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Publication Number: FHWA-RD-03-083
Date: June 2003

Bridge Scour in Nonuniform Sediment Mixtures and in Cohesive Materials: Synthesis Report

6. EFFECT OF COHESION ON ABUTMENT

SCOUR

In this chapter, effects of cohesion on local abutment scour are investigated experimentally for Montmorillonitic and Kaolinitic clay mixtures using larger scale, 1.2-m and 2.4-m wide test flumes at the Engineering Research Center, CSU. For cohesive soils with significant clay content (30 percent for the present mixtures), soil parameters such as compaction, initial water content, degree of saturation, shear strength, and type of clay mineral dominate the abutment scour. In this study these effects are quantified for flow conditions with Froude numbers ranging from 0.2 to 0.9. Equations relating flow and selected cohesive soil parameters to abutment scour were developed to explain the variability of abutment scour with cohesion properties. These equations express abutment scour in cohesive soils relative to clear-water scour in noncohesive material for the same flow and geometry conditions. Under the same geometric and flow conditions, measured scour in cohesive materials varies from 7 percent to 140 percent of that measured in medium sand.

6.1 GENERAL

Flow structure around abutments and the resulting local scour were studied in the past in numerous experimental, numerical, and analytical investigations for noncohesive materials. As a result, series of empirical and semiempirical prediction equations were developed to relate the scour depth at bridge abutments to different approach flow conditions, to sediment size and gradations, and to different abutment types and sizes.

The mechanism of cohesive-material scour is significantly different from scouring of alluvial noncohesive materials. The process involves not only the balancing of flow-induced shear stresses and the shear strength of soils to withstand scour, but also the chemical and physical bonding of individual particles and the properties of the eroding fluid. Cohesive materials, once eroded, remain in suspension. As a result, the phenomenon identified as clear-water local scour in noncohesive materials always prevails. Along with the eroding fluid properties, the scour process in cohesive soils is strongly affected by the amount of cohesive material present in the soil mixture as well as the type of mineral clay, initial water content, soil shear strength, and compaction of the clay. The objectives of this paper are to apply the knowledge gained in the past in cohesive material scour to study local scour around abutments and to analyze effects of compaction, initial water content, soil shear strength, and the approach flow conditions on abutment scour. For this purpose two different types of clay mixtures were used. The first cohesive mixture was a naturally occurring soil that contained 32 percent Montmorillonite mineral clay with almost equal amounts of fine sand and silt. The second cohesive mixture was prepared by blending 30 percent pure Kaolinite clay with medium sand. Experiments using the first soil were conducted under unsaturated and saturated soil conditions. The Kaolinite clay scour experiments were limited to unsaturated conditions where compaction and initial water content of the mixture were varied. As a result of this experimental study, empirical relationships were developed relating the scour in cohesive material to that observed in the noncohesive material that was used in preparing the mixtures under the same flow and geometric conditions.

6.2 EXPERIMENTAL SETUP AND MEASUREMENTS

The two categories of abutment scour experiments presented in this paper are classified as Montmorillonite and Kaolinite clay experiments. In each category of experiments, series of runs utilizing two experimental flumes were conducted by varying the clay properties under different flow conditions. A total of 126 experiments were conducted covering a wide range of flow and soil conditions. Details of the experiments are presented by Yakoub(22) and Molinas and Reiad (5).

Flumes

Experiments were conducted in two different larger scale test flumes housed at the Engineering Research Center at CSU to achieve desired flow intensities. These flumes are identified as the sediment transport flume and the steep flume. The sediment transport flume is 2.4 m wide by 60 m long, and the steep flume is 1.2 m wide by 12 m long. The flow depths used in the experiments varied between 0.12 m and 0.3 m, and approach Froude numbers ranged from 0.1 to 0.9.

