Relationship Between Erodibility and Properties of Soils (2019)

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11 1.1 Definition of Erosion The phenomenon of erosion is the result of interaction between three main components: the erodible material, the eroding fluid (in most cases water), and the geometry of the obstacle affect- ing the flow. In this process, the fluid generates the “load,” the erodible material provides the resistance, and the obstacle induces the disturbance. Briaud (2008) divided erodible materials into three categories: • Soil: those earth elements that can be classified by the Unified Soil Classification System (USCS); • Rock: those earth elements that have an unconfined compressive strength of the intact rock core of more than 500 kPa with joint spacing of at least 0.1 m; • Intermediate geomaterials: any earth material between rock and soil. Erodibility can be defined as the behavior of the eroding material when subjected to the flow of the eroding fluid. Eroding water is quantified by its velocity, and the geometry of the obstacle is characterized by its dimensions. Figure 1 shows the forces acting on a soil particle at the surface of the interface between the water and the soil. Given their application in nature, erosion phenomena can be divided into two groups: 1. Internal erosion, which is important for seepage through embankment dams, levees, and canal side embankments, and 2. Surface erosion, which is important for bridge scour, overtopping of levees, dams, highway embankments, and meander migration. 1.1.1 Internal Erosion The type of erosion in which the soil particles are transported within the body of an earth structure, such as an embankment dam from the upstream source to the downstream by the eroding fluid is known as “internal erosion” (Wan and Fell 2002). On the basis of the process in which the eroded particles are carried from an embankment dam or its foundation, internal erosion is subdivided into two types: piping and suffusion. 1.1.1.1 Piping Piping is mainly the result of backward erosion due to the high exit gradient at the down- stream part of an embankment or the boundary between a coarse-grained downstream zone of a rockfill dam and its core. Basically, the high exit gradient detaches the particles and initi- ates the internal erosion. This erosion process leads to the formation of a continuous tunnel C H A P T E R 1 Introduction

12 Relationship Between Erodibility and Properties of Soils in the embankment, which is known as a “pipe.” Other factors, such as hydraulic fracturing or poor compaction of the soil, also potentially might cause some cracking through the core of the dam, which can result in piping. Similar to the definition made by Terzaghi and Peck (1948), the phenomenon of heave in dams can be named as a special case of piping that happens when the effective stress of the soil at the toe is decreased due to a high seepage gradient. 1.1.1.2 Suffusion The internal instability of fusion mostly happens in soils in which the distribution of grain size does not meet the requirements of self-filtering conditions, such as poorly graded soils (Wan and Fell 2002). Suffusion is the result of replacement and erosion of very fine soils that exist in a matrix of coarser particles by the eroding flow. The Comité Français des Grande Barrages (1997) reports several dam failures in France that were caused mainly by suffusion. Von Thun (1996) describes seepage and piping failures as the primary dam safety problem in the western United States. Indeed, a study on the relative risk of failure of dams in the United States revealed that 60% of all failures of embankment dams higher than 15.2 m (50 ft) in the western United States were caused by piping. 1.1.2 Surface Erosion Surface erosion occurs on the surface of the soil, such as in river beds and during overtopping flow of levees and embankments, wave action, and plunge pools. Similar to the erosion shown in Figure 1, surface erosion happens in three main stages: 1. A drag force and the resulting shear stress are developed on the surface at the interface between the soil particles/rock block and the eroding fluid. 2. The eroding fluid causes a decrease in the normal stress induced on the surface of the soil particles/rock block; that is, as the velocity of the eroding fluid increases in the space surrounding the soil particles, given to the rule of conservation of energy and Bernoulli’s principle, the normal pressure induced by the eroding fluid decreases to maintain the flow. (a) (b) Figure 1. Free body diagram of a soil particle or rock block in two different stages: (a) no-flow condition and (b) with water flow (Briaud 2008).

