Relationship Between Erodibility and Properties of Soils (2019)

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1 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. Many researchers have attempted to develop equations quantifying the erodibility of soils without much success. One problem is that erodibility is not a single number, but a relation- ship 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 many erosion tests, such as 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, these include the JET, the North Carolina State University in situ scour evaluation probe test, and the Texas A&M University (TAMU) borehole erosion test and pocket erodometer test. All these tests measure 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 tasks were as follows: Phase I Task 1: Identification of current knowledge on soil erosion and soil properties. Task 2: Identification of current soil erodibility data and correlations. Task 3: Assessment of current and promising erosion tests. Phase II Task 4: Performance of erosion tests with different devices on the same prepared soils. Task 5: Performance of erosion tests on many different soils to develop erodibility equations. Task 6: Development of regression equations and validation. Task 7: Verification, synthesis, and analysis of all data to propose the best solution. A summary of each chapter is given below. Chapter 1. Introduction Chapter 1 is divided into two parts. The first part presents a definition of erosion and intro- duces different types of erosion. The general parameters for quantifying soil erodibility and the constitutive models for erosion are briefly discussed. The second part presents the research S U M M A R Y Relationship Between Erodibility and Properties of Soils

2 Relationship Between Erodibility and Properties of Soils approach. The project tasks are described and a summary of how and where within the report each of the tasks is addressed is provided. Chapter 2. Existing Erosion Tests Chapter 2 presents a comprehensive literature review on different soil erosion tests. Tests developed all over the world in the past few decades are discussed in terms of their application in the lab or in the field and of their application to surface erosion or internal erosion problems. The advantages and disadvantages of the most important tests are explained, and a summary table about the tests used in statistical analyses in this report is provided at the end of the chapter. The advantages, disadvantages, and applications of the three major erosion tests used in this study—the EFA, the JET, and the HET—are presented in Table S-1. Chapter 3. Existing Correlations Between Soil Erodibility and Soil Properties Chapter 3 provides 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 are summarized. The influence factors on erosion, including the less easily obtained engineering properties, are presented and discussed in detail. Table S-2 summarizes these parameters. Chapter 4. Erosion Experiments Chapter 4 begins by describing the TAMU Soil Erosion Laboratory. The erosion testing devices built as part of this research project as well as the refurnished and armored erosion function apparatus are presented. The test plan matrix proposed for the project and the results of the hundreds of erosion tests performed during the project are then presented and discussed. Finally, an example of the spreadsheet of geotechnical engineering properties created for each tested sample obtained at TAMU is presented. Appendices 1 and 2 of this report contain the spreadsheets for the erosion test results and soil geotechnical properties, respectively, for all samples tested in this project. [Note: Five appendices to NCHRP Research Report 915 are gathered in an Appendices Report that is available on the NCHRP Project 24-43 page on the TRB website (trb.org).] Chapter 5. Organization and Interpretation of the Data Chapter 5 is largely dedicated to the organization and description of the erosion spreadsheet developed for this project and named “NCHRP-Erosion.” NCHRP-Erosion includes the results of nearly 1,000 erosion tests—approximately 250 erosion tests performed as part of this project and nearly 750 erosion tests collected from all over the world—along with the geotechnical properties of each sample. The process used to compile erosion test data from all over the world is explained, and the contact people and organizations who helped gather the information are mentioned. All the erosion data in NCHRP-Erosion were 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 discusses the column contents in detail and concludes with the Inquiry Operation Manual that explains

