Relationship Between Erodibility and Properties of Soils (2019)

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138 As discussed in Chapters 1 and 2, one of the critical issues associated with all erosion test devices is that they do not give the same erosion parameters and, therefore, do not lead to the same type of results. To overcome this issue, all tests need to be studied in the same fashion. In Chapter 2, all available erosion tests, their applications, test results, and physical specifications are discussed in detail. Table 4 (Chapter 2) lists all the types of erosion tests discussed in this report. Performing numerical studies for all tests would be cost prohibitive; therefore, the investigators decided to study a selected number of the most common tests: erosion function apparatus (EFA), jet erosion test (JET), hole erosion test (HET), and borehole erosion test (BET). The numerical simulations presented in this chapter are divided into two sections: 1. The evolution of the hydraulic shear stress at the soil–water interface in nonerodible soils and 2. Monitoring the variation in shear stress at the soil–water interface including the erosion process. Section 6.1 presents the results of numerical simulations for the JET, EFA, HET, and BET prior to erosion. Section 6.2 presents a novel technique using numerical simulations to compare the results of the EFA with those of the JET, BET, and HET, including the erosion process. 6.1 Results of Numerical Simulation for Nonerodible Soils 6.1.1 CHEN4D Code For this task, computational fluid dynamics (CFD) is used together with a code called Computational Hydraulic Engineering in 4 Dimensions (CHEN4D), which was developed by H. C. Chen (Chen et al. 1990). The goal is to simulate each erosion test and develop data reduction techniques that will give the same soil erosion information from these tests without changing the test. CHEN4D is used to perform CFD simulations of the JET, the HET, and the BET and backcalculate the erosion function, which leads to proper matching of the results of these tests with the erosion function from the EFA. These simulations are expected to lead to a common data reduction process of erosion tests and a common output of all erosion tests, to bring uniformity in erosion studies, and to keep all soil erosion testing options open for the engineer. The CHEN4D code solves unsteady three-dimensional Navier–Stokes equations together with advanced near-wall turbulence closure and sediment transport models for fluid–structure interaction problems around complex configurations. A moving overset (chimera) grid approach is implemented to accommodate time domain simulation of arbitrary body motions and grid C H A P T E R 6 Comparison of Selected Soil Erosion Tests by Numerical Simulation

Comparison of Selected Soil Erosion Tests by Numerical Simulation 139 deformations such as those encountered in multiple-ship and floating pier interactions; green water and slamming impact of ships in random waves; vortex-induced motion of offshore platforms; and pier scour, abutment scour, and bridge scour, including overtopping. Both the soil roughness and bed load transport models are incorporated in CHEN4D for the simulation of erosion and accretion of deformable soils. The industry standard CFD models such as FLUENT and CD-adapco’s (2016) STAR Computational Continuum Mechanics (STAR-CCM+) have limited capability in dealing with arbitrary multiple-body motions or large grid deformations (Chen et al. 2013). 6.1.2 JET Simulations This section discusses the results of numerical simulations of the JET. The simulations were based on the large laboratory JET device developed by Hanson and Hunt (2007) (Figure 97). The goal for this phase of the work was to simulate the submerged jet test with the CHEN4D code to obtain the hydraulic shear stress distribution on the surface of the sample prior to any erosion of the soil. Therefore, the soil was assumed to be nonerodible, and the distribu- tion of jet flow velocity and shear stress on the surface of the soil were obtained. Two cases were assumed for the surface of the soil: (1) a smooth surface to represent a clayey soil and (a) (b) 0.25 " 4.584 " 2.4685 " 16.5 " Ø4.0000 4.5 " 1.9685 " 16.5 " Ø12.0000 1.5 " 12 " Ø4.5000 8.25 " 4 " 16.5 " Ø12.5000 8.25 " Figure 97. Large laboratory JET device used in the numerical simulations: (a) photograph and (b) schematic diagram with dimensions in inches (Hanson and Hunt 2007).

