Dynamic pressures on a pair of rigid walls retaining poroelastic soil

This work deals with the evaluation of the dynamic pressures and the associated forces on a pair of rigid vertical cantilever walls retaining a uniform, fully saturated poroelastic layer of soil. Hysteretic damping in the soil skeleton may also be present. Wall pressures and forces are induced by horizontal ground shaking harmonically varying with time and spatially invariant. The problem is solved analytically under conditions of plane strain. The governing partial differential equations of motion, after separation of variables and the simplifying assumptions of zero vertical normal stresses and zero horizontal variation of vertical displacements, reduce to a system of two ordinary differential equations for the amplitudes of the solid skeleton horizontal displacement and the pore water pressure, which are easily solved. The parameters examined include the ratio of the distance between walls to the height of the retained soil material and the soil material properties such as porosity, permeability and damping. The comprehensive numerical data presented indicate that the displacements, wall pressures and resultant forces are highly dependent on the distance between the walls for any values of porosity and permeability.     

Application of Biot's poroelasticity to some soil dynamics problems in civil engineering

This review type of paper shows how the poroelastodynamic theory of Biot can be applied to some soil dynamics problems encountered in transportation engineering, which have been solved by the present authors. These problems involve rigid walls retaining poroelastic soil and subjected to harmonic seismic waves and moving loads on poroelastic soil. Both classes of problems involve a soil layer over bedrock, are of the plane strain type and are solved analytically by two methods: a direct (almost exact and exact for the above two classes of problems) method and an approximate method. The effects of shear modulus, porosity, permeability and hysteretic damping of the soil medium as well as the seismic frequency for retaining walls and velocity for moving loads on the dynamic response are numerically evaluated in order to assess their relative importance on that response.     

Seismic Displacement of Gravity Walls by a Two-body Model

Gravity walls retaining dry soil are modeled as a system of two bodies: (a) the gravity wall that slides along the wall-foundation soil boundary and (b) the critical soil wedge in the soil behind the wall. The strength of the system is defined by both the frictional and the cohesional components of resistance. The angle of the prism of the critical soil wedge behind the wall is obtained using the limit equilibrium method. The model accounts for changes in the geometry of the backfill soil behind the wall by considering the displacements at the end of each time step under limit equilibrium. The model shows that the standard (single) block model is over-conservative for the extreme case of critical-to-applied-seismic acceleration ratios less than about 0.30, but works well for cases where this ratio ranges between 0.5 and 0.8. The model is applied to predict the seismic displacement of gravity walls (a) tested in the shaking-table and (b) studied numerically by elaborate elasto–plastic analyses.     

Seismic behaviour of flexible retaining systems subjected to short-duration moderately strong excitation

Using finite-element modelling, this paper explores the magnitude and distribution of dynamic earth pressures on several types of flexible retaining systems: L-shaped reinforced-concrete walls, piled walls with horizontal or with strongly inclined anchors, and reinforced-soil walls. The utilized base excitation is typical of earthquake motions of either high or moderately low dominant frequencies having a peak ground acceleration (PGA) of 0.40 g and relatively short duration. Linear as well as non-linear (Mohr–Coulomb) soil behaviour is investigated, under dry conditions. The results show that, as the degree of realism in the analysis increases, we can explain the frequently observed satisfactory performance of such retaining systems during strong seismic shaking.     

A new limit equilibrium method for the pseudostatic design of embedded cantilevered retaining walls

This paper describes a new pseudostatic limit equilibrium method for the design of cantilevered retaining walls under seismic actions. The method has been applied in a parametric study of the effects of the geometry of the wall, considering different excavated and embedded depths, of the strength of the soil, and of the contact between the soil and the wall. The pseudostatic predictions are in very good agreement, both in terms of horizontal contact stress and bending moment distributions, with the results of truly dynamic 2-D finite difference analyses and published experimental data. It is found that for increasing strengths of the soil–wall system both the critical acceleration and the maximum bending moment on the wall increase. In other words, a stronger soil–wall system will experience smaller displacements during the earthquake, but this is paid for by increasing internal forces in the wall.     

