Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

PUBLICATION NO. FHWA-HRT-23-014 JANUARY 2023 

NextScour Case Study: The Lafayette 

Avenue Bridge Over the Saginaw River 

in Bay City, Michigan
FOREWORD 

The Federal Highway Administration (FHWA) is developing the NextScour Research Initiative 

with the goal of improving scour analysis and providing more accurate scour depth estimates for 

bridge foundation design. This initiative is an interdisciplinary effort between hydraulics and 

geotechnical engineers to address the existing knowledge gaps surrounding traditional methods 

of scour analysis. In 2020, FHWA established a Transportation Pooled Fund study to collaborate 

with State departments of transportation on future bridge projects at sites with layers of cohesive 

soils that could potentially provide resistance to hydraulic loads. This report documents one of 

the case studies, Lafayette Avenue Bridge in Michigan, and provides an example of how the 

NextScour approach can assist practitioners as they calculate scour depths and conduct bridge 

foundation design. 

Mark E. Swanlund 

Acting Director, Office of Infrastructure 

Research and Development 

Notice 

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

(USDOT) in the interest of information exchange. The U.S. Government assumes no liability for 

the use of the information contained in this document. 

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document. 

Quality Assurance Statement 

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement. 

.
TECHNICAL REPORT DOCUMENTATION PAGE 

1. Report No. 

FHWA-HRT-23-014 

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

4. Title and Subtitle 

NextScour Case Study: The Lafayette Avenue Bridge Over the 

Saginaw River in Bay City, Michigan 

5. Report Date 

January 2023 

6. Performing Organization Code: 

7. Author(s) with ORCID numbers. 

Haoyin Shan (0000-0002-6358-5347), James Pagenkopf 

(0000-0001-5392-8628), Chen Li (0000-0001-6915-9368), 

Nasi Zhang (0000-0002-1175-6909), Daniel Pastrich (0000-

0003-1417-1989), Otto Wiblishauser (0000-0002-1257-8163), 

Chao Huang (0000-0002-6034-8637), and Kornel Kerenyi 

(0000-0002-7363-2223). 

8. Performing Organization Report No. 

9. Performing Organization Name and Address 

Genex Systems, LLC 

11848 Rock Landing Drive, Suite 303 

Newport News, VA 23606 

10. Work Unit No. 

11. Contract or Grant No. 

693JJ320F000313 

12. Sponsoring Agency Name and Address 

Office of Research, Development, and Technology 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101-2296 

13. Type of Report and Period Covered 

Research Report; 

October 2020–August 2022 

14. Sponsoring Agency Code 

HRDI-40

15. Supplementary Notes 

The Contracting Officer’s Representative was Kornel Kerenyi (HRDI-40, 0000-0002-7363-2223). The authors thank 

Dr. Zhaoding Xie and Ms. Xinya Liu for their technical assistance with two- and three-dimensional computational 

fluid dynamics modeling, and Mr. Nandor Nagy for his assistance on preparing figures in this paper. 

16. Abstract 

The Michigan Department of Transportation (MDOT) plans to replace the Lafayette Avenue Bridge over the 

Saginaw River in Bay City, MI. Hydraulic scour analysis of the planned bridge replacement resulted in deep scour 

depths, which MDOT believed were excessive due to a subsurface layer of cohesive soil that existed across the 

bridge site. MDOT reached out to the Federal Highway Administration (FHWA) to inquire if FHWA’s NextScour 

Research Initiative could potentially reduce the scour design depths. Additionally, both the existing bridge and 

proposed bridge replacement featured large bascule piers, and MDOT asked if FHWA could conduct physical 

modeling of the piers in their flume to study scour formations around the piers. 

Through a Transportation Pooled Fund study, TPF-5(461), FHWA was able to perform five tasks for MDOT that 

are summarized in this report (FHWA 2020). Task 1: Perform hydraulic modeling of the site to obtain flow 

velocities and bed shear stresses. Task 2: Perform soil erosion testing on the cohesive soil to determine the clay’s 

critical shear stress. Task 3: Develop decay functions to establish the relation between hydraulic loads and depth. 

Task 4: Conduct computational fluid dynamics scour modeling in sand and clay soils. Task 5: Conduct a 

probabilistic scour analysis to quantify the risk levels for the various scour analysis methods. This research study 

showed that the cohesive layer of clay at the site could potentially stop the scour at this bridge site, and the 

NextScour methodology is a developing tool to improve accuracy for bridge foundation design. 

17. Key Words 

NextScour, scour design, hydraulic modeling, soil 

erosion testing, computational fluid dynamics, and 

probabilistic analysis 

18. Distribution Statement 

No restrictions. This document is available to the 

public through the National Technical Information 

Service, Springfield, VA 22161. 

http://www.ntis.gov 

19. Security Classif. (of this report)

Unclassified 

20. Security Classif. (of this page)

Unclassified 

21. No. of Pages 

57

22. Price 

N/A 

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

ii

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m

2

yd2 square yard 0.836 square meters m

2

ac acres 0.405 hectares ha 

mi2square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m

3 

yd3 cubic yards 0.765 cubic meters m

3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) 

oF Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx 

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA 

mm2square millimeters 0.0016 square inches in2 

m

2

square meters 10.764 square feet ft2 

m

2

square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac 

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m

3 cubic meters 35.314 cubic feet ft3 

m

3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees)

oC Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2candela/m20.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International e System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)
iii

TABLE OF CONTENTS 

CHAPTER 1. INTRODUCTION ................................................................................................ 1

CHAPTER 2. PROJECT BACKGROUND ............................................................................... 3

Subsurface Soil Profile and Geotechnical Properties ............................................................ 4

Summary of Current Hydraulic Analysis............................................................................... 5

CHAPTER 3. TASK 1. HYDRAULIC MODELING ................................................................ 7

Nominal CFD Bed Shear Stress ............................................................................................... 9

CHAPTER 4. TASK 2. EROSION TESTING ......................................................................... 11

ESTD Summary ...................................................................................................................... 11

ESTD Erosion Data Analysis ................................................................................................. 13

Critical Shear Stress Distribution ......................................................................................... 15

CHAPTER 5. TASK 3. DECAY FUNCTIONS ....................................................................... 19

Flume Scour Tests ................................................................................................................... 19

Decay Function Development ................................................................................................ 22

CHAPTER 6. TASK 4. CFD SCOUR ....................................................................................... 27

CHAPTER 7. TASK 5. PROBABILISTIC SCOUR ANALYSIS .......................................... 33

Deterministic Scour Analysis ................................................................................................. 33

Probabilistic Scour Analysis Concept ................................................................................... 34

Probabilistic Scour Analysis by using HEC-18 Equations.................................................. 39

CHAPTER 8. SUMMARY......................................................................................................... 45

REFERENCES ............................................................................................................................ 47
iv

LIST OF FIGURES 

Figure 1. Schematic. Plan and profile views of the proposed Lafayette Avenue Bridge. .............. 3

Figure 2. Schematic. Subsurface profile of the bridge site. ............................................................ 4

Figure 3. Image. LiDAR topography and the CFD simulation domain with the proposed bridge 

model. .................................................................................................................................... 7

Figure 4. Image. Velocity distributions of SRH-2D and the single-phase model. ......................... 8

Figure 5. Image. Bed shear stress distributions of SRH-2D and the single-phase model. ............. 9

Figure 6. Drawing. Locations and elevations of MDOT Shelby tube samples. ........................... 11

Figure 7. Photo. Labeled parts of the ESTD. ................................................................................ 12

Figure 8. Photo. The laser scanner measuring the soil surface and digitized soil surface (inset). 12

Figure 9. Graph. Erosion rates of nine tested Shelby tube samples. ............................................. 14

Figure 10. Graph. Erosion rates of samples with corresponding erosion categories. ................... 14

Figure 11. Graph. Logarithmic best fit of the erosion data. .......................................................... 16

Figure 12. Graph. Bootstrapping technique showing 50,000 linear fittings. ................................ 17

Figure 13. Graph. Histogram of the 50,000 critical shear stresses. .............................................. 17

Figure 14. Image. Scaled bridge models in MFS.......................................................................... 20

Figure 15. Image. A typical scour bathymetry scanning result. ................................................... 21

Figure 16. Graph. Scour depths progress of set L.2...................................................................... 22

Figure 17. Photos. Final scour hole around: (a) Set L, and (b) Set R. .......................................... 22

Figure 18. Image. (a) Experimental bathymetry scan at 0 percent scour depth and (b) resulting 

CFD bed shear stress distribution........................................................................................ 23

Figure 19. Image. (a) Experimental bathymetry scan at 21 percent scour depth and (b) resulting 

CFD bed shear stress distribution........................................................................................ 23

Figure 20. Image. (a) Experimental bathymetry scan at 51 percent scour depth and (b) resulting 

CFD bed shear stress distribution........................................................................................ 23

Figure 21. Image. (a) Experimental bathymetry scan at 81 percent scour depth and (b) resulting 

CFD bed shear stress distribution........................................................................................ 24

