Pseudostatic Seismic Loading Research Articles

Seismic Bearing Capacity of Eccentrically and Obliquely Loaded Strip Footings on Geosynthetic-Reinforced Soil

The paper aims to evaluate the pseudostatic seismic bearing capacity of shallow foundations on geosynthetic-reinforced granular soil subjected to inclined/eccentric combined loading. This is achieved through a comprehensive set of lower-bound finite-element limit analysis (LB FELA) simulations adopting the second-order cone programming. The pseudostatic seismic loading is incorporated into the element equilibrium equations as body forces. Both sliding and structural modes of geosynthetic failure are simulated within the FELA framework. The influences of pseudostatic acceleration, embedment depth (u), and the ultimate tensile strength (Tu) of the reinforcement layer on the failure mechanism, bearing capacity ratio, and failure envelope of the overlying obliquely/eccentrically loaded shallow foundation are thoroughly investigated and discussed. It is generally concluded that at a given reinforcement embedment depth, failure envelopes shrink substantially with the increase of the seismic horizontal acceleration and the reduction of the geosynthetic ultimate tensile strength.

Centrifuge model studies on the performance of earthen dams with geocomposite internal drain subjected to pseudostatic seismic loading

This paper evaluates geocomposite (GC) as an internal drain for seepage control in earthen dams subjected to upstream impoundment and inertial loading through centrifuge model tests. A total of five centrifuge tests were performed on a homogeneously built small earthen dam section having prototype height of 7.2 m with 1H:1V side slopes at 30 g-level using a 4.5 m radius large beam geotechnical centrifuge available at the Indian Institute of Technology Bombay, India. The studied earthen dam models had an internal drain in the form of (a) a geocomposite horizontal drain (GC HD); (b) a sand-sandwiched geocomposite horizontal drain (SSGC HD); (c) a geocomposite chimney drain (GC CD); and (d) a sand-sandwiched geocomposite chimney drain (SSGC CD). The seepage-deformation response of the GC equipped earthen dam models is presented in terms of the development of pore-water pressure (PWP), phreatic surfaces, surface settlements (sc), and downstream slope face movements (sf). The behavior of the earthen dam model without any internal drain is also presented for comparison. In the case of an earthen dam with GC internal drain both as HD and CD, it was found to be efficient up to some extent in restricting phreatic surfaces, but phreatic surfaces were observed to be close to downstream side slope. However, a sand-sandwiched GC internal drain HD and CD seemed more promising in restricting the phreatic surface much within the downstream region and imparting higher stability even during sustained inertial loading conditions. The study concludes that SSGC chimney drain can be safely adopted for seepage control in small earthen dams and similar geotechnical structures viz levees, raw water reservoirs (RWRs), coastal protection structures, etc.

Seismic Response of Embedded Retaining Wall for Excavation Support

A comparative analysis of the solutions for the seismic impact on a flexible retaining wall designed to strengthen the construction excavation for a multi-storey building in Sofia has been performed. For this purpose, the following FEM calculation models of the interaction of the wall with the surrounding soil body were compiled: (1) a 1D beam-column-spring model of the wall, including spring support in its embedded length and pseudostatic seismic loading of the wall with active earth pressure, determined by the Mononobe-Okabe method; (2) a 2D model of the wall and soil body, with pseudostatic seismic loading in the form of inertial forces applied at the finite element nodes; (3) a time history FE analysis conducted with the accelerograms of two landmark earthquakes from the Balkan Peninsula - the 1976 Vrancea (Romania) earthquake and the 1986 Kalamata (Greece) earthquake. The pseudostatic seismic loading in analyzes (1) and (2) was determined on the basis of the reference pseudostatic acceleration of 2.3 m/s2, determined for the city of Sofia according to the seismic hazard map for Bulgaria. The accelerograms in analysis (3) were scaled to a maximum value of acceleration of PGA = 2.3 m/s2. The physical modelling of the soil body uses the HSM and HSsmall advanced constitutive laws, implemented in the Plaxis software.

