**Suggested Citation:**"Chapter 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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 9. Conclusions and Recommendations." 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.

324 CHAPTER 9 9. CONCLUSIONS AND RECOMMENDATIONS The goal of this project is to develop reliable and simple equations quantifying the erodibility of soils based on 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 (sand, clay) therefore erodibility is tied to soil properties. On the other hand, 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, they include many erosion tests such as the pinhole test, the hole erosion test, the jet erosion test, the rotating cylinder test, the erosion function apparatus test. In the field, they include the jet erosion test, the NC State in situ scour evaluation probe test, the TAMU borehole erosion test and pocket erodometer test, and etc. All these tests measure the soil erodibility but give different results. It is important to give the engineers options so that she or he 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 summary of the findings for each chapter is discussed below. 9.1. Chapter 1 - Introduction This chapter was divided into two halves. The first half presented a definition for the erosion phenomenon and introduced different types of erosion. The general parameters to quantify the soil erodibility and the constitutive models for erosion were briefly discussed. The second half of this chapter presented the research approach. The project tasks were described one by one, and a summary of how and where within the report each one of the tasks are addressed was provided. 9.2. Chapter 2 - Existing Erosion Tests This chapter presented a comprehensive literature review on different soil erosion tests. The tests developed all over the world in the last few decades were discussed in terms of their application in the lab or in the field, as well as their application in surface erosion or internal erosion problems. Advantages and disadvantages of the most important tests were explained, and a summary table about selected tests was provided at the end of this chapter. The advantages, the disadvantages, and the applications of the three major erosion tests (i.e. EFA, JET, HET) that are used in this study were presented in Table 90, which is also repeated below. Table 90 (REPEATED). Comparison of the EFA, the JET, and the HET

325 Erosion Test Advantages Drawbacks Applications EFA 1) Minimize the sample disturbance effect, as it takes the un-extruded 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. , , , , and ). Can give the erosion function directly. 4) Can monitor the erosion rate in real- time rather than 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 (Chapter 6 of HEC-18). 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 m/s up 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 in size cannot be tested with confidence as the diameter of the sampling tube is 75 mm. 4) The EFA device is fairly expensive (around $50k 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 to other types of erosion test. 3) Can be performed on any surface vertical, horizontal, and inclined. 4) Very good as an index erodibility test. 1) Particles larger than 30 mm in size cannot be tested with confidence because of the small size of the sample. 2) Coarse grained soils (i.e. non-cohesive 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 are more difficult to test 5) The flow within the eroded hole and at the soil boundary is complex and difficult to analyze. 6) Only gives three of the erodibility parameters ( , , and ) out of the five possible parameters. 7) The elements of erosion are inferred rather than measured directly. 8) There are multiple interpretation techniques to predict the critical shear stress which 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 wide range of 1) The sample needs to be cohesive and strong enough to stand under its own weight. Therefore, the test cannot be run on loose cohesion-less soils or soft cohesive soils. 1) Internal erosion of earth dams 2) Suffusion 3) Levee breach 4) Soil improvement

326 hydraulic shear stress at the soil-water interface. 2) Very difficult to run on intact samples in Shelby tubes from the field. Only good for remolded re-compacted samples in the lab. 3) Difficult and time-consuming preparation of the test. 4) No direct monitoring of the erosion process. The erosion rate needs to be inferred and extrapolated. 5) The hydraulic shear stress is inferred, and not directly measured. 6) The data reduction process is quite subjective. 7) Only gives three of the erodibility parameters ( , , and ) out of the five possible parameters. 8) The flow within the eroded hole and at the soil boundary is complex. 9.3. Chapter 3 â Existing Correlations between Soil Erodibility and Soil Properties This chapter 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 last century were summarized. The influence factors on erosion including the less-easily- obtained engineering properties were presented and discussed in detail. A summary of these influencing parameters was presented in Table 10, which is also repeated below. Table 10 (REPEATED). Influencing soil and water properties in erosion resistance of soils More typically obtained properties ï· Plasticity index ï· Liquidity Index ï· Unit weight ï· Water content ï· Undrained shear strength ï· Percent passing sieve #200 ï· Percent clay particles ï· Percent silt particles ï· Mean grain size ï· Coefficient of uniformity ï· Percent compaction (for man-made soils only) ï· Soil swell potential ï· Soil void ratio Less easily obtained properties ï· Specific gravity of solids ï· Soil dispersion ratio ï· pH (flowing water and pore water) ï· Salinity of eroding fluid ï· Organic content ï· Soil cation exchange capacity ï· Soil clay minerals ï· Soil sodium adsorption ratio ï· Potassium intensity ï· Aggregate stability ï· Soil activity ï· Soil temperature ï· Density of cracks