140 Relationship Between Erodibility and Properties of Soils (2) a surface with 5% roughness to represent coarse sand and gravel. Figure 98 shows the dis- tribution of shear stress versus the distance away from the centerline of the soil surface for the smooth case (clayey soils) and the shear stress distributions in different time steps, as well as the time-averaged shear stress. The time-averaged shear stress distribution for the smooth and 5% roughness surfaces are shown in Figure 99. The results are in general agreement with the shape of Hanson’s shear stress distribution shown in Figure 11 (Chapter 2). The shear stress Figure 98. Shear stress distribution on the soil surface from the center of the surface to the sides in different time steps. Figure 99. Average time shear stress distribution for smooth surfaces and surfaces with 5% roughness.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 141 on the point of impingement is zero, while the maximum shear stress occurs at a short distance from the center. Figure 99 shows that for soil with a smooth surface (clayey soil), the maximum is less as compared with the case where the soil surface is rough. Also, it is observed that the maximum shear stress happens farther from the center for the rough soil surface than for the smooth one. Figure 100 shows the evolution of the jet on the smooth surface as the steady state jet condition develops. Figure 101 shows the evolution of the jet on the rough surface as the steady state jet condition develops. The next step is to replace the soil (white block) with an erodible surface to obtain the erodibility parameters of different soils for different hydraulic conditions. Figure 100. Velocity results of submerged jet evolution in different time steps for the smooth surface (from top left to bottom right).

142 Relationship Between Erodibility and Properties of Soils 6.1.3 HET Simulations CFD numerical simulations were performed for the Wan and Fell (2002) HET. Figure 102 shows the geometry of the HET used in the numerical simulations. The HET is discussed in greater detail in Chapters 1 and 2 of this report. As in the case of the JET simulations, the soil was assumed to be nonerodible. The water flow velocity and shear stress distributions through the HET hole were obtained. The initial stresses were evaluated for the 6-mm-diameter hole in the center of the sample at an average Figure 101. Velocity results of submerged jet evolution in different time steps for the rough surface (from top left to bottom right).

Comparison of Selected Soil Erosion Tests by Numerical Simulation 143 velocity (in the hole) of 2.5 m/s. For the HET simulations, the same two cases as considered in the JET were tested: (1) smooth soil representing clayey soils and (2) a surface with 5% rough- ness, representing sandy soils. It is worth mentioning that in the HET, the soil is compacted in a compaction mold with an inner diameter of 4 in. (101.6 mm), and a 6-mm hole is drilled in the center of the sample. The time-averaged shear stress distribution through the 6-mm hole along the 101.6-mm length of the sample was obtained. Figure 103 shows that the shear stress along the hole was approximately 30 Pa for the coarser surface (sandy soils). As expected, the shear stress was less when the surface was smooth (clayey soils). The flow condition at the beginning of the hole is not constant. The existence of negative shear stress at the beginning is due to a small region of recirculation right where flow impinges on the hole. Due to this separate region, contraction occurs and, consequently, flow starts recirculating to get into the hole. The shear stress along the drilled hole can also be estimated by using Moody charts (Figure 104). Assuming a flow velocity of 2.5 m/s and diameter of 6 mm, the discharge is 7.1 × 10–5 m3/s. Reynolds number (Re) is calculated to be 14,670 by using Equation 58. Re (58) vDw= r µ (a) (b) 63.5 90 .0 50 .8 90.0 180.0 53 .0 18 0. 0 55.5 56 .5 CROSS SECTION A-A LONGITUDINAL SECTION 6. 0 A A 35 mm DIA. HOLE FOR OUTLET PIPE Figure 102. HET used in numerical simulations at Texas A&M University: (a) photographs and (b) schematic diagram with dimensions in millimeters (Wan and Fell 2002).

144 Relationship Between Erodibility and Properties of Soils Figure 103. Shear stress distribution through the drilled hole along the length of the sample for both smooth and 5% rough surfaces, considering an average velocity of 2.5 m/s in the hole. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.015 0.01 103 104 105 106 107 108 5x10–4 2x10–4 5x10–5 5x10–6 10–6 10–4 10–5 0.05 0.04 0.03 0.02 0.015 0.01 0.005 0.002 0.001 R elative Pipe R oughness d Re = VdReynolds Number, Fr ic tio n Fa ct or Transition Region Complete turbulence Smooth Pipe Laminar Flow 64 Re Friction Factor = 2d V 2l P Material (mm) Figure 104. Moody diagram (Moody 1944).

