**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

**Suggested Citation:**"Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulations." National Academies of Sciences, Engineering, and Medicine. 2019.

*Relationship Between Erodibility and Properties of Soils*. Washington, DC: The National Academies Press. doi: 10.17226/25470.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

141 CHAPTER 6 6. COMPARISON OF SELECTED SOIL EROSION TESTS BY NUMERICAL SIMULATIONS As discussed in Chapters 1 and 2, one of the critical issues associated with all different erosion test devices is that they do not give the same erosion parameters; they 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, as well as their physical specifications are discussed in detail. Table 4 shows all different types of erosion tests explained in this report. Performing numerical studies for all tests would be cost prohibitive; therefore, we decided to study a selected number of tests among the most common ones: 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 separate sections: 1) evolution of the hydraulic shear stress at the soil-water interface in non-erodible 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 JET, BET, and HET, including the erosion process. 6.1. Results of Numerical Simulation on Non-Erodible Soils CHEN4D Code For this task, computational fluid dynamics (CFD) is used together with a code called CHEN4D. The goal is to simulate each test and develop data reduction techniques which will give the same soil erosion information from these erosion tests without changing the test. CHEN4D (Computational Hydraulic Engineering in 4 Dimensions) was developed by H.C. Chen. It is used to perform CFD simulations of the JET test, the HET test, the BET test and back calculate the erosion function which leads to proper matching of these test results with the erosion function from the EFA. These simulations are expected to lead to a common data reduction process of erosion tests, a common output of all erosion tests, bring uniformity in erosion studies, and keep all soil erosion testing options open for the engineer. The CHEN4D code solves unsteady 3D 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 deformations such as those encountered in multiple-ship and floating pier interactions, greenwater and slamming impact of ships in random waves, vortex-induced motion of offshore platforms, pier-scour, abutment

142 scour, and bridge scour including overtopping. Both the soil roughness and bed load transport models have been incorporated in CHEN4D for the simulation of erosion and accretion of deformable soils. The industry standard CFD models such as FLUENT and STAR-CCM+ have limited capability dealing with arbitrary multiple-body motions or large grid deformations. JET Simulations In this section, results of numerical simulations on the JET are discussed. The simulations are 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 through 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 is assumed to be non-erodible, and the distribution of jet flow velocity and shear stress on the surface of the soil is obtained. Two cases are assumed for the surface of the soil: 1) smooth surface which can represent a clayey soil, and 2) 5% roughness which can represent a coarse sand and gravel. Figure 98 shows the distribution of shear stress versus the distance away from the center line of the soil surface for the smooth case (clayey soils). The shear stress distributions in different time steps, as well as the time-averaged shear stress are depicted in Figure 98. 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 Hansonâs shear stress distribution shown in Figure 11. The shear stress 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 a smooth surface soil (clayey soils), the maximum is less compared to 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.

143 Large laboratory JET (Hanson and Hunt, 2007) Schematic diagram of the large laboratory JET with the dimensions in inches Figure 97. Photograph of large laboratory JET device used in the numerical simulations, along with a schematic diagram of that with dimensions 0.25 " 4.584 " 2.4685 " 16.5 " Ã4.0000 4.5 " 1.9685 " 16.5 " Ã12.0000 1.5 " 12 " Ã4.5000 8.25 " 4 " 16.5 " Ã12.50008.25 "

144 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 and with 5% roughness surfaces. 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 will be to replace the soil (white block) with an erodible surface to obtain the erodibility parameters of different soils for different hydraulic conditions.

