider 1993 

Schneider, J. F. 1993, Guidelines for determining design basis ground motions. Volume 1: Method 

and guidelines for estimating earthquake ground motion in eastern North America, EPRI TR102293: Electric Power Research Institute, Palo Alto, CA 

Schwartz 1988 

Schwartz, D.P. 1988. Geologic Characterization of Seismic Sources: Moving Into The 1990's, 

Proceedings, Earthquake Engineering and Soil Dynamics II --Recent Advances in Ground-Motion 

Evaluation, ASCE Geotechnical Special Pub. No. 20, pp. 1-42 

 B-2 
APPENDIX B-2 

BIBLIOGRAPHY 

CONCRETE GRAVITY DAMS, ARCH DAMS, BUTTRESS 

DAMS AND STRUCTURES APPURTENANT TO DAMS 

Chandrashaker and Humar 1993 

Chandrashaker, R. and Humar, J.L. 1993. Fluid-Foundation Interaction in the Seismic Response of 

Gravity Dams, Earthquake Engineering and Structural Dynamics, Vol. 22, pp. 1067-1084 

Chavez and Fenves 1994 

Chavez, J.W. and Fenves, G.L. 1994. EGAD-SLIDE: A Computer Program for the Earthquake 

Analysis of Concrete Gravity Dams Including Base Sliding, Rept. UCB/SEMM-94/02, Dept. of 

Civil Engrg., Univ. of California at Berkeley, Berkeley, CA 

Chavez and Fenves 1995 

Chavez, J.W. and Fenves, G.L. 1995. Earthquake Response of Concrete Gravity Dams Including 

Base Sliding, Journal of Structural Engineering, ASCE, Vol. 121, No. 5, pp. 865-875 

Chopra 1967 

Chopra, A.K. 1967 (Dec). Hydrodynamic Pressures on Dams During Earthquakes, ASCE, Journal 

of Engineering Mechanics Division, Vol. 93, No. EM6, pp. 205-223 

Chopra 1978 

Chopra, A.K. 1978 (Jun). Earthquake Resistant Design of Concrete Gravity Dams, ASCE, Journal 

of the Structural Division, Vol. 104, No. ST6, pp. 953-971 

Chopra 1992 

Chopra, A.K. 1992 (July). Earthquake Analysis, Design, and Safety Evaluation of Concrete Arch 

Darns, paper presented at Tenth World Conference on Earthquake Engineering, Madrid, Spain, and 

Published in report entitled Earthquake Engineering Research at Berkeley -1992, Rept. 

UCBfEERC-92/13, University of California, Berkeley CA. 

Chopra 1995 

Chopra, A. 1995. Dynamics of Structures -Theory and Applications to Earthquake Engineering, 

Prentice-Hall, p. 29 

Chopra and Tan 1989 

Chopra, A.K. and Tan, H. 1989 (Mar). Simplified Earthquake Analysis of Gated Spillway 

Monoliths of Concrete Gravity Darns, U.S. Army Corps of Engineers, Waterways Experiment 

Station Technical Report SL-89-4, Vicksburg, MS

Chopra and Tan 1992 

Chopra, A. K. and Tan, H. 1992. Modeling of Dam Foundation Interaction in Analysis of Arch 

Dams, Proc. 10th World Conference on Earthquake Engineering, Madrid, Spain 

 B-3 
Chopra and Zhang 1991 

Chopra, A.K. and Zhang, L. 1991 (May). Base Sliding Response of Concrete Gravity Dams to 

Earthquakes, Rept. UCBiEERC-91/05, Univ. of California, Berkeley, CA

 

Chopra and Zhang 1991 

Chopra, A. K. and Zhang, L. 1991 (Dec). Earthquake-Induced Base Sliding of Concrete Gravity 

Dams, Journal of Structural Engineering, ASCE, Vol. 117, No. 12, pp. 3698-3719 

Clough and Ghanaat 1993 

Clough, R. W. and Ghanaat, Y. 1993. Concrete Dams: Evaluation for Seismic Loading, in Dam 

Safety Evaluation Proceedings, Vol. 4, Grindelwald, Switzerland, pp. 137-169 

Clough and Zienkiewicz 1982 

Clough, R. W. and Zienkiewicz, O. C. 1982. Finite Element Methods in Analysis and Design of 

Dams, Committee on Analysis and Design of Dams

Damay and Adegha 1993 

Danay, A. and Adeghe, L. N. 1993 (Jan). Seismic-Induced Slip of Concrete Gravity Dams, Journal 

of Structural Engineering, ASCE, Vol. II 9, No. 1, pp. 108-129 

Department of the Army 1993 

Department of the Army 1993. Engineering Manual-Arch Dam Design, EM 1110-2-2201, Office, 

Chief of Engineers, Washington, D.C. 