Comparison of Selected Soil Erosion Tests by Numerical Simulation 145 where rw = density of water (kg/m3), v = flow velocity (m/s), D = diameter of flow channel (m), and µ = viscosity of water (1.027 × 10–3 kg/m/s). On the basis of the knowledge that the surface roughness is 5%, the friction factor is obtained as approximately 0.075 from the Moody diagram. By using Equation 7 (Chapter 2), the shear stress is calculated to be 50 Pa, which is greater than the 25 Pa obtained through the numerical analysis results shown in Figure 103. The differ- ence shows that there is a discrepancy between the Moody chart predictions and the numerical simulations and that the Moody charts overestimated the shear stress by 100% in this case. For the case of a smooth pipe, on the basis of the knowledge that Re = 14,670, the friction factor is 0.028 on the basis of the Moody chart (see Figure 104). By using Equation 7, the shear stress is calculated as 21.875 Pa, which is larger than the 10 Pa obtained through the numerical simula- tion shown in Figure 103. Again, the Moody diagram gives a higher value. The evolution of the velocity for the smooth case is shown in Figure 105. 6.1.4 EFA Simulations The EFA geometry used in the simulations is described in Chapter 2. As mentioned earlier, the EFA comprises a rectangular channel approximately 1.24 m long. On the bottom surface, a sample the size of a Shelby tube with an outer diameter of 76.2 mm is extruded. The surface of the conduit is assumed to be smooth. Three target velocities (U = 1 m/s, 3 m/s, and 6 m/s) are considered in the results. The channel height is used as the characteristic length in the simula- tions instead of the channel hydraulic diameter (Dh = 67.33 mm). The roughness of the soil surface is 5% (of the channel height) in all cases. Figure 106 to Figure 108 show the shear stress distribution on both the top and bottom surfaces of the channel for U = 1 m/s, 3 m/s, and 6 m/s, respectively. In these figures, both the smooth (upper half) and rough (lower half) results on the same figure are plotted to facilitate a direct comparison of the effect of surface roughness. The shear stresses were also calculated by using the Moody chart (Figure 104). Re can be calculated by using rw = 1,000 kg/m3, D = 0.00508 m, and µw = 1.027 × 10–3 kg/m/s. The friction factors for the case of 5% roughness were then obtained as 0.079, 0.075, and 0.073 for U = 1 m/s, 3 m/s, and 6 m/s, respectively. Equation 7 was then used to measure the shear stresses for each velocity. The resulting shear stresses from the Moody chart are 9.875 Pa, 84.375 Pa, and 324 Pa for U = 1 m/s, 3 m/s, and 6 m/s, respectively. Comparison of the shear stress results obtained from the numerical simulations with the Moody chart shows that as in the case of the HET results, the Moody chart overestimates the shear stress values by about 25%. Figure 109 to Figure 111 show the shear stress evolution when the velocity is 1 m/s, 3 m/s, and 6 m/s, respectively. The soil surface roughness is 5% in all cases. 6.1.5 BET Simulations Numerical simulations were also performed for the BET, assuming a nonerodible soil for the purpose of obtaining the shear stress distribution at the soil surface. The geometry of the BET is described in Chapter 2. For the following simulations, two flow rates—23 gallons per minute (gpm) and 90 gpm—were considered. Also, three distances between the jet orifice and the bottom surface of the borehole were considered (1 in., 3 in., and 6 in.). Figure 27 (Chapter 2)

146 Relationship Between Erodibility and Properties of Soils Figure 105. Velocity evolution for the smooth case.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 147 Figure 106. Shear stress distribution on both top surface (which is smooth) and bottom surface (which encompasses the rough soil surface) for U = 1 m/s. Figure 107. Shear stress distribution on both top surface (which is smooth) and bottom surface (which encompasses the rough soil surface) for U = 3 m/s. Figure 108. Shear stress distribution on both top surface (which is smooth) and bottom surface (which encompasses the rough soil surface) for U = 6 m/s.

148 Relationship Between Erodibility and Properties of Soils Figure 109. Shear stress evolution captured in six time steps when the flow velocity in the conduit is 1 m/s (from top left to bottom right).

Comparison of Selected Soil Erosion Tests by Numerical Simulation 149 Figure 110. Shear stress evolution captured in six time steps when the flow velocity in the conduit is 3 m/s (from top left to bottom right).