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example.     

1D harmonic response of layered inhomogeneous soil: Analytical investigation

The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.     

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.     

On the effective seismic input for non-linear soil-structure interaction systems

Two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately. The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free-field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil-structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil-structure interface of the complete system. It is shown, further, that the free-field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free-field ground motion at a site is usually specified at a single reference point.     

Vertical and rocking impedances for rigid rectangular foundations on soils with bounded non-homogeneity

The vertical and rocking response of rigid rectangular foundations resting on a linear-elastic, compressible, non-homogeneous half-space soil model is studied. The non-homogeneity is described by a continuous yet bounded increase of shear modulus with depth. The mixed boundary value problem is solved by means of the semi-analytical method of the subdivision of the foundation/soil contact area whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green's functions for the particular soil model. Impedance functions are given for representative values of the non-homogeneity parameters, the Poisson's ratio and the foundation geometry over a wide range of frequencies. Significant features associated with the soil non-homogeneity are pointed out. Copyright © 1999 John Wiley & Sons Ltd.     

Seismic active thrust on cantilever walls with short heel

This note presents an analytical solution of the thrust on retaining walls with short heel, where the seismic action is simulated through the pseudo-static approach. The critical shape of the thrust wedge is assumed to be that minimizing the safety factor against wall sliding. This procedure is also congruent with the original method of Coulomb. The problem is mathematically expressed by a system of two equations, the first cubic and the second quadratic, whose solution converges quickly.     

地下隧道轴向地震动土作用分析

以弹性基岩上覆层状场地中刚性衬砌隧道为模型,采用间接边界元方法求解衬砌隧道所受的沿轴向地震动土作用,通过参数分析揭示轴向动土作用的幅值大小、空间分布等基本规律。研究表明,土-隧道动力相互作用对地震动土作用的空间分布形式影响较小,但对地下隧道所受地震动土作用峰值大小具有显著影响,隧道主要位置点的地震动土作用峰值与隧道相应位置处自由场土层应力相比放大1.7~2.4倍。论文最后提出一个轴向地震动土作用的简化计算方法。     

水平成层均质土地震反应非线性分析的半解析算法

采用动态应力-应变关系及其推广的Masing加卸载准则,考虑土体在地震等不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解相结合,提出了该动力非线性方程的半解析时域算法,以水平成层场地一维剪切梁模型为例,建立了求解土体地震反应的非线性分析技术。针对Seed-Idriss给出的砂土平均曲线,分析计算了非均匀层状密砂的线性和非线性地震反应。     

Earthquake-induced displacements of gravity retaining walls and anchor-reinforced slopes

This paper examines in terms of seismic performance, the effectiveness of anchor reinforcement against gravity retaining walls used to stabilize a dry homogenous fill slope in earthquake-prone environment. Both analyzed stabilizing measures have the same design yield acceleration estimated from a limit equilibrium approach. The earthquake-induced displacements are calculated using a sliding block formulation of the equation of motion. Sliding failure along the base of the gravity retaining wall and rotational failure of the soil active wedge behind the wall, as well as rotational failure of the slide mass of the anchor-reinforced slope were considered in the present formulation. For the specific characteristics of the analyzed fill slope and input horizontal ground motion, the slope reinforced with anchors appears to experience vertical and horizontal seismic displacements at slope crest smaller by 12% and respectively, 32% than the vertical and horizontal earthquake-induced deformations estimated at the top of the active wedge behind the gravity retaining wall.     

