Stochastic model predictive approach for seismic lateral displacement of geosynthetic- reinforced soil slopes based on Newmark's sliding block analysis

doi:10.21203/rs.3.rs-3973399/v1

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Stochastic model predictive approach for seismic lateral displacement of geosynthetic- reinforced soil slopes based on Newmark's sliding block analysis

https://doi.org/10.21203/rs.3.rs-3973399/v1

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As a result of technological advances, geosynthetic reinforced soil (GRS) slopes have been constructed more frequently in recent decades, which have been used extensively in landslide stabilization, highway construction, and geological disaster prevention. A new formula was developed for predicting the probabilistic sliding displacement of GRS slopes in this paper. An example of a model based on numerical simulation (Slide) was illustrated to calculate seismic displacement based on three types of Newmark analysis. A synthetic dataset including 972 numerical simulations was generated for statistical analysis by data derived from real-time strong-ground motions of 30 worldwide earthquakes. An investigation into the relationship between reinforced slope properties and motion characteristics was performed using a parametric analysis. It was concluded that coupled analysis calculated higher values for earthquake-induced sliding displacement of GRS slope. Also, statistical analysis indicated that soil friction angle is more influential on sliding displacement than the other random variables. A cumulative distribution function was constructed for estimating probabilistic seismic displacement based on 5000 Latin-hypercube sampling.

Earthquake

Newmark slope sliding model

Geosynthetic reinforced soil slope

Probabilistic assessment

Sliding displacement

Landslide is one of the earth's most destructive disasters, is often triggered by major earthquakes. Among all the damages caused by earthquakes, landslides constitute a significant portion [1, 2]. There has been continuous progress in the development of methods for estimating landslide displacement during an earthquake since Newmark [3] proposed the sliding block method for predicting the cumulative permanent displacement of a slope [1, 4]. A numerical study utilizing the Newmark slope sliding model is presented in Fig. 1, which depicts the different displacement values and failure surfaces associated with both geosynthetic-reinforced and unreinforced slopes. The displacement evaluated by the Newmark slope sliding method is merely a design parameter determined by an artificially simplified slope model ignoring several important mechanisms; for example, continuous shear failure rather than a fixed slip surface, cyclic deterioration of soil materials (including pore-pressure buildup) rather than a fixed friction angle, etc. It is assumed that once soil has yielded, its resistance remains constant as displacement increases. However, this method may not accurately model the system without structural elements (such as geosynthetics) that restrain ground movement. Displacement will stretch geosynthetic reinforcements, thereby increasing their restraint capacity (it is mandatory that they are designed not to yield/rupture when subjected to full displacement). Accordingly, the primary Newmark method does not accurately represent the slope's deformation. Thus, it is essential to develop equations that are easier to understand and more effective as well. In this regard, several modifications have been suggested to the primary Newmark slope sliding model to achieve a more accurate estimation of slope displacement by modeling the dynamic slope response. Generally, these approaches can be categorized into three types:

i. “Rigid-block analysis”, discrete-element assembly is a structure made from rigid components without glue or other joining mechanisms. In the approach, compressive forces occur at the vertices of the interface to model a unilateral contact between blocks. Originally, rigid-body assumed that normal forces could occur without deformation. Once the shaking has stopped, a permanent displacement will result from accumulated unrecoverable deformations. In this theory, a sliding soil mass can be regarded as an object subject to seismic forces.

ii. Based on the rigid block analysis, Makdisi and Seed [5] presented the “Decoupled approach”. The dynamic response is calculated to measure the block's displacement based on the system's equivalent acceleration [6]. Additionally, in decoupled procedures, the dynamic response of the embankment is computed independently of the sliding mass displacement.

iii. “Coupled analysis”, in which deformation of the sliding mass is calculated concurrently with its dynamic response [7, 8]. Then, the ground motions are investigated regarding the plastic sliding displacements [8, 9].

It is widely used by researchers to assess earthquake landslide hazards using the Newmark sliding displacement method. Many assumptions are involved in the traditional Newmark slope sliding model, which results in various levels of uncertainty in displacement results. There have been several research studies based on ground-motion intensity such as critical acceleration to develop regression-based Newmark slope sliding prediction equations for slope displacements.

Ambraseys and Menu [10] proposed the first equation to predict displacement within the framework of the Newmark slope sliding models (D_n). The consequence Eq. (1) describes their work in the best possible light:

Log D_n = 0.9 + Log ((1 - a_c / a_max) ^2.53 × (a_c / a_max) ^−1.09) ± 0.3; (1)

where the term a_c represents the critical acceleration (measured in g), a_max represents the maximum acceleration recorded in a strong-motion record, D_n is in centimeter units, and the last term indicates the model’s estimation error. According to Newmark analysis, sliding is caused by input accelerations exceeding critical accelerations (a_c), and the block keeps sliding until zero relative velocity is achieved between the block and the ground surface [11, 12]. The critical acceleration is the acceleration that causes the factor of safety to reach 1.0:

a _c = (F.S − 1) gsin α; (2)

where g is the acceleration of gravity, F.S is safety factor, and α is angle between the sliding surface and the horizontal. Jibson [12] derived the following regression Eq. (3) by analyzing 11 strong-motion records:

Log D_n = 1.46 Log Ia − 6.642 a_c + 1.546 ± 0.409; (3)

where Ia is the Arias intensity (in meters per second). In light of that, the in situ measurements have shown that critical acceleration can be effectively normalized by the maximum ground acceleration (a_max). Therefore, Jibson [2] developed the regression Eq. (4) with all logarithmic terms:

Log D_n = 0.561 Log Ia − 3.833 Log (a_c / a_max) -1.474 ± 0.616 (4)

Rathje and Saygili [13] proposed Eq. (5) by interfering combinations of M_w, Ia, and a_max:

Ln D_n = 4.89–4.85 (a_c / a_max) − 19.64 (a_c / a_max)² + 42.49 (a_c / a_max)³ − 29.06 (a_c / a_max)⁴ + 0.72Ln (a_max) + 0.89 (M_w -6) + 0.789 (a_c / a_max) − 0.539 (a_c / a_max)² + 0.732; (5)

In this case, the scalar model standard deviation as a second-order polynomial is represented by the last three terms. Hsieh and Lee [1] developed regression equations for both global and local purposes. They also considered both soil and rock site conditions. Eq. (6) has the goodness of fit and less estimation error:

Log D_n = 0.847 Log Ia − 10.62 a_c + 6.587 a_c × Log Ia + 1.84 ± 0.295 (6)