150 Relationship Between Erodibility and Properties of Soils Figure 111. Shear stress evolution captured in six time steps when the flow velocity in the conduit is 6 m/s (from top left to bottom right).

Comparison of Selected Soil Erosion Tests by Numerical Simulation 151 shows the schematic diagram of the BET: the jet induces shear stress both at the circular bottom surface and along the side walls in the z-direction. Shear stress results for both regions are presented below for the two aforementioned flow rates. Figure 112 shows the shear stress distribution along the radius of the circular bottom surface of the borehole when the flow rate is 90 gpm. When the gap between the jet orifice and the bottom surface is smaller, the maximum induced shear stress will be larger and farther from the jet’s impingement point. Figure 113 shows the shear stress distribution along the side wall of the drilled hole for the same three gap intervals when the flow rate is 90 gpm. The maximum shear stress is largest when the gap between the discharge orifice and the bottom surface is 3 in. The same approach was used for a flow rate of 23 gpm. Figure 114 and Figure 115 show the results for the shear stress on the circular bottom surface and on the side wall, respectively. In these figures, the effect of a 2% roughness is shown only when the gap between the discharge orifice and the bottom surface is 1 in. It should be noted that zero elevations are set as the bottom of the borehole in Figure 113 and Figure 115. Figure 114 shows that the shear stress is higher when the gap is small (1 in.), and decreases when the gap increases. Also, the shear stress distribution is slightly different when a 2% roughness is considered for the bottom surface (coarser soils). Comparison of Figure 114 and Figure 112 shows that the shear stress distribution is smoother at higher flow rates. Figure 115 shows the measured shear stress along the side wall of the borehole. The maximum shear stress, similar to the case in which the flow rate was 90 gpm, occurred when the gap between the jet orifice and bottom of the borehole was 3 in. It is also observed that 2% roughness on the sides results in a slightly higher shear stress value as compared with the smooth side. Figure 115 also shows that after about 0.5 m above the bottom discharge, the shear stress on the borehole wall has become constant. 90 gpm, 6-inch gap 90 gpm, 3-inch gap 90 gpm, 1-inch gap Figure 112. Shear stress distribution within the circular bottom surface of the drilled hole with 1-in., 3-in., and 6-in. gap between the jet orifice and borehole bottom surface when the flow rate is 90 gpm.

152 Relationship Between Erodibility and Properties of Soils 90 gpm, 6-inch gap 90 gpm, 3-inch gap 90 gpm, 1-inch gap Figure 113. Shear stress distribution along the side wall surface of the drilled hole with 1-in., 3-in., and 6-in. gap between the jet orifice and borehole bottom surface when the flow rate is 90 gpm. 23 gpm, 6-inch gap, smooth 23 gpm, 1-inch gap, 2% roughness 23 gpm, 3-inch gap, smooth 23 gpm, 1-inch gap, smooth Figure 114. Shear stress distribution within the circular bottom surface of the drilled hole with 1-in., 3-in., and 6-in. gap between the jet orifice and borehole bottom surface when the flow rate is 23 gpm.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 153 Figure 116 shows an example of the numerical simulations in four different time steps. In this example, the gap between the discharge orifice and the bottom of the borehole is 1 in. and the flow rate is 23 gpm. Velocities range from 0 to 6 m/s at the bottom of the borehole and from 0 to 2 m/s on the sides. 6.2 Results of Numerical Simulation Including Erosion 6.2.1 Methodology In the previous section, the development of shear stress on the soil–water interface was simulated and discussed for the EFA, JET, HET, and BET on the basis of the assumption that the soil was not erodible. This section presents the results of numerical simulations including the erosion process. The STAR-CCM+ was used for this purpose. The STAR-CCM+ can generate the CFD in soil–fluid interaction problems such as the erosion process. The primary goal of using numerical simulations was to compare the results of the four erosion testing methods (EFA, HET, JET, and BET) in similar soil samples. As discussed in Chapter 1, the results of each erosion test can be translated into a relationship between the shear stress/velocity and the erosion rate. In fact, the erosion rate (z . ) is a function of shear stress/velocity (see Chapter 1, Equations 1 and 2). The relationship between the erosion rate and the shear stress (or velocity) is called the erosion function. The numerical simulations were concentrated on finding out how the JET, the HET, and the BET would react to the erosion function obtained from the EFA on one common soil sample. The results of the numerical simulations were compared with the actual test results obtained through experiments. The soil surface in the JET, the HET, and the BET was defined as a moving boundary. The erosion process was simulated by using the movement of these boundaries. This movement develops according to the erosion function equation that is obtained from the EFA 23 gpm, 6-inch gap, smooth 23 gpm, 1-inch gap, 2% roughness 23 gpm, 3-inch gap, smooth 23 gpm, 1-inch gap, smooth Figure 115. Shear stress distribution along the side wall surface of the drilled hole with 1-in., 3-in., and 6-in. gap between the jet orifice and borehole bottom surface when the flow rate is 23 gpm.