Introduction 13 3. Due to the turbulence in the water, the normal stress and the induced shear stress on the hydraulic interface between the eroding fluid and soil fluctuate. At high velocities, these fluc- tuations create cyclic loading of the soil particle, which allows erosion to occur more easily (Croad 1981; Hofland et al. 2005). The combination of the drag shear force, the uplift normal force, and their fluctuations acts together to remove the soil particle/rock block and initiate the surface erosion process. The process outlined above is mainly observed in granular soils and fractured cohesive soils. In intact unfractured clayey soils, the individual clay particles can form microaggregates (from a single to dozens of micrometers) and macroaggregates (from dozens to thousands of micro- meters) (Osipov et al. 1989). The erosion behavior of clayey soils depends on the presence of these micro and macroaggregates in the matrix, on the ability of the particles to coagulate, on the size and shape of the particles, and on the clay’s ability to resist disaggregation when sub- merged in water. The nature and the magnitude of the structural or cohesion forces also play a very important role in understanding the erodibility of clayey soils. The strength of the structural forces can vary significantly and depends on their nature and on the soil properties. Surface erosion is the key element in bridge scour. Scour around bridge supports is the most common cause of bridge failure (Arneson et al. 2012). More than 80% of all bridges in the United States (approximately 500,000 bridges) are located over water that highlights the signifi- cance of studying surface erosion. Studies have shown that in 60% of the cases where bridge col- lapse has happened, the failure was due to the scour at and beneath the bridge supports (Briaud et al. 1999). 1.2 Soil Erodibility and Constitutive Models This project dealt with the first category of erodible materials defined by Briaud (2008): soils. It is well understood that knowledge of the erodibility of soil is the key step in probing and controlling the serious safety hazards caused by erosion, such as bridge scour, embankment and floodwall overtopping erosion, dam spillway erosion, and stream stability. Despite the large number of contributions to soil erosion and despite the development of several testing methods, both in the field and in laboratories, no unified method for estimating the erodibility characteristics of soils has been achieved so far. One of the complexities in trying to unify methods of measuring erodibility is that some researchers have tested man-made soils to impose specific conditions or have reproduced field conditions in the lab, while others have tested samples collected from the field. Intact samples from the field and reproduced/remolded samples in the laboratory are often different in some aspects, such as stress history and chemical and organic content. These differences can sometimes lead to different erodibility characteris- tics. It is critical to learn about as many engineering properties of the tested soils as possible to achieve all different factors that influence the erosion resistance of soils. The only way to come up with a common reliable model for estimating the erodibility char- acteristics of each soil is to first identify the major parameters involved in the erosion process. The erodibility of a material can be defined as the relationship between the erosion rate of the material (z . ) and the velocity (v) of eroding fluid at the interface between the material and water.  (1)z f v( )= where z . is the erosion rate (depth/time) and v is the velocity of eroding fluid (length/time). Equation 1, however, is not satisfactory enough, because the velocity varies in direction and intensity in the flow field (Briaud 2008). Indeed, the water velocity profile reaches a value of zero