In addition, Paulsen and Kramer [14] developed a practical model for assessing post-earthquake serviceability after earthquakes by estimating the permanent displacement of reinforced slopes. As a result of their study, it was demonstrated that the model is capable of predicting critical acceleration and permanent displacement reasonably well. Mojallal et al. [15] proposed an approach for calculating the coefficient of critical acceleration and displacements in the permanent phase of GRS walls. In this way, in accordance with Newmark’s sliding block method and upper-bound theory, groups of charts have been proposed to predict the permanent displacements due to sliding. Using the horizontal slice method and limit equilibrium. Varzaghani and Ghanbari [16] proposed a novel approach to investigate displacement of slope-adjacent foundations due to seismic activity. It is determined that the critical failure surface for different failure surfaces is the surface with the maximum strain calculated dynamically. According to the comparison, the suggested model can accurately predict seismic displacements. In addition, it was demonstrated that with an increase in slope angle and decreasing distance between the slope edge and foundation, seismic displacement increased in a non-linear manner. Du et al. [11] evaluated different types of Newmark analysis using intensity measures (IMs) considering uncertainty sources. It was found, indeterminacy for the vector-IM remains stable during ground motions magnitude and site conditions. In the end, a procedure is carried out to arithmetic uncertainty sources for a completely probabilistic Newmark slope sliding model, also it was shown that unit weight would not noticeable effects on the displacement. Liu et al. [17] employed a FEM procedure to study the seismic responses of GRS walls in the presence of different near-field earthquakes. The study investigated interaction between the ground-motion parameters, reinforcement’s forces, and lateral displacement. It was concluded that the Arias intensity is associated with the maximum reinforcement tensile strength, and the displacement is also influenced by these two parameters. Song et al. [18] investigated the effect of earthquake orientations on the probabilistic seismic displacement of slopes. Anticipant correlation of orientation- independent seismic deformation are expanded for various kind of earthquake. Statistical evaluation of ground motion-induced landslide risk was carried out for assumptive slopes, and the sliding landslide risk maps and the earthquake selection method for site condition assessment of slopes were introduced by including the impact of earthquake orientation in various kind of earthquakes. Geotechnical engineering faces a number of significant challenges when it comes to slope stability analysis since it is mathematically challenging to determine the critical slip surface of earth slopes. In an unreinforced earth slope, several methods can be used to estimate the minimum factor of safety for non-circular slip surfaces; however, for a reinforced soil slope, it cannot easily be calculated due to the additional effect of reinforcement. The particle swarm optimization (PSO) method can be used to search the critical slip surface efficiently. Shinoda and Miyata [19] calculated the slope safety factors for both reinforced and unreinforced soil slopes by considering force and moment equilibrium. To begin, sensitivity analyses were conducted to investigate the effects of PSO parameters on safety factors. An appropriate PSO parameter range for calculating the safety factor in unreinforced and reinforced soil slopes was determined based on this analysis. Sharafi and Maleki [20] employed a reinforced slope to multi-dimensional seismic loading combinations in order to assess seismic performance of the reinforced sandy slopes. They implemented reduced-scale laboratory models of a shaking table alongside the 3D explicit finite difference method. They concluded that the long-term lateral sliding displacement of the slope has the greatest impact among the combination of the axial components of motion records. The findings have also demonstrated a straightforward logarithmic connection between several intensity indicators and the lateral displacement of a reinforced sandy slope. Because of the mechanism of slope movement caused by earthquakes, and the criteria for seismic performance or failure state, assessing the seismic stability of earth slopes has long been a challenge in geotechnical engineering. A study of rotational sliding mass failures on seismic slopes was performed by Ji et al. [21] in order to resolve these issues. By integrating Newmark's sliding block theory with rotational displacement computations, the authors extended Newmark's analysis of permanent displacement. In addition, they proposed a simplified relationship between a circular failure mass's rotational and horizontal motions. To calculate the reliability index, which can be viewed as a substitute for the probability of failure, uncertainties of soil properties were introduced. A substantial amount of research has been conducted in geotechnical engineering regarding evaluation of seismic stability. In order to address this issue, Ji et al. [22] developed a revised sliding block model incorporating shear strength and dynamic critical acceleration. Additionally, the probabilistic seismic slope displacement distribution was recalculated by incorporating the uncertainties associated with the ground motion. According to their findings, displacement and Arias intensity are approximately linearly correlated on a logarithmic scale. Choudhuri and Chakraborty [23] conducted an analysis of a two-layer cohesive-frictional soil system to determine its probabilistic bearing capacity based on soil spatial variability. It is considered that the cohesion and friction angle of both layers are random fields with lognormal distributions. Numerical analyses were performed using the finite difference code. In order to estimate the bearing capacity of the footing, the Monte-Carlo simulation technique was used. Additionally, the study reviewed the effects of cross-correlation between friction angle and cohesion on the probabilistic properties of bearing capacity and failure probability. Due to significantly high estimates for the standard deviation of existing prediction equations, Nayek and Gade [24] prompted to develop new data-driven prediction models based on artificial neural network technology. Predicting slope displacement is accomplished by combining parameters associated with ground-motion characteristics with the slope's critical acceleration value. A dataset containing 13,707 data points of slope displacement was used to generate several prediction models, including scalars and vectors. The models perform well according to their efficiency. Tiwari and Lam [25] analyzed the displacement of retaining walls (RW) with base restraints during an earthquake. After shaking table experiments were performed on a reduced-scale RW model, an exhaustive finite element analysis (FE) was carried out. There were also investigations into the impact of different backfills on the seismic performance of RWs. Based on the observations, cohesionless backfill may slightly affect the displacement of base restrained RWs. An analytical model has been developed for estimating earthquake-induced displacement of base restrained RW based on results from shaking table experiments and FE simulations. In practice, soils are usually unsaturated, but the traditional approach to evaluating the stability of geosynthetic-reinforced soil structures (GRSSs) is conducted under either completely dry or saturated conditions. Because of suction-induced effects, Deng and Yang [26] developed a useful analytical method for determining the reinforcement strength required for preventing slope failure of unsaturated GRSSs under steady infiltration conditions, based on the reinforcement effect of geosynthetics. According to the results, suction stress plays a more significant role in determining the required normalized reinforcement than tensile strength cut-offs. Nazari et al. [27] examined the probabilistic stability of tiered GRS walls under seismic loads, taking into account soil spatial variability and cross-correlation between input variables. The critical slip surface was identified using random limit equilibrium methods (RLEM). Based on the results, increasing the coefficient of variation from 5 to 15% increased the failure probability from zero to around 9%, raising serious concerns about the stability of the GRS walls. Additionally, it was determined that the probability of failure decreased as the negative cross-correlation between soil cohesion (c) and soil friction angle (φ) increased. Furthermore, the random finite element method (RFEM) approach produces a higher factor of safety in comparison to circular and non-circular RLEMs, with a difference of approximately 6% from Sarma's method. The proposed formula develops a shear strength reduction method and incorporates the effects of the inertial forces acting on the reinforced soil. This allows for a more accurate estimation of the sliding displacement of the reinforced soil. A novel numerical-simulation-based slope reliability analysis (NSB-SRA) method was proposed by Chen et al. [28] to decrease the time required for slope reliability assessment when considering spatial variability. In the first step of building a multivariate adaptive regression spline (MARS) model, the dual dimensionality reduction technique was employed to greatly reduce random variables. Following that, NSB-SRA was performed on samples selected by response conditioning method based on MARS models predictions. As a final step, two examples of slopes with spatially variable slopes are presented in order to validate the proposed method. According to the results, MARS in combination with FDM can perform NSB-SRA efficiently. Co-seismic landslides are often triggered by earthquake-induced soil displacement on slopes. In this regard, Ji et al [29] developed Newmark slope sliding model that takes into account both vertical and horizontal ground motions when estimating dynamic pore water pressure. Using the proposed model, the continuous variations in seismic yield acceleration at almost saturated and unrestricted soil slopes can be quantitatively described. As a result, the frequency distribution characteristics of the ground motions can be reasonably used to predict the accumulated seismic displacement. Various researchers used the modified Newmark sliding displacement method in order to identify slopes at risk for landslides resulting from a future earthquake. Using the Newmark slope sliding displacements method, Cheng et al. [30] developed a deep neural network (DNN) prediction and a hybrid prediction models using ground-motion severity indicators. Across a broad range of slope conditions, a significant number of ground motions and critical accelerations (a_c) samples were used to generate the proposed model. Comparing the proposed model with conventional regression models, significant reductions in standard deviation can be achieved. To demonstrate its effectiveness in engineering applications, the proposed model were applied in probabilistic slope displacement hazard analyses. Furthermore, geosynthetic-reinforced pile-supported embankments (GPEs) are currently the most commonly used method for practical projects. Xie et al. [31] proposed pile-supported geosynthetic-reinforced soil wall (PGSW) technology for widening embankments using a centrifugal model. Additionally, the cut slope ratio of the existing embankment in PGSW was analyzed using finite difference numerical models. In the PGSW-based technology, the settlements of the existing embankment and the widened portion were smaller than in the GPE-based technology.

