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.     

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.     

非极限状态挡土墙主动土压力研究

利用薄层单元法对挡土墙非极限状态主动土压力进行研究,认为挡土墙土压力是由墙后填土在平衡状态下出现的楔形土体产生,取挡土墙后楔形土体沿平行于填料坡面的薄层作为微分单元体,通过作用在微分单元体的力和力矩平衡条件,建立挡土墙非极限状态主动土压力微分方程,得到非极限状态土侧压力系数、土压力强度、土压力合力和作用点的理论公式。根据非极限状态摩擦角与墙体位移关系,分析填土内摩擦角、墙土摩擦角和挡土墙位移比对土侧压力系数、土压力分布、土压力系数和作用点的影响。分析表明采用极限平衡理论计算平动模式下刚性挡土墙非极限状态时的抗倾覆稳定性偏于危险。另外,公式计算结果与实测模型试验进行对比分析,主动土压力分布曲线吻合良好。     

各向异性砂土主动土压力的离心模型试验研究

 利用新研制的土压力离心模型试验设备,通过土压力盒测量作用在挡土墙上的土压力分布,利用非接触图像测量系统(GIPS)测量土体位移,对各向异性的南京云母砂分别进行沉积面铅直和水平两个方向的土压力离心模型试验。通过对比试验得到的土压力分布与理论公式计算得到的各向同性砂土土压力分布,以及两种沉积方向的砂土的滑裂面位置,对各向异性砂土的土压力及土体变形破坏问题进行初步研究。结果表明：随着挡土墙向远离墙后填土方向运动的位移不断增大,作用在挡土墙上的土压力逐渐减小,墙后填土中各点的位移不断增大,在墙后土体中逐渐形成滑裂面。当挡土墙的位移量达到10－3H(H为试样模型高度)时,墙后填土达到主动极限平衡状态。受到片状云母颗粒排列方向的影响,沉积面铅直的土体滑裂面比沉积面水平的滑裂面略显平缓。     

基坑地连墙后有限土受力特性试验研究

为了研究城市基坑施工地连墙后有限宽度无黏性土的破坏模式及其压力分布特征,依托可模拟不同复杂工况的试验模型箱,开展地连墙平动模式下的主动土压力模型试验。通过数码相机记录填土随地连墙平行移动过程中的破坏全过程,采用颗粒图像测速技术分析有限宽度无黏性填土的变形特性和有限填土的破坏形式,并将测得的主动土压力与理论解进行对比。试验结果表明：有限填土几何条件的变化将影响填土的破坏模式,两侧边界的限制是地连墙平动模式下有限填土内部产生多道滑动面的主要原因,滑动面以曲面形式呈现;主动土压力值随填土宽高比的增大而增大,半无限土体状态下,主动土压力值接近库伦土压力值;第一个“反射点”随自然坡面倾角的增大而上移;随着有限填土区域的增大,主动土压力值也逐渐增大。     

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.     

平动模式下考虑剪应力作用的刚性挡土墙主动土压力计算

以墙后为无黏性填土的刚性挡土墙为研究对象,假定破裂面为通过墙踵的平面,且墙后土体中形成圆弧形土拱,考虑滑动土楔内水平土层间的平均剪应力,修正水平层分析法,得到平动模式下主动土压力的表达式。通过与文献中模型试验结果和现有理论成果的对比分析证明了修正方法的合理性。参数分析表明,水平土层间的平均剪应力和主动土压力一样,沿墙高为非线性分布,主要受墙背倾角、墙土摩擦角、填土内摩擦角等因素的影响。对于墙背竖直或墙背较陡且比较粗糙的挡土墙,考虑水平土层间平均剪应力作用算得的主动土压力合力作用点位置高于库仑解且低于不考虑剪应力作用的理论解答,而对墙背较缓且比较光滑的挡土墙,情况则正好相反。而且,不论是否考虑水平土层间的平均剪应力,主动土压力合力作用点位置都会随墙背变缓而降低。     

