Relationship Between Erodibility and Properties of Soils (2019)

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301 The goal of this project was to develop reliable and simple equations quantifying the erod- ibility of soils on the basis of soil properties. The reliability must take into account the accuracy required for erosion-related projects, while the simplicity must consider the economic aspects of erosion-related projects. Different soils exhibit different erodibility (e.g., sand, clay); therefore, erodibility is tied to soil properties. However, many researchers have attempted to develop such equations without much success. One problem is that erodibility is not a single number, but a relationship between the erosion rate and the water velocity or the hydraulic shear stress. This erosion function is a curve, and it is difficult to correlate a curve to soil properties. Another problem that needs to be solved is associated with the availability of several erosion testing devices. In the laboratory, these include the pinhole test, the hole erosion test (HET), the jet erosion test (JET), the rotating cylinder test, and the erosion function apparatus (EFA) test. In the field, they include the JET, the North Carolina State University in situ scour evalu- ation probe test, the Texas A&M University (TAMU) borehole erosion test (BET) and pocket erodometer test, and others. All these tests measure the soil erodibility but give different results. It is important to give engineers options so that they can choose one test or another. Therefore, it would be helpful if all these tests could give the same answer. Indeed, the soil does not know the difference between erosion tests, and the erosion function is a fundamental property of the soil. Experimental and numerical efforts were made to advance in this direction. The findings for each chapter are summarized below. 9.1 Summary of Chapters 1 Through 8 9.1.1 Chapter 1: Introduction Chapter 1 is divided into two parts. The first part presented a definition for the erosion phe- nomenon and introduced different types of erosion. The general parameters for quantifying soil erodibility and the constitutive models for erosion were briefly discussed. The second part of the chapter presented the research approach. The project tasks were described, and a summary of how and where within the report each one of the tasks is addressed was provided. 9.1.2 Chapter 2: Existing Erosion Tests Chapter 2 presented a comprehensive literature review on different soil erosion tests. Tests developed all over the world in the past few decades were discussed in terms of their application in the lab or in the field and their application in surface erosion or internal erosion problems. The advantages and disadvantages of the most important tests were explained, and a table sum- marizing selected tests was provided at the end of the chapter. The advantages, drawbacks, and C H A P T E R 9 Conclusions and Recommendations

302 Relationship Between Erodibility and Properties of Soils applications of the three major erosion tests (EFA, JET, and HET) used in this study are pre- sented in Table 90 (Chapter 8). 9.1.3 Chapter 3: Existing Correlations Between Soil Erodibility and Soil Properties Chapter 3 provided a literature review of the existing correlations between soil erodibility and soil properties. The observations and correlation equations proposed by various researchers in the past century were summarized. The factors that influence erosion, including the less easily obtained engineering properties, were presented and discussed in detail. Table 10 (Chapter 3) summarizes these parameters. 9.1.4 Chapter 4: Erosion Experiments Chapter 4 began with a description of the Soil Erosion Laboratory at TAMU. The erosion testing devices built as part of this research project, as well as the refurnished and armored EFA, were presented. The test plan matrix proposed for this project was presented and discussed. Next, the results of the hundreds of erosion tests performed during this project were presented and discussed. The chapter concludes with a discussion of how the geotechnical engineering properties associated with each tested sample were obtained at TAMU and presented in the form of a spreadsheet of soil geotechnical properties for each sample. The erosion spreadsheets and geotechnical properties spreadsheets for all samples tested in this project are available in Appendices 1 and 2. 9.1.5 Chapter 5: Organization and Interpretation of the Data Chapter 5 introduced NCHRP-Erosion, the erosion spreadsheet developed for this project. NCHRP-Erosion includes records of the geotechnical properties of each sample from nearly 1,000 erosion tests: approximately 750 tests collected from literature review and from contacts with researchers and organizations around the world and the approximately 250 erosion tests performed during this project. The chapter explained the process of collecting and compiling the worldwide data and lists the people and organizations who helped gather the information. In NCHRP-Erosion, all the erosion data are analyzed according to the procedures described in the report for five erodibility parameters: 1. Critical shear stress, tc, 2. Critical velocity, vc, 3. Initial slope of velocity, Ev, 4. Initial slope of shear stress, Et, and 5. Erosion category, EC. NCHRP-Erosion includes 50 columns and nearly 1,000 rows. Chapter 5 discussed the column contents in detail. The chapter also included the Inquiry Operation Manual that explains how to search for specific data within NCHRP-Erosion. 9.1.6 Chapter 6: Comparison of Selected Soil Erosion Tests by Numerical Simulation Chapter 6 presented a comparison of selected soil erosion tests (EFA, HET, JET, and BET) with results obtained with numerical simulation software. This chapter was divided into two sec- tions: (1) numerical simulations on nonerodible soils and (2) numerical simulations including

