Microsoft Word - numero_67_art_09_4517.docx A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 118 Impact of earthquake’s epicenter distance on the failure of the embankment – A seismic prediction Abdoullah Namdar School of Civil Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, Iran Omer Mughieda* Department of Civil Engineering, Abu Dhabi University, Abu Dhabi, UAE omer.mughieda@adu.ac.ae Ts Haji Azahar Bin Mohd Yasin Faculty of Civil Engineering Technology, Universiti Malaysia Pahang, Malaysia Falak Azhar Independent researcher, Dubai, UAE KEYWORDS. Embankment, Pre-existing Crack, Displacement, ANN, Damage prediction. Citation: Namdar, A., Mughieda, O., Yasin, T.H.A.B.M., Azhar, F., Impact of earthquake’s epicenter distance on the failure of the embankment – A seismic prediction, Frattura ed Integrità Strutturale, 67 (2024) 118-136. Received: 30.08.2023 Accepted: 31.10.2023 Online first: 03.11.2023 Published: 01.01.2024 Copyright: © 2024 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/z4GYgk-jkcA A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 119 INTRODUCTION racks in clay have undergone investigation through numerous experimental studies [1-3]. Rankine's theory and XFEM are generally applied to simulate cracks and predict the crack propagation angle and shape, respectively [4, 5]. One of the earlier observed experimental outcomes concluded that the angle of crack propagation in the clay is related to the brittleness of the clay [1]. In this regard, to validate the results of XFEM in crack propagation, the numerical simulation results [5] agreed with the experimental outcome [1]. Additionally, clay is used to build the embankment core due to its low permeability characteristics [6, 7], and by applying seismic acceleration to the ground, the crack in clay causes severe damage to the core of the embankment [8]. The impact of cracks on any embankment location requires thorough investigation. It is unclear whether the displacement's time and magnitude change with distance from the earthquake epicenter. Seismic accelerations create nonlinear displacement on the embankment [9]. Various methodologies have been used to improve the stability of the embankment [10-14]. The stability of embankments can be increased with the use of several techniques, such as embankment fill, geosynthetic reinforcement, sheet piles and column installation, geogrid installation, and replacement fill [10-14]. Minimal research has been conducted on embankment distance from the earthquake epicenter for damage assessment of the embankment with the cracked core. However, some studies have analyzed pre-existing cracks on the embankment to apply feasible techniques for improving embankment stability. The tension crack on the embankment usually occurs before applying seismic loading [15-18]. The top surface of the bentonite-sand mixture can crack due to shrinkage and desiccation [15]. Other reasons include erosion, swelling of soil [16], thaw settlement [17], and nonlinear volumetric deformation of soil in permafrost regions [18]. Pre-existing tension cracks extend with the application of seismic load. The geogrid and crushed-rock interlayers cannot prevent embankment cracking from the thaw settlement [17]. Therefore, it becomes necessary to simulate an embankment with pre-existing cracks for a smooth assessment of the seismic stability of the embankment. Generally, a tension crack occurs in the crest of the embankment [8, 10, 19-22]. Several studies have concluded that pre- existing cracks on the embankment and earth structure reduce stability [23-26]. Field monitoring methods help classify embankment damage and the development of tensile cracks [27-30]. Numerical simulations and experimental work analyze the impact of the cracks on the instability of the embankment [31] and can assess crack propagation due to seismic acceleration [32]. Additionally, it is crucial to thoroughly investigate the differential displacement of embankment with pre- existing cracks related to the magnitude of seismic acceleration. During an earthquake, the seismic response of an embankment is related to the seismic acceleration's magnitude. Classifying earth structure damage as subjected to seismic acceleration from an earthquake is important. In the present study, ANNs were used to predict displacement obtained by XFEM in association with the varying distances from the embankment model to the earthquake's epicenter. Additionally, the study has predicted how earthquake epicenter distance impacts the displacement's time and magnitude. These two essential parts of geotechnical engineering design have not been reported in the literature. The objectives of this research work are;  To assess applying the seismic acceleration of an earthquake with varying distances to the embankment model.  