The current study developed a performance function for slopes with geosynthetic reinforcement layers. The approach used numerical simulations, statistical analysis, and ground-motion data, which designed 12 control parameters for the slope. Even though the present study followed the same directions as previous investigations, it has undergone an evolutionary phase. Several important differences distinguish the present study from previous research. This study provides a computation programming code using Wolfram Mathematica for calculating displacement based on double integration of acceleration time-history. Consequently, this approach is able to estimate the maximum sliding displacement of reinforced slopes for varying soil, geosynthetics, and seismic conditions. By developing a stochastic model predictive approach and integrating advanced optimization search techniques, an innovative framework for estimating probabilistic lateral sliding displacement of GRS slopes is proposed, utilizing Newmark's sliding block analysis as a basis. The complementary optimization search techniques in conjunction with non-circular methods in this study are part of a comprehensive investigation that improves the accuracy of seismic sliding displacement measurements compared with previous studies. As part of this study, a synthetic dataset containing 972 data points was also generated regarding the seismic sliding of geosynthetic-reinforced soil slopes under strong-ground motion data based on numerical analysis results. Unlike previous studies that focused mostly on unreinforced slopes, this study simulates the realistic behavior of GRS slopes taking into account several uncertainty sources such as soil spatial variabilities, reinforcement properties, and failure surfaces. It also examined combinations of seismic characteristics relating to displacement (Log D_n) as well as Housner intensity (HI), moment magnitude (M_w), closest distance to the rupture surface (R_rup), and significant duration (T_5 − 75). Furthermore, this study examined the critical accelerations and cumulative permanent displacements of GRS slopes based on slope properties and seismic motion characteristics. A further originality is that the study illustrates the relationship between motion characteristics such as Arias intensity and critical acceleration ratio on a logarithmic scale. It was concluded, the slope performance is strongly influenced by this factor under operational conditions. Using Spearman correlation coefficients, the most influential motion characteristics are identified, and further insight is gained into geosynthetic-reinforced soil slope dynamics. As a result of the verification, it is confirmed that the proposed formula is well adapted to previous research results.

This study evaluated probabilistic estimates of Newmark slope sliding analyses using 5000 Latin-hypercube samples through surface altering optimization based on the limit equilibrium method. There is a constraint on the bottom boundary condition of the model in both x and y directions, whereas the lateral boundary conditions are only fixed in x-direction. There are 50 slices in the slope across the geometry of the model. In order to generate formulation, four multi-level variables including soil friction angle (φ), length of the geogrid (L/H), geogrid tensile strength (T), and vertical space of the geogrid layers (S_v) were defined. The soil friction angle (φ) is varied from 35 to 45 degrees. The normalized length of the geogrid (L/H) is varied between 0 to 1.6. The vertical space of the geogrid layers (S_v) is varied between 0.4 to 0.8 meters, and the tensile strength of the geogrid reinforcement is varied between 0 to 100 kN/m. A numerical model is developed using the software Slide 2018 [32]. It is possible to identify the critical slip surface with the lowest safety factor through advanced search algorithms. Properties of the selected geosynthetics, derived from several manufacturers, including Maccaferri and Tensar, will be provided. Further information is available on the manufacturer's specification sheet. In its offering of numerical modeling, the authors employed the most comprehensive and practical solutions. As the highest quality assurance practices are utilized throughout the manufacturing, Tensar uniaxial geogrids are designed to provide high tensile strength at low strains, which is ideal for mechanically stabilizing earth walls and reinforced soil slopes. The authors are confident that their model is based on robust technology, profound expertise, and extensive field experience. This confidence stems from the longstanding industry leadership of Tensar, which has set the industry standard for over three decades.

A schematic form of the geogrid-reinforced slope is shown in Fig. 2. The tags were added to Fig. 2 to indicate the numerical domain size. Furthermore, the numerical model should be sufficiently large to avoid being affected by dimensional constraints. The slope is inclined at an angle of 60 degrees to the ground surface. Given the constraints of the fixed slope angle, it was normalized using integration, as follows:

\({\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\text{T}\text{a}\text{n} {\alpha }\) = - ln |cos(α)| \({|}_{\frac{\pi }{6}}^{\frac{\pi }{3}}\) (7)

This normalization process mitigates the influence of slope angle and achieves a more generalized result across various GRS slope angles from 30̊ (π/6) to 60̊ (π/3). This general solution is truly independent of geometric configurations due to its dimensionless parameters.

This investigation was conducted using Spencer's method, which produces accurate results, especially under seismic conditions. Seismic records are examined for both positive and negative acceleration data points to compute displacement. The displacement direction is further defined by the downslope. There are three major factors considered in coupled and decoupled approaches, including shear wave velocity (material above/below slip surface), damping ratio (ζ = 5%), and reference strain (0.05%). Shear strength of the soil mass as well as reinforcement elements, are considered in calculating yield acceleration. Ultimately, it is worth noting that the analysis in slide 2018 is based on the program slammer, developed by the U.S. Geological Survey.

2.1. Materials

A c-φ soil similar to Firuzkuh 161 crushed silica sand, used for reinforced and backfill soil zone [33]. For numerical modeling of the soil, the Mohr-Coulomb failure criterion was used. The material properties and detailed information about the variable parameters is listed in Table 1 to generate a synthetic dataset. The soil unit weight (γ), soil cohesion (c), soil friction angle (φ), and geogrid tensile strength (T) modeled as normally and log-normally distributed random variables. The CVs and types of distribution for γ, c, φ, and T are given in Table 2.