14 Relationship Between Erodibility and Properties of Soils at the interface between the water and the soil. A more fundamental definition is the relationship between the erosion rate and the shear stress at the soil–water interface. z f ( )= t (2) where z . is the erosion rate (depth/time), and t is the hydraulic shear stress at the interface (force/length square). However, the velocity is often used because it is easier to get a feel for velocity than for shear stress. In an effort to normalize Equation 1, the erodibility of a soil can be defined as the relationship between the erosion rate z . and the mean depth velocity v of the water in excess of the critical velocity vc (Figure 2). The following equation is proposed by Shafii et al. (2016) as an example of a relationship between soil erodibility and mean depth velocity: z v v v vc c c m  ( )( )= α − (3) where α and m are unitless coefficients depending on the properties of the soil. Also, a normal- ized version of Equation 2 has been proposed: z vc c c m  ( )( )= ′α t − t t ′ (4) where α′ and m′ are unitless coefficients depending on the properties of the soil. The erosion function described by Equation 4 represents the constitutive law of the soil for erosion problems, much as a stress–strain curve would represent the constitutive law of the soil for a settlement problem. While a definition based on shear stress is an improvement over one based on veloc- ity, it is still not completely satisfactory, as the shear stress is not the only stress that contributes to the erosion rate. Indeed, the fluctuations in normal stress and shear stress due to turbulence intensity apply pulsations that can suck the soil particle or cluster of soil particles out of posi- tion and then entrain it in the flow through the drag force. A more complete description of the erosion function is proposed in Equation 5 (Shafii et al. 2016): z v v v v c m n p = α t − t r     + β Dt r     + γ Ds r     (5) 2 2 2 where z . = erosion rate (mm/h), v = mean depth water velocity (m/s), t = hydraulic shear stress (N/m2), E ro si on R at e (m m /h r) Velocity (m/s) E ro si on R at e (m m /h r) Shear Stress (N/m2) Figure 2. Examples of erosion function (Briaud 2013).

Introduction 15 tc = threshold or critical shear stress (N/m2) below which no erosion occurs, r = mass density of water (kg/m3), Dt = turbulent fluctuation of hydraulic shear stress (N/m2), and Ds = turbulent fluctuation of net uplift normal stress (N/m2). All other quantities are parameters characterizing the soil being eroded. While this model is quite thorough, it is rather impractical at this time to determine all the parameters needed in Equation 5 on a site-specific and routine basis. At present, Equations 3 and 4 are broadly accepted and form the basis of this project (Shafii et al. 2016). After using a video analysis tech- nique to investigate and measure the hydrodynamic forces on gravel particles, Shafii et al. (2019) have recently introduced a more practical erosion model: z c c  = t t     × s s     α β 0.1 (6) where z . = erosion rate (mm/h), tc = critical shear stress (Pa) associated with an erosion rate of 0.1 mm/h, sc = critical normal stress (Pa) associated with an erosion rate of 0.1 mm/h, and α and β = unitless erosion model parameters. Equation 6 is expected to capture the influence of both shear and normal stresses during erosion. One example application of erosion functions is to model the development of scour holes in bridges. Li et al. (2002) at Texas A&M University (TAMU) developed a method for calculating the maximum scour depth around bridge piers. In this method, the eroding flow generates a shear stress on the soil–water interface that initiates the scour. The shear stress generated at the bottom of the scour hole decreases as the scour depth increases. This pro- cess continues until there is an equilibrium depth in which the erosion resistance of the soil (critical shear stress) at the soil–water interface equals the shear stress imposed by the eroding flow. This idea has recently been endorsed by the Federal Highway Administration (FHWA). 1.3 Erodibility Parameters The erosion functions presented in Section 1.2 (Equation 2 to Equation 6) can all be used to help quantify the erosion behavior of soils; however, none of these equations has been able to capture erodibility with 100% accuracy. Therefore, the model parameters defined in these equa- tions (i.e., α′ and m′ in Equation 4; α and β in Equation 6) cannot be determined definitively. One of the important goals of this study was to organize and analyze many different erosion test results in a way such that these data would become comparable. The following erodibility parameters have been used because they are widely accepted among hydraulic and geotechnical engineers and have simple and easily understood definitions. 1.3.1 Erosion Rate The erosion rate of a soil can be identified in many different ways, depending on the erosion testing method. This rate can be generally expressed in three main forms: 1. Rate of change in the depth of a soil surface under a specific hydraulic shear stress induced by the eroding fluid flow (e.g., erosion function apparatus, jet erosion test, etc.);

