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'''Abstract:''' The suffusion susceptibility of the soil samples is evaluated through an erosion resistance index. Thanks to existing statistical analyses, the erosion resistance index is estimated from several soil parameters. In actual exploitation, the soil properties with the input parameters related to the grain distribution of the soil… vary greatly from the original design value due to the influence of many factors. One of the factors is the inherent variability. Inherent soil variability is modeled as a random field. The usual problems used to assess the suffusion susceptibility may be not give accurate results or fully evaluate the actual working ability of the ground in each case. This is one of the reasons why dams are still eroded when they are put into use. The paper aims assess the suffusion susceptibility of the earth dam body using two-dimensional (2D) Stochastics random field, modelling the initial problem, considering the variability spatial of soil properties, using the assumption of a Normal random field of soil characteristics parameters. An illustration of a numerical simulation of homogeneous earth dam body is presented in this paper. The paper shows the predicted results of the two-dimensional spatial variability of erosion resistance index and probability of suffusion susceptibility of the homogeneous earth dam body.
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'''Keywords:''' Internal erosion, suffusion susceptibility, numerical simulation, random field, forecasting
  
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''' ASSESS OF STABILITY FOR RELIABILITY THEORY'''<big>''' '''</big>'''IN CONSIDERATION OF CHANGE OF SHEAR RESISTANCE BY DEPTH'''
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1. Introduction
  
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 Internal erosion is one of the main causes of instabilities within hydraulic earth structures such as dams, dikes, or levees in [1]. According to reference [2], there are four types of internal erosion: concentrated leak erosion, backward erosion, contact erosion and suffusion. Concentrated leak erosion may occur through a crack or hydraulic fracture. Backward erosion mobilizes all the grains in regressive way (i.e., from the downstream part of earth structure to the upstream part) and includes backward erosion piping and global backward erosion. Contact erosion occurs where a coarse soil is in contact with a fine soil. The phenomenon of suffusion corresponds to the process of detachment and then transport of the finest particles within the porous network under seepage flow. The finer fraction eroded and leaving the coarse matrix of the soil will further modify the hydraulic conductivity and mechanical parameters of the soil. This suffusion process may result in an increase of hydraulic conductivity, seepage velocities and hydraulic gradients, possibly accelerating the rate of suffusion in [3]. The development of suffusion may cause the incidents of dam including piping and sinkholes.
  
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Tran Vu DOAN 1, Trung Viet TRAN 1, Van Thao LE 1.*, Thuy Kim Phương DOAN1
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In the literature, some researchers assume that suffusion is best represented by its initiation. Reference [4] take into account the main initiation conditions for suffusion include three components: material susceptibility, critical hydraulic load and critical stress condition. Several methods have been proposed to characterize the initiation of suffusion confronting material susceptibility criteria and hydraulic criteria in [5].
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1 University of Science and Technology –The University of Danang
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54 Nguyen Luong Bang Street, Lien Chieu District, Danang city
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In the literature, the suffusion susceptibility characterization was mainly researched through grain size based on criteria for the initiation of process. Several criteria based on the study of grain size distribution have been proposed in literature in [6–7]. Reference [8] concluded that the most widely used methods based on particle size distribution are conservative. In the case, the geometrical conditions allow particle movements, the hydraulic conditions must be studied in [9]. The hydraulic loading on the grains is often described by three distinct parameters characterizing the hydraulic loading: the hydraulic gradient in [10], the hydraulic shear stress in [11] and the pore velocity in [12]. The critical values of these three quantities can then be used to characterize the suffusion initiation in [10, 13, 12]. However, suffusion tests carried out with permeameters of different sizes indicate that scale effects exist when measuring critical hydraulic criteria in [14].
  
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Reference [14] showed the critical hydraulic gradient concept depends on the length of the seepage path. Moreover, the value of critical hydraulic gradient is affected significantly by the hydraulic loading history in [15]. Therefore, the suffusion susceptibility of dam scales cannot be evaluated by these approaches. Besides, Reference [16] focused on the estimation of whole suffusion process. Reference [17] proposed a new analysis based on the energy expended by the seepage flow which is a function of both the flow rate and the pressure gradient. Reference [18] performed many the suffusion tests to “final state”. This ‘final state’ is obtained towards the end of each test when the hydraulic conductivity is constant while the rate of erosion decreases. The expended energy E<sub>flow</sub> is the time integration of the instantaneous power dissipated by the water seepage for the test duration. For the same duration the cumulative eroded dry mass is determined, the erosion resistance index is expressed by:                                                         
  
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Depending on the values of Iα index, Reference [19] proposed six categories of suffusion susceptibility from highly erodible to highly resistant (corresponding susceptibility categories: highly erodible for Iα < 2; erodible for 2 ≤ Iα < 3; moderately erodible for 3 ≤ Iα < 4; moderately resistant for 4 ≤ Iα < 5; resistant for 5 ≤ Iα < 6; and highly resistant for Iα ≥ 6). Since the erosion resistance index Iα has been proven to be intrinsic, i.e., independent of the sample size in [20] and of the loading path in [15], at least at the laboratory scale, it may be applied to the structure scale of a dam. Reference [21] gave a method to assess the suffusion susceptibility of low permeability core soil in compacted dams based on construction data. They showed the one-dimensional (1D) spatial variability of all material parameters, in particular the hydraulic conductivity, the dry unit weight and the grain size distribution which affect the erosion resistance index. However, the suffusion susceptibility of earth dam body through the erosion resistance index needs to be assess the two-dimensional spatial variability. A two-dimensional contour map of the erosion resistance index would provide additional valuable information.
  
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==Corresponding Author: ==
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Reference [22] showed the disparate sources of uncertainties. One of the primary sources of geotechnical uncertainties is inherent soil variability. When we repeat the experiment many times at the same location, or at different locations, we always don't get the same result. To suppress or eliminate the influence of this source, we often use a very large number of samples. However, in practice, this implementation is not feasible because the experimental conditions do not allow, or the cost is too great. So, in the current calculation, there is always this random source. The objectives of the paper are to assess the suffusion susceptibility of earth dam considering variability spatial of soil properties. To tackle this objective, the contour map of 2D spatial variability of erosion resistance index of earth dam body is presented. This approach is based on two-dimensional Stochastics random field.
  
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==Dr. Van Thao LE==
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2. Description
  
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The University of Danang-Danang University of Science and technology
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                            ''2.1 Assessment of soil suffusion susceptibility''
  
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54 Nguyen Luong Bang Street, Danang city, Vietnam
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Reference [18] performed many suffusion tests on 32 different soils to measure the value of erosion resistance index. For each test, the erosion resistance index Iα was measured at the ‘final state’ in [15]. From the study of several grain size-based criteria, a statistical analysis was developed to predict the erosion resistance index Iα. Reference [23] described the key influence of the grain size distribution on the suffusion process and they distinguished three main gradation curves: linear distribution, discontinuous distribution and upwardly concave distribution. The concave distribution consists of a poorly graded coarse fraction associated to a highly graded fine fraction. The soils that are likely to suffer from suffusion are, according to reference [24] “internally unstable”, i.e., their grain-size distribution curve is either discontinuous or upwardly concave. Based on this information, several criteria have been proposed in literature, and recently reference [25] proposed three categories of soil erodibility from the comparison of criteria of Istonima, Kézdi and Kenney and Lau. They defined P as the mass fraction of particles finer than 0.063mm. For gap-graded soil, Chang and Zhang defined the gap ratio as: Gr = d<sub>max</sub>/d<sub>min</sub> (d<sub>max</sub> and d<sub>min</sub>: maximal and minimal particle sizes characterizing the gap in the grading curve). For P less than 10%, the authors assumed that the stability is correctly assessed using the criterion G<sub>r</sub> < 3. For P higher than 35%, the gap graded soil is reputed stable, and with P in the range 10% to 35% the soil is stable if G<sub>r</sub> < 0.3P. According to Chang and Zhang, their method is only applicable to low plasticity soils.
  