327 9.4. Chapter 4 â Erosion Experiments This chapter started by describing the soil erosion laboratory at Texas A&M University. The erosion testing devices built as part of this research project as well as the refurnished and armored Erosion Function Apparatus 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. Finally, the geotechnical engineering properties associated with each tested sample were obtained at Texas A&M University and presented in the form of a soil geotechnical properties spreadsheet for each sample. It should be noted that Appendix 1 and 2 of this report contain the erosion spreadsheets as well as the geotechnical properties spreadsheets for all tested samples in this project. 9.5. Chapter 5 â Organization and Interpretation of the Data This chapter was largely dedicated to the organization and description of the erosion spreadsheet developed for this project and named âTAMU-Erosionâ. TAMU-Erosion includes nearly 1000 erosion tests with the geotechnical properties of each sample, and is comprised of the two hundred erosion tests performed as part of this project as well as eight hundred erosion tests collected from all over the world. The compilation and collection process of erosion test data from all over the world was explained, and the contact people and organization who helped gather the information were mentioned. In TAMU-Erosion, all the erosion data are analyzed according to the procedures described in the report for the five erodibility parameters: 1) critical shear stress ( ), 2) critical velocity ( ), 3) initial slope of velocity ( ), 4) initial slope of shear stress ( ), and 5) erosion category (EC). TAMU-Erosion includes 50 columns and nearly 1000 rows. The column contents were discussed in detail. Finally, an inquiry operation manual explained how to search for specific data within TAMU-Erosion. 9.6. Chapter 6 â Comparison of Selected Soil Erosion Tests by Numerical Simulations This chapter presented the comparison of selected soil erosion tests (i.e. EFA, HET, JET, and BET) with the use of numerical simulations software. This chapter was divided into two sections: 1) numerical simulations on non-erodible soils, 2) numerical simulations including the erosion process. The first part of the chapter dealt with the evolution of hydraulic shear stress and velocity profile with the assumption that the soil is not erodible. It was observed that there is a discrepancy between the Moody chart predictions and the numerical simulations, and that the Moody charts generally overestimate 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 cases). In the second part, the erosion function was assigned to the water-soil interface, and the erosion was numerically simulated with a moving boundary for selected erosion tests. The results of 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

328 can be reasonably used to produce a similar âscour versus timeâ plot to what the JET, the 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). 9.7. Chapter 7 â Correlation Equation Development This chapter was dedicated to the main goal of this study which is the development of correlation equations. This chapter was divided into four major parts. The first part presented a preliminary and quick method to determine the erosion resistance of a soil using only the Unified Soil Classification System (USCS) of the soil and associated erosion categories. The plot of erosion rate vs. velocity based on the USCS categories is shown in Figure 145, which is also repeated below. The width of each box, that 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 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 the TAMU-Erosion) fall into the Category II (high erodibility). Figure 145 (REPEATED). Erosion Category Charts with the USCS Symbols The second part of Chapter 7 dealt with improving existing plots of the critical velocity/critical shear stress versus the mean particle size. It was observed that for soils with mean particle size larger than 0.3 mm, following relationships exist between the critical velocity/shear stress and 0.1 1 10 100 1000 10000 100000 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 (150-1500 mm Spacing) -Intact Rock -Jointed Rock (Spacing > 1500 mm) MH SP-SM ML-CL Rock SW SW-SM SP-SC SP SM SC-SM SC ML GC CL GP CH

