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12 CHAPTER 1 1. INTRODUCTION 1.1. Erosion Definition The phenomenon of erosion is the result of interaction between three main components including the erodible material, the eroding fluid (in most cases water), and the geometry of the obstacle impacting the flow. In this process the fluid generates the âloadâ, the erodible material provides the resistance while the obstacle induces the disturbance. Briaud (2008) divided the erodible materials into three categories: ï· Soil: those earth elements which can be classified by the Unified Soil Classification System (USCS). ï· 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. ï· Intermediate geomaterials: any earth material intermediate between rock and soils. Erodibility can be defined as the behavior of the eroding material when subjected to the flow of the eroding fluid. The eroding water is quantified by its velocity, and the obstacle geometry is characterized by its dimensions. Figure 1 shows the forces acting on a soil particle at the interface surface between the water and the soil. a) No-flow condition b) With the water flow Figure 1. Free body diagram of a soil particle or rock block in two different stages a) no-flow condition, b) with the water flow (Briaud, 2008) Given to its application in the nature, erosion phenomenon can be divided into two different groups: 1) Internal erosion which is important for seepage through embankment dams, levees, canal sides embankments 2) Surface erosion which is important for bridge scour, overtopping of levees, dams, highway embankments, meander migration.
13 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). Due to the process in which the eroded particles are carried from an embankment dam or its foundation, internal erosion is subdivided into two different types: piping and suffusion. The first type is piping. This phenomenon is mainly the result of a backward erosion due to the high exit gradient at the downstream part of embankments or the boundaries between the coarse downstream of a rockfill dam and its core. Basically, this high exit gradient detaches the particles and initiates the internal erosion. This erosion process leads to the formation of a continuous tunnel in the embankment which is known as a pipe. It is also worth mentioning that other factors such as hydraulic fracturing or poor compaction of the soil might cause some potential crack 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, which happens when the effective stress of the soil at the toe is decreased due to high seepage gradient. The other type of internal erosion is suffusion. This internal instability mostly happens in those soils whose grain size distribution 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 existing in the matrix of coarser particles by the eroding flow. CFGB (1997) reports several dam failures in France which were caused mainly by suffusion. Von Thun (1996) describes seepage and piping failures as the No. 1 dam safety problem in the western USA. Indeed, a study on the relative risk of failure of dams in the USA revealed that 60% of all failures of embankment dams higher than 15.2m (50 feet) in the western USA were due to piping. Surface Erosion Surface erosion occurs on the surface of the soil such as in river beds and during overtopping flow of levee and embankments, wave action, plunge pools, etc. Similar to the erosion shown in Figure 1, the 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 particle/ rock block. In other words, as the velocity of the eroding fluid increases in the space surrounding the soil particles, given to the rule of conservation of energy and Bernoulliâs principle, the normal pressure induced by the eroding fluid decreases to maintain the flow. 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 fluctuations create cyclic loading of the soil particle which makes erosion easier to occur (Croad, 1981; Hofland et al., 2005). The combination of the drag shear force, the uplift normal force, and their fluctuations act together to remove the soil particle/rock block and initiate the surface erosion process.
14 The above outlined process is mainly observed in granular soils and/or fractured cohesive soils. In intact unfractured clayey soils, the individual clay particles can form micro-aggregates (from single to dozens of micrometers) and macro-aggregates (from dozens to thousands of micrometers) (Osipov et al., 1989). The erosion behavior of clayey soils depends on the presence of these micro- and macro- aggregates in the matrix, on the ability of the particles to coagulate, on the size and shape of the particles, and on the clay ability to resist disaggregation when submerged 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 percent of all bridges in the United States (approximately 500,000 bridges) are located over water which highlights the significance of studying surface erosion. Studies have shown that in 60 percent of the cases where bridge collapse has happened, the failure was due to the scour at and beneath the bridge supports (Briaud et al., 1999). Scour of bearing material is a serious and costly problem and leads to severe disasters such as the one reported in 159 counties of Georgia in 1994 (CDC, 1994). 1.2. Soil Erodibility and Constitutive Models This project deals with the first category of erodible materials defined by Briaud (2008): soils. It is well understood that knowledge of erodibility of soil is the key step to probe and control 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 developing several testing methods both in the field and laboratories, no unified method for estimating the erodibility characteristics of soils has been achieved so far. One of the complexities in trying to unify erodibility measurement methods is that some researchers have tested man-made soils to impose specific condition, or have reproduced the 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, chemical and organic content, etc. These differences can sometimes lead to different erodibility characteristics. 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 to estimate the erodibility characteristics of each soil is to first identify the major parameters involved in the erosion process. The erodibility of the material can be defined as the relationship between the erosion rate of material and the velocity (v) of eroding fluid at the interface between material and water. (1) Where, is the erosion rate (depth/time), and v is the velocity of eroding fluid (length/time). Eq. 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 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 water-soil interface.