145 Figure 100. Velocity results of submerged jet evolution in different time steps for the smooth surface (starting from top left to bottom right)

146 Figure 101. Velocity results of submerged jet evolution in different time steps for the rough surface (starting from top left to bottom right) 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. For more details about the HET, please refer to Chapters 1 and 2 of this report. As in the case of the JET simulations, it is assumed that the soil is non-erodible. The water flow velocity and shear stress distributions through the HET hole are obtained. The initial stresses were evaluated for the 6 mm diameter hole in the center of the sample at an average velocity (in the hole) of 2.5 m/s. For the HET simulations, the same two cases as the JET are considered: 1) smooth soil which represents clayey soils, and 2) surface with 5% roughness which implies sandy soils. It is worth mentioning that in the HET, the soil is compacted in a 4 in (101.6 mm) inner diameter compaction mold, and a 6 mm hole is drilled in the center of the sample. The time- averaged shear stress distributions 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 is approximately 30 Pa for coarser surface (sandy soils). As expected, the shear stress is less when the surface is smooth (clayey soils).

147 Two photographs of HET at Texas A&M University Schematic diagram of the HET with the dimensions in mm Figure 102. Photograph and diagram of the HET used in numerical simulations 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 6. 0 63.5 90 .0 50. 8 90.0 A 180.0 53 .0 A 35 mm DIA. HOLE FOR OUTLET PIPE 18 0. 0 55.5 56 .5 LONGITUDINAL SECTION CROSS SECTION A-A

148 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 into the hole. Due to this separate region, contraction happens, and consequently flow starts recirculating to get into the hole. The shear stress along the drilled hole can also be estimated 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 / . Reynolds Number (Re) is calculated to be 14670 using Eq. 58. (58) Where, (kg/m3) is density of water, (m/s) is the flow velocity, D (m) is the diameter of flow channel, and is viscosity of water (1.027 10 kg/m/s). Knowing that the surface roughness is 5%, the friction factor is obtained approximately 0.075 from the Moody diagram. Figure 104. Moody diagram (Moody, 1944) Using Eq. 7, the shear stress is calculated to be 50 Pa which is larger than the 25 Pa obtained through the numerical analysesâ results shown in Figure 103. The difference shows that there is a discrepancy between the Moody chart predictions and the numerical simulations and that Moody charts overestimate the shear stress by 100% in this case. For the case of a smooth pipe, knowing that the Reynolds Number (Re) is 14670, the friction factor is 0.028 from the Moody Diagram (See Figure 104). Using Eq. 7, the shear stress is calculated as 21.875 Pa which is larger than the 10 Pa obtained through the numerical simulation shown in Figure 103. Again, the Moody Diagram gives higher values. The evolution of the velocity for the smooth case is shown in Figure 105, as an illustration.

149 Figure 105. Velocity evolution for the smooth case EFA Simulations

150 The EFA geometry used in the simulations is as described in Chapter 2. As mentioned earlier, EFA comprises of a rectangular channel which is approximately 1.24 m long. On the bottom surface, Shelby tube size sample 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 instead of the channel hydraulic diameter (Dh = 67.33 mm) in the simulations. The roughness of the soil surface is 5% (of the channel height) in all the cases. Figure 106 to Figure 108 show the shear stress distribution on both top and bottom surface 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. Figure 106. Shear stress distribution on both top surface (which is smoot) and bottom surface (which encompasses the rough soil surface) for the U = 1 m/s

151 Figure 107. Shear stress distribution on both top surface (which is smoot) and bottom surface (which encompasses the rough soil surface) for the U = 3 m/s Figure 108. Shear stress distribution on both top surface (which is smoot) and bottom surface (which encompasses the rough soil surface) for the U = 6 m/s The shear stresses are also calculated using Moody chart (Figure 104). Reynolds number can be calculated using =1000 kg/m3, D = 0.00508 m, and 1.027 10 kg/m/s. The friction factors for the case of 5% roughness are then obtained as 0.079, 0.075, and 0.073 for U = 1 m/s, 3 m/s, and 6 m/s, respectively. Eq. 7 is then used to measure the shear stresses for each velocity. The resulting shear stresses from 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. Comparing the shear stress results obtained from the numerical