幂函数剪切模量成层土非线性地震反应的半解析算法

运用文献[1]所建议的动态应力一应变关系及其推广的Masing加卸载准则,考虑土料在地震等产生的不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解[2]相结合,提出了该动力非线性方程的半解析时域算法,基于改进的一维剪切梁模型,对剪切模量是其深度的某一幂函数的成层非均质土层,建立了求解土体地震反应的非线性分析技术。针对文献[2]中的土层剖面,做了计算、分析和讨论。     

Dynamic pressures on rigid cantilever walls retaining poroelastic soil media. Part I. First method of solution

The problem of the determination of dynamic pressures and the associated forces on a rigid, vertical cantilever wall retaining a semi-infinite, uniform, fully-saturated poroelastic layer of soil is solved analytically under conditions of plane strain. Hysteretic damping in the soil skeleton may also be present. The rigid wall and the base of the soil layer are both excited by an acceleration harmonically varying with time and spatially invariant. The governing partial differential equations of motion, after separation of variables and the simplifying assumption of zero vertical normal stresses, reduce to a system of two ordinary differential equations for the amplitudes of the horizontal solid skeleton displacement and the pore water pressure, which are easily solved. Soil displacements and stresses, wall pressures and resultant forces as well as the pore water pressure are explicitly expressed. Their variation with frequency, hysteretic damping, porosity and permeability is numerically computed in order to assess the relative importance of the various parameters on the response.     

Use of rubberised backfills for improving the seismic response of integral abutment bridges

Reuse of the 1.5 billion waste tyres that are produced annually is a one of the major worldwide challenges, as waste tyres are toxic and cause pollution to the environment. In recognition of this problem, this paper introduces the reuse of tyres, in the form of derived aggregates in mixtures with granulated soil materials, as previous studies indicated the potential benefits of these materials in the seismic performance of structures. The objective of the present research study is to investigate whether use of rubberised backfills benefits the seismic response of Integral Abutment Bridges (IABs) by enhancing soil-structure interaction (SSI) effects. Numerical models including typical integral abutments on surface foundation with nonlinear conventional backfill material and its alternative form as soil-rubber mixtures are analysed and their response parameters are compared. The research is conducted on the basis of parametric analysis, which aims to evaluate the influence of different rubber-soil mixtures on the dynamic response of the abutment-backfill system under various seismic excitations, accounting for dynamic soil-abutment interaction. The results provide evidence that the use of rubberised backfill leads to reductions in the backfill settlements, the horizontal displacements of the bridge deck, the residual horizontal displacements of the top of the abutment and the pressures acting on the abutment, up to 55, 18, 43 and 47 % respectively, with respect to a conventional backfill comprising of clean sand. Small change in bending moments and shear forces on the abutment wall is also observed. Therefore, rubberised backfills offer promising solution to mitigate the earthquake risk, towards economic design with minimal damage objectives for the resilience of transportation networks.     

Spatially coupled vibrations of a suspension bridge under random highway traffic

The problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single-span thin-walled beam underslung to two cables. The response of the bridge in the space-time domain is described by a coupled system of non-linear, integro-differential equations. The dynamic influence functions of vertical and horizontal deflections at each cross-section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer-oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs.     

双层打包带加固窗间墙抗震性能试验研究

地震时砌体结构窗间墙易发生破坏,为了提高其抗震性能,对高宽比为1的2组共4片墙体,其中:2片为双层打包带加固墙体,2片为原墙,进行了拟静力试验,研究墙体的破坏形态、水平承载力、滞回曲线和耗能等抗震性能。试验发现原墙发生剪切破坏,加固后墙体发生摇摆破坏,加固改变了墙体破坏模式,加固后墙体滞回曲线饱满但有捏笼,破坏荷载、延性和耗能能力都有提高,破坏时未发生剥离,表明双层打包带加固法有效地提高了窗间墙体抗震性能,对承受较大竖向应力墙体效果更好,建议加固时要加强加固层与窗下和窗上墙体的连接。     

软土场地地铁车站抗震计算的等代地震加速度法

将软土地层中地铁车站结构与周围土体地震时产生的水平加速度,以静态的水平加速度代替,使两者作用下结构内力最大值相等、出现部位相同,实现将动力问题转化为静力问题。结果表明,该方法能反映软土地层中两层三跨地铁车站的在地震时的动力响应,是适用于工程设计的简单、实用的数值方法。