154 Relationship Between Erodibility and Properties of Soils test performed on the same soil sample. Figure 117 shows a flowchart describing the procedure for each numerical simulation. The numerical simulations according to the procedure shown in Figure 117 are presented in the following three forms: 1. EFA’s erosion function on the JET, 2. EFA’s erosion function on the HET, and 3. EFA’s erosion function on the BET. Before the results of these comparisons are discussed, the details of the mesh created for the JET, the HET, and the BET in STAR-CCM+ are presented. Figure 116. Example of velocity results of jet evolution in different time steps for the rough surface when the gap between the orifice and bottom surface is 1 in. (from top left to bottom right).

Comparison of Selected Soil Erosion Tests by Numerical Simulation 155 6.2.2 Mesh Geometry and Soil–Water Interface For all three erosion tests (JET, HET, and BET), two-dimensional axisymmetric models were created. The mesh used in these models was quadrilateral. Detailed information on the mesh used for each erosion test is presented in Table 30 below. Figure 118, Figure 119, and Figure 120 show the axisymmetric models created for the JET, the HET, and the BET, respectively. The dimensions used for the models are in accordance with the dimensions of these testing devices in the Soil Erosion Laboratory at Texas A&M University. For detailed information on dimensions of each test device, see Chapter 4, Section 4.1 of this report. One of the important laws in the fluid dynamics is the law of the wall. This law states that in turbulent flow, the mean velocity at a specific point and the logarithm of the distance between that point and the fluid region boundary (or wall) are proportional. The effect of this law is very significant, especially for those parts of the flow that are closer than 20% of the flow height to the 1. Obtain the erosion function equation from the EFA test for one soil sample. 2. Assign the erosion function from Step 1 to the soil–water interface in the desired test (JET, HET, BET). 3. Develop the velocity (v) and shear stress (τ) profiles at the soil– water interface by using CFD. 4. Calculate the erosion rate (z . ) using the erosion function assigned to the interface in Step 2. 5. Move the boundary according to the z . calculated in the previous step. Figure 117. Procedure for numerical simulations conducted to compare the results of the EFA with the results of the JET, HET, and BET. Erosion Test Type of Mesh Number of Cells Number of Faces Number of Vertices JET Quadrilateral 8,809 17,501 9,115 HET Quadrilateral 22,918 45,151 23,673 BET Quadrilateral 31,765 62,244 33,054 Table 30. Detailed information on mesh created for each erosion test.