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Email: [mailto:lvthao@dut.udn.vn lvthao@dut.udn.vn]
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By using a triaxial erodimeter, reference [14] determined the suffusion susceptibility of three mixtures of kaolin and aggregates. The results indicate that suffusion process depends on the grain angularity of coarse fraction. With a same grain size distribution, angularity of coarse fraction grains contributes to increase the suffusion resistance. Thus, the parameter of shape of grains plays an important role on suffusion susceptibility.
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==Abstract==
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The physicochemical characteristics of the fluid and solid phases are also crucial, particularly in the case of cohesive soils. For the same type of clay, several tests performed in clayey sands have shown that suffusion decreases with the increase of the clay content in [26].
  
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Slope stability problem is one of the most common problems in construction design. The application of tools often follows a pattern, using only fixed input parameters and resulting in a factor of safety according to the parameters themselves. This calculation model is only correct during the time when the shear resistance parameter (c, &#x03c6;) of the ground does not change and is no accurate after the structure put into use, leading to slope instability, causing landslides and damage to the slope after a period of exploitation and use. The experimental studies have shown that the shear resistance parameter (c, &#x03c6;) of the soil ground changes randomly with depth. As a result, current mechanical computational models are no accurate. This paper proposes a new model to analyze stability based on reliability theory with the change of shear resistance parameters by depth. Firstly, by using Karhunen – Loeve series, the result of slope stability coefficient of proposed model is smaller than these when not considering the change of shear resistance (c, &#x03c6;) by depth. Then, by using Monte - Carlo simulations (n=1000) combined Karhunen – Loeve series, the forecast results are different from those only considering the static problem and the problem of random quantities, the probability of failure increase significantly.
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In addition, with material susceptibility, reference [4] consider two others main initiation conditions for suffusion: the stress condition and the hydraulic load. For the same material susceptibility, the modification of the effective stress can induce grain rearrangements. Several tests performed in oedometric conditions on unstable soils showed that a rise in the effective stress causes an increase of the soils’ resistance to suffusion in [14]. In the same manner, when tests were carried out under isotropic confinement in [26], the increase in the confinement pressure, and then the increase of soil density allowed a decrease in the suffusion rate.
  
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'''Key words: '''reliability,''' '''slope stability, shear resistance, simulation,
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Reference [18] showed the correlation equation between physical parameters and erosion resistance index Iα for all soils
  
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==Introduction==
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Iα = –13.57+0.43g<sub>d</sub> + 0.18j – 0.02Finer KL +0.49V<sub>BS</sub> + 189.70k<sub>i</sub>+3.82 min(H/F)                             
  
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The problem of slope stability is one of the most common problems in construction design. The years of the twentieth century have researchers and methods proposed by Bishop (1955) [1] , Janbu (1954) [2]. From limit equilibrium theory to complex methods with high accuracy of Morgenstern - Price (1965) [3], Spencer (1973) [4], Janbu (1973) [5], the application of the above methods through the commercial software such as: Slope/W, Plaxis-2D or Plaxis-3D…However the input is static parameters. According to the method of dividing soil columns, the sliding mass above each hypothetical sliding surface divided into vertical soil columns, then analyze the force and moment balance conditions for the force system acting on the earth column to find the slope stability coefficient (FoS). Stability coefficient defined as the ratio of the total shear resistance moment to the total shearing moment acting on the sliding surface. After that, the researchers improved, supplemented, and proposed new calculation methods suitable to the real situation such as Janbu method (1954), Bishop method (1955), Spencer method (1973). The Janbu method does not completely satisfy the force and moment balance equations. Characteristic for the line of action method, in cases it is difficult to converge. At the same time, Janbu gave the coefficient ƒo without any specific basis, so it does not use in practice. The Bishop method is a popular method today, however, this method does not fully consider the vertical forces on both sides of the soil mass, and at the same time it is necessary to find out which sliding arc (sliding center) is the most dangerous, having the lowest factor of safety to evaluate the instability of the slope, so further research is needed. The Spencer method is a method that fully considers the force components of a soil element, strictly satisfies the static equilibrium, fully considers the force and moment balance equations, and may be use for circular sliding surfaces and not round. However, Spencer only calculates the moment equilibrium equation at the bottom of the soil column, thereby not simulating the sliding center and dangerous sliding arc of the slope. This method is quite complicated when the unknowns and the number of equations is large. Zhang and Zhou (2018) [6] use Monte - Carlo (MC) simulation, the LEM limit balance method finds the FoS factor of safety and the failure probability P<sub>f</sub>, then compares their method with the classical methods of Bishop and Janbu. The obtained FoS factor of the UD-LASSO method is lower than that of Bishop and Janbu. The simple Bishop and Janbu methods of slope stability analysis have widely used since their presentation in the 1950s. Although Bishop's method does not satisfy the lateral force balance and the method of Janbu does not satisfy moment equilibrium, but FoS factor can easily calculated for most slope types. However, FoS values can differ by up to ±15% from results calculated by methods that satisfy force and moment balance such as Spencer's method or the Morgenstern-Price method. Although a direct comparison between different methods is not always possible, the FoS value determined using Bishop's simplified method for the expected circular sliding surface may differ slightly 5% more than the Spencer or Morgenstem - Price methods. The simple Janbu method used for non-circular surfaces, often giving FoS values up to 30% lower for the more rigorous methods. In contrast, the simplified Janbu method can give up to 5% higher FoS values for slopes and uncommon sliding surface shapes (Fredlund and Krahn, 1977) [7]. Currently, in the world, the researchers more fully evaluate the factors when calculating slope stability, considering the random change of shear resistance (c, &#x03b3;, &#x03c6;) of the soil as well as determining the probability of failure, however, very few studies have considered the random variation in depth. Therefore, the article proposes to simulate and evaluate the behavior of random factors in depth. These models usually adopt fixed input parameters for one or more separate locations, then through calculation methods to make general conclusions about the ability to ensure the overall stability of the slope.
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+0.18P +0.28G<sub>r</sub> +19.51d<sub>5</sub> +1.06d<sub>15</sub> - 0.84d<sub>20</sub>+0.81d<sub>50</sub> -0.98 d<sub>60</sub> -0.10d<sub>90</sub>                            (1)
  
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Soil is a natural material and is sensitive to its surroundings, so its physical properties change from one location to another. This variation can be as part of a heterogeneous soil state. The random change of the shear resistance parameters of the soil is one of the most important problems in the analysis of geotechnical works. The field experiments with different soils have shown that the shear strength of the soil can view as a random quantity and simulated by the Normal distribution function (Lumb, 1966 [8]; Tan et al., 1993 [9]). This random variation characterized by the coefficient of variation (COV).
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  Where: dry unit weight g<sub>d</sub>, blue methylene value V<sub>BS</sub>, internal friction angle j, initial hydraulic conductivity k<sub>i</sub>, minimum value of ratio H/F, percentage of finer fraction (based on Kenney and Lau’s criteria) Finer KL, gap ratio G<sub>r</sub>, d<sub>5</sub>, d<sub>15</sub>, d<sub>20</sub>, d<sub>50</sub>, d<sub>60</sub>, d<sub>90</sub> (diameters of the 5%, 15%, 20%, 50%, 60%, 90% mass passing, respectively) and P (percentage of finer than 0.063mm)
  