Department of the Army 1995 

Department of the Army 1995. Engineering Manual-Gravity Dam Design, EM 1110-2-2200, 

Office, Chief of Engineers, Washington, D.C. 

Dowling and Hall 1989 

Dowling, M. J. and Hall, J. F. 1989 (Apr). Nonlinear Seismic Analysis of Arch Dams, Journal of

Engineering Mechanics, ASCE, Vol. II 5, No. 4, pp. 768-789 

El-Aidi and Hall 1989 

El-Aidi, B. and Hall, J. 1989. Non-Linear Earthquake Response of Concrete Gravity Dams Part 1: 

Modeling, Earthquake Engineering and Structural Dynamics, Vol. 18, pp. 837-851 

El-Aidi and Hall 1989 

El-Aidi, B. and Hall, J. 1989. Non-Linear Earthquake Response of Concrete Gravity Dams Part 2: 

Behavior, Earthquake Engineering and Structural Dynamics, Vol. 18, pp. 853-865 

Fenves and Chopra 1983 

Fenves, G. and Chopra, A. K. 1983 (Nov-Dec). Effects of Reservoir Bottom Absorption on 

Earthquake Response of Concrete Gravity Dams, Vol. 11, No. 6, pp. 809-829 

 B-4 
Fenves and Chopra 1984 

Fenves, G. L. and Chopra, A. K. 1984. EGAD-84: A Computer Program for the Earthquake 

Analysis of Concrete Gravity Dams, Rept. UC/EERC-84/11, Univ. of California, Berkeley, CA 

Fenves and Chopra 1984 

Fenves, G. and Chopra, A. K. 1984 (Sept-Oct). Earthquake Analysis of Concrete Gravity Dams

Including Reservoir Bottom Absorption and Dam-Water-Foundation Rock Interaction, Earthquake 

Engineering and Structural Dynamics, Vol. 12, No. 5, pp. 663-680 

Fenves and Chopra 1985 

Fenves, G. and Chopra, A. K. 1985 (Jan-Feb). Effects of Reservoir Bottom Absorption and DamWater-Foundation Rock Interaction on Frequency Response Functions for Concrete Gravity Dams, 

Earthquake Engineering and Structural Dynamics, Vol. 13, No. 1, pp. 13-31 

Fenves and Chopra 1985 

Fenves, G. and Chopra, A.K. 1985. Reservoir Bottom Absorption Effects in Earthquake Response 

of Concrete Darns, Journal of Structural Engineering, ASCE, Vol. 111, No. 3, pp. 545-562 

Fenves and Chopra 1986 

Fenves, G. and Chopra, A.K. 1986 (June). Simplified Analysis for Earthquake Resistant Design of 

Concrete Gravity Dams, Rept. UCB/EERC-85/10, Univ. of California, Berkeley, CA

Fenves and Chopra 1985 

Fenves, G. and Chopra, A. K. 1985 (June). Simplified Earthquake Analysis of Concrete Gravity 

Dams: Separate Hydrodynamic and Foundation Interaction Effects, Journal of Engineering 

Mechanics, ASCE, Vol. 111, No. 6, pp. 715-735 

Fenves and Chopra 1985 

Fenves, G. and Chopra, A.K. 1985 (June). Simplified Earthquake Analysis of Concrete Gravity 

Dams: Combined Hydrodynamic and Foundation Interaction Effects, Journal of Engineering 

Mechanics, ASCE, Vol. 111, No. 6, pp. 736-756 

Fenves and Chopra 1987 

Fenves, G.L. and Chopra, A.K. 1987. Simplified Analysis of Concrete Gravity Dams, Journal of 

Structural Engineering, ASCE, Vol. 113, No. 8, pp. 1688-1708 

Fenves and Others 1992 

Fenves, G.L., Mojtahedi, S. and Reimer, R.B. 1992 (Apr). Effect of Contraction Joints on quake 

Response of an Arch Dam, Journal of Structural Engineering, ASCE, Vol. II 8, No. 4, pp. 1039-

1055 

Ghanaat 1993 

Ghanaat, Y. 1993. Theoretical Manual for Analysis of Arch Dams, U.S. Army Corps of Engineers, 

Waterways Experiment Station Technical Report ITL 93- 1, Vicksburg, MS 

 B-5 
Ghanaat 1993 

Ghanaat, Y. 1993. User's Manual-GDAP, Graphics-Based Dam Analysis Program Version 3.25, 

U.S. Army Corps of Engineers, Waterways Experiment Station Instruction Report IT 93-3, 

Vicksburg, MS 

Hall and Others 1991 

Hall, J.F., Dowling, M.J. and El-Aidi, B. 199 1. Defensive Design of Concrete Gravity Darns, 

Report No. EERL 91-02, California Inst. of Technology, Pasadena, CA 

Janson 1988 

Janson, R. B. (editor) 1988. Advanced Dam Engineering for Design, Construction and 