Conclusions and Recommendations 303 the erosion process. The first part of the chapter dealt with the evolution of hydraulic shear stress and the velocity profile with the assumption that the soil was not erodible. A discrepancy was observed between the Moody chart predictions and the numerical simulations, and the Moody charts were found generally to overestimate shear stress. This discrepancy was more pronounced in higher shear stress values (up to 100% difference between the Moody chart pre- diction and the numerical simulation in one case). In the second part of the chapter, the erosion function was assigned to the soil–water interface, and the erosion was numerically simulated with a moving boundary for selected erosion tests. The results of the numerical simulations were compared with the actual observations for each test. The findings showed 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 JET, the HET, and the BET experiments would produce. However, the variety of interpretation techniques 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). 9.1.7 Chapter 7: Development of Correlation Equations Chapter 7 was dedicated to the main goal of this study: the development of correlation equa- tions. The chapter was divided into four major parts. The first part presented a preliminary and quick method for determining the erosion resistance of a soil using only the Unified Soil Clas- sification System (USCS) of the soil and associated erosion categories. The plot of erosion rate versus velocity based on the USCS categories is shown in Figure 145 (Chapter 7). In the figure, the width of each box is associated with a USCS category represents the zone in which 90% of the EFA results performed on such samples would fall in the Erosion Category Chart. For instance, if the soil type of a location in an arbitrary geotechnical site were classified as SM (silty sand) according to the USCS, it would most likely (with close to 90% confidence based on the EFA results compiled in NCHRP-Erosion) fall within Category II (high erodibility). The second part of Chapter 7 dealt with improving existing plots of critical velocity/critical shear stress versus mean particle size. It was observed that for soils with mean particle size greater than 0.3 mm, the following relationships exist between the critical velocity/shear stress and mean particle size: vc (m/s) = 0.315(D50 (mm))0.5 and tc (Pa) = D50 (mm). It was also concluded that for fine-grained soils, there is no direct relationship between critical velocity/shear stress and mean particle size. However, the data could be bracketed with an upper bound and a lower bound equation. The third part of this chapter presented the frequentist regression technique. The step-by-step procedure for implementing the frequentist regression technique, the experimental design, and the model selection process were discussed, and the results of the regressions were presented. The best correlation equations were selected after passing through a four-filter process including 1. R2, 2. Mean square error (MSE), 3. Statistical F-test, and 4. Cross-validation test. POO and POU plots were also presented for the selected equations. Table 102 to Table 106 show the selected equations for each erodibility parameter and for each data set. The last part of this chapter dealt with a probabilistic approach as opposed to the determin- istic approach presented in the previous section. The probabilistic approach was based on the Bayesian inference method. The methodology of the Bayesian inference method and its results were presented in Section 7.4 and are also given in Appendix 5.

304 Relationship Between Erodibility and Properties of Soils aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table 102. Selected models for critical shear stress, tc. aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table 103. Selected models for critical velocity, vc. aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table 104. Selected models for erosion category, EC.

Conclusions and Recommendations 305 9.1.8 Chapter 8: Most Robust Correlation Equations Chapter 8 began with a summary of the advantages, disadvantages, and applications of the three major erosion tests used in this study—the EFA, the JET, and the HET [see Table 90 (Chapter 8)]. The chapter then presented correlation equations recommended on the basis of the work discussed in Chapter 7 (see Tables 102 to 106) and provided instructions on how best to use them. Table 100 (Chapter 8) shows an example of the proposed equation chart for erosion category based on the JET data. This table presents the recommended cor- relation equation for predicting the erosion category in for D50 < 0.3 mm. Along with each proposed equation, the tables in Chapter 8 that present proposed equations give one or two plots showing the probability of underpredicting (POU)—or, where applicable, the prob- ability of overpredicting (POO)—versus a correction factor, as well as a plot of predicted versus measured values. Such plots provide great insight into the use of each equation. A column to the right of each equation offers a few remarks on the proposed equation, the value of R2, and the cross-validation score. aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table 105. Selected models for velocity slope, Ev. aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table 106. Selected models for shear stress slope, Et.