Figure 118. Axisymmetric model for the JET. Figure 119. Axisymmetric model for the HET. Figure 120. Axisymmetric model for the BET.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 157 wall. The general formulation of the law of the wall (Equation 59) solves for the average velocity parallel to the wall in turbulent flows (high Reynolds numbers). 1 ln (59)u y C= k ++ + + where u+ = dimensionless velocity parameter = u (average velocity parallel to the wall) ÷ the uT (friction velocity); y+ = dimensionless wall coordinate, obtained by using Equation 60; k and C + = constants equal to 0.41 and 0.5, respectively, for a smooth wall according to Schlichting and Gersten (2000). (60)y y u v T= ++ where v = local kinematic viscosity of the fluid, uT = friction velocity at closest fluid region boundary, and y = distance of the point to the nearest wall. The parameter y+ is one of the most important parameters in defining the law of the wall and conducting the fluid mechanics numerical simulations. For this study, the value of y+ was designed to be <1 to achieve a very small cell distance between the wall and the point of flow (y < 10–6 m). 6.2.3 Model Development Numerical simulations were performed for the JET, HET, and BET as explained in the previous sections (Figure 117). The results of comparisons between the EFA test and the other erosion tests are presented separately in the following sections. 6.2.3.1 EFA’s Erosion Function on the JET As discussed in Section 6.2.1, the erosion rate can be written as a function of shear stress. For the purpose of comparing the EFA test results with the JET results, the procedure described in Figure 117 was followed for four samples: two sand, one silt, and one clay. The name of these samples are Sand #1 and Sand #2 (sand samples), FHWA Sample 2 (silt sample), and B-1 (4–6 ft) Beaumont (clay sample). As presented in Figure 117, the first step was to obtain the relationship between the erosion rate, z . , and the shear stress for each sample in the EFA. This relationship, also called the erosion function, was obtained after testing each of the four samples in the EFA and then assigned to the soil–water interface in the JET simulation, which is defined in the form of a moving boundary. Once the shear stress was developed on the soil–water interface, the erosion rate at the boundary was calculated by using the assigned erosion function and the boundary moves accordingly. This process repeats itself and the boundary keeps moving until the developed shear stress on the interface becomes equal to or less than the critical shear stress for the tested soil. To distinguish between smooth clay and rough sand surface, the roughness height (RH) was defined in STAR-CCM+. RH is the height of the roughness of the soil particles (equivalent

158 Relationship Between Erodibility and Properties of Soils to ε defined in the Moody diagram shown in Figure 104). For each simulation in this study, whether the sample was clay, silt, or sand, four RH values were considered: 1. RH = 0 mm, or smooth surface; 2. RH = 0.5 mm; 3. RH = 1 mm; and 4. RH = 3 mm. Figure 121 shows the results of the numerical simulations for the Sand #1 sample when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface in the JET model. The observed JET results (black circles) were slightly overestimated through STAR-CCM+ when their erosion function obtained from the EFA was assigned to the soil–water interface. This overestimation was less pronounced when the RH was close to 0 mm (smooth surface). The actual average roughness height (D50/2) for Sample SE-1 was about 0.14 mm; therefore, smooth surface results would be a relatively reasonable assumption. Figure 122 shows an example of the numerical simulations in four different time steps for the Sand #1 sample. In this example, the soil–water interface was defined as a moving boundary. The velocity profile of the flow is shown for each time step. Velocity for this example ranged from 0 to 3.2 m/s. The highest velocity was at the jet nozzle, and when the water reached the soil surface, its velocity became less. This process continued until the shear stress induced on the boundary (i.e., the soil–water interface) became less than the measured critical shear stress from the EFA’s erosion function. Figure 123 shows the results of the numerical simulations for the Sand #2 sample when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface in the JET model. The observed JET results (black circles) were slightly underestimated through STAR-CCM+ when their erosion function obtained from the EFA was assigned to the Observed STAR-CCM+ Roughness Height = 3 mm STAR-CCM+ Roughness Height = 1 mm STAR-CCM+ Roughness Height = 0.5 mm STAR-CCM+ Smooth Figure 121. Scour depth versus time for observed JET and simulated JET for Sand #1.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 159 (1) Time = 4.5 min (2) Time = 9 min (3) Time = 13.5 min (4) Time = 18 min Figure 122. Example of moving boundary for Sand #1 with RH = 0.5 mm.

