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.     

Boundary differential equation method: simplified dynamic soil stiffnesses for embedded rigid foundations

With a simplified model and Galerkin's weighted residual procedure, two simple differential equations of dynamic behavior of a bounded rectangular medium are established along the boundaries in the x- and y-direction in the medium. Solutions of these equations yield closed form expressions of soil stiffnesses for various cases of a partially embedded rigid foundation, including the stiffnesses per depth of foundation with rectangular base area and the stifnesses of strip foundation. The developed procedure provides the definition of the weight functions, which are used in Galerkin's method for weighted residual. In addition to these weight functions, their conjugators are also suitable for weight functions. When the soil depth is finite, the original weight functions fail to produce physically meaningful results in some frequency range but the conjugators do not fail at any frequencies. The developed equations to compute soil stiffnesses for embedded foundations are simple yet capable of calculating the responses close to those computed by the much more elaborated finite element method.     

Seismic response of isolated bridges with soil–structure interaction

The modern transportation facilities demand that the bridges are to be constructed across the gorges that are located in seismically active areas and at the same time the site conditions compel the engineers to rest the pier foundation on soil. The purpose of this study is to assess the effects of soil–structure interaction (SSI) on the peak responses of three-span continuous deck bridge seismically isolated by the elastomeric bearings. The emphasis has been placed on gauging the significance of physical parameters that affect the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. The soil surrounding the foundation of pier is modelled by frequency independent coefficients and the complete dynamic analysis is carried out in time domain using complex modal analysis method. In order to quantify the effects of SSI, the peak responses of isolated and non-isolated bridge (i.e. bridge without isolation device) are compared with the corresponding bridge ignoring these effects. A parametric study is also conducted to investigate the effects of soil flexibility and bearing parameters (such as stiffness and damping) on the response of isolated bridge system. It is observed that the soil surrounding the pier has significant effects on the response of the isolated bridges and under certain circumstances the bearing displacements at abutment locations may be underestimated if the SSI effects are not considered in the response analysis of the system.     

Seismic behavior of a post-tensioned integral bridge including soil–structure interaction (SSI)

Current practice usually pays little attention to the effect of soil–structure interaction (SSI) on seismic analysis and design of bridges. The objective of this research study is to assess the significance of SSI on the modal with geometric stiffness and seismic response of a bridge with integral abutments that has been constructed using a new bridge system technology. Emphasis is placed on integral abutment behavior, since abutments together with piers are the most critical elements in securing the integrity of bridge superstructures during earthquakes. Comparison is made between analytical results and field measurements in order to establish the accuracy of the superstructure–abutment model. Sensitivity studies are conducted to investigate the effects of foundation stiffness on the overall dynamic and seismic response of the new bridge system.     

Seismic analysis of lock–soil–fluid systems by hybrid BEM–FEM

A study of soil–structure–fluid interaction (SSFI) of a lock system subjected to harmonic seismic excitation is presented. The water contained lock is embedded in layered soils supported by a half-space bedrock. The ground excitation is prescribed at the soil–bedrock interface. The response is numerically obtained through a hybrid boundary element (BEM) finite element method (FEM) formulation. The semi-infinite soil and the fluid are modeled by the BEM and the lock is modeled by the FEM. The equilibrium equation for the lock system is obtained by enforcing compatibility and equilibrium conditions at the fluid–structure, soil–structure and soil–layer interfaces under conditions of plane strain. To the authors’ knowledge this is the first study of a lock system that considers the effects of dynamic soil–fluid–structure interaction through a BEM–FEM methodology. A numerical example and parametric studies are presented to examine the effects of the presence of water, lock stiffness, and lock embedment on the response.     

Seismic response analysis of pipes by a probabilistic approach

Seismic response of buried pipes in longitudinal direction is studied. The effect of the variation of geotechnical properties of the surrounding soil on the stiffness, mass and damping of the soil is considered. The soil–structure interaction depends on pipe stiffness, joint stiffness, the variation of the soil stiffness and the soil mass and damping. Variations of the properties of the surrounding soil along the pipe are described by the random field theory. A numerical model is developed in order to simulate the effects of the variation of the soil on displacements, bending moments in the pipe and also to carry out a statistical analysis. The influence of different parameters regarding design and safety level of the pipe is conducted.     