306 Relationship Between Erodibility and Properties of Soils 9.2 Recommendations on How to Approach Erosion-Related Design Problems One of the key missions of this project was to provide engineers in charge of erosion problems with a set of correlation equations for predicting erosion parameters without the need to per- form multiple and costly erosion tests. In this section, a step-by-step approach is presented. It must be noted that each step can stand alone by itself and help solve the problem; however, the combination of all four steps would lead to the most accurate results. While Steps 1 and 2 yield more preliminary estimates of the erodibility parameters, Steps 3 and 4 provide more detailed insights in obtaining the erodibility parameters. It is recommended that the engineer consider all four steps prior to making a final decision. 9.2.1 Step 1. Probe NCHRP-Erosion Chapter 5 of this report discussed the development of the NCHRP-Erosion database. This global spreadsheet is a searchable tool and allows the engineer to filter the data according to multiple criteria. The first preliminary approach to evaluating the erodibility of a desired site is through probing NCHRP-Erosion. The engineer can use information on as many geo technical properties as possible from the site (i.e., USCS category, AASHTO classification, Atterberg limits, unit weight, and so forth), and filter NCHRP-Erosion on the basis of those criteria with the goal of finding soil samples that are similar to the target soil. After the filtering, the soil samples obtained might be tested with more than one erosion test (e.g., EFA, BET, JET, HET). The engineer then can see for himself or herself what erodibility parameters he or she must expect from the soil without having to conduct different erosion tests. Probing the NCHRP- Erosion database can also help the engineer to compare the results of these different erosion tests on similar soil samples. 9.2.2 Step 2. Use the USCS Erosion Charts to Estimate Erosion Resistance Chapter 7, Section 7.1, showed that the erosion functions for soils with a given USCS category do not generally fall distinctly into a single erosion category but rather seem to plot approxi- mately across two categories. Figure 145 (Chapter 7) summarizes all results into erosion category charts. Figure 145 can be used as another preliminary tool for estimating the erodibility of any sample by using only the USCS category. In this figure, the width of each box associated with a USCS category represents the zone in which the results of 90% of the EFA tests performed on such samples would fall in the erosion category chart. For instance, if the soil type of a location in an arbitrary geotechnical site is classified as SM (silty sand) according to the USCS, it would most likely (with close to 90% confidence based on the EFA results compiled in NCHRP-Erosion) fall into Category II (high erodibility) in Figure 145. Similarly, a soil classified as CH (fat clay) would most likely fall into Category III (medium erodibility), and an SP (poorly graded sand) would fall within Categories I and II (very high to high erodibility). The wider the box is for a USCS category, the greater the variability of the erosion category (EC) is for that particular soil type. Knowledge of the erosion category of a soil can lead to much useful information about the erosion resistance of that soil; however, it should be noted that such results are not accurate enough for design purposes. 9.2.3 Step 3. Use the Deterministic Regression Results Chapter 7, Section 7.3, presented a comprehensive deterministic approach to selecting the best correlation equations between the geotechnical properties and the erodibility parameters.

Conclusions and Recommendations 307 The most robust equations were repeated in Chapter 8, Section 8.2. The proposed equations were developed on the basis of data obtained in different erosion tests (i.e., EFA, JET, and HET); therefore, advance knowledge of each test is extremely useful in choosing the best equa- tion. Table 90 (Chapter 8) shows a list of advantages, disadvantages, and applications for the EFA, JET, and HET. The content of this table should be studied carefully before the proposed equations in Section 8.2 are used. POU/POO plots are presented with the best equations. These plots help the engineer find the correction factor needed to reach a certain confidence that the predicted value is under- or overpredicted. The POU/POO plots can be very useful for design purposes. 9.2.4 Step 4. Use the Bayesian Inference Results One of the issues with conventional deterministic approaches is that they fail to capture uncer- tainty by accounting only for the mean value of the unknown parameter. Therefore, Chapter 7, Section 7.4, was dedicated to performing a probabilistic analysis using the Bayesian inference approach. The comprehensive deterministic frequentist regression analysis performed in Sec- tion 7.3 was the foundation of the Bayesian inference analysis performed in Section 7.4. The selected correlation equations using the deterministic approach were analyzed using Bayesian inference. The engineer can evaluate the sensitivity of the predicted value with regard to one or more model parameters. All possible values that an erodibility parameter can get for each selected equation are presented in the form of a probability distribution. Examples of the Bayesian inference analysis are presented in Section 7.4. Appendix 5 presents the complete results of the Bayesian inference analysis. 9.3 Example Applications This section consists of generic examples illustrating the use of the approach to evaluating soil erosion resistance presented in Section 9.2. Four geotechnical sites (gravel, sand, silt, and clay sites) were studied to examine their resistance to potential surface erosion caused by an arbitrary upcoming flood. In these examples, earlier geotechnical explorations have included sieve and hydrometer analysis, unit weight test, and, where applicable, Atterberg limit tests and unconsoli- dated undrained tests. Table 107 shows selected geotechnical properties of the upper soil layer (first 2 m) in each site. In these examples, the use of the first three steps discussed in Section 9.2 are illustrated. For Step 4 (Bayesian inference), the user is referred to Section 7.4. The geotechnical properties shown in Table 107 help the user search NCHRP-Erosion and find soil samples that are very similar to the existing soil for each site. Using NCHRP- Erosion, the user can see the results of different erosion tests performed on similar samples Site USCS Category Unit Weight (kN/m3) PL (%) PI (%) Percent Finer Than #200 Mean Particle Size (mm) Vane Shear Test (kPa) WC (%) Cu Clay Percentage (< 0.002 mm) (%) Gravel GP 18.5 na na 0 14 na 6 0.4 0 Sand SP-SM 16 25 4 11 0.2 12 11 4.5 1.5 Silt ML 20 23 7 60 0.037 29 30 na 15 Clay CH 18 25 26 100 0.001 75 23 na 42 Note: na = not applicable. Table 107. Selected geotechnical properties of upper soil layer at each site.