152 simulations with Moody chart shows that as in the case of the HET results, Moody chart overestimate the shear stress values by about 25%. Figure 109 to Figure 111 shows 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 the cases. Figure 109. Shear stress evolution captured in six time steps, when the flow velocity in the conduit is 1 m/s (starting from top left to bottom right)

153 Figure 110. Shear stress evolution captured in six time steps, when the flow velocity in the conduit is 3 m/s (starting from top left to bottom right)

154 Figure 111. Shear stress evolution captured in six time steps, when the flow velocity in the conduit is 6 m/s (starting from top left to bottom right) BET Simulations Numerical simulations were also performed for the Borehole Erosion Test (BET), assuming a non-erodible soil with 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 gpm and 90 gpm) are considered. Also, three distances between the jet orifice and the bottom surface of the borehole are considered (1 inch, 3 inches, and 6 inches). Figure 27 shows the schematic diagram of the BET. As shown in Figure 27, the jet is inducing 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 for the two aforementioned flow rates.

155 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. Obviously, 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 impingement point. Figure 112. Shear stress distribution within the circular bottom surface of the drilled hole with 1 inch, 3-inch, and 6-inch gap between the jet orifice and borehole bottom surface, when the flow rate is 90 gpm Figure 113 also 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. It is observed that the maximum shear stress is largest when the gap between the discharge orifice and the bottom surface is 3 inches. Figure 113. Shear stress distribution along the side wall surface of the drilled hole with 1 inch, 3- inch, and 6-inch gap between the jet orifice and borehole bottom surface, when the flow rate is 90 gpm

156 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 inch. It should be noted that zero elevations in Figure 113 and Figure 115 are set as the bottom of the borehole. Figure 114 shows that the shear stress is higher when the gap is small (1 inch), 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 between 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 that flow rate was 90 gpm, happens when the gap between the jet orifice and bottom of the borehole is 3 inches. Also, it is observed that 2% roughness on sides will result in a slightly higher shear stress values compared to the smooth side. It also shows that after about 0.5 m above the bottom discharge the shear stress on the borehole wall has become constant. Figure 116 shows an example of the numerical simulations in four different time steps. In this example, the gap between discharge orifice and the bottom of the borehole is 1 inch, and the flow rate is 23 gpm. Velocities range from 0 to 6 m/s at the bottom of the borehole, and 0 to 2 m/s on the sides. Figure 114. Shear stress distribution within the circular bottom surface of the drilled hole with 1 inch, 3-inch, and 6-inch gap between the jet orifice and borehole bottom surface, when the flow rate is 23 gpm

157 Figure 115. Shear stress distribution along the side wall surface of the drilled hole with 1 inch, 3- inch, and 6-inch gap between the jet orifice and borehole bottom surface, when the flow rate is 23 gpm

158 Figure 116. An example of velocity results of jet evolution in different time steps for the rough when the gap between orifice and bottom surface is 1 inch (starting from top left to bottom right) 6.2. Results of Numerical Simulation Including Erosion 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, with an assumption that the soil is not erodible. This section presents the results of the numerical simulations including the erosion process. The software used for this purpose is CD-adapcoâs Star Computational Continuum Mechanics (Star CCM+) (2014). Star CCM+ can generate the computational fluid dynamics (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 aforementioned erosion testing methods (i.e. 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

159 between the shear stress/velocity and the erosion rate. In fact, the erosion rate ( ) is a function of shear stress/velocity (See Eqs. 1 and 2). The relationship between the erosion rate and the shear stress (or velocity) is called the âErosion Functionâ. The numerical simulations are concentrated on finding out that 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 are compared with the actual test results obtained through experiments. The soil surface in the JET, the HET, and the BET is defined as a moving boundary. The erosion process is simulated using the movement of these boundaries. This movement develops according to the erosion function equation that is obtained from the EFA test performed on the same soil sample. Figure 117 shows a flowchart describing the procedure for each numerical simulation. Figure 117. The procedure of the numerical simulations conducted to compare the results of the EFA with the results of the HET, the JET, and the BET The numerical simulations according to the procedure shown in Figure 117 are presented in the three following forms: 1) EFAâs Erosion Function on the JET 2) EFAâs Erosion Function on the HET 3) EFAâs Erosion Function on the BET 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 desire test (i.e. JET, HET, BET) 3- Develop the velocity (v) and shear stress ( ) profiles at the soil- water interface using CFD 4- Calculate the erosion rate ( ) using the erosion function assigned to the interface in step 2 5- Move the boundary according to the calculated in the previous step