329 mean particle size: ï¨ ï©0.5500.315 ( )( / )c D mmv m s ï½ and 50( ( ))c D mPa mï´ ï½ . It was also concluded that for fine-grained soils there is no direct relationship between critical velocity/shear stress and the 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 âFrequentistsâ Regressionâ technique. The step-by- step procedure for implementing the frequentistsâ regression technique, the experimental design, and the model selection process were discussed, and the results of the regressions were presented. The best correlations equations were selected after passing through a four-filter process including: 1) R2, 2) mean squared error (MSE), 3) statistical F-test, and 4) the cross-validation test. Plots of the âProbability of Over-Predictingâ and âUnder-Predictingâ were also presented for the selected equations. Table 102 to Table 106 show the selected equations for each erodibility parameter and for each dataset. Table 102. Selected models for critical shear stress Ïc Group No. Independent variables Dataset/ No. of data Model expression (parameter values given by deterministic regression) R Cross- validation score 124 Î³, A, WC, Su, PF, D50 EFA/Fine 44 Ï 158.06 Î³ A . WC . S . PF . D50 . 0.94 0.66 77 Cu, Î³, D50 EFA/Coarse 28 Ï 1.58 C . Î³ . D50 . 0.93 0.99 113 PC, Î³, WC, Su, D50 JET/Global 28 Ï 0.248 PC 1.23 Î³ 0.21 WC 0.07 S 36.89 D50 31.82 0.50 0.10 19 PI, Su, D50 HET/Global 21 Ï 25.07 PI . S . D50 . 0.64 0.43 Table 103. Selected models for critical velocity vc Group No. Independent variables Dataset/ No. of data Model expression (parameter values given by deterministic regression) R Cross- validation score 117 PC, WC, Su, D50 EFA/Fine 46 v 2.518 10 PC . WC . S . D50 . 0.80 0.80 27 PI, , WC, D50 EFA/Coarse 15 3 10 . . . 50 . 0.88 0.72

330 Table 104. Selected models for erosion category EC Group No. Independent variables Dataset/ No. of data Model expression (parameter values given by deterministic regression) R Cross- validation score 132 A, WC, Su, D50 EFA/Fine 44 EC 0.1933 A . WC . S . D50 . 0.55 0.53 91 Cu, WC, VST, D50 EFA/Coarse 11 EC 1.12 C . WC . VST . D50 . for 0.074 D50 0.3 0.92 0.80 88 PL, Su, D50 JET/Global 28 EC 0.022 PL 0.0031 S 5.5 D50 3.34 0.70 0.58 12 PI, Î³, Su HET/Fine 21 EC 1.67 PI . Î³ . S . 0.70 0.54 48 Cc, , WC HET/Coarse 28 1.045 . . . 0.77 0.78 Table 105. Selected models for velocity slope Ev Group No. Independent variables Dataset/ No. of data Model expression (parameter values given by deterministic regression) R Cross- validation score 86 Cu, Î³, WC, D50 EFA/Coarse 28 E 88969.4 C . Î³ . WC . D50 . 0.86 0.64 126 D50, , WC, PF, A EFA/Fine 74 1.682339 10 50 . . . . . 0.79 0.52 Table 106. Selected models for shear stress slope EÏ Group No. Independent variables Dataset/ No. of data Model expression (parameter values given by deterministic regression) R Cross- validation score 77 Cu, Î³, D50 EFA/Coarse 28 E 3228.7 C . Î³ . D50 . 0.91 0.64 134 A, , PF, D50 EFA/Fine 72 1.429078 10 . . . 50 . 0.90 0.51 40 Î³, WC, PF, D50 HET/Coarse 62 E 2.951 Î³ . WC . PF . D50 . 0.86 0.55 108 LL, PL, , PC, Su HET/Fine 21 9 10 . . . . . 0.81 0.51 5 PI, , WC JET/Coarse 25 55637006351614 . . . 0.90 0.67 15 PI, WC, Su JET/Fine 24 396599.6 . . . 0.93 0.23 The last part of this chapter dealt with a probabilistic approach as opposed to the deterministic approach presented in the previous section. The probabilistic approach was based on the âBayesian inferenceâ method. The methodology of the Bayesian inference method and its results were presented in Section 7.4 as well as in the Appendix 5 of the appendices report.

