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.     

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     

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.     

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.     

预应力返包式加筋土挡墙的动力响应分析

在地震作用下,返包式加筋土挡墙作为一种柔性结构常因侧向变形较大或局部产生破坏而影响其正常使用。为解决该问题,提出了预应力返包式加筋土挡墙结构。为完善预应力返包式加筋土挡墙的设计理论,运用拟动力法和附加应力法理论,以预应力返包式加筋土挡墙作为研究对象,结合现有的加筋土挡墙侧向动土压力和侧向位移计算理论,提出了一套用于计算预应力返包式加筋土挡墙侧向动土压力和侧向位移的理论公式。结合室内振动台模型试验验证了所提理论方法的可行性和合理性。该方法计算简洁,适用性广,能够较好地计算预应力返包式加筋土挡墙的侧向动土压力和侧向位移,对完善预应力返包式加筋土挡墙的设计理论具有一定的指导和借鉴意义。     

地震荷载下的土压力线性分布解

Mononobe-Okabe土压力理论广泛应用于地震效应下的土压力计算,但由于其理论基础为库伦理论,因而只能计算土压力合力。基于Mononobe-Okabe土压力理论的平面滑裂面假设,在拟静力分析法的基础上采用斜向条分法,推导了考虑多种复杂条件下的地震土压力合力及其作用点位置、土压力强度计算式,并给出临界破裂角的显式解答。分析表明:斜向条分法能够有效验证Mononobe-Okabe理论假设土压力强度沿墙高线性分布的合理性,且在相应简化条件下,该公式给出的土压力合力与Mononobe-Okabe理论的计算结果完全一致。通过探讨水平和竖向地震荷载对土压力的影响初步获得了地震土压力的变化规律。     

预应力锚索桩板墙地震响应的振动台试验研究

作为一种轻型支挡结构,预应力锚索桩板墙具备安全、可靠、造价低等优势,汶川地震也证明了它具有良好的抗震性能。但由于此结构体系的受力复杂,目前一系列基础研究问题仍没有解决,理论研究远落后于工程实践,特别是在抗震设计理论研究方面。通过最直接的室内研究手段——大型振动台试验对预应力锚索桩板墙进行了地震响应研究,输入加速度时程选取卧龙台站实测水平向和竖直向地震波,并按相似比处理,测试了桩身6个高度位置的地震土压力、2个高度位置的位移、边坡中5个高度位置的加速度以及锚索预应力的时程变化。试验结果揭示了预应力桩板墙在地震作用下的土压力分布规律、桩身位移和锚索预应力的地震响应特征以及加固边坡的动力特性和加速度放大效应,为深入了解预应力锚索桩板墙的抗震表现和抗震机理提供了可靠的依据。     

SV波作用下刚性挡土墙地震主动土压力时频域计算方法

 基于弹性波动理论,概化刚性挡土墙的动力分析模型,利用水平分层法,建立单元体的受力平衡微分方程,借助Hilbert-Huang变换,提出地震作用下刚性挡土墙地震主动土压力的时频域计算方法,并通过与振动台试验结果的对比验证该方法的合理性。分析输入波频率对刚性挡土墙墙后填土的临界破裂角、地震主动土压力合力以及作用点的影响,结果表明：随着地震烈度的增大,临界破裂角逐渐减小,地震主动土压力合力逐渐增大,合力作用点位置略有上移;随着输入波频率的增大,临界破裂角和地震主动土压力合力分别呈“倒马鞍型”和“正马鞍形”分布,并且均在输入波频率与刚性挡土墙系统自振频率相近时达到最大,而地震主动土压力合力的作用点则基本上不变;按照现有规范不考虑输入波频率进行刚性挡土墙地震稳定性设计,可能会降低挡墙的地震安全储备。刚性挡土墙地震主动土压力的时频域计算方法不仅能够考虑地震波三要素(峰值、频率以及持时)对挡墙土压力的影响,同时也能够为其他类型支挡结构的抗震时频设计提供一定的参考。     

多级拼装悬臂式挡墙地震响应振动台模型试验

多级拼装悬臂式挡墙是一种可用于高填方工程的新型轻型支挡结构.为确定墙-坡系统的地震动力响应特征,进行几何、重度和时间相似比分别为1 ∶ 10,1 ∶ 1和1 ∶ 3.162的三级拼装悬臂墙支挡边坡的水平振动台模型试验.结果表明:坡体加速度沿墙高呈明显的非线性放大效应;墙后静止土压力和动土压力均呈"三峰型"分布模式,各级...     

水平柔性拉筋式重力墙地震土压力拟静力分析方法

水平柔性拉筋式重力墙是一种新型耐震结构,为研究墙后地震土压力,运用拟静力法并基于塑性极限分析上限原理,采用平面滑动破坏机构,考虑拉筋拔出和拉断两种破坏模式,推导墙后地震土压力的计算公式,并通过数值模拟方法进行验证,且讨论了填土内摩擦角、黏聚力、墙背外摩擦角、拉筋间距、极限拉力以及拉筋长度对地震土压力的影响特征。实例分析结果表明：随填土强度参数的增大地震土压力总体呈非线性减小,墙背外摩擦角对地震土压力的影响较小;随拉筋竖向间距增大,土压力呈非线性增大,但增幅渐小;拉筋极限拉力达到一定值后,对土压力没有影响;随拉筋长度在一定范围内的增加,墙后土压力逐渐减小。     