To predict displacement in critical points of the embankment model.  To study the time for the maximum negative and positive displacement occurrence. MODELING AND SIMULATION amage in an earthquake-impacted area is not linear. Therefore, the factors that lead to damage need precise assessment. The earth structure's distance from the earthquake location must be studied to analyze the model's seismic response, and the numerical simulation needs to be investigated for the model's simulated earthquake response. The numerical simulation to explain this problem has the cost-effective, easy performance and quickly producing information advantage over the experimental simulation. The selected design parameters include the mechanical properties of the clay, sandstone, and recycled aggregate, the boundary condition of the model, and multidirectional applied seismic loading. In addition, according to theoretical concepts, clay is a non-tensile material. The simulated model has been subjected to seismic acceleration at different distances from the earthquake's epicenter. XFEM was used to produce ANNs with two hidden layers designed to predict the displacement based on the results. In order to validate the results of the numerical simulation, the outcome of the simulation has been compared to available data in the literature. C D A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 120 The geometry of the embankment impacts the model displacement [48]. As a matter of fact, when simulating problems with seismic waves, the edge effect can be present and should be taken into account in a complete model. However, in the present work, the influence of the model's dimensions is not taken into account for the sake of simplicity, although it is well-known that the geometric dimensions assumed for the foundation may affect the results. Fig. 1 is a demonstration of the model used in the numerical simulation. Part (a) is the simulated model, including the embankment and its foundation. The embankment is modeled from recycled material. The core and the foundation of the embankment are made of impermeable clay and sandstone, respectively. Parts (b) and (c) illustrate the model's boundary conditions, where the core of the embankment with cracks was simulated. In the seismic analysis of the model, the core embankment is critical, as the pre- existing crack of the model is located in the area. Fig. 1 part (d) graphically represents the application of seismic acceleration to each point at a model, where multi-directional seismic acceleration is applied to the model. The lateral and vertical displacements on the embankment are linked to the soil's mechanical properties [9]. As this study considers the materials used to construct different embankment areas, it is necessary to analyze the displacement at the critical point of the model. The vertical displacement that occurs at the embankment’s crest reduces the seismic safety of the embankment [28]. In the current study, points located in the crest and center of the embankment’s slope have been considered for investigation of the seismic vertical displacement. Figure 1: Model and boundary conditions, a) simulation of the embankment and its foundation models, b) core of the embankment at Y-Z plane, c) core of the embankment at Y-X plane, d) the application of seismic acceleration to each point of the model. Material Friction angle, ϕ (deg) Cohesion, Cu (kPa) Poisson’s ratio, ν Unit weight, γ (kN/m3) Modulus elasticity, E (MPa) Ref Clay (Undrained) - 25 0.3 18 12.5 [34] Recycle aggregate 40.6 - 0.25 23.3 27620 [35] Sandstone - - 0.25 24 35000 [36] Table 1: Mechanical properties of clay, recycled material, and sandstone [34-36]. MECHANICAL PROPERTIES n the geo-structure seismic simulation, the type of the geomaterials impact the embankment's displacement. The material's location also influences the model's mechanical properties and displacement [33]. The embankment is made of two types of materials. Clay was used to build the embankment's core, and the recycled aggregate was used in other areas. A sandstone foundation was used for embankment installation. I 54 (m) 10 ( m ) 5 (m ) 7 (m) 7 (m)15 (m) 15 (m)10 (m) Embankment foundation Embankment X = U1 = UR2 = UR3 = 0 Z Y Z Y X Y Z = U3 = UR1 = UR2 = 0 Y = U 2 = U R 1 = U R 3 = 0 Preexisting crack Y X Z S ei sm ic a cc el er at io n (g ) ap pl ie d at a p oi nt Core of embankment Y Y Y = U 2 = U R 1 = U R 3 = 0 X C or e of e m ba nk m en t C or e of e m ba nk m en t Y = U 2 = U R 1 = U R 3 = 0 X = U1 = UR2 = UR3 = 0 (a) (b) (c) (d) 3(m) P re ex is ti ng c ra ck A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 121 Tab. 1 describes the mechanical properties of clay, recycled aggregate, and sandstone used in the simulation