331 9.8. Chapter 8 â Most Robust Correlation Equations This chapter focused on the recommended correlation equations (Table 102 to Table 106) based on the work presented in Chapter 7, and provided instructions on how best to use them. Table 100, which is also repeated below, shows an example of the proposed equation charts for erosion category based on the JET data. This table presents the recommended correlation equations to predict erosion category in different D50 ranges. It should be noted that alongside with each proposed equation, these tables often give two plots showing the POU (or POO, where applicable) vs. correction factor, as well as the âpredictedâ vs. âmeasuredâ. 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 score (named as C.V in the tables). Same sorts of tables were proposed for different erodibility parameters and different erosion tests. Table 100 (REPEATED). Proposed equations for erosion category (EC) based on the JET data JET 50 0.3 . . . . Remarks R2 = 0.70 C.V Score = 0.58 1- Refer to the Group 88 in Table 76 for further information on the statistical significance of the proposed equation. 2- The âPOU vs. Correction Factorâ plot is based on the data used to develop the proposed equation. 3- In order to reach a 90% confidence that the predicted EC is smaller than the actual EC, the predicted value should be multiplied by 0.85.

332 9.9. Recommendations on How to Approach the Erosion-Related Design Problems One of the key missions of this project was to provide the engineers in charge of erosion problems with a set of correlation equations to predict erosion parameters without having to perform 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, a 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 considers all four steps prior to making a final decision. Step 1- Probe the TAMU-Erosion Chapter 5 of this report discussed the development of the TAMU-Erosion database. This global spreadsheet is a searchable tool and allows the engineer to filter the data based on multiple criteria. The first preliminary approach to evaluate the erodibility of a desired site is through probing TAMU-Erosion. The engineer can use as many geotechnical properties information as possible from the site (i.e. the USCS category, the AASHTO classification, the Atterberg limits, the unit weight, etc.), and filter the TAMU-Erosion based on those criteria with the goal of finding the soil samples that are similar to the target soil. After filtering, the obtained soil samples might be tested with more than one erosion test (i.e. EFA, BET, JET, HET, etc.). The engineer then can see for his/herself that what erodibility parameters he/she must expect from the soil without the need to conduct different erosion tests. Probing the TAMU-Erosion also helps the engineer to compare the results of these different erosion test on the similar soil samples. Step 2- Use the USCS-Erosion Charts to estimate the erosion resistance 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 approximately across two categories. Figure 145 summarized all results into the erosion category charts. Figure 145 can be used as another preliminary tool to estimate the erodibility of any sample, using only the USCS category. In this figure, the width of each box, that 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 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 the TAMU-Erosion) fall into the Category II (high erodibility) on Figure 145. Similarly, a soil classified as CH (fat clay) would most likely fall into the Category III (medium erodibility), and a SP (poorly graded sand) would fall within the Categories I and II (very high to high erodibility). The wider the box is for a USCS category, the more the variability of the erosion category (EC) is for that particular soil type. Knowledge of the

333 erosion category of a soil can lead to many useful information 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 presented a comprehensive deterministic approach to select the best correlation equations between the geotechnical properties and the erodibility parameters. The most robust equations were repeated and tabulated in Section 8.2. The proposed equations are developed based on the data obtained in different erosion tests (the EFA, the JET, and the HET); therefore, the in- advance knowledge on each test is extremely useful to choose the best equation. Table 90 showed a list of advantages, disadvantages, and application for the EFA, the JET, and the HET. The content of this table should be studied carefully before using the proposed equations in Section 8.2. Plots of âprobability of under/over-predictingâ (POU/POO) were 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/over predicted. They 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 the uncertainty by only accounting for the mean value of the unknown parameter. Therefore, Section 7.4 was dedicated to performing a probabilistic analysis using the Bayesian inference approach. The comprehensive deterministic frequentistsâ regression analysis performed in Section 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 the 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 were presented in Section 7.4. Appendix 5 of the appendices report presents the entire results of the Bayesian inference analysis. 9.10. Example Applications This section consists of generic examples illustrating the use of the presented approach in Section 9.9 to evaluate soil erosion resistance. Four different geotechnical sites (i.e. gravel, sand, silt, and clay sites) are being studied to examine their resistance against 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 unconsolidated undrained (UU) tests. Table 107 shows selected geotechnical properties of the upper soil layer (first 2 meters) in each site. In these examples, use of the first three steps discussed in Section 9.9 are illustrated. For step 4 (Bayesian inference), the user is referred to Section 7.4.