Measurements

Flow and sediment parameters measured in experiments were velocity distribution (vertical, longitudinal, and lateral), depth of flow, depth of scour, initial water content of soil, Torvane shear strength, and degree of compaction. Velocity measurements were carried out by the use of a magnetic flow-meter. In the experiments, approach velocity to each abutment was determined by depth- and width-integrated average of vertical velocity profiles. Similarly, the approach depth was determined from a width- and length-averaged value of water surface and bed elevation measurements. The bed elevations were measured along the flumes across the flow channel before and after each experiment. The depth of abutment scour was measured during and at the end of each experiment; it was determined by the difference between the minimum bottom elevation at the nose region of abutment and the maximum elevation away from the structure.

Cohesive soils

In this study, two cohesive soil mixtures were used. The first is a naturally occurring homogeneous soil containing 32 percent clay, 30 silt, and 38 percent fine sand particles. Utilizing the X-Ray Diffraction Test, the dominant clay mineral was found to be Montmorillonite. According to the unified soil classification system, the cohesive soil is classified as medium plasticity clay and the texture as clay loam. The second cohesive soil mixture was prepared by blending commercially obtained pure Kaolinite clay with medium sand. This mixture was composed of 30 percent clay and 70 percent sand. Montmorillonite clay experiments studied the effects of compaction, initial water content, and shear strength for unsaturated and saturated soil conditions. This was achieved by compacting the cohesive material placed around the abutments at various degrees of compaction and by using soils of different initial water content, whereas Kaolinite clay experiments investigated the effects of initial water content on unsaturated clay erosion by preparing mixtures with varying initial water contents. In these experiments compaction was also varied over a narrow range of conditions.

Abutments

In the experiments, rectangular vertical-wall abutments constructed of clear Plexiglas with protrusion lengths of 0.22 m and 0.11 m were used. Lengths of these abutments in the direction of flow were 0.44 m and 0.22 m, respectively. The scour depth development was measured against time utilizing three measuring tapes attached to the interior wall of each abutment and by the use of a small inclined mirror.

6.3 EXPERIMENTAL RESULTS

Results of abutment scour experiments in cohesive materials are presented in tables 29 through 32. These tables present the flow conditions and volumetric scour measurements along with cohesive soil properties and measured maximum local scour values. The clay mineral present in the cohesive soil mixtures used in set 1 and set 2 experiments (given in tables 29 and 30) was Montmorillonite. Tables 31 and 32 present results of experiments utilizing Kaolinite clay mixtures. The analysis that is presented in this study is aimed at quantifying cohesive material effects in terms of easily obtainable soil parameters. For this purpose, the parameters selected to represent the scour resistance of cohesive materials were limited to those given in tables 29 through 32. They were: clay content, compaction, initial water content, shear strength, and clay mineral. The effects of clay content on bridge scour are treated in a separate chapter in this report. In the following analysis, effects due to cohesive material properties other than clay content are investigated. In the past, erodibility of cohesive soils was also related to surrounding fluid, disturbed versus undisturbed soils, sodium adsorption ratio, plasticity, etc. Due to the complexities involved in quantifying these effects (a much larger variety of clays), these parameters were excluded from the present analysis.

Table 29. Results of Montmorillonite clay experiments conducted in the 2.44-m wide sedimentation flume using a 0.22-m abutment protrusion length.

