Generalized solution to Coulomb’s seismic active earth pressure acting on rigid retaining wall with cohesive backfill and trial application for evaluation of seismic performance of retaining wall

In this paper, a general solution for evaluating the Coulomb-type seismic active earth pressure that acts on a rigid retaining wall from the cohesive backfill soil is shown together with its derivation process. In the proposed solution, the mobilization of the cohesion on the failure plane in the backfill soil of the retaining wall and the associated increase in shear strength are considered in the pseudo-static limit equilibrium approach under the assumption that the cohesion is uniformly distributed in the backfill soil. The angle of the failure plane and the seismic active earth pressure calculated by the proposed equation completely agree with the calculation results by the trial wedge method, which shows the validity of the proposed solution. In addition, by combining the concept of the Modified Mononobe-Okabe method and the proposed equation, a calculation method for the seismic active earth pressure is proposed. It can consider the effect of backfill cohesion and can be applied even under a large seismic load. Furthermore, a series of trial analyses on the effect of backfill cohesion on the seismic performance of the retaining wall is also conducted using the proposed equation. A series of analyses using the case of a retaining wall damaged during the 1995 Hyogo-ken Nanbu earthquake shows that the effect of backfill cohesion is significant in the seismic performance evaluation and the design of aseismic reinforcements.     

Seismic earth pressures on flexible cantilever retaining walls with deformable inclusions

In this study, the results of 1-g shaking table tests performed on small-scale flexible cantilever wallmodels retaining composite backfill made of a deformable geofoam inclusion and granular cohesionlessmaterial were presented. Two different polystyrene materials were utilized as deformable inclusions.Lateral dynamic earth pressures and wall displacements at different elevations of the retaining wallmodel were monitored during the tests. The earth pressures and displacements of the retaining wallswith deformable inclusions were compared with those of the models without geofoam inclusions.Comparisons indicated that geofoam panels of low stiffness installed against the retaining wall modelaffect displacement and dynamic lateral pressure profile along the wall height. Depending on the inclusioncharacteristics and the wall flexibility, up to 50% reduction in dynamic earth pressures wasobserved. The efficiency of load and displacement reduction decreased as the flexibility ratio of the wallmodel increased. On the other hand, dynamic load reduction efficiency of the deformable inclusionincreased as the amplitude and frequency ratio of the seismic excitation increased. Relative flexibility ofthe deformable layer （the thickness and the elastic stiffness of the polystyrene material） played animportant role in the amount of load reduction. Dynamic earth pressure coefficients were compared withthose calculated with an analytical approach. Pressure coefficients calculated with this method werefound to be in good agreement with the results of the tests performed on the wall model having lowflexibility ratio. It was observed that deformable inclusions reduce residual wall stresses observed at theend of seismic excitation thus contributing to the post-earthquake stability of the retaining wall. Thegraphs presented within this paper regarding the dynamic earth pressure coefficients versus the wallflexibility and inclusion characteristics may serve for the seismic design of full-scale retaining walls withdeformable polystyren     

循环荷载作用下黏性土加筋挡墙有限元动力特性分析

在循环荷载作用下,对加筋土挡墙进行有限元模拟分析,研究黏性土加筋土挡墙的动力特性.重点研究挡墙回填土为黏性土条件下,不同加筋材料、动荷载峰值加速度对加筋土挡墙的影响.由计算结果认为在循环荷载作用下加筋土挡墙水平位移受动荷载峰值加速度影响较大,加筋土挡墙最大位置出现在挡墙下部,黏性回填土的加筋土挡墙变形量要小于砂土回填的加筋土挡墙.     