Figure 22. Image. (a) Experimental bathymetry scan at 100 percent scour depth and (b) resulting 

CFD bed shear stress distribution........................................................................................ 24

Figure 23. Graph. Decay function for MDOT sets L and R. ........................................................ 25

Figure 24. Image. The (a) surveyed riverbed, (b) clear-water scoured riverbed with sand, and (c) 

the riverbed with clay layer inserted at 530 ft. .................................................................... 28

Figure 25. Image. Bed shear stress distributions on scoured riverbed with clay layer for (a) Q100

discharge and (b) Q500 discharge. ........................................................................................ 29

Figure 26. Image. Bed shear stress distributions under increasing flows. .................................... 30

Figure 27. Image. Clay scour depth of 5 ft after Q500+35 percent for 75 yr. ................................ 31

Figure 28. Graph. Deterministic scour analysis using decay function and clay resistance for Q100

and Q500. .............................................................................................................................. 34

Figure 29. Graph. (a) Load distribution, resistance distribution, and exceedance probability of 

scour. (b) Exceedance probability versus scour depth. ....................................................... 35

Figure 30. Graph. PMF of annual maximum discharge and maximum annual discharge in every 

75 yr for the Lafayette Avenue Bridge (station 140). ......................................................... 36

Figure 31. Graph. Bed shear stress distribution for total pier (fender) scour. .............................. 38

Figure 32. Graph. Exceedance probability for total pier scour at various scour elevations. ........ 39

Figure 33. Graph. Exceedance probability of contraction scour at various scour elevations. ...... 42

Figure 34. Graph. Exceedance probability of local pier scour at various scour elevations. ......... 42
v

Figure 35. Graph. Exceedance probability of total pier scour at various scour elevations........... 43

Figure 36. Graph. Comparison of exceedance probability of total pier scour. ............................. 44

 
vi

LIST OF TABLES 

Table 1. Flow conditions and representative shear stresses for different flows. .......................... 10

Table 2. Elevations of ESTD erosion test samples and basic soil geotechnical information. ...... 13

Table 3. Flow conditions of flume scour tests. ............................................................................. 21

Table 4. Flow conditions and representative shear stresses for increasing flows......................... 30

Table 5. Peak-flood statistics at station 140 from HEC-RAS model............................................ 36

Table 6. Regressed sample parameters for Log-Pearson Type III distribution. ........................... 36

Table 7. Comparison of the exceedance probability: Theoretical versus Monte Carlo. ............... 37

Table 8. Pe,scour of total pier scour at each scour elevation. .......................................................... 38

Table 9. Design scour depth for Q100 and Q500 flood. ................................................................... 43
vii
1

CHAPTER 1. INTRODUCTION 

The Michigan Department of Transportation (MDOT) is investigating a replacement bridge for 

the existing Lafayette Avenue Bridge over the Saginaw River in Bay City, MI. Like the current 

bridge, the proposed bridge features two large bascule piers, which may create complex flow 

patterns due to their wide widths. MDOT calculated the scour depths using the current standard 

practice, which assumes a uniform layer of bed material, in this case, sand. The scour 

calculations, however, seemed excessive to MDOT, as they were aware of a thick, subsurface 

clay layer extending across the entire site channel. Cohesive materials, such as clay, are typically 

more resistant to scour compared to sandy materials due to higher critical shear stresses, but the 

critical shear value of cohesive materials is preferable to be obtained through erosion testing 

(Arneson et al. 2012). 

In 2020, the Federal Highway Administration (FHWA) established a Transportation Pooled Fund 

(TPF) study, TPF-5(461) Soil and Erosion Testing Services for Bridge Scour Evaluations 

(FHWA 2020). This study is a collaborative effort between the Hydraulics and Geotechnical 

Research Programs at Turner-Fairbank Highway Research Center (TFHRC) and includes support 

from the FHWA Resource Center. The study allows State departments of transportation to 

partner with FHWA to perform the soil and erosion testing required to determine material 

properties, such as critical shear stress, which are needed to calculate scour depths more 

accurately. With a potential layer of cohesive material within the calculated scour depth, the 

Lafayette Avenue Bridge was an excellent candidate for this TPF study. The study also aligns 

with FHWA’s NextScour research initiative, which seeks to improve scour analysis and provide 

more accurate scour depth estimates for foundation design (Shan et al. 2021a).

In addition to providing soil erosion testing, researchers at the FHWA J. Sterling Jones 

Hydraulics Research Laboratory proposed to model the flow around the Lafayette Avenue 

Bridge’s wide bascule piers. The Hydraulics Laboratory researchers have extensive experience 

conducting computational fluid dynamics (CFD) modeling, which can capture the complex 

three-dimensional (3D) flow at the piers. The team also proposed conducting physical modeling 

of the bridge piers and abutments using flume testing to calibrate and verify the CFD models. 

Additionally, both the laboratory and FHWA Resource Center personnel could help verify the 

traditional one- and two-dimensional (1D and 2D) hydraulic modeling performed for the site. 

The Hydraulics Laboratory team presented a study approach on October 15, 2020, to MDOT, 

which contained the following five tasks: 

• Task 1. Hydraulic modeling to obtain the representative initial bed shear stress. 

• Task 2. Erosion testing to obtain the distribution of clay critical shear stress. 

• Task 3. Decay functions, developed from the flume test and CFD shear stresses, to model 

the hydraulic loading. 

• Task 4. CFD scour to model the scour progress in clay and sand. 

• Task 5. Probabilistic scour analysis to develop probabilistic distributions of the maximum 

scour depths considering the uncertainties from the flood discharge, roughness on the 

main channel and the floodplain, and soil erosion resistance. 
2

This report references measurements and calculations in both English and International System 

of Units (SI). References to bridge plans, hydraulic analysis, and geotechnical studies typically 

use English units. References to laboratory equipment, laboratory tests, and CFD modeling 

typically use SI units. Conversions from SI to English units are provided when appropriate.
3

CHAPTER 2. PROJECT BACKGROUND 

The Lafayette Avenue Bridge carries SR M-13 and SR M-84 over the east channel (or main 

channel) of the Saginaw River in Bay City, MI. The west abutment rests on Middle Ground 

Island, and a second fixed bridge connects to Salzburg Avenue over the smaller west channel of 

the river. Originally opened in 1938, the Lafayette Avenue Bridge features two bascule piers that 

support a 184-ft-long bascule span. The bridge was rehabilitated in 1987 to replace the 

superstructure, but the existing substructure was retained. 

MDOT’s newly proposed bridge, shown in figure 1, will replace the entire substructure and 

superstructure in the current location of the existing bridge. The proposed piers are larger than 

the current piers and are spaced farther apart to maintain a bascule span distance of 190 ft. Both 

the proposed left and right abutments are set further back into the embankment compared to the 

original abutments to provide additional relief to the main channel. The proposed left abutment is 

a spill-through abutment, while the right abutment is a vertical-wall abutment carrying a 

pedestrian path under the approach span. The proposed foundations feature H-piles support for 

all piers and abutments. In addition to the H-piles, MDOT plans on installing cofferdams around 

the perimeter of each pier to protect the piles. 

© 2020 MDOT. Modifications by FHWA. 

Figure 1. Schematic. Plan and profile views of the proposed Lafayette Avenue Bridge. 

To protect the bascule piers from passing vessels, MDOT plans to install a fender system with a 

151-ft clearance between the piers. Each fender features a 25-ft-diameter cell up and downstream 

of the pier. The fender channel is aligned with the main channel of the Saginaw River and is at a 

slight 7.5-degree skew with the centerline of the deck and the bascule span. 
4

SUBSURFACE SOIL PROFILE AND GEOTECHNICAL PROPERTIES 

The subsurface soil profile at the site was determined from a 2016 geotechnical site investigation 

conducted by MDOT. Five soil borings were conducted in the floodplain surrounding each 

abutment. Sediment probes were conducted upstream and downstream of each pier, as well as 

two additional borings in the channel. The investigation revealed that the subsurface soils at both 

overbanks had an initial layer of fill consisting of loose sand and silt, followed by a layer of 

decomposed wood, sawdust, sand, and silt, with traces of gravel. The right overbank then 

transitioned to a 15-ft-thick layer of poorly graded sand. The left overbank (part of Middle 

Ground Island) was found to have silt and sand layers at this level. Starting at an elevation of 

around 553 ft in the right overbank and around 533 ft in the left overbank, the soil profile 

transitioned to a thick layer of stiff, gray, lean clay that continued down to an elevation of 485 ft, 

where it reached a layer of shale. 

The main channel bed featured a thin layer of river sediment that consisted of clayey/sandy silt. 

MDOT found the corresponding median grain size (D50) of this fine silty sand to be 0.1 mm. 

Beneath the sediment was the layer of poorly graded, loose sand and silty sand, which varied in 

thickness between 5 and 10 ft. Between elevations 533 and 540 ft, the sand layer transitioned to 

the thick layer of lean clay. The borings suggested that this clay layer was continuous across the 

entire profile of the channel. A generalized subsurface profile at the center line of the existing 

bridge was created using the boring data and is shown in figure 2. 