Rehabilitation, Van Nostrand Reinhold, p. 811 

Leger and Katsoull 1989 

Leger, P. and Katsoull, M. 1989. Seismic Stability of Concrete Gravity Dams, Earthquake 

Engineering and Structural Dynamics, Vol. 18, pp. 889-902 

Panel on Earthquake Engineering for Concrete Dams 1990 

Earthquake Engineering for Concrete Dams: Design, Performance, and Research Needs, National 

Academy Press, Washington, D.C., p. 143 

Priscu and Others 1985 

Priscu, R., Popovici, A., Stematiu, D. and Stere, C., 1985. Earthquake Engineering for Large Dams, 

John Wiley, 2nd edition 

Scott and Dreher 1983 

Scott, G. A., and Dreher, K. J. 1983. Dynamic Stability of Concrete Darn Foundations, 5th 

International Society for Rock Mechanics Congress, Melbourne, Australia, Proceedings, pp. C227-

C233 

Touhei and Ohmachi 1993 

Touhei, T. and Ohmachi, T. 1993. A FE-BE Method for Dynamic Analysis of Dam-FoundationReservoir Systems in the Time Domain, Earthquake Engineering and Structural Dynamics, Vol. 22, 

pp. 195-209 

Yang and Others 1996 

Yang, R., Tsai, C. S. and Lee, G. C. 1996 (Feb). Procedure for Time-Domain Seismic Analyses of 

Concrete Dams, Journal of Engineering Mechanics, ASCE, Vol. 122, No. 2, pp. 116-126 

USCOLD 1995 

Guidelines for Earthquake Design and Evaluation of Structures Appurtenant to Dams

 B-6 
APPENDIX B-3 

BIBLIOGRAPHY 

EARTHEN DAMS, ROCKFILL DAMS & LIQUEFACTION HAZARD ANALYSIS 

Ambraseys and Sanna 1967 

Ambraseys, N. N. and Sanna, S. K. 1967. "The Response of Earth Dams to Strong Earthquakes," 

Geotechnique, Vol. 17, No. 2, pp. 181-213 

Banerjee and Others 1979 

Banerjee, N. G., Seed, H. B., and Chan, C. K. 1979. "Cyclic Behavior of Dense Coarse-Grained 

Materials in Relation to the Seismic Stability of Dam,” Report No. UCB/EERC-79/13, University 

of California, Berkeley, CA 

Bureau and Other 1985 

Bureau, G., Volpe, R.L., Roth, W. H., and Udaka, T. 1985. Seismic Analysis of Concrete Face 

Rockfill Dams, Proc. of Geotechnical Engineering, Division of ASCE Symposium on Concrete 

Face Rockfill Dams-Design, Construction, and Performance, pp. 479-508 

Byrne 1991 

Byrne, P. M., “A Model for Predicting Liquefaction Induced Displacement,” Proceedings: Second

International Conference on Recent Advances in Geotechnical Engineering & Soil Dynamics, 

March, 1991 

Castro and Others 1985 

Castro, G., Poulos, S. J., and Leathers, F. D. 1985. "A Re-examination of the Slide of the Lower 

San Fernando Dam," Journal of Geotechnical Engineering, American Society of Civil Engineers, 

Vol. 111, No. 9, pp 1093-1107 

Chugh 1982 

Chugh, A.K. 1982. Slope Stability Analysis for Earthquakes, International Journal for Numerical 

and Analytical Methods for Geomechanics, Vol. 6, No. 3, pp. 307-322 

Department of the Army 1970 

Department of the Army 1970. Laboratory Soil Testing, Engineer Manual EM II 10-2-1906, 1980 

Revision, Office, Chief of Engineers, Washington, D.C. 

Department of the Army 1979 

Department of the Army. 1979. Geophysical Exploration, Engineer Manual EM II I0-I-1802, 

Office, Chief of Engineers, Washington, D.C. 

Department of the Army 1993 

Department of the Army. 1993. Slope Stability Manual, Engineer Manual EM II I0-I-1902, Office, 

Chief of Engineers, Washington, D.C. 

 B-7 
Duncan and Others 1980 

Duncan, J. M., Byrne, P., Wong, K. S., and Mabry, P. 1980. "Strength, Stress-Strain and Bulk 

Modulus Parameters for Finite Element Analysis of Stresses and Movements in Soil Masses," 

Report UCB/GT/80-0 1, University of California, Berkeley, CA

Duncan and Others 1984 

Duncan, J. M., Seed, R. B., Wong, K. S., and Ozawa, Y. 1984. "FEADAM84: A Computer 

Program for Finite Element Analysis of Dams," Research Report SU/GT/84-03, Stanford 

University, Stanford, CA 

Edris and Wright 1992 

Edris, E. V., Jr. and Wright, S. G. 1992. "User's Guide: UTEY-AS3 Slope stability package," 