Run
ID
Flow
Discharge
Q
(l/s)
Percent
Clay
Content
CC
(%)
Initial
Water
Content
IWC
(%)
Dry
Density
dry
(t/m3)
Compaction
C
(%)
Torvane
Shear
Strength
S
(kPa)
Flow
Depth
Y
(m)
Approach
Velocity
V
(m/s)
Scour
Depth
Dsc
(m)
Scour
Volume
Vsc
(l)
Flow
Temp.
T
(oC)
8-12-MA 144.42 0 4.0 1.758 91.4 3.655 0.311 0.171 0.020 1.812 17.2
8-13-MA 184.06 0 4.0 1.758 91.4 3.655 0.312 0.223 0.058 4.106 17.2
8-14-MA 176.98 0 4.0 1.758 91.4 3.655 0.320 0.207 0.047 3.313 17.2
8-15-MA 198.22 0 4.0 1.758 91.4 3.655 0.309 0.235 0.060 4.191 17.2
8-16-MA 229.37 0 4.0 1.758 91.4 3.655 0.319 0.250 0.069 4.899 17.2
8-17-MA 257.12 0 4.0 1.758 91.4 3.655 0.322 0.287 0.110 9.090 17.2
8-18-MA 295.63 0 4.0 1.758 91.4 3.655 0.326 0.317 0.171 14.102 17.2
8-19-MA 242.39 0 4.0 1.758 91.4 3.655 0.327 0.253 0.087 3.398 17.2
8-20-MA 172.73 10 5.5 1.510 74.2 9.204 0.275 0.171 0.088 5.607 17.2
8-21-MA 147.25 10 5.5 1.510 74.2 9.204 0.282 0.162 0.027 2.039 17.2
8-22-MA 202.47 10 5.5 1.510 74.2 9.204 0.296 0.210 0.049 3.511 17.2
8-23-MA 232.20 10 5.5 1.510 74.2 9.204 0.289 0.229 0.061 4.304 17.2
8-24-MA 263.35 10 5.5 1.510 74.2 9.204 0.307 0.271 0.066 4.587 16.7
8-25-MA 311.49 10 5.5 1.510 74.2 9.204 0.298 0.341 0.142 10.987 16.7
8-26-MA 368.12 10 5.5 1.510 74.2 9.204 0.307 0.424 0.204 25.287 16.7
8-27-MA 311.49 32 29.7 1.483 85.8 9.786 0.245 0.448 0.000 0.000 13.3
8-27-MB 311.49 32 13.1 1.266 73.2 44.037 0.258 0.378 0.110 9.005 13.3
8-28-MA 518.20 32 27.5 1.483 85.8 14.679 0.248 0.704 0.000 0.000 12.2
8-28-MB 518.20 32 38.1 1.363 78.8 2.936 0.242 0.646 0.107 2.492 12.2
8-29-MA 792.87 32 27.5 1.091 63.1 14.679 0.244 0.869 0.000 0.000 12.2
8-29-MB 792.87 32 38.1 1.141 66.0 2.936 0.258 0.674 0.162 8.495 12.2
8-30-MA 368.12 32 16.7 1.271 73.5 46.973 0.252 0.549 0.249 15.489 12.8
8-30-MB 368.12 32 20.8 1.295 74.9 44.037 0.260 0.479 0.122 3.993 12.8
8-31-MA 368.12 32 17.7 1.000 57.9 17.615 0.257 0.451 0.354 54.000 12.2
8-31-MB 368.12 32 13.4 1.110 64.3 10.765 0.273 0.415 0.271 47.997 12.2
8-32-MA 254.85 13 8.7 1.581 80.0 11.743 0.252 0.351 0.140 10.506 13.3
8-32-MB 254.85 5 6.1 1.691 86.5 5.872 0.264 0.314 0.107 9.005 13.3
8-33-MA 311.49 13 6.4 1.352 68.4 11.743 0.253 0.436 0.277 28.005 12.8
8-33-MB 311.49 5 4.0 1.432 73.3 5.872 0.265 0.390 0.195 24.013 12.8
8-34-MA 424.75 13 2.4 1.420 71.9 9.786 0.233 0.646 0.445 95.003 13.3
8-34-MB 424.75 5 3.1 1.501 76.8 7.829 0.238 0.558 0.366 78.013 13.3
8-35-MA 424.75 32 17.1 1.306 75.5 48.930 0.245 0.631 0.198 25.995 13.3
8-35-MB 424.75 32 16.4 1.260 72.9 34.251 0.244 0.594 0.357 44.995 13.3
8-36-MA 501.21 32 34.4 1.380 79.8 2.936 0.246 0.838 0.155 16.509 15.0
8-36-MB 501.21 32 44.6 1.240 71.7 0.979 0.230 0.799 0.238 25.995 15.0
8-37-MA 736.24 32 35.7 1.363 78.8 2.936 0.306 0.911 0.082 2.407 15.0
8-37-MB 736.24 32 45.3 1.329 76.9 0.979 0.292 0.951 0.271 44.004 15.0
8-38-MA 948.61 32 36.8 1.340 77.5 2.936 0.351 0.997 0.091 4.502 15.6
8-38-MB 948.61 32 44.4 1.237 71.6 0.979 0.320 1.039 0.338 95.994 15.6

