Evaluation of seismic displacements of quay walls

A new simplified dynamic analysis method is proposed to predict the seismic sliding displacement of quay walls by considering the variation of wall thrust, which is influenced by the excess pore pressure developed in backfill during earthquakes. The method uses the Newmark sliding block concept and the variable yield acceleration, which varies according to the wall thrust, to calculate the quay wall displacement.A series of 1 g shaking table tests were executed to verify the applicability of the proposed method, and a parametric study was performed. The shaking table tests verified that the proposed method properly predicts the wall displacement, and the parametric study showed that the evaluation of a realistic wall displacement is as important as the analysis of liquefaction potential for judging the stability of quay walls.     

Numerical analysis of deformation behaviour of quay walls under earthquake loading

In the last 50 years, there have been many incidences of failure of gravity quay walls. These failures are often associated with significant deformation of liquefiable soil deposits. Gravity quay wall failures have stimulated great progress in the development of deformation-based design methods for geotechnical structures. In this paper, the effective-stress analysis method has been used in conjunction with a generalised elasto-plasticity constitutive model implemented into a finite element procedure. Various monotonic and cyclic triaxial paths are simulated in order to demonstrate the capabilities of the constitutive model. The FEM is validated by back analysis of a typical Port Island PC1 caisson type quay wall, which was damaged during the 1995 Hyogoken-Nanbu earthquake. The numerical results are compared with the observed data obtained consisting of seaward displacement, settlement and tilting. In addition, both the influence of permeability, on the generation of pore water pressure and the influence of the relative density of the backfill and foundation layers, on the residual deformation of gravity quay walls are investigated.     

Static and dynamic behavior of hunchbacked gravity quay walls

One of the parameters that can affect the lateral pressures behind a retaining wall is the back-face shape of the wall, which can be controlled by the designer, and has not been investigated experimentally. Therefore, in order to study this behavior, a set of 1g shaking table tests was carried out on hunched back gravity type quay walls made of concrete blocks. Crushed stone and silica sand were used in the backfill and subsoil, respectively. The subsoil was prepared by moist tamping. The models were fully instrumented and beside each earth pressure transducer a pore water pressure sensor was also installed behind the wall therefore the lateral effective stress acting on the wall could be calculated. Tests were performed with various base accelerations on models with different subsoil relative densities. The results show that the earth pressure increases at upper portions of the wall and decreases by the leaning slope at lower elevations. Depending on the back-face shape of the wall the total thrust and overturning moment would be increased or decreased after an earthquake. However, the hunched back-shape of the wall tends to raise the point of application of the total thrust exerted on the wall. Other advantages of hunched back walls are demonstrated as well.     

Evaluation of force components acting on gravity type quay walls during earthquakes

In the analysis of the seismic stability of gravity type quay walls, the magnitudes of force components acting on quay walls during earthquakes and the phase relationships among these force components must be properly evaluated. In general, the force components include inertia force of the wall, lateral earth force, and water force. The magnitude and the phase relationship of each force component vary with time, and are largely affected by the magnitude of excess pore pressure developed in the backfill soil of the quay wall. The dynamic thrust develops at the contact surface between the backfill soil and the wall as a result of the interaction among these force components. In this study, a simple model is proposed to evaluate the magnitude and the phase variation of the dynamic thrust on the back of the wall. The proposed model computes the dynamic thrust by using the force components calculated from existing equations. We verified the proposed model by comparing its results with those obtained from a series of shaking table tests.     

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.     

Phasing issues in the seismic response of yielding,gravity-type earth retaining walls – Overview and results from a FEM study