16 Relationship Between Erodibility and Properties of Soils 2. Rate of change in the soil volume during a specific time period while the soil is subjected to a hydraulic shear stress induced by the eroding fluid flow; and 3. Rate of change in the eroded soil mass, which is sometimes presented as the rate of mass removal per unit area (e.g., hole erosion test). 1.3.2 Slope of Erosion Function Another important erodibility parameter is the normalized erosion rate against the flow velocity or the hydraulic shear stress. As shown in Figure 2, the result of an erosion test can be presented in two different forms: erosion rate versus velocity and erosion rate versus hydraulic shear stress. There are different methods for determining the slope of erosion function. In this report, the slope of the erosion rate versus velocity curve is designated as Ev and the slope of erosion rate versus shear stress is designated as Et. In Chapter 5, the procedure for determining Ev and Et is detailed for each test result. 1.3.3 Critical Velocity/Shear Stress Critical velocity/shear stress refers to the initiation of the erosion process. Basically, the criti- cal velocity (vc) in an erosion test refers to the maximum velocity that the soil can resist without getting eroded. In terms of the hydraulic shear stress, this value is known as “critical shear stress” (tc). Depending on the type of erosion test, researchers have used different definitions and dif- ferent techniques to identify the critical velocity and critical shear stress. In this study, critical velocity and critical shear stress were determined by using the same procedure independent of the type of erosion test. This procedure is discussed in Chapter 5. 1.3.4 Erosion Category Briaud (2008) and Hanson and Simon (2001) developed category charts to make it easier to identify the erodibility of soils. Figure 3 shows the erosion categories developed by Briaud (2008) in his 2007 Ralph B. Peck Lecture. In that chart, the erosion categories are bound by lines in the z . versus v and the z . versus t plots. These charts were based on many years of erosion testing at TAMU. The lines giving the boundaries between categories originate at the critical velocity and critical shear stress. Table 1 shows the critical values for the velocity and the shear stress for each erosion category in Figure 3. (a) (b) 100,000 10,000 1,000 100 10 1 0.1 EROSION RATE (mm/hr) 100101.00.1 VELOCITY (m/s) 100,000 10,000 1,000 100 10 1 0.1 100,00010,0001,0001001010 EROSION RATE (mm/hr) SHEAR STRESS (Pa) Figure 3. Erosion categories for soils and rocks on basis of (a) velocity and (b) shear stress, as proposed by Briaud (2008).

Introduction 17 1.4 Research Approach and Project Tasks The goal of this project was to develop reliable and simple equations that link the erodibil- ity of soils to commonly determined soil properties. The use of the results is to provide valu- able input in erosion studies on topics such as bridge scour, river meander migration, roadway embankment overtopping, and others. The equations optimize the balance between reliability and simplicity. Reliability must take into account the accuracy required for highway projects, while simplicity must consider the economic aspects of such projects. During this study, the following seven tasks were accomplished: 1. Identification of current knowledge on erosion and soil properties; 2. Identification of current soil erodibility data correlations; 3. Assessment of current and promising erosion tests; 4. Performance of erosion tests with different devices on the same soils; 5. Performance of erosion tests on many different soils to develop erodibility equations; 6. Development of regression equations and validation; and 7. Verification, synthesis, and analysis of all data to propose the best solution. 1.4.1 Identification of Current Knowledge on Erosion and Soil Properties Defining erodibility was the first step. Soil erodibility is not a single number, but a relation- ship between the hydraulic load (water velocity or shear stress) and the soil resistance (erosion rate). The relationship equations proposed in this study link the elements of the erosion function (critical velocity, critical shear stress, and initial slope of the erosion rate versus velocity or shear stress curve) to various soil properties. In the identification of current geotechnical laboratory tests, this study focused on the most typically obtained soil properties in regression equations. Among those soil properties are mean grain size, plasticity index, water content, percentage passing the #200 sieve, unit weight, and undrained shear strength. In the identification of current practices for testing erosion, the objec- tive was to learn about all of the available erosion testing devices and then to focus on the most commonly used erosion tests, both in the laboratory and in the field. This knowledge is docu- mented in Chapter 2 of this report. Category Number Erosion Category Description (m/s) (Pa) I Very high erodibility geomaterials 0.1 0.1 II High erodibility geomaterials 0.2 0.2 III Medium erodibility geomaterials 0.5 1.3 IV Low erodibility geomaterials 1.35 9.3 V Very low erodibility geomaterials 3.5 62.0 VI Nonerosive materials 10.0 500.0 Source: Briaud 2008. Table 1. Threshold velocity and shear stress associated with each erosion category.