© 2020 MDOT. Modifications by FHWA. 

Figure 2. Schematic. Subsurface profile of the bridge site. 

The clay layer started out very stiff at the right overbank, with standard penetration tests (SPTs) 

producing blow counts (N-values) of 30 blows per ft at an elevation of 550 ft. These values 

dropped quickly to around 10 blows per ft at an elevation of 540 ft. Beginning at this depth, the 

clay experienced similar N-values across the entire profile of the channel, varying between 7 and 

12 before increasing again near the shale layer. MDOT believed that this thick layer of lean clay 

could potentially provide sufficient erosive resistance to the design floods and reduce the original 

values of the design scour depths. 
5

SUMMARY OF CURRENT HYDRAULIC ANALYSIS

MDOT prepared a hydraulic scour report to calculate scour depths for the proposed bridge. The 

hydrological analysis determined a drainage area of 6119.5 mi2, and Q100 and Q500 flow 

discharges of 56,770 and 67,740 cubic ft per second (cfs), respectively. 

The flow parameters at the bridge site were calculated using the U.S. Army Corps of Engineers 

(USACE) Hydrologic Engineering Center’s River Analysis System (HEC-RAS) software

(USACE 2022). The model considered 12 cross sections in the west channel of the Saginaw 

River, 13 cross sections in the east channel (including the cross section of the proposed Lafayette 

Avenue Bridge), and 3 cross sections in the combined lower reach. The HEC-RAS model 

considered a Manning’s n value of 0.030 for the main channel and varied between 0.06 and 0.14 

in the left and right overbanks. HEC-RAS returned an average velocity at the cross section 

directly upstream of the bridge of 5.27 ft/s and a hydraulic depth of 23.80 ft for the Q100 flow and 

6.10 ft/s and 24.29 ft for the Q500.

The material in the riverbed was very fine sand with a D50 of 0.1 mm. Using the methodology 

from Hydraulic Engineering Circular No. 18 (HEC-18), the calculated critical velocity of the bed 

material was less than the mean velocity in the channel for the Q100 discharge, indicating that 

Laursen’s live-bed scour equation should be used to calculate contraction scour (Arneson et al. 

2012). The predicted contraction scour depth was rounded to 5 ft for the Q100 flow and 6 ft for 

the Q500.

Local scour was also calculated at the piers using HEC-18 methodology. The proposed pier 

geometry and the flow parameters were entered into the pier scour equations, and a correction 

factor was applied to account for the wide piers in shallow flow. The resulting pier scour depths 

were 31 ft for the Q100 flow and 35 ft for the Q500. Local scour equations for the proposed 

abutments predicted flow would remain in the main channel and that zero abutment scour would 

occur for either flow.

The total scour calculation combined the contraction and pier scour values and resulted in a 36-ft 

scour depth for the Q100 flow and 41-ft scour depth for the Q500. Considering an average channel 

bed elevation of 550 ft, these scour depths corresponded to elevations of 514 and 509 ft, 

respectively. For comparison, the clay layer at the site began at elevations between 530–540 ft.

In addition to the conventional hydraulic analysis, 6 mi downstream of the bridge is the Saginaw 

Bay, which is part of Lake Huron. Although the Great Lakes do not experience coastal tides, the 

water elevation on the lake can fluctuate due to seiches, which are standing waves produced by 

wind and atmospheric pressure. If the crest of a standing wave recedes at the river outlet, it could 

potentially lower the water surface elevation (WSE) at the downstream boundary of the 

HEC-RAS model. Lower water surface elevations could produce increased velocities at the 

bridge site. Fluctuating boundary conditions at the bridge site due to lowering lake water 

elevation levels were a subject for further investigation in the study.

7

CHAPTER 3. TASK 1. HYDRAULIC MODELING 

Hydraulic modeling for this study aimed to predict the flow depths, velocities, and bed shear 

stresses at the bridge. This task used a 2D riverine and 3D coastal model to study the complex 

flow at the bridge site that is influenced by the Middle Ground Island dividing the Saginaw River 

into two channels, a river confluence near the south end of the island, and water level 

fluctuations of Lake Huron several miles downstream. Data from the 2D riverine and 2D/3D 

coastal model established the boundary conditions for the CFD model that included an area 

approximately 1,000 ft upstream and downstream of the bridge. The CFD model computed bed 

shear stresses in the bridge opening and around the proposed bascule piers. 

The 3D CFD model was developed by combining the light detection and ranging (LiDAR) 

topography (exported from the Sedimentation and River Hydraulics – Two Dimension 

(SRH-2D) model from MDOT) and the computer-aided design (CAD) model of the proposed 

bridge (U.S. Bureau of Reclamation 2022). Multiple flow conditions were simulated, including 

the Q100 and Q500. CFD simulation focused on the region around the bridge (figure 3).

Source: FHWA.

Figure 3. Image. LiDAR topography and the CFD simulation domain with the proposed 

bridge model. 

A volume of fluid (VOF) model was first evaluated, which simulated two-phase flow (air and 

water) in a 3D volume to better predict the water surface elevation. The inlet boundary was set as 

a uniform velocity inlet, and the outlet boundary was set as a pressure outlet. The riverbed was 

modeled as a rough wall with a roughness height of two times the riverbed surface sand D50. 

Corresponding single-phase models were developed to simplify the simulations. A CFD singlephase model does not incorporate air in the simulation. Instead, a top wall is placed at the 

expected water surface elevation (obtained from the HEC-RAS model). It is set as a symmetrical 

boundary to simulate the water surface. The inlet was set as a flow rate inlet, while the outlet 

boundary and riverbed were identical to the VOF model. The Unsteady Reynolds-Average 
8

Navier-Stokes (URANS) solver with a k-epsilon turbulence model was selected to solve the 

momentum equations. 

Initial test runs showed that the VOF and single-phase models produced similar results, so the 

single-phase model was adopted for the remaining CFD simulations. The simulation results of 

flow velocities and bed shear stresses of the single-phase model were compared with SRH-2D 

results. As shown in Figure 4, velocity distributions between both models were similar. The 

upstream approach velocity in each case was almost the same. But the water flow around the 

piers was different in the SRH-2D model because it cannot accurately simulate the 3D flow 

pattern around the bridge. Figure 5 compares the bed shear stresses. The SRH-2D model showed 

relatively larger bed shear stresses upstream and downstream of the bridge compared to the CFD 

model but had comparable stresses closer to the bridge. 

Source: FHWA. 

Figure 4. Image. Velocity distributions of SRH-2D and the single-phase model. 
9

Source: FHWA. 

1 Pa = 0.021 lb/ft2(psf). 

Figure 5. Image. Bed shear stress distributions of SRH-2D and the single-phase model. 

NOMINAL CFD BED SHEAR STRESS 

The riverbed in a CFD model is composed of millions of cells, with each cell outputting a single 

shear stress value. In order to determine a relevant average shear stress value adjacent to the 

bridge pier, an area of interest must be identified. Then the shear stress values from cells in that 

area can be averaged. A flow separation zone forms when water passes an obstruction. Bed shear 

stresses in the separation zone are amplified compared to upstream approach shear stresses, 

which initiate the scour process. CFD simulation results indicated that the flow separation zone 

is similar in size to the blockage area due to the obstruction. The blockage area is equal to the 

obstruction width times the flow depth. Therefore, the flow separation zone is the area of 

interest, where bed shear stresses are averaged to determine the representative shear stress due to 

the obstruction. This averaged representative bed shear stress can then be compared to shear 

stresses calculated from HEC-RAS output flow parameters to complete the probabilistic scour 

analysis in Task 5, which is discussed in chapter 7. 

For the Lafayette Avenue Bridge, the proposed upstream fender would have the deepest scour 

hole, where the blockage area was considered the fender diameter times the flow depth. Because 

the piers were close to the river banks, only bed shear stresses from cells adjacent to the bridge 

pier and elevations below the pier pile cap were collected. The shear stresses were ranked from 

largest to smallest until the cumulative cell area equaled the blockage area. Area-weighted 

average shear stress was then calculated to be the nominal bed shear stress. Table 1 lists the 

nominal shear stresses at the two fenders for increasing flows. 
10

Table 1. Flow conditions and representative shear stresses for different flows. 