考虑邻近地下室外墙侧压力影响的平动模式挡土墙主动土压力研究

 对于挡土墙距既有地下室很近,墙后填土宽度有限的情形,采用经典的库仑、朗肯土压力理论计算挡墙主动土压力是不严格的。通过有限元数值分析发现,当挡墙平动、填土达到主动极限状态时,无黏性土滑动土楔与邻近地下室外墙并未脱开,地下室外墙上全深度承受侧压力;随着填土宽高比n的不同,挡墙与地下室外墙间土体内将形成一道或多道滑裂面,且最靠近地表的滑裂面与挡墙或地下室外墙交点以上的土压力近似为库仑主动土压力。由此建立新的土压力计算模型,给出了挡墙主动土压力系数 和第一道滑裂面倾角 的求解方法,采用水平薄层单元法,得到了挡土墙主动土压力的分布以及合力作用点相对高度 的理论公式,并通过典型算例,与经典土压力理论、前人理论方法及有限元数值解进行对比。研究发现,挡土墙土压力为非线性的鼓形分布,当土体内摩擦角 和墙土摩擦角 取定值且 0°时, 随着n的增大而增大,而 和 随着n的增大而减小,当 时, 和 值与库仑解一致;当 0°时,不论n取何值, 和 值恒等于朗肯理论解,且 。     

无黏性有限土体主动破坏及土压力离散元分析

建立在半无限土体假定上的朗肯土压力理论和库伦土压力理论,在挡土墙后填土有限的情况下不再适用。针对墙后无黏性填土,采用离散元方法分别对光滑、粗糙墙面平动模式下墙后有限宽度土体主动破坏的过程进行研究,分析了挡土墙运动过程中滑裂带发展、土体位移规律以及墙后水平土压力分布的情况。研究结果表明,墙体光滑情况下,滑裂带呈直线,墙后填土宽高比较小时,可以观察到滑裂带的反射,墙后土体呈多折线破坏模式,滑裂带倾角基本与库伦理论滑裂带倾角相等,且与土体宽高比无关,水平土压力合力受土体宽高比影响亦不大。墙体粗糙情况下,滑裂带呈曲线,反射现象随墙体粗糙程度增加而减弱,滑裂带倾角随土体宽高比增大而减小,最终落于库伦理论滑裂带内侧。此时,存在一临界宽高比,当墙后土体宽高比小于此值时,主动土压力随宽高比增大而增大,大于此值时,主动土压力不受宽高比影响。而无论墙体粗糙与否,墙后土体宽高比越小,达到极限状态所需墙体位移均越小。     

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。     

复杂条件下挡土墙主动土压力解析解

基于库仑理论的平面滑裂面假设,综合考虑填土具有黏聚力和内摩擦角、挡土墙墙背和填土面均倾斜、填土与墙背间具有摩擦和黏着力、填土浅表具有张拉裂缝和表面有连续均布超载的复杂情况,采用薄层单元法,导出了作用于挡土墙上的主动土压力的解析解,可适用于黏性和无黏性填土的复杂条件;且证明现行经典朗肯理论和库仑理论主动土压力是解析解相应简化假设下的特例。多个工程实例计算均表明,公式计算结果与实测主动土压力非线性分布曲线吻合良好,因而解析解对实际工程中主动土压力的计算精度是可靠的,具有推广应用价值。     

Active earth pressure of narrow cohesive backfill on rigid retaining wall of rotation about the bottom

Retaining wall construction often encounters narrow cohesive backfill and the traditional theories are no longer suitable. Hence, analytical solutions for active earth pressure of narrow cohesive backfill on a rigid retaining wall rotating about the bottom are proposed in this paper. The principle stress rotation caused by interface friction is also included. Through a typical FEM analysis and analytical derivation, the multi-segmented failure surface composed of a logarithmic spiral curve in the lower part and a tangent line in the upper part is quantitatively determined. According to the aspect ratio of the narrow backfill, three basic failure models of the narrow cohesive backfill are found together with three types of differential elements. A program is coded to automatically identify these three failure models to quickly obtain the distribution, the resultant and the application point of the active earth pressure. The proposed analytical solutions are then verified through a two-step procedure of elaborate comparisons with the FEM results and good agreements are observed. Subsequently, a parametric investigation indicates the active earth pressure is positively correlated to the aspect ratio and slope inclination angle, while is negatively correlated to the soil cohesion and interface friction.     