Note:

Duration of experiments varied between 12 to 16 hours.


Table 30. Results of Montmorillonite clay experiments conducted in the 1.22-m wide flume using a 0.11-m abutment protrusion length.

Run
ID
Flow
Discharge
Q
(l/s)
Percent
Clay
Content
CC
(%)
Initial
Water
Content
IWC
(%)
Dry
Density
gdry
(t/m3)
Compaction
C
(%)
Torvane
Shear
Strength
S
(kPa)
Flow
Depth
Y
(m)
Approach
Velocity
V
(m/s)
Scour
Depth
Dsc
(m)
Scour
Volume
Vsc
(l)
Flow
Temp.
T
(oC)
4-39 36.81 32 20.2 1.363 78.8 34.251 0.140 0.149 0.025 0.113 13.3
4-40 59.47 32 19.7 1.369 79.2 31.316 0.143 0.271 0.064 1.161 13.3
4-41 48.14 32 19.8 1.300 75.2 34.251 0.146 0.198 0.041 0.510 13.3
4-42 70.79 32 19.6 1.317 76.2 40.123 0.144 0.360 0.109 4.191 13.3
4-43 39.64 32 20.0 1.088 63.0 13.113 0.135 0.165 0.029 0.255 13.3
4-44 55.78 32 19.6 1.139 65.9 13.700 0.140 0.256 0.063 1.104 13.9
4-45 67.96 32 20.2 1.134 65.6 14.092 0.140 0.351 0.137 8.495 13.9
4-46 90.61 32 19.5 1.409 81.5 66.056 0.129 0.503 0.168 9.486 13.9
4-47 49.55 32 12.3 1.214 70.2 37.187 0.131 0.238 0.081 3.398 13.9
4-48 36.81 32 12.3 1.168 67.6 36.209 0.129 0.192 0.049 1.246 13.9
4-49 55.22 32 11.1 1.139 65.9 27.401 0.132 0.311 0.145 9.713 13.9
4-50 66.54 32 10.8 1.141 66.0 23.487 0.135 0.372 0.193 17.500 13.9
4-51 45.31 5 6.2 1.472 75.3 5.480 0.130 0.223 0.031 0.425 13.9
4-52 70.79 5 6.2 1.472 75.3 5.480 0.131 0.378 0.130 11.497 13.9
4-53 53.80 5 6.2 1.472 75.3 5.480 0.130 0.305 0.071 1.897 13.9
4-54 35.40 5 6.2 1.472 75.3 5.480 0.126 0.168 0.030 0.113 13.9
4-55 87.78 5 6.2 1.472 75.3 5.480 0.130 0.506 0.209 25.513 13.9
4-56 38.23 13 11.2 1.478 74.8 27.401 0.132 0.198 0.030 0.113 13.3
4-57 48.14 13 11.2 1.478 74.8 27.401 0.129 0.226 0.055 0.850 13.3
4-58 56.63 13 11.2 1.478 74.8 27.401 0.135 0.308 0.096 3.200 13.9
4-59 65.13 13 11.2 1.478 74.8 27.401 0.130 0.357 0.130 5.493 13.3
4-60 82.12 13 11.2 1.478 74.8 27.401 0.129 0.491 0.137 7.108 12.8
4-61 80.70 32 35.6 1.371 79.3 4.698 0.129 0.482 0.081 0.595 13.3
4-62 101.94 32 30.4 1.413 81.7 4.893 0.131 0.616 0.066 1.897 13.3
4-63 120.35 32 29.0 1.420 82.1 5.480 0.134 0.683 0.034 2.209 13.3
4-64 106.19 32 35.3 1.380 79.8 3.327 0.134 0.637 0.085 3.511 13.3
4-65 121.76 32 34.8 1.415 81.9 4.306 0.133 0.686 0.107 3.908 14.4
4-66 52.39 32 43.3 1.323 76.5 1.566 0.129 0.287 0.074 1.388 14.4
4-67 65.13 32 40.3 1.363 78.8 1.175 0.130 0.384 0.093 2.209 14.4
4-68 82.12 32 44.5 1.323 76.5 1.370 0.128 0.482 0.119 5.409 13.9
4-69 48.14 32 45.8 1.351 78.1 1.370 0.131 0.250 0.044 0.311 13.3
4-70 104.77 32 45.8 1.351 78.1 1.370 0.141 0.619 0.172 5.805 13.9