An overview of past and recent developments on the subject of seismic earth pressures on yielding, gravity-type walls, retaining cohesionless backfill, is first presented, focusing on available data on the issue of phase difference that develops between the peak values of wall inertia and seismic earth thrust increment. The results of a FEM parametric study are next presented regarding the dependence on the resulting dynamic earth thrust reduction – acting on the time of peak wall inertia – on backfill rigidity, wall height, and shaking characteristics. The reliability of the numerical analyses was verified by modeling centrifuge tests reported by Nakamura [24] and successfully comparing measured vs. computed behavior. The results of the parametric analyses indicate that the seismic active earth thrust, acting on the wall at the time of maximum wall inertia, is significantly reduced (compared to its peak value) with increasing shaking intensity of backfill, increasing wall displacements, increasing wall height, and decreasing backfill rigidity. No systematic dependence on the ratio of input motion frequency to the natural frequency of the backfill (f/f₁) was observed. The above findings: (1) verify earlier experimental and numerical results, (2) explain the reported lack of damage to retaining walls under strong ground shaking, and (3) indicate the need for revising the pertinent provisions of current seismic codes. Graphs summarizing the results of the numerical analyses are presented which may be used as a guide for selecting the magnitude of seismic active earth thrust that needs to be taken into account in the design of the examined type of earth retaining walls.     

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.     

三个抗震问题简析及新型挡墙地震反应评述

水平地震作用沿墙高的分布、弱粘性土地震土压力、和挡墙体系考虑水的作用是挡土墙抗震研究中的三个重要问题。首先对其研究进展进行了简要总结。然后针对近年来大量涌现的新型、异型、轻型挡土墙的抗震研究现状进行了评述，包括现场地震调查、振动台及离心机试验、悬臂L型挡土墙、锚杆式及土钉式挡土墙、加筋土挡土墙和地下室挡墙。最后，指出了存在的问题和提出今后的研究方向。     

地基条件对仰斜式挡墙地震响应影响及墙高限值研究

地基条件和墙高是影响挡土墙地震响应特征的重要因素。建立不同地基条件的仰斜式挡土墙有限元时程分析模型,以墙身外倾最大危险状态为最不利时刻,研究地基条件和墙高对挡墙动力响应及墙-土相互作用的影响特征,并以满足力学检算和墙身位移限值为出发点,提出同时考虑地基条件和地震峰值加速度PGA的仰斜式挡墙墙高控制建议。结果表明：岩质地基挡墙墙背动土压力沿墙高呈中部大、上下小的凸形分布,大震下土压力较中震时有小幅减小;基底反力呈墙踵为0、墙趾集中的三角形图式,且随PGA和墙高的增加踵部脱空趋势更为明显;土质地基挡墙因墙底地基土变形对墙后填土的牵连作用,填土跟随墙身运动的趋势加剧,墙背动土压力与PGA呈正相关并沿墙高近似呈线性分布,于墙底处最大;墙身往复摆动使踵趾端地基土体塑性变形较基底中部明显,基底反力峰值向中部转移;根据最不利时刻稳定性、承载力检算,考虑对墙身位移合理限制,提出地震区仰斜式挡墙的允许墙高在设防PGA不超过0.2g时为8 m, 0.4g大震下硬质岩地基挡墙可达8 m,软质岩地基挡墙不宜超过6 m,碎石土、砂质黏土地基挡墙不宜超过4 m。     

基于P-Z模型的直立墙振动台试验数值模拟

基于块石静、动室内三轴试验确定的广义塑性模型参数,对直立墙结构振动台试验进行有限元数值模拟,并与试验结果进行对比分析,进一步探讨直立墙结构在地震荷载作用下的破坏过程和破坏特征。计算表明:该模型可较合理地模拟直立墙结构的地震反应特性和破坏特征,计算结果与试验现象基本相符。位于抛石基床上的直立墙结构破坏模式为直立墙向外海侧的滑移、倾斜和竖向沉降,其破坏过程为:当输入加速度较小时,直立墙处于稳定状态;随着输入加速度逐渐增大,直立墙在自身惯性力和墙后回填块石的动土压力作用下缓慢向外海侧水平滑移、倾斜和竖向沉降,墙后回填块石出现沉陷,但变形较小;当加速度达到一定值时,直立墙向外海侧移动和回填块石沉陷速率急剧增加,变形较大。     

Mitigation measures for pile groups behind quay walls subjected to lateral flow of liquefied soil: Shake table model tests