基于性能的重力式挡墙地震易损性分析

位于高烈度地震区的支挡结构时刻面临着特大震灾的严峻考验,迄今国内外还没有人针对重力式挡墙系统地做过易损性方面的研究工作。采用增量动力分析方法,考虑地震动输入的不确定性,选取PGA为地震强度参数,挡墙的位移指数D_I为性能参数,基于振动台模型试验划分了挡墙的抗震性能水准,利用FLAC^3D对8 m高的重力式挡墙进行了地震动力响应分析和地震易损性分析,通过易损性曲线对挡墙在不同地震动作用下的易损性进行了评估和对比分析。研究表明：PGA与挡墙的位移指数近似呈指数关系,当地震动加速度小于0.4g时,场地条件对墙体位移指数的影响不显著,当地震动加速度大于0.4g时,土质场地挡墙位移指数与岩石场地挡墙相比显著增大,墙体位移指数受场地条件的影响显著。当PGA<0.4g时,挡墙基本保持完好或以轻微损伤破坏为主;当PGA>0.6g时,挡墙已完全损伤,发生严重损坏的概率也较大;当PGA>0.8g时,会造成挡墙的严重损坏,甚至可能造成整体倒塌,需要采取一定的抗震加固措施。     

强地震荷载作用下临水挡土墙的拟动力法稳定性分析

 假设墙后填土破坏面为曲面,用正弦波模拟地震加速度时程曲线,采用拟动力法对临水挡土墙进行稳定性分析,确定了挡土墙和墙后填土所受的阻尼力和惯性力,获得地震荷载作用下挡土墙的被动土压力、抗滑和抗倾覆稳定性系数的封闭形式解析解。定量分析地震加速度、放大系数、墙后填土的物理力学参数和动水压力对挡土墙的滑动位移、挡土墙的抗滑和抗倾覆稳定性系数的影响,得出当地震加速度、放大系数越大,水位越高,内摩擦角越小,临水挡土墙的稳定性越差。     

1 g Shaking table model tests on seismic active earth pressure acting on retaining wall with cohesive backfill soil

The effects of backfill cohesion on the seismic behavior of a retaining wall are discussed on the basis of a series of 1 g shaking table model tests. The model test results show that a retaining wall having cohesive backfill soil is more stable than a wall without it. The following aspects are observed in the cases of cohesive backfill soil from a detailed analysis using the measured seismic active earth pressure acting on the retaining wall: 1) the existence of a stable region at the top part of the backfill soil, 2) the increase in shear force acting on the boundary between the back face of the wall and the backfill soil, and 3) the mobilization of cohesion along the failure plane in the backfill soil.The existence of a stable region results in reductions in both the driving force and the overturning moment, while it tends to disappear under a high seismic load. The increase in shear force acting on the back face of the wall contributes to an increase in the resistant moment against the overturning of the wall with respect to the base of the footing, and it mobilizes even under a high seismic load. Mobilized cohesion along the failure plane contributes to the support of the soil wedge, resulting in a decrease in the seismic active earth pressure. It also continuously mobilizes even under a high seismic load.These observations indicate that giving consideration to the backfill cohesion when calculating the seismic active earth pressure leads to the rationalization of the evaluation of the seismic performance of the retaining wall even though further study is required, namely, carrying out the validation in the prototype scale and setting the applicable conditions for the seismic design.     

Reexamination of Mononobe-Okabe Theory of Gravity Retaining Walls Using Centrifuge Model Tests

Gravity retaining walls are widely used in Japan because of their simplicity of structure and ease of construction. In design procedure, the seismic coefficient method is widely employed, in which the earth pressure and inertia force are calculated by converting the seismic force into a static load. Earth pressure is usually calculated by the Mononobe-Okabe formula, which applies Coulomb's earth pressure computed from the equilibrium of forces in the static state. However, the Hyogoken-Nambu Earthquake of 1995 prompted the need to reexamine seismic design methods for various civil engineering structures. Gravity retaining wall is one of such structures whose seismic design has to be reexamined and rationalized. At this moment there is no clear empirical basis for converting the seismic force into a static load. The design method has to take into account the behavior of gravity retaining walls during earthquakes. At the Public Works Research Institute, model tests were conducted on gravity retaining walls using a centrifuge. The acceleration and displacement of a retaining wall and its backfill as well as the earth pressure acting on the wall were measured simultaneously together with the deformation behavior of the wall and its backfill, using a high-precision high-speed camera. The data show that the hypothetical conditions of the Mononobe-Okabe formula do not appropriately express the real behavior of backfill and gravity retaining walls during earthquakes.     