Seismic Bearing Capacity of Shallow Foundations Placed on an Anisotropic and Nonhomogeneous Inclined Ground

In the present study, the limit equilibrium method combined with the pseudo-static seismic loading approach and applying the simplified Coulomb failure mechanism were employed for calculating the bearing capacity of nonhomogeneous and anisotropic soils on slopes. It was assumed that the cohesion coefficient was nonhomogeneous and anisotropic and anisotropy effect was ignored for the friction angle. For estimating optimal bearing capacity values, the particle swarm optimization algorithm was used. Comparing the results of previous researchers with those of the present study for isotropic and homogeneous soils indicated that the present solution provided acceptable values for the bearing capacity of shallow foundations. The effect of anisotropy ratio and the nonhomogeneous coefficient on the seismic bearing capacity was evaluated and found that decreasing the anisotropy ratio and increasing the nonhomogeneous coefficient cause an increase in the seismic bearing capacity. Furthermore, the results showed that the depth of the failure zone decreases with increasing the nonhomogeneous coefficient, the anisotropy ratio, and the seismic acceleration coefficient, while the depth of the failure zone increases with an increase in the slope inclination.

Seismic Bearing Capacity of Shallow Strip Footings on Sand Deposits with Weak Inter-layer

The main objective of this study is to evaluate the ultimate seismic bearing capacity of a shallow strip footing resting on a frictional soil stratum containing a weak intervening layer. The majority of the studies throughout the literature pertain to the static loading condition. The previous seismic analyses have also been devoted to the studies on the bearing capacity of shallow strip footings resting on a two-layered soil. The influence of weak middle layer on the pseudo-static seismic bearing capacity of shallow foundations is the main focus of the present study. To determine the seismic bearing capacity, the limit equilibrium method (LEM) was combined with the pseudo-static seismic loading approach. Bearing capacity was defined by a single equivalent coefficient which combines the contributions of cohesion, surcharge and soil weight. A two-wedge failure surface, known as the Coulomb failure mechanism, was adopted to model the slip lines in each layer to calculate the seismic bearing capacity of the overlying shallow strip footing. The Particle Swarm Optimization (PSO) algorithm was invoked to seek the optimal bearing capacity value under different strength and loading conditions. In order to verify the validity of the presented formulations, the results were compared with some Finite Elements Method (FEM) analyses available in literature. Furthermore, the influence of the embedment depth, thickness, and strength of the weak inter-layer on the seismic bearing capacity of the shallow footing is investigated in the presence of different seismic loading arrangements. The results of this study could be very helpful in the seismic analysis and design of shallow foundations overlying a soil medium containing a weak layer of various strengths.

Seismic bearing capacity of shallow strip foundations in the vicinity of slopes using the lower bound finite element method

The seismic bearing capacity of shallow strip foundations in the vicinity of slopes was investigated by the use of the lower bound limit analysis in conjunction with the finite element method and the linear programming technique. The combination of the most probable failure modes including slope instability and ultimate bearing capacity makes the problem difficult to solve by conventional approximate methods such as the limit equilibrium, the bound theorems of the limit analysis, and the slip line methods since these are based on assumptions about either kinematically admissible failure mechanisms or statically admissible stress fields. The pseudo-static seismic loading scheme was adopted in the presence of both horizontal and vertical acceleration fields, and the soil-foundation interface was assumed perfectly rough. Parametric analyses were conducted to evaluate the most effective factors in the form of the dimensionless strength and geometry parameters. The results of the current study were found comparable with those in the literature, and the consistency of the results confirmed the robustness of the extended finite element lower bound formulation. It was shown that the normalized limit pressure is dramatically reduced as the earthquake acceleration coefficients increases, and that it increases with higher the soil strength parameters. Moreover, the threshold distance at which the influence of the slope diminishes was found to be a function of the soil strength parameters and the slope geometry.