Technical Report GL-87- 1, Vol. IV, U.S. Army Corps of Engineers, Waterways Experiment 

Station, Vicksburg, MS

Evans 1993 

Evans, M.D. 1993 (May). Gravelly Soil Liquefaction, Proceedings, 1993 National Earthquake 

Conference -Earthquake Hazard Reduction in the Central and Eastern United States: A Time for 

Examination and Action, Memphis, pp. 57-66 

Evans and Seed 1987 

Evans, M.D., and Seed, H.B. 1987. "Undrained Cyclic Triaxial Testing of Gravels--The Effects of 

Membrane Compliance," Report No. UCB/EERC-87/08, University of California, Berkeley, CA 

Federal Highway Administration 1978 

Guidelines for Cone Penetration Test Performance and Design, Report No. FHWA-TS-78-209, 

Prepared for the US Department of Transportation by Dr. John H. Schmertmann, University of 

Florida 

Fear and McRoberts 1995 

Fear, L. and McRoberts, E. “Reconsideration of Initiation of Liquefaction in Sandy Soils,” ASCE 

Geotechnical Journal, Vol. 121, #3, March 1995 

Finn 1990 

Finn, W. D. L. 1990. "Analysis of Post-Liquefaction Deformations in Soil Structures" Proceeding 

H. Bolton Seed Memorial Symposium, Vol. 2, University of California, Berkeley, CA, May 10 and 

11, 1990, pp. 291-311 

Finn and Others 1994 

Finn, W.D.L., Ledbetter, R.H. and Marcuson, W.F. 1994. Seismic Deformations in Embankments 

and Slopes, Proceedings Symposium on Developments in Geotechnical Engineering from Harvard 

to New Delhi 1936-1994, Bangkok, Thailand, edited by A.S. Balasubramaniam, and others, 

Balkema Publication, ISBN 90 5410 522 4, pp. 233-264 

 B-8 
Finn and Others 1986 

Finn, W. D. L., Yogendrakumar, M., Yoshida, N., and Yoshida, H. 1986. "TARA-3: A Program to

Compute the Response of 2-D Embankments and Soil-Structure Interaction Systems to Seismic 

Loadings," Department of Civil Engineering, University of British Columbia, Vancouver, B.C. 

Franklin and Chang 1977 

Franklin, A. G. and Chang, F. K. 1977. "Earthquake Resistance of Earth and Rock-Fill Dams; 

Permanent Displacements of Earth Embankments by Newmark Sliding Block Analysis," 

Miscellaneous Paper S-71-17, Report 5, U. S. Army Corps of Engineers, Waterways Experiment 

Station, Vicksburg, MS

Gazetas and Uddin 1994 

Gazetas, G. and Uddin, N. 1994 (Nov). Permanent Deformation on Preexisting Sliding Surfaces in 

Dams, Journal of Geotechnical Engineering, ASCE, Vol. 120, No. I 1, pp. 2041-2061 

Houston and Others 1987 

Houston, S. L., Houston, W. N., and Padilla, J. M. 1987. "Microcomputer-Aided Evaluation of 

Earthquake-Induced Permanent Slope Displacements," Microcomputers in Civil Engineering, 

Elsevier Science Publishing Co., Inc., Vol. 2, pp. 207-222 

Hynes and Franklin 1984 

Hynes, M. E. and Franklin, A. G. 1984. "Rationalizing the Seismic Coefficient Method," 

Miscellaneous Paper GL-84-13, US Army Corps of Engineers, Waterways Experiment Station, 

Vicksburg, MS 

Idriss and Others 1992 

Idriss, I.M. and Sun, J.I, 1992 (Nov). User's Manual for SHAKF-91-A Computer Program for 

Conducting Equivalent Linear Seismic Response Analyses of Horizontally Layered Soil Deposits, 

Center for Geotechnical Modeling, Dept. of Civil & Environmental Engineering, University of 

California, Davis, CA 

Ishihara 1993 

Ishihara, K. 1993. Liquefaction and Flow Failure During Earthquakes, 33rd Rankine Lecture, 

British Geotechnical Society, Geotechnique, Vol. 43, No. 3, pp. 351-415 

Itasca Consulting Group 2002 

Itasca Consulting Group, Inc. 2002, User's Guide for FLAC3D - Fast Lagrangian Analysis of 

Continua in 3 Dimensions, Version 2.1. Minneapolis 

Koester 1992 

Koester, J.P. 1992 (Dec). The Influence of Test Procedure on Correlation of Atterberg Limits With 

Liquefaction in Fine-Grained Soils, Geotechnical Testing Journal, ASTM, GTODJ, Vol. 15, No. 4, 

pp. 352-361 

 B-9 
Koester 1994 

Koester, J.P. 1994 (Jul). Pre-and Post-Liquefaction Behavior of Fine-Grained Soils, SF session 

paper No. 00347, presented at the Fifth US National Conference on Earthquake Engineering, EERI, 