Exact solution for horizontal displacement at center of the surface of an elastic half space under horizontal impulsive punch loading

The exact analytical solution for the horizontal displacement at the center of the surface of an elastic half space under an impulsive loading having the same spatial distribution as the contact stresses that arise underneath a rigid disk when subjected to a static, horizontal load, is obtained using the Cagniard–De Hoop method. The solution can be used to study the dynamical interaction between soil and structures, and can also be used to assess numerical computations with a finite element or a boundary element program.     

Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations

The paper provides state-of-the-art information on the following aspects of seismic analysis and design of spread footings supporting bridge piers: (1) obtaining the dynamic stiffness (“springs” and “dashpots”) of the foundation; (2) computing the kinematic response; (3) determining the conditions under which foundation–soil compliance must be incorporated in dynamic structural analysis; (4) assessing the importance of properly modeling the effect of embedment; (5) elucidating the conditions under which the effect of radiation damping is significant; (6) comparing the relative importance between kinematic and inertial response. The paper compiles an extensive set of graphs and tables for stiffness and damping in all modes of vibration (swaying, rocking, torsion), for a variety of soil conditions and foundation geometries. Simplified expressions for computing kinematic response (both in translation and rotation) are provided. Special issues such as presence of rock at shallow depths, the contribution of foundation sidewalls, soil inhomogeneity and inelasticity, are also discussed. The paper concludes with parametric studies on the seismic response of bridge bents on embedded footings in layered soil. Results are presented (in frequency and time domains) for accelerations and displacements of bridge and footing, while potential errors from some frequently employed simplifications are illustrated.     

Calibration of dynamic analysis methods from field test data

In view of the heterogeneity of natural soil deposits and approximations made in analysis methods, in situ methods of determining soil parameters are highly desirable. The problem of interest here is the nonlinear dynamic behavior of pile foundations. It is shown in this paper that soil parameters needed for simplified dynamic analysis of a single pile may be back-calculated from the dynamic response of the pile measured in the field. A pile was excited by applying a large horizontal dynamic force at the pile-head level, and the response measured. In this paper, two different (simplified) methods of modeling the dynamic response of the pile are considered. One of the methods is based on the Winkler foundation approach, with the spring constant characterized by the so-called nonlinear p–y springs. The second method is based on the equivalent-linear finite element approach, with the nonlinearity of shear modulus and damping accounted for by employing the so-called degradation relationships. In the latter, the effect of interface nonlinearity is also considered. Starting with best estimates of soil parameters, the experimental data on the response of pile is used to fine-tune the values of the parameters, and thereby, to estimate parameters that are representative of in situ soil conditions.     

Seismic response of slender rigid structures with foundation uplifting

The rocking of rigid structures uplifting from their support under strong earthquake shaking is investigated. The structure is resting on the surface of either a rigid base or a linearly elastic continuum. A large-displacement approach is adopted to extract the governing equations of motion allowing for a rigorous calculation of the nonlinear response even under near-overturning conditions. Directivity-affected near-fault ground motions, idealized as Ricker wavelets or trigonometric pulses, are used as excitation. The conditions under which uplifting leads to large angles of rotation and eventually to overturning are investigated. A profoundly nonlinear rocking behavior is revealed for both rigid and elastic soil conditions. This geometrically nonlinear response is further amplified by unfavorable sequences of long-duration pulses in the excitation. Moreover, through the overturning response of a toppled tombstone, it is concluded that the practice of estimating ground accelerations from overturning observations is rather misleading and meaningless.     

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.     

