Two-layered Slopes Research Articles

Upper Bound Analysis of Two-Layered Slopes Subjected to Seismic Excitations Using the Layer-Wise Summation Method

Due to natural sedimentation and artificial filling, slopes exhibit heterogeneity in the form of multi-layer soils, namely, layered slopes. Compared with homogenous slopes, the failure mechanism of layered slopes is more complex owing to the different shear strengths of each soil layer. Therefore, it is of great importance to gain insight into the stability of layered slopes. In this study, the upper bound theorem of limit analysis incorporated with a pseudo-static approach is utilized to investigate the seismic stability of two kinds of two-layered slopes: one with a stiff lower soil layer and the other with a weak lower soil layer. Three failure patterns, namely face failure, toe failure and base failure, are taken into account. A depth coefficient (Δ) is introduced to describe the distribution of two soil layers. The layer-wise summation method is adopted to calculate the safety factor and yield acceleration coefficient more conveniently. Based on Newmark’s method, the earthquake-induced horizontal displacement is estimated. The calculated results are validated by comparisons with published literature and the numerical method in terms of safety factor, critical failure surface and yield acceleration coefficient. The results show that the depth coefficient has a significant influence on the failure mechanism of two-layered slopes by determining whether the stability of upper-layered soil is dominant in the overall slope stability or not. Inaccurately identifying the failure patterns will overestimate the seismic performance of two-layered slopes in the aspects of safety factor and yield acceleration coefficient, leading to an underestimation of earthquake-induced horizontal displacement.

Efficient reliability assessment of slope stability with insightful sensitivity analysis concerning the safety factor

The limit state functions (LSFs) of slope stability are nonlinear, implicit, or derived from numerical simulations, and additional surrogate models are usually used for its reliability problems. Alternatively, an efficient numerical procedure using a variant of the HLRF-BFGS algorithm is proposed to address this issue without additional surrogate models. This proposed procedure simultaneously conducts reliability assessment and sensitivity analysis concerning the safety factor by suggested calculations of partial derivatives using the finite difference method (FDM). Two highly nonlinear numerical examples are presented to validate its convergence and to investigate the step length of the FDM. Results show that the proposed procedure can get considerable accuracy while the HLRF algorithm cannot converge, and its required iterations are about 30% and 81% less than those of the limited step-size iteration algorithm. In addition, a step length not greater than 0.1 is suggested after investigations. Application to a classical two-layered slope is illustrated. Reliability results show that the proposed procedure can get the same accuracy as those of surrogate models after only 5 iterative steps. Sensitivity results show that the cohesion of the upper soil is the only sensitivity factor, and the most possible potential slide surface lies in the upper soil.

Three-dimensional stability analysis of two-layer slope based on GIS under rainfall conditions

ABSTRACT Geographical Information System (GIS), as a computer-based tool, allows easy data processing, and complex geospatial data management and analysis, making it a suitable environment for 3D slope stability analysis. The study proposed an integral scheme for 3D stability analysis of a two-layer slope under rainfall conditions based on GIS. To construct the 3D model of the slope and the sliding surface in GIS, a method was proposed in which a grid is divided into four sections to improve the accuracy of calculation, and the extension of the Hovland model and the Janbu model in unsaturated soil was discussed. The transformation equations between the global coordinates and the ellipsoid local coordinates were derived to locate the critical sliding surface, and how to apply constraints of parameters to improve search efficiency was put forward. An infiltration model for a two-layer slope was built so that the changes in water content in slope at the both stages of rainwater infiltration and redistribution can be determined, and the model was integrated into the GIS-based scheme to assess the impact of rainfall on slope stability. Finally, two case studies were implemented to demonstrate the validity and correctness of the proposed scheme.

Quantitative bearing capacity assessment of strip footings adjacent to two-layered slopes considering spatial soil variability

Quantitative bearing capacity assessment of strip footings adjacent to two-layered slopes considering spatial soil variability

Risk assessment of a layered slope considering spatial variabilities of interlayer and intralayer

While many studies have analyzed the effects of spatial variabilities of intralayer soil parameters on the probability of failure and risk of layered slopes, there is a paucity of research on the effects of interlayer variability. This paper is intended to investigate the influence of interlayer variability on the mechanical responses of a layered slope, as well as the effects of spatial variabilities of strength parameters of intralayer soils. To characterize the uncertainty of intralayer and interlayer spatial variabilities of layered geologic profiles, an integrated random field is developed using the program of FLAC based on both the two-dimensional random field theory and one-dimensional random process theory. Particularly, the random field for the interlayer transition zone is generated by a linear interpolation technique. Within the framework of Monte-Carlo simulation, a large number of stochastic calculations for a two-layered slope are conducted to evaluate the influences of spatial variabilities of both interlayer and intralayer on the stability and risk of the slope. The results show the failure mode of a two-layered slope changes greatly due to the stochastic layered boundary. It is also noted that the probability and risk of slope failure might be underestimated if ignoring the uncertainty arising from layered boundary and layered transition zone. The proposed equations can provide helpful information when investigating the probability and risk associated with layered slopes.