Flow 

Flow 

Rate 

(cfs) 

WSE 

(ft)

Average 

Velocity 

(ft/s) 

Blockage 

Area

(ft2) 

Shear Stress 

at Left Fender 

(Pa) 

Shear Stress at 

Right Fender 

(Pa) 

Q10 42,785 580.9 4.4 865.7 8.2 7.1

Q50 54,510 581.3 5.5 875.7 12.1 11.6

Q100 59,360 581.5 5.9 880.5 14.5 14.1

Q500 70,130 582.0 6.8 893.2 20.2 19.7

Q2000 79,295 582.3 7.5 899.3 26.2 24.5
11

CHAPTER 4. TASK 2. EROSION TESTING 

MDOT collected 27 Shelby tube soil samples in three boreholes at the bridge site. The first two 

boreholes were downstream of the bridge at each of the existing piers (BB101 and BB102), and 

the third borehole was located at the left abutment upstream of the bridge (MB1). MDOT 

shipped the Shelby tubes to the Hydraulics Laboratory at TFHRC for erosion testing using the 

Ex-situ Scour Testing Device (ESTD). Figure 6 shows the Shelby tube sampling depths with the 

nine tubes tested in the ESTD highlighted. The erosion testing results determined a critical shear 

stress distribution of the medium-to-hard lean clay layer and was later used for the probabilistic 

scour analysis discussed in Task 5 in chapter 7. 

© 2020 MDOT. Modifications by FHWA. 

Figure 6. Drawing. Locations and elevations of MDOT Shelby tube samples. 

ESTD SUMMARY 

The ESTD, shown in figure 7, is an automated erosion device developed by FHWA that 

measures the erodibility of a cylindrical soil sample under well-controlled flow conditions (Shan 

et al. 2011). The ESTD features a 4.7-inch wide by 0.75-inch-high rectangular acrylic test 

channel that is 3-ft long. The maximum flow capacity of the pump is 0.5 cfs, which translates to 

a maximum flow velocity of 20 ft/s. An underwater laser scanner mounted on an industrial 

robotic arm scans the soil surface every 20 s (figure 8), sending a quasi-instantaneous signal to 

the control program. The control program averages the scan data and compares it to a reference 

point on the surface of the test channel. If the average value is less than this reference point, a 

command is sent to the piston to extrude the sample to maintain the soil surface flush with the 

test channel bed. The control program records the extrusion data from the piston, which is used 

to calculate the erosion rate. Flow circulation is continuously measured using an electromagnetic 

flow meter, and two filtration tanks are used to capture the eroded clay particles and keep the 

water clear for the laser scanner. An electromagnetic shear sensor located just upstream of the 

piston directly measures the shear stress of the soil sample in a separate series of tests after 

erosion testing is completed. The relationship between erosion rates and shear stresses was

developed by comparing results at similar flow rates, which is then used to determine the critical 

shear stress of the soil. Shan et al. (2021b) outlined in detail the ESTD test procedures. 
12

Source: FHWA.

A = robotic arm; B = laser scanner; C = flow channel; D = 3-inch Shelby 

tube sample; E = hydraulic piston; F = shear sensor; G = flow pump; 

H = flow meter; and I = filter cylinders.

Figure 7. Photo. Labeled parts of the ESTD.

Source: FHWA. 

Figure 8. Photo. The laser scanner measuring the soil surface and digitized soil surface 

(inset). 

For ESTD erosion tests, one or two 1-ft sections were cut from each Shelby tube, usually from 

the tube bottom. On top of each tube sample, lab engineers performed the rapid strength tests 

using a pocket penetrometer (PP) and a vane shear tester. After extracting and removing the 

disturbed soil surface from these strength tests, lab engineers conducted erosion tests on the 

remaining soil in the tube. Only the top 9–10 inches of soil were tested because the bottom 2‒3 

inches had a greater propensity to dislodge from the tube in the flow due to decreased friction 

surface area between the soil and the Shelby tube. Table 2 shows the elevation ranges of ESTD 

test tubes, strength test results, and water content of each Shelby tube sample. FHWA’s 

Geotechnical Laboratory provided soil classifications for three of the tested samples, including 

MB1 ST1, MB1 ST2, and BB102 ST14, and determined they were all low-plasticity clay. They 

then tested an additional six samples not included in ESTD erosion testing and found those were 

also all classified as low-plasticity clay. 
13

The typical duration of an erosion test for one flow rate/velocity setting was 10 min. A linear 

best fit line was applied to the erosion data (recorded position of the soil surface versus time) for 

each flow rate, where the slope represented the erosion rate. Hydraulic shear stresses on soil 

samples were recorded separately from the erosion tests using 0.6-inch-thick soil samples 

confined in stainless steel rings. The ring is mounted to a small bowl that attaches directly to the 

sensor disk. The bowl’s interior features a raised circular platform, which pushes the soil out 

about 0.08 inches above the edge of the ring. After the ring is mounted on the shear sensor, the 

sensor disk height is adjusted until the soil surface is flush with the test channel surface. The 

shear stress data were used to convert flow rates into equivalent shear stress values.

Table 2. Elevations of ESTD erosion test samples and basic soil geotechnical information.

Tube 

Number

Elevation 

(ft)

Elevation of 

1-ft Test 

Tube (ft)

Elevation

of Strength 

Test (ft)

PP 

(kPa)

Vane 

Shear 

Strength 

(kPa)

Water 

Content 

(percent)

MB1 ST1 526.1-523.6 524.6–523.6 524.7 119.7 64 8.7

MB1 ST2 523.6-521.1 522.1–521.1 523.2 105.3 40 13.6–14.9

MB1 ST4 518.6-516.1 517.1–516.1 518.2 143.6 48 20.5–23.4

MB1 ST8 508.6-506.1 507.2–506.2 507.2 71.8 36 28.2–29.8

BB101 ST12 522.1-520.1 520.8–519.8 520.7 80 22 14.9

BB101 ST15 507.6-505.1 507.1–506.1 507.1 76.5 44 23.5

BB102 ST5 542.9-540.4 541.9–540.9 540.9 57.5 40 28.2

BB102 ST11 527.9-525.4 526.5–525.5 526.5 167.6 86 14.9–17.7

BB102 ST14 517.9-515.4 517.9–515.4 516.6 167.6 62 26.6

ST = Shelby tube; 1 kPa = 21 psf.

ESTD EROSION DATA ANALYSIS

Generally, the soils within all nine Shelby tube samples had higher erosion rates as the flow rates 

increased, i.e., increased shear stresses, as shown in figure 9. Figure 9 also revealed that Shelby 

tubes ST5 and ST14 from borehole BB102 had much higher erosion rates at the same shear 

stresses than other tubes, indicating lower critical shear stresses for these two tubes. Figure 10

shows the erosion data in log-log scale along with the erosion categories proposed by Briaud 

(2011). Outside of ST5 and ST14, most data points fall within the low erodibility category. 

Because of data scatter in figure 9 and figure 10, it was very difficult to fit the data using a single 

curve. Therefore, alternative methods were considered to derive a shear stress distribution for the 

entire clay layer instead of only finding a deterministic value of the critical shear stress value.
14 

Source: FHWA.

Figure 9. Graph. Erosion rates of nine tested Shelby tube samples.

Source: FHWA.

Note: Dashed lines represent boundaries of erosion categories.

Figure 10. Graph. Erosion rates of samples with corresponding erosion categories.
15

CRITICAL SHEAR STRESS DISTRIBUTION 

Because the ESTD can produce a wide range of flow rates and erosion rates, a probabilistic 

analysis method was considered to determine the critical shear stress value along with a 

confidence interval, which is typically expressed as a coefficient of variation (COV). FHWA 

considered multiple methods to determine these values. Before any method was applied, the data 

were broken down into smaller time windows. It is not unusual during the 10-min erosion test for 

the soil to erode at different rates throughout the run. The simplest method to interpret the 

erosion rate was to calculate a best fit line across the entire length. But if the data are broken 

down into smaller time windows, varying from 1–4 min, with overlaps of 50 percent, more data 

points are generated that better represent the full range of erosion seen in the original 10-min run.

There were two methods considered for determining the critical shear stress of the soil using a 

probabilistic analysis. The first method was the bin method. The set of data points was separated 

into a series of horizontal bins containing a certain range of erosion rates, where the total number 

of bins was equal to the log-base 2 value of the number of datapoints. Each bin contained an 

equal amount of data points. For each bin, the mean, standard deviation, and COV were 

calculated for both erosion rates and shear stress values. Then the mean values were plotted and 

fitted using the erosion power function to find a resulting critical shear stress. 

The second method was the bootstrapping method (Stine 1989). In this method, the data are 

plotted on a log-log plot, and from the cloud of data points, a subset is selected at random. From 

this subset, a log-log best fit line is calculated. This process is repeated N number of times, 

anywhere from 5,000 to 50,000. For this method, a nonzero erosion rate must be selected to find 

the critical shear stress value, typically 0.1 mm/h (0.0039 inch/h), which matches the definition 

used by Briaud et al. (2011). The intersection of the best fit lines at the selected erosion rate 

results in a distribution of critical shear stress values from which a COV can also be calculated. 

Both methods were tested by FHWA to evaluate the optimal way to determine the probabilistic 

distribution of critical shear stress values for a tested soil. The bootstrapping method was 

eventually selected because it generated more reliable and reproducible distributions from the 

erosion datasets. 

The first step of the bootstrapping method was to apply a power function to describe the erosion 

function of the cohesive soil tested as follows: 

(1)

Where: 

ė = erosion rate. 