Three-dimensional internal stability analysis of geosynthetic-reinforced earth structures considering seismic loading

The seismic internal stability analysis of geosynthetic-reinforced earth structures (GRESs) is typically conducted under idealized two-dimensional conditions. Though this assumption simplifies the analysis and design procedure, GRESs are three-dimensional in nature. In addition, existing seismic internal stability analyses of three-dimensional GRESs focus on the required strength of reinforcement, ignoring potential pullout failure of reinforcement. This may result in potentially underconservative design as the required length of reinforcement is a vital part of the internal stability analysis of GRESs. In this study, both the required strength and length of reinforcement of three-dimensional GRESs are calculated considering pseudostatic seismic loading. The results are compared with idealized two-dimensional solutions and presented in the form of stability charts for illustrative purposes and ease of application. It shows that seismic loads amplify the effects stemming from consideration of three-dimensional conditions.

Ultimate seismic bearing capacities and failure mechanisms for strip footings placed adjacent to slopes

Assessment of the ultimate bearing capacity of foundations adjacent to slopes is complex as it is highly dependent on the slope geometry and soil properties. Seismic loading may impact both the critical failure mechanism and its associated bearing capacity. The existing approaches for analyzing the seismic bearing capacity of footings near slopes typically employ coefficients developed to fit the conventions of Terzaghi’s bearing capacity equation, herein referred to as the “superposition method.” In this study, a rigorous assessment of the seismic bearing capacity is performed using an upper-bound limit state plasticity framework known as discontinuity layout optimization (DLO), which makes few prior assumptions concerning the failure geometry. Results show that soil properties, slope configuration, and pseudostatic seismic loading all influence the realized failure mechanism and associated bearing capacity. The use of bearing capacity coefficients that fit within the conventional superposition method may underestimate limit loads when the underlying soil provides a relative increase in resistance, but may greatly overestimate bearing capacity when the self-weight of the soil is destabilizing in nature. A set of design charts using direct computational methods for a variety of geometric, geotechnical, and seismic conditions is provided.

Finite element-based probabilistic stability analysis of rock-fill tailing dam considering regional seismicity

The recent tailing dam failure in Brazil has again emphasized the need of performing robust stability analysis prior to construction. This paper demonstrates the probabilistic dynamic stability analysis of tailing dams considering an existing rock-fill tailing dam in India. The stability analysis was performed using 2D finite element-based package RS2. In the probabilistic analysis, the strength parameters such as cohesion (c) and the friction angle (φ) were considered as random variables. In total, 3000 numbers of samples were generated assuming a normal distribution. Monte Carlo simulation was used to evaluate the probability of failure (PoF) and reliability index. Strength reduction method was used for the finite element analyses. A pseudo-static seismic loading was incorporated in the strength reduction analysis to check the seismic stability of the dam. A factor of safety (FoS) of 1.15 was observed from the deterministic analysis for downstream slope. For the same case, the probabilistic analysis provided a mean FoS of 1.19 with 5.46% probability of failure. The FoS values and the locations of the critical failure surface obtained by the limit equilibrium method and finite element method were compared. The observed FoS values were found to be higher than the values specified in the IS 7894-1975 (reaffirmed in 1997) and ANCOLD (1999). In the case of pseudo-static approach, the maximum displacement of 0.53 m was observed in the slope. Furthermore, nonlinear dynamic stability analysis was performed to simulate a true earthquake event. The permanent deformation of the slope after the earthquake was found to be 0.40 m. The zone of failure observed in both pseudo-static and nonlinear dynamic stability analyses was found to be the same. Overall, the results revealed that the spatial variability of the soil significantly influences the FoS values.