Note:

Duration of experiments varied between 12 to 16 hours.


Table 31. Results of Montmorillonite clay experiments conducted in the 2.44-m wide flume using a 0.1-m abutment protrusion length.

Run
ID
Flow
Discharge
Q
(l/s)
Percent
Clay
Content
CC
(%)
Initial
Water
Content
IWC
(%)
Dry
Density
gammadry
(t/m3)
Compaction
C
(%)
Torvane
Shear
Strength
S
(kPa)
Flow
Depth
Y
(m)
Approach
Velocity
U
(m/s)
Scour
Depth
Dsc
(m)
Scour
Volume
Vsc
(l)
Flow
Temp.
T
(oC)
8-80-MA 356.79 32 46.7 1.226 70.9 0.979 0.177 0.664 0.113 4.899 20.0
8-81-MA 240.69 0 4.0 1.758 91.4 3.655 0.155 0.503 0.253 21.011 18.3
8-81-MB 240.69 5 6.9 1.363 69.7 1.957 0.148 0.433 0.210 5.097 18.3
8-81-MC 240.69 10 11.4 1.463 71.9 7.829 0.155 0.384 0.131 0.963 18.3
8-81-MD 240.69 13 11.0 1.254 63.5 7.829 0.146 0.366 0.140 1.161 18.3
8-82-MA 172.73 0 4.0 1.758 91.4 3.655 0.152 0.360 0.158 16.990 18.9
8-82-MB 172.73 5 4.3 1.389 71.1 1.957 0.148 0.308 0.104 3.596 18.9
8-82-MC 172.73 10 10.1 1.449 71.2 7.829 0.158 0.277 0.073 1.104 18.9
8-82-MD 172.73 13 5.6 1.329 67.3 7.829 0.155 0.250 0.067 1.246 18.9
8-83-MA 133.09 0 4.0 1.758 91.4 3.655 0.143 0.280 0.113 6.513 19.4
8-83-MB 133.09 5 4.2 1.300 66.5 1.957 0.145 0.229 0.094 1.897 19.4
8-83-MC 133.09 10 8.5 1.320 64.9 7.829 0.148 0.204 0.067 0.850 19.4
8-83-MD 133.09 13 9.9 1.335 67.6 7.829 0.146 0.177 0.052 0.453 19.4
8-84-MA 300.16 0 4.0 1.758 91.4 3.655 0.155 0.680 0.274 63.996 20.0
8-84-MB 300.16 5 6.2 1.289 66.0 1.957 0.151 0.591 0.262 32.989 20.0
8-84-MC 300.16 10 11.3 1.193 58.7 7.829 0.151 0.533 0.152 16.990 20.0
8-84-MD 300.16 13 9.8 1.286 65.1 7.829 0.149 0.454 0.165 19.001 20.0

Note:

Duration of experiments varied between 12 to 16 hours.


