Proceedings of the 6th

International Conference on the Application

of Physical Modelling in Coastal and Port Engineering and Science

(Coastlab16)

Ottawa, Canada, May 10-13, 2016

Copyright ©: Creative Commons CC BY-NC-ND 4.0

1

Critical shear stress of silts and clays used in levees during floodwall

overtopping S. MEHDI MOUSAVI

1, ABDOLREZA OSOULI

2, ERGYS BORAJ

3, FRANCISCO LAGUNAS

4 SINA NASIRI

5

1 Graduate research Assistant, Texas Tech University, U.S.A, m.mousavi-ghorabaee@ttu.edu

2 Assistant Professor, Southern Illinois University Edwardsville, U.S.A, aosouli@siue.edu

3 Undergraduate research assistant, Sothern Illinois University Edwardsville, U.S.A, eboraj@siue.edu

4 Undergraduate research assistant, Sothern Illinois University Edwardsville, U.S.A, flaguna@siue.edu

5 Graduate research assistant, Sothern Illinois University Edwardsville, U.S.A, snasiri@siue.edu

ABSTRACT

Prediction of scour in levees during the floodwall overtopping is critical. One of the key components in predicting the

scour depth and erosion rate is the critical shear stress of the soil. Critical shear stress is the stress that if exceeded, the

erosion starts. The resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding

at particle contacts. There are several empirical and analytical procedures to predict the critical shear stress of cohesive

soils. The empirical methods usually consider the effect of each contributing parameter separately. The effect of saturation

ratio of soils is usually neglected in determining erosion rates. Through a series of lab scaled levee tests, an equation is

developed for predicting critical strength of the cohesive soils. The considered contributing factors in this study are

plasticity index, compaction level, and median particle diameter together and saturation ratio. Results show that higher

compaction level and higher plasticity will result in higher critical shear stress and higher saturation ratio decreases the

critical shear stress. A method is proposed to identify the critical shear stress and verified by laboratory tests for levee

applications.

KEWORDS: Levee, Overtopping, Erodibility, Critical shear stress, Cohesive soil

1 INTRODUCTION

Overtopping has always been of principal concern for coastal structures constructed to defend against flooding. A

sample of these constructions is shown in Figure 1 (Guy, 2014). Similar structures may also be used to provide protection

against coastal erosion. Other structures may be built to protect ship navigation or mooring within ports, harbours or

marinas formed by breakwaters. Within river banks, harbours, or along shorelines, reclaimed areas must be defended

against flooding and erosion. (William Allsop, 2008)

Figure 1. Levee and floodwall system (Guy, 2014)

2

Levees are one of the earthen structures constructed across rivers or in the vicinity of lakes and seas to protect lands

while floods, storm surges and hurricanes occur. Due to global warming and changes in sea level and weather, the number

and the intensity of these natural disasters have increased demand for more stable and stronger protection structures on the

bank of the rivers. Levee failures during hurricane Katrina in 2005 in New Orleans are the famous classical examples.

(Mazdak Karimpour, 2014)

Among various failure mechanisms that cause levee breaches, soil erosion is one of the most important factors

(Kamalzare, 2013). Predicting soil erosion and scour generation when overtopping happens is important in order to design

stable levee and floodwalls. One of the key components in predicting the scour depth and erosion rate is the critical shear

stress of the soil. Critical shear stress is the stress that if exceeded, the erosion starts. The resistance of soil is a result of

friction and interlocking of particles, and possibly cementation or bonding at particle contacts.

There are several approaches for determining�� . Critical shear stress can be determined via flume tests using soil parameters such as particle size and soil specific gravity, measured in situ with a submerged jet test device, or it can be

assumed zero. For cohesionless soils, Shields’ diagram provides estimates of critical shear stress based on particle size using

a representative particle diameter and assuming no interaction among the sediment particles (Ing. A. Shields, 1936). The

diagram then was extended to be used for fine grained materials but due to lack of enough experimental verification, its use

can result in significant underestimation. Visually,�� is determined by measuring the shear stress at failure (L. A. Clark, 2007).

