Seismic lateral movement prediction for gravity retaining walls on granular soils

At present, methods based on allowable displacements are frequently used in the seismic design of earth retaining structures. However, these procedures ignore both the foundation soil deformability and the seismic amplification of the soil placed behind the retaining wall. Thus, they are not able to predict neither a rotational failure mechanism nor seismic induced lateral displacements with an acceptable degree of accuracy for the most general case. In this paper, a series of 2D finite-element analyses were carried out to study the seismic behavior of gravity retaining walls on normally consolidated granular soils. Chilean strong-motion records were applied at the bedrock level. An advanced non-linear constitutive model was used to represent both the backfill and foundation soil behavior. This elastoplastic model takes into account both the stress dependency of soil stiffness and coupling between shear and volumetric strains. In unloading–reloading cycles, the non-linear shear-modulus reduction with shear strain amplitude is considered. Interface elements were used to model soil–structure interaction. Routine-design charts were derived from the numerical analyses to predict the lateral movements at the base and top of gravity retaining walls located at sites with similar seismic characteristics to the Chilean subduction zone. Thus, wall seismic rotation can also be obtained. The developed charts consider wall dimensions, granular soil properties, bedrock depth, and seismic input motion characteristics. As shown, the proposed charts match well with available experimental data.     

Bounding surface plasticity model for the seismic liquefaction analysis of geostructures

This paper presents the constitutive relations and the simulative potential of a new plasticity model developed mainly for the seismic liquefaction analysis of geostructures. The model incorporates the framework of critical state soil mechanics, while it relies on bounding surface plasticity with a vanished elastic region to simulate the non-linear soil response. Key constitutive ingredients of the new model are: (a) the inter-dependence of the critical state, the bounding and the dilatancy (open cone) surfaces on the basis of the state parameter ψ, (b) a (Ramberg–Osgood type) non-linear hysteretic formulation for the “elastic” strain rate, (c) a discontinuously relocatable stress projection center related to the “last” load reversal point, which is used for mapping the current stress point on model surfaces and as a reference point for introducing non-linearity in the “elastic” strain rate and finally (d) an empirical index of the directional effect of sand fabric evolution during shearing, which scales the plastic modulus. In addition, the paper outlines the calibration procedure for the model constants, and exhibits its accuracy on the basis of a large number of laboratory element tests on Nevada sand. More importantly, the paper explores the potential of the new model by presenting simulations of the VELACS centrifuge tests of Models No 1 and 12, which refer to the free-field liquefaction response of Nevada sand and the seismic response of a rigid foundation on the same sand, respectively. These simulations show that the new model can be used successfully for the analysis of widely different boundary value problems involving earthquake soil liquefaction, with the same set of model constants calibrated on the basis of laboratory element tests.     

A modified ISBA surface scheme for modeling the hydrology of Athabasca River Basin with GCM-scale data

A soil–vegetation–atmosphere transfer model (SVAT), interactions between the soil–biosphere–atmosphere (ISBA) of Météo France, is modified and applied to the Athabasca River Basin (ARB) to model its water and energy fluxes. Two meteorological datasets are used: the archived forecasts from the Meteorological Survey of Canada’s Global Environmental Multiscale Model (GEM) and the European Centre for Mid-range Weather Forecasts global re-analysis (ERA-40), representing spatial scales typical of a weather forecasting model and a global circulation model (GCM), respectively. The original treatment of soil moisture and rainfall in ISBA (OISBA) is modified to statistically account for sub-grid heterogeneity of soil moisture and rainfall to produce new, highly non-linear formulations for surface and sub-surface runoff (MISBA). These new formulations can be readily applied to most existing SVATs. Stand alone mode simulations using the GEM data demonstrate that MISBA significantly improves streamflow predictions despite requiring two fewer parameters than OISBA. Simulations using the ERA-40 data show that it is possible to reproduce the annual variation in monthly, mean annual, and annual minimum flows at GCM scales without using downscaling techniques. Finally, simulations using a simple downscaling scheme show that the better performance of higher resolution datasets can be primarily attributed to improved representation of local variation of land cover, topography, and climate.     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

A SANISAND model with anisotropic elasticity

Numerous experimental studies indicate that as a result of shear stress, the elastic behavior of granular media becomes both non-linear and anisotropic. This paper presents a simple constitutive model for sands with respect to anisotropic elasticity. To this aim, using the concept of second order fabric tensor, a simplified elasticity theory is presented which is capable of considering the effect of induced anisotropy on the elastic response. SANISAND is the name used for a family of simple anisotropic sand models developed in the framework of critical state soil mechanics and bounding surface plasticity. An existing SANISAND model is modified in order to include the proposed anisotropic elasticity. The modified model simulations are compared with those obtained from the other members of this family. It is shown that considering anisotropic elasticity can take part in explanation of drastic loss of mean principal stress when sand is subjected to reverse loading in dilative branch of behavior and as a result, improve the liquefaction simulations.     