τ = shear stress. 

ka, kb = equation constants. 
16

By taking the logarithm of both sides, equation 1 converts to a linear relationship (as shown in 

equation 2), and a linear best fit was applied to the data to obtain constants ka and kb. After fitting 

both constants, the critical shear stress was defined as the shear stress when the erosion rate 

equaled 0.1 mm/h, as follows: 

(2)

The erosion data were divided into 4-min time windows, with 2-min overlaps between adjacent 

windows. A linear best fit function was applied to each window, where the slope of the linear fit 

was equal to the erosion rate. For very low flows, where erosion may not be detectable by the 

laser, a lower boundary for erosion was set at 0.016 mm/h (6.3×10-4 inch/h), which was based on 

the resolution of the laser scanner. In total, 1,127 erosion data points were collected (figure 11). 

The solid line represents the linear fit function for the entire dataset. With the corresponding 

fitted constants ka of 0.00033 and kb of 1.89, the critical shear stress was calculated to be 20.5 Pa 

(0.431 psf). 

Source: FHWA. 

Figure 11. Graph. Logarithmic best fit of the erosion data.

The second step of the bootstrapping method was to randomly select a subset of data points from 

the total set and apply the logarithmic best fit equation. A script randomly selected 40 out of the 

1,127 total data points and then applied the best fit function to calculate a corresponding critical 

shear stress. This process was then repeated 50,000 times to get a distribution of critical shear 

stresses (figure 12). The two dashed lines represent the 95-percent confidence limits on the linear 

fit of the mean critical shear stress, and the solid line is the mean linear fit of the 50,000 

iterations. Figure 13 plots a histogram of all 50,000 critical shear stresses. The mean value of the 

critical shear stresses was 20.5 Pa (0.431 psf), which matched the value calculated previously for 

the entire 1,127-point dataset. The standard deviation was 6.56 Pa (0.138 psf), and the coefficient 

of variation was 0.32. Both mean and COV were used as the critical shear stress distribution 

parameters. Since the erosion rates follow a lognormal distribution, the distribution of the critical 

shear stress was also assumed lognormal. 
17

Source: FHWA. 

Note: Dashed lines represent the 95-percent confidence interval on the mean linear fit. 

Figure 12. Graph. Bootstrapping technique showing 50,000 linear fittings. 

Source: FHWA. 

Figure 13. Graph. Histogram of the 50,000 critical shear stresses. 

19

CHAPTER 5. TASK 3. DECAY FUNCTIONS 

Physical experiments were conducted in the Hydraulic Laboratory’s 6-ft-wide Multi-functional 

Flume System (MFS) using scaled Lafayette Avenue Bridge models to understand where scour 

holes would form and the depths they would reach. Multiple model configurations were tested, 

including pier with embankment and abutment. Flume tests ran for 70 h minimum, but could last 

up to 120 h, and were paused at regular intervals to scan the bathymetry to measure the 

incremental progress of the scour hole. These scans were then used to calculate the decay of the 

hydraulic loads and calibrate the computer models of the experiments. 

FLUME SCOUR TESTS 

The Froude criterion was used to determine the geometric scale of the model because the 

governing force is gravity and open channel flow aspects dominate. A geometric scale factor 

(model:prototype) of 1:50 was selected for the flume tests, which provided a reasonable 

experimental flow depth and an appropriate model size of the bridge components without 

significant influence from the flume sidewalls. At this scale, the entire bridge was separated into 

two models: (a) Set L: left half-bridge with pier and abutment, and (b) Set R: right half-bridge 

with pier and abutment. The model pier was about 1.1 ft wide, and the model fender cylinder had 

a diameter of 6 inches. The prototype river cross sections were simplified and reproduced in the 

MFS. Four cross sections upstream of the bridge, two cross sections at the bridge, and five cross 

sections downstream of the bridge were exported from the LiDAR topography. The average 

riverbed elevation from these cross sections was 550.2 ft. The averaged left and right bank slopes 

were 0.13 and 0.22, respectively, with a standard deviation of 0.03. 

Figure 14 shows the simplified and scaled model setups in the MFS looking downstream. The 

7.5-deg skew angle was kept in the scaled models. The floodplain at the left abutment had an 

elevation of 576.3 ft. The horizontal distance between the main channel edge and the left 

floodplain edge measured approximately 154.6 ft. This geometry resulted in a left bank slope of 

0.169. Similarly, the right floodplain had an elevation of 582 ft, which resulted in a right bank 

slope of 0.25. For both sets L and R, a minimum distance of 2 ft was maintained between the 

fender and the MFS wall to minimize any contraction effects between both. 
20

Source: FHWA. 

A. Left half bridge. 

Source: FHWA. 

B. Right half bridge. 

Figure 14. Image. Scaled bridge models in MFS. 

Since both test setups were part of a compound channel, two transition structures were designed 

and 3D-printed to ensure the rectangular channel smoothly transitioned to the compound 

channels without introducing scour at the very upstream of the sand recess section. Both sets 

modeled half of the bridge, but the two models were not split from the centerline of the main 

channel. Therefore, the flow rate percentage of Q100 was estimated from the CFD simulation of 

the full-scaled geometry. The flow rate ratio of Sets L and R was 64.1 and 59.4 percent, 

respectively, indicating that the two model sections partially overlapped at the center of the 

channel. 

The Saginaw River bed has very fine sands with a D50 of 0.1 mm (0.0039 inch), which are 

impossible to scale down in flume tests. Uniform sands with a D50 of 1.15 mm (0.045 inch) were 

used instead. The flume-scale flow rate, flow depth, and upstream approach velocity were 

calculated from the scaling factor, a Q100 discharge of 56,770 cfs, and a WSE of 585.5 ft. Table 3

lists the flow conditions. As shown in the table, two different approach velocities were used for 

each set to ensure the scour depth was accurately measured and the effect of the flume walls was 

minimized. 
21

Table 3. Flow conditions of flume scour tests. 

Cases 

Flow 

Rate 

(cfs) 

Water 

Depth (ft) 

Scaled 

VQ100,approach

(ft/s) 

Vapproach

(ft/s) 

V Ratio 

(percent) 

Run 

Time 

(h) 

Scour 

Depth 

(ft)

Set L.1 2.1 0.71 0.49 0.49 100 70 0.18 

Set L.2 2.5 0.71 0.49 

0.45 

0.58 120 124 0.38 

Set R.1 2.1 0.71 0.45 0.49 108 87 0.20 

Set R.2 2.3 0.71 0.45 0.54 120 85 0.35 

The experiment was prepared by positioning the models in the MFS according to the design 

drawings. The sediment was then placed around the models, compacted by hand, and shaped 

with the assistance of a robotic arm mounted on a linear carriage over the MFS. The robotic arm 

could be programmed to repeatedly form complex sediment formations, which included the 

channel slope. 

Each experiment started by scanning the initial bathymetry using an underwater laser scanner. 

Water was slowly introduced into the flume with a near-zero flow rate to minimize disturbance 

of the bed material. The flow depth was then increased until the scanner was submerged. Once 

the laser scan was completed, the experiment began by decreasing the flow depth while 

gradually increasing the flow rate. Each test required two runs. The first run established the 

equilibrium scour depth, and the total run time was logged in table 3, and the final bathymetry 

was scanned. Then a second run was repeated and paused at approximately 20, 40, 60, and 

80 percent of the equilibrium scour depth. When the targeted scour depth was reached, the flow 

was reduced to standing water, and then the laser scanner collected the bathymetry. After the 

scan was finished, the flow resumed, and the run continued until the next incremental scour 

depth was reached. Figure 15 shows a typical scanned 3D point cloud. 

Source: FHWA. 

Figure 15. Image. A typical scour bathymetry scanning result. 

Figure 16 shows a typical measured scour depth over time, indicating that the scour generally 

reached equilibrium after about 80 h. Figure 17 shows the equilibrium scour hole around the pier 

and fender. Water flows from right to left, and the deepest scour hole appears upstream of the 

upstream fender cylinder. 
22

Source: FHWA. 

Figure 16. Graph. Scour depths progress of set L.2. 

All photos source: FHWA. 

Note: Flow is from right to left. 

Figure 17. Photos. Final scour hole around: (a) Set L, and (b) Set R. 

DECAY FUNCTION DEVELOPMENT 

The incremental scour bathymetries collected by the laser scanner were post-processed and 

exported into CFD to compute the nominal bed shear stress to develop the decay function. The 

nominal bed shear stress at each incremental scour bathymetry was calculated following the 

procedure outlined in Task 1. Figure 18 to figure 22 illustrate the bed shear stress distributions 

for Set L.2 on the scanned incremental scour bathymetries. The figures show that two zones of 

high shear stress appear on either side of the fender and pier at the initial riverbed. As the scour 

hole deepens, shear stress magnitude decreases until most of the area around the fender and the 

pier are lighter intensity, close to the critical shear stress of the 1.15 mm (0.045 inch) sand. This 

result reflects the trend of shear stress decay within the developing scour hole. 
23

All images source: FHWA. 