Table 32. Results of Kaolinite clay experiments in the 2.44-m wide flume, with 0.22-m abutment width.

Run
ID
Flow
Discharge
Q
(l/s)
Percent
Clay
Content
CC
(%)
Initial
Water
Content
IWC
(%)
Dry
Density
gammadry
(t/m3)
Compaction
C
(%)
Torvane
Shear
Strength
S
(kPa)
Flow
Depth
Y
(m)
Approach
Velocity
V
(m/s)
Scour
Depth
Dsc
(m)
Scour
Volume
Vsc
(l)
Flow
Temp.
T
(oC)
8-71-MA 157.16 30 14.8 1.661 84.1 30.337 0.177 0.308 0.015 0.453 19.4
8-71-MB 157.16 30 13.4 1.672 84.7 41.101 0.173 0.262 0.000 0.000 19.4
8-71-MC 157.16 30 13.3 1.684 85.3 42.080 0.168 0.238 0.055 1.303 19.4
8-72-MA 421.92 30 15.4 1.707 86.4 23.487 0.191 0.811 0.030 0.793 19.4
8-72-MB 421.92 30 14.7 1.758 89.0 41.101 0.183 0.820 0.037 0.963 19.4
8-72-MC 421.92 30 15.4 1.707 86.4 16.636 0.175 0.960 0.070 1.897 19.4
8-73-MA 286.00 30 20.1 1.741 88.2 7.829 0.159 0.637 0.021 0.651 18.9
8-73-MB 286.00 30 26.5 1.621 82.1 3.914 0.157 0.527 0.040 1.048 18.9
8-73-MC 286.00 30 29.7 1.523 77.1 1.957 0.165 0.457 0.037 0.991 18.9
8-74-MA 351.13 30 18.8 1.732 87.7 10.765 0.165 0.719 0.030 0.850 20.0
8-74-MB 351.13 30 23.4 1.641 83.1 4.893 0.155 0.686 0.046 1.189 20.0
8-74-MC 351.13 30 27.5 1.541 78.0 2.936 0.139 0.777 0.058 1.388 20.0
8-75-MA 237.86 30 21.8 1.695 85.8 4.893 0.158 0.512 0.000 0.000 20.0
8-75-MB 237.86 30 25.1 1.641 83.1 1.957 0.161 0.460 0.000 0.000 20.0
8-75-MC 237.8 30 29.7 1.532 77.6 0.979 0.170 0.439 0.000 0.000 20.0
8-76-MA 489.88 30 21.8 1.695 85.8 4.893 0.193 0.817 0.037 0.963 20.0
8-76-MB 489.88 30 25.1 1.641 83.1 1.957 0.177 0.808 0.067 1.812 20.0
8-76-MC 489.88 30 29.7 1.532 77.5 0.979 0.167 1.201 0.158 9.486 20.0
8-77-MA 170.75 10 15.5 1.695 85.8 2.936 0.152 0.030 0.146 8.014 19.4
8-77-MB 170.75 20 17.1 1.741 84.5 3.914 0.158 0.223 0.012 0.396 19.4
8-77-MC 170.75 50 16.6 1.552 85.2 45.016 0.173 0.195 0.094 3.511 19.4
8-77-MD 170.75 50 27.1 1.478 81.1 2.936 0.174 0.171 0.000 0.000 19.4
8-78-MA 235.03 10 13.5 1.692 85.6 2.936 0.155 0.512 0.229 13.989 19.4
8-78-MB 235.03 20 14.7 1.518 73.6 3.914 0.155 0.460 0.046 0.481 19.4
8-78-MC 235.03 50 15.7 1.335 73.3 45.016 0.168 0.439 0.192 6.513 19.4
8-78-MD 235.03 50 25.8 1.586 87.0 2.936 0.171 0.372 0.000 0.000 19.4
8-79-MA 288.83 10 16.2 1.841 93.2 2.936 0.162 0.582 0.256 21.011 20.0
8-79-MB 288.83 20 16.8 1.775 86.1 3.914 0.161 0.479 0.052 1.359 20.0
8-79-MC 288.83 50 15.7 1.335 73.3 45.016 0.174 0.424 0.177 12.006 20.0
8-79-MD 288.83 50 30.9 1.455 79.9 2.936 0.174 0.357 0.000 0.000 20.0
8-80-MB 356.79 20 16.8 1.775 86.1 3.914 0.170 0.607 0.152 10.987 20.0
8-80-MC 356.79 50 15.7 1.335 73.3 45.016 0.176 0.539 0.226 18.010 20.0
8-80-MD 356.79 50 30.9 1.455 79.9 2.936 0.168 0.472 0.000 0.000 20.0