Analog circuit to simulate dynamic soil–structure interaction in shake table test

A soil medium at the side of an embedded structure is treated as mutually uncoupled horizontal layers of a unit thickness. A plane strain condition is assumed within each individual layer such that the medium responses do not vary along the thickness. According to previous work by the authors and also a new formulation given herein, the impedance of the above layer at the structure can be produced by frequency-independent simple mechanical models for all three modes of foundation responses. Similar frequency-independent models are also presented for the impedance at the foundation base. These models are made of two different basic elements and a mass interconnected in series. Their arrangements directly indicate the wiring of electric circuits which generate signals corresponding to the transient soil–structure interaction responses. To all intents and purposes, electric circuits do not loose time in responding to the inputs. Therefore, they allow us to simulate the soil–structure interaction response in shake table model tests, which are commonly conducted at relatively high excitation frequencies for earthquake simulation.     

A simplified model for lateral response of large diameter caisson foundations—Linear elastic formulation

The transient response of large embedded foundation elements of length-to-diameter aspect ratio D/B=2–6 is characterized by a complex stress distribution at the pier–soil interface that cannot be adequately represented by means of existing models for shallow foundations or flexible piles. On the other hand, while three-dimensional (3D) numerical solutions are feasible, they are infrequently employed in practice due to their associated cost and effort. Prompted by the scarcity of simplified models for design in current practice, we here develop an analytical model that accounts for the multitude of soil resistance mechanisms mobilized at their base and circumference, while retaining the advantages of simplified methodologies for the design of non-critical facilities. The characteristics of soil resistance mechanisms and corresponding complex spring functions are developed on the basis of finite element simulations, by equating the stiffness matrix terms and/or overall numerically computed response to the analytical expressions derived by means of the proposed Winkler model. Sensitivity analyses are performed for the optimization of the truncated numerical domain size, the optimal finite element size and the far-field dynamic boundary conditions to avoid spurious wave reflections. Numerical simulations of the transient system response to vertically propagating shear waves are next successfully compared to the analytically predicted response. Finally, the applicability of the method is assessed for soil profiles with depth-varying properties. The formulation of frequency-dependent complex spring functions including material damping is also described, while extension of the methodology to account for nonlinear soil behavior and soil–foundation interface separation is described in the conclusion and is being currently investigated.     

Investigation of non-linear site amplification at two downhole strong ground motion arrays in Taiwan

Non-linear seismic response of soil is studied by comparing the spectral ratios of surface to downhole horizontal accelerations on weak and strong motion. Data from two boreholes are analysed. One is drilled in the alluvial deposits in the south–west quadrant of the SMART 1 array. The second one penetrates Pleistocene terrace deposits in the northern part of the SMART2 array. Observed weak and strong motion spectral ratios are compared with the theoretical ones predicted by the geotechnical soil model which postulates a hysteretic constitutive law. A significant non-linear response is found at the first site for the events with surface peak acceleration exceeding roughly 0–15g. Deamplification of the strong motion occurred in the frequency range from approximately 1 to 10 Hz. The maximum observed difference between the average weak and strong motion amplification functions of an 11 m-thick near-surface stratum is a factor of 2–3. Nonlinear response characteristics are in qualitative agreement with the model. An additional corollary is that the amplification function calculated from the shear wave coda is equivalent to the average amplification calculated over the ensemble of small earthquakes. No statistically significant non-linear response is detected on the second array, that is tentatively accounted for by the stiffer soil conditions and weaker accelerations achieved at the SMART2 site. The results indicate that the non-linear amplification can be detectable at certain soil conditions above a threshold acceleration level.     