Table 1

Reinforced slope geometry and material properties values
Parameter	Value
Reinforced slope height, H (m)	6
Slope batter (degree)	60
Soil properties
Internal friction angle, φ (degree)^{a, b}	35, 40, 45
Young’s modulus, E (MPa)	40
Poisson’s ratio, ν	0.3
Unit weight, γ (kN/m³)^b Cohesion, c (kPa)^b	17.325 5
Reinforcement properties
Reinforcement type	Geogrid
Tensile strength, T (kN/m) ^{a, b}	10, 20, 30
Shear strength type	Linear elastic
Vertical space, S_v (m) ^a	0.4–0.8
Reinforcement length, L/H ^a	0.4-1.0
Note: Cohesion and friction angle are spatially correlated (coefficient of correlation: − 0.5)
^a Parameters used to generate a synthetic database parametric study
^b Random variables with uncertainty sources

Table 2

CV values and distribution types of random variables
Random variable	CV (%)	Distribution	Source
Soil unit weight, γ (kN/m³)	5	Normal	[34]
Soil friction angle, φ (degree)	10	Log-Normal	[35]
Geogrid tensile strength, T (kN/m) Soil cohesion, c (kPa)	10 30	Normal Log-Normal	[36] [34]

2.2. Ground motion data

A list of thirty earthquake strong-motion records used in this study is presented in Table 3. The maximum velocity (v_max) ranges between 0.13 m/s and 1.24 m/s, and its moment magnitude (M_w) lies between 5.4 and 7.9. Over 26.6% of the records in the generated dataset have maximum acceleration in excess of 0.7g, and about one-third of the records are located within 5 km of the source (R_rup). There are several earthquake records with significant time durations (T_5–95) between 2.9 and 31.2 seconds have been considered in this study, and T_5–75 in the bandwidth of 1.0 to 20.8s. Figure 3 shows the moment magnitude range and fault mechanism types of earthquakes. The Housner intensity (or response spectrum intensity) variations considered in Eq. (6), which defined as follows:

Table 3

Strong ground motions data used in the present study
Earthquake	Maximum acceleration, a_max (g)	Arias intensity, Ia (m/s)	Significant period, T_5 − 75 (s)	Maximum velocity, V_max (m/s)	Housner intensity, HI (m)
Bam, Iran, 2003	0.80766	8	5.6	1.24	3.89
Cape Mendocino, USA, 1992	0.59079	3.8	6.5	0.49	1.61
Chi-Chi, Taiwan, 1999	0.35869	2	20.8	1.1	1.76
Christchurch, New Zealand, 2011	0.37135	3.6	4.4	0.48	2.53
Chuetsu-oki, Japan, 2007	0.30313	2.3	7.3	0.49	1.62
Coyote Lake, USA, 1979	0.23291	0.6	5	0.26	0.70
Darfield, New Zealand, 2010	0.7645	4.7	5.6	1.16	3.70
Denali, Alaska, 2002	0.3326	1.9	9.1	1.16	3.28
Duzce, Turkey, 1999	0.30336	1.86	3.5?	0.39	0.72
El Mayor-Cucapah, Mexico, 2010	0.25507	1.9	10.1	0.55	1.06
Honduras-Guatemala, 1986	0.70423	2.5	1.3	0.8	2.22
Imperial Valley, USA, 1979	0.34081	1.7	2.8	0.51	1.23
Irpinia, Italy, 1980	0.12965	0.4	5.2	0.23	0.80
Kalamata, Greece, 1986	0.16137	0.3	1	0.13	0.31
Kermanshah, Iran, 2017	0.6844	3.3	10	0.57	1.65
Kobe, Japan, 1995	0.83423	8.4	4.3	0.91	3.63
Kocaeli, Turkey, 1999	0.22675	1.3	7	0.7	1.55
Landers, USA, 1992	0.13046	0.2	12.3	0.2	0.52
L'Aquila, Italy, 2009	0.66405	2.8	4.9	0.4	1.31
Loma Prieta, USA, 1989	0.55912	2.1	3.1	0.36	0.95
Montenegro, Yugoslavia, 1979	0.29275	1.8	9	0.43	1.59
Morgan Hill, USA, 1984	0.71338	3.9	3	0.53	1.59
Niigata, Japan, 2004	1.74227	10	2	0.54	1.07
Northridge, USA, 1994	0.55745	3.1	4.8	0.76	2.45
Parkfield, USA, 2004	0.31762	0.8	3.1	0.27	0.90
San Fernando,USA, 1971	1.21904	8.9	5.8	1.14	3.52
Superstition Hills, USA, 1987	0.11387	0.3	10.6	0.18	0.79
Tabas, Iran, 1978	0.85398	11.8	8.3	0.99	3.28
Tottori, Japan, 2000	0.31988	1.8	6.2	0.35	1.44
Westmorland, USA,1981	0.23208	0.7	6.2	0.56	1.24

HI= \(\underset{0.1}{\overset{2.5}{\int }}PSV \left(T,5\%\right) dT\) (8)

where PSV represents the pseudo-velocity response spectrum, T and ξ are the structural natural period and damping, respectively. An earthquake's magnitude of seismic motion severity measures the potential damage that may result from the earthquake. It is important to note that Housner intensity and displacement are measured in the same units. Figure 4 shows the Spectral response acceleration of earthquakes used in the present study.

In slope design, failure risk is evaluated based on the displacement calculation. The GRS slope properties and motion characteristics were analyzed to develop a suitable formula for predicting displacement. Based on the sensitive analysis results, four key control parameters were chosen as random variables. The variables included soil friction angle, soil cohesion, soil unit weight, and reinforcement tensile strength. To begin with, the slope geometry, boundary conditions, seismic loads, and material properties were specified. In the next step, random variables were analyzed using statistical measures such as means (µ), CVs, distribution type (normal, or log-normal), and cross-correlation coefficients. Afterward, slide software was used to conduct probabilistic numerical simulations. Accordingly, as discussed in the numerical modeling section, 5000 sets of random variables were generated using Latin hypercube sampling by means of simulated annealing optimization. Following the simulation, a revised dataset consisting of 972 numerical modeling analyses was then adjusted. Thereafter, the dataset was subjected to several regression analyses using SPSS software. In subsequent calibration steps, the coefficients are then calculated using threshold values of earthquake-induced displacements as measures of seismic slope performance. After fitting a regression-based equation, a proper equation was developed to predict the seismic sliding displacement of reinforced slopes considering soil spatial variability. For a better understanding of the methodology, an illustration of the steps involved in fitting a regression model and establishing a computational framework for GRS slopes is shown in Fig. 5. As a result of this study, a model consists of 12 variables can be formulated as follows:

Y = 𝛽 ₀ + \(\sum _{i=1}^{i=12}\beta\)_iX_i (9)

where Y represents the normalized displacement of the slope expressed on the logarithmic scale (Y = Log D_n/H), 𝛽₀ represents constant value, and 𝛽_i is deterministic coefficients. In contrast, X_i represents a set of parameters such as slope geometry, geogrid specifications, and motion characteristics as presented in Table 4. The values of deterministic coefficients are listed in Table 4, which aren't mentioned here to avoid overcrowding. Table 4 also offers an approximation for fast computation of seismic sliding displacement of geosynthetic-reinforced soil slopes. For each of the three types of analysis, the calculated results (D_n) are compared with the predicted values as illustrated in Fig. 6. Data plots should be attentively aligned around the one-to-one correspondence line, demonstrating that the described formula is accurate. The correlation coefficients are tagged to indicate the significance of parameters. According to Fig. 6, the displacement of reinforced slopes can be predicted well with a small scatter, especially if the displacement ranges between %0.01H and %1.0H. Table 5 describes Spearman correlation coefficients of motion characteristics with Newmark displacement on the logarithmic scale.