Static and Seismic Stability Charts for Three‐Dimensional Cut Slopes and Natural Slopes under Short‐Term Undrained Conditions

In the strict framework of limit analysis, an analytical approach is derived to obtain the upper bound solutions for three‐dimensional inhomogeneous slopes in clays under undrained conditions. Undrained strength profiles increasing linearly with depth below the crest of the slope and below the outline surface of the slope are assumed representative of cut slopes and natural slopes, respectively. Stability charts are produced for the cut slopes and the natural slopes under both static and pseudostatic seismic loading conditions. The presented charts are convenient to assess the preliminary and short‐term stability for 3D slopes in practical applications, such as rapid excavation or buildup of embankments and slopes subjected to earthquakes. Compared with the available results from the finite element limit analysis method, a better estimate of the slope safety is obtained from the analytical approach.

Parallel numerical analysis of the failure characteristics of earthquake-induced landslides

Earthquake-induced landslides are serious natural hazards that shocked us with tremendous casualties and great economic losses in many mountainous areas around the world. However, predicting and preventing the earthquake-induced landslides is very difficult due to the complicated relationship between seismic dynamics and coseismic landsliding. Comprehensive understanding of earthquake-induced landslides from the perspective of seismic dynamic mechanism remains inadequate at present. This study employs an elastoplastic spectral element method incorporating parallel computing and represents a realistic three-dimensional slope model via a semi-structured hexahedral mesh to investigate the dynamic failure characteristics of earthquake-induced landslides. Dynamic behaviours of slopes are simulated using a continuumbased approach with a Mohr-Coulomb yield criterion. Displacement fields are calculated using the shear strength reduction technique. Pseudo-static seismic loading is performed to assess the slope stability quantitatively and complex topography is taken into consideration. The Xinzhong landslide that occurred in Beichuan Country is one of destructively collapsing landslides triggered by the Wenchuan earthquake and is therefore selected as a case study for discussion. Three-dimensional visualization of the calculated results quantitatively demonstrated that the three-dimensional numerical model well reproduced the coseismic landsliding response and its essential dynamic failure pattern, which could not be purely captured by Geographic Information Systems (GIS) and Remote Sensing (RS) technologies and calculated using simply two-dimensional numerical model. The numerical results also showed that tensile and shear fractures had significant influences on the nature of the failed surface development. In addition, the presence of seismic loading in the slope could cause obvious disturbances for the slope stability. Comparative analysis indicated that the shear surface of the earthquake-induced slope was shorter and the tension crack surface was deeper than that of the normal gravity condition. Moreover, the landslide mainly occurred in the transition from the upper to lower part of the slope, indicating that the slope topography was one of the crucial factors resulting in slope failure. Although the model was constructed without the presence of a pre-existing failure surface, comparative analysis addressed that the failure surface obtained by the numerical simulation was in close agreement with that by the post-failure investigations. The results could provide insight into better understanding of the relationship between landslide and seismic dynamic mechanism. The study has practical significance for the effective prevention and mitigation of earthquake-induced landslide hazards.

Stability Charts for 3D Failures of Homogeneous Slopes

A three-dimensional (3D) kinematically admissible rotational failure mechanism is extended from toe failure to include face failure and base failure for homogeneous slopes in both purely cohesive and frictional/cohesive soils. In the strict framework of limit analysis, an analytical approach is derived to obtain the upper bounds on slope stability and the corresponding type of the critical failure mechanism. Compared with the available results from the finite-element limit-analysis method, the 3D rotational failure mechanisms give the best estimate on the upper bound. A set of stability charts is presented in a wide range of parameters for 3D homogeneous slopes under both static and pseudostatic seismic loading conditions. This set is useful in assessing the safety of the 3D homogeneous slopes in practical applications.