Multi-objective optimization design of pile-anchor structures for slopes based on reliability theory considering the spatial variability of soil properties

Pile-anchor structures (PAS) are emerging as a promising tool for slope stabilization and landslide mitigation. However, the optimized design of PAS is an essential yet challenging issue. In particular, there is an irreconcilable contradiction between the safety and cost-efficiency in PAS design, and a coordinated balance between these two factors is critical for safe and practical applications. Previous optimization design studies rarely considered the uncertainty of PAS-reinforced slope systems while the spatial variability of soil properties has a significant impact on the optimization design. This study, therefore, proposes a framework for the multi-objective optimization design of PAS in slopes based on reliability theory and in consideration of the spatial variability of soil properties. The study is automated by coupling a multi-objective optimization design using Pareto optimality theory and PAS-reinforced slope simulations using Monte Carlo simulations to consider the spatial variability of soil properties. An illustrative example of the PAS design for a two-layer slope is provided to demonstrate the proposed framework. The results suggest that the optimal PAS design achieved meets the minimum failure probability and has the lowest total cost. This study aims to motivate the subsequent development of optimization design for slope engineering.

Risk assessment of soil slope failure considering copula-based rotated anisotropy random fields

In natural slopes, apart from isotropic and transversely anisotropic soil fabric, rotated anisotropic soil fabric is also commonly observed due to deposition and weathering. Previous studies mainly focused on the effects of copula selection on transversely anisotropic soil slope stability. However, the influence of copula selection on rotated anisotropically deposited soil slope stability is still not clear. This study develops a new method to generate copula-based rotated anisotropy random fields for characterizing the spatial variability of soil properties. The index associated with the failure probability and consequence is employed to assess the risk of failure of two cohesive-frictional slopes in spatially variable soils (i.e., a single- and a two-layer slope). The results reveal that the commonly-used Gaussian copula may underestimate the risk of failure of both the single- and two-layer slopes at any soil deposition orientation. The risk of slope failure calculated by four candidate copulas shows a great difference. This difference is mainly affected by slope failure probability. For a single-layer cohesive-frictional slope, the slope with the highest risk of failure occurs at a rotational angle β = 150°. The corresponding soil deposition orientation (30°) is slightly smaller than the slope inclination (45°), independent of copula types. Additionally, when a slope fails, it can be found that the Gaussian copula corresponds to the largest sliding volume for some combination anisotropy cases, which is in reverse to the failure probability. Therefore, for a cohesive-frictional slope, it is suggested to consider both failure probability and failure consequence to assess the potential slope failure risk. Furthermore, the No.16 copula can give a more conservative risk assessment when dependence structure between cohesion and friction angle is uncertain.

Undrained seismic bearing capacity of strip footings horizontally embedded in two-layered slopes

This study investigated the undrained seismic bearing capacity of strip footings embedded in two-layered slopes by finite element limit analysis (FELA); in particular, a pseudostatic method was specified to seismic loads. Lower bound theory (LB), upper bound theory (UB), and adaptive meshing technique are employed for exploring the effect of the shear strength ratio of top layer and bottom layer, cu1/ cu2; the horizontal embedment depth of footings, b/ B; the footing locations (in bottom layer or top layer); seismic coefficient kh; and the slope gradient β on seismic bearing capacity. Results indicated that the seismic bearing capacity would increase with the growth of horizontal embedment depth of footings. The comparison between the predictions obtained from the proposed method and the existing method was presented, and the failure mechanisms are further summarized.

Development of three-dimensional failure mechanisms and genetic algorithm for limit analysis of two-layer slopes

This paper develops general three-dimensional kinematically rotational failure mechanisms for two-layer soil slopes, which not only considers the back slope angle but also involves the face-failure, toe-failure and base-failure mechanisms. Although the failure mechanisms are developed for two-layer soil slopes, it is easy to extend for multilayer soil slopes with the framework proposed in this study. Genetic algorithm (GA), which poses the advantages of highly computational efficiency over the traditional loop searching method, is developed to search for the upper bound of the critical height of slope. The proposed mechanisms could perfectly reduce to the failure mechanism of single-layer slopes, and the results generated from the GA algorithm are more critical than those of other available approaches, which indirectly identifies the validity of the current analysis and shows the advantage of the GA algorithm. Parametric studies, which cover a wide range of soil slope angle, back slope angle, relative layer thickness and soil strength as well as the width of restriction, are performed to investigate the transformation of the failure mechanism and the corresponding the critical height of two-layer slopes.