Table S-1. Comparison of EFA, JET, and HET. Advantages Drawbacks Applications EFA 1. Minimizes the sample disturbance effect, as it takes the unextruded Shelby tube sample directly from the field. 2. Can be used on natural samples as well as man-made samples 3. Gives all five erodibility parameters (i.e., , τ , , , and EC). Can give the erosion function directly. 4. Can monitor the erosion rate in real time rather than by interpolating or extrapolating using indirect equations. 5. EFA test results are directly used as input to the TAMU-SCOUR method for bridge scour depth predictions (Arneson et al. 2012, Chapter 6). 6. EFA can test the erodibility of the soil at any depth as long as a sample can be recovered. 7. Gives the erosion function, which is a fundamental measure of erodibility at the element level. 8. Can be used to test very soft to hard soils. Very broad applications. The velocity range is from 0.2 to 6 m/s. 1. Shear stress is indirectly measured from velocity using Moody charts, which might not be accurate. Also, the average flow velocity is used in the calculation. 2. In some cases, obtaining samples is difficult and costly. The test needs to be done on the sample before the sample is affected by long periods of storage. 3. Particles larger than about 40 mm cannot be tested with confidence, as the diameter of the sampling tube is 75 mm. 4. The EFA device is fairly expensive (around $50,000 in 2018). 1. Bridge scour. 2. Meander migration. 3. Levee overtopping. 4. Soil improvement. 5. Internal erosion of dams. JET 1. Can be run both in the field and in the lab. 2. The latest version of the JET, the mini- JET, is simple, quick, and inexpensive compared with other types of erosion tests. 3. Can be performed on any surface— vertical, horizontal, or inclined. 4. Very good as an index erodibility test. 1. Particles larger than 30 mm cannot be tested with confidence because of the small size of the sample. 2. Coarse-grained soils (i.e., noncohesive sand and gravel) tend to fall back into the open hole during the jet erosion process, thereby making the readings dubious. 3. Very small-scale test application. 4. Typically used for man-made samples. Natural samples are more difficult to test. 5. The flow within the eroded hole and at the soil boundary is complex and difficult to analyze. 6. Gives only three of the five possible erodibility parameters (τ , , and EC). 7. The elements of erosion are inferred rather than measured directly. 8. There are multiple interpretation techniques for predicting the critical shear stress, and these give significantly different results. 1. Agriculture erosion. 2. Levees. HET 1. Direct similitude with piping erosion in earth dams. 2. Can apply to a wide range of pressure heads and therefore a wide range of hydraulic shear stress at the soil–water interface. 1. The sample needs to be cohesive and strong enough to stand under its own weight. Therefore, the test cannot be run on loose cohesionless soils or soft cohesive soils. 2. Very difficult to run on intact samples in Shelby tubes from the field. Only good for remolded, recompacted samples in the lab. 3. Preparation of the test is difficult and time consuming. 4. No direct monitoring of the erosion process. The erosion rate needs to be inferred and extrapolated. 5. The hydraulic shear stress is inferred rather than directly measured. 6. The data reduction process is quite subjective. 7. Gives only three of the five possible erodibility parameters (τ , , and EC). 8. The flow within the eroded hole and at the soil boundary is complex. 1. Internal erosion of earth dams. 2. Suffusion. 3. Levee breach. 4. Soil improvement.

4 Relationship Between Erodibility and Properties of Soils how to search for specific data within the spreadsheet. NCHRP-Erosion can be downloaded from the TRB website (trb.org) by searching for “NCHRP Research Report 915”. Chapter 6. Comparison of Selected Soil Erosion Tests by Numerical Simulation Chapter 6 presents a comparison of selected soil erosion tests [i.e., EFA, HET, JET, and the borehole erosion test (BET)] by means of numerical simulations software. The chapter is divided into two sections: (1) numerical simulations for nonerodible soils and (2) numerical simulations including the erosion process. The first part of the chapter deals with the evolu- tion of hydraulic shear stress and the velocity profile with the assumption that the soil is not erodible. It is observed that there was a discrepancy between the Moody chart predictions and the numerical simulations and that the Moody charts generally overestimated the shear stress. This discrepancy was more pronounced in higher shear stress values (up to 100% difference between the Moody chart prediction and the numerical simulation in one case). In the second part of the chapter, the erosion function is assigned to the water–soil interface, and the erosion is numerically simulated with a moving boundary for selected erosion tests. The results of the numerical simulations are compared with the actual observations for each test. 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, HET, and 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). Chapter 7. Development of Correlation Equations Chapter 7 is dedicated to the main goal of the study, namely, the development of correlation equations. This chapter is divided into four major parts. The first part presents a preliminary and quick method for determining the erosion resistance of a soil by using only the Unified Soil Classification System (USCS) classification of the soil and associated erosion categories. The plot of the erosion rate versus velocity based on the USCS categories is shown in Figure S-1. The width of each box associated with a USCS category represents the zone in which 90% of the EFA results for such samples would fall within the erosion category chart. For instance, More Typically Obtained Properties Less Typically Obtained Properties • Plasticity index • Liquidity index • Unit weight • Water content • Undrained shear strength • Percentage passing sieve #200 • Percentage of clay particles • Percentage of silt particles • Mean grain size • Coefficient of uniformity • Percentage of compaction (for man-made soils only) • Soil swell potential • Soil void ratio • Specific gravity of solids • Soil dispersion ratio • pH (flowing water and pore water) • Salinity of eroding fluid • Organic content • Soil cation exchange cap • Soil clay minerals • Soil sodium adsorption ratio • Soil activity • Soil temperature • Density of cracks Table S-2. Soil and water properties that influence the erosion resistance of soils.