308 Relationship Between Erodibility and Properties of Soils from different projects. (Chapter 5 of this report includes the Inquiry Operation Manual for NCHRP-Erosion.) The user is then referred to Chapter 2 of this report and to Table 90 (Chap- ter 8) to study the advantages, drawbacks, and applications of each test. The user can then use his or her engineering judgment to decide which results would be an appropriate match to the existing problem. It is recommended that the engineer carry out all four steps to confirm his or her findings in Step 1 and also have a more thorough examination of the erodibility of the existing soil, in case there are not enough samples in NCHRP-Erosion for that particular soil. The second step is to use the USCS erosion charts (Figure 145, Chapter 7) as a preliminary estimate of the erosion category at each site. Section 9.2.2 gives a few examples of how to use these charts. In this example applica- tion, the gravel site soil is classified as GP. Figure 145 (Chapter 7) shows that this soil would most likely fall into a zone in the vicinity of the boundary between Category II and Category III (high to medium erodibility). In addition to the erosion category, the user can use the plot to deter- mine approximately the erosion rate he or she should expect at the site given the flow conditions (i.e., velocity) of the upcoming flood. For example, Figure 145 shows that, assuming the GP soil in this example would fall very close to the boundary between Category II and Category III, for a flow velocity of 2 m/s, an erosion rate of approximately 100 mm/h erosion rate would be expected. Similarly, Figure 145 shows that the example sand site (SP-SM), silt site (ML), and clay site (CH) would likely fall into Category I (very high erodibility), Categories II to III (high to medium erodibility), and Category III (medium erodibility), respectively. The erosion rate expected for each site can then be determined in a manner similar to that of the case of the gravel site (GP), by considering an average line in the appropriate zone and the flow conditions of the upcoming flood. In Step 3, the user is recommended to use the selected correlation equations to evaluate his or her findings during the first two steps and improve his or her decision, where applicable. Dif- ferent equations are used to predict the erodibility parameters, depending on the erosion test data (EFA, JET, or HET) used to develop them (see Tables 102 to 106 and Chapter 8). Therefore, knowledge of the strength points and limitations of each test is a vital step prior to choosing an equation. Table 90 (Chapter 8) helps readers identify and understand the differences between the erosion tests. The user is free to select the best equation according to his or her objective and consideration of the differences between the equations. 9.3.1 Gravel Site Table 91 (Chapter 8) shows that for soils with D50 greater than 0.3 mm, the recommended equation for obtaining the critical shear stress is tc = D50. Therefore, for the case of this example site, critical shear stress is tc = 14 Pa. The critical velocity can be defined from equations shown in Table 94 (Chapter 8). For soils with D50 greater than 0.3 mm, it is recommended to use Therefore, for the case of this example site, the critical velocity is Table 95 (Chapter 8) shows the recommended equations for the slope of the shear stress– erosion rate plot (Et) according to the EFA test data. For soils with D50 greater than 0.074 mm, 0.315 50 0.5v Dc ( )= × 0.315 14 1.18 m/s0.5vc ( )= × = 3,228.7 2.8 1.58 502.91E C Du( )= × × γ ×t - - -