Table 4

Coefficient values for the proposed formula
Model Summary	Rigid analysis	Coupled analysis	Decoupled analysis
Model Summary	β Coefficients	β Coefficients	β Coefficients
(Constant)	-10.519	-7.336	-7.250
X₁: S_v/H	-10.244	-4.847	-4.971
X₂: T/γH²	23.608	12.385	13.708
X₃: L/H	1.731	0.719	0.790
X₄: Tan φ	4.442	1.147	1.303
X₅: log Ia (m/s)	0.832	0.919	0.703
X₆: log a_c/a_max	-15.957	-11.025	-11.863
X₇: Log Ia ×Log a_c/a_max (m/s)	1.365	1.105	1.527
X₈: Moment magnitude (M_w)	0.449	0.382	0.340
X₉: a_max (g)	-4.412	-2.566	-2.659
X₁₀: Housner intensity (m)	0.301	0.296	0.354
X₁₁: V_max (m/s)	-0.946	-0.856	-0.949
X₁₂: T_5 − 75 (s)	-0.112	-0.090	-0.106

Table 5

Spearman correlation coefficients of motions characteristics with log D_n/H
Correlation coefficient	log Ia	log a_c/a_max	Log Ia × Log a_c/a _max	M_w	a_max	Housner intensity	v_max	T ₍₅₋₇₅₎
Rigid	0.722	-0.826	-0.792	.122	0.669	0.347	0.407	− .067
Coupled	0.728	-0.844	-0.806	.117	0.677	0.343	0.4	− .060
Decoupled	0.678	-0.828	-0.778	.051	0.658	0.336	0.395	− .105

The material properties of twelve selected outcrop models and their respective applied earthquakes are provided in Table 6. In all cases, the critical acceleration is less than that of the peak ground acceleration, except for case number 5th, which led to zero sliding displacement. Additionally, statistical comparisons between the numerical sliding displacement computed by programmed code measures and the Newmark double integration procedure were provided in Table 6.

Table 6

Properties of twelve defined GRS slope models used for verification of programmed code measured
Case No.	Earthquake	Model configure				Result
		T (kN/m)	L/H	S_v (m)	φ (degrees)	a_c (g)	Displacement (mm)
		T (kN/m)	L/H	S_v (m)	φ (degrees)	a_c (g)	Slide software (Coupled approach)	Programmed code measured*
1	Cape Mendocino	10	0.7	0.6	40	0.418	4.19	4.35
2	Tabas	20	0.7	0.6	40	0.481	32.42	25.81
3	Tabas	30	0.7	0.6	40	0.52	20.15	21.52
4	Tabas	30	0.4	0.6	40	0.437	54.41	38.67
5	Landers	30	0.7	0.6	40	0.52	0	0
6	San Fernando	30	1.0	0.6	40	0.624	16.85	13.95
7	Bam	30	0.7	0.4	40	0.586	3.44	2.7
8	San Fernando	30	0.7	0.6	40	0.52	26.15	27.79
9	Niigata	30	0.7	0.8	40	0.47	101.94	104.802
10	Northridge	30	0.7	0.6	35	0.441	3.03	3.077
11	San Fernando	30	0.7	0.6	40	0.522	26.15	27.42
12	Niigata	30	0.7	0.6	45	0.614	59.99	48.97
Note: c = 5 kPa and γ = 17.325 kN/m³ for all cases.
* Programmed computation code using Wolfram Mathematica is provided in appendix

In Table 7 comparison has been made between the proposed formula in this study with those reported by equations conducted by others to predict earthquake-induced displacement. All researchers' equations (Eq. 1 - Eq. 5) are discussed and referenced in the introduction section. The presented equation includes more parameters than the previous ones, which only considered a few seismic motion characteristics, such as maximum acceleration or Arias intensity. Consequently, the authors strongly believe that the proposed regression-based equation provides the best representation for computing seismic lateral displacements of GRS slope. According to Table 7, the proposed model demonstrated satisfactory prediction accuracy compared with existing proposed equations, which is consistent with most engineering practices regarding displacement patterns. As previously mentioned, Table 6 provided a detailed description of the GRS properties case number.

Table 7

Comparison between the sliding displacement by proposed formula and results reported by other researchers.
Case No.	Displacement (mm)
Case No.	Ambraseys & Menu [10]	Hsieh & Lee [1]	Jibson [2]	Jibson [12]	Rathje & Saygili [13]^a	Proposed model
1	5.11	2.09	2.50	3.53	12.10	3.25
2	18.26	109.36	12.11	8.26	70.34	28.63
3	12.68	79.47	8.98	4.55	38.06	21.01
4	26.88	156.76	17.50	16.20	77.51	70.76
5	0	0	0	0	0	0
6	26.93	8.52	14.99	0.61	52.01	14.20
7	4.25	7.41	3.67	0.93	6.58	4.42
8	49.35	24.17	30.16	3.03	96.30	53.25
9	149.54	62.16	185.46	7.67	438.76	229.09
10	1.93	1.04	1.56	2.19	2.47	3.14
11	48.79	23.69	29.72	2.93	95.14	51.25
12	82.46	16.34	66.58	0.84	222.83	38.93
^a Scalar Model

Figure 7 shows schematic instrumentation of centrifuge model tests those of Nova-Roessig and Sitar [37], and a comparison of the proposed formula in the current study and their results. Their study evaluated the dynamic response of soil slopes supported by geosynthetics materials and metal grids using centrifuge tests. This study used prototypes with heights of 7.3 m and slope angles of 1H:2V (63.4°), also the four larger-scale tests (Nat1-N/S) which were verified to the proposed formula in this study were spun up to 19.2g. It should be noticed that critical acceleration in three levels of model height (at foundation, mid-height, and top) changes between 0.05g to 0.32g. According to the comparison with other methods, the proposed technique is able to predict the GRS slope sliding displacement with an acceptable level of accuracy.

The values in Table 4 provide an approximation of the fast estimate of the GRS slopes based on Newmark analysis. Using normalized slope properties enhances the utility of Eq. (9), which facilitates the comparison of predicted displacements. To gain a deeper understanding, based on coupled approach, Eq. (10) predicts normalized seismic sliding displacement of the GRS slope as follows, resulting in better fit (R²: 0.867) and less estimation error (0.323):

Log D_n/H =- 4.847 (S_v/H) + 12.385 (T/γH²) + 0.719 (L/H) + 1.147 (Tan φ) + 0.919 (Log Ia) − 11.025 (Log a_c/a_max) + 1.105 (Log Ia)× (Log a_c/a_max) + 0.382 (M_w) − 2.566 (a_max) + 0.296 (HI) − 0.856 (V_max) − 0.090 (T_5 − 75) − 7.336 ± 0.323 (10)

There is a finite sum of terms in this series expansion. Calculating the seismic sliding displacement of the GRS slope requires only inserting value of the parameters into the proposed series expansion. This study utilizes standardization terms to improve the applicability of seismic lateral displacement predictions. Academics and practitioners may find this equation useful and interesting.