15 (2) Where, is the erosion rate (depth/time), and 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 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: / / (3) Where, Î± and m are unit-less coefficients depending on the properties of the soil. Also, a normalized version of Eq. 2 has been proposed (Figure 2). / â² / (4) Where, Î±â and mâ are unit less coefficients depending on the properties of the soil. The erosion function described by Eq. 4 represents the constitutive law of the soil for erosion problems much like a stress strain curve would represent the constitutive law of the soil for a settlement problem. While a shear stress based definition is an improved definition over a velocity based definition, it is still not completely satisfactory as the shear stress is not the only stress which contributes to the erosion rate. Indeed, the fluctuations in normal stress and shear stress due to turbulence intensity apply pulsations which can suck the soil particle or cluster of soil particles out of position and then entrain it in the flow through the drag force. A more complete description of the erosion function is proposed in Eq. 5 (Shafii et al., 2016): (5) Where is the erosion rate (mm/hr), the mean depth water velocity (m/s), ï´ the hydraulic shear stress (N/m2), ï´c the threshold or critical shear stress (N/m2) below which no erosion occurs, ï² the mass density of water (kg/m3), Îï´ the turbulent fluctuation of the hydraulic shear stress (N/m2), and Îï³ the turbulent fluctuation of the 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 Eq. 5 on a site specific and routine basis. Today, Eq. 3 and 4 are broadly accepted and will form the basis of this project (Shafii et al., 2016). After investigating and measuring the hydrodynamic forces on gravel particles using a video analysis technique, Shafii et al. (2018) have recently introduced a more practical erosion model (Eq. 6). . (6) Where, is the erosion rate (mm/hr), (Pa) and (Pa) are the critical shear stress and critical normal stress associated with 0.1 mm/hr erosion rate, and and are the unit-less erosion model parameters. Eq. 6 is expected to capture the influence of both shear and normal stresses during erosion.
16 Figure 2. Examples of erosion function (Briaud, 2013) One example application of erosion functions is to model the scour hole development in bridges. Li et al. (2002) at Texas A&M University developed a method to calculate the maximum scour depth around bridge piers. In this method, the eroding flow generates a shear stress on the soil-water interface which initiates the scour. The shear stress generated at the bottom of the scour hole decreases as the scour depth increases. This process 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 that are presented in Section 1.2 (Eq. 2 to Eq. 6) can all be used to help quantify the erosion behavior of soils; however, none of these equations has been able to capture the erodibility with 100% accuracy. Therefore, the model parameters defined in these equations (i.e. â² and â² in Eq. 4; and in Eq. 6) cannot be determined definitively. One of the important goals of this study is to organize and analyze many different erosion test results in a way that these data become comparable. The following erodibility parameters have been used because they are widely accepted among hydraulic and geotechnical engineers and have a simple and easily understood definition. 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 depth of a soil surface under a specific hydraulic shear stress induced by the eroding fluid flow (i.e. Erosion Function Apparatus, Jet Erosion Test, etc.). 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. 3) Rate of change in the eroded soil mass which is sometimes presented as the rate of mass removal per unit area (i.e. Hole Erosion Test).