The most widely used erosion measurement technique, particularly for cohesive soils, involves an open-channel flow

test with soil forming the bed. The critical stress �� is then determined visually or graphically. Smerdon and Beasley (1961) conducted a flume study on eleven cohesive Missouri soils to relate basic soil properties to ��. The empirical relations developed between the soil properties and �� are shown by Equations 1 to 4 (L. A. Clark, 2007):

�� = �. ��(�)�.�1

�� = ��. �(��)��.��2

�� = �. �� × ����.����3

�� = �. ��� × ���.����4

Where

��= Critical shear stress (pa) ��= Plasticity index � =Dispersion ratio �!�=Mean particle size (m) ��=Percent clay by weight (%)

Niel (1973) incorporated the depth of flow as well as soil properties and presented Eq 5 (L. A. Clark, 2007):

�� = �. "����#$(%& − �)����/�)�/�

5

Where

��= Critical shear stress (pa) +,= Specific weight of water (N/m3) -&=Specific Gravity of soil

�!�=Mean particle size (m) d=Depth of flow (m)

In a more recent relevant study, Julian and Torres (2006) estimated critical shear stress based on the percentage of silt

and clay (SC) (L. A. Clark, 2007):

.� = �. � + �. �""�(01) + �. ���(01)� − �. ��2 − �(01)�6

Where

3

��= Critical shear stress (pa) 45= Silt-clay content defined as particle sizes less than 0.063 mm Submerged Jet Test is another way to calculate the critical shear stress. The jet scours the soil until the maximum scour

depth is reached, and the rate of scour approaches to zero. At this equilibrium condition, the critical shear stress can be

computed (Hanson, 1990).

To consider all relevant soil properties (i.e., Plasticity Index (PI), Compaction Level (CL), and Saturation Ratio (SR),

mean particle size) in critical shear stress estimation of fine grain soils, the erosion of levee soils were studied in a series of

lab-scaled levee-floodwall simulation tests. A strain-measuring device has been developed to measure the applied stresses

by freefall water from overtopped floodwalls. The results were used to develop a formula for �� based on all soil properties mentioned above from some of the conducted tests. Then, the developed equation was verified by using the other tests

results which were not used in its development. At the end, the results from the verified equation was compared to other

proposed equations from literature.

2 Methodology

In this study the critical shear stress of levee soils due to overtopping was investigated by running lab scale models and

using a strain measuring device. The 1 to 20 scaled physical models, constructed in laboratory, represent typical levees

across Mississippi river. All the tests included a floodwall, which was represented by a wooden plate at the crest of the

levee. A box with dimensions of 0.9 m (3ft) wide, 2.4 m (8 ft) long and 1.8m (6 ft) high was constructed using plywood and

clear acrylic plastic material. The modeled levees inside this box were 0.23 m (9 in) wide, 0.18 m (7 ft) long and the top of

the levee was 0.35 m (14 in) high. Figure 2 shows the constructed levee in the box and the scour width and depth

definitions.

Figure 2. The simulator box used for constructing the levees

Induced Stresses have been measured using a strain-measuring device, which was calibrated to measure the induced

stresses of falling water on the soil surface. Figure 3 shows the strain-measuring device and the installation of the device

inside the box. Figure 4 shows a sketch of the device during floodwall overtopping. The strain gauge is mounted on a

cantilever beam and the stresses applied to the beam from water freefall is measured using the strain gauge. The cantilever

beam was positioned at different elevations to measure the applied stresses induced by various height of water freefall.

Since, during floodwall overtopping usually a scour hole is developed behind the floodwall, the freefall water impinges to a

pool. In order to represent the difference of the pool depth above the soil surface during overtopping when stresses are

measured using the device, a plastic container was attached on top of the beam to allow a formation of a pool. The strain

gauge reading of the device was calibrated for the “with pool” and “without pool” scenarios. Different dead weights were

hung from the tip of the beam and the generated strains were calibrated to develop a correlation of applied load versus strain

reading. There, the force applied by the free waterfall could be estimated using the calibrated strain gauge. Once the loads

acting on the beam is known, the applied stress will be calculated using equation 7:

67789:)%;�:%%(7��:)(8?)@=;C:%;�

4

Figure 3. The strain gauge measurement device

Figure 4. The strain gauge device under the floodwall during floodwall overtopping

The soil used for these tests was classified as low plasticity silty soil (ML) and called borrow material in this paper.

Also low plastic clay (CL) was mixed with silty soil to have variation in plasticity of levee soil. Therefore, besides the ML

soils, two other soil mixtures were prepared. First mixture included 1 to 1 ratio of silty soil (ML) to clayey soil (CL), and

the second mixture consisted of 1 to 2 ratio of silty soil (ML) to clayey soil, respectively. Therefore, total of three soils were

used in levee tests. Sieve Analysis (ASTM D1921), Compaction (ASTM D698), Plasticity index tests (ASTM D4318) were

performed on both of these soils and the mixtures. The plasticity of borrow material (ML) and the 1:1, and 1:2 ML to CH

soil mixtures were 0%, 6% and 9%, respectively. The compaction tests were based on standard proctor test.