Note:

Duration of experiments varied between 12 to 16 hours.


6.4 ANALYSIS

The functional relationship between the maximum depth of abutment scour and the parameters defining the soil, fluid, and the geometry of the abutment is derived through dimensional analysis. The depth of abutment scour in cohesive material (Dsc) is expressed as a function of the following independent variables:

Equation 36. D sub lowercase S and C equals lowercase F open parenthesis D sub lowercase S, Y, lowercase A, L, V, IWC, C, CC, S, M lowercase N, T, lowercase T, lowercase G, Greek alpha, Greek phi, Greek rho, Greek N closed parenthesis.
(36)

in which Ds = depth of abutment scour in noncohesive material for conditions corresponding to Dsc; Y = depth of approach flow; a = abutment protrusion length; L = length of abutment in the direction of flow; V = velocity of approach flow; IWC = initial water content; C = compaction related to the optimum compaction; CC = clay content; S = Torvane shear stress, Mn = type of clay (e.g., Kaolinite, Illite, Montmorillonite); T = water temperature; t = duration of experiment; g = gravitational acceleration, alpha symbol = angle of attack; abutment shape factor symbol = abutment shape factor; rho symbol = fluid density; and L = kinematic viscosity of fluid.

Applying the dimensional analysis using Ds, V, and D as repeating variables, and using appropriate simplifications, the following set of dimensionless parameters can be obtained:

Equation 37. D sub lowercase S and C divided by D sub lowercase S equals lowercase F open parenthesis IWC, S divided by open parenthesis Greek rho times V squared closed parenthesis, C, M lowercase N closed parenthesis.
(37)

In the derivation of equation 37, the CC was eliminated as a variable since, as shown in Chapter 4, the effects of this parameter was found to be an independent factor up to 12 percent clay content. In the cohesive abutment scour experiments, the clay content was kept above 30 percent. In abutment scour experiments the variation of scour with time was measured. This relationship was shown by Molinas and Reiad to be an asymptotic function with a sharp initial scour development followed by a gradual increase(5). The initial rate of scour hole development is generally controlled by the nature of the clay mineral and other cohesive material parameters such as compaction, initial water content, etc. Experimental and theoretical studies have shown that the velocity at the nose region of a vertical wall abutment is amplified by a factor of 1.2 to 1.8 times the approach V. According to Molinas, Khereldin, and Wu, bottom shear stresses that are related to V2 are also amplified (by up to 11 times) and cause local scour in the affected zone(26). If approach velocities are increased beyond a threshold value defined as critical velocity, the entire approach channel bottom becomes subject to general scour in addition to the local scour. Under these conditions, the scour hole development process continues until equilibrium slopes are attained for the entire reach and may last indefinitely. The experimental study presented in this report limited itself to conditions in which the oncoming flows do not scour the approach reach (clear water conditions). Under these conditions, as soon as the scour hole reaches a depth where the shear stress within the base becomes equal to the critical shear stress of the cohesive material, local scouring ceases. The duration of experiments in the study were long enough to maintain the equilibrium condition for at least 4 hours. The final scour depth values obtained under these conditions are independent of time, and therefore in deriving equation 37 the time parameter, t, is eliminated. Additionally, the dimensionless S can be related to C and IWC, further reducing the number of parameters.