Application of an elastoplastic spectral‐element method to 3D slope stability analysis

SUMMARYWe implement a spectral‐element method for 3D time‐independent elastoplastic problems in geomechanics. As a first application, we use the method for slope stability analyses ranging from small to large scales. The implementation employs an element‐by‐element preconditioned conjugate‐gradient solver for efficient storage. The program accommodates material heterogeneity and complex topography. Either simple or complex water table profiles may be used to assess effects of hydrostatic pressure. Both surface loading and pseudostatic seismic loading are implemented. For elastoplastic behavior of slopes to be simulated, a Mohr–Coulomb yield criterion is employed using an initial strain method (i.e., a viscoplastic algorithm). For large‐scale problems, the software is parallelized on the basis of domain decomposition using Message Passing Interface. Strong‐scaling measurements demonstrate that the parallelized software performs efficiently. We validate our spectral‐element results against several other methods and apply the technique to simulate failure of an earthen embankment and a mountain slope.Copyright © 2012 John Wiley & Sons, Ltd.

Seismic Bearing Capacity of a Rigid Footing Adjacent to a Cohesionless Slope

At present, analytical or empirical formula for seismic bearing capacity of footings adjacent to slopes is not available. This study uses a pseudo-static-based approach in conjunction with rigorous Janbu's slice method to derive analytical values of seismic bearing capacity factors (Nγ) and correction factors for the effects of inertia of soil mass and load inclinations for a rigid footing adjacent to cohesionless slopes. It is shown that both the bearing capacity factors (Nγ) and the correction factors for the seismic bearing capacity of footings placed on level ground derived herein are comparable with those reported in the literature. Empirical equations regarding the effects of slope angles and load inclinations, expressed using generalized forms of those proposed in the literature, are also derived. It is also found that the empirical equations derived in the present study provide values of correction factors in good agreements with the analytical ones, indicating the validity of using these empirical equations for assessing the bearing capacity of rigid footings situated on the slope subjected to pseudo-static seismic loading.

Reliability-Based Analysis and Design of Strip Footings against Bearing Capacity Failure

This paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to a vertical load with or without pseudostatic seismic loading. Only the punching failure mode of the ultimate limit state is studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters and the horizontal seismic coefficient. The Hasofer-Lind reliability index and the failure probability are determined. A sensitivity analysis is also performed. The influence of the applied footing load on the reliability index and the corresponding design point is presented and discussed. It was shown that the negative correlation between the soil shear strength parameters highly increases the reliability of the foundation and that the failure probability is highly influenced by the coefficient of variation of the angle of internal friction of the soil and the horizontal seismic coefficient. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability.

Reliability of Shallow Foundations Subjected to Multidirectional Seismic Loading

A method of assessing the probability of failure of shallow foundations in saturated fine-grained soil under multidirectional seismic loading is presented. The method uses the distributions of two variables, the spectral acceleration at the fundamental period of the structure and the shear strength of the foundation soil, to form the joint probability density function. The performance function, which defines the required soil strength for the foundation to equilibrate the applied loading, is mapped on this domain. Numerical integration is used to ascertain the probability of failure. A bounded probability density function is used, namely a Pearson Type 1 (Beta) distribution, for soil strength. This distribution provides an upper and lower limit to in situ shear strength. The spectral acceleration is represented by the complementary cumulative distribution function of a Type 1 asymptotic extreme value (Gumble) distribution. Such a distribution is shown to be an accurate representation of real earthquake loading and may be found by a probabilistic seismic hazard analysis for a region. The method is based on pseudostatic seismic loading of the foundation and accounts for spectral acceleration acting along the two horizontal axes. The influence of the orientation of the foundation to the earthquake source is incorporated using the concept of principal directions of ground motion. The performance function is formulated for shallow foundations under eccentric and inclined loading using the recommendations in Eurocode 7. The function is shown to be nonlinear and compound, one part pertaining to the bearing mode of failure (for lower values of acceleration) and the remaining part pertaining to the sliding mode of failure (for higher values of acceleration). An equation is presented for the transition acceleration that separates the performance function into the two parts. A case study is presented and conclusions are drawn about the role of the bearing and sliding modes of failure.