334 Table 107. Selected geotechnical properties of the upper soil layer in each site 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 - - 0 14 - 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 - 15 Clay CH 18 25 26 100 0.001 75 23 - 42 Geotechnical properties shown in Table 107 help the user search into TAMU-Erosion and find the soil samples that are very similar to the existing soil for each site. As discussed earlier, Chapter 5 presents an inquiry operation manual. By using TAMU-Erosion, the user can see different erosion testsâ results performed on similar samples from different projects. The user is then referred to Chapter 2 of this report and Table 90 to study the advantages, drawbacks and applications of each test. Then, the user can use his/her engineering judgement and decide which results would be an appropriate match to the existing problem. It is recommended that the engineer carries out all four steps to confirm his/her findings in the first step and also have a more thorough examination of erodibility of the existing soil, in case there is not enough samples in TAMU-Erosion for that particular soil. The second step is to use USCS-Erosion Charts (Figure 145) as a preliminary estimate of the erosion category in each site. Section 9.9.2 shows a few examples of how to use these charts. In this example application, the gravel site soil is classified as GP. Figure 145 shows that this soil would most likely fall into a zone in the vicinity of the boundary between Category II and III (high to medium erodibility). In addition to the erosion category, the user can use the plot to approximately determine how much erosion rate he/she should expect in the site considering the flow conditions (i.e. velocity) of the upcoming flood. For example, Figure 145 shows that assuming our GP soil would fall very close to the boundary between category II and III, for a flow velocity of 2 m/s, it is expected to observe approximately 100 mm/hr erosion rate. Similarily, 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 amount of erosion rate expected for each site can then be determined similar to 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 the third step, the user is recommended to use the selected correlation equations to evaluate his/her findings during the fisrt two steps and improve his/her decision, where applicable. The erodibility parameters are predicted using different equations depending on what erosion test data (EFA, JET, or HET) are used to develop them (Chapter 8 and Table 102 to Table 106). Therefore, the knowledge on the strength points/limitations of each test is a vital step prior to choosing an equation. Table 90 helps the readers identify and understand the differences between the erosion tests. The user is free to select the best equation according to his/her objective and considering the differences between the equations.

335 Gravel Site Table 91 shows that for soils with D50 greater than 0.3 mm, the recommended equation for obtaining the critical shear stress is Ï D50. Therefore, for the case of this example site, critical shear stress is Ï 14 Pa. The critical velocity can be defined from equations shown in Table 94. For soils with D50 greater than 0.3 mm, it is recommended to use v 0.315 D50 . . Therefore, for the case of this example site, critical velocity is v 0.315 14 . 1.18 / . Table 95 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the EFA test data. For soils with D50 greater than 0.074 mm, 3228.7 . . 50 . . Therefore, 3228.7 0.4 . 18.5 . 14 . 0.19 mm/hr-Pa. The POO plot shown in Table 95 shows that in order to reach an 80% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2.5 (2.5 0.19 0.475 mm/hr-Pa). Table 96 and Table 97 show the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the JET and HET data, respectively. Since performing the JET and HET on gravel is not feasible, equations given in Table 96 and 97 cannot be used for this example site. Table 98 shows the recommended equations for the slope of velocity-erosion rate plot ( ) according to the EFA test data. For soils with D50 greater than 0.074 mm, 88969.4 . . . 50 . . Therefore, 88969.4 0.4 . 19.5 . 6 . 14 . 11.6 mm-s/m-hr. The POO plot shown in Table 98 shows that in order to reach an 80% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 5 (5 11.6 58 mm-s/m-hr). Table 99, Table 100, and Table 101 show that there is no strong equation for obtaining EC for soils with D50 greater than 0.3 mm. 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 based on the EFA, JET and HET data; however, as mentioned earlier, the user is referred to Table 90 to select the best equation according to his/her objective and considering the differences between the equations. Table 91 shows the recommended equations for the critical shear stress ( ) according to the EFA test data. For soils with D50 between 0.074 mm and 0.3 mm, 1.58 . . 50 . . Therefore, 1.58 4.5 . 16 . 0.2 . 0.46 . The POU plot shown in Table 91 shows that in order to reach an 80% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.82 (0.82 0.46 0.38 ). Table 92 shows the recommended equations for the critical shear stress ( ) according to the JET data. For soils with D50 smaller than 0.3 mm, 0.248 1.23 0.21 0.07 36.89 50 31.82. Therefore, 0.248 1.5 1.23 16 0.21 11 0.07 12 36.89 0.2 31.82 7.54 . The POU plot shown in Table 92 shows that in