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{| class="formulaSCP" style="width: 100%; text-align: center;"
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For widely graded soils, the correlation of physical parameters with the erosion resistance index: (N=10, R<sup>2</sup> =0.99)
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{| style="text-align: center; margin:auto;"
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| <math display="inline">COV=\frac{\sigma }{\mu }</math>
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| style="width: 5px;text-align: right;white-space: nowrap;" | (1)
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      Iα = -26.34+0.43g<sub>d</sub> + 0.66 j – 0.16Finer KL + 1.15V<sub>BS</sub> +0.37P +6.82d<sub>5</sub> -1.26d<sub>60</sub>
  
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As in slope stability calculations, resistance parameters, soil bearing capacity are the most important indicators in geotechnical design. The calculation methods are based on the input parameters of the soil. Therefore, it is important to identify certainly these parameters.
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                                                                                                                         (2) 
  
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Through the research results on the change index of the soil's physical parameters in the calculation of geotechnical works, it is necessary to consider the physical properties of the soil as a random variable and accurately reflect the working condition of the soil. Phoon and Kulhawy (1999) [10] confirmed that the use of the Normal distribution model to simulate the random changes of mechanical properties is consistent with the experimental results.
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For gap-graded soils, the correlation of physical parameters with the erosion resistance index: (N=21, R<sup>2</sup>=0.90)
  
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==Building a model to calculate the stability coefficient ==
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Iα = -37.62+0.67 g<sub>d</sub> + 0.64 j + 0.09Finer KL - 0.03V<sub>BS</sub> -1.43P + 0.63G<sub>r</sub> + 0.76d<sub>5</sub> -0.97d<sub>60</sub> +0.61d<sub>90</sub>                                                           (3)                                                                                                                             
  
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Within the scope of the paper, the Bishop method to determine the slope stability coefficient is used and the problem considers the following parameters: weight density γ; unit cohesion c; internal friction angle φ; soil element width b; soil element self-weight W; inclined angle of the soil element to the horizontal θ; frictional force T; elemental force U; reaction N to give the factor of safety FoS without considering the shear force S between the soil elements, passive and active soil pressures E1, E2, and the presence of water in the slope.
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The distinction between widely graded or gap-graded is based on the gap-ratio in [24] and in [18]). Gap-graded soils are defined by G<sub>r</sub> > 1. If this distinction is not obvious, the smallest value of Iα should be taken from the two values calculated by equations (2) and (3) to ensure a conservative estimation. The equation (2) may be viewed as a resilient tool that can be adapted to the available parameters of a given construction site.
  
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Consider the slope ABCD as shown in Figure 1, with a dangerous sliding arc EF. To determine the FoS coefficient by the Bishop method, the sliding arc region will be divided into n different pieces and the stability coefficient FoS is determined. The Bishop method does not take into account the variation of shear resistance with depth. However, when considering the change with depth of the soil shear resistance parameter in the same i<sup>th</sup> piece, according to the depth, the soil shear resistance parameter (c, &#x03c6;) is different (Fig 1). This change is simulated by Karhunen-Loeve series and simulated by Matlab software. At this time, the stability coefficient FoS will be redefined as follow :
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  ''2.2 Assessment of the relative suffusion potential''
  
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Considering the i<sup>th</sup> element fragment is divided into m subdivisions according to the depth (∆y), then the weight of the soil block i (Wi) is calculated :
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The erosion resistance index (Iα) is just a material parameter that characterizes the susceptibility of a given soil to suffusion. Hence, it cannot be interpreted as a ‘security factor’ to distinguish between ‘probable occurrence of erosion’ and ‘no erosion’ in [21], This distinction requires additionally the estimation of the hydraulic loading. The erosion resistance index is estimated from several soil parameters using 2D Stochastics random field. Therefore, the relative suffusion potential of the earth dam body may be characterized by the 2D contour map of the erosion resistance index Iα. A contour map shows the suffusion susceptibility at locations in the homogeneous earth dam body through the erosion resistance index value Iα. Cross-section of the earth dam will be pointed out with the spatial variability of Iα, may be low of high resistance to suffusion. Two other maps show the 2D spatial variability of density, internal friction angle.            
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{| class="formulaSCP" style="width: 100%; text-align: center;"
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| <math>{W}_{i}=\sum _{j=1}^{m}{\Delta x\times \Delta y\times \gamma }_{ij}</math>
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3. Numerical simulation
  
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Where: <big>&#x0394;xﾸﾧõ;&#x00a0;&#x0394;y </big>- width and thickness of element ij,
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                            ''3.1 A numerical example of homogeneous earth dam body''
  
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''&#x03b3;<sub>ij</sub> ''- density of the ij<sup>th</sup> soil element corresponding to the depth Yj
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This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.
  
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At the position of the sliding surface of the i<sup>th</sup> soil element, we will have the values of the cohesion force Ci and the internal friction angle &#x03c6; which are different according to the depth Yi of the i<sup>th </sup>fragment sliding arc. At this time, the shear resistance of the i<sup>th</sup> soil element is determined as follow :
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The earth dam has the structure homogeneous with assumed parameters: the height of dam crest: +21.1 m, the width of dam crest is 6.0 m. The dam slope in upstream: m = 3.5 ¸ 3.0 and in downstream: m = 2.5 ¸ 3.0. The data of dam include full grain size distributions with widely graded soil, dry unit weight, internal friction angle, initial hydraulic conductivity, and other parameters with the following assumed average values: dry unit weight  g<sub>d</sub> =17 kN/m<sup>3</sup>; internal friction angle j=27<sup>0</sup>; percentage of fines (%) (based on Kenny &Lau, 1985 criterion) Finer KL=20%; the percentage finer than 0.063 mm P=24%; d<sub>5</sub> =0.1mm; d<sub>60</sub> =1mm. The suffusion susceptibility will be estimated through erosion resistance index.
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{| class="formulaSCP" style="width: 100%; text-align: center;"
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| <math>{T}_{i}={C}_{i}\times \Delta x\times Sec{\theta }_{i}+{W}_{i}\times Cos{\theta }_{i}\times tan{\varphi }_{i}</math>
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''3.2 Simulation methodology''
  
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The stability factor FoS is determined in this case :
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              In this paper, the soil characteristic parameters are modeled as a random field. These parameters are inputted in the model using the two-dimensional (2D) Stochastics random field which is researched in [27]. In a random finite element method, the spatial variability g, j, Finer KL, P, d<sub>5</sub>, d<sub>60</sub> are simulated by a random field with assumed coefficient of variance (cov) cov = 0.05 and mapped onto the finite element mesh. This estimation is based on equation (2) since all soil samples are widely graded. Among the seven parameters of equation (2), the blue methylene value (V<sub>BS</sub>) was considered constantly V<sub>BS</sub>=0.5g/100g in the dam. The forecasting result of spatial variability of erosion resistance index with the contour map 2D is showed.
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{| class="formulaSCP" style="width: 100%; text-align: center;"
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| <math>FoS=\frac{\sum _{i=1}^{n}\left[ {C}_{i}\times \Delta x\times Sec{\theta }_{i}+{W}_{i}\times Cos{\theta }_{i}\times tan{\varphi }_{i}\right] }{\sum _{i=1}^{n}{W}_{i}\times Sin{\theta }_{i}}</math>
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  ''3.3 Numerical results''
  
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{| style="width: 100%;border-collapse: collapse;"
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3.3.1 Forecasting the erosion resistance index and the probability of suffusion susceptibility
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|  style="vertical-align: top;width: 100%;"|[[Image:Draft_Thao_708187998-image2.png|450px]]
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The result of erosion resistance index with contour map 2D is showed in figure 2. Several locations in the map pointed out with a low resistance to suffusion (blue color). Some zones with yellow color represent the high resistance to suffusion. The predicted values of Iα lies within the range from 2 to more than 9. The result of map shows the spatial variability of erosion resistance index. These results may be explained by soil spatial variability. According to reference [21], they show the one-dimensional spatial variability of erosion resistance index which erosion resistance index is estimated equally for one layer in the dam core. These results may be not given accurate results at different locations. Based on two- dimensional random field model, the two- dimensional spatial variability of erosion resistance index is predicted in the whole dam.
  