A representation of soil spatial variables is illustrated in Fig. 8(a) and Fig. 8(b) provides an overview of the failure surface and critical acceleration. Based on the analysis of soil spatial variation, a failure surface with a minimum factor of safety perfectly matches with potential failure surface that shows with red color cells. Detailed results of the slope sliding displacements based on rigid, coupled, and decoupled approaches are provided in Table 8, consistent with codes and standards for specified horizontal sliding displacement as mentioned in Table 9.

Table 8

Displacement of reinforced slope based on the three types of Newmark method (a_c = 0.522 g)
Analysis	Displacement (mm)
Rigid	13.4
Coupled	19.5
Decoupled	9.8

Table 9

Codes or standards for specified horizontal sliding displacement
Codes or standards	Maximum lateral displacements
BS8006 [38]	0.5%
Geoguide6 [39]	0.5%
NGG [40]	0.1% − 0.3%
WSDOT [41]	0.4% in 3 m
EN 14475 [42]	50 mm
FHWA [43]	0.9% − 4%
AASHTO [44]	0.9% − 4%

5.1. Parametric study

An illustration of the critical acceleration of a reinforced slope varies as a function of the vertical distance between layers of geogrid can be seen in Fig. 9(a). According to Fig. 9(b), the critical acceleration increases as the tensile strength of geogrid increases to a maximum of T = 30 kN/m. After the value of T = 20 kN/m, critical acceleration increased slowly. Figure 9(c) shows the influence of normalized reinforcement length (L/H) on slope critical acceleration. As shown in this figure, increasing normalized reinforcement length ratio from 0.4 to 1.0 induced a fast increase in critical acceleration, especially from 0.7 to 1.0 an increase in growth rate was observed. Figure 9(d) shows the influence of the soil’s friction angle. This figure indicates that increasing the soil friction angle resulted in higher critical acceleration values (almost linear trend) resulting in lower slope displacements.

5.2. Statistical analysis

As shown in Fig. 10(a), using 5000 Latin-hypercube samples, the histogram provides the relative frequency distribution of the normalized displacement (D_n/H) taking uncertainty into account. As can also be seen in this figure, displacement follows a log-normal distribution. It is possible to estimate the probability of exceeding a given value using the cumulative distribution function (CDF) plots as shown in Fig. 10(b), which is useful for the development of performance-driven designs [45]. Integrating the probability density function (PDF) of the displacement results in a CDF [46]. In this case, a normalized displacement (D_n/H) of less than 0.72% is 90% likely, while there is no more than 10% probability that the displacement will be less than 0.12%.

A scatter plot obtained from the Slide software is shown in Fig. 11 to depict data from various random variables such as soil friction angle (φ), soil unit weight (γ), soil cohesion (c), and geogrid tensile strength (T) versus displacement. There were no specific values assigned to parameters with uncertainty sources. According to previous research (Table 2), the authors considered a normal or log-normal distribution for each of them in the numerical simulations. To clarify further, Latin-hypercube samples assigned random variable values for the parameters mentioned above. Consequently, Eq. (10) was derived through data analysis. According to this figure, an increase in the soil friction angle, as well as the tensile strength of the reinforcement will result in a decrease in displacement. In contrast, displacement is positively correlated with soil unit weight.

Based on the three types of Newmark slope sliding model, Fig. 12 shows the effect of four parameters on the displacement of geosynthetic-reinforced soil slopes. The following charts illustrate the average displacement caused by thirty earthquakes. It should be noted that due to small values for maximum acceleration (a_max) and high values for critical acceleration (a_c) of some earthquakes, there is no sliding displacement induced, resulting in lower average values. Meanwhile, some earthquakes such as Niigata, Kobe, Tabas, and Bam, induced more displacements. Based on the results shown in Fig. 12, coupled analysis results in higher sliding displacement for the GRS slope, whereas rigid analysis results in lower sliding displacement.

5.3 Effects of earthquakes motion characteristics on sliding displacement

In this study, a dataset based on 30 worldwide earthquakes is used to examine relationships between motion characteristics and slope displacements. According to the Jibson 93 and Jibson 98 models, when a_c is fixed, it is established that Log Ia and Log D_n are related. The Jibson 98 model also modified the relationship between the a_c and Log D_n [47]. In light of the fact that there is a relationship between Log D_n with respect to Log a_c and Log Ia, it can be concluded that there must be a relationship (linear or non-linear) between Log a_c × Log Ia, as well as other combinations of these two parameters concerning Log D_n. For each type of Newmark displacement analysis, the goodness of trend line fit was calculated separately for a_c/a_max × Log Ia, Ia × Log a_c/a_max, and Log Ia × Log a_c/a_max with log D_n. The relationship between motion characteristics and sliding displacement is plotted in Fig. 13. Therefore, the authors strongly believe that the logarithmic scale is ideal for showing the relationship between motion characteristics. In part, this is consistent with most engineering practices. Figure 14(a) shows the relationship between motion characteristics. This was accomplished by establishing a power trendline. The results were enhanced by creating a linear trendline on a logarithmic scale, as depicted in Fig. 14(b).

The proposed framework is expected to be more accurate and efficient than traditional methods, providing a reliable prediction of sliding displacement for geosynthetic reinforced soil slopes subjected to sliding forces. Sliding displacement is the movement of a slope or part of a slope when it can no longer support the weight of the material above it. This study systematically examined uncertainties and variabilities associated with the Newmark slope sliding models to predict displacements during an earthquake. A 2D simplified GRS slope was utilized to investigate factors such as the soil type, reinforcement, motion data characteristics, and other environmental variables on the critical acceleration and slope long-term displacement. This makes it more accurate than previous models that only considered a few of these factors. This approach could provide a deeper statistical perspective of slope displacements incorporating attribute effects of geosynthetic reinforcement within the Newmark slope sliding model framework. The authors have also found some gaps in our knowledge concerning geosynthetic reinforced soil slopes, which should be addressed in further research. A further investigation of soil constitutive models would be beneficial. Moreover, studying partially saturating soils would also be helpful, as fully saturating soils and dry soil mass would be less likely to occur. Based on the findings of this study, the following conclusions can be stated:

The proposed framework developed a stochastic model predictive approach to provide reliable probabilistic estimates of lateral sliding displacement for GRS slopes based on Newmark's sliding block analysis. In addition, a programming code was presented to compute fast sliding displacements of GRS slopes. Comparing the results of the provided equation in this study with the work of other researchers indicates the high accuracy of Eq. (10).
The seismic sliding displacement of the GRS slope can be calculated by inserting the value of the parameters into the proposed series expansion (Eq. 10).
Based on Fig. 12, coupled analysis computes a higher earthquake-induced sliding displacement of the GRS slope. In particular, this difference is reflected significantly by the soil friction angle changes. In some cases, the divergence between coupled and rigid values reaches up to one-third.
It has been demonstrated in previous studies that displacement in the logarithmic scale is closely related to Arias intensity in the logarithmic scale as well as critical acceleration ratio in the logarithmic scale. This study aimed to examine the relationship between GRS slope displacement in the logarithmic scale and combinations of Arias intensity and critical acceleration ratio (Log Ia × Log a_c/a_max). Results demonstrated that the interaction of earthquake characteristics is also associated with displacement in a reasonable manner.
Based on Spearman correlation coefficients for motion characteristics, Log Ia and Log a_c/a_max are more correlated with Log D_n/H than moment magnitude, significant duration, and maximum velocity (according to Table 5).
Regarding soil spatial variation of model properties, sliding displacement is most affected by the soil friction angle. For instance, in the Coupled method, increasing the soil friction angle from 35 ̊ to 40 ̊ will increase the critical acceleration by 0.08g, resulting in a decrease in normalized displacement (D_n/H) from % 0.734 (D_n = 4.404 cm) to % 0.335 ( D_n = 2.01 cm).
Housner intensity, a measure of possible damage resulting from an earthquake, is considered an important parameter to estimate seismic displacement of the GRS slope in this study. The Spearman correlation coefficient is estimated at 0.343 for this parameter in Table 5.
Using the proposed approach, predicting seismic sliding displacements of the geosynthetic-reinforced slopes with a small scatter is possible, especially when the displacement is between %0.01H and %1.0H (according to Fig. 6)

H: Slope height (= 6m) φ: Soil friction angle c: Soil cohesion γ_s: Soil unit weight D_n: Newmark slope sliding displacement FS: Factor of safety g: Acceleration due to gravity (= 9.81m/s²) v_max: Maximum velocity a_max: Maximum acceleration a_c: Critical acceleration M_w: Moment magnitude ν: Poisson ratio T_P: Predominant period T_m: Mean period T_5-75: Significant time duration Ia: Arias intensity R_rup: Closest distance to the rupture surface L/H: Normalized length of the geogrid ξ: Damping ratio S_v: Vertical space T: Tensile strength J: Axial stiffness R²: Goodness of fit ρ: Cross-correlation E: Elastic modulus k_h: Horizontal pseudo-static acceleration coefficient V_s: Shear wave velocity α: slope angle IM_S: Intensity measures HI: Housner intensity Y: Normalized displacement (logarithmic scale) β₀: Constant value β_i: Unknown deterministic coefficients X_i: Model parameter D_r: Relative density 2D: Two-dimensional GRS: Geosynthetic reinforced soil PDF: Probability density function RSM: Response surface method CDF: Cumulative distribution function CV: Coefficient of variation LEM: Limit equilibrium method RLEM: Random Limit Equilibrium Method FEM: Finite element method RFEM: Random Finite Element Method RBD: Reliability-Based Design FORM: first-order reliability method PSV: Pseudo-velocity response spectrum DNN: Deep Neural Network

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author Contribution

All authors contributed to the study including conception, methodology, numerical modeling, and data analysis. The first draft of the manuscript was written by Reza A. Nazari and all authors commented on the previous version of manuscript. All authors reviewed and approved the revised manuscript.

Acknowledgment

It is with great pleasure that the authors extend their deep profound gratitude to Rocscience Inc, especially Dr. Sina Javankhoshdel for their assistance. In addition, we also grateful to the Pacific Earthquake Engineering Research Center (PEER) at the University of California, Berkeley, for providing strong-motion recordings.