墙后有限宽度无黏性土主动土压力试验研究

针对无黏性土体,开展了刚性挡墙平动、绕墙底转动和绕墙顶转动3种墙体主动变位模式情况下墙后有限宽度土体土压力试验。通过观察墙后不同宽度土体的破坏过程及对土压力的全程量测,对其破坏模式及土压力分布规律进行了探讨。试验结果表明,墙后有限宽度土体的破坏面为一连续曲面,随着墙后土体宽度的增加,土体破坏面逐渐向外侧偏移,最终趋于某一固定位置,但始终位于库仑破坏面内侧。土压力值监测表明,库仑土压力理论并不适用于有限宽度土体。当填土宽度为有限宽度时,土压力值小于库仑主动土压力值,其差距随土体宽度减小而逐渐增大。当墙体平动时,土压力值沿墙高先增大后减小;墙体绕墙底转动时土压力值则呈线性增长趋势;而当墙体绕墙顶转动时,在挡墙上部出现了明显的土拱效应。     

竖向分层非饱和土主动土压力的计算与分析

为了减小经典库仑土压力理论与实际工程中竖向分层土压力之间的误差,在传统库仑土压力理论和有限土压力理论的基础上,考虑了非饱和土的强度特性,建立了挡土墙后竖向分层填土的静力学平衡关系,得到了竖向分层填土的主动土压力的计算公式.通过与现有理论对比分析,验证了本文理论的正确性.分别分析了填土性质参数及挡土结构几何参数对土压力的...     

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。     

单元集成法及其在土压力计算中的应用

基于塑性力学上限定理的土压力计算，在数值上可以通过单元集成法来实现。它采用类似于有限元网格划分的方式离散墙背土体，并设定一个机动许可的滑动机构。在此滑动模式下，可以求得每个单元贡献的外力功率和内能耗散率。所有单元的能量变化率的总和就是墙背土滑裂体的总能量变化率。然后，根据上限定理可以求得与滑动机构相对应的极限外载荷，并通过非线性数学规划法找到其最小值。采用平面和对数螺旋滑裂面的单滑块机制，对典型的二维土压力问题进行分析，其结果说明该方法的有效性。     

挡土墙后粘性填土的主动土压力计算

根据库伦土压力的计算原理,从滑动楔体处于极限平衡状态时力的静力平衡条件出发,推导出了计算粘性土或无粘性土主动土压力的公式。该公式适用于均布荷载作用于挡土墙后任意位置。对重力式挡土墙设计中土压力的计算具有一定参考价值。     

挡土墙地震主动土压力的库仑解

传统的Mononobe-Okabe法在实际工程中有着广泛应用,但它仅适用于无黏性土的极限土压力计算,且不能给出土压力分布。基于极限平衡理论,视墙后填土为服从Mohr-Coulomb屈服准则的理想弹塑性材料,假定墙后塑性区的一簇滑移线为直线即平面滑裂面,考虑墙背倾角、地面倾角、土黏聚力和内摩擦角、墙土之间黏结力和外摩擦角、地面均布超载、塑性临界深度以及水平和竖向地震系数等因素的影响,建立较为完善的塑性滑楔分析模型,进而采用极限平衡法求解挡土墙地震主动土压力、滑裂面土反力及其分布,并且通过量纲一化的分析首次提出几何力学相似原理。研究结果表明,总地震主动土压力随水平地震系数代数值的增大而增大;但随竖向地震系数代数值的增大并非总是减小,当水平地震系数较大时,可能出现先减后增的情况。     

Upper bound solution to seismic active earth pressure of submerged backfill subjected to partial drainage

In waterfront geotechnical engineering, seismic and drainage conditions must be considered in the design of retaining structures. This paper proposes a general analytical method to evaluate the seismic active earth pressure on a retaining wall with backfill subjected to partial steady seepage flow under seismic conditions. The method comprises the following steps: i) determination of the total head, ii) upper bound solution of seismic active earth thrust, and iii) deduction for the earth pressure distribution. The determination of total head h(x,z) relies on the Fourier series expansions, and the expressions of the seismic active earth thrust and pressure are derived by using the upper bound theorem. Parametric studies reveal that insufficient drainage and earthquakes are crucial factors that cause unfavorable earth pressure. The numerical results confirm the validity of the total head distribution. Comparisons indicate that the proposed method is consistent with other relevant existing methods in terms of predicting seismic active earth pressure. The method can be applied to the seismic design of waterfront retaining walls.     

Modellversuche zum Erd‐ und Auflastdruck auf Winkelstützwände

Model tests on earth pressure and load pressure on cantilever retaining walls. Design‐ing the sections of cantilever retaining walls, it is required to know the earth pressure acting directly on the wall stem and the load pressure acting directly on the wall heel. Large scale model tests are presented, which aim to determine the development of the contact pressures due to dead load of the backfill as well as due to uniform surface loads. The model tests simulate the construction as well as the backfilling process. Wall geometry and subsoil flexibility are varied. The principal behaviour of cantilever retaining walls is presented. The test results are used to derive basic properties of the earth pressure and the load pressure.