336 order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.6 (0.6 7.54 4.54 ). Performing the HET on SP-SM samples is typically not feasible; therefore, Table 93 equation cannot be used for this site. Table 94 shows the recommended equations for the critical velocity ( ) according to the EFA test data. For soils with D50 greater than 0.074 mm, 3 10 . . . 50 . . Therefore, 3 10 4 . 16 . 11 . 0.2 . 0.016 / . The POU plot shown in Table 94 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.7 (0.7 0.016 0.01 / ). This very low critical velocity implies that this siteâs resistance to erosion initiation is significantly low. Table 95 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the EFA test data. For soils with D50 greater than 0.074 mm, 3228.7 . . 50 . . Therefore, 3228.7 4.5 . 16 . 0.2 . 64.8 mm/hr-Pa. The POO plot shown in Table 95 shows that in order to reach an 80% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2.5 (2.5 64.8 162 mm/hr-Pa). Table 96 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the JET data. For soils with D50 greater than 0.074 mm, 55637006351614 . . . . Therefore, 55637006351614 4 . 16 . 11 . 130.2 mm/hr-Pa. The POO plot shown in Table 95 shows that in order to reach a 90% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 1.4 (1.4 130.2 184.8 mm/hr-Pa). Due to the low fine content of the upper soil in this example site, Table 97 equation cannot be used. Table 98 shows the recommended equations for the slope of velocity-erosion rate plot ( ) according to the EFA test data. For soils with D50 greater than 0.074 mm, 88969.4 . . . 50 . . Therefore, 88969.4 4.5 . 16 . 11 . 0.2 . 404.6 mm-s/m-hr. The POO plot shown in Table 98 shows that in order to reach an 80% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 5 (5 404.6 2023 mm-s/m-hr). Table 99 shows the recommended equations for the erosion category ( ) according to the EFA test data. For soils with D50 between 0.074 mm and 0.3 mm, 1.12 . . . 50 . . Therefore, 1.12 4.5 . 11 . 12 . 0.2 . 1.42. The POU plot shown in Table 99 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , 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 ( ) according to the JET data. For soils with D50 smaller than 0.3 mm, 0.022 0.0031 5.5 50 3.34. Therefore, 0.022 25 0.0031 12 5.5 0.2 3.34 1.73. The POU plot shown in Table 100 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.85 (0.85 1.73 1.47). Table 101 equation is based on the HET data, and since performing the HET is not feasible on SP-SM, using this equation is not recommended.

337 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 based on 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/her objective. Table 91 shows the recommended equations for the critical shear stress ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 158.06 . . . . 50 . . Soil activity (A) is obtained as PI/PC. Therefore, 158.06 20 0.47 . 30 . 29 . 60 . 0.037 . 0.74 . The POU plot shown in Table 91 shows that there is 90% chance that the predicted is smaller than the actual . Table 92 shows the recommended equations for the critical shear stress ( ) according to the JET data. For soils with D50 smaller than 0.3 mm, 0.248 1.23 0.21 0.07 36.89 50 31.82. Therefore, 0.248 15 1.23 20 0.21 30 0.07 29 36.89 0.037 31.82 10.47 . The POU plot shown in Table 92 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.6 (0.6 10.47 6.28 ). Table 93 shows the recommended equations for the critical shear stress ( ) according to the HET data. For soils with D50 smaller than 0.3 mm, 25.07 . . 50 . . Therefore, 25.07 7 . 29 . 0.037 . 51.9 . The POU plot shown in Table 93 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.6 (0.6 51.9 31.1 ). Table 94 shows the recommended equations for the critical velocity ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 2.518 10 . . . 50 . . Therefore, 2.518 10 15 . 30 . 29 . 0.037 . 0.41 / . The POU plot shown in Table 94 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.8 (0.8 0.41 0.33 / ). Table 95 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 1.429078 10 . . . 50 . . Therefore, 1.429078 10 0.47 . 20 . 60 . 0.037 . 0.78 mm/hr-Pa. The POO plot shown in Table 95 shows that in order to reach an 87% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2 (2 0.78 1.56 mm/hr-Pa). Table 96 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the JET data. For soils with D50 smaller than 0.074 mm, 396599.6 . . . . Therefore, 396599.6 7 . 30 . 29 . 1088 mm/hr-Pa. The POO plot shown in Table 96 shows that in order to reach an 88% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2 (2 1088 2176 mm/hr-Pa).