Figure 18. Image. (a) Experimental bathymetry scan at 0 percent scour depth and (b) 

resulting CFD bed shear stress distribution. 

All images source: FHWA. 

Figure 19. Image. (a) Experimental bathymetry scan at 21 percent scour depth and (b) 

resulting CFD bed shear stress distribution. 

All images source: FHWA. 

Figure 20. Image. (a) Experimental bathymetry scan at 51 percent scour depth and (b) 

resulting CFD bed shear stress distribution. 
24

All images source: FHWA. 

Figure 21. Image. (a) Experimental bathymetry scan at 81 percent scour depth and (b) 

resulting CFD bed shear stress distribution. 

All images source: FHWA. 

Figure 22. Image. (a) Experimental bathymetry scan at 100 percent scour depth and (b) 

resulting CFD bed shear stress distribution. 

The representative bed shear stresses at incremental scour depths were normalized by the 

upstream approach shear stress. Because the flume tests had zero slope, the approach shear stress 

τa was computed using equation 3 with the friction factor f obtained from Moody’s Diagram 

(Moody 1944). Reynolds number and relative roughness were needed to determine the friction 

factor. For rectangular channels, the characteristic length in Reynolds number is the hydraulic 

diameter, i.e., four times the hydraulic radius. The relative roughness was assumed as the ratio of 

0.5D50 to the hydraulic diameter. 

(3)

Where: 

ρ = water density. 

U = average approach velocity. 

The incremental scour depths were normalized by the obstruction projected width, B, which was 

used in the Nominal Bed Shear Stress section to calculate the blockage area. Because scour 

mainly occurs around the upstream fender cylinder for Sets L and R, the projected width was set 
25

as the fender diameter. An exponential function was fitted through the data 

for all four cases (figure 23), where ys is the incremental scour depth, and a and b are fitting 

constants. 

Source: FHWA. 

Figure 23. Graph. Decay function for MDOT sets L and R. 

Figure 23 indicates that the data from these four cases generally align, and the best fit and the 

more conservative design decay functions are given in equations 4 and 5, respectively. Shan et 

al. (2016) used a reliability index (RI) to measure the reliability and accuracy of an equation. The 

same RI analysis was performed here to make sure the design decay function had an RI of 2.0. 

To reach that threshold, the best-fit equation was multiplied by a safety factor of 1.23, which 

resulted in equation 5.

(4)

(5)

27

CHAPTER 6. TASK 4. CFD SCOUR

A preliminary NextScour CFD scour simulation tool was developed by researchers at FHWA 

using OpenFOAM, which is open-sourced CFD software (OpenFOAM Foundation Ltd. 2022). A

scour model for the simulation tool was written in Python (Python Software Foundation 2022). 

OpenFOAM was used to simulate the flow condition near the bridge, and the scour model 

updated the scour bathymetry based on the flow condition output at a given time. The time step 

for flow simulation varied from 1 to 10 ms, while the scour model ranged from 1 to 30 min. 

First, the original riverbed information was imported into OpenFOAM as a solid boundary. After 

one time step of flow calculation, shear stress on the riverbed was extracted and exported to the 

scour model. The bed surface was deformed to reflect the changing scour depths using the 

erosion functions for the clay layer (equation 1). The maximum scour depth for one cell in the 

bed surface was limited to 10 mm per time step. OpenFOAM then resumed the flow simulation 

with the updated river bathymetry. This iteration between OpenFOAM and the scour model 

continued until the shear stress in the scour hole equaled the estimated critical shear stress of the 

soil, i.e., the condition where no further erosion happened. 

The average approach bed shear stress in the full-scaled Saginaw River CFD simulation is about 

2.7 Pa (0.057 psf) for Q100 flow and 3.6 Pa (0.076 psf) for Q500 flow. These shear stresses are 

larger than the critical shear stress of the riverbed sand with a D50 of 0.1 mm (0.0039 inch). 

Therefore, live-bed scour would occur. However, because the current CFD scour tool does not 

have a sediment transport module, live-bed conditions cannot be simulated. Instead, the critical 

velocity of the 0.1 mm (0.0039 inch) sand was calculated using the flow depth from Q100. An 

approach velocity of 0.4 m/s (1.3 ft/s) was used in OpenFOAM simulation, which generated a 

clear-water flow condition. Due to the shear amplification of the bridge, the flow still eroded 

sands near the pier and the fender. Once the scour around the bridge pier reached equilibrium, 

the clay layer at 530 ft was reinserted into the model to generate a new bathymetry, and the bed 

material properties were updated from 0.1 mm (0.0039 inch) sand to the clay properties 

measured in Task 2 (figure 24).
28

Source: FHWA. 

Figure 24. Image. The (a) surveyed riverbed, (b) clear-water scoured riverbed with sand, 

and (c) the riverbed with clay layer inserted at 530 ft. 

Figure 25 illustrates the bed shear stress distributions in the updated bathymetry with the exposed 

clay layer, and table 4 gives the nominal shear stress magnitudes. Note that the average shear 

stress value of the left pier consisted of only the exposed clay area, while the average shear stress 

value of the right pier was bounded by the size of the blockage area. All shear stresses 

surrounding the two piers under both the Q100 and Q500 flows were smaller than the critical shear 

stress of the clay, which was 20.5 Pa (0.431 psf). This result confirmed that scour would stop 

once the clay layer was exposed. As an exercise, the researchers continuously increased the Q500

flow velocity by 10 to 35 percent in increments of 5 while keeping the same WSE to see when 

flow would start to erode the clay and how much it would erode over time. 
29

Source: Argonne National Laboratory (ANL). Modifications by FHWA. 

Figure 25. Image. Bed shear stress distributions on scoured riverbed with clay layer for (a) 

Q100 discharge and (b) Q500 discharge. 

The shear stress distributions under the increased flows (figure 26) indicated that bed shear stress 

started to exceed the clay critical shear stress when the flow reached Q500+30 percent. Under the 

flow condition of Q500+35 percent, the scour depth in the clay reached 5 ft in a 75-yr simulation 

near the right upstream fender cylinder (figure 27).
30

Table 4. Flow conditions and representative shear stresses for increasing flows. 

Flow 

Flow 

Rate 

(cfs) 

WSE 

(ft)

Average 

Velocity 

(ft/s) 

Clay 

Exposed 

Area at 

Left Pier 

(ft2) 

Average 

Shear 

Stress at 

Left Pier 

(Pa) 

Flow 

Blockage 

Area at 

Right Pier

(ft2) 

Average 

Shear 

Stress at 

Right Pier

(Pa) 

Q100 59,360 581.3 5.9 523.1 6.5 890.6 10.1 

Q500 70,130 582 6.8 525.6 8.7 892.6 12.9 

Q500+10% 77,143 582 7.48 525.6 10.7 893.4 15.9 

Q500+15% 80,650 582 7.82 525.6 11.8 892.0 17.6 

Q500+20% 84,156 582 8.16 525.6 12.9 890.3 19.2 

Q500+25% 87,663 582 8.5 525.6 13.9 893.0 20.8 

Q500+30% 91,169 582 8.84 525.6 15.0 893.0 22.4 

Q500+35% 94,676 582 9.18 525.6 16.2 893.0 24.2 

Source: ANL. Modifications by FHWA. 

Figure 26. Image. Bed shear stress distributions under increasing flows. 
31

Source: ANL. Modifications by FHWA. 

Figure 27. Image. Clay scour depth of 5 ft after Q500+35 percent for 75 yr.

33

CHAPTER 7. TASK 5. PROBABILISTIC SCOUR ANALYSIS 

DETERMINISTIC SCOUR ANALYSIS 

The deterministic scour analysis was conducted once the decay function and critical shear stress 

of the clay layer were known. The design decay function (equation 5) should be used to check 

whether the clay layer would erode under a given flow. 

First, the upstream approach shear stresses, τa, for Q100 and Q500 were computed using equation 6 

(equation 6.7 in HEC-18) with given HEC-RAS flow parameters at the approach cross section of 

station 90 (Arneson et al. 2012). 

(6)

Where:

γ = unit weight of water. 

y = approach flow depth. 

n = Manning n.

V = average approach velocity. 

Ku = 1.486 for English Units and 1.0 for SI Units. 

This calculation resulted in approach shear stress values of 11.6 Pa (0.244 psf) and 14.9 Pa 

(0.313 psf) for the Q100 and Q500 flows, respectively. The calculated approach shear stress was 

then converted to bed shear stress at the fender using the ratio from the design equation from 

equation 5. It should be noted that the approach shear stresses calculated from equation 6 

generally overestimate the shear stress compared to the results from CFD simulations because it 

is averaged over the entire cross section and relies heavily on the estimation of Manning’s n

value. Alternatively, the CFD calculation considers the velocity profile of the flow and computes 

the shear stress in the boundary layer of the surface. The values of 11.6 and 14.9 Pa (0.244 and 

0.313 psf) were about 4 to 4.5 times greater than the approach shear stress calculated using CFD. 