The local abutment scour analysis in this study was conducted separately for the two clay types. This distinction is made since the type of clay mineral (Mn) was found to have a dominant effect on the scourability of bed material.

Montmorillonite Scour

The measured values of (Dsc /Ds) were regressed against the remaining dimensionless groups in equation 37 using nonlinear multiple regression analysis. The best-fit regression equations resulting from the statistical analysis of experimental data were reported earlier by Molinas, Reiad, and Jones(27) and are given below.

For unsaturated clays with initial water content less than 25 percent:

Equation 38. D sub lowercase S and C divided by D sub lowercase S equals open parenthesis 2.186 minus 0.05342 times IWC closed parenthesis times open parenthesis 15.407 minus 0.522 times C plus 0.006087 times C squared minus 0.0000235 times C cubed closed parenthesis.
(38)

where the IWC and C are in percent.

For saturated clays with initial water content in the range of 28 to 45 percent:

Equation 39. D sub lowercase S and C divided by D sub lowercase S equals open parenthesis 4.76 minus 0.451 times IWC plus 0.01361 times IWC squared minus 0.000126 times IWC cubed closed parenthesis times open parenthesis 0.339 plus 0.01744 times C closed parenthesis.
(39)

In deriving equations 38 and 39, IWC ranged from 12 to 45 percent, and C ranged from 58 to 89 percent. Equations 38 and 39 were developed based on laboratory tests in which Froude numbers ranged from 0.1 to 0.6 and soil shear strength values ranged from 0.1 to 0.63 kg/cm2. The plot of equations 38 and 39 with observed data is presented in figure 36.

Figure 36. Graph. Computed and measured relative abutment scour for Montmorillonite clay. This figure shows measured relative scour on the X axis and computed relative scour on the Y axis. The data lie along a straight line at 45 degrees with some minor scatter.

Figure 36. Computed and measured relative abutment scour for Montmorillonite clay.

Figure 37. Graph. Computed and measured relative abutment scour for Kaolinite clay.  This figure shows measured relative scour on the X axis and computed relative scour on the Y axis. The data lie along a straight line at 45 degrees with some minor scatter.

Figure 37. Computed and measured relative abutment scour for Kaolinite clay.

Kaolinite Scour

For unsaturated Kaolinite clay soils, the basic form of equation 37 was retained. For the cohesive soil consisting of 30 percent Kaolinite clay and 70 percent medium sand with a median diameter of 0.81 mm, the best-fit regression equation from the statistical analysis of experimental data is:

Equation 40. D sub lowercase S and C divided by D sub lowercase S equals open parenthesis 0.12 plus 0.014 times IWC minus 0.00205 times IWC squared minus 0.000057 times IWC cubed closed parenthesis times open parenthesis 0.4 plus 0.017 times C closed parenthesis.
(40)

Scour initiating velocities for the Kaolinite clay mixture were experimentally determined to be 0.6 m/s. For velocities smaller than this value, the scour ratio is zero. The plot of equation 40 with observed data is presented in figure 37.

6.5 CONCLUSIONS

Abutment scour in cohesive soils shows a wide range of variability depending on the properties of soils. In the experiments, under the same geometric and flow conditions, measured scour in cohesive materials varied anywhere from 7 percent to 140 percent of that measured in medium sand. This is due to initial water content, soil shear strength, degree of compaction, and type of clay mineral present in the soil. For Montmorillonitic soils, the relative scour depth is expressed in terms of initial water content and degree of compaction. For unsaturated Montmorillonitic mixtures, abutment scour depth decreases as the compaction and initial water content increases. For saturated cohesive soils, however, the scour depth is mainly a function of initial water content and is inversely proportional to initial water content. For unsaturated Kaolinitic mixtures the initiation of scour takes place under higher flow intensities, and under same flow conditions, the total scour may be up to 80 percent smaller than the corresponding scour encountered in noncohesive material.

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