Chicago, IL

Koester 1994 

Koester, J.P. 1994 (Oct). The Influence of Fines Type and Content on Cyclic Strength, 

Geotechnical Special Publication No. 44, ASCE Convention Specialty Session on Ground Failures 

in Silty Soils 

Kramer 1996 

Kramer, S.L., 1996. Geotechnical Earthquake Engineering, Prentice-Hall, Upper Saddle River NJ, 

653 pages 

Liao and Whitman 1985 

Liao, S. C. and Whitman, R. V. 1985. "Overburden Correction Factors For SPT in Sand," Journal 

of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 112, No. 3, 

pp 373-377 

Liao and Others 1988 

Liao, S., Veneziano, D., and Whitman, R.V., “Regression Models for Evaluating Liquefaction 

Probability,” ASCE Journal Geotechnical Engineering, Vol.114, #4, April 1988 

Lysmer and Others 1973 

Lysmer, J., Udaka, T., Tsai, C., and Seed, H. 1973. "FLUSH: A Computer Program for 

Approximate 3-D Analysis of Soil-Structure Interaction Problems," Report No. EERC 75-30, 

Earthquake Engineering Research Center, Berkeley, CA 

Makdisi and Seed 1979 

Makdisi, F.I., and Seed, H.B. 1979 (Jul). Simplified Procedure for Estimating Dam and 

Embankment Earthquake-Induced Deformations, ASCE Journal of the Geotechnical Engineering 

Division, Vol. 104, No. GT7, pp. 849-867 

Marcuson and Others 1990 

Marcuson, W.F., Hynes, M.E. and Franklin, A.G. 1990 (Aug). Evaluation and Use of Residual 

Shear Strength in Seismic Safety Analysis of Embankments, Earthquake Spectra, pp. 529-572 

Mejia and Others 1982 

Mejia, L.H. and Seed, H.B. and Lysmer, J.L. 1982 (Dec). Dynamic Analysis of Earth Dams in 

Three Dimensions, Journal of Geotechnical Engineering Division, ASCE, Vol. 108, No. 12, pp. 

1586-1604 

 B-10 
Mejia and Seed 1983 

Mejia, L.H. and Seed, H.B. 1983 (Sep). Comparison of 2-D and 3-D Dynamic Analysis of Earth 

Dams, Journal of Geotechnical Engineering Division, ASCE, Vol. 109, No. I 1, pp. 1383-1398 

Mitchell and Tseng 1990 

Mitchell, J.K., and Tseng, D.J. 1990. Assessment of Liquefaction Potential by Cone Penetration 

Resistance, Proceedings of the H.B. Seed Memorial Symposium, Bi Tech Publishing, Vol. II, pp. 

335-350 

National Research Council 1985 

National Research Council. 1985. Liquefaction of Soils During Earthquakes: National Academy 

Press, Washington, D.C., p. 240 

Okamoto 1984 

Oakamoto, S. 1984. Introduction to Earthquake Engineering, second edition, University of Tokyo 

Press, p. 629 

Olsen 1994 

Olsen, R.S. 1994. Normalization and Prediction of Geotechnical Properties Using the Cone 

Penetrometer Test (CPT), Technical Report GL-94-29, U.S. Army Corps of Engineers, Waterways 

Experiment Station, Vicksburg, MS

Olsen and Koester 1995 

Olsen, R.S., and Koester, J.P. 1995 (Oct). "Prediction of Liquefaction Resistance Using the CPT,” 

Proceedings, CPT ‘95 -International Conference on Cone Penetration Testing, Linkopping, Sweden 

Prevost 1989 

Prevost, J. 1989. DYNARD-A Computer Program for Nonlinear Seismic Site Response Analysis, 

XI Technical Report NCEER-89-0025, National Center for Earthquake Engineering Research, 

University of Buffalo 

Robertson and Others 

Robertson, P. K., Woeller, D. J. and Finn, W. D. L., “Seismic Cone Penetration Test for Evaluating 

Liquefaction Potential Under Cyclic Loading,” Canadian Geotechnical Journal, Vol. 29, pp. 686-

695 

Sarma 1975 

Sarma, S. K. 1975. "Seismic Stability of Earth Dams and Embankments," Geotechnique, Vol. 25, 

No. 4, pp 743-761 

Sarma 1979 

Sarma, S. K. 1979. Response and Stability of Earth Dams During Strong Earthquakes, 

Miscellaneous Paper GL-79-13, USAE Waterways Experiment Station, Vicksburg, MS 

 B-11 
Schnabel and Others 1972 

Schnabel, P. B., Lysmer, J., and Seed, H. B. 1972. "SHAKE, A Computer Program for Earthquake 

I Response Analysis of Horizontally Layered Sites," Report EERC 72-12, Earthquake Engineering 