The levee models constructed using 70, 80 and 90 percent compaction levels. Ten different lab scaled levee-floodwall

erosion tests were conducted. These ten tests are specified in Table 1. In each test, the targeted compaction levee of the

material was accomplished by the use of a hand tamper on several thin lifts. After compaction of each layer, 3 samples were

taken from the compacted layer to verify the targeted compaction level.

In order to run the tests, first the reservoir behind the levee was filled up to the top of the floodwall level. The flooding

process started by pumping water to the reservoir. The resulted overtopping nappe initiated the scour generation. The

overtopped water was drained at the downstream of the levee and was circulated to the reservoir. In order to monitor the

erosion of levee material due to floodwall overtopping, three camcorders were used to monitor the generated scour from

side, top and front angles.

The vertical velocity of the water was calculated by using Equation 8 (free fall equation) (Johnson, 2012).

$ = G�DC8

Where w is the vertical speed at the point where water impinges the soil, g is the gravity acceleration and h is the

distance from top of the floodwall to the levee surface.

5

Table 1. Tests used for creation and verification of the proposed equation

Test

Number

Test Usage Saturation

Ratio (SR)

(%)

��� (mm) Compaction Level (CL)

(% )

Plasticity

Index (PI)

(%)

1 Equation

Development

19 0.035 70 0

2 Equation

Development

75 0.035 70 0

3 Equation

Development

36 0.035 90 0

4 Equation

Development

80 0.035 90 0

5 Equation

Development

19 0.02 70 6

6 Equation

Development

30 0.02 80 6

7 Equation

Development

47 0.02 90 6

8 Equation

Verification

47 0.02 70 0

9 Equation

Verification

70 0.02 70 0

10 Equation

Verification

38 0.015 80 9

3 Results

Figure 5 shows the erosion-applied stress results of the 7 tests. Using the results of this figure, the trend line of each

data set could be obtained. The results show that with an increase of the plasticity index and compaction level the critical

shear stress increases. The results also show that with an increase in the saturation ratio from Test 5 to 4, the critical shear

stress decreases. Although the change of mean particle size had the smallest effect on the critical stress, it is observed that

with an increase in the soil particle diameter there is a reduction in critical shear stress. The observations of the effect of PI

and mean particle size on critical shear stress are in agreement with previous studies in this area (Kimiaghalam, 2014).

Table 2 presents all the variable considered for developing the final equation with each test’s trend line. A linear trend

line was used for all the tests because of the good agreement with the test results. Trend lines then extended to intercept with

applied stress axis to find the critical shear stress.

Using the results of these tests, Equation 9 is proposed for determining the critical shear stress of the fine grain soils of

levees during overtopping. The cumulative variance of the calculated �� and the measured �� from the tests is 0.14 pascal. Table 2 shows the calculations of the variance.

.� = �. ��(IJ) × (1K)�.�� × (�. ���)��� × (�. ��)0L 9

Where

PI= Plasticity index

CL= Compaction Level

D50= Mean Particle size (mm)

SR= Saturation ratio

6

Figure 5. Erosion rate-Applied stress results of the tests used for creation of the proposed equation

Table 2. Variances of the outcome of the figures vs. the proposed equation

Test

Number

(SR)

%

��� (mm)

(CL)

%

(PI) Erosion rate (ER)-. trend line equation

.� from Fig. 5 (Pa) .� From Eq. 9

(pa)

Variance

(Pa)

1 19 0.035 80 0 ER=51.425τ - 28.566 0.87 1.20 0.056

2 75 0.035 80 0 ER=60.707τ - 20.129 0.33 0.52 0.017

3 36 0.035 90 0 ER=42.624τ - 71.945 1.687 1.36 0.052

4 80 0.035 90 0 ER=42.624τ - 71.945 0.82 0.70 0.007

5 19 0.02 70 6 ER=47.774τ - 39.062 2.6 2.47 0.008

6 30 0.02 80 6 ER=52.437τ - 172.06 3.28 3.23 0.001

7 47 0.015 90 6 ER=98.492τ - 261.11 3.65 3.66 0.000

Equation 9 was verified using 3 other levee-floodwall tests shown in Table 3. Equation 9 was used to predict the .� and the results were compared with the .� calculated from the trend lines. As the results show there is a good agreement between calculated critical shear stresses from equation with the measured ones from Figure 5. The biggest difference was

observed on the 2CL: 1ML soil combination, which was about 1 Pa lower than the trend line. This is probably because no

tests with PI of 9% was used in development of Eq 9.