Conclusions and Recommendations 309 Therefore, The POO plot in Table 95 shows that to reach 80% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2.5 (2.5 × 0.19 = 0.475 mm/h-Pa). Tables 96 and 97 (Chapter 8) show the recommended equations for the slope of the shear stress–erosion rate plot (Et) according to the JET and HET data, respectively. However, because performing the JET and HET on gravel is not feasible, the equations given in Tables 96 and 97 cannot be used for this example site. Table 98 (Chapter 8) shows the recommended equations for the slope of velocity–erosion rate plot (Ev) according to the EFA test data. For soils with D50 greater than 0.074 mm, Therefore, The POO plot in Table 98 shows that to reach 80% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 5 (5 × 11.6 = 58 mm-s/m-h). Tables 99, 100, and 101 (Chapter 8) show that there is no strong equation for obtaining the erosion category (EC) for soils with D50 greater than 0.3 mm. 9.3.2 Sand Site Table 107 shows that the upper soil layer in the example sand site has an average mean particle size of 0.2 mm. In this example, the erodibility parameters are calculated using the equations developed on the basis of the EFA, JET, and HET data; however, as noted above, the user is referred to Table 90 to select the best equation according to his or her objective and with regard to the differences between the equations. Table 91 shows the recommended equations for critical shear stress (tc) according to the EFA test data. For soils with D50 between 0.074 mm and 0.3 mm, Therefore, The POU plot in Table 91 shows that to reach 90% confidence that the predicted tc is less than the actual tc, the predicted value should be multiplied by 0.82 (0.82 × 0.46 = 0.38 Pa). Table 92 (Chapter 8) shows the recommended equations for critical shear stress (tc) accord- ing to the JET data. For soils with D50 less than 0.3 mm, Therefore, E 3,228.7 0.4 18.5 14 0.19 mm/h-Pa2.8 1.58 2.91( ) ( ) ( ) ( )= × × × =t - - - 88,969.4 WC1.77 2.26 0.34 501.69E C Dv u( )= × × γ × ×- - - 88,969.4 0.4 19.5 6 14 11.6 mm-s/m-h1.77 2.26 0.34 1.69Ev ( )= × × × × =- - - 1.58 0.04 0.02 500.77C Dc u( )t = × × γ ×- 1.58 4.5 16 0.2 0.46 Pa0.04 0.02 0.77c ( )t = × × × =- S Dc u0.248 PC 1.23 0.21 WC + 0.07 36.89 31.8250t = - × - × γ + × × - × + c 0.248 1.5 1.23 16 0.21 11 + 0.07 12 36.89 0.2 31.82 7.54 Pat = - × - × + × × - × + =

310 Relationship Between Erodibility and Properties of Soils The POU plot in Table 92 shows that to reach 90% confidence that the predicted tc is less than the actual tc, the predicted value should be multiplied by 0.6 (0.6 × 7.54 = 4.54 Pa). Performing the HET on SP-SM samples is typically not feasible; therefore, the equation in Table 93 cannot be used for this site. Table 94 shows the recommended equations for critical velocity (vc) according to the EFA test data. For soils with D50 greater than 0.074 mm, Therefore, The POU plot in Table 94 shows that to reach 90% confidence that the predicted vc is less than the actual vc, the predicted value should be multiplied by 0.7 (0.7 × 0.016 = 0.01 m/s). This very low critical velocity implies that this site’s resistance to initiation of erosion is significantly low. Table 95 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the EFA test data. For soils with D50 greater than 0.074 mm, Therefore, The POO plot in Table 95 shows that to reach 80% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2.5 (2.5 × 64.8 = 162 mm/h-Pa). Table 96 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the JET data. For soils with D50 greater than 0.074 mm, 55,637,006,351,614 PI WC0.19 6.39 3.67E ( )= × × γ ×t - - - Therefore, The POO plot in Table 96 shows that to reach 90% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 1.4 (1.4 × 130.2 = 184.8 mm/h-Pa). Due to the low fine content of the upper soil in this example site, the equation in Table 97 cannot be used. Table 98 shows the recommended equations for the slope of velocity–erosion rate plot (Ev) according to the EFA test data. For soils with D50 greater than 0.074 mm, Therefore, The POO plot in Table 98 shows that to reach 80% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 5 (5 × 404.6 = 2,023 mm-s/m-h). 3 10 PI WC15 1.24 8.11 0.54 502.35v Dc ( )= × × × γ × ×- - 3 10 4 16 11 0.2 0.016 m/s15 1.24 8.11 0.54 2.35vc ( )= × × × × × =- - 3,228.7 2.8 1.58 502.91E C Du( )= × × γ ×t - - - E 3,228.7 4.5 16 0.2 64.8 mm/h-Pa2.8 1.58 2.91( ) ( ) ( ) ( )= × × × =t - - - 55,637,006,351,614 4 16 11 130.2 mm/h-Pa0.19 6.39 3.67E ( )= × × × =t - - - E C Dv u88,969.4 WC1.77 2.26 0.34 501.69( )= × × γ × ×- - - Ev 88,969.4 4.5 16 11 0.2 404.6 mm-s/m-h1.77 2.26 0.34 1.69( )= × × × × =- - -