Undrained stability analysis of eccentrically loaded strip footing lying on layered slope by finite element limit analysis

In this study, the undrained stability of eccentrically loaded strip footing lying on two-layered slopes was investigated by self-developed adaptive finite element limit analysis (AFELA) code. Upper bound (UB) and lower bound (LB) results of bearing capacity factors Nc within 5% relative error were obtained to quantify the effects of several factors, including the strength ratio, the undrained shear stress ratio, the thickness of the top layer, the slope angle, the edge distance, the load eccentricity, and especially the different load eccentricity was analyzed. Typical failure patterns were also discussed for deeper insight into the footing-slope system. Meanwhile, the results from AFELA code were compared with previous studies to verify the reliability of this investigation.

Undrained seismic bearing capacity of strip footings lying on two-layered slopes

Abstract In this study, finite element limit analysis (FELA) is employed to investigate the undrained seismic bearing capacity of strip footings placed on two-layered slopes. Upper bound theorem (UB), lower bound theorem (LB) and adaptive meshing technique were used in parametric studies to investigate the effects of various factors on seismic bearing capacity Ncs and failure mechanism, especially the seismic coefficient kh and the shear strength ratio of top layer and bottom layer cu1/cu2. The angle of the slope β, the absolute strength of top layer cu/γB, horizontal offset distance b and the thickness of top layer D are also taken into consideration. Furthermore, the comparisons between present study and previous studies are provided. Detailed design tables are presented to distinguish the failure patterns and estimate the seismic bearing capacity of slopes under different conditions.

Robust Geotechnical Design for Soil Slopes considering Uncertain Parameters

Designing the geometry of soil slope is an effective treatment for preventing slope failure. How to deal with the uncertainties involved in soil parameters in geotechnical design is a main concern of geotechnical engineers. In this study, a robust geotechnical design for soil slopes (RGDS) approach was proposed, in which the Uncertainty Theory was introduced to describe explicitly the uncertainties involved in soil parameters. The uncertain reliability is often used to describe the risk of slope failure. The design robustness describing the insensitivity between the variation in the system response and the variation of input uncertain soil parameters was evaluated by the signal-to-noise ratio. The objectives of this design are to maximize the design robustness, minimize the excavation cost, and guarantee the safety (maximize the uncertain reliability). Therefore, the RGDS was formulated as a multiobjective optimization, and the optimal design can be determined based on the concepts of Pareto front and knee point. The proposed RGDS approach was illustrated through a numerical case of a two-layer slope design. The numerical results indicate that the RGDS approach is not only more intuitive and easier to follow but also more computationally efficient.

Stability Analysis of a Two‐Layered Slope with Cracks by Finite Element Limit Analysis

In this study, to support slope stability estimating engineering, the stability of a slope with cracks lying on two‐layered slopes was investigated by a self‐developed adaptive element limit analysis (AFELA) code. Upper bound (UB) and lower bound (LB) results of soil additional gravity factor SF within 4% relative error were obtained to quantify the effects of several factors, including the Moore‒Cullen strength ratio, angle of the slope, thickness of the top layer, length of the crack, angle of the crack, and crack’s distance from the edge. Typical failure patterns were also discussed for deeper insight into the two‐layered slope stability with cracks. In addition, the results of the AFELA code were compared with the actual situation of the slope and existing commercial calculation software to verify the reliability of this investigation.

Failure Mechanism of Two-Layered Slopes Subjected to the Surcharge Load

AbstractFor some two-layered slopes subjected to the surcharge load, the soil mass undergoes rotational or translational movement. Thus, the conventional failure mechanism of homogeneous slopes is ...