160 Before discussing the results of these comparisons, the details of the mesh created for the JET, the HET, and the BET in Star CCM+ are presented below. Mesh Geometry and Soil-Water Interface For all the three erosion tests (JET, HET, and BET), two-dimensional axisymmetric models were created. The mesh used in these models is quadrilateral. The detailed information on the mesh used for each erosion test is presented in Table 30 below. Also, Figure 118, Figure 119, and Figure 120 show the axisymmetric models created for the JET, the HET, and the BET, respectively. It should be noted that the dimensions used for the models are in accordance with the dimension of these testing devices in the Erosion Laboratory at Texas A&M University. For detailed information on dimensions of each test device, please refer to the Section 4.1 of this report. Table 30. Detailed information on the created mesh for each erosion test Erosion Test Type of Mesh Number of Cells Number of Faces Number of Vertices JET Quadrilateral 8809 17501 9115 HET Quadrilateral 22918 45151 23673 BET Quadrilateral 31765 62244 33054 Figure 118. The axisymmetric model for the JET

161 Figure 119. The axisymmetric model for the HET Figure 120. The axisymmetric model for the BET One of the important laws in the fluid dynamics is the law of the âwallâ. 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 the âwallâ) 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

162 to the wall. The general formulation of the law of the wall (Eq. 59) solves for the average velocity parallel to the wall in turbulent flows (high Reynoldâs numbers). ln (59) Where is a dimension-less velocity parameter and equals (average velocity parallel to the wall) divided by the (friction velocity); refers to the dimension-less wall coordinate, and is obtained using Eq. 60. The parameters and are two constants that are equal to 0.41 and 0.5, respectively, for a smooth wall according to Schlichting and Gersten (2000). (60) Where is the local kinematic viscosity of the fluid; is mentioned earlier is the friction velocity at the closest fluid region boundary, and is the distance of the point to the nearest wall. 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 is designed to be less than 1 to achieve very small cell distance between the wall and the point of flow ( 10 ). 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 with other erosion tests are presented separately in the following sections. EFAâs 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, a procedure as described in Figure 117 was followed for four different samples (2 sand, 1 silt, and 1 clay). The name of these samples are: Sand #1 & Sand #2 (sand samples), FHWA Sample 2 (silt sample), and B-1 (4â-6â) Beaumont (clay sample). As presented in Figure 117, the first step was to obtain the relationship between the erosion rate ( ) and the shear stress for each sample in the EFA. This relationship, also called the erosion function, is 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 is developed on the soil-water interface, the erosion rate at the boundary is calculated 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 or less than the critical shear stress for the tested soil. In order to distinguish between smooth clay and rough sand surface, the Roughness Height (RH) is defined in Star CCM+. RH is the height of the roughness of the soil particles (equivalent to Æ defined in Moody diagram shown in Figure 104). In this study, for each simulation whether the sample is 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 sample Sand #1 when the erosion function obtained from the EFA test on the exact same sample is used at the soil-water