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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.4.  Conclusions
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Fig 1.Schematic of determining the stability coefficient FoS by Bishop's method considering the depth variation of the soil's physical properties</div>
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==Results and conclusions==
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The result of paper assesses the suffusion susceptibility of the dam body using two-dimensional random field considering soil spatial variability. With illustration of a numerical simulation, the predicted result of spatial variability of erosion resistance index is showed in a contour map 2D. Furthermore, the probability of suffusion susceptibility is also forecasted correspond to classification of suffusion susceptibility. This result demonstrates that the actual state of practice would be to account for the two-dimensional spatial variability.
  
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==Analyze stability coefficient using Kahunen -Loeve serives==
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1.       Foster, M., Fell, R., and Spanagle, M. 2000. The statistics of embankment dam failures and accidents. Canadien Geotechnical Journal, 37: 1000-1024
  
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A numerical example of slope is considered in Fig 2. The avaraged values of weight of density, cohension, internal friction angle are hypothesized in Table 1. The value of CoV and width b is also selected in Table 1.
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2.       Fell, R., and Fry, J. J. 2013. Erosion in geomechanics applied to dams and levees. Bonelli S. Editor. ISTE-Wiley. pp.1-99
  
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{| style="width: 100%;border-collapse: collapse;"
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3.       Icold. (2013). Internal erosion of existing dams, levees and dykes, and their foundations.Bulletin. Internal Erosion Processes and Engineering Assessment (Vol. 1, pp. 164).
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|  style="text-align: center;vertical-align: top;"|''' [[Image:Draft_Thao_708187998-image3.png|528px]] '''
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4.       Garner, S.J., and Fannin, R.J. 2010. Understanding internal erosion: a decade of research following a sinkhole event. The International J. on Hydropower and Dams 17: 93-98.
  
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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5.       Marot, D., & Benamar, A. (2012). Suffusion, transport and filtration of fine particles in granular soil. Erosion of Geomaterials, 39–79.
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Fig 2.Analysis slope diagram</div>
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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6.       Kenney, T. C., and Lau, D. (1985). Internal stability of granular filters. Canadien Geotechnical Journal, 22: 215-225.
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Table 1.'' ''Soil's physical properties</div>
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{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
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7.       Li, M., & Fannin, R. J. (2008). Comparison of two criteria for internal stability of granular soil. Canadian Geotechnical Journal, 45(9), 1303–1309.
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Physical properties
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''Average'''
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''CoV'''
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|'''b (m)'''
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Weight Density (KN/m<sup>3</sup>)
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|19.5
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|0.1
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|1
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Cohension (KN/cm<sup>2</sup>)
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|18.4
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|0.1
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|1
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Internal friction angle (<sup>o</sup>)
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|18.4
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|0.1
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|1
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|}
+
  
 +
8.       Wan, C. F., & Fell, R. (2008). Assessing the potential of internal instability and suffusion in embankment dams and their foundations. Journal of Geotechnical and Geoenvironmental Engineering, 134(3), 401–407.
  
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Simulation results of the change with depth of cohesion C by Kahunen -Loeve serives are showed in Fig 3. The changed value of cohesion from 13 to 22 kN/m<sup>3</sup><sub>. </sub>The blue area show cohesion is smaller than the average value.
+
9.       Kovács, G. (2011). Seepage hydraulics (Vol. 10). Amsterdam: Elsevier Scientific Publishing Co.
  
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{| style="width: 100%;border-collapse: collapse;"
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10.     Skempton, A. W., and Brogan, J. M. 1994. Experiments on piping in sandy gravels. Géotechnique, 44(3): 440-460.
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|-
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|  style="vertical-align: top;width: 100%;"|[[Image:Draft_Thao_708187998-image4-c.png|600px]]
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|}
+
  
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11.     Reddi, L. N., Lee, I., and Bonala, M. S. 2000. Comparision of internal and surface erosion using flow pump test on a sandkaolinite mixture. Geotechnical Testing Journal, 23(1): 116-122.
  
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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12.     Perzlmaier, S. 2007. Hydraulic criteria for internal erosion in cohesionless soil. In Internal erosion of dams and their Foundations. Editors R. Fell and J.J. Fry. Taylor & Francis: 179-190.
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Fig 3.Simulation results of the change with depth of cohesion C by Karhunen – Loeve series</div>
+
  
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<div id="_Hlk112512369" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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13.     Moffat, R., and Fannin, J. 2006. A large permeameter for study of internal stability in cohesionless soils. Geotechnical Testing Journal, 29(4): 273-279.
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''
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[[Image:Draft_Thao_708187998-picture-Group 1.svg|center|98px]]
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''</div>
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{| style="width: 100%;border-collapse: collapse;"
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14.     Marot, D., Bendahmane, F., and Nguyen, H. H. 2012. Influence of angularity of coarse fraction grains on internal process. La Houille Blance, International Water Journal, 6(2012): 47-53.
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|  style="text-align: center;vertical-align: top;"|<span id='_Hlk112512311'></span>
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[[Image:Draft_Thao_708187998-image5-c.png|600px]]
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15.     Rochim, A., Marot, D., Sibille, L., & Le, V. T. (2017). Effects of hydraulic loading history on suffusion susceptibility of cohesionless soils. Journal of Geotechnical and Geoenvironmental Engineering, 143(7), 04017025.
  
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(4a)
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16.     Marot, D., Bendahmane, F., and Konrad, J. M. (2011a). Multichannel optical sensor to quantify particle stability under seepage flow. Canadian Geotechnical Journal, 48: 1772-1787.
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|-
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|  style="text-align: center;vertical-align: top;width: 100%;"|
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[[Image:Draft_Thao_708187998-picture-Text Box 2.svg|center|97px]]
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[[Image:Draft_Thao_708187998-image6-c.png|600px]]
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(4b)
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17.     Marot, D., Regazzoni, P. L., and Wahl, T. 2011b. Energy based method for providing soil surface erodibility rankings. Journal of Geotechnical and Geoenvironmental Engineering (ASCE), 48:1772-1787.
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|}
+
  
 +
18.     Le, V. T., D. Marot, A. Rochim, F. Bendahmane, and H. H. Nguyen. 2018. “Suffusion Susceptibility Investigation by EnergyBased Method and Statistical Analysis.” Canadian Geotechnical Journal 55, no. 1 (January): 57–68.
  
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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19.     Marot, D., Rochim, A., Nguyen, H. H., Bendahmane, F., & Sibille, L. (2016). Assessing the susceptibility of gap graded soils to internal erosion characterization: proposition of a new experimental methodology. Nat Hazards (first online), 1-24.
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Fig 4.Comparison of results with consideration (proposed model) and without considering the change in soil shear resistance parameter with depth (GeoStudio 2020'')''</div>
+
  
−
After using the Karhunen-Loeve series to simulate the change of parameters (&#x03b3;, c, &#x03c6;), we have the coefficient FoS is 1.48. This value is smaller than results (1.68) run using software GeoStudio 2020. These results showed in Fig 4a and Fig 4b). The results compared with the case that do not consider this change show that there is a difference in the sliding arc and the stability coefficient. This is explained because in the area of sliding arc, there are many values of density larger than the average value, while in the area of sliding arc, the load capacity is smaller than the average value (blue area in Fig 3) which make decrease in the load capacity of the slope.
+
20.     Zhong, C., V. T. Le, F. Bendahmane, D. Marot, and Z.-Y. Yin. 2018. “Investigation of Spatial Scale Effects on Suffusion Susceptibility.” Journal of Geotechnical and Geoenvironmental Engineering 144, no. 9 (September): 04018067.
  