This paper presents experimental results of a series of 1g shake table tests on mitigation measures for a model consisting of a 3×3 pile group and a sheet-pile quay wall in which the pile group was subjected to liquefaction-induced lateral spreading. First, general observations associated with the mechanism of lateral spreading and pile response are presented based on tests without remedial measures, followed by in depth discussions. Second, three remedial techniques were deployed to provide an adequate seismic performance of the pile group and the quay wall: (i) mitigating sheet pile of floating type, (ii) mitigating sheet pile of fixed end type, and (iii) anchoring the quay wall to a new pile row. The main objective of these mitigation methods was to restrict ground distortion behind the quay wall, enhancing seismic response of pile group and quay wall. This mitigation philosophy was decided based on the outcome of the first part, which consisted of a series of tests without mitigation measures. In addition, it should be noted that the proposed countermeasures were selected to be applicable for existing vulnerable pile groups, which are at risk of liquefaction and lateral spreading. Results of different mitigation tests are comparatively examined using a parameter called reduction factor, and the effectiveness of each countermeasure is discussed in detail. The results demonstrate that by applying the proposed mitigation measures the seismic performance of both pile group and quay wall can be improved, as a result of reduction in soil displacement and velocity of soil flow.     

Plastic hinge analysis for lightly reinforced and unconfined concrete structural walls

Poor performance of lightly reinforced and unconfined concrete structural walls have been observed in recent earthquake events. This research investigates the displacement capacity of such walls by comparing the results of a series of state-of-the-art finite element analyses for a range of different structural walls to that estimated using plastic hinge analyses. The common expressions used in estimating the yield curvature, yield displacement and plastic displacement are scrutinised for these types of walls. Some recommendations are given to improve the prediction of the displacement capacity of lightly reinforced and unconfined rectangular and C-shaped walls for flexural actions using a plastic hinge analysis. Importantly, a parameter has been recommended to be used in a “modified” approach for estimating the nominal yield displacement of lightly reinforced concrete walls. Different expressions are also recommended depending on the amount of longitudinal reinforcement used in the wall in comparison to that required to initiate secondary cracking. This is important for providing better estimations of the displacement capacity of RC structural wall buildings in low-to-moderate seismic regions such that vulnerability studies can be conducted.     

Centrifuge modeling of the behavior of caisson-type quay walls during earthquakes

A series of 2-D centrifuge modeling tests with an in-flight shaker were carried out in order to model both the deformation characteristics of backfill and the seismic responses of caisson-type walls embedded in soils with various permeabilities. The rotational and translational modes were found to be in phase or various degrees out of phase with each other for quay walls embedded in soils with varying permeabilities. The alternative pumping and suction processes in excess pore water pressure that are caused by a wall's vibrations increase the level of damage because large amounts of backfill are forcedly leaked into the sea. The test results show that the rotational mode makes the dominant contribution to the changes in excess pore water pressure and in the earth pressure in the deep layers of soil, but the translational mode makes the dominant contribution to these pressures in the shallow layers. The average shear wave velocities were found to decrease rapidly to values as low as 1/8th of the velocity measured at the beginning of shaking.     

Numerical analysis of reinforced soil walls with granular and cohesive backfills under cyclic loads

Novel approaches to the dynamic analysis of the reinforced soil walls have been reported in the literature. Use of marginal soils reduces the cost of geosynthetic reinforced soil walls if proper drainage measures are taken. Therefore the affect of using cohesive marginal soils as backfill in geosynthetic reinforced retaining structures were investigated in this research. The dynamic response of reinforced soil walls was investigated in a similar focus, using finite element analysis. The results obtained from walls with cohesive backfill were compared to the results obtained from walls with granular backfill. The height of the wall was chosen as 6 m in the two-dimensional plane strain finite element model and the base acceleration was chosen to be a harmonic motion. The effects of various parameters like the backfill type, facing type, reinforcement stiffness, and peak ground acceleration on the cyclic response of reinforced soil retaining walls were investigated. After analyzing the wall response for end of construction and dynamic excitation phases, it was determined that the deformations and reinforcement tensile loads increased during the cyclic load application and that the amount of additional deformation that occurred during cyclic load application was strongly related to backfill soil type, facing type, reinforcement type and peak ground acceleration. It was determined that a cohesive backfill and geotextile reinforcement was a good combination to reduce the deformations of geosynthetic reinforced walls during cyclic loading for medium height walls.     