of the embankment and subsoil [34-36]. Clay limits water flow due to its impermeable nature [37]. The material is considered low in strength. Recycled aggregate can be utilized for embankment construction as it can provide acceptable seismic resistance to the embankment [33]. Compared to the embankment, the foundation behaves with the solidified part of the model. SEISMIC DATA n 21 March 2023, an earthquake with 5.6 MWW occurred in the Melipilla region of Chile. The earthquake's epicenter was measured at a depth of 65 (km) and coordinates of -33.6103 and -71.3517. Four different acceleration histories (registered at four different stations located at a distance of 24.9 (km), 38.3 (km), 65.9 (km), and 84.5 (km) from the epicenter of the earthquake) are here considered and used as input data in four different models. These histories are shown in Fig. 2. This numerical simulation aims to assess the impact of the epicenter distance on the seismic response of the embankment. The acceleration changes as it shifts farther from the earthquake epicenter. The multi- directional seismic acceleration must be applied to the model to improve the results' accuracy in the numerical simulation [39]. Fig. 1 depicts that appropriate modeling was done considering the nature of the seismic acceleration occurring in the field. The seismic acceleration of the earthquake with 5.6 MWW at 0°, 90°, and 360° has been applied to the model. 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 0° 0.05 (g) - 0.05 (g) Distance to epicenter = 24.9 (km) Station = Santo Domingo, Chile(a) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 90° 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 A cc el er at io n [g ] A cc el er at io n [g ] A cc el er at io n [g ] Time [s] Time [s] Time [s] Recorded in 360° 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Distance to epicenter = 38.3 (km) Recorded in 0° 0.05 (g) - 0.05 (g) Station = Talagante, Chile(b) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 90° 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 360° Time [s] Time [s] Time [s] A cc el er at io n [g ] A cc el er at io n [g ] A cc el er at io n [g ] 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 0° 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 A cc el er at io n [g ] A cc el er at io n [g ] A cc el er at io n [g ] Time [s] Time [s] Recorded in 90° 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Time [s] Recorded in 360° Distance to epicenter = 65.9 (km) 0.05 (g) - 0.05 (g) Station = Casona(c) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 0° Time [s] Time [s] 0.05 (g) - 0.05 (g) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Recorded in 90° A cc el er at io n [g ] A cc el er at io n [g ] A cc el er at io n [g ] 0.05 (g) - 0.05 (g) (d) 0 5 10 15 20 25 30 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Distance to epicenter = 84.5 (km) Recorded in 360° Time [s] 0.05 (g) - 0.05 (g) Station = Hacienda Santa Martina Figure 2: The acceleration history (g) for different distances from the epicenter CRACK THEORETICAL CONCEPTS, SIMULATION IN FEM, AND REALITY ccording to Rankine’s theory (1857), the pre-existing cracks on clay are simulated [5], and crack propagation is predicted by using the XFEM [4]. The crack propagation angle in the brittle clay sample is higher than in the ductile clay sample [1]. This phenomenon was simulated and proved using the XFEM. It was observed that the clay with higher brittleness faces the crack propagation with a higher angle when subjected to seismic acceleration [4]. The failure O A A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 122 model of the clay model with pre-existing cracks is associated with the brittleness of the clay. Fig. 3 shows the type of crack that occurred on the Akitsu River embankment due to the Kumamoto earthquake in Japan in 2016 [8]. Based on theoretical concepts and evidence based on reports, Fig. 3 illustrates the embankment crack, which is simulated and presented in Fig. 1. This study simulated the single longitudinal pre-existing crack on the embankment. It assumed the location of the crack at the center of the embankment’s crest. Simulation of the crack shape was followed by simulating the crack depth, which was calculated using Rankine’s theory. Using Rankine’s theory for undrained clay, Eqns. 1 and 2 are applied to calculate the length of the pre-existing crack and identify the solid zone in the core of the embankment [40]. u   Length of the preexisting crack  2c  /  γ Z   (1) z 0S  Solid zone    H    Z   (2) Fig. 3 depicts the pre-existing crack on the clayey core of the embankment. It assumed the core of the embankment is under undrained conditions. The fully saturated undrained clay has ϕu equal to zero. Figure 3: The preexisting