Table 3. Detailed information of verification tests

Test

Number

(SR)

%

��� (mm)

(CL)

%

(PI) Erosion rate (ER)-. trend line equation

.� from trend line (pa)

.� from equation

9 (pa)

Variance

(Pa)

1 047 0.02 70 6 ER=109.72τ – 143.42 1.31 1.19 0.12

2 70 0.02 70 0 ER=143.15τ – 40.92 0.28 0.36 0.08

3 38 0.015 80 9 ER=25.92τ -199 7.67 6.05 1.62

At the end for comparison with other proposed equations, results from Equation 9 were compared with the results from

Equation 1, 3 and 5. A mean depth of flow of 1 inch that represented the test conditions for the levee-floodwall systems was

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40

Ero

sio

n R

ate

(m

m/h

r)

Applied stress (Pa)

PI=0 CL=80% SR=19%

PI=0 CL=90% SR=36%

PI=6 CL=70% SR=19%

PI=6 CL=80% SR=30%

PI=6 CL=90% SR=47%

PI=0 CL=80% SR=75%

PI=0 CL=90% SR=80%

7

considered in Equation 5. Results are shown in Table 4 with all the participating variables. All equations except Equation 9

are insensitive to soil properties. It is also worth noting that the only equation that considers almost vertical impingement of

water freefall is Eq 9. The other equations assume horizontal flow of water on the soil.

Table 4. Comparing the results of different equations

Test

Number

(SR)

%

��� (mm)

(CL)

%

(PI) .� Eq 1 (pa) .� Eq 3 (pa) .� Eq 5 (pa) .� Eq 9 (pa)

1 19 0.035 80 0 0.29 3.53 1.27 1.20

2 75 0.035 80 0 0.29 3.53 1.27 0.52

3 36 0.035 90 0 0.29 3.53 1.27 1.36

4 80 0.035 90 0 0.29 3.53 1.27 0.70

5 19 0.02 70 6 0.76 3.54 0.75 2.47

6 30 0.02 80 6 0.76 3.54 0.75 3.23

7 47 0.02 90 6 0.76 3.54 0.75 3.66

Figure 6 shows the results of proposed equation comparing to other equations. It can be seen that the proposed

equation is sensitive to change in alteration in soil properties and provides an interval of critical shear stress from 0.52 Pa to

3.66 Pa. Equation 1 which only considers plasticity index provides the lowest critical shear stress of 0.29. The average

critical shear stress from Equation 1 is 0.53 Pa. Equation 3 provides larger critical shear stress comparing to the other

equations with a mean of 3.54 Pa. Equation 5 provides a mean of 1 Pa for critical shear stresses. Finally, the mean critical

shear stress based on Equation 9 for the seven tests is 1.9 Pa.

Figure 6. Comparing results of proposed equation vs. other equations

4 Summary and Conclusion

The goal of this study was to propose a new equation for predicting critical shear stress of the silty and clayey soils

used in levees during floodwall overtopping. The proposed equation unlike previous equations takes into account the

plasticity index, saturation ratio, mean particle size and compaction level of the soil in predicting critical shear stress and is

more appropriate for erosions due to free fall water. Levees with larger compaction levels and percentage of plastic

material will have higher resistance against shear stresses induced by water overtopping from floodwall while increase in

saturation ratio and mean grain size results in reduction of critical shear stress of the levee’s soil.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

1 2 3 4 5 6 7

Cri

tica

l S

he

ar

stre

ss (

Pa

)

Test number

Proposed Equation Eq1 Eq3 Eq5

8

REFERENCES

Guy, A. (2014, September 17). Climate London. Retrieved from Climate London:

http://climatelondon.org.uk/articles/climate-change-and-the-thames-estuary/

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Transactions of the ASAE, 132-137.

Ing. A. Shields, W. P. (1936). Application of Similarity Principles and Turbulence Research to Bed-load Movement. Soil

Conservation Service Cooperative Laboratory, California Institute of Technology.

Johnson, E. B. (2012). Levee scour from overtopping storm waves and scour counter measures. Ocean Engineering, 72-78.

Kamalzare, M. H. (2013). Computer Simulation of Levee Erosion and Overtopping. Geo-Congress at Stability and

Performance of Slopes and Embankments. San Diego.

L. A. Clark, T. M. (2007). Methods for determining streambank critical shear stress and soil erodibility: implications for

erosion rat e predictions. American Society of Agricultural and Biological Engineers, 95-106.

Mazdak Karimpour, A. O. (2014). Levee erosion and scour potential due to floodwall overtopping. XV Danube. Vienna.

Navid Kimiaghalam, S. P. (2014). An experimental study on the effects of physical, mechanical,and electrochemical

properties of natural cohesive soils on critical shear stress and erosion rate. International Journal of Sediment

Research.

William Allsop, T. B. (2008). Direct hazards from wave overtopping – the forgotten aspect of coastal flood risk assessment?

Flood and Coastal Management Conference. Manchester.