Conclusions and Recommendations 311 Table 99 shows the recommended equations for the erosion category (EC) according to the EFA test data. For soils with D50 between 0.074 mm and 0.3 mm, Therefore, The POU plot in Table 99 shows that to reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.84 (0.84 × 1.42 = 1.19). Table 100 shows the recommended equations for the erosion category (EC) according to the JET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 100 shows that to reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.85 (0.85 × 1.73 = 1.47). The equation in Table 101 is based on the HET data, and because performing the HET is not feasible on SP-SM, use of this equation is not recommended. 9.3.3 Silt Site Table 107 shows that the upper soil layer in the example silt site has an average mean particle size of 0.037 mm. In this example, the erodibility parameters are calculated using the equations developed on the basis of the EFA, JET, and HET data; however, as also mentioned above, the user is referred to Table 90 to select the best equation according to his or her objective. Table 91 shows the recommended equations for critical shear stress (tc) according to the EFA test data. For soils with D50 less than 0.074 mm, Soil activity (A) is obtained as PI/PC. Therefore, The POU plot in Table 91 shows that there is a 90% chance that the predicted tc is less than the actual tc. Table 92 shows the recommended equations for critical shear stress (tc) according to the JET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 92 shows that to reach 90% confidence that the predicted tc is less than the actual tc, the predicted value should be multiplied by 0.6 (0.6 × 10.47 = 6.28 Pa). EC 1.12 WC VST0.1 0.28 0.02 500.44C Du( )= × × × ×- - EC 1.12 4.5 11 12 0.2 1.420.1 0.28 0.02 0.44( )= × × × × =- - EC 0.022 PL + 0.0031 5.5 3.3450S Du= - × × - × + EC 0.022 25 + 0.0031 12 5.5 0.2 3.34 1.73= - × × - × + = 158.06 WC PF5 0.46 10.03 1.83 18.28 504.21A S Dc u( )t = × γ × × × × ×- - - 158.06 20 0.47 30 29 60 0.037 0.74 Pa5 0.46 10.03 1.83 18.28 4.21c ( )t = × × × × × × =- - - 0.248 PC 1.23 0.21 WC + 0.07 36.89 31.8250S Dc ut = - × - × γ + × × - × + 0.248 15 1.23 20 0.21 30 + 0.07 29 36.89 0.037 31.82 10.47 Pact = - × - × + × × - × + =

312 Relationship Between Erodibility and Properties of Soils Table 93 shows the recommended equations for critical shear stress (tc) according to the HET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 93 shows that to reach 90% confidence that the predicted tc is less than the actual tc, the predicted value should be multiplied by 0.6 (0.6 × 51.9 = 31.1 Pa). Table 94 shows the recommended equations for critical velocity (vc) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, The POU plot in Table 94 shows that to reach 90% confidence that the predicted vc is less than the actual vc, the predicted value should be multiplied by 0.8 (0.8 × 0.41 = 0.33 m/s). Table 95 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, The POO plot in Table 95 shows that to reach 87% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2 (2 × 0.78 = 1.56 mm/h-Pa). Table 96 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the JET data. For soils with D50 less than 0.074 mm, Therefore, The POO plot in Table 96 shows that to reach 88% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2 (2 × 1,088 = 2,176 mm/h-Pa). Table 97 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the HET data. For soils with D50 less than 0.074 mm, Therefore, 25.07 PI0.27 0.55 500.5S Dc u( )t = × × × 25.07 7 29 0.037 51.90.27 0.55 0.5c ( )t = × × × = 2.518 10 PC WC5 0.2 2.06 0.51 500.13v S Dc u( )= × × × × ×- - 2.518 10 15 30 29 0.037 0.41 m/s5 0.2 2.06 0.51 0.13vc ( )= × × × × × =- - E A D1.429078 10 PF13 0.47 10.43 6.14 507.52( )= × × × γ × ×t - - E 1.429078 10 0.47 20 60 0.037 0.78 mm/h-Pa13 0.47 10.43 6.14 7.52( )= × × × × × =t - - 396,599.6 PI WC2.54 4.58 4.91E Su( )= × × ×t - - 396,599.6 7 30 29 1088 mm/h-Pa2.54 4.58 4.91E ( )= × × × =t - - 9 10 LL PL PC6 0.35 1.59 3.3 0.48 0.19E Su( )= × × × × γ × ×t - - - - 9 10 30 23 20 15 29 1.13 mm/h-Pa6 0.35 1.59 3.3 0.48 0.19E ( )= × × × × × × =t - - - -

Conclusions and Recommendations 313 The POO plot in Table 97 shows that to reach 90% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 1.45 (1.45 × 1.13 = 1.64 mm/h-Pa). Table 98 shows the recommended equations for the slope of velocity–erosion rate plot (Ev) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, The POO plot in Table 98 shows that to reach 80% confidence that the predicted Ev is greater than the actual E, the predicted value should be multiplied by 2 (2 × 4.3 = 8.6 mm-s/m-h). Table 99 shows the recommended equations for the erosion category (EC) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, The POU plot in Table 99 shows that to reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.75 (0.75 × 2.3 = 1.73). Table 100 shows the recommended equations for the erosion category (EC) according to the JET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 100 shows that to reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.85 (0.85 × 2.72 = 2.31). Table 101 shows the recommended equations for the erosion category (EC) according to the HET data. For soils with D50 less than 0.074 mm, Therefore, The POU plot in Table 101 shows that to reach 100% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.95 (0.95 × 3.1 = 2.95). 9.3.4 Clay Site Table 107 shows that the upper soil layer in this site has an average mean particle size of 0.001 mm. In this example, the erodibility parameters are calculated using the equations 1.682339 10 WC PF13 505.1 9.2 1.13 4.69 0.01E D Av ( )= × × × γ × × ×- - - Ev 1.682339 10 0.037 20 30 60 0.47 4.3 mm-s/m-h13 5.1 9.2 1.13 4.69 0.01( )= × × × × × × =- - - EC 0.1933 WC0.06 0.51 0.09 500.12A S Du( )= × × × ×- - EC 0.1933 0.47 30 29 0.037 2.30.06 0.51 0.09 0.12( )= × × × × =- - EC 0.022 PL + 0.0031 5.5 3.3450S Du= - × × - × + EC 0.022 23 + 0.0031 29 5.5 0.037 3.34 2.72= - × × - × + = EC 1.67 PI0.04 0.15 0.03Su( )= × × γ × EC 1.67 7 20 29 3.10.04 0.15 0.03( )= × × × =