Summary 5 0.1 1 10 100 1,000 10,000 100,000 0.1 1.0 10 100 VELOCITY (m/s) EROSION RATE (mm/hr) Very High Erodibility I High Erodibility II Medium Erodibility III Low Erodibility IV Very Low Erodibility V -Fine Sand -Non-plastic Silt -Medium Sand -Low-Plasticity Silt - Increase in Compaction (well-graded soils) -Increase in Density -Increase in Water Salinity (clay) Non-Erosive VI -Fine Gravel -High-Plasticity Silt -Low-Plasticity Clay -All fissured clays -Jointed Rock (spacing < 30 mm) -Cobbles -Coarse Gravel -High-Plasticity Clay -Jointed Rock (30–150 mm spacing) -Riprap -Jointed Rock (150–1,500 mm spacing) -Intact Rock - Jointed Rock (spacing > 1,500 mm) MH SP-SM ML-CL Rock SW SW-SM SP-SC SP SM SC-SM SC ML GC CL GP CH 0.1 1 10 100 1,000 10,000 100,000 EROSION RATE (mm/hr) Very High Erodibility I High Erodibility II Medium Erodibility III Low Erodibility IV Very Low Erodibility V 0.1 1 10 100 1,000 10,000 100,000 SHEAR STRESS (Pa) -Fine Sand -Non-plastic Silt -Medium Sand -Low-Plasticity Silt - Increase in Compaction (well-graded soils) - Increase in Density - Increase in Water Salinity (clay) -Fine Gravel -High-Plasticity Silt -Low-Plasticity Clay -All fissured clays -Jointed Rock (spacing < 30 mm) -Cobbles -Coarse Gravel -High-Plasticity Clay -Jointed Rock (30–150 mm spacing) -Riprap -Jointed Rock (150–1,500 mm spacing) -Intact Rock -Jointed Rock (spacing > 1,500 mm) MH SP-SM ML-CL Rock SW SW-SM SP-SC SP SM SC-SM SC ML GC CL GP CH Figure S-1. Erosion category charts with USCS symbols.