Experimental developments for studying static and seismic behavior of retaining walls with liquefiable backfills

The effects of earthquakes on cantilever retaining walls with liquefiable backfills were studied. The experimental techniques utilized in this study are discussed here. A series of centrifuge tests was conducted on aluminum, fixed-base, cantilever wall models retaining saturated, cohesionless backfills. Accelerations on the walls and in the backfill, static and excess pore pressures in the soil, and deflections and bending strains in the wall were measured. In addition, direct measurements of static and dynamic lateral earth pressures were made. In some tests, sand backfills were saturated with the substitute pore fluid metolose. Modeling of model type experiments were conducted. The experimental measurements were found internally consistent and repeatable. Both static and dynamic earth pressure measurements were determined to be reliable. It was also observed that for the test configuration adopted, a special boundary treatment such as the use of duxseal is optional. Static and seismic modeling of models were also successful, which indicated that the assumed scaling relations were essentially correct.     

Seismic analysis of infinite pile groups in liquefiable soil

Numerical analysis of an infinite pile group in a liquefiable soil was considered in order to investigate the influence of pile spacing on excess pore pressure distribution and liquefaction potential. It was found that an optimal pile spacing exists resulting in minimal excess pore pressure. It was also found that certain pile group configurations might reduce liquefaction potential, compared to free field conditions. It was observed that for closely spaced piles and low frequency of loading, pile spacing has little influence on the response of the superstructure.     

Magma contamination by direct wall rock interaction: constraints from xenoliths from the walls of a carbonate-hosted magma chamber (Vesuvius 1944 eruption)

During the 1944 eruption of Vesuvius different types of xenoliths were ejected. They represent fragments of the walls of a low volume (<0.5 km³) shallow (3–4 km depth) magma chamber. The study of these xenoliths enables us to estimate the amount of contamination occurring at the boundary of a high-T alkaline magma chamber hosted in carbonate rocks. The process of contamination of the magma by carbonates can be modelled, using isotopic and chemical data, as a mixing between magma and marbles. Mass exchanges occur at the boundary between the crystallizing magma and marble wall rocks, where endoskarn forms. The contamination of the solidification front of the chamber is very limited. The solidification front and the skarn shell effectively isolate the interior of the magma chamber from new inputs of contaminants from the carbonate wall rocks. Therefore, the main volume of magma, hosted in the magma chamber, did not undergo any significant mass exchange with the wall rocks.     

Seismic response of base-isolated liquid storage tanks considering fluid–structure–soil interaction in time domain

The seismic response analysis of a base-isolated liquid storage tank on a half-space was examined using a coupling method that combines the finite elements and boundary elements. The coupled dynamic system that considers the base isolation system and soil–structure interaction effect is formulated in time domain to evaluate accurately the seismic response of a liquid storage tank. Finite elements for a structure and boundary elements for liquid are coupled using equilibrium and compatibility conditions. The base isolation system is modeled using the biaxial hysteretic element. The homogeneous half-space is idealized using the simple spring-dashpot model with frequency-independent coefficients. Some numerical examples are presented to demonstrate accuracy and applicability of the developed method.Consequently, a general numerical algorithm that can analyze the dynamic response of base-isolated liquid storage tanks on homogeneous half-space is developed in three-dimensional coordinates and dynamic response analysis is performed in time domain.     

Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: Shaking in the direction perpendicular to ground flow

The 1995 Kobe earthquake seriously damaged numerous buildings with pile foundations adjacent to quay walls. The seismic behavior of a pile group is affected by movement of quay walls, pile foundations, and liquefied backfill soil. For such cases, a three-dimensional (3-D) soil–water coupled dynamic analysis is a promising tool to predict overall behavior. We report predictions of large shake table test results to validate 3-D soil–water coupled dynamic analyses, and we discuss liquefaction-induced earth pressure on a pile group during the shaking in the direction perpendicular to ground flow. Numerical analyses predicted the peak displacement of footing and peak bending moment of the group pile. The earth pressure on the pile in the crustal layer is most important for the evaluation of the peak bending moment along the piles. In addition, the larger curvatures in the bending moment distribution along the piles at the water side in the liquefied ground were measured and predicted.     