Design and commissioning of a laminar soil container for use on small shaking tables

This paper describes the design, fabrication and commissioning of a single axis laminar shear box for use in seismic soil–structure interaction studies. A laminar shear box is a flexible container that can be placed on a shaking table to simulate vertical shear-wave propagation during earthquakes through a soil layer of finite thickness. The laminar shear box described in this paper was designed to overcome the base shear limitations of a small shaking table at The University of Western Ontario. The design details of the box are provided in addition to results of dynamic tests performed to commission the box. A synthetic clay comprising sodium bentonite mixed with diluted glycerin was used as the model soil and 1-G similitude theory was employed to maintain model to prototype similarity. The model soil was compacted into the container in lifts to achieve soil stiffness that increased with depth. A series of shaking table tests and numerical analyses that were performed to study the performance of the laminar box and non-linear seismic behavior of the model clay are described. The results of this study show that the laminar box does not impose significant boundary effects and is able to maintain 1-D soil column behavior. In addition, the dynamic behavior of the model clay during scaled model tests was found to be consistent with the behavior measured during cyclic laboratory tests.     

Influence of plasticity on the seismic soil–micropiles–structure interaction

This paper includes an analysis of the influence of soil plasticity on the seismic response of micropiles. Analysis is carried out using a global three-dimensional modeling in the time domain. The soil behavior is described using the non-associated Mohr–Coulomb criterion. Both the micropiles and the superstructure are modeled as three-dimensional beam elements. Proper boundary conditions are used to ensure waves transmission through the lateral boundaries of the soil mass. Analyses are first conducted for harmonic loadings and then for real earthquake records. They show that plasticity could have a significant influence on the seismic response of the soil–micropiles–structure systems. This influence depends on the amplitude of the seismic loading and the dominant frequencies of both the input motion and the soil–piles–structure system.     

Soil–structure interaction in the time domain using halfspace Green's functions

A time-domain formulation is proposed for the transient response analysis of general, three-dimensional structures resting on a homogeneous, elastic halfspace subjected to either external loads or seismic motions. The formulation consists of two parts: (a) the time domain formulation of the soil behaviour and (b) the coupling of the corresponding soil algorithms to the Finite Element Code ANSYS. As far as the structure is concerned, this coupling opens the way for the analysis of non-linear soil–structure interaction. The approach is based on halfspace Green's functions for displacements elicited by Heaviside time-dependent surface point loads. Hence, the spatial discretisation can be confined to the contact area between the foundation and the soil, i.e. no auxiliary grid beyond the foundation as for conventional boundary element formulations is required. The method is applied to analyse the dynamic response of a railway track due to a moving wheel set by demonstrating the influence of ‘through-the-soil coupling’.     

Effects of soil cracking on the seismic response of soil–structure systems

A numerical study on the influence that cracks and discontinuities (closed cracks) can have on the seismic response of a hypothetical soil–structure system is presented and discussed. A 2-D finite-difference model of the soil was developed, considering a bilinear failure surface using a Mohr–Coulomb model. The cracks are simulated with interface elements. The soil stiffness is used to characterize the contact force that is generated when the crack closes. For the cases studied herein, it was considered that the crack does not propagate during the dynamic event. Both cases, open and closed cracks, are considered. The nonlinear behavior was accounted for approximately using equivalent linear properties calibrated against several 1-D wave propagation analyses of selected soil columns with variable depth to account for changes in depth to bed rock. Free field boundaries were used at the edges of the 2-D finite-difference model to allow for energy dissipation of the reflected waves. The effect of cracking on the seismic response was evaluated by comparing the results of site response analysis with and without crack, for several lengths and orientations. The changes in the response obtained for a single crack and a family of cracks were also evaluated. Finally, the impact that a crack may have on the structural response of nearby structures was investigated by solving the seismic-soil–structure interaction of two structures, one flexible and one rigid to bracket the response. From the results of this investigation, insight was gained regarding the effect that discontinuities may have both on the seismic response of soil deposits and on nearby soil–structure systems.     

Effect of non-linear soil–structure interaction on seismic response of tall slender structures

Some structures may be very massive and may have to be located on relatively soft soil. In such cases, the soil adjacent to the structure behaves in a non-linear fashion and affects the response of the structure to the dynamic loading. An approximate hybrid approach to analyse soil–structure systems accounting for soil non-linearities has been developed in this paper. The approach combines the consistent infinitesimal finite-element cell method (CIFECM) and the finite-element method (FEM). The CIFECM is employed to model the non-linear (near-field) zone of the soil supporting the structure as a series of bounded media. The material properties of the bounded media are selected so that they are compatible with the average effective strains over the whole bounded medium during the excitation. The linear zone of soil away from the foundation, the far-field, is modelled as an unbounded medium using the CIFECM for unbounded media. The structure itself is represented by the FEM. The proposed method is used to model the dynamic response of a one-mass structure and a TV-tower supported on a homogenous stratum and excited by an earthquake. It was found that the secondary soil non-linearity might increase or decrease the base forces of tall slender structures depending on the type of structure, frequency content of the input motion and the dynamic properties of the near-field soil.     