338 Table 97 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the HET data. For soils with D50 smaller than 0.074 mm, 9 10 . . . . . . Therefore, 9 10 30 . 23 . 20 . 15 . 29 . 1.13 mm/hr-Pa. The POO plot shown in Table 97 shows that in order to reach an 90% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 1.45 (1.45 1.13 1.64 mm/hr-Pa). Table 98 shows the recommended equations for the slope of velocity-erosion rate plot ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 1.682339 10 50 . . . . . . Therefore, 1.682339 10 0.037 . 20 . 30 . 60 . 0.47 . 4.3 mm-s/m-hr. The POO plot shown in Table 98 shows that in order to reach an 80% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2 (2 4.3 8.6 mm- s/m-hr). Table 99 shows the recommended equations for the erosion category ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 0.1933 . . . 50 . . Therefore, 0.1933 0.47 . 30 . 29 . 0.037 . 2.3. The POU plot shown in Table 99 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , 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 ( ) according to the JET data. For soils with D50 smaller than 0.3 mm, 0.022 0.0031 5.5 50 3.34. Therefore, 0.022 23 0.0031 29 5.5 0.037 3.34 2.72. The POU plot shown in Table 100 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , 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 ( ) according to the HET data. For soils with D50 smaller than 0.074 mm, 1.67 . . . . Therefore, 1.67 7 . 20 . 29 . 3.1. The POU plot shown in Table 101 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.95 (0.95 3.1 2.95). 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 developed based on 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/her objective. Table 91 shows the recommended equations for the critical shear stress ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 158.06 . . . . 50 . . Soil activity (A) is obtained as PI/PC. Therefore, 158.06 18 0.62 . 23 . 75 . 100 . 0.001 . 53.7 . The POU

339 plot given in Table 91 shows that there is 90% chance that the predicted is smaller than the actual . Table 92 shows the recommended equations for the critical shear stress ( ) according to the JET data. For soils with D50 smaller than 0.3 mm, 0.248 1.23 0.21 0.07 36.89 50 31.82. Therefore, 0.248 42 1.23 18 0.21 23 0.07 75 36.89 0.001 31.82 9.3 . The POU plot shown in Table 92 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.6 (0.6 9.3 5.6 ). Table 93 shows the recommended equations for the critical shear stress ( ) according to the HET data. For soils with D50 smaller than 0.3 mm, 25.07 . . 50 . . Therefore, 25.07 26 . 75 . 0.001 . 20.5 . The POU plot shown in Table 93 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.6 (0.6 20.5 12.3 ). Table 94 shows the recommended equations for the critical velocity ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 2.518 10 . . . 50 . . Therefore, 2.518 10 42 . 23 . 75 . 0.001 . 0.75 / . The POU plot shown in Table 94 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.8 (0.8 0.75 0.6 / ). Table 95 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 1.429078 10 . . . 50 . . Therefore, 1.429078 10 0.62 . 18 . 100 . 0.001 . 7 10 mm/hr-Pa. The POO plot shown in Table 95 shows that in order to reach an 87% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2 (2 7 10 14 10 mm/hr-Pa). This very low implies the fact that once the erosion is inititated, 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 ( ) according to the JET data. For soils with D50 smaller than 0.074 mm, 396599.6 . . . . Therefore, 396599.6 26 . 23 . 75 . 0.1 mm/hr-Pa. The POO plot shown in Table 96 shows that in order to reach an 88% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2 (2 0.1 0.2 mm/hr-Pa). Table 97 shows the recommended equations for the slope of shear stress-erosion rate plot ( ) according to the HET data. For soils with D50 smaller than 0.074 mm, 9 10 . . . . . . Therefore, 9 10 51 . 25 . 18 . 42 . 75 . 0.39 mm/hr-Pa. The POO plot shown in Table 97 shows that in order to reach an 90% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 1.45 (1.45 0.39 0.57 mm/hr-Pa). Table 98 shows the recommended equations for the slope of velocity-erosion rate plot ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 1.682339 10 50 . . . . . . Therefore,