18 Relationship Between Erodibility and Properties of Soils 1.4.2 Identification of Current Soil Erodibility Data Correlations In the identification of current erodibility data correlations, available data on the following subjects were collected: soil erodibility parameters (i.e., critical velocity, critical shear stress, ini- tial slope of the erosion rate versus velocity or shear stress curve), and common soil properties. The existing erodibility correlations are documented in Chapter 3 of this report. Additionally, a global spreadsheet developed as part of this study is presented in Chapter 5. 1.4.3 Assessment of Current and Promising Erosion Tests The most commonly available laboratory and in situ erosion tests are reviewed in Chapter 2. Each test has advantages and limitations. These tests were also assessed with respect to issues such as the range of soil types that can be tested, the cost of the test, the cost of the device, and the best applications. These comparisons help the engineer select the best tests for a given situation. The assessment is documented at the end of Chapter 2. The critical issue associated with these different devices and tests is that they do not give the same erosion parameters; that is, they do not lead to the same type of results. To solve this problem, numerical simulations were used. These simulations led to a common data reduction process of erosion tests and a common output of all erosion tests, brought uniformity to ero- sion studies, and kept all soil erosion testing options open for the engineer. Information on the numerical simulations is documented in Chapter 6 of this report. 1.4.4 Performance of Erosion Tests with Different Devices on the Same Soils This task was dedicated to testing the same soil with different erosion testing devices. The soils tested were man-made soils because the use of such soils was the only way to be sure that identical and reproducible samples could be prepared and tested. These soils included, at a mini- mum, a gravel, a compacted sand, a compacted silt, and a compacted high-plasticity clay. All soil properties tests, all pocket erodometer tests, and all erosion function apparatus, jet erosion, and hole erosion tests were performed at the Erosion Laboratory at TAMU. For the in situ tests, the borehole erosion test and the pocket erodometer test were conducted at the RELLIS sand and clay sites at TAMU. These results are documented in Chapter 4 of this report. 1.4.5 Performance of Erosion Tests on Many Different Soils to Develop Erodibility Equations This task was dedicated to testing the different soil samples with different erosion testing devices at TAMU. The data obtained from the erosion tests performed during this project, along with data collected from all over the world, were used to develop the regressions equations. Chapter 4 of this report as well as Appendices 1 and 2 document the results of the erosion and geotechnical tests performed in this study. [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).] 1.4.6 Development of Regression Equations and Validation This task was dedicated to developing regression equations correlating the erodibility param- eters and the geotechnical properties of soils. Two major statistical methods were used: 1. A frequentist approach with plots of probability of overpredicting and probability of under- predicting for the selected models. As part of this approach, first- and second-order statistical

Introduction 19 analyses were conducted. This analysis was followed by regression and optimization tech- niques (i.e., cross validation). 2. A probabilistic approach using Bayesian inference. The main benefit of the use of Bayesian inference is the definition of a metric of confidence on the model predictions. The results of these statistical approaches are extensively documented in Chapter 7 of this report and in Appendices 3 to 5. 1.4.7 Verification, Synthesis, and Analysis of All Data to Propose the Best Solution Once all the testing and the statistical/correlation analysis were conducted, all aspects of the project were synthesized and analyzed to present a complete solution package to address the main objective of this research. Also, the classification charts presented in Figure 3, which link the likely soil erosion function to the soil classification as a first step in any soil erosion problem, were updated. These results are documented in Chapter 8 of this report.