Undrained Bearing Capacity of Strip Footings Placed Adjacent to Two-Layered Slopes

Undrained Bearing Capacity of Strip Footings Placed Adjacent to Two-Layered Slopes

Analysis of Slope Stability with Imprecise Soil Properties Using Uncertain Sets

There are many uncertainties with respect to the assessment of slope stability, and those associated with soil properties should be given particular attention. The uncertainty theory provides an alternative to treat these uncertainties using parochial cognitive sources. A novel methodology is proposed to evaluate the stability of slopes based on an uncertain set. The soil properties involved in the deterministic methods, i.e., shear strength parameters and unit weight, are expressed as uncertain sets, and their membership functions can be assumed to be triangular or trapezoidal for a homogeneous or two-layered slope, respectively. The parameter values of membership functions are designed according to the means and variations of the soil properties, and then the expected safety factor can be calculated through the operational laws. Two numerical examples including a homogeneous slope and a two-layered slope illustrate the suitability of the proposed methodology. The relationship between the variation in the safety factor and the changes in the soil properties is investigated; moreover, the determination of the parameter values of membership is also discussed.

Stability analysis of two-layered non-homogeneous slopes

Natural slopes are non-homogeneous in nature, which behave differently than homogeneous slopes. The non-homogeneity in slopes exist in various ways, which include change in stratifications and/or shear strength parameters (cohesion, friction angle) with depth, presence of saturated–unsaturated zones, etc. This study is performed to show the effect of non-homogeneity due to different types of soils on the stability of two-layered slopes. Homogeneous and two-layered non-homogeneous models of soil slope are prepared with three different fine-grained and coarse-grained types of soils. Both the limit equilibrium method and finite element methods were used to evaluate the stability of the slopes and the results are presented in terms of safety factors along with the corresponding critical slip surfaces. Slopes with coarse-grained soil showed translational type of failure, while rotational failure was observed for fine-grained slopes.

Simplified slope reliability analysis considering spatial soil variability

Due to inherent spatial variability, soil properties vary from one location to another even within one soil layer. Such spatial variability of soils gives rise to scale-dependency in slope safety evaluation. This paper presents a simplified reliability method for slopes considering spatial soil variability. In this method, equivalent homogeneous random soil parameters are used in a single random variable (SRV) method (e.g., the first-order reliability method) to evaluate the slope reliability. Spatial variability is considered by using the equivalent parameters such that a SRV method with these equivalent parameters produces a comparable failure probability as that calculated using a more rigorous random finite element/difference method (RFEM/RFDM) with the original spatially variable parameters. Empirical equations for determining the statistics (mean value and standard deviation) of the equivalent parameters are derived through extensive RFDM analyses. The proposed method is found to be valid for both single-layered and two-layered slopes.

Response of heterogeneous slopes to increased surcharge load

Slope stability analysis generally considers a homogeneous slope composed of either soil or rock. There is no definitive criterion to distinguish homogeneous and heterogeneous slopes. This paper presents five model tests on two-layered slopes with different interface subjected to surcharge load. Numerical simulations were performed to capture the behaviors observed. Given the satisfactory reproduction of the model tests, a parametric study was then conducted to investigate the impact of the interface, slope angle and strength parameters. Finally, a set of criteria based on the relative cohesion ratio was proposed to characterize a distinct change in the nature of the slope.

Influence of transport Layer on Transient Suction Distribution in a Two-Layered Slope

Residual soil slope failure due to rainfall infiltration is one of geotechnical hazards receiving much attention in many tropical climate countries. The infiltrating water eliminates matric suction in the residual soil slope and results in slope failure. A capillary barrier is used to prevent excessive rainfall infiltration and preserve matric suction in the residual soil slope and hence prevent rainfall-induced slope failure. A numerical study to examine the performance of a transport layer in a two-layered slope using capillary barrier principle was presented in this paper. Material properties of tropical residual soils consisting of Grade V (silty gravel) and Grade VI (sandy silt) were used and modelled a two-layered slope. These material properties were obtained from representative soil sample of Balai Cerapan slope in Universiti Teknologi Malaysia, Johor Bahru campus. A granite chips (Gravel) was also incorporated to act as a transport layer in the numerical model. The simulated slope model was then subjected to three different rainfall intensities of 9 mm/h (rainfall 1), 22 mm/h (rainfall 2) and 36 mm/h (Rainfall 3) representing short, medium and high intensity rainfalls, respectively. A total of six numerical schemes were performed by restricting the thickness of the transport layer to 0.1 m. However, to assess the effect of the transport layer thickness on suction distribution; the thickness was increased to 0.2 m. The results of the study show that inclusion of gravelly transport layer enables the top layer of fine sandy silt residual soil to retain the infiltrating water as a result of capillary break developed at the interface and also divert it above the interface towards the direction of the toe of the slope. Similarly the transport layer is found to be effective in preventing water breakthrough occurrence into the underlying coarser soil layer of the two-layered slope, especially when the thickness of the transport layer is optimum.