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==Reliability analysis of slope stability considering the random change by depth of shear resistance==
+
21.     Zhang. L, R. Gelet, D. Marot, M. Smith & J-M.Konrad (2018): A method to assess the suffusion susceptibility of low permeability core soils in compacted dams based on construction data, European Journal of Environmental and Civil Engineering. ISSN: 1964-8189 (Print) 2116-7214.
  
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To analyze the reliability of the problem, using Karhunen - Loeve series to simulate the change with depth of the soil shear resistance. After using the Karhunen - Loeve series, we get the following results as Fig 5a and Fig 5b. The results of simulation times for shear resistance parameters are different. From this result, it is necessary to perform simulations for accurate analysis results, according to previous studies, the number of simulations from 1000 to 10000 will give reliable results.
+
22.    Phoon,K.K; Kulhawy, F.H. (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal, vol. 36(4): 612-624
  
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{| style="width: 100%;border-collapse: collapse;"
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23.     Lafleur, J., Mlynarek, J., and Rollin A.L. (1989). Filtration of broadly graded cohesionless soils. Journal of Geotechnical Engineering 115(12): 1747-1768.
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|-
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|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<big> [[Image:Draft_Thao_708187998-chart1.svg|288px]] </big>
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(5a)
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24.     Fell, R., and Fry, J.J. editors 2007. The state of the art of assessing the likelihood of internal erosion of embankment dams, water retaining structures and their foundations. In internal erosion of dams and their foundations. Editors R.Fell and J.J Fry Taylor & Francis, London. 1-24.
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|  style="border: 1pt solid black;vertical-align: top;"|<big> [[Image:Draft_Thao_708187998-chart2.svg|234px]]    </big>
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<big>                          (</big>5b<big>)</big>
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25.     Chang, D. S., and Zhang, L. M. 2013. Critical hydraulic gradients of internal erosion under complex stress states. Journal of Geotechnical and Geoenvironmental Engineering, 139(9), 1454-1467.
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|}
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26.     Bendahmane, F., Marot, D., and Alexis, A. 2008. Experimental parametric study of suffusion and backward erosion. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 134(1):57-67.
  
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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27.     Vanmarcke, E.H. 1977. Probability modeling of soil profiles. Journal of the Geotechnical Engineering Division, ASCE, 103(11): 1227–1246
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Fig 5. Simulation of change <big>''c, &#x03c6; ''</big>of soil with depth </div>
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After simulation, the process of determining the stability coefficient (FOS) performed. However, because the properties of the soil change randomly (with constraints), for analysis and evaluation, it is necessary to use Monte - Carlo simulation to predict all possible cases, in the article, we use 1000 times of Monte - Carlo simulation to change the quantity ξ_i (θ) in the Karhunen - Loeve simulation and the result is 1000 FoS values. The analysis process shows in Fig 6.
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[[Image:Draft_Thao_708187998-picture-Group 22.svg|center|600px]]
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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Fig 6. Schematic of the problem of random parameters</div>
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To determine the reliability, from the results of 1000 FOS values, the failure probability value P<sub>f</sub> is determined as in the following formula:
+
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+
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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<math display="inline">P_f=P\left[FOS\leq 1,4\right]=\int_{-\infty }^{1.4}\frac{1}{{\sigma }_{FOS}\times \sqrt{2\pi }}\times e^{-\frac{{\left(FOS-{\mu }_{FOS}\right)}^2}{2{\sigma }_{FOS}^2}}dx</math> </div>
+
−
 
+
−
In which: mean  <math>{\mu }_{FOS}</math> and standard deviation  <math>{\sigma }_{FOS}</math> are determined from 1000 analyzed FOS values based on the formula:
+
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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<math display="inline">{\mu }_X=\frac{1}{n}\sum_{i=1}^nx_i</math> </div>
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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<math display="inline">{\sigma }_X=\sqrt{\frac{1}{n-1}{\sum_{i=1}^n\left(x_i-{\mu }_X\right)}^2}</math> </div>
+
−
 
+
−
The steps to analyze the reliability in the above problem are as follows:
+
−
 
+
−
Step 1: Input the parameter values from geological data.
+
−
 
+
−
Step 2: Use the Karhunen - Loeve series to simulate a random field X that varies with the depth of the roadbed with the following characteristics: mean (&#x03bc;), standard deviation (&#x03c3;) and correlation characteristic (b).
+
−
 
+
−
Step 3: From the combination of variables {c, φ, γ} randomly generated in step 2, using the Bishop problem and Matlab software to calculate the factor of safety FOS<sub>min</sub>
+
−
 
+
−
Step 4: Use the Monte - Carlo simulation to repeat steps 2 and 3 with the number of simulations n=1000, the result will be a set of 1000 FOS<sub>min</sub> values.
+
−
 
+
−
Step 5: Apply the theory of reliability and failure probability to evaluate the influence of shear resistance on slope stability.
+
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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Table 2. Data needed to simulate random parameters</div>
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{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
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|-
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|  style="border: 1pt solid black;text-align: center;"|'''Parameters'''
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|  style="border: 1pt solid black;text-align: center;"|'''µ'''
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|  style="border: 1pt solid black;text-align: center;"|σ=0.1µ
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|  style="border: 1pt solid black;text-align: center;"|σ=0.2µ
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|  style="border: 1pt solid black;text-align: center;"|σ=0.3µ
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−
|  style="border: 1pt solid black;text-align: center;"|'''µ'''
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|  style="border: 1pt solid black;text-align: center;"|σ=0.1µ
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|  style="border: 1pt solid black;text-align: center;"|σ=0.2µ
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|  style="border: 1pt solid black;text-align: center;"|σ=0.3µ
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−
|-
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|  style="border: 1pt solid black;text-align: center;"|Density  γ (kN/m<sup>3</sup>)
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|  style="border: 1pt solid black;text-align: center;"|19.58
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|  style="border: 1pt solid black;text-align: center;"|1.958
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|  style="border: 1pt solid black;text-align: center;"|3.916
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|  style="border: 1pt solid black;text-align: center;"|5.874
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|  style="border: 1pt solid black;text-align: center;"|19.54
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|  style="border: 1pt solid black;text-align: center;"|1.954
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|  style="border: 1pt solid black;text-align: center;"|3.908
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|  style="border: 1pt solid black;text-align: center;"|5.862
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|-
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|  style="border: 1pt solid black;text-align: center;"|Cohesion
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{| class='formulaSCP' style='width: 100%;'
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|-
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|
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{| style='margin:auto;width: 100%; text-align:center;'
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|-
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| <math display="inline">c</math>
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|}
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| style='width: 5px;text-align: right;white-space: nowrap;' | (kPa)
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|}
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|  style="border: 1pt solid black;text-align: center;"|18.4
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|  style="border: 1pt solid black;text-align: center;"|1.84
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|  style="border: 1pt solid black;text-align: center;"|3.68
+
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|  style="border: 1pt solid black;text-align: center;"|5.52
+
−
|  style="border: 1pt solid black;text-align: center;"|18.4
+
−
|  style="border: 1pt solid black;text-align: center;"|1.84
+
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|  style="border: 1pt solid black;text-align: center;"|3.68
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|  style="border: 1pt solid black;text-align: center;"|5.52
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|-
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|  style="border: 1pt solid black;text-align: center;"|Internal friction angle  <math display="inline">\varphi </math> (độ)
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|  style="border: 1pt solid black;text-align: center;"|18.4
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|  style="border: 1pt solid black;text-align: center;"|1.84
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|  style="border: 1pt solid black;text-align: center;"|3.68
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−
|  style="border: 1pt solid black;text-align: center;"|5.52
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−
|  style="border: 1pt solid black;text-align: center;"|18.4
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|  style="border: 1pt solid black;text-align: center;"|1.84
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|  style="border: 1pt solid black;text-align: center;"|3.68
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|  style="border: 1pt solid black;text-align: center;"|5.52
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−
|}
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−
 
