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.     

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。     

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.     

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。     

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。     

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。     

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。     

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.     

粘性土主动土压力库仑精确解的改进

基于库仑理论的平面滑裂面假设,考虑滑裂面上填土凝聚力及填土与挡土墙墙背接触面上粘着力,对粘性土主动土压力的库仑精确解算法进行了改进。改进的库仑精确解算法对超载的处理及裂缝深度的计算简单;对按不考虑填土表面出现裂缝的情况,只需取Z0=0,与按出现裂缝情况完全相同。公式计算简便,精度可靠,易于推广应用。     

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。     

地震荷载下重力式挡土墙的抗倾覆稳定性分析

基于平面滑裂面假设,采用水平层分析法推导了地震荷载作用下的主动土压力计算公式,并给出了地震土压力沿墙高的分布及土压力合力作用点的位置。在此基础上提出了重力式挡土墙的抗倾覆稳定性验算公式,为实际工程中挡土墙抗震设计提供了理论依据。稳定性分析结果表明,随着水平地震荷载的增大,抗倾覆稳定性显著降低。     

Seismic Earth Pressure Exerted on Retaining Walls Under a Large Seismic Load

In recent years, serious damage has been done to retaining structures because of large earthquakes. In order to establish practical methods for evaluating the seismic earth pressure, which is one of the important external forces acting on retaining structures during large earthquakes, a series of shaking table tests was conducted on retaining wall (RW) models. The experiments revealed that the seismic active earth pressure was considerably smaller than that obtained by the Mononobe-Okabe theory, particularly under a large seismic load. Furthermore, it was demonstrated that the seismic earth pressure had an upper limit, which was determined by the force equilibrium of the soil wedge at the critical state when the RW lost its stability. On the basis of the test results, a new method to evaluate the seismic earth pressure for practical designs under a large seismic load has been suggested. This proposed method provides a reasonable earth pressure as well as an angle of failure plane, those of which depend on the seismic stability of the retaining wall. It has been confirmed that earth pressure obtained by the proposed method agrees well with the measured seismic earth pressure exerted on several retaining walls with different degrees of stability.     

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。     

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。     

临近地下室外墙的挡土墙主动土压力研究

关于考虑土拱效应的临近地下室外墙影响下的挡土墙主动土压力的研究目前已经取得了很多成果,但对考虑地表附加应力影响时的研究还有较多的不足。研究发现,考虑地表附加应力时挡土墙后破裂土体的平均竖向应力σ_v的求解公式与地表到墙后土体破裂面的最短距离H₁和张拉裂缝的深度zc的正负以及两者之间的关系有关,以此为基础将该问题分为4种情况进行研究,推导出了各情况下相应的σ_v的求解公式,并得得到了其相应的主动土压力计算公式;同时,通过对主动土压力积分推导出了各情况下相应的主动土压力合力和倾覆力矩的计算公式,由此可以计算合力作用点的高度。算例表明,地表附加应力的存在会对主动土压力的分布以及合力作用点的位置有较大的影响,证明了本文研究的必要性。     

车辆荷载和静荷载对路肩式挡墙影响的研究

按JTGD30-2004《公路路基设计规范》规定,车辆荷载作用在挡土墙背土上所引起的附加土体侧压力可以换算成等代均布土层厚度后,按库伦土压力理论计算,并且抗倾覆系数取值1.5。研究车辆行车荷载对挡土墙的影响,对原有的设计理论进行分析完善,既能够优化结构又能提高经济效益。为研究在车辆荷载的作用下挡土墙的受力特点及影响,设计了试验模型;通过试验测出挡土墙在不同的轴载作用下应力的分布图以及计算出总合力、合力矩,并且与静荷载作用下挡墙的受力状态进行对比,据此提出了减小土压力、改进挡土墙的措施。     

粘性土回填高挡土墙土压力计算探讨

针对粘性土回填高挡土墙的土压力计算问题,通过工程实例,分析探讨了用综合内摩擦角法和力多边形法计算粘性土主动土压力的差异性,并引入一折减系数使综合内摩擦角法更完善,以便为工程应用提供参考依据。     

New procedure for active earth pressure calculation in retaining walls with reinforced cohesive-frictional backfill

A new approach is suggested to determine the active earth pressure on retaining walls with reinforced and unreinforced cohesive-frictional backfill based on the horizontal slices method. A 4n formulation for unreinforced backfill and a 5n formulation for reinforced backfill are introduced and the tensile forces of the reinforcements and angle of failure wedge are calculated. The proposed method shows that the variation of active earth pressure by the depth of the wall in cohesive-frictional soils has a non-linear distribution. Also, the point of application of the pressure always shifts to the lower two-thirds of the wall height. The angle of failure wedge for cohesive-frictional soils increases linearly with an increase in the cohesive strength of the soil. A comparison of the analytical results obtained from the proposed method with those of previous research and AASHTO method results shows a negligible difference. The analytical method presented can be used to calculate the active earth pressure, tensile force of reinforcements and angle of failure wedge for unreinforced and reinforced walls in cohesive-frictional soil.     

基于库仑理论的主动土压力非线性分布特征

基于库仑土压力理论的假设,挡土墙土压力是由墙后填土在极限平衡状态下出现的滑动楔体产生,对局部三角形滑楔体进行力和力矩平衡分析,建立挡土墙上土压力强度的两个基本微分方程式;比较两式得到了主动土压力分布系数,由此推导了土压力强度和土压力合力作用点高度的理论公式,并分析了填土内摩擦角、墙背摩擦角、填土倾角、墙背倾角和填土表面...     

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。