Effects of spatial variation of soil properties on seismic performance of port structures

From past seismic events such as the 1995 Kobe (Hyogoken-Nanbu) and 2001 Nisqually earthquakes, it was found that liquefaction-induced lateral spread has caused significant damage to structures such as buildings and bridges, in addition to underground utility facilities like pipelines. In this respect, seaport facilities are particularly vulnerable to these liquefaction-related damages, because they are usually constructed on poorly consolidated natural deposit or fills. This study investigates the effect of the liquefaction and lateral spread on the seismic response of caisson type quay walls. For this purpose, 2D nonlinear dynamic analyses of soil–structure system are carried out with the aid of finite difference software, FLAC. The unique feature of this study lies in the fact that the 2D soil system is idealized as homogeneous non-Gaussian random field. A simulation algorithm is then used to generate a set of digital realizations of 2D random field sample. Each realization is used for the dynamic analysis to generate a unique response of the soil–structure system. Repeating this analysis for the entire set of realizations, the probabilistic nature of the response is characterized in the Monte Carlo sense. This result based on random field is compared with the response obtained under the uniform field assumption with the mean value of soil property. The comparison shows that in general the uniform model provides unconservative result compared with the response from the random field model due to nonlinear behavior of the soil–structure system. It is also found that the consideration of spatial variation of soil can capture the dispersion of observed response of quay walls.     

Seismic soil–structure interaction of massive flexible strip-foundations embedded in layered soils by hybrid BEM–FEM

A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response.     

Non-linear dynamic earth dam–foundation interaction using a BE–FE method

A general, rigorous, coupled Boundary Element–Finite Element (BE–FE) formulation is presented for non-linear seismic soil–structure interaction in two dimensions. The BE–FE method is applied to investigate the inelastic response of earth dams to transient SV waves. The dam body, consisting of heterogeneous materials modelled with a simple non-linear hysteretic model, is discretized with finite elements, whereas the elastic half-space is discretized with boundary elements. The study focuses on the combined effects of the material non-linearity and foundation flexibility. The results show the significant effect of the foundation flexibility in reducing the response through radiation of energy. For excitations with peak ground accelerations from 0·2gto 0·6g, the crest acceleration amplification ranges from 2·5 to 1·4 and seems to be comparable with field observations and results from other studies. Deamplification increasing with strain is reported at the lower part of the dam. The method is computationally powerful and can be used for efficient non-linear analysis of complex soil–structure systems. The efficiency of the BE–FE method allows further improvements with incorporation of a more advanced constitutive model and consideration of the generation and dissipation of pore-water pressures during the earthquake. © 1998 John Wiley & Sons, Ltd.     

A modified lumped parametric model for nonlinear soil-structure interaction analysis

Most soil—structure interaction (SSI) analyses are still conducted assuming linear material behavior or simulating nonlinear effects through an equivalent linearization and the structure (foundation) being closely welded with the surrounding soil. It is recognized, however, that nonlinearities can play a significant role in the results. Two kinds of nonlinearities must be considered: those associated with inelastic soil behavior and those resulting from loss of contact between the foundation and the surrounding soil. In the present paper a modified lumped parametric model for the analysis of nonlinear SSI effects has been proposed. In the model both nonlinearities are taken into account. The results of tests of the soil-structure system model have been presented, which agree well with those obtained from analysis by using the proposed model.     

Dynamic soil–structure interaction effects on the seismic response of asymmetric buildings

An approach is formulated for the linear analysis of three-dimensional dynamic soil–structure interaction of asymmetric buildings in the time domain, in order to evaluate the seismic response behaviour of torsionally coupled buildings. The asymmetric building is idealized as a single-storey three-dimensional system resting on different soil conditions. The soil beneath the superstructure is modeled as linear elastic solid elements. The contact surface between foundation mat and solid elements of soil is discretised by linear plane interface elements with zero thickness. An interface element is further developed to function between the rigid foundation and soil. As an example, the response of soil–structure interaction of torsionally coupled system under two simultaneous lateral components of El Centro 1940 earthquake records has been evaluated and the effects of base flexibility on the response behaviour of the system are verified.