160 Relationship Between Erodibility and Properties of Soils soil–water interface. This underestimation was more pronounced when the RH was close to 0 mm (smooth surface). The actual average RH (D50/2) for Sample SE-2 was about 0.122 mm. At the end of the 40-min JET, the observed scour hole was 2.2 cm, while the STAR-CCM+ simulations (using the EFA erosion function assigned to the soil–water interface) resulted in an almost 1.4-cm scour hole in the smooth surface case. Figure 123 also shows that for higher RHs (near 3 mm), the results of the numerical simulations tended to be closer to the observation for Sample SE-2. Figure 124 shows the results of the numerical simulations for Sample B-1 (4–6 ft) when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface in the JET model. The observed JET results (black circles) were slightly overestimated through STAR-CCM+ when their erosion function obtained from the EFA was assigned to the soil–water interface. This overestimation was more pronounced when the RH was greater. The actual average RH (D50/2) for B-1 (4–6 ft) was about 0.0024 mm. At the end of the 40-min JET, the observed scour hole was 0.62 cm, while the STAR-CCM+ simulations (using the EFA erosion function assigned to the soil–water interface) resulted in an almost 1.0-cm scour hole in the smooth surface case. Figure 125 shows the results of the numerical simulations for FHWA Sample 2 when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface in the JET model. The observed JET results (black circles) were slightly underestimated through STAR-CCM+ when their erosion function obtained from the EFA was assigned to the soil–water interface. This underestimation was less observed when the RH was greater. The actual average RH (D50/2) for FHWA Sample 2 was about 0.0031 mm. At the end of the 40-min JET, the observed scour hole was 1.6 cm, while the STAR-CCM+ simulations (using the EFA erosion function assigned to the soil–water interface) resulted in an almost 0.8-cm scour hole in the case of a smooth surface. STAR-CCM+ Smooth STAR-CCM+ Roughness Height = 0.5 mm STAR-CCM+ Roughness Height = 1 mm STAR-CCM+ Roughness Height = 3 mm Observed Figure 123. Scour depth versus time for observed JET and simulated JET for Sand #2.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 161 STAR-CCM+ Smooth STAR-CCM+ Roughness Height = 0.5 mm STAR-CCM+ Roughness Height = 1 mm STAR-CCM+ Roughness Height = 3 mm Observed Figure 124. Scour depth versus time for observed JET and simulated JET for B-1 (4–6 ft). STAR-CCM+ Smooth STAR-CCM+ Roughness Height = 0.5 mm STAR-CCM+ Roughness Height = 1 mm STAR-CCM+ Roughness Height = 3 mm Observed Figure 125. Scour depth versus time for observed JET and simulated JET for FHWA Sample 2.

162 Relationship Between Erodibility and Properties of Soils 6.2.3.2 EFA’s Erosion Function on the HET The approach outlined in Figure 117 was used to compare the results of the EFA with the HET on the same soil samples. The erosion process for two samples (one silt and one clayey sand) was simulated by using STAR-CCM+ after the EFA erosion function was assigned to the soil–water interface in the HET model. The name of these samples are SH-1 (sand sample) and Teton Sample (silt sample). The results of the numerical simulations were compared with the observations of the enlargement of the hole diameter during the HET for the same samples. As in the EFA–JET comparison, four different RHs were considered for each simulation: smooth, 0.5 mm, 1 mm, and 3 mm. Figure 126 shows the results of the numerical simulations for SH-1 when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface in the HET model. It was shown that the observed evolution of the average hole diameter during the HET would lie between the results of the STAR-CCM+ numerical simulations for the smooth to 0.5-mm RH surface. The actual average RH (D50/2) for SH-1 was about 0.1 mm. At the end of the 1,500-s (25-min) HET, the average diameter of the initial hole had become around 13 mm. The STAR-CCM+ simulations (using the EFA erosion function assigned to the soil–water interface) also resulted in an almost average 13-mm hole diameter in the case of an RH of 0.5 mm. It is worth mentioning that at the beginning of the test, when the longitudinal wall of the hole was smoother, the observed evolution of the hole’s diameter tended to better match the results of the numerical simulations for the case of a smooth surface. Figure 127 shows an example of the numerical simulations in three time steps for SH-1. In this example, the soil–water interface was defined as a moving boundary. The velocity profile of the flow is also shown for each time step. The velocity for this example ranged between 0 and 3.75 m/s. Figure 128 shows the results of the numerical simulations for the Teton sample when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface in the HET model. The observed HET results (black circles) were underestimated through STAR-CCM+ when their erosion function obtained from the EFA was assigned to the H ol e D ia m et er (m ) Time (s) Figure 126. Average hole diameter versus time for observed HET and simulated HET for SH-1.

Time = 350 s Time = 700 s Time = 1,400 s Figure 127. Example of moving boundary for SH-1 with RH = 0.5 mm.