314 Relationship Between Erodibility and Properties of Soils developed on the basis of the EFA, JET, and HET data; however, as also mentioned previously, the user is referred to Table 90 to select the best equation according to his or her objective. Table 91 shows the recommended equations for critical shear stress (tc) according to the EFA test data. For soils with D50 less than 0.074 mm, Soil activity (A) is obtained as PI/PC. Therefore, The POU plot given in Table 91 shows that there is an almost 90% chance that the predicted tc is less than the actual tc. Table 92 shows the recommended equations for critical shear stress (tc) according to the JET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 92 shows that to reach 90% confidence that the predicted tc is less than the actual tc, the predicted value should be multiplied by 0.6 (0.6 × 9.3 = 5.6 Pa). Table 93 shows the recommended equations for critical shear stress (tc) according to the HET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 93 shows that to reach 90% confidence that the predicted tc is less than the actual tc, the predicted value should be multiplied by 0.6 (0.6 × 20.5 = 12.3 Pa). Table 94 shows the recommended equations for critical velocity (vc) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, The POU plot in Table 94 shows that to reach 90% confidence that the predicted vc is less than the actual vc, the predicted value should be multiplied by 0.8 (0.8 × 0.75 = 0.6 m/s). Table 95 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the EFA test data. For soils with D50 less than 0.074 mm, 158.06 WC PF5 0.46 10.03 1.83 18.28 504.21A S Dc u( )t = × γ × × × × ×- - - 158.06 18 0.62 23 75 100 0.001 53.7 Pa5 0.46 10.03 1.83 18.28 4.21c ( )t = × × × × × × =- - - Dc u0.248 PC 1.23 0.21 WC + 0.07 S 36.89 31.8250t = - × - × γ + × × - × + c 0.248 42 1.23 18 0.21 23 + 0.07 75 36.89 0.001 31.82 9.3 Pat = - × - × + × × - × + = Dc 25.07 PI S .0.27 u0.55 500.5( )t = × × × 25.07 26 75 0.001 20.5 Pa0.27 0.55 0.5c ( )t = × × × = 2.518 10 PC WC5 0.2 2.06 0.51 500.13v S Dc u( )= × × × × ×- - 2.518 10 42 23 75 0.001 0.75 m/s5 0.2 2.06 0.51 0.13vc ( )= × × × × × =- - 1.429078 10 PF13 0.47 10.43 6.14 507.52E A D( )= × × × γ × ×t - -

Conclusions and Recommendations 315 Therefore, The POO plot in Table 95 shows that to reach 87% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2 (2 × 7 × 10-11 = 14 × 10-11 mm/h-Pa). This very low Et implies the fact that once the erosion is initiated, the erosion rate increases at a significantly low rate with increase in velocity/shear stress. Table 96 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the JET data. For soils with D50 less than 0.074 mm, Therefore, The POO plot in Table 96 shows that to reach 88% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2 (2 × 0.1 = 0.2 mm/h-Pa). Table 97 shows the recommended equations for the slope of shear stress–erosion rate plot (Et) according to the HET data. For soils with D50 less than 0.074 mm, Therefore, The POO plot in Table 97 shows that to reach 90% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 1.45 (1.45 × 0.39 = 0.57 mm/h-Pa). Table 98 shows the recommended equations for the slope of velocity–erosion rate plot (Ev) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, The POO plot in Table 98 shows that to reach 80% confidence that the predicted Et is greater than the actual Et, the predicted value should be multiplied by 2 (2 × 1.6 × 10-6 = 3.2 × 10-6 mm-s/m-h). This low Ev is consistent with the very low Et for this site. Table 99 shows the recommended equations for the erosion category (EC) according to the EFA test data. For soils with D50 less than 0.074 mm, Therefore, 1.429078 10 0.62 18 100 0.001 7 10 mm/h-Pa13 0.47 10.43 6.14 7.52 11E ( )= × × × × × = ×t - - - 396,599.6 PI WC2.54 4.58 4.91E Su( )= × × ×t - - 396,599.6 26 23 75 0.1 mm/h-Pa2.54 4.58 4.91E ( )= × × × =t - - 9 10 LL PL PC6 0.35 1.59 3.3 0.48 0.19E Su( )= × × × × γ × ×t - - - - 9 10 51 25 18 42 75 0.39 mm/h-Pa6 0.35 1.59 3.3 0.48 0.19E ( )= × × × × × × =t - - - - 1.682339 10 WC PF13 505.1 9.20 1.13 4.69 0.01E D Av ( )= × × × γ × × ×- - - 1.682339 10 0.001 18 23 100 0.62 1.6 10 mm-s/m-h13 5.1 9.20 1.13 4.69 0.01 6Ev ( )= × × × × × × = ×- - - - EC 0.1933 WC0.06 0.51 0.09 500.12A S Du( )= × × × ×- - EC 0.1933 0.62 23 75 0.001 3.30.06 0.51 0.09 0.12( )= × × × × =- -