163 interface in the JET model. It is shown that the observed JET results (black circles) are slightly over-estimated through Star CCM+ when their erosion function obtained from the EFA is assigned to the soil-water interface. This over-estimation is less pronounced when the roughness height is close to 0 mm (smooth surface). The actual average roughness height (D50/2) for SE-1 is 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 is defined as a moving boundary. Also the velocity profile of the flow is shown for each time step. Velocity for this example ranges between 0 to 3.2 m/s. The highest amount of velocity is of course at the jet nozzle and when the water reaches the soil surface, its velocity becomes less. This process continues until the shear stress induced on the boundary (soil-water interface) becomes less than the measured critical shear stress from the EFAâs erosion function. Figure 121. The scour depth versus time for observed JET & simulated JET for Sand #1

164 1) Time = 4.5 min 2) Time = 9 min 3) Time = 13.5 min 4) Time = 18 min Figure 122. An example of the moving boundary for Sand #1 with RH = 0.5 mm.

165 Figure 123 shows the results of the numerical simulations for the sample Sand #2 when the erosion function obtained from the EFA test on the exact same sample is used at the soil-water interface in the JET model. It is shown that the observed JET results (black circles) are slightly under-estimated through Star CCM+ when their erosion function obtained from the EFA is assigned to the soil-water interface. This under-estimation is more pronounced when the roughness height is close to 0 mm (smooth surface). The actual average roughness height (D50/2) for SE-2 is about 0.122 mm. At the end of the 40 minutes 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 almost 1.4 cm scour hole in the smooth surface case. Figure 123 also shows that in higher roughness heights (near 3 mm), results of the numerical simulations tend to be closer to the observation for the sample SE-2. Figure 123. The scour depth versus time for observed JET & simulated JET for Sand #2 Figure 124 shows the results of the numerical simulations for the sample B-1 (4â-6â) when the erosion function obtained from the EFA test on the exact same sample is used at the soil-water interface in the JET model. It is shown that the observed JET results (black circles) are slightly over-estimated through Star CCM+ when their erosion function obtained from the EFA is assigned to the soil-water interface. This over-estimation is more pronounced when the roughness height is greater. The actual average roughness height (D50/2) for B-1 (4â-6â) is about 0.0024 mm. At the end of the 40 minutes JET, the observed scour hole was 0.62 cm, while the Star CCM+ simulations

166 (using the EFA erosion function assigned to the soil-water interface) resulted in almost 1.0 cm scour hole in the smooth surface case. Figure 124. The scour depth versus time for observed JET & simulated JET for B-1 (4â-6â) 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 is used at the soil-water interface in the JET model. It is shown that the observed JET results (black circles) are slightly under-estimated through Star CCM+ when their erosion function obtained from the EFA is assigned to the soil-water interface. This under-estimation is less observed when the roughness height is greater. The actual average roughness height (D50/2) for FHWA Sample 2 is about 0.0031 mm. At the end of the 40 minutes 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 almost 0.8 cm scour hole in the case of smooth surface.

167 Figure 125. The scour depth versus time for observed JET & simulated JET for FHWA Sample 2 EFAâs Erosion Function on the HET Similar approach, as outlined in Figure 117, was taken to compare the results of the EFA with the HET on same soil samples. The erosion process for two different samples (1 silt and 1 clayey sand) was simulated using Star CCM+ after assigning the EFA erosion function to the soil-water interface in the HET model. The name of these samples are: SH-1 (sand samples) and Teton Sample (silt sample). The results of the numerical simulations were compared with the observations of the hole diameter enlargement during the HET for the same samples. Similar to the case of EFA-JET comparison, four different roughness heights (RH) were considered: smooth, 0.5 mm, 1 mm, and 3 mm for each simulation. 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 is used at the soil-water interface in the HET model. It is shown that the observed average hole diameter evolution during the HET would lie between the results of the Star CCM+ numerical simulations for the cases of smooth to 0.5 mm RH surface. The actual average roughness height (D50/2) for SH-1 is about 0.1 mm. At the end of the 1500 seconds (25 minutes) HET, the average diameter of the initial hole has become around 13 mm. The Star CCM+ simulations (using the EFA erosion function assigned to the soil-water interface) also resulted in almost an average 13 mm hole diameter in the case of 0.5 mm roughness height. It is worth mentioning that in the beginning of the test where the hole longitudinal wall is