6 Relationship Between Erodibility and Properties of Soils if the soil type at a geotechnical site is classified as SM (silty sand) according to the USCS, it would most likely (with close to 90% confidence on the basis of the EFA results compiled in NCHRP-Erosion) fall into Category II (high erodibility). 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 second part of Chapter 7 deals with improving existing plots of critical velocity/critical shear stress versus mean particle size (D50). It is observed that for soils with a 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 is 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 Chapter 7 presents the frequentist regression technique. The step-by-step procedure for implementing the frequentist regression technique, the experimental design, and the model selection process are discussed, and the results of the regressions are presented. The best correlation equations are determined by a four-filter process including (1) R2, (2) the mean square error, (3) the statistical F-test, and (4) the cross-validation test. Plots of the probability of overpredicting (POO) and probability of underpredicting (POU) are also presented for the selected equations. Tables S-3 to S-7 show the selected equations for each erodibility parameter and for each data set. Group No. Independent Variablesa Data Setb Model Expressionc Cross- Validation Score 124 γ, A, WC, Su, PF, D50 EFA/Fine (n = 44) τ = (158.06) × γ × . × WC . × . × PF . × – . 0.94 0.66 77 Cu, γ, D50 EFA/Coarse (n = 28) τ = (1.58) × . × γ . × . 0.93 0.99 113 PC, γ, WC, Su, D50 JET/Global (n = 28) τ = − 0.248 × PC − 1.23 × γ + 0.21 × WC + 0.07 × − 36.89 × + 31.82 0.50 0.10 19 PI, Su, D50 HET/Global (n = 21) τ = (25.07) × PI . × . × . 0.64 0.43 aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table S-3. Selected models for critical shear stress, sc. aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Group No. Independent Variablesa Data Setb Model Expressionc Cross- Validation Score 117 PC, WC, Su, D50 EFA/Fine (n = 46) = (2.518 × 10 ) × PC . × WC . × . × – . 0.80 0.80 27 PI, γ, WC, D50 EFA/Coarse (n =15) = (3 × 10 ) × PI . × γ . × WC . × – . 0.88 0.72 Table S-4. Selected models for critical velocity, vc.

Summary 7 Group No. Independent Variablesa Data Setb Model Expressionc Cross- Validation Score 132 A, WC, Su, D50 EFA/Fine (n = 44) EC = (0.1933) × . × WC . × . × – . 0.55 0.53 91 Cu, WC, VST, D50 EFA/Coarse (n = 11) EC = (1.12) × . × WC . × VST . × – . for 0.074 < < 0.3 0.92 0.80 88 PL, Su, D50 JET/Global (n = 28) EC = − 0.022 × PL + 0.0031 × − 5.5 × + 3.34 0.70 0.58 12 PI, γ, Su HET/Fine (n = 21) EC = (1.67) × PI . × γ . × . 0.70 0.54 48 Cc, γ, WC HET/Coarse (n = 28) EC = (1.045) × . × γ . × WC . 0.77 0.78 aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table S-5. Selected models for erosion category, EC. Group No. Independent Variablesa Data Setb Model Expressionc Cross- Validation Score 86 Cu, γ, WC, D50 EFA/Coarse (n = 28) = (88,969.4) × . × γ . × WC . × – . 0.86 0.64 126 D50, γ, WC, PF, A EFA/Fine (n = 74) = (1.682339 × 10 ) × . × γ . × WC . × PF . × . 0.79 0.52 aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table S-6. Selected models for velocity slope, Ev. Group No. Independent Variablesa Data Setb Model Expressionc Cross- Validation Score 77 Cu, γ, D50 EFA/Coarse (n = 28) = (3,228.7) × . × γ . × – . 0.91 0.64 134 A, , PF, D50 EFA/Fine (n = 72) = (1.429078 × 10 ) × . × γ . × PF . × . 0.90 0.51 40 γ, WC, PF, HET/Coarse = (2.951) × γ . × WC . × PF . 0.86 0.55 D50 (n = 62) × – . 108 LL, PL, , PC, Su HET/Fine (n = 21) = (9 × 10 ) × LL . × PL . × γ . × PC . × . 0.81 0.51 5 PI, , WC JET/Coarse (n = 25) = (55,637,006,351,614) × PI . × γ . × WC . 0.90 0.67 15 PI, WC, Su JET/Fine (n = 24) = (396,599.6) × PI . × WC . × . 0.93 0.23 aSee Chapter 7, Section 7.3.1. bn = number of data points. cParameter values given by deterministic regression. Table S-7. Selected models for shear stress slope, Et.