316 Relationship Between Erodibility and Properties of Soils The POU plot in Table 99 shows that to reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.75 (0.75 × 3.3 = 2.48). Table 100 shows the recommended equations for the erosion category (EC) according to the JET data. For soils with D50 less than 0.3 mm, Therefore, The POU plot in Table 100 shows that to reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.85 (0.85 × 3.0 = 2.6). Table 101 shows the recommended equations for the erosion category (EC) according to the HET data. For soils with D50 less than 0.074 mm, Therefore, The POU plot in Table 101 shows that to reach 100% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.95 (0.95 × 3.34 = 3.17). 9.4 General Observations on the Effect of Geotechnical Properties on Soil Erodibility Out of all the findings of this study, the correlation matrices [such as Figure 152 (Chapter 7)], along with the equations proposed in Chapter 8, may be the best measures for understanding the effect of each geotechnical property on each soil erodibility parameter. Appendix 3 presents all correlation matrices for the 12 groups shown in Figure 148 (Chapter 7). As discussed in Chapter 7, Section 7.3.2, the correlation matrices also show the Pearson correlation coefficient for each plot. The Pearson correlation coefficient was used to reflect the linear dependency between two variables, with +1 indicating a strong positive relationship, –1 indicating a solid negative relationship, and 0 indicating no relationship at all. In general, the geotechnical properties that, by increasing, lead to an increase of the critical shear stress (tc), the critical velocity (vc), and the erosion category (EC) and to a decrease in the shear stress slope (Et) and the velocity slope (Ev) are considered to be parameters that have a pos- itive impact on erosion resistance. However, those geotechnical properties that, by increasing, lead to a decrease of tc, vc, and EC and to an increase in Et and Ev are considered to be parameters that have a negative impact on soil erosion resistance. The following observations were made regarding the effect of each soil property on the erodibility of soils: • An increase in mean particle size (D50) leads to an increase in the erosion resistance of soils with D50 greater than 0.3 mm. However, regardless of the erosion test type, an increase in D50 leads to a decrease in the erosion resistance of soils with D50 less than 0.3 mm. • In fine-grained soils (D50 < 0.074 mm), a decrease in the coefficient of curvature or coefficient of uniformity (Cc and Cu) leads to an increase in soil erosion resistance. • In both fine- and coarse-grained soils, an increase in the percentage of clay leads to an increase in the erosion resistance of the soil. EC 0.022 PL + 0.0031 5.5 3.3450S Du= - × × - × + EC 0.022 25 + 0.0031 75 5.5 0.001 3.34 3.0= - × × - × + = EC 1.67 PI0.04 0.15 0.03Su( )= × × γ × EC 1.67 26 18 75 3.340.04 0.15 0.03( )= × × × =

Conclusions and Recommendations 317 • An increase in the plasticity index (PI) in general leads to an increase in the erosion resistance in both coarse-grained and fine-grained soils (especially soils with D50 less than 0.3 mm); however, there are a few exceptions to this statement. • An increase in the plastic limit (PL) leads to an increase in the erosion resistance in fine- grained soils. This influence was found to be more pronounced in the EFA data set than in the JET and HET data sets. • In many cases, the wet unit weight (γ) and the undrained shear strength (Su) (for soils with D50 less than 0.3 mm) were directly proportional to the erosion resistance. • Water content (WC) seemed to have a positive impact on the erosion resistance of finer soils in general. However, WC showed a negative effect on the erosion resistance of coarse-grained soils in the EFA test. It appears that WC alone is poorly correlated with the erosion resistance. Overall, the geotechnical properties were found to have a mixed and complex relationship with erosion resistance in general. Nevertheless, the aforementioned observations as well as the proposed equations can be used as a first step in estimating the erosion resistance of many soils. If, by using such relationships, the erosion issue is clearly not a problem, it is unlikely that further effort is necessary. However, if the use of such equations leads to uncertainty, it is desirable to run erosion tests on site-specific samples.