+
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With data in table 2, after performing the five above steps, we get the result as shown in Fig 7a and Fig 7b. From the analysis results, we find that, when not considering random change, value FoS=1.68 > 1.4, slope ensures stability, however, when considering random change of basic properties, we found up to 12.95% ability of failure of the slope. This shows that when considering the random change with the depth, the slope is unstable, and the distribution is stable when considering the random change with the depth of the shear resistance parameter (c, &#x03c6;) of the soil is need.
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(7a)
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|  style="text-align: center;vertical-align: top;width: 100%;"|[[Image:Draft_Thao_708187998-image15.png|600px]]
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(7b)
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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Fig 7. ''' '''Results of reliability analysis of slope stability: CoV = 0.2, b = 2m</div>
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+
−
==Conclusions==
+
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+
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The article has built a model to analyze the slope stability when considering the change of shear resistance with depth based on the Bishop’s equation using Karhunen – Loeve series. With a proposed numerical model, the results compared with the case that do not consider this change (results run using software GeoStudio 2020) show that there is a difference in the sliding arc and the stability coefficient. Specifically, the results show that the value of the stability coefficient of the proposed model is 1.48, which is smaller than 1.68 of the models run with GeoStudio 2020 software. By using Monte - Carlo simulations combined with Karhunen - Loeve series, when considering the random change in depth of soil shear resistance, the forecast results are different from those only when considering the static problem and random quantity problems, the probability of failure will increase significantly (12.95%). The research results open a new direction in the calculation and quality control of slope stability.
+
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+
−
==Acknowledgements==
+
−
 
+
−
The authors thank the Ministry of Education and Training of Vietnam, the University of Danang, University of Science and Technology, Vietnam, for supporting for this work.
+
−
 
+
−
==Conflict of interest==
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+
−
All authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, all authors also certify that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in the Indian Geotechnical Journal.
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+
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==References==
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1. Bishop. A.W. (1955) The Use of the Slip Circle in the Stability Analysis of Slope. Geotechnique, 10, 129-150.
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2.  Janbu. N (1954). Application of composite slip surfaces for stability analysis. Eur Conf Stabil Earth Slopes 3 pp 43–49
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3.  Morgenstern. N.  R. and Price, V.  E. (1965).  The Analysis of the Stability of General Slip Surfaces. Geotechnique, Vol. 15, No. 1 pp. 77‐93.
+
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4. Spencer. (1973). Thrust line criterion in embankment stability analysis. <br/>Géotechnique. Volume 23 Issue 1, March 1973, pp. 85-100
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5.  Janbu. N. (1973). Slope Stability Computations. Embankment Dam Engineering, Casagrande Volume, pp. 47‐86.
+
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6.  Zhang. X, Zhou. X. (2018) Analysis of the numerical stability of soil slope using virtual-bond general particle dynamics Eng. Geol., 243 (2018), pp. 101-110.
+
−
 
+
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7.  Fredlund. D.G. and Krahn, J. (1977) Comparison of Slope Stability Methods of Analysis. Canadian Geotechnical Journal, 14, 429-439.
+
−
 
+
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8.  Lumb. P (1966). The variability of natural soils. Can Geotech J3(2):74–97.
+
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+
−
9. Tan. CP, Donald. IB, Melchers. RE (1993) Probabilistic slip circleanalysis of earth and rockfill    dams. In: Proceedings of theconference on probabilistic methods in geotechnicalengineering, Canberra, Australia, pp 281–288.
+
−
 
+
−
10. Phoon. K.K; Kulhawy. F.H. (1999b). [https://www.nrcresearchpress.com/doi/abs/10.1139/t99-039 Evaluation of geotechnical property variability]. Canadian Geotechnical Journal, vol. 36(4): 625-639.
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Latest revision as of 00:27, 17 May 2023

Abstract: The suffusion susceptibility of the soil samples is evaluated through an erosion resistance index. Thanks to existing statistical analyses, the erosion resistance index is estimated from several soil parameters. In actual exploitation, the soil properties with the input parameters related to the grain distribution of the soil… vary greatly from the original design value due to the influence of many factors. One of the factors is the inherent variability. Inherent soil variability is modeled as a random field. The usual problems used to assess the suffusion susceptibility may be not give accurate results or fully evaluate the actual working ability of the ground in each case. This is one of the reasons why dams are still eroded when they are put into use. The paper aims assess the suffusion susceptibility of the earth dam body using two-dimensional (2D) Stochastics random field, modelling the initial problem, considering the variability spatial of soil properties, using the assumption of a Normal random field of soil characteristics parameters. An illustration of a numerical simulation of homogeneous earth dam body is presented in this paper. The paper shows the predicted results of the two-dimensional spatial variability of erosion resistance index and probability of suffusion susceptibility of the homogeneous earth dam body.

Keywords: Internal erosion, suffusion susceptibility, numerical simulation, random field, forecasting

1. Introduction

 Internal erosion is one of the main causes of instabilities within hydraulic earth structures such as dams, dikes, or levees in [1]. According to reference [2], there are four types of internal erosion: concentrated leak erosion, backward erosion, contact erosion and suffusion. Concentrated leak erosion may occur through a crack or hydraulic fracture. Backward erosion mobilizes all the grains in regressive way (i.e., from the downstream part of earth structure to the upstream part) and includes backward erosion piping and global backward erosion. Contact erosion occurs where a coarse soil is in contact with a fine soil. The phenomenon of suffusion corresponds to the process of detachment and then transport of the finest particles within the porous network under seepage flow. The finer fraction eroded and leaving the coarse matrix of the soil will further modify the hydraulic conductivity and mechanical parameters of the soil. This suffusion process may result in an increase of hydraulic conductivity, seepage velocities and hydraulic gradients, possibly accelerating the rate of suffusion in [3]. The development of suffusion may cause the incidents of dam including piping and sinkholes.

In the literature, some researchers assume that suffusion is best represented by its initiation. Reference [4] take into account the main initiation conditions for suffusion include three components: material susceptibility, critical hydraulic load and critical stress condition. Several methods have been proposed to characterize the initiation of suffusion confronting material susceptibility criteria and hydraulic criteria in [5].

In the literature, the suffusion susceptibility characterization was mainly researched through grain size based on criteria for the initiation of process. Several criteria based on the study of grain size distribution have been proposed in literature in [6–7]. Reference [8] concluded that the most widely used methods based on particle size distribution are conservative. In the case, the geometrical conditions allow particle movements, the hydraulic conditions must be studied in [9]. The hydraulic loading on the grains is often described by three distinct parameters characterizing the hydraulic loading: the hydraulic gradient in [10], the hydraulic shear stress in [11] and the pore velocity in [12]. The critical values of these three quantities can then be used to characterize the suffusion initiation in [10, 13, 12]. However, suffusion tests carried out with permeameters of different sizes indicate that scale effects exist when measuring critical hydraulic criteria in [14].