crack on the clayey core of the embankment. In a realistic crack simulation model, the crack orientation should be free to rotate. The model should comprehend that pre- existing crack and crack propagation behave differently. Furthermore, it should be able to identify tensile and shear failure [41]. XFEM is a feasible platform to simulate crack propagation to satisfy these requirements. Fig. 3 (b) shows a type of crack in case of two earthquakes occurring subsequently in a short time. The crack created in the first earthquake will be a pre-existing crack for the second earthquake. Assuming the crack opening occurs parallel to the major principal tensile stress, the crack strain in this direction can be calculated [42], in addition, the finite elements were applied to crack growth [43-44]. A 2004 study proposed the phantom paired element approach for crack propagation, using node generation according to the material's properties [45]. The phantom node method describes the node generation in the crack opening and propagation. A later research study in 2016 used the ABAQUS to implement XFEM to simulate the crack opening and propagation process [46]. The current study used ABAQUS to perform the phantom node method to simulate crack opening and propagation. Fig. 4 depicts the function of the phantom node method for generating mesh in crack opening and propagation. Fig. 5 illustrates the simulated model using ABAQUS to perform the nonlinear numerical simulation. Nodes 192 and 1434 have been selected as critical points of the model. Evaluating the displacement in these two points helps with the model's stability analysis and prediction failure. The number of nodes and elements for the models are 10212 and 8690 respectively. The type of the mesh is C3D8R. The mesh dimension for the model is 1350 mm. Due to the preexisting crack in the embankment model, the extended finite elements method was used in performing ABAQUS. Different parts of the embankment model interaction were modeled using the contact algorithm presented in ABAQUS by creating a tangential interface. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 123 Figure 4: The phantom node method for generating mesh in crack opening and propagation [45]. Figure 5: Model in the numerical simulation. ARTIFICIAL NEURAL NETWORKS tatistical analysis is usually preferred for predicting and classifying results in geotechnical engineering [33, 47-48]. Artificial neural networks (ANN) can significantly support geotechnical engineering designs as they can be used for the integration, prediction, and classification of results [49-52]. ANN is also commonly used for results of investigation forecasting, categorization outcome of a phenomenon study, association of data, and filtering interpreted data for solving several engineering problems [53-57]. An ANN is created from input, hidden, and output layers, with neurons performing at each layer [52]. In a recent 2020 study, ANN was proposed with two hidden layers with an architecture of 6:7:5:1 for the input layer, first hidden layer, second hidden layer, and output layer, respectively [58]. The multilayer perceptron (MLP) is a wholly associated class of feedforward ANN [59]. This study used the MLP method with the Levenberg-Marquardt algorithm to project the ANN for the classification and prediction of the displacement in a selected model point. The following equations were used in ANN [60]: 2 2   1  1  j Zjf e    (3) S A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 124 1       n j ij i j i Z W x b    (4)  1 2 tanh   tanh( [ ])  1 W X f w    (5) 1 1 1 2 2 2 3 3 3, , , , , , , , , , 1   T X t l x y l x y l x y    (6) where; jf is output of jth neuron jZ is data gathering of jth neuron ix is input ijw is weigh jb is bias 1w is weight matrices linking the input and hidden layers 2w is weight matrices linking the hidden and output layers X is the augmented input vector In reference to the literature [61], Eqns. 7-8 are used to control prediction quality.  2 1 1         n p i RMSE d d n    (7)     2 12 2 1         1         n pi n oi d d R d D           (8) d is the obtained displacement by XFEM, dp is the forecasted displacement by ANNs and oD is the mean of displacement from FEM. The quantity of neurons in the hidden layer design significantly affects the output accuracy of prediction and classification performed by the ANN model [62]. In this investigation, two hidden layers were selected for ANN. RESULTS AND DISCUSSION he earthquake's impact on embankment damage was numerically investigated by assessing displacement, stress, and strain in nodes 192 and 1434 of the model in the crest and middle of the embankment's slope. The results of the nonlinear numerical simulation revealed that the location of the embankment and its distance