The CFD simulation can more accurately capture the 3D flow pattern near the fender and the 

bridge piers compared to equation 6. Additionally, because CFD modeling of bed shear stresses 

at the fender and the piers already considered the contraction effect, no separate contraction 

scour analysis was needed. Therefore, the initial bed shear stresses calculated near the fender on 

the riverbed in Task 1 were used as the initial starting condition for the deterministic analysis. 

These values, originally listed in Table 1, were 14.5 Pa (0.305 psf) for the Q100 and 20.2 Pa 

(0.424 psf) for the Q500 flood event. These values were then multiplied by the safety factor of 

1.23 used to get the design decay function (equation 5) from the best fit decay function (equation 

4). This factor increased the initial bed shear stresses at the pier to 17.8 and 24.8 Pa (0.374 and 

0.521 psf). FHWA recognizes that CFD simulations will not be available for all bridge designers, 

so future research will focus on determining a table of shear stress modification factors to get 

appropriate initial bed shear stress values at the piers from the approach shear stress calculated in 

equation 6. 
34

With initial bed shear stress values selected, the decayed shear stress was computed at 1-ft 

incremental scour depths using equation 5. These shear stresses were compared with clay critical 

shear stress in the clay layer. Figure 28 reveals that at 530-ft elevation, the decayed shear stress 

was 13.0 Pa (0.273 psf) for Q500, less than the design clay erosion resistance, which was equal to 

the mean shear stress minus one standard deviation. Therefore, the total pier scour would stop at 

530 ft. This result confirmed the CFD scour results in Task 4. 

Source: FHWA. 

τdesign for the clay layer = τmean − 1 standard deviation (6.6 Pa). 

Figure 28. Graph. Deterministic scour analysis using decay function and clay resistance for 

Q100 and Q500. 

PROBABILISTIC SCOUR ANALYSIS CONCEPT 

In the current American Association of State and Highway Transportation Officials (AASHTO) 

Load Factor Resistance Design (LRFD) bridge design specifications (2020), the load and 

resistance generally refer to the forces applied on a bridge structure by internal or external 

sources and the capability of the designed structure to resist such forces. A typical design limit 

state equation is as follows: 

(7)
35

Where: 

ηi = load modifier. 

γi = load factor. 

Li = load effect. 

φ = resistance factor. 

Rn = nominal resistance. 

Scour is analogous to LRFD, where the load refers to the bed shear stress produced by the flow, 

and the resistance is the critical shear stress of the soil. When the flow-induced bed shear stress is 

larger than the critical shear stress of the soil, scour happens. Probability of exceedance, Pe,scour, 

represents the probability of the scour going beyond a predicted scour depth. Figure 29(a) shows 

the concept of load (L) and resistance (R) distribution and Pe,scour for a preset scour depth. The 

distribution of the load, w, is calculated from a Monte Carlo simulation considering various 

uncertainties in the flood event. The distribution of the resistance c, is obtained from soil erosion 

tests. The shaded area where the difference between the resistance and load (R - L) is Pe,scour. A 

relationship between Pe,scour and incremental scour depths can be established, as shown in figure 

29(b).

Source: FHWA. 

Figure 29. Graph. (a) Load distribution, resistance distribution, and exceedance 

probability of scour. (b) Exceedance probability versus scour depth. 

The probabilistic scour analysis was performed on the proposed new bridge using a 10,000-point 

Monte Carlo simulation for a 75-yr bridge design life (Doucet et al. 2001). The HEC-RAS model 

for this project was provided by MDOT. It was a three-reach model with five discharge control 

cross sections. The HEC-RAS model was revised to a one-reach model with one inlet upstream 

of the east channel to simplify the probabilistic study. 

Step 1: Generate annual maximum discharge. 

The U.S. Geological Survey (USGS) gage 04157005 is about 12.5 miles upstream of the 

Lafayette Avenue Bridge, which does not represent the discharge at the bridge. Therefore, the 

sample mean (X̅), the sample standard deviation (S), and the sample skewness (G) for 

Log-Pearson Type III distribution were calculated using the peak floods provided in the 

HEC-RAS model (table 5), and the results were shown in table 6 (Beard 1962; England et al. 

2019). The R

2 value for the regression curves was 1.0, which indicated the regression was 
36

accurate. The regressed parameters were used to generate the population mean  population 

standard deviation , and population skewness . N is the number of the annual peak discharges 

of the historical record, which was required when determining the distribution of   and , and 

SG. In this case, N was assumed to be 101, the total available annual peak discharges recorded at 

gage 04157005. 

Table 5. Peak-flood statistics at station 140 from HEC-RAS model. 

Flow Q10 Q50 Q100 Q500

Discharge (cfs) 42,785 54,510 59,360 70,130 

Table 6. Regressed sample parameters for Log-Pearson Type III distribution. 

Parameters X̅ S G 

Station 140 4.446 0.146 -0.112 

For 10,000 points Monte Carlo simulation, 10,000 sets of i i i (i = 1, 2, ... 10,000) were 

generated. For each set of i i i, 75 exceedance probabilities (Pe,(i, j), j = 1, 2, ... 75) were 

randomly selected to represent each year of the 75 yr of bridge design life. In total, 750,000 

discharges were generated. Figure 30 shows the probability mass function (PMF) of the 750,000 

annual maximum discharge and the PMF of the 10,000 maximum annual discharge in every 

75 yr at the inlet (station 140). 

Source: FHWA. 

Figure 30. Graph. PMF of annual maximum discharge and maximum annual discharge in 

every 75 yr for the Lafayette Avenue Bridge (station 140). 

The exceedance probability of various flood frequencies calculated from the generated data and 

the theoretical values were compared in table 7. Generally, the exceedance probability of 

generated floods in one year was close to the theoretical values. Similarly, the exceedance 
37

probability for 75 yr was also close to the theoretical value for generated floods of Q50 and Q100. 

In contrast, the generated floods of Q200 and Q500 had a larger exceedance probability in 75 yr 

than their theoretical values. This result was due to the small number of N used in discharge 

generation. If N was larger, e.g., N = 1,000 or higher, the Monte Carlo simulation results and the 

theoretical value would be closer. 

Table 7. Comparison of the exceedance probability: Theoretical versus Monte Carlo. 

Flood 

Exceedance Probability of 

Flood Frequency in 1 yr 

Exceedance Probability of 

Flood Frequency in 75 yr 

Theoretical 

Value 

(percent) 

Monte 

Carlo 

(percent) 

Theoretical 

Value 

(percent) 

Monte 

Carlo 

(percent) 

Q50 2 2.2 78 73.3

Q100 1 1.2 52.9 52.3

Q200 0.5 0.7 31.3 35.2

Q500 0.2 0.3 13.9 19.9

Step 2: Generate Manning’s n. 

Manning’s n is the only random variable considered in the hydraulic model uncertainty, and it is 

considered constant in the bridge design life. The Transportation Research Board’s National 

Cooperative Highway Research Program (NCHRP) Report 761 indicates that Manning’s n 

follows a lognormal distribution with a COV of 0.015 (Lagasse et al. 2013). Manning’s n was 

given by MDOT as 0.03 for the main channel and 0.08 for the overbanks in the revised 

HEC-RAS model. 

Step 3: Compute the flow conditions in HEC-RAS. 

There were 750,000 sets of discharges, and 10,000 Manning’s n were submitted to the revised 

HEC-RAS model via a batch job to compute the flow velocity (V) and flow depth (y0) at the 

approach cross section (station 90). 

Step 4: Select the scour elevations. 

The selected scour elevations were 550, 540, 530, 520, and 510 ft for the total pier scour. 

Step 5: Determine the load distribution: Distribution of bed shear stress. 

For each scour elevation, 750,000 sets (10,000 sets for each 75-yr bridge design life) of bed 

shear stresses for the total pier scour (τb,total) were calculated by using the flow parameters 

obtained from HEC-RAS (equation 6) and the decay function (equation 4). The load distribution 

was the distribution of the 10,000 maximum bed shear stresses. Figure 31 shows the probability 

density function (PDF) of the bed shear stresses at selected scour elevations. 
38

Source: FHWA. 

Figure 31. Graph. Bed shear stress distribution for total pier (fender) scour. 

Step 6: Distribution of critical shear stress. 

It was assumed that the critical shear stress followed a lognormal distribution, whose parameters 

were calculated from the mean and COV of critical shear stress obtained in Task 2. In that task,

10,000 critical shear stresses were generated according to the obtained lognormal distribution. 

The “clay erosion resistance” curve in figure 31 shows the PDF of the generated critical shear 

stresses.

Step 7: Calculate Pe,scour at scour elevations.

The load distribution of total pier scour was compared against the resistance distribution. Pe,scour

was calculated as the probability of critical shear stress being less than the decayed bed shear 

stress at each target scour elevation. Pe,scour at each target scour depth are listed in table 8, as well 

as shown in figure 32. 

Table 8. Pe,scour of total pier scour at each scour elevation. 

