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1 SUMMARY 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 tasks are 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: Perform erosion tests with different devices using the same prepared soils Task 5: Perform erosion tests using many different soils to develop the erodibility equations Task 6: Development of regression equations and validation Task 7: Verification, synthesis and analysis of all data to propose best solution The summary of the findings for each chapter is discussed below. Chapter 1 - Introduction: This chapter is divided into two halves. The first half presents a definition for erosion, and introduces different types of erosion. The general parameters to quantify soil erodibility and the constitutive models for erosion are briefly discussed. The second half of this chapter presents the research approach. The project tasks are described one by one, and a summary of how and where within the report each one of the tasks are addressed is provided.
2 Chapter 2 - Existing Erosion Tests: This chapter presents a comprehensive literature review on different soil erosion tests. The tests developed all over the world in the last few decades are 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 are explained, and a summary table about the tests used in statistical analyses in this report is 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 are presented in Table 90, which is also repeated below. Table 90 (REPEATED). Comparison of the EFA, the JET, and the HET 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. 1) Agriculture erosion 2) Levees
3 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. 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 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 cohesion-less soils or soft cohesive soils. 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. 1) Internal erosion of earth dams 2) Suffusion 3) Levee breach 4) Soil improvement Chapter 3 â Existing Correlations between Soil Erodibility and Soil Properties: This chapter 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 last century are summarized. The influence factors on erosion including the less-easily- obtained engineering properties are presented and discussed in detail. A summary of these influencing parameters is presented in Table 10, which is also repeated below.
4 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 Chapter 4 â Erosion Experiments: This chapter starts 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 are presented. The test plan matrix proposed for this project is presented and discussed. Next, the results of the hundreds of erosion tests performed during this project are presented and discussed. Finally, the geotechnical engineering properties associated with each tested sample are 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. Chapter 5 â Organization and Interpretation of the Data: This chapter is 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 is explained, and the contact people and organization who helped gather the information are 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 are discussed in detail. Finally, an inquiry operation manual explains how to search for specific data within TAMU-Erosion.
5 Chapter 6 â Comparison of Selected Soil Erosion Tests by Numerical Simulations: This chapter presents the comparison of some selected soil erosion tests (i.e. EFA, HET, JET, and BET) with the use of numerical simulations software. This chapter is divided into two sections: 1) numerical simulations on non-erodible soils, 2) numerical simulations including the erosion process. The first part of the chapter deals 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 is assigned to the water soil interface, and the erosion is 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 show that the erosion function obtained from the EFA test for each sample can be reasonably used to produce a similar âscour versus timeâ plot to what the results of the JET, the HET, and the BET experiments would produce. 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). Chapter 7 â Correlation Equation Development: This chapter is dedicated to the main goal of this study which is the development of correlation equations. This chapter is divided into four major parts. The first part presents 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 at a 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).
6 Figure 145 (REPEATED). Erosion Category Charts with the USCS Symbols The second part of Chapter 7 deals 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, the following relationships exist between the critical velocity/shear stress and 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 presents the âFrequentistsâ Regressionâ technique. The step-by- step procedure for implementing the frequentistsâ regression technique, the experimental design, and the model selection process are discussed, and the results of the regressions are 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 (POO) and âUnder-Predictingâ (POU) are also presented for the selected equations. Table 102 to Table 106 show the selected equations for each erodibility parameter and for each dataset. 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
7 Table 102 (REPEATED). Selected models for critical shear stress 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 (REPEATED). Selected models for critical velocity 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 Table 104 (REPEATED). 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 (REPEATED). Selected models for velocity slope 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
8 Table 106 (REPEATED). Selected models for shear stress slope 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 deals with a probabilistic approach as opposed to the deterministic approach presented in the previous section. The probabilistic approach is based on the âBayesian inferenceâ method. The methodology of the Bayesian inference method and its results are presented in Section 7.4 as well as in the Appendix 5 of the appendices report. Chapter 8 â Most Robust Correlation Equations: This chapter focuses on the recommended correlation equations (Table 102 to Table 106) based on the work presented in Chapter 7, and provides 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 sort of tables are proposed for different erodibility parameters and different erosion tests.
9 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. Chapter 9 â Conclusions and Recommendations: This chapter presents the general conclusions as a result of the work done in this project, and discusses how to approach the erosion-related design problems in four different steps: Step 1- Probe TAMU-Erosion: Chapter 5 of this report discussed the development of 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 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 TAMU-Erosion
10 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. The proposed erosion category-USCS category chart can be used as another preliminary tool to estimate the erodibility of any sample, using only the USCS category. In this chart, 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). 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 erosion category of a soil can lead to 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 in order to choose the best equation. The advantages and disadvantages of each erosion test should be studied carefully before using the proposed equations in Section 8.2. Plots of âprobability of under/over-predictingâ (POU/POO) 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 perform 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.
11 Also, the following findings on the relationships between the geotechnical properties and the erodibility parameters are reported: 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 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.