考虑变形影响的重力式挡墙地震土压力分布

利用汶川地震丰富的近场实震资料,分析总结了地震作用下挡墙的变形破坏模式,指出挡墙的变形模式与地基基础关系最为密切。位于岩质地基上的挡墙主要发生倾斜变形,位于土质地基上的挡墙则主要发生推移变形。在此基础上,基于温克勒地基模型,将土体看做是一系列弹簧和理想刚塑性体的组合体,分析得到了不同变形模式下挡墙地震土压力及其合力作用点的计算方法。结果表明：不同变形模式下挡墙的地震土压力分布特征各异,除平移模式外,其余变形模式下挡墙地震土压力随深度都呈非线性分布;位于岩质地基上的挡墙发生变形后地震土压力的合力作用点要比土质地基上的挡墙高。通过开展位于岩质地基和土质地基上挡墙的振动台模型试验,对文中提出的挡墙地震土压力计算方法进行了验证,发现试验结果和理论分析结果较相吻合。     

RT模式下考虑主应力偏转的刚性挡墙地震主动土压力

依据拟静力学理论,考虑主应力偏转的影响,推导了绕墙顶转动模式(RT模式)下的地震主动土压力的计算公式。通过旋转挡土墙的解析模型,将地震问题转化为静力问题,并根据库仑土压力理论得到地震主动破裂角。在此基础上改进圆弧形小主应力偏转迹线,利用摩尔应力圆得到了RT模式下地震主动侧压力系数和水平微元土层间摩擦系数公式,提出基于微分薄层法的地震主动土压力解析式。分析了主要参数对地震主动破裂角、地震主动侧压力系数、水平微元土层间摩擦系数、地震主动土压力分布和侧向土压力作用位置的影响。将解析结果与其他土压力理论及试验数据进行对比,结果表明本文方法更为可靠。     

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。     

Current Status of Ductility Design of Abutment Foundations Against Large Earthquakes

This paper describes a new ductility design method of abutment foundations in soil liquefaction situations under large earthquakes. The proposed method was developed for introducing it to the 2002 Japanese Specifications for Highway Bridges. Based on past damage case histories, several failure scenarios were assumed that are, as a result, associated with soil liquefaction. Then the proposed design method was made to control damage against soil liquefaction situations. The load combinations considered in the proposed method are based on one of the assumed failure scenarios. A practical seismic earth pressure evaluation for high peak ground acceleration levels, as observed in the 1995 Hyogo-ken Nanbu (Kobe) earthquake, has been newly introduced. Back-analyses of 14 damage case histories of abutments were conducted using the proposed method, and a design threshold value was explored accounting for the performance-based design concept. The back-analyses also unveiled remaining issues and the current status of abutment design against large earthquakes.     

地震作用下模块式面板土工合成材料加筋土挡墙的内部稳定分析

由于造价低廉,性能优良且外表美观,模块式面板土工合成材料加筋土挡墙在我国交通及城建等领域有着广泛的应用前景。大量的工程实践证明,土工合成材料加筋土挡墙的抗震性能良好,但仍有必要进行合理的抗震设计,而内部稳定校核是加筋土挡墙抗震设计的一个重要环节,它一定程度上决定了高烈度地震区加筋土挡墙的配筋方式及配筋密度。应用非线性动力有限元法分析不同加筋长度、加筋间距及不同地震作用下模块式土工合成材料加筋土挡墙在地震作用下的内部稳定,研究了筋材蠕变对加筋土挡墙动力内部稳定的影响,并将有限元分析的结果与国外规范建议的内部稳定校核结果进行比较。研究结果表明,在正常配筋密度条件下,各层筋材最大内力的位置与规范建议的位置有一定的区别,墙体下部更加远离面板;且筋材的最大内力沿高度的分布与该规范计算结果差别较大;而筋材蠕变使筋材的内力出现重分布。     

地震作用下挡土墙动土压力分布研究

自日本学者Mononobe、Matuo和Okabe首先提出了基于Coulomb土压力理论的静力方法——物部-冈部(M-O)公式后,国内外学者就挡土墙地震土压力理论和模型试验进行了很多研究,并取得了很多成果。在简要地对挡土墙在地震作用下的破坏形式、地震土压力分布的研究进展和地震土压力分布的研究趋势进行总结后,对其发展方向进行了分析和讨论。     

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。     

地震作用下土钉支护边坡动力分析

应用动力弹塑性有限元方法,研究了双向地震激励下土钉支护边坡动力响应。考虑土体与支护结构相互作用及其协同工作建立三维有限元模型。给出了地震波和阻尼的选取方法。应用了非线性静动力性能的弹塑性模型模拟土体;采用了可以描述土钉在进入塑性阶段强化性质的双线形弹塑性模型模拟土钉;土与结构的相互作用由接触单元模拟。研究内容包括边坡竖向地震响应、水平地震响应,土钉的地震响应,土压力地震响应。结果表明土钉支护边坡延性大,有很好的抗震性能;地震作用后各层土钉轴力都增大;边坡在地震作用下产生永久位移;地震作用下土压力峰值形状与地震作用前的土压力形状相似。这些结论对土钉支护边坡的抗震设计与动力分析有较高的参考价值。     

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。     

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。