Scour Elevation 

(ft)

Pe,scour for Total Pier Scour 

(percent) 

550 31.6

540 11.5

530 3.3

520 0.7

510 0.2
39

Source: FHWA. 

Figure 32. Graph. Exceedance probability for total pier scour at various scour elevations. 

PROBABILISTIC SCOUR ANALYSIS BY USING HEC-18 EQUATIONS 

A probabilistic scour analysis based on the scour design equations in HEC-18 was performed to 

identify the exceedance probability of scour depths and compare results with the proposed 

NextScour decay function method. 

For direct comparison, the same distribution on discharge and Manning’s n and the flow 

conditions calculated from the HEC-RAS models that were used in the previous probabilistic 

analysis were adopted here to calculate the exceedance probability for the HEC-18 equations. 

For contraction scour, critical velocity, which is calculated by equation 8, was used to determine 

whether clear water or live-bed condition would apply. 

(8)

Where:

Vc = critical velocity above which bed material of size D50 and smaller will be 

transported. 

y = average depth of flow upstream of the bridge. 

D50 = particle size in a mixture of which 50 percent are smaller. 

Ku = 11.17 for English units or 6.19 for SI units. 

According to HEC-18, if the critical velocity of the bed material Vc is larger than the mean 

velocity upstream of the bridge, the clear water contraction scour equation (equation 9) was used 

to calculate the contraction scour. Otherwise, the live-bed contraction scour equations 

(equation 10), were applied. 
40

(9)

Where: 

ys,contr = contraction scour depth. 

y0 = existing depth in the contracted section before scour. 

Q = discharge through the bridge associated with the width W. 

W = bottom width of the contracted section less pier widths. 

Ku = 0.0077 for English units and 0.025 for SI units. 

fEq,contr = equation uncertainty factor for contraction scour. 

(10)

Where: 

y1 = average depth in the upstream main channel. 

Q1 = flow in the upstream channel. 

Q2 = flow in the contracted channel. 

W1 = bottom width of the upstream main channel. 

W2 = bottom width of main channel in contracted section less pier width. 

k1 = 0.69 for this project. 

fEq,contr in equations 9 and 10 is a factor to account for the equation uncertainty of the contraction 

scour equations. According to NCHRP Report 761, fEq follows a normal distribution with the 

mean and COV of 0.92 and 0.21, respectively (Lagasse et al. 2013). 

The local pier scour depth was calculated using equation 11: 

(11)

Where: 

ys,pier = local pier scour depth. 

y1 = flow depth directly upstream of the pier. 

K1 = correction factor for pier nose shape (K1 = 1.0 for this project). 

K2 = correction factor for angle of attack of flow (K2 = 1.2 for this project). 

K3 = correction factor for bed condition (K3 = 1.1 for this project). 

a = pier width (a = 53.75 ft for this project). 

Fr = Froude number. 

Kw = correction factor for wide piers.

fEq,pier = equation uncertainty factor for pier scour. 
41

Fr is calculated using equation 12: 

(12)

Where: 

V = flow velocity directly upstream of the pier. 

y1 = flow depth directly upstream of the pier. 

g = gravitational constant. 

Kw, the correction factor for wide piers, is calculated by equation 13 for clear-water conditions 

and equation 14 for live-bed conditions, respectively. 

(13)

(14)

fEq,pier in equation 11 is a factor to account for the equation uncertainty of the local pier scour 

equation. According to NCHRP Report 761, fEq,pier follows a normal distribution with the mean 

and COV of 0.82 and 0.23, respectively (Lagasse et al. 2013). 

The total pier scour (ys,total) was the sum of the contraction scour and local pier scour depth, as 

shown in equation 15: 

(15)

A total of 750,000 contraction (ys,contr), local pier (ys,pier), and total pier scour depths (ys,total) were

calculated from 750,000 flow conditions obtained at Step 3 in the previous section by using 

equations 9 or 10, equation 11, and equation 15. For every 75-yr bridge life, 10,000 maximum 

contraction (ys,contr,max), local pier (ys,pier,max), and total pier scour depth (ys,total,max) values were 

obtained. The exceedance probability of scour depth was computed by 1 minus the empirical 

cumulative distribution function of the 10,000 maximum scour depth for each scour component, 

and the results are shown in figure 33 through figure 35. 
42 

Source: FHWA.

Figure 33. Graph. Exceedance probability of contraction scour at various scour elevations.

Source: FHWA.

Figure 34. Graph. Exceedance probability of local pier scour at various scour elevations.
43 

Source: FHWA.

Figure 35. Graph. Exceedance probability of total pier scour at various scour elevations.

A summary of the original MDOT scour analysis is shown in table 9. It was observed that the 

exceedance probability of the design contraction scour depth for Q100 and Q500 flood is 28.8 and 

8.6 percent, respectively; the exceedance probability of the design local pier scour depth for Q100

and Q500 flood is 21.3 and 8.8 percent, respectively; and the exceedance probability of the design 

total pier scour depth for Q100 and Q500 flood is 19.8 and 6.9 percent, respectively.

Table 9. Design scour depth for Q100 and Q500 flood. 

Scour 

Component

Q100 Q500

Scour 

Depth

(ft)

Elevation 

(ft)

Exceedance 

Probability 

(percent)

Scour 

Depth

(ft)

Elevation 

(ft)

Exceedance 

Probability 

(percent)

Contraction 

scour 

5 545 28.8 6 544 8.6 

Local pier 

scour 

31 519 21.3 35 515 8.8 

Total pier 

scour 

36 514 19.8 41 509 6.9 

Figure 36 compares the exceedance probabilities calculated by using the NextScour decay 

function method and HEC-18 equations. The deterministic analysis with the NextScour decay 

function method shows that the scour elevation for Q100 and Q500 flood can be increased from 

514 ft and 509 ft (determined by HEC-18 equation) to 530 ft (determined by decay function). 

With the probabilistic analysis, the exceedance probabilities of the total pier scour depth for Q100

and Q500 flood can be reduced from 19.8 and 6.9 percent to 3.3 percent. The significant 

improvement mainly attributes to the consideration of soil erosion resistance at the clay layer 

when using the decay function. It was found that the proposed decay function method was able 

to achieve a shallower scour depth with less uncertainty compared to the scour design by using 

the existing HEC-18 equations, which assume a uniform sand layer. 
44 

Source: FHWA.

Figure 36. Graph. Comparison of exceedance probability of total pier scour.
45

CHAPTER 8. SUMMARY

The Lafayette Avenue Bridge replacement project provided an excellent candidate for the TPF 

study. CFD modeling, physical flume scour testing, and soil erosion testing were all conducted 

by researchers in the FHWA Hydraulics Laboratory.

Hydraulic modeling using 2D and 3D models found an initial representative CFD shear stress of 

14.5 Pa (0.305 psf) for Q100 and 20.2 Pa (0.424 psf) for Q500 at the riverbed near the left upstream 

fender cylinder. Physical modeling included fabricating two 1:50 scale half-bridge models for 

flume scour tests. Various approach velocities were used to observe the scour around fender 

cylinders, piers, and abutments. Scour tests revealed that the deepest scour happened upstream of 

the fender cylinders, and abutment scour was minimal. 

CFD-computed bed shear stresses on incremental scour bathymetries, which were collected from 

the flume scour tests, were used to develop the decay functions of scour at the fenders. Soil 

erosion tests identified that the clay below the 530-ft elevation had a mean critical shear stress of 

20.5 Pa (0.431 psf) with a COV of 0.32. 

A probabilistic scour analysis approach was considered using the Monte Carlo simulation. 

Nearly a million flow discharges were generated using a batch HEC-RAS computation that 

considered various statistical uncertainties in the flood event and a distribution of Manning’s n

values. With the decay function equations and the computed approach shear stresses from the 

resulting Monte Carlo flow parameters, the distribution of decayed shear stress at 1-ft 

incremental scour depth was calculated. The exceedance probability of the total fender scour for 

a continuous depth was determined by comparing the decayed shear stress against the soil 

resistance distribution at each depth. The exceedance probability of the total fender scour 

reaching the clay layer at 530 ft was determined to be 3.3 percent in the 75-yr bridge design life. 

For comparison, the probabilistic scour analysis was also performed by using the HEC-18 

equation, in which the exceedance probability of the design total fender scour depth was 19.8

and 6.9 percent for Q100 and Q500 flood, respectively. It was found that by using the decay 

function, which considered the resistance of the clay layer, the exceedance probability of total 

fender scour depth for Q100 and Q500 flood reduced from 19.8 and 6.7 percent, respectively, to 

3.3 percent.

This study result provides MDOT with a research tool to quantify a risk level in bridge 

foundation design. It also demonstrated NextScour could significantly improve the accuracy of 

bridge scour estimates. Future monitoring of the bridge site is recommended, however, to verify 

the scour predictions after a flood event.

47

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Recyclable

Recommended citation: Federal Highway Administration, 

NextScour Case Study: The Lafayette Avenue Bridge 

Over the Saginaw River in Bay City, Michigan

(Washington, DC: 2023) https://doi.org/10.21949/1521957