Seismic behavior of bridges with pier and foundation strengthening: PsD tests and analytical study

By means of a simplified three degrees of freedom model, seismic behavior of reinforced concrete bridge piers and foundations were evaluated based on pseudo‐dynamic (PsD) tests for cases where pier strengthening and foundation strengthening are implemented. In addition, analysis based on PsD test results was conducted to investigate the influence of pier strengthening on seismic damage to the foundation. The PsD tests and the analysis show that the foundation suffers increased hysteretic response when pier strengthening is applied. The results also show that the foundation strengthening can prevent foundation damage. Copyright © 2011 John Wiley & Sons, Ltd.     

Response of three Athens metro underground structures in the 1999 Parnitha earthquake

The M_s 5.9 earthquake of 1999 produced valuable records in three underground structures, as follows: (a) in the just completed cut-and-cover station of Sepolia two accelerographs recorded the free-field and the station-base motion; (b) in the still under-construction tunnelled station of Monastiraki an accelerograph recorded the ground surface motion, and (c) in the nearby Kerameikos station, abandoned for non-technical reasons, the temporary prestressed-anchor piled (PAP) wall was still in place and produced a record of total seismic displacement at its top. Directly or indirectly utilising these records, the article outlines the results of numerical analyses aimed at ‘recovering’ the complete seismic response of the three underground structures. Particular emphasis is given to Sepolia station, where the developed accelerations (with PGA of about 0.17 g at the station base and 0.43 g at the station roof) are shown to have been almost exactly equal to the design accelerations according to the seismic code under the assumption that the station responds as an aboveground structure. The successful performance of the two temporary structures, in Monastiraki and Kerameikos (which had been designed against minimal acceleration levels but experienced ground-surface high-frequency accelerations of the order of 0.50 g) is explained through dynamic response analyses.     

Seismic behaviour of shallow foundations: Shaking table experiments vs numerical modelling

The capability of a simplified approach to model the behaviour of shallow foundations during earthquakes is explored by numerical simulation of a series of shaking table tests performed at the Public Works Research Institute, Tsukuba, Japan. After a summary of the experimental work, the numerical model is introduced, where the whole soil–foundation system is represented by a multi‐degrees‐of‐freedom elasto‐plastic macro‐element, supporting a single degree‐of‐freedom superstructure. In spite of its simplicity and of the large intensity of the excitation involving a high degree of nonlinearity in the foundation response, the proposed approach is found to provide very satisfactory results in predicting the rocking behaviour of the system and the seismic actions transmitted to the superstructure. The agreement is further improved by introducing a simple degradation rule of the foundation stiffness parameters, suitable to capture even some minor details of the observed rocking response. On the other hand, the performance of the model is not fully satisfactory in predicting vertical settlements. Copyright © 2007 John Wiley & Sons, Ltd.     

地震发生过程的有限单元法模拟——以苏门答腊俯冲带上的大地震为例

地震预报由目前的经验预报走向物理预报,数值模拟地震过程是其中的关键.文中应用统一的数学公式表述了速率相关的摩擦接触中黏着（sticking）和滑移(sliding)这两种不同的运动状态;有限元计算中采用静力显示的时间积分方法,基于R最小策略,控制时间步长以保持力学状态变化稳定,从而保证有限元计算过程平稳、收敛.以2004年发生过Mm=9.3特大地震的苏门答腊俯冲带为例,模拟了俯冲带上俯冲板片与上伏板块之间的闭锁、解锁、滑动到再闭锁这一准周期性过程,即地震的孕育、发生过程.计算结果表明,俯冲带上具有较大尺度、介质均匀、摩擦系数相同的区域是产生大规模、大幅度整体突然滑动（即大地震）的条件;模拟的苏门答腊俯冲带上的大地震在时间上有准周期性,空间上有迁移特征,破裂由深部向浅部进行;此外,俯冲带的几何特征对大地震的震源位置有很大的影响.