to the earthquake's epicenter is critical. According to Fig. 6, with an increase in the distance of the embankment to the earthquake's epicenter, the time for the occurrence of the maximum negative and positive displacement in the selected points is nonlinear. The time and magnitude of the maximum displacement at each model are different. The maximum negative and positive displacements in the Y direction of nodes 192 and 1434 were observed at 24.9 kilometers from the earthquake's epicenter. Additionally, the measurements of displacement against distance from the epicenter can be observed to follow a nonlinear pattern. Model - 1, Model - 2, Model - 3, and Model - 4 are located at distances of 24.9 (km), 38.3 (km), 65.9 (km), and 84.5 (km) from the earthquake's epicenter, respectively. T A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 125 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 Displacement at node 192 Displacement at node 192 Displacement at node 192 Displacement at node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 Model - 1 Model - 2 Model - 3 Model - 4 D is pl ac em en t ( m m ) D is pl ac em en t ( m m ) D is pl ac em en t ( m m ) D is pl ac em en t ( m m ) Time [s] Time [s] Time [s] Time [s] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 Model - 1 Model - 2 Model - 3 Model - 4 Displacement at node 1434 Displacement at node 1434 Displacement at node 1434 Displacement at node 1434 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 D is pl ac em en t ( m m ) D is pl ac em en t ( m m ) D is pl ac em en t ( m m ) D is pl ac em en t ( m m ) Time [s] Time [s] Time [s] Time [s] Figure 6: Displacement in models 1 - 4, at selected points Vertical displacement occurs at the embankment's crest, and there is no seismic safety for the embankment when faced with unallowable displacement [28]. In the current study, node 192 is located in a critical part of the embankment and has been considered for investigation of the seismic vertical displacement in previous research work [14]. The slope movement accelerates the displacement of the crest [10], and nodes 192 and 1434 present the displacement of the crest and slope vertical movement. The displacement in node 192 differs from the displacement in node 1434 within all models. Fig. 7 shows the maximum deformation against the first maximum multidirectional displacement in models 1– 4. In model 1, maximum multidirectional displacement occurs at 8.4 seconds, at a distance of 24.9 km from the earthquake's epicenter, while in models 2-4, the maximum displacement occurred at 5.8 seconds, 12.2 seconds, and 14 seconds, at distances of 38.3 km, 65.9 km, and 84.5 km from the earthquake's epicenter, respectively. The distance from the earthquake's epicenter mostly leads to a delay in maximum multidirectional displacement. Model 2 follows faster displacement and a higher deformation level than models 1, 3, and 4. The deformation based on the shear strain occurs at different times for each model. Figure 7: Maximum deformation against first maximum multidirectional displacement in models 1 – 4. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 126 As part of a 2023-based study by Namdar et al., prediction of the cracked soil using XFEM was reported [5], and the type of crack was analyzed by considering crack propagation and mechanical properties of the material. The crack propagation angle is more prominent for a brittle material in comparison to a ductile material [1]. The crack will be propagated based on the mechanical properties of the material. The shape of the cracks and the possibility of crack propagation are associated with the mechanical properties of the materials [5]. In the present study, due to the nature of the seismic acceleration, mechanical properties of the soil, and geometry of different sections of the model constructed from the soil and recycled aggregate, the crack has not been propagated during the application of seismic load on the model. The lateral force from the slope of the embankment does not allow the crack propagation. Figs. 8 and 9 show the fluctuation of maximum dynamic nonlinear deformation produced by stress and strain in nodes 192 and 1434 of models 1-4. The maximum intensity of the stress and strain is observed when the model is located at a 24.9 km distance from the earthquake's epicenter. The deformation speed changes as the model's location from the earthquake's epicenter changes. An increase in displacement of the model leads to faster deformation. By comparing all models, it can be observed that the distribution of the deformation is nonlinear. Maximum deformation for all models was observed in the crest. Vertical strain and stress values vary for each model at nodes 192 and 1434. Tension cracks occur at the top of