8 Relationship Between Erodibility and Properties of Soils The last part of Chapter 7 deals with a probabilistic approach as opposed to the deterministic approach presented in the previous section. The probabilistic approach is based on the Bayesian inference method. The methodology of the Bayesian inference method and its results are presented in Section 7.4 as well as in Appendix 5. Chapter 8. Most Robust Correlation Equations This chapter focuses on the recommended correlation equations (Tables S-3 to S-7) based on the work presented in Chapter 7 and provides instructions on how best to use them. Table S-8 shows an example of the proposed equation charts for erosion category based on the JET data. This table presents the recommended correlation equation for predicting the erosion category for D50 < 0.3 mm. Along with each proposed equation, these tables give two plots: one showing the POU (or the POO, where applicable) versus the correction factor and one showing the predicted EC versus the measured EC. Such plots provide great insight on using each equation. Also, a column containing some remarks is provided on the right side of each equation. This column includes the values of R2 and the cross-validation (C.V.) score. The same sort of table is presented for different erodibility parameters and different erosion tests. < . = − . × + . × − . × + . Remarks R2 = 0.70 C.V. score = 0.58 1. Refer to Group 88 in Table 76 for further information on the statistical significance of the proposed equation. 2. The POU versus correction factor plot is based on the data used to develop the proposed equation. 3. To reach 90% confidence that the predicted EC is less than the actual EC, the predicted value should be multiplied by 0.85. Table S-8. Proposed equation for erosion category (EC) based on the JET data.

Summary 9 Chapter 9. Conclusions and Recommendations Chapter 9 presents the general conclusions resulting from the work done in this project, recommendations on how to approach erosion-related design problems, and general observa- tions on the effect of geotechnical properties on soil erodibility. Recommendations on How to Approach Erosion-Related Design Problems Step 1. Probe NCHRP-Erosion Chapter 5 of this report discusses the development of the NCHRP-Erosion database. This global spreadsheet is a searchable tool that allows the engineer to filter the data on the basis of multiple criteria. The first approach to evaluating the erodibility of a desired site is through probing NCHRP-Erosion. The engineer can use information on as many geotechnical properties as are available for the site (e.g., 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 obtained soil samples may be tested with one or more erosion tests (e.g., EFA, BET, JET, HET). The engineer then can see which erodibility parameters he or she must expect from the soil without having to conduct different erosion tests. Probing NCHRP-Erosion also helps the engineer compare the results of these different erosion tests on similar soil samples. Step 2. Use the USCS Erosion Charts to Estimate Erosion Resistance Section 7.1 shows 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 approximately across two categories. As discussed in the summary of Chapter 7 above, the proposed erosion category–USCS category chart can be used as another preliminary tool for estimating the erodibility of any sample. Knowledge of the erosion category of a soil can lead to useful informa- tion about the erosion resistance of that soil; however, it should be noted that such results are not accurate enough for design purposes. Step 3. Use the Deterministic Regression Results Section 7.3 presents a comprehensive deterministic approach for selecting the best correlation equations between geotechnical properties and erodibility parameters. The most robust equations were repeated and are presented in a tabulated format in Section 8.2. The proposed equations were developed on the basis of the data obtained in different erosion tests (EFA, JET, and HET). The advance knowledge on each test is extremely useful in choosing the best equation. Before the proposed equations in Section 8.2 are used, the advantages and disadvantages of each erosion test should be studied carefully. POU/POO plots help the engineer find the correction factor needed to reach a certain confidence that the predicted value is under- or overpredicted. These plots can be very useful for design purposes. Step 4. Use the Bayesian Inference Results One of the issues with conventional deterministic approaches is that they fail to capture uncertainty by accounting only for the mean value of the unknown parameter. Therefore, Section 7.4 is dedicated to the performance of a probabilistic analysis with the Bayesian infer- ence approach. The comprehensive deterministic frequentist regression analysis performed in Section 7.3 is the foundation of the Bayesian inference analysis performed in Section 7.4. The selected correlation equations that use the deterministic approach are analyzed by Bayesian

10 Relationship Between Erodibility and Properties of Soils 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 entire results of the Bayesian inference analysis. General Observations on the Effect of Geotechnical Properties on Soil Erodibility The following findings on the relationships between geotechnical properties and erodibility parameters are also reported in Chapter 9: • 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. • 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.