168 smoother, the observed evolution of hole diameter tends to be more matching with the results of numerical simulations for the case of smooth surface. Figure 127 shows an example of the numerical simulations in three different time steps for SH- 1. In this example, the soil-water interface is defined as a moving boundary. Also the velocity profile of the flow is shown for each time step. Velocity for this example ranges between 0 to 3.75 m/s. Figure 126. The average hole diameter versus time for observed HET & simulated HET for SH-1

169 Time = 350 sec Time = 700 sec Time = 1400 sec Figure 127. An example of the moving boundary for SH-1 with RH = 0.5 mm Figure 128 shows the results of the numerical simulations for Teton Sample when the erosion function obtained from the EFA test on the exact same sample is used at the soil-water interface in the HET model. It is shown that the observed HET results (black circles) are under-estimated

170 through Star CCM+ when their erosion function obtained from the EFA is assigned to the soil- water interface. This under-estimation is even more pronounced when the surface is smoother. The actual average roughness height (D50/2) for SH-1 is about 0.015 mm. At the end of the 175 seconds (almost 3 minutes) HET, the diameter of the initial hole has 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 smooth surface. Figure 128. The average hole diameter versus time for observed HET & simulated HET for Teton Sample EFAâs Erosion Function on the BET Similar approach, as outlined in Figure 117, was taken to compare the results of the EFA with the BET on same soil samples. The erosion process for one clay sample (CBH3) was simulated using Star CCM+ after assigning the EFA erosion function to the soil-water interface in the BET model. The results of the numerical simulations were compared with the observations of the borehole diameter enlargement at depth 8 to 10 ft during the BET for the same samples. Three different roughness heights (RH) were considered: smooth, 0.5 mm, 1 mm for each simulation. 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 is used at the soil-water interface. It was observed that 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. Also, it must be

171 noted that 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 in comparison. The difference between the initial borehole profiles in the numerical simulations and the actual BET field measurement resulted in different scour profiles after 20 minutes of test; 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 is defined as a moving boundary. Also, the velocity profile of the flow is shown for each time step. Velocity for this example ranges between 0 to 3.75 m/s. Figure 129. Results of the BET numerical simulation after 20 minutes using the EFAâs erosion function

172 1) Time = 5 min 2) Time = 10 min 3) Time = 15 min 4) Time = 20 min Figure 130. An example of the moving boundary for the Riverside Sample with RH = 0.5 mm Comparison and Uniformity The results of the numerical simulations on the JET, HET, and BET were presented in the previous 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, is assigned to the soil-water interface. Consequently, the results of numerical simulations were compared with the actual observations for each test. In this section, a summary of the findings is presented. Table 31 shows a summary of the numerical simulation results as discussed in the Section 6.2 of this report. The findings show that the erosion function obtained from the EFA test for each sample can be reasonably used to produce a similar âscour versus timeâ plot to what the JET, the

173 HET, and the BET experiments would result. However, the variety of interpretation techniques that are used for 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 for 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. Table 31. Summary of the numerical simulation results Sample Name Roughness Height (mm) Final observed scour (mm) Final Calculated Scour using the EFA Erosion Function (mm) Figure 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 Figure 121 Sand #2 0.122 23 13.8 16.8 20 20.3 Figure 123 B-1 (4-6) 0.0024 7 10.8 14.3 17.5 18.5 Figure 124 FHWA S2 0.0031 17 8 10.8 12.8 14.6 Figure 125 HET SH-1 0.1 13.4 12.5 13.5 14 14.2 Figure 126 Teton 0.015 35 19 20 21 22.5 Figure 128 BET Riverside 0.00038 201 20.31 20.35 20.40 - Figure 129 1 The scour values shown for the BET are in fact the maximum diameter enlargements in 8â-10â depth of the borehole