340 1.682339 10 0.001 . 18 . 23 . 100 . 0.62 . 1.6 10 mm- s/m-hr. The POO plot shown in Table 98 shows that in order to reach an 80% confidence that the predicted is greater than the actual , the predicted value should be multiplied by 2 (2 1.6 10 3.2 10 mm-s/m-hr). This low is consistent with the very low for this site. Table 99 shows the recommended equations for the erosion category ( ) according to the EFA test data. For soils with D50 smaller than 0.074 mm, 0.1933 . . . 50 . . Therefore, 0.1933 0.62 . 23 . 75 . 0.001 . 3.3. The POU plot shown in Table 99 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , 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 ( ) according to the JET data. For soils with D50 smaller than 0.3 mm, 0.022 0.0031 5.5 50 3.34. Therefore, 0.022 25 0.0031 75 5.5 0.001 3.34 3.0. The POU plot shown in Table 100 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , 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 ( ) according to the HET data. For soils with D50 smaller than 0.074 mm, 1.67 . . . . Therefore, 1.67 26 . 18 . 75 . 3.34. The POU plot shown in Table 101 shows that in order to reach a 90% confidence that the predicted is smaller than the actual , the predicted value should be multiplied by 0.95 (0.95 3.34 3.17). 9.11. 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), alongside with the proposed equations in Chapter 8, may be the best measures to understand the effect of each geotechnical property on each soil erodibility parameter. Appendix 3 of the Appendices Report presents all correlation matrices for the 12 groups shown in Figure 148. As discussed in Section 7.3.2, the correlation matrices also show the Pearsonâs Correlation Coefficient (PCC) for each plot. PCC was used to reflect the linear dependency between two variables, with +1 showing a strong positive relationship, -1 indicating a solid negative relationship, and 0 referring to no relationship at all. In general, the geotechnical properties that, by increasing, lead to an increase of the critical shear stress ( ), the critical velocity ( ), and the erosion category ( ), and to a decrease in the shear stress slope ( ) and the velocity slope ( ) are considered as parameters that have a positive impact on the erosion resistance. On the other hand, those geotechnical properties that, by increasing, lead to a decrease of , , , and and to an increase in and are considered as parameters that have a negative impact on the soil erosion resistance. The following observations were made regarding the effect of each soil property on the erodibility of soils: ï· An increase in the mean particle size (D50) leads to an increase in the erosion resistance for soils with D50 larger than 0.3 mm. On the other hand, regardless of the erosion test type, an

341 increase in D50 leads to a decrease of the erosion resistance of soils with D50 smaller than 0.3 mm. ï· 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 the soil erosion resistance. ï· In both fine and coarse-grained soils, an increase in percent clay leads to an increase in the erosion resistance of the soil. ï· 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 smaller than 0.3 mm); however, there are a few exceptions to this statement. ï· 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 dataset than in the JET and the HET datasets. ï· In many cases, the wet unit weight ( ) and the undrained shear strength (Su) (for soils with D50 smaller than 0.3 mm) showed to be directly proportional to the erosion resistance. ï· The 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 the water content alone is poorly correlated with the erosion resistance. Overall, the geotechnical properties were found to have a mixed and complex relationship with the erosion resistance in general. Nevertheless, the aforementioned observations as well as the proposed equations can be used as a first step to estimate 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.