Data Availability Statement

The dataset generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Hsieh SY, Lee CT (2011) Empirical estimation of the Newmark displacement from the Arias intensity and critical acceleration. Eng Geol 122(1–2):34–42. https://doi.org/10.1016/j.enggeo.2010.12.006
Jibson RW (2007) Regression models for estimating coseismic landslide displacement. Eng Geol 91(2–4):209–218. https://doi.org/10.1016/j.enggeo.2007.01.013
Newmark NM (1965) Effects of earthquakes on dams and embankments. Geotechnique 15(2):139–160
Roy R, Ghosh D, Bhattacharya G (2016) Influence of strong motion characteristics on permanent displacement of slopes. Landslides 13(2):279–292. https://doi.org/10.1007/s10346-015-0568-3
Makdisi FI, Seed HB (1978) Simplified procedure for estimating dam and embankment earthquake-induced deformations. J Geotech Eng Div 104(7):849–867. https://doi.org/10.1061/AJGEB6.0000668
Lin JS, Whitman RV (1983) Decoupling approximation to the evaluation of earthquake-induced plastic slip in earth dams. Earthq Eng Struct dynamics 11(5):667–678. https://doi.org/10.1002/eqe.4290110506
Lashgari A, Jafarian Y (2013) Role of sliding block rotation on earthquake induced permanent displacement of earth slopes. In 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Kos Island, Greece
Rathje EM, Bray JD (2000) Nonlinear coupled seismic sliding analysis of earth structures. Journal of Geotechnical and Geoenvironmental Engineering 126(11): 1002–1014. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:11(1002)
Bray JD, Rathje EM (1998) Earthquake-induced displacements of solid-waste landfills. J Geotech GeoEnviron Eng 124(3):242–253. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:3(242)
Ambraseys NN, Menu JM (1988) Earthquake-induced ground displacements. Earthq Eng Struct dynamics 16(7):985–1006. https://doi.org/10.1002/eqe.4290160704
Du W, Huang D, Wang G (2018) Quantification of model uncertainty and variability in Newmark displacement analysis. Soil Dyn Earthq Eng 109:286–298. https://doi.org/10.1016/j.soildyn.2018.02.037
Jibson RW (1993) Predicting earthquake-induced landslide displacements using Newmark's sliding block analysis. Transp Res Rec 1411:9–17. http://onlinepubs.trb.org/Onlinepubs/trr/1993/1411/1411-002.pdf
Rathje EM, Saygili G (2009) Probabilistic assessment of earthquake-induced sliding displacements of natural slopes. Bull New Z Soc Earthq Eng 42(1):18–27. https://doi.org/10.5459/bnzsee.42.1.18-27
Paulsen SB, Kramer SL (2004) A predictive model for seismic displacement of reinforced slopes. Geosynthetics Int 11(6):407–428. https://doi.org/10.1680/gein.2004.11.6.407
Mojallal M, Ghanbari A, Askari F (2012) A new analytical method for calculating seismic displacements in reinforced retaining walls. Geosynthetics Int 19(3):212–231. https://doi.org/10.1680/gein.2012.12.00010
Varzaghani MI, Ghanbari A (2014) A new analytical model to determine dynamic displacement of foundations adjacent to slope. Geomech Eng 6(6):561–575. http://dx.doi.org/10.12989/gae.2014.6.6.561
Liu H, Hung C, Cao J (2018) Relationship between Arias intensity and the responses of reinforced soil retaining walls subjected to near-field ground motions. Soil Dyn Earthq Eng 111:160–168. https://doi.org/10.1016/j.soildyn.2018.04.022
Song J, Gao Y, Feng T (2018) Probabilistic assessment of earthquake-induced landslide hazard including the effects of ground motion directionality. Soil Dyn Earthq Eng 105:83–102. https://doi.org/10.1016/j.soildyn.2017.11.027
Shinoda M, Miyata Y (2019) PSO-based stability analysis of unreinforced and reinforced soil slopes using non-circular slip surface. Acta Geotech 14:907–919. https://doi.org/10.1007/s11440-018-0678-x
Sharafi H, Maleki YS (2019) Evaluation of the lateral displacements of a sandy slope reinforced by a row of floating piles: a numerical-experimental approach. Soil Dyn Earthq Eng 122:148–170. https://doi.org/10.1016/j.soildyn.2019.04.007
Ji J, Zhang W, Zhang F, Gao Y, Lü Q (2020) Reliability analysis on permanent displacement of earth slopes using the simplified bishop method. Comput Geotech 117:103286. https://doi.org/10.1016/j.compgeo.2019.103286
Ji J, Wang CW, Gao Y, Zhang L (2021) Probabilistic investigation of the seismic displacement of earth slopes under stochastic ground motion: a rotational sliding block analysis. Can Geotech J 58(7):952–968. https://doi.org/10.1139/cgj-2020-0252
Choudhuri K, Chakraborty D (2022) Probabilistic analyses of three-dimensional circular footing resting on two-layer c–ϕ soil system considering soil spatial variability. Acta Geotech 17(12):5739–5758. https://doi.org/10.1007/s11440-022-01701-7
Nayek PS, Gade M (2022) Artificial neural network-based fully data-driven models for prediction of newmark sliding displacement of slopes. Neural Comput Appl 34(11):9191–9203. https://doi.org/10.1007/s00521-022-06945-8
Tiwari R, Lam N (2022) Displacement based seismic assessment of base restrained retaining walls. Acta Geotech 17(8):3675–3694. https://doi.org/10.1007/s11440-022-01467-y
Deng B, Yang M (2022) Stability analysis of geosynthetic-reinforced soil structures under steady infiltrations. Acta Geotech 17(1):205–220. https://doi.org/10.1007/s11440-021-01195-9
Nazari RA, Sharafi H, Jafari H (2022) Probabilistic Assessment on the Performance of Tiered Geosynthetic Reinforced Soil Walls Using RLEM and RFEM. Int J Geosynthetics Ground Eng 8(6):74. https://doi.org/10.1007/s40891-022-00418-7
Chen L, Zhang W, Paneiro G, He Y, Hong L (2023) Efficient numerical-simulation-based slope reliability analysis considering spatial variability. Acta Geotech 1–23. https://doi.org/10.1007/s11440-023-02138-2
Ji J, Zhang W, Zhang T, Song J (2023) Seismic displacement of earth slopes incorporating co-seismic accumulation of dynamic pore water pressure. Earthq Eng Struct Dynamics 52(6):1884–1907. https://doi.org/10.1002/eqe.3851
Cheng Y, Wang J, He Y (2023) Prediction Models of Newmark Sliding Displacement of Slopes Using Deep Neural Network and Mixed-effect Regression. Comput Geotech 156:105264. https://doi.org/10.1016/j.compgeo.2023.105264
Xie M, Li L, Cao W, Zheng J, Dong X (2023) Centrifugal and numerical modeling of embankment widening over soft soils treated by pile-supported geosynthetic-reinforced soil wall. Acta Geotech 18(2):829–841. https://doi.org/10.1007/s11440-022-01611-8
Rocscience (2018) Slide2 Version 2018–2D Limit Equilibrium Slope Stability Analysis. Toronto, Ontario, Canada. https://www.rocscience.com/
Yazdandoust M (2017) Investigation on the seismic performance of steel-strip reinforced-soil retaining walls using shaking table test. Soil Dyn Earthq Eng 97:216–232. https://doi.org/10.1016/j.soildyn.2017.03.011
Duncan JM (2000) Factors of safety and reliability in geotechnical engineering. J Geotech GeoEnviron Eng 126(4):307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
Phoon KK, Kulhawy FH (1999) Evaluation of geotechnical property variability. Can Geotech J 36(4):625–639. https://doi.org/10.1139/t99-039
Low BK, Tang WH (1997) Reliability analysis of reinforced embankments on soft ground. Can Geotech J 34(5):672–685. https://doi.org/10.1139/t97-032
Nova-Roessig L, Sitar N (2006) Centrifuge model studies of the seismic response of reinforced soil slopes. Journal of Geotechnical and Geoenvironmental Engineering 132(3): 388–400. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:3(388)
BS8006 (1995) Code of practice for strengthened/reinforced soil and other fills. British Standards Institution, Milton Keynes, U.K. https://books.google.com/books?id=2PbgPQAACAAJ
Geoguide 6 (2002) Guide to reinforced fill structure and slope design. Geotechnical Engineering Ofce, Civil Engineering Department, Hong Kong, China. https://www.cedd.gov.hk/flemanager/eng/content_116/eg6_200212.pdf: Accessed Dec 2002
Nordic Geosynthetic Group (NGG) (2005) Nordic guidelines for reinforced soils and flls. Nordic Geosynthetic Group, www.sgf.net. Accessed May 2015
WSDOT (2005) Geotechnical Design Manual, M 46–03, Chap. 15 Abutments, retaining walls, and reinforced slopes. Washington State Department of Transportation, Olympia, Washington, USA
EN 14475 (2006) Execution of special geotechnical works – reinforced fill. European Standard. https://books.google.com/books?id=LpQQAAAACAAJ. Accessed 31 Oct 2006
Holtz RD, Christopher BR, Berg RR (2008) Geosynthetic design and construction guidelines. US Department of Transportation, Federal Highway Administration, Washington DC, pp 07–092
American Association of State Highway and Transportation Officials (AASHTO) (2009) Interim LRFD bridge design specifications. 4th ed., Washington, D.C., USA
Lin BH, Yu Y, Bathurst RJ, Liu CN (2016) Deterministic and probabilistic prediction of facing deformations of geosynthetic-reinforced MSE walls using a response surface approach. Geotext Geomembr 44(6):813–823. https://doi.org/10.1016/j.geotexmem.2016.06.013
Huang Y, Hu H, Xiong M (2018) Probability density evolution method for seismic displacement-based assessment of earth retaining structures. Eng Geol 234:167–173. https://doi.org/10.1016/j.enggeo.2018.01.019
Jibson RW, Harp EL, Michael JA (2000) A method for producing digital probabilistic seismic landslide hazard maps. Engineering geology 58(3–4): 271–289.
https://doi.org/10.1016/S0013-7952(00)00039-9

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Stochastic model predictive approach for seismic lateral displacement of geosynthetic- reinforced soil slopes based on Newmark's sliding block analysis

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Abstract

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1. Introduction

2. Numerical modeling

2.1. Materials

2.2. Ground motion data

3. Proposed model to estimate the Newmark displacements for GRS slopes

4. Verification

5. Results and Discussion

5.1. Parametric study

5.2. Statistical analysis

5.3 Effects of earthquakes motion characteristics on sliding displacement

6. Conclusions

Notation

Declarations

Competing Interests

Funding

Author Contribution

Acknowledgment

Data Availability Statement

References

Additional Declarations

Supplementary Files

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