the embankment and not the bottom. When the embankment is subjected to seismic loading, the crest of the embankment fails due to tensile force, and the bottom part fails due to shear force [8]. Tensile failure precedes shear failure with low vertical stress. Due to this phenomenon, the crack will not be propagated in the embankment model when a preexisting crack during the embankment model is subjected to seismic acceleration. In this study, the crack has not been propagated from an initial condition of the model. The maximum intensity of the stress and strain is observed when the model is located at a 24.9 km distance from the earthquake's epicenter. The distance of the model plays an essential role in seismic stability. The stress-strain curve does not present shearing tensile in the model. When the compressive stress governs the model deformation, it does not cause crack propagation. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Model-1, Node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Model-2, Node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Model-3, Node 192 S tr es s (M P a) Time [s] S tr es s (M P a) S tr es s (M P a) S tr es s (M P a) Time [s] Time [s] Time [s] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Model-4, Node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Model-1, Node 1434 Time [s] Time [s] Time [s] S tr es s (M P a) S tr es s (M P a) S tr es s (M P a) S tr es s (M P a) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Model-2, Node 1434 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Node-1434 Model-3, Node 1434 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 Node-1434 Model-4, Node 1434 Time [s] Figure 8: Stress in models 1 – 4 at selected points. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-1, Node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-2, Node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-3, Node 192 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-4, Node 192 S tr ai n Time [s] Time [s] Time [s] Time [s] S tr ai n St ra in St ra in 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-1, Node 1434 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-2, Node 1434 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-3, Node 1434 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.00010 -0.00005 0.00000 0.00005 0.00010 Model-4, Node 1434 S tr ai n S tr ai n S tr ai n St ra in Time [s] Time [s] Time [s] Time [s] Figure 9: Strain in models 1 - 4 at selected points. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 127 A 1988 research study by Vallejo stated that the propagation angle of the secondary cracks in the ductile samples of clay is a function of the water content in the samples [1]. In addition, large tensile strains do not aid in the development of crack openings. In a model, tensile cracks occur when one of the principal stresses is tensile [31]. Therefore, the stress-strain relation is vital in crack opening and propagation. The preexisting crack minimizes the seismic stability of the embankment. The nature of the seismic acceleration interaction in developing tensile strain and stress in a location of the model causes crack propagation. Under compressive stress-strain conditions, the crack propagation was not observed in the numerical simulation. As part of the conventional design, only the strength and magnitude of the ground motion are considered. The distance of the embankment to the earthquake's epicenter causing changes in the results is not taken into consideration. According to the present study, there is a need for the seismic embankment to assume different distances from the epicenter of the earthquake and integrate the results by applying ANN. APPLICATION OF ARTIFICIAL NEURAL NETWORKS s stated in the literature, in many cases, a tension crack occurs in the crest of the embankment [8, 10, 19 - 22]. As part of the current study, ANN has been applied to four models, and the displacement in the crest of the embankment has been assessed. The ANN has been designed with two hidden layers. The prediction accuracy needs to be improved due to the complex failure mechanism of the model. The parameters in ANN input are the vertical peak, strain, displacement, and times of peak occurrence. Using Abalone Data Analysis in performing Levenberg-Marquardt algorithms, 3927 data values in the data ring value were observed to predict displacement. The data in ANN is divided into training, testing, and validation. These three groups of data are representative of the sample population in the ANN. In applying ANN to geotechnical engineering data are randomly divided into three subsets: training, testing, and validation with different percentages. In the presented work data was subdivided to obtained data from