164 Relationship Between Erodibility and Properties of Soils soil–water interface. This underestimation was even more pronounced when the surface was smoother. The actual average RH (D50/2) for SH-1 was about 0.015 mm. At the end of the 175 (almost 3-min) HET, the diameter of the initial hole had become around 32 mm. However, the STAR-CCM+ simulations (using the EFA erosion function assigned to the soil–water interface) resulted in almost half of the enlargement in the hole diameter for the case of a smooth surface. 6.2.3.3 EFA’s Erosion Function on the BET The approach outlined in Figure 117 was used to compare the results of the EFA with the BET on the same soil samples. The erosion process for one clay sample (CBH3) was simulated by using STAR-CCM+ after the EFA erosion function was assigned to the soil–water interface in the BET model. The results of the numerical simulations were compared with the observa- tions of the borehole diameter enlargement at the depth of 8 to 10 ft during the BET for the same samples. Three different RHs were considered for each simulation: smooth, 0.5 mm, and 1 mm. Figure 129 shows the results of the numerical simulations for CBH3 when the erosion function obtained from the EFA test on the exact same sample was used at the soil–water interface. Change in the RH did not make a noticeable difference in the diameter enlargement profile; therefore, only one line represents the scour profile in the three cases. In the numerical simulations, the initial borehole profile had to be considered as a straight vertical line (dashed line in Figure 129), whereas in reality, the borehole profile was very irregular. The difference between the initial borehole profiles in the numerical simulations and the actual BET field measurement resulted in different scour profiles after 20 min of testing; however, both results confirmed two common observations: (1) the maximum scour happens close to the bottom of the borehole (z = 9.8 ft) and (2) the maximum diameter enlargement is close to 2 cm. Figure 130 shows an example of the numerical simulations in three different time steps for the Riverside sample. In this example, the soil–water interface was defined as a moving boundary. The velocity profile of the flow is shown for each time step. The velocity for this example ranged between 0 and 3.75 m/s. H ol e D ia m et er (m ) Time (s) Figure 128. Average hole diameter versus time for observed HET and simulated HET for the Teton sample.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 165 Figure 129. Results of BET numerical simulation after 20 min using the EFA’s erosion function. 6.2.4 Comparison and Uniformity The results of the numerical simulations of the JET, HET, and BET are presented in the pre- vious section. The goal, as discussed earlier, was to investigate how the JET, the HET, and the BET would react if the erosion function equation obtained from the EFA test on the same soil were assigned to the soil–water interface. Consequently, the results of numerical simulations were compared with the actual observations for each test. This section presents a summary of the findings. Table 31 summarizes the numerical simulation results presented in Section 6.2.3. The findings show that the erosion function obtained from the EFA test for each sample can reasonably be used to produce a scour-versus-time plot similar to what the results of the JET, the HET, and the BET experiments would produce. However, the variety of interpretation techniques used in each test to obtain the shear stress in the soil–water interface leads to different erosion functions. Therefore, one must be aware of the interpretation techniques that each test uses to obtain the erosion function (erosion rate versus shear stress). It is also worth noting that, in the case of the HET results, the scour values actually refer to the average diameter of the drilled hole in the center of the sample.

166 Relationship Between Erodibility and Properties of Soils (1) Time = 5 min (2) Time = 10 min (3) Time = 15 min (4) Time = 20 min 1.3660 Figure 130. Example of moving boundary for the Riverside sample with RH = 0.5 mm.

Comparison of Selected Soil Erosion Tests by Numerical Simulation 167 Sample Name RH (mm) Final Observed Scour (mm) Final Scour Calculated Using EFA Erosion Function (mm) Figure No. RH = 0 mm RH = 0.5 mm RH = 1 mm RH = 3 mm JET Sand #1 0.14 40 40.8 43.5 43.1 48 121 Sand #2 0.122 23 13.8 16.8 20 20.3 123 B-1 (4-6) 0.0024 7 10.8 14.3 17.5 18.5 124 FHWA S2 0.0031 17 8 10.8 12.8 14.6 125 HET SH-1 0.1 13.4 12.5 13.5 14 14.2 126 Teton 0.015 35 19 20 21 22.5 128 BET Riverside 0.00038 20a 20.31 20.35 20.40 - 129 aScour values shown for BET are the maximum diameter enlargements in the 8- to 10-ft depth of the borehole. Table 31. Summary of the numerical simulation results.