Reference [14] showed the critical hydraulic gradient concept depends on the length of the seepage path. Moreover, the value of critical hydraulic gradient is affected significantly by the hydraulic loading history in [15]. Therefore, the suffusion susceptibility of dam scales cannot be evaluated by these approaches. Besides, Reference [16] focused on the estimation of whole suffusion process. Reference [17] proposed a new analysis based on the energy expended by the seepage flow which is a function of both the flow rate and the pressure gradient. Reference [18] performed many the suffusion tests to “final state”. This ‘final state’ is obtained towards the end of each test when the hydraulic conductivity is constant while the rate of erosion decreases. The expended energy Eflow is the time integration of the instantaneous power dissipated by the water seepage for the test duration. For the same duration the cumulative eroded dry mass is determined, the erosion resistance index is expressed by:                                                         

Depending on the values of Iα index, Reference [19] proposed six categories of suffusion susceptibility from highly erodible to highly resistant (corresponding susceptibility categories: highly erodible for Iα < 2; erodible for 2 ≤ Iα < 3; moderately erodible for 3 ≤ Iα < 4; moderately resistant for 4 ≤ Iα < 5; resistant for 5 ≤ Iα < 6; and highly resistant for Iα ≥ 6). Since the erosion resistance index Iα has been proven to be intrinsic, i.e., independent of the sample size in [20] and of the loading path in [15], at least at the laboratory scale, it may be applied to the structure scale of a dam. Reference [21] gave a method to assess the suffusion susceptibility of low permeability core soil in compacted dams based on construction data. They showed the one-dimensional (1D) spatial variability of all material parameters, in particular the hydraulic conductivity, the dry unit weight and the grain size distribution which affect the erosion resistance index. However, the suffusion susceptibility of earth dam body through the erosion resistance index needs to be assess the two-dimensional spatial variability. A two-dimensional contour map of the erosion resistance index would provide additional valuable information.

Reference [22] showed the disparate sources of uncertainties. One of the primary sources of geotechnical uncertainties is inherent soil variability. When we repeat the experiment many times at the same location, or at different locations, we always don't get the same result. To suppress or eliminate the influence of this source, we often use a very large number of samples. However, in practice, this implementation is not feasible because the experimental conditions do not allow, or the cost is too great. So, in the current calculation, there is always this random source. The objectives of the paper are to assess the suffusion susceptibility of earth dam considering variability spatial of soil properties. To tackle this objective, the contour map of 2D spatial variability of erosion resistance index of earth dam body is presented. This approach is based on two-dimensional Stochastics random field.

2. Description

                            2.1 Assessment of soil suffusion susceptibility

Reference [18] performed many suffusion tests on 32 different soils to measure the value of erosion resistance index. For each test, the erosion resistance index Iα was measured at the ‘final state’ in [15]. From the study of several grain size-based criteria, a statistical analysis was developed to predict the erosion resistance index Iα. Reference [23] described the key influence of the grain size distribution on the suffusion process and they distinguished three main gradation curves: linear distribution, discontinuous distribution and upwardly concave distribution. The concave distribution consists of a poorly graded coarse fraction associated to a highly graded fine fraction. The soils that are likely to suffer from suffusion are, according to reference [24] “internally unstable”, i.e., their grain-size distribution curve is either discontinuous or upwardly concave. Based on this information, several criteria have been proposed in literature, and recently reference [25] proposed three categories of soil erodibility from the comparison of criteria of Istonima, Kézdi and Kenney and Lau. They defined P as the mass fraction of particles finer than 0.063mm. For gap-graded soil, Chang and Zhang defined the gap ratio as: Gr = dmax/dmin (dmax and dmin: maximal and minimal particle sizes characterizing the gap in the grading curve). For P less than 10%, the authors assumed that the stability is correctly assessed using the criterion Gr < 3. For P higher than 35%, the gap graded soil is reputed stable, and with P in the range 10% to 35% the soil is stable if Gr < 0.3P. According to Chang and Zhang, their method is only applicable to low plasticity soils.

By using a triaxial erodimeter, reference [14] determined the suffusion susceptibility of three mixtures of kaolin and aggregates. The results indicate that suffusion process depends on the grain angularity of coarse fraction. With a same grain size distribution, angularity of coarse fraction grains contributes to increase the suffusion resistance. Thus, the parameter of shape of grains plays an important role on suffusion susceptibility.

The physicochemical characteristics of the fluid and solid phases are also crucial, particularly in the case of cohesive soils. For the same type of clay, several tests performed in clayey sands have shown that suffusion decreases with the increase of the clay content in [26].

In addition, with material susceptibility, reference [4] consider two others main initiation conditions for suffusion: the stress condition and the hydraulic load. For the same material susceptibility, the modification of the effective stress can induce grain rearrangements. Several tests performed in oedometric conditions on unstable soils showed that a rise in the effective stress causes an increase of the soils’ resistance to suffusion in [14]. In the same manner, when tests were carried out under isotropic confinement in [26], the increase in the confinement pressure, and then the increase of soil density allowed a decrease in the suffusion rate.

Reference [18] showed the correlation equation between physical parameters and erosion resistance index Iα for all soils

Iα = –13.57+0.43gd + 0.18j – 0.02Finer KL +0.49VBS + 189.70ki+3.82 min(H/F)                             

+0.18P +0.28Gr +19.51d5 +1.06d15 - 0.84d20+0.81d50 -0.98 d60 -0.10d90                            (1)

  Where: dry unit weight gd, blue methylene value VBS, internal friction angle j, initial hydraulic conductivity ki, minimum value of ratio H/F, percentage of finer fraction (based on Kenney and Lau’s criteria) Finer KL, gap ratio Gr, d5, d15, d20, d50, d60, d90 (diameters of the 5%, 15%, 20%, 50%, 60%, 90% mass passing, respectively) and P (percentage of finer than 0.063mm)

For widely graded soils, the correlation of physical parameters with the erosion resistance index: (N=10, R2 =0.99)

      Iα = -26.34+0.43gd + 0.66 j – 0.16Finer KL + 1.15VBS +0.37P +6.82d5 -1.26d60

                                                                                                                         (2) 

For gap-graded soils, the correlation of physical parameters with the erosion resistance index: (N=21, R2=0.90)

Iα = -37.62+0.67 gd + 0.64 j + 0.09Finer KL - 0.03VBS -1.43P + 0.63Gr + 0.76d5 -0.97d60 +0.61d90                                                           (3)                                                                                                                             

The distinction between widely graded or gap-graded is based on the gap-ratio in [24] and in [18]). Gap-graded soils are defined by Gr > 1. If this distinction is not obvious, the smallest value of Iα should be taken from the two values calculated by equations (2) and (3) to ensure a conservative estimation. The equation (2) may be viewed as a resilient tool that can be adapted to the available parameters of a given construction site.

  2.2 Assessment of the relative suffusion potential

The erosion resistance index (Iα) is just a material parameter that characterizes the susceptibility of a given soil to suffusion. Hence, it cannot be interpreted as a ‘security factor’ to distinguish between ‘probable occurrence of erosion’ and ‘no erosion’ in [21], This distinction requires additionally the estimation of the hydraulic loading. The erosion resistance index is estimated from several soil parameters using 2D Stochastics random field. Therefore, the relative suffusion potential of the earth dam body may be characterized by the 2D contour map of the erosion resistance index Iα. A contour map shows the suffusion susceptibility at locations in the homogeneous earth dam body through the erosion resistance index value Iα. Cross-section of the earth dam will be pointed out with the spatial variability of Iα, may be low of high resistance to suffusion. Two other maps show the 2D spatial variability of density, internal friction angle.            

3. Numerical simulation

                            3.1 A numerical example of homogeneous earth dam body

This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.