回填EPS混合土的防滑悬臂式挡墙地震稳定性分析

以一种带防滑齿的"T"型悬臂式挡土墙为对象,采用振动台模型试验揭示了分别回填EPS混合土和天然南京细砂时的挡墙地震稳定性特征。分析并比较了墙–土体系的地震反应以及墙背动土压力分布,重点讨论了试验的防滑悬臂式挡墙位移模式以及回填土性质对墙背动土推力的影响。试验结果表明,回填EPS混合土时,填土地表加速度反应相对更小。回填土的动土推力对墙体转动位移的贡献随激励峰值的增大而增大;墙–土惯性相互作用效应与回填土的动力变形模式密切相关。两种回填料下的墙背动土压力分布形态具有显著差异;砂土–挡墙体系的动土推力与地表峰值加速度间趋向非线性关系,作用点接近2/3墙高。回填EPS混合土时两者更接近线性关系,且动土推力作用点接近1/3墙高。两种体系的动土推力作用点随地表峰值加速度增大均略有下移。基于试验结果与几种经典的解析方法预测结果比较,给出了EPS混合土柔性挡墙抗震分析的几点建议。     

Seismic analysis of semi-gravity RC cantilever retaining wall with TDA backfill

The seismic behavior of Tire Derived Aggregate (TDA) used as backfill material of 6.10 m high retaining walls was investigated based on nonlinear time-history Finite Element Analysis (FEA). The retaining walls were semi-gravity reinforced concrete cantilever type. In the backfill, a 2.74 m thick conventional soil layer was placed over a 3.06 m thick TDA layer. For comparison purpose, a conventional all soil-backfill model was also developed, and the analysis results from the two models under the Northridge and Takatori earthquakes were compared. The FEA results showed that both models did not experience major damage in the backfill under the Northridge earthquake. However, under the Takatori earthquake, the TDA-backfill model developed substantially large displacement in the retaining walls and in the backfill compared with the soil-backfill model. Regions of large plastic strain were mainly formed in the TDA layer, and the soil over the TDA layer did not experience such large plastic strain, suggesting less damage than the soil-backfill model. In addition, the acceleration on the backfill surface of the TDA-backfill model decreased substantially compared with the soil-backfill model. If an acceleration sensitive structure is placed on the surface of the backfill, the TDA backfill may induce less damage to it.     

Sliding stability and lateral displacement analysis of reinforced soil retaining walls

Field observations have demonstrated that reinforced soil retaining walls generally have superior seismic performance when compared to traditional gravity retaining walls. However, current design guidelines for reinforced soil retaining walls are typically based on pseudo-static methods of analysis, which involve simplifying assumptions. For instance, the reinforced zone is usually assumed as a rigid body in external stability calculations. As a result, the influences of reinforcement arrangement and properties on the sliding stability and displacement of the wall cannot be accounted for in their design. Additionally, the soil shear strength is assumed to be constant in conventional displacement calculations using the Newmark sliding block method. In this paper, an analysis method is proposed to determine the yield acceleration and lateral displacement of reinforced soil walls that includes soil shear strength mobilization and a two-part wedge planar failure mechanism. The proposed method is validated against the results of laboratory model tests, and influences of factors such as ground acceleration coefficients, and reinforcement and backfill properties on the stability of the wall are examined.     

地震作用下饱和回填砂土重力式挡土结构滑动与转动位移分析

 预测地震作用下重力式挡土结构的位移是基于位移抗震设计方法的关键。基于Newmark滑动理论、超孔隙水压力应力模型和累积损伤原理,建立饱和回填砂土中超孔压比时程计算模型,以及墙体滑动和转动临界加速度时程计算模型。基于所建立的模型,提出用于计算饱和回填砂土重力式挡土结构滑动和转动位移的计算方法。采用该方法,分析土体参数和地震动参数对墙体滑动及转动位移的影响,并对墙体滑动与转动的耦合作用进行研究。结果表明,填土不发生液化的情况下,滑动位移对土体相对密度和墙体与地基土间的摩擦角十分敏感;转动位移对输入地震的震级、水平加速度和竖向加速度、填土的内摩擦角、墙背摩擦角和相对密度均较为敏感。超孔隙水压力对墙体滑动和转动位移的影响不可忽视。在地震作用下墙体与墙后填土破坏土楔体共同运动的假设条件下,墙体滑动与墙体转动相互抑制。     