Research Center, University of California, Berkeley, CA 

Seed 1979 

Seed, H. B. 1979. "19th Rankine Lecture: Considerations in the Earthquake Resistant Design of 

Earth and Rockfill Dams," Geotechnique, Vol. 29, No. 3, pp 215-263 

Seed 1987 

Seed, H. B. 1987 (Aug). Design Problems in Soil Liquefaction, Journal, Geotechnical Engineering 

Division, ASCE, Vol. 11 3, No. 8, pp.827-845 

Seed and Idriss 1970 

Seed, H. B., and Idriss, I.M. 1970. Soil Moduli and Damping Factors for Dynamic Response 

Analysis, Report EERC-70/1 0, Earthquake Engineering Research Center, Berkeley, CA 

Seed and Idriss 1982 

Seed, H. B., and Idriss, I. M. 1982. Ground Motions and Soil Liquefaction During Earthquakes, 

Earthquake Engineering Research Institute, 499 14th Street, Oakland, CA, pp. 134 

Seed and Others 1983 

Seed, H. B., Idriss, I. M., and Arango, I. 1983. "Evaluation of Liquefaction Potential Using Field 

Performance Data.” Journal of Geotechnical Engineering, American Society of Civil Engineers, 

Vol. 109, No. 3, pp 458-482 

Seed and Others 1975 

Seed, H. B., Lee, K. L., Idriss, I. M., and Makdisi, F. I. 1975. "The Slides in the San Fernando 

Dams During The Earthquake of February 9, 1971," Journal of the Geotechnical Engineering 

Division, American Society of Civil Engineers, Vol. 101, No. GT7, pp 651-688 

Seed and Others 1985 

Seed, H. B., Tokimatsu, K., Harder, L. F., and Chung, R. 1985. "Influence of SPT Procedures in 

Soil Liquefaction Resistance Evaluations," Journal of the Geotechnical Engineering Division, 

American Society of Civil Engineers, Vol. 111 No. 12, pp 861-878 

Seed and Others 1986 

Seed, H. B., Wong, R., Idriss, I. M., and Tokimatsu, K. 1986. Moduli and Damping Factors for 

Dynamic Analysis of Cohesionless Soils, Journal, Geotechnical Engineering Division, ASCE, Vol. 

112, No. 11, pp. 1016-1032 

Seed and Harder 1990 

Seed, R. B. and Harder, L. F. 1990. SPT-Based Analysis of Cyclic Pore Pressure Generation and 

Undrained Strength, Proceedings of the H. B. Seed Memorial Symposium, Bi Tech Publishing, 

Vol. 11, pp. 351-376 

 B-12 
Sherard and Dunnigan 1985 

Sherard and Dunnigan 1985. Filters and Leakage Control in Embankment Dams, Proceedings, 

Symposium on Seepage and Leakage from Dams and Impoundments, R. L. Volpe and W. E. Kelly, 

eds, ASCE, pp. 1-30, reprinted in Embankment Dams-James L. Sherard Contributions, S. Singh, 

ed, ASCE Geotechnical Special Publication No. 32, 1992 

Stark and Mesri 1994 

Stark, T. D. and Mesri, G. 1994. Undrained Shear Strength of Liquefied Sands for Stability 

Analysis, Journal Geotechnical Engineering Division, ASCE, Vol. 118, No. 11, pp. 1727-1747, and 

Field Case Histories 

Stark and Olson 1995 

Stark, T.D. and Olson, S.M. 1995. Liquefaction Resistance Using CPT Journal Geotechnical 

Engineering Division, ASCE, Vol. 121, No. 12, pp. 856-869 

Sun and Others 1988 

Sun, J. I., Golesorkhi, R., and Seed, H. B. 1988. Dynamic Moduli and Damping Ratios for 

Cohesive Soils, Report EERC-88/15, Earthquake Engineering Research Center, Berkeley, CA 

Sykora 1987 

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Correlations in Soils," U.S. Army Corps of Engineers, Waterways Experiment Station, 

Miscellaneous Paper GL-87-22 

Tokimatsu and Seed 1988 

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Vol. 113, No. 8, pp 861-878 

Tokimatsu and Yoshimi 1983 

Tokimatsu, K. and Yoshimi, Y. 1983. "Empirical Correlation of Soil Liquefaction Based on SPT 

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 B-14 
APPENDIX C 

GLOSSARY 

Active Fault - A fault, which, because of its present tectonic setting, can undergo 

movement from time to time in the immediate geologic future. 

 Comment: For the purpose of earthquake engineering application, it is a 

seismogenic or earthquake fault and is distinct from other types of faults such as 

landslides, ice thrusting, groundwater withdrawal effects, etc. 

Attenuation - A decrease in amplitude of the seismic waves with distance due to 

geometric spreading, energy absorption, and scattering. 