XFEM, forecasting data, standard deviation, and mean data for all sets of the training, testing, and validation with different percentages. These data values are efficient and applicable to the prediction process. The ANN for the classification and prediction of the displacement in a selected model point. Tabs. 2-5 present the data used in the ANN. Fig. 10 shows regression analysis for displacement prediction at the Y direction in models 1-4 at node 192. Data separation is divided into training, testing, and validation. The combination of all these parts is presented in a new figure. The testing set performs the ANN, and subsequently, the training is stopped by the validation set. The training process is crucial in finding regression results in an ANN model. The RMSE and regression value R indicate performance assessment of the ANN for comparison statistical analysis. It has been observed that the prediction of ANN for each model has a different quality according to the data quality provided by FEM. Accurate predictions using FEM results can be challenging. In the adjustment of the model parameters, a training set will be employed. The testing set is used to control the quality function of the ANN model at different steps of training to avoid overfitting. In the organized ANN architectural design, the validation set is used to assess the function of the trained network [63]. The overfitting takes place when the data points in the training set are small [64]. In the present work, to perform the ANN based on Levenberg-Marquardt Algorithm, the Abalone Rings Data Set mode was used, and based on the selected technique 3927 data values were generated. The increasing number of data values supports avoiding overfitting. By designing an accurate ANN, overfitting will be avoided, and an accurate relationship between input and output will be constructed [65–66]. In addition, overfitting may occur when the training error is smaller than the validation error [67]. The RMSE for all models is summarized in Tab. 6. There is no overfitting in models 1-4 during all phases of the ANNs. The overfitting represents an error in the networking. The diagram of the cost function variations from RMSE has been revealed in Fig. 11. This cost function variations chart has been depicted for each model concerning the training, validation, and test data. Fig. 11 shows the prediction accuracy of displacement in the Y direction for models 1-4 at node 192. Tab. 6 presents R2 and RMSE obtained for models 1-4 in the ANN. The regression value indicates that the displacement is well predicted. Based on the results of the ANN, the prediction outcomes are acceptable. A A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 128 No Time (s) of Peak Strain Vertical Peak Strain Time (s) of Peak Displacement Vertical Peak Displacement (mm) 1 9 3.66158E-5 1.2 0.00353 2 9 3.66158E-5 2.8 0.01323 3 10.2 1.11211E-5 5.1 -0.0551 4 10.2 1.11211E-5 6.1 -0.08055 5 10.6 2.48084E-5 6.6 -0.08583 6 11.7 2.55166E-5 7 -0.08054 7 12.6 -1.73152E-6 7.4 -0.05559 8 12.9 -1.67194E-5 7.8 -0.07243 9 13.5 -3.9369E-5 8.4 0.50558 10 14.4 -5.43946E-5 9.3 -0.44701 11 14.4 -5.43946E-5 9.7 0.28515 12 15.4 2.92603E-5 10.2 0.18595 13 15.6 -3.05468E-6 10.6 -0.4731 14 15.9 -4.24715E-5 10.9 0.0273 15 16.4 1.2962E-5 11.2 0.13593 16 17.3 4.15847E-5 11.6 0.41824 17 17.5 -1.91974E-5 12.5 -0.80471 18 17.6 -1.25472E-5 13 0.66525 19 17.9 -3.90044E-5 13.9 -0.72156 20 17.9 -3.90044E-5 14.7 0.27817 21 18 -3.43934E-5 15 0.2971 22 18.5 -4.52935E-5 15.2 -0.22274 23 18.5 -4.52935E-5 15.7 -0.43133 24 18.6 1.81624E-5 16.1 0.07363 25 18.9 -3.79437E-5 16.4 0.08212 26 18.9 -3.79437E-5 16.5 -0.07664 27 19 -1.29523E-5 16.7 0.09019 28 19.2 -2.36419E-5 17.2 -0.33251 29 19.3 -4.2118E-5 17.8 0.33712 30 19.3 -4.2118E-5 18.1 0.17749 31 19.8 2.72532E-5 18.4 -0.47448 32 19.9 -3.69108E-5 18.9 -0.55117 33 20 -1.3475E-5 19.7 0.39952 Table 2: Data used in ANNs for model 1 at node 192. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 129 No Time (s) of Peak Strain Vertical Peak Strain Time (s) of Peak Displacement Vertical Peak Displacement (mm) 1 4.2 -1.3028E-5 0.8 -0.00193 2 8.7 2.55742E-5 1.4 0.039 3 10 -2.30875E-5 2 0.04645 4 11.4 2.36953E-5 2.4 0.012 5 11.9 3.09427E-5 2.5 0.03858 6 12.1 8.26371E-6 2.9 -0.02446 7 12.2 2.12201E-6 3.5 -0.01487 8 12.9 -2.63654E-5 4.1 -0.01416 9 13.3 -2.56894E-5 4.5 0.07741 10 13.7 -3.55372E-5 5.2 -0.10697 11 14.2 2.24323E-5 5.9 0.23836 12 14.5 1.98749E-5 6.4 0.20091 13 14.8 3.11179E-5 7.2 -0.20553 14 15.1 2.28205E-5 8.3 0.23569 15 16.1 -4.67412E-5 9.1 -0.05504 16 16.4 -1.81681E-5 9.7 0.06633 17 16.5 3.34733E-5 10 0.0091 18 16.6 -2.73132E-5 10.2 0.03745 19 16.8 2.01654E-6 10.6 -0.09899 20 17.1 2.96615E-5 11.9 0.34158 21 17.8 -2.63391E-5 12.9 -0.39836 22 18.1 -2.40995E-5 13.8 0.40224 23 18.1 -2.40995E-5 14.4 -0.17259 24 18.2 4.54628E-5 15.1 0.3185 25 18.3 1.11294E-6 16.1 -0.26687 26 18.6 -1.49689E-5 16.8 0.23331 27 18.7 -2.27521E-5 17.1 0.21027 28 19.1 -2.19045E-5 17.3 -0.05233 29 19.2 -1.07561E-6 17.9 0.16137 30 19.3 -4.97683E-5 18.2 0.29323 31 19.4 -9.87762E-6 18.5 0.24324 32 19.6 -3.51647E-5 19.1 -0.2389 33 19.7 3.44068E-5 19.8 0.22637 Table 3: Data used in ANNs for model 2 at node 192. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 130 No Time (s) of Peak Strain Vertical Peak Strain Time (s) of Peak Displacement Vertical Peak Displacement (mm) 1 11.8 2.07563E-5 1.1 -9.31982E-4 2 11.9 -2.14757E-5 2.2 0.04912 3 12.8 -1.19775E-5 3.2 -0.04446 4 13.7 -8.5937E-8 4 0.04448 5 13.9 -4.18506E-6 4.6 -0.02776 6 14 1.74155E-5 5.4 0.08549 7 14.1 2.52645E-5 6.1 -0.07784 8 14.7 5.44731E-7 6.9 0.1135 9 15 3.02762E-5 7.8 -0.06366 10 15.3 4.2301E-5 8.5 0.14371 11 15.9 -1.88E-5 9.3 -0.07478 12 16.1 1.99012E-5 10.3 0.16302 13 16.4 2.78226E-5 11.3 -0.27656 14 16.8 -2.01119E-5 12.3 0.46863 15 16.9 -1.24433E-5 13.1 -0.34137 16 17 2.35534E-5 13.8 0.35243 17 17.4 -2.04325E-5 14.1 0.24636 18 17.4 -2.04325E-5 14.5 -0.18729 19 17.6 2.17913E-5 14.9 -0.10603 20 17.6 2.17913E-5 15.3 0.40707 21 17.7 -2.68727E-5 15.6 0.40274 22 18 -4.45752E-5 16.3 -0.50955 23 18.1 1.64394E-5 17 0.54821 24 18.4 4.00299E-5 17.9 -0.35257 25 18.7 6.92011E-6 18.4 0.22553 26 18.9 1.47135E-5 18.7 0.27565 27 19 -6.47186E-6 19 0.22177 28 19.2 -6.47131E-6 19.4 -0.0398 29 19.4 -3.17943E-5 19.7 0.07224 30 19.7 -1.95444E-5 19.8 0.00777 31 19.7 -1.95444E-5 1.1 -9.31982E-4 32 19.9 4.86036E-7 2.2 0.04912 33 20 2.75958E-5 3.2 -0.04446 Table 4: Data used in ANNs for model 3 at node 192. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 131 No Time (s) of Peak Strain Vertical Peak Strain Time (s) of Peak Displacement Vertical Peak Displacement (mm) 1 13.5 3.49656E-5 3.7 -0.02382 2 13.9 4.56664E-5 5.1 0.03901 3 15.1 6.21655E-5 5.4 0.0315 4 15.3 4.32877E-5 6 -0.0352 5 15.5 3.55169E-5 6.8 0.02722 6 15.5 3.55169E-5 7 -0.03207 7 15.6 -3.81852E-5 7.6 -0.03201 8 15.9 5.5054E-5 7.8 0.04521 9 16.1 -3.8902E-5 8.3 0.0512 10 16.2 4.48545E-5 9 -0.02201 11 16.3 -5.66588E-5 9.8 0.02609 12 16.5 7.32731E-5 9.9 -0.02686 13 16.9 -4.22031E-5 10.5 0.05561 14 17 2.61352E-5 10.9 -0.02357 15 17.1 6.98217E-5 11.7 0.06574 16 17.2 6.9958E-5 12.1 0.09113 17 17.3 4.10507E-5 13.1 -0.30422 18 17.3 4.10507E-5 13.5 0.03494 19 17.5 1.67097E-5 13.7 -0.1781 20 17.8 1.21767E-5 13.9 0.5977 21 17.9 4.85343E-5 14.6 0.14167 22 18.1 -8.11604E-5 14.9 -0.3594 23 18.2 8.66784E-5 15.3 0.07141 24 18.4 -5.18286E-5 15.6 -0.12681 25 18.7 -5.93208E-5 15.9 0.37987 26 18.8 4.26183E-5 16.1 -0.26379 27 19.1 2.64145E-5 16.5 0.22709 28 19.2 4.78482E-5 16.7 -0.38467 29 19.4 -6.44013E-5 17.4 0.40609 30 19.4 -6.44013E-5 17.6 -0.1747 31 19.5 -7.55963E-5 18.1 -0.64465 32 19.7 5.7718E-5 18.9 0.39326 33 19.8 -4.45848E-5 19.4 -0.15696 Table 5: Data used in ANNs for model 4 at node 192. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 132 Figure 10: Regression analysis for displacement prediction in Y direction in models 1- 4 at node 192. A.Namdar et alii, Frattura ed Integrità Strutturale, 67 (2023) 118-136; DOI: 10.3221/IGF-ESIS.67.09 133 Figure 11: Prediction of displacement in Y direction for models 1-4 at node 192. - Training Validation Test Number of layers in ANNs Model- 1 R2 0.76728 0.77483 0.81098 2 RMSE 4.2872 4.0429 3.353 2 Model- 2 R2 0.75463 0.80366 0.77366 2 RMSE 4.5024 3.0944 4.0887 2 Model- 3 R2 0.76064 0.78967 0.77881 2 RMSE 4.3886 3.9027 3.8994 2 Model- 4 R2 0.76198 0.76098 0.763 2 RMSE 4.3759 4.3814 3.9123 2 Table 6: R2 and RMSE outcomes of ANNs for models 1-4 at node 192. CONCLUSION nonlinear numerical simulation was conducted to assess the impact of the earthquake's distance on the crack propagation of soil. The numerical modeling of soil categorized as a no-tensile material was adopted to explain the deformation of the crack-growing path simulated using the XFEM. ANN was used to predict maximum displacement in a selected point of each model.  In the event of an earthquake, the acceleration history (g) characteristics for different distances from the epicenter can vary. The nature of applying seismic load on the model at a different distance from the earthquake's epicenter is different.  It was observed that the model's failure pattern changes with the earthquake's associated distance. The seismic resistance of the embankment is related to the distance from the epicenter of the earthquake and the soil layers that seismic waves transfer from the earthquake's epicenter to the embankment.  By increasing the distance of the embankment to the earthquake's epicenter, the time for the occurrence of the maximum negative and positive displacement exhibits nonlinearity. 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