Active static and seismic earth pressure for c–φ soils

Rankine classic earth pressure solution has been expanded to predict the seismic active earth pressure behind rigid walls supporting c–φ backfill considering both wall inclination and backfill slope. The proposed formulation is based on Rankine's conjugate stress concept, without employing any additional assumptions. The developed expressions can be used for the static and pseudo-static seismic analyses of c–φ backfill. The results based on the proposed formulations are found to be identical to those computed with the Mononobe–Okabe method for cohesionless soils, provided the same wall friction angle is employed. For c–φ soils, the formulation yields comparable results to available solutions for cases where a comparison is feasible. Design charts are presented for calculating the net active horizontal thrust behind a rigid wall for a variety of horizontal pseudo-static accelerations, values of cohesion, soil internal friction angles, wall inclinations, and backfill slope combinations. The effects of the vertical pseudo-static acceleration on the active earth pressure and the depth of tension cracks have also been explored. In addition, examples are provided to illustrate the application of the proposed method.     

路堤震害风险概率评价与管理研究

 路堤震害在破坏性地震中十分普遍,开展路堤震害风险概率评价并提出合理的震害风险管理方法对提高公路抗震能力和区域防灾减灾能力具有重要意义。进行路堤震害等级划分,选取路堤震害损伤参数,建立路堤震害等级与震害损伤参数的对应关系;以连霍高速公路西宝段K1125+470处路堤为例开展基于CPSHA的公路地震危险性评价,基于IDA和PSDA的路堤震害易损性评价以及基于危险性曲线的路堤震害风险概率评价;在明确路堤震害风险可接受度的基础上提出路堤震害风险管理方法,验证挡土墙对提高路堤抗震性能的积极作用。研究结果表明：连霍高速公路西宝段地震危险性评价结果比第四代地震区划图略高,这与目前渭河断陷盆地地震活跃的现实是一致的;PGA(PGA为地震动峰值加速度)达到0.6 g时,路堤超越严重损伤的概率为65.910%,达到0.8 g时,超越严重损伤的概率为99.995%,说明路堤震害易损性较高;路堤未来50 a超越严重损伤的风险概率为36.46%,发生基本完好和轻微损伤的风险概率为28.49%;以路堤未来50 a发生毁坏的风险概率40%为风险可接受度,路堤震害风险管理方法适用于新建路堤的抗震设计和已建路堤的抗震加固;未来50 a有挡土墙路堤超越严重损伤的风险概率比无挡土墙路堤低15.29%,发生基本完好和轻微损伤的风险概率比无挡土墙路堤高15.62%。     

A Displacement Prediction Method for Retaining Walls Under Seismic Loading

This paper describes a new calculation method for seismic displacement of retaining walls. A macroscopic failure surface and a plastic displacement potential in the general load space are considered in the method to evaluate the subgrade reaction force from foundation ground. The method is capable of calculating not only horizontal, vertical or rotational displacement alone, but also their combined effect. The method is validated through comparison with centrifuge test results of a gravity retaining wall with dense backfill sand subjected to strong base shaking. The calculated displacement components, that is vertical, horizontal and rotational displacement at the end of shaking, compared well with those measured. It also appeared that previously proposed conventional displacement calculation methods based on Newmark’s sliding block analogy might underestimate the displacement. The assumption of the constant frictional coefficient may be responsible for this.The proposed method is limited to retaining walls resting on soils where dramatic degradation of soil strength due to the generation of excess pore pressure does not occur.     

地震动土压力水平层分析法

Mononobe-Okabe公式是挡土结构设计中关于侧向动土压力计算的常用方法。但Mononobe-Okabe公式的诸多假设使得其公式适用范围受限,而且无法给出地震动土压力合力作用点位置及地震动土压力强度沿墙背分布情况。为弥补以上不足,基于Mononobe-Okabe平面破裂面假设,采用水平层分析法推导地震条件下主动和被动土压力合力及其作用点位置、土压力强度分布公式,并采用图解法得到临界破裂角的显式解答。公式考虑水平和垂直地震加速度、墙背倾角、挡墙墙背与填料黏结力和外摩擦角、均布超载等诸多因素,可以适用于黏性土和无黏性土的主动和被动土压力计算。分析结果表明,地震条件下土压力强度沿墙高为非线性分布,在相应简化假设条件下公式与Mononobe-Okabe公式完全一致。     

Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.     