Bedrock - Any sedimentary, igneous, or metamorphic material represented as a unit in 

geology; being a sound and solid mass, layer, or ledge of mineral matter; and with shear 

wave threshold velocities greater than 2500 feet/second. 

Bedrock Motion Parameters - Numerical values representing vibratory ground motion, 

such as particle acceleration, velocity, and displacement, frequency content, predominant 

period, spectral intensity, and a duration which define a design earthquake. (These may 

also be used in a more general sense for ground motion.) 

Body Waves - Waves propagated in the interior of the earth, i.e., the compression (P) and 

shear (S) waves of an earthquake. 

Capable Fault - An active fault that is judged capable of producing macroearthquakes and 

exhibits one or more of the following characteristics: 

• Movement at or near the ground surface at least once within the past 35,000 years. 

• Macroseismicity (3.5 magnitude or greater) instrumentally determined with records of 

sufficient precision to demonstrate a direct relationship with the fault. 

• A structural relationship to a capable fault such that movement on one fault could be 

reasonably expected to cause movement on the other. 

• Established patterns of microseismicity which define a fault, with historic 

macroseismicity that can reasonably be associated with the fault. 

Critical Damping - the minimum amount of damping that prevents free oscillatory vibration. 

Cyclic Mobility - A phenomenon in which a cohesionless soil loses shear strength during 

earthquake ground vibrations and acquires a degree of mobility sufficient to permit 

intermittent movement up to several feet as contrasted to liquefaction where continuous 

movements of several hundred feet are possible. 

Damping - Resistance which reduces vibrations by energy absorption. There are different 

types of damping such as viscous, Coulomb, and geometric damping. 

Damping Ratio - the ratio of the actual damping to the critical damping. 

Duration of Strong Ground Motion - The "bracketed duration" or the time interval between the 

first and last acceleration peaks that are equal to or greater than 0.05g. 

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 Comment: There are other definitions that, if used, should be clearly defined. 

Epicenter - The point on the earth's surface located vertically above the point where the first 

rupture and the first earthquake motion occur. 

Fault - A fracture or fracture zone in the earth along which there has been displacement of the 

two sides relative to one another and which is parallel to the fracture. 

Hypocenter - The location where the slip responsible for an earthquake originates; the focus of 

an earthquake. 

Intensity - A numerical index describing the effects of an earthquake on man, manmade 

structures,or other features of the earth's surface. 

Comment: There are several intensity scales, but the most commonly used scale in the 

U.S. is the Modified Mercalli Intensity scale (Richter, C. F., Elementary Seismology, 

W.H. Freeman and Company, San Francisco, 1958). Historically, the epicentral intensity 

(lo) has been used to designate the size of an earthquake due to the lack of instrumental 

data. 

 

Limits of Near-Field Motion: 

Richter Magnitude, M Modified Mercalli, To Radius of Near Field, Km 

Maximum Intensity 

 5.0 VI 5 

 5.5 VII 15 

 6.0 VIII 25 

 6.5 IX 35 

 7.0 X 40 

 7.5 XI 45 

Comment: These limits of near-field motions are for earthquakes in the Western United 

States. There are no established limits of near-field motions in the Eastern United States. 

Liquefaction - Denotes a condition where a soil will undergo continued deformation at a 

constant low residual stress or with low residual resistance due to the buildup and maintenance 

of high pore water pressures, which reduces the effective confining pressure to a very low value. 

Pore pressure buildup leading to liquefaction may be due either to static or cyclic stress 

applications and the possibility of its occurrence will depend on the void ratio or relative density 

of a cohesionless soil and the confining pressure. 

Magnitude - A measure of the earthquake size related to the strain energy released by it, based 

on the displacement amplitude, period of the seismic waves, and distance from the earthquake 

epicenter. 

Comment: There are several magnitude designations, some of which are listed below. 

Therefore, the type of magnitude used and how it was determined should be clearly 

designated. 

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• Body Wave Magnitude (mb) - The magnitude of an earthquake measured as the 

common logarithm of the maximum displacement amplitude (microns) and period 

(seconds) of the body waves. 

Comment: Developed to measure the magnitude of deep focus earthquakes, which do 

not ordinarily set up detectable surface waves with long periods. Magnitudes can be 

assigned from any suitable instrument whose constants are known. The body waves can 

be measured from either the first few cycles of the compression waves (mb) or the 1-

second period surface waves (Mb, g).

• Richter or Local Magnitude (ML) - The magnitude of an earthquake measured as a 

common logarithm of the displacement amplitude, in microns, of a standard Wood 

Anderson seismograph located on firm ground 100 km from the epicenter and having a 

magnification of 2800, a natural period 0.8 second and a damping coefficient of 80 

percent. 