The earth dam has the structure homogeneous with assumed parameters: the height of dam crest: +21.1 m, the width of dam crest is 6.0 m. The dam slope in upstream: m = 3.5 ¸ 3.0 and in downstream: m = 2.5 ¸ 3.0. The data of dam include full grain size distributions with widely graded soil, dry unit weight, internal friction angle, initial hydraulic conductivity, and other parameters with the following assumed average values: dry unit weight  gd =17 kN/m3; internal friction angle j=270; percentage of fines (%) (based on Kenny &Lau, 1985 criterion) Finer KL=20%; the percentage finer than 0.063 mm P=24%; d5 =0.1mm; d60 =1mm. The suffusion susceptibility will be estimated through erosion resistance index.

3.2 Simulation methodology

              In this paper, the soil characteristic parameters are modeled as a random field. These parameters are inputted in the model using the two-dimensional (2D) Stochastics random field which is researched in [27]. In a random finite element method, the spatial variability g, j, Finer KL, P, d5, d60 are simulated by a random field with assumed coefficient of variance (cov) cov = 0.05 and mapped onto the finite element mesh. This estimation is based on equation (2) since all soil samples are widely graded. Among the seven parameters of equation (2), the blue methylene value (VBS) was considered constantly VBS=0.5g/100g in the dam. The forecasting result of spatial variability of erosion resistance index with the contour map 2D is showed.

  3.3 Numerical results

3.3.1 Forecasting the erosion resistance index and the probability of suffusion susceptibility

The result of erosion resistance index with contour map 2D is showed in figure 2. Several locations in the map pointed out with a low resistance to suffusion (blue color). Some zones with yellow color represent the high resistance to suffusion. The predicted values of Iα lies within the range from 2 to more than 9. The result of map shows the spatial variability of erosion resistance index. These results may be explained by soil spatial variability. According to reference [21], they show the one-dimensional spatial variability of erosion resistance index which erosion resistance index is estimated equally for one layer in the dam core. These results may be not given accurate results at different locations. Based on two- dimensional random field model, the two- dimensional spatial variability of erosion resistance index is predicted in the whole dam.

.4. Conclusions

The result of paper assesses the suffusion susceptibility of the dam body using two-dimensional random field considering soil spatial variability. With illustration of a numerical simulation, the predicted result of spatial variability of erosion resistance index is showed in a contour map 2D. Furthermore, the probability of suffusion susceptibility is also forecasted correspond to classification of suffusion susceptibility. This result demonstrates that the actual state of practice would be to account for the two-dimensional spatial variability.

1.       Foster, M., Fell, R., and Spanagle, M. 2000. The statistics of embankment dam failures and accidents. Canadien Geotechnical Journal, 37: 1000-1024

2.       Fell, R., and Fry, J. J. 2013. Erosion in geomechanics applied to dams and levees. Bonelli S. Editor. ISTE-Wiley. pp.1-99

3.       Icold. (2013). Internal erosion of existing dams, levees and dykes, and their foundations.Bulletin. Internal Erosion Processes and Engineering Assessment (Vol. 1, pp. 164).

4.       Garner, S.J., and Fannin, R.J. 2010. Understanding internal erosion: a decade of research following a sinkhole event. The International J. on Hydropower and Dams 17: 93-98.

5.       Marot, D., & Benamar, A. (2012). Suffusion, transport and filtration of fine particles in granular soil. Erosion of Geomaterials, 39–79.

6.       Kenney, T. C., and Lau, D. (1985). Internal stability of granular filters. Canadien Geotechnical Journal, 22: 215-225.

7.       Li, M., & Fannin, R. J. (2008). Comparison of two criteria for internal stability of granular soil. Canadian Geotechnical Journal, 45(9), 1303–1309.

8.       Wan, C. F., & Fell, R. (2008). Assessing the potential of internal instability and suffusion in embankment dams and their foundations. Journal of Geotechnical and Geoenvironmental Engineering, 134(3), 401–407.

9.       Kovács, G. (2011). Seepage hydraulics (Vol. 10). Amsterdam: Elsevier Scientific Publishing Co.

10.     Skempton, A. W., and Brogan, J. M. 1994. Experiments on piping in sandy gravels. Géotechnique, 44(3): 440-460.

11.     Reddi, L. N., Lee, I., and Bonala, M. S. 2000. Comparision of internal and surface erosion using flow pump test on a sandkaolinite mixture. Geotechnical Testing Journal, 23(1): 116-122.

12.     Perzlmaier, S. 2007. Hydraulic criteria for internal erosion in cohesionless soil. In Internal erosion of dams and their Foundations. Editors R. Fell and J.J. Fry. Taylor & Francis: 179-190.

13.     Moffat, R., and Fannin, J. 2006. A large permeameter for study of internal stability in cohesionless soils. Geotechnical Testing Journal, 29(4): 273-279.

14.     Marot, D., Bendahmane, F., and Nguyen, H. H. 2012. Influence of angularity of coarse fraction grains on internal process. La Houille Blance, International Water Journal, 6(2012): 47-53.

15.     Rochim, A., Marot, D., Sibille, L., & Le, V. T. (2017). Effects of hydraulic loading history on suffusion susceptibility of cohesionless soils. Journal of Geotechnical and Geoenvironmental Engineering, 143(7), 04017025.

16.     Marot, D., Bendahmane, F., and Konrad, J. M. (2011a). Multichannel optical sensor to quantify particle stability under seepage flow. Canadian Geotechnical Journal, 48: 1772-1787.

17.     Marot, D., Regazzoni, P. L., and Wahl, T. 2011b. Energy based method for providing soil surface erodibility rankings. Journal of Geotechnical and Geoenvironmental Engineering (ASCE), 48:1772-1787.

18.     Le, V. T., D. Marot, A. Rochim, F. Bendahmane, and H. H. Nguyen. 2018. “Suffusion Susceptibility Investigation by EnergyBased Method and Statistical Analysis.” Canadian Geotechnical Journal 55, no. 1 (January): 57–68.

19.     Marot, D., Rochim, A., Nguyen, H. H., Bendahmane, F., & Sibille, L. (2016). Assessing the susceptibility of gap graded soils to internal erosion characterization: proposition of a new experimental methodology. Nat Hazards (first online), 1-24.

20.     Zhong, C., V. T. Le, F. Bendahmane, D. Marot, and Z.-Y. Yin. 2018. “Investigation of Spatial Scale Effects on Suffusion Susceptibility.” Journal of Geotechnical and Geoenvironmental Engineering 144, no. 9 (September): 04018067.

21.     Zhang. L, R. Gelet, D. Marot, M. Smith & J-M.Konrad (2018): A method to assess the suffusion susceptibility of low permeability core soils in compacted dams based on construction data, European Journal of Environmental and Civil Engineering. ISSN: 1964-8189 (Print) 2116-7214.

22.    Phoon,K.K; Kulhawy, F.H. (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal, vol. 36(4): 612-624

23.     Lafleur, J., Mlynarek, J., and Rollin A.L. (1989). Filtration of broadly graded cohesionless soils. Journal of Geotechnical Engineering 115(12): 1747-1768.

24.     Fell, R., and Fry, J.J. editors 2007. The state of the art of assessing the likelihood of internal erosion of embankment dams, water retaining structures and their foundations. In internal erosion of dams and their foundations. Editors R.Fell and J.J Fry Taylor & Francis, London. 1-24.

25.     Chang, D. S., and Zhang, L. M. 2013. Critical hydraulic gradients of internal erosion under complex stress states. Journal of Geotechnical and Geoenvironmental Engineering, 139(9), 1454-1467.

26.     Bendahmane, F., Marot, D., and Alexis, A. 2008. Experimental parametric study of suffusion and backward erosion. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 134(1):57-67.

27.     Vanmarcke, E.H. 1977. Probability modeling of soil profiles. Journal of the Geotechnical Engineering Division, ASCE, 103(11): 1227–1246

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