Experimental study on seismic response of soilbags-built retaining wall

The seismic performance of soilbags-built retaining wall model was studied experimentally. A series of small-scale shaking table tests with the input of different amplitude sinusoidal waves and a large-scale shaking table test in a designed laminar shear box with the input of the Wenchuan earthquake wave were carried out on soilbags' retaining wall models. For comparison, the small-scale shaking table tests were also conducted on horizontally reinforced retaining wall models. The horizontal acceleration responses, the Fourier spectra, the dynamic earth pressure and the lateral displacements of soilbags' retaining wall models were investigated in shaking table tests. The results show that the seismic response of the soilbags' retaining wall is equivalent to or even slightly better than that of the horizontally reinforced retaining wall. The fundamental frequency and the Fourier spectral characteristics of the soilbags’ retaining wall are similar to those of backfill sands. The dynamic earth pressure of the wall model fluctuates almost synchronously with the input Wenchuan wave and no residual earth pressure is induced by the seismic loading. The permanent lateral displacements are small when subjected to multiple shakings, providing a proof that the retaining wall of soilbags has a good seismic performance.     

地震作用下挡土墙抗倾覆稳定安全系数研究

基于拟动力法,考虑墙背面和填土面倾斜的工况,推导出挡土墙在地震作用下的抗倾覆稳定安全系数的计算表达式。数值算例结果表明,稳定安全系数随着填土内摩擦角、墙土外摩擦角和墙背面倾角的增大而增大,随地震放大系数、水平加速度影响系数和填土面倾角的增大而减小。其中,只有在地震作用较大时,放大系数的影响才逐渐显现,同时,摩擦角的影响却相对减弱;墙背面倾角和填土面倾角不同时,稳定系数随地震作用的变化趋势基本一致。通过对比2种计算方法的结果可知,拟动力法由于考虑了地震周期和地震波效应的影响,计算得到的稳定安全系数比拟静力法大。     

考虑土拱效应的黏性填土挡土墙主动土压力研究

 以墙后填土为黏性土的刚性挡土墙为研究对象,考虑挡土墙后的土拱效应,以及墙土摩擦角、墙土黏结力、墙后填土黏聚力的影响,推导挡土墙在平动模式下的主动土压力系数和主动土压力解析解。结果表明,考虑土拱效应的主动土压力系数和主动土压力均与墙土摩擦角、计算点深度以及墙后填土的内摩擦角、黏聚力及重度有关。通过将求解的主动土压力系数和主动土压力与现有经典理论解及前人理论研究成果对比,发现结果完全吻合,验证该研究结果的正确性。     

挡土墙与土界面摩擦角为负的地震被动土压力解析解

目前大多数被动土压力问题研究的是挡土墙背与土界面摩擦角为正的情况（墙身相对土体向下移动）,而挡土墙与土界面摩擦角为负(墙身相对土体向上移动)的被动土压力问题则研究的较少。在平面滑裂面假设的基础上,利用散粒体Kötter方程得到破裂面土抗力的分布,结合拟静力法通过极限平衡分析得到了挡土墙与土界面摩擦角为负时的地震被动土压力系数、被动土压力合力和被动土压力合力作用点高度的理论公式。在地震荷载作用下,竖向地震加速度系数总是减小被动土压力,水平向地震加速度系数或减小或增加被动土压力系数取决于挡土墙倾角、挡土墙背与填土界面摩擦角、填土摩擦角。随地震加速度系数的增加,地震被动土压力系数变化越明显。利用破坏土楔弯矩平衡条件得到了地震被动土压力的作用点高度,且土压力作用点高度随水平向地震加速度系数的增加而减小。地震被动土压力系数和土压力作用点高度与相关文献结果吻合较好,可为锚、输电线路等基础受上拔荷载时设计所采用。