Analytical and empirical models for predicting the drift capacity of modern unreinforced masonry walls

Displacement‐based seismic assessment of buildings containing unreinforced masonry (URM) walls requires as input, among others, estimates of the in‐plane drift capacity at the considered limit states. Current codes assess the drift capacity of URM walls by means of empirical models with most codes relating the drift capacity to the failure mode and wall slenderness. Comparisons with experimental results show that such relationships result in large scatter and usually do not provide satisfactory predictions. The objective of this paper is to determine trends in drift capacities of modern URM walls from 61 experimental tests and to investigate whether analytical models could lead to more reliable estimates of the displacement capacity than the currently used empirical models. A recently developed analytical model for the prediction of the ultimate drift capacity for both shear and flexure controlled URM walls is introduced and simplified into an equation that is suitable for code implementation. The approach follows the idea of plastic hinge models for reinforced concrete or steel structures. It explicitly considers the influence of crushing due to flexural or shear failure in URM walls and takes into account the effect of kinematic and static boundary conditions on the drift capacity. Finally, the performance of the analytical model is benchmarked against the test data and other empirical formulations. It shows that it yields significantly better estimates than empirical models in current codes. The paper concludes with an investigation of the sensitivity of the ultimate drift capacity to the wall geometry, static, and kinematic boundary conditions.     

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.     

地震与海啸作用下重力式岸墙旋转位移拟静力分析

被动状态下位移预测是挡墙地震工程设计中的关键,而岸墙后回填土的孔隙水压力对墙体运动具有一定影响。采用拟静力法计算墙后部分浸水土体的被动动土压力,根据静力水压力理论近似计算土颗粒里的动水压力;同时考虑地震荷载和海啸力的作用,根据力矩极限平衡确定旋转门槛加速度系数,采用旋转块体方法计算岸墙被动旋转运动下的地震位移。探讨回填砂土内摩擦角、墙体与土间摩擦角、地震加速度系数、回填土地下水位、海啸波浪高度等参数对旋转位移的影响。     

挡土墙地震反应非线性波动模拟

本文运用解耦近场非线性波动数值模拟方法研究挡土墙地震反应，为反映墙土体系在地震作用下的位移机制，引入了Desai薄层单元模拟墙土间接触面，并采用双线型本构关系作为接触面单元和土体的非线性模型，在此基础上给出了解决P—SV问题的非线性显式有限元时域递推公式，为进一步发展非线性波动数值模拟技术提供了有益经验。为验证本文方法及适用性，将数值模拟结果与Zeng，X．和Madabhushi，X．P．G．等的离心机试验和弹塑性数值模拟结果进行对比。结果表明：墙土体系加速度、挡土墙顶底相对滑移、沉降和墙体倾角等同离心机试验模拟结果基本吻合，与弹塑性数值模拟结果相似。     

轻质砌块填充墙对钢框架地震反应影响分析

本文根据现有的填充墙钢框架结构试验和理论研究成果,提出了一种适用于结构整体分析的框架填充墙有限元模型。采用杆系模型并编制了相应的弹塑性地震反应分析程序。通过对空框架和带填充墙钢框架的地震反应分析,研究了轻质砌块填充墙的存在对钢框架顶层位移反应、底层柱弯矩及柱轴力反应的影响,得出了有益的结论。为进一步完善钢结构抗震设计提供了理论基础。     

Analytical solution of seismic pseudo-static active thrust acting on fascia retaining walls

This paper presents a limit equilibrium method, based on the approach of Mononobe and Okabe, for calculating the active thrust on fascia retaining walls, where common methods cannot be used owing to the narrowness of the backfill which does not permit the development of the thrust wedge in the shape and sizes predicted by these methods. The proposed method examines three distinct failure mechanisms, called Mechanism 1, Mechanism 2 and Mechanism 3, where the thrust wedge is formed by one, two or three blocks, respectively; separated by plane slip surfaces. The seismic forces have been simulated with the pseudo-static method. For all three mechanisms, the active thrust is obtained in closed form: in particular, with a cubic equation for Mechanism 2, and with a system of two equations, one cubic and the other quartic, for Mechanism 3. Mechanisms with more than three blocks cannot have analytical solutions. The study is completed by an examination of some significant cases from which the higher attenuation of the seismic thrust, with respect to the static, emerges as the backfill width reduces.