Comment: Empirical charts and tables are available to correct for epicentral distances 

from 100 km, other types of seismographs, and various conditions of the ground. The 

correction charts and the definition itself apply strictly only to earthquakes having focal 

depths smaller than about 30 km. The correction charts are relatively accurate up to 

epicentral distances of about 600 km. These correction charts are site dependent and 

have to be developed for each recording site. This is commonly used up to magnitude 

ML equal to 6.5. Above the MS is used to define magnitude. 

• Surface Wave Magnitude (MS) - The magnitude of an earthquake measured as the 

common logarithm of the resultant of the maximum mutually perpendicular horizontal 

displacement amplitudes, in microns, of the 20-second period surface waves. 

Comment: Developed to measure the magnitude of shallow focus earthquakes at 

relatively long distances. Magnitudes can be assigned from any suitable instrument 

whose constants are known. 

Maximum Credible Earthquake (MCE) - The earthquake(s) associated with specific 

seismotectonic structures, source areas, or provinces that would cause the most severe vibratory 

ground motion or foundation dislocation capable of being produced at the site under the currently 

known tectonic framework. It is determined by judgment based on all known regional and local 

geological and seismological data. 

Comment: In general, each seismotectonic province, source area or structure considered 

will have an MCE associated with it. In the present context these multiple MCEs are used 

to define the controlling MCE for the site of interest. 

Maximum Design Earthquake (MDE) - A postulated seismic event, specified in terms of

specific bedrock motion parameters at a given site, which is used to evaluate the seismic 

resistance of manmade structures or other features at the site. 

Comment: The maximum design earthquake is the earthquake that is used to evaluate the 

seismic resistance of the structure and is usually equated with the controlling MCE. 

However, where the failure of the dam presents no hazard to life, a lesser earthquake may 

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be justified, provided there are cost benefits and the risk of property damage is 

acceptable. 

Operating Basis Earthquake (OBE) - The earthquake(s) for which the structure is designed to 

resist and remain operations. It reflects the level of earthquake protection desired for operational 

or economic reasons and may be determined on a probabilistic basis considering the regional and 

local geology and seismology. 

 

Predominant Period - The period(s) at which maximum spectral amplitudes are shown on 

response spectra. Normally, acceleration response spectra are used to determine the predominant 

period(s) of the earthquake ground motion. 

Response Spectrum - A plot of the maximum values of acceleration, velocity, and/or 

displacement response of an infinite series of single-degree-of-freedom systems subjected to a 

time-history of earthquake ground motion. The maximum response values are expressed as a 

function of natural period for a given damping. 

Comment: The response spectrum acceleration, velocity, and displacement values may 

be calculated from each other assuming a sinusoidal relationship between them. When 

calculated in this manner, these are sometimes referred to as pseudoacceleration, 

pseudovelocity, or pseudodisplacement response spectrum values. 

Scaling - An adjustment to an earthquake time-history or response spectrum where the amplitude 

of acceleration, velocity and/or displacement is increased or decreased, usually without change to

the frequency content of the ground motion. 

Comment: There are other methods to scale earthquakes and, if used, they should be 

clearly defined. The earthquake time-history or response spectrum can be scaled based on 

ground motion parameters of peak acceleration, peak velocity, peak displacement, 

spectrum intensity, or other appropriate parameters. 

Seismic Moment (M0) - A measure of the earthquake size containing information on the rigidity 

of the elastic medium in the source region, average dislocation and area of faulting. It determines 

the amplitude of the long-period level of the spectrum of ground motion. It is calculated as: 

 MO = Shear Modulus of Faulted Rock (Dynes/cm2

) 

x Length of Fault Rupture Zone (cm)

x Width of Fault (cm)

x Displacement of Fault (cm)

Seismotectonic Province - A geologic area characterized by similarity of geologic structure and 

tectonic and seismic history. 

Seismotectonic Source Area - An area of known or potential seismic activity that may lack a 

specific identifiable seismotectonic structure. 

 Comment: Several source areas may occur within a seismotectonic province. 

Seismotectonic Structure - An identifiable dislocation or distortion within the earth's crust 

resulting form recent tectonic activity or revealed by seismologic or geologic evidence. 

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Smooth Response Spectrum - A response spectrum devoid of sharp peaks and valleys that 

specifies the amplitude of the spectral acceleration, velocity and/or displacement to be used in 

the analyses of the structure. 

Spectrum Intensity - The integral of the pseudovelocity response spectrum taken over the range 

of structural vibration periods from 0.1 to 2.5 seconds. 

Surface Waves - Waves that travel along or near the surface and include Rayleigh (Sv) and Love 

(SH) Waves of an earthquake. 

Synthetic Earthquake - Earthquake time history records developed from mathematical models 

that use white noise, filtered white noise and stationary and non-stationary filtered noise, or 

theoretical seismic source models of failure in the fault zone. 

 Comment: White noise is random energy containing all frequency components in equal 

proportions. Stationary white noise is random energy with statistical characteristics that 

do not vary with time. 

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