17 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 to determine the slope of erosion function. In this study, the slope of the erosion rate versus velocity curve will be designated as Ev, and the slope of erosion rate versus shear stress will be designated as . In Chapter 5, the procedure for determining Ev and is detailed for each test result. Critical Velocity/ Shear Stress These values of the critical velocity/ shear stress refer to the initiation of the erosion process. Basically, the critical velocity ( ) 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 ( ). Depending on the type of erosion test, researchers have used different definitions and different techniques to identify the critical velocities and critical shear stress. In this study, the critical velocity and critical shear stress will be determined using the same procedure independent of the type of erosion test. This procedure will be discussed in Chapter 5. Erosion Category Briaud (2008) and Hanson and Simon (2001) have 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 versus v and the versus Ï plots. These charts were based on many years of erosion testing at Texas A&M University. 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. Figure 3. Erosion category for soils and rocks based on velocity and shear stress proposed by Briaud (2008)
18 Table 1. Threshold velocities and shear stress associated with each erosion category Category No. 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 Non-erosive materials 10 500 1.4. Research Approach and Project Tasks The goal of this project is to develop reliable and simple equations which link the erodibility of soils to commonly determined soil properties. The use of the results are to provide valuable input in erosion studies such as bridge scour, river meander migration, roadway embankment overtopping and others. The equations will optimize the balance between reliability and simplicity. The reliability must take into account the accuracy required for highway projects while the simplicity must consider the economic aspects of highway projects. During this project, the seven following tasks were accomplished: Identification of current knowledge on erosion and soil properties Erodibility definition was the first step. The soil erodibility is not a single number but a relationship 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 the regression equations. Among those soil properties are the mean grain size, the plasticity index, the water content, the percent passing sieve #200, the unit weight, the undrained shear strength, etc. In the identification of the current erosion testing practices, the objective was to learn about all of the available erosion testing devices, and next to place a focus on the most commonly used erosion tests both in the laboratory and in the field. This knowledge is documented in the Chapter 2 of this report. Identification of current soil erodibility data correlations In the identification of current erodibility data correlations, available data on soil erodibility parameters (namely critical velocity, critical shear stress, initial slope of the erosion rate vs. velocity or shear stress curve) and common soil properties were collected. The existing erodibility
19 correlations are documented in the Chapter 3 of this report. Additionally, a global spreadsheet is developed as part of this study, and presented in the Chapter 5 of this report. 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 are also assessed with respect to issues such as ârange of soil types that can be testedâ, âcost of the testâ, âcost of the deviceâ, âbest applicationsâ, etc. These comparisons help the engineer select the best tests to be chosen 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; they do not lead to the same type of results. To solve this problem, numerical simulations are used. These simulations lead to a common data reduction process of erosion tests, a common output of all erosion tests, bring uniformity in erosion studies, and keep all soil erosion testing options open for the engineer. Information on the numerical simulations is documented in the Chapter 6 of this report. Perform erosion tests with different devices using the same soils This task was dedicated to testing the same soil with different erosion testing devices. The soils to be tested were man-made soils because it is the only way to be sure that identical and reproducible samples can be prepared and tested. These soils included as a minimum: a gravel, a compacted sand, a compacted silt, and a compacted high plasticity clay. All soil properties tests, all pocket erodometer tests, and all EFA tests, JET tests, and HET tests were performed at the Erosion Laboratory at Texas A&M University. For the in situ tests, the borehole erosion test and the pocket erodometer test were conducted at the RELLIS Sand and Clay sites at Texas A&M University. These results are documented in the Chapter 4 of this report. Perform erosion tests using many different soils to develop the erodibility equations This task was dedicated to testing the different soil samples with different erosion testing devices at Texas A&M University. The data obtained from the erosion tests performed during this project, alongside with the collected data from all over the world, are used to develop the regressions equations. Chapter 4 of this report as well as the Appendixes 1 and 2 document the results of the erosion and geotechnical tests performed in this study. Development of regression equations and validation This task was dedicated to develop the regressions equations correlating the erodibility parameters and the geotechnical properties of soils. Two major statistical methods were used: 1) A frequentistsâ approach with the plots of âprobability of over-predictingâ and âprobability of under-predictingâ for the selected models. As part of this approach, first and second order statistical analyses were conducted. This was followed by the regression and optimization
20 techniques (i.e. cross-validation). 2) A probabilistic approach using the Bayesian inference. The main benefit of the use of the Bayesian inference is the definition of a metric of confidence on the model predictions. The results of these statistical approaches are extensively documented in the Chapter 7 of this report, as well as in the Appendices 3 to 5. Verification, synthesis and analysis of all data to propose best solution Once all the testing was conducted and the statistical/correlation analysis was 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, are updated. These results are documented in the Chapter 8 of this report.