A Generalized Limit Equilibrium Method for the Solution of Active Earth Pressure on a Retaining Wall

In this paper, a generalized limit equilibrium method of solving the active earth pressure problem behind a retaining wall is proposed.Differing from other limit equilibrium methods, an arbitrary slip surface shape without any assumptions of pre-defined shapes is needed in the current framework, which is verified to find the most probable failure slip surface. Based on the current computational framework, numerical comparisons with experiment, discrete element method and other methods are carried out. In addition, the influences of the inclination of the wall, the soil cohesion, the angle of the internal friction of the soil, the slope inclination of the backfill soil on the critical pressure coefficient of the soil, the point of application of the resultant earth pressure and the shape of the slip surface are also carefully investigated. The results demonstrate that limit equilibrium solution from predefined slip plane assumption, including Coulomb solution, is a special case of current computational framework. It is well illustrated that the current method is feasible to evaluate the characteristics of earth pressure problem.

Improved method for determining active earth pressure considering arching effect and actual slip surface

To determine the distribution of active earth pressure on retaining walls, a series of model tests with the horizontally translating rigid walls are designed. Particle image velocimetry is used to study the movement and shear strain during the active failure of soil with height H and friction angle φ. The test results show that there are 3 stages of soil deformation under retaining wall translation: the initial stage, the expansion stage and the stability stage. The stable sliding surface in the model tests can be considered to be composed of two parts. Within the height range of 0.82 H-1.0 H, it is a plane at an angle of π/4+φ/2 to the horizontal plane. In the height range of 0-0.82 H, it is a curve between a logarithmic spiral and a plane at an angle of π/4+φ/2 to the horizontal. A new method applicable to any sliding surface is proposed for active earth pressure with the consideration of arching effect. The active earth pressure is computed with the actual shape of the slip surface and compared with model test data and with predictions obtained by existing methods. The comparison shows that predictions from the newly proposed method are more consistent with the measured data than the predictions from the other methods.

Estimation of active earth pressure based on pseudo-dynamic approach and discretization technique

A method combining the pseudo-dynamic approach and discretization technique is carried out for computing the active earth pressure.Instead of using a presupposed failure mechanism,discretization technique is introduced to generate the potential failure surface,which is applicable to the case that soil strength parameters have spatial variability.For the purpose of analyzing the effect of earthquake,pseudo-dynamic approach is adopted to introduce the seismic forces,which can take into account the dynamic properties of seismic acceleration.A new type of micro-element is used to calculate the rate of work of external forces and the rate of internal energy dissipation.The analytical expression of seismic active earth pressure coefficient is deduced in the light of upper bound theorem and the corresponding upper bound solutions are obtained through numerical optimization.The method is validated by comparing the results of this paper with those reported in literatures.The parametric analysis is finally presented to further expound the effect of diverse parameters on active earth pressure under non-uniform soil.

DISTRIBUTION OF ACTIVE EARTH PRESSURE OF RETAINING WALL WITH WALL MOVEMENT OF ROTATION ABOUT TOP

Based on the Coulomb's theory that the earth pressure against the back of a retaining wall is due to the thrust exerted by the sliding wedge of soil from the back of the wall to a plane which passes through the bottom edge of the wall and has an inclination equal to the angle of θ, the theoretical answers to the unit earth pressure, the resultant earth pressure and the point of application of the resultant earth pressure on a retaining wall were obtained for the wall movement mode of rotation about top. The comparisons were made among the formula presented here, the formula for the wall movement mode of translation, the Coulomb's formula and some experimental observations. It is demonstrated that the magnitudes of the resultant earth pressures for the wall movement mode of rotation about top is equal to that determined by the formula for the wall movement mode of translation and the Coulomb's theory. But the distribution of the earth pressure and the points of application of the resultant earth pressures have significant difference.

Comparative study of different theories on active earth pressure

Determination of distribution and magnitude of active earth pressure is crucial in retaining wall designs. A number of analytical theories on active earth pressure were presented. Yet, there are limited studies on comparison between the theories. In this work, comparison between the theories with finite element analysis is done using the PLAXIS software. The comparative results show that in terms of distribution and magnitude of active earth pressure, RANKINE＇s theory possesses the highest match to the PLAXIS analysis. Parametric studies were also done to study the responses of active earth pressure distribution to varying parameters Increasing soil friction angle and wall friction causes decrease in active earth pressure. In contrast, active earth pressure increases with increasing soil unit weight and height of wall. RANK/NE＇s theory has the highest compatibility to finite element analysis among all theories, and utilization of this theory leads to proficient retaining wall design.

Active earth pressure acting on retaining wall considering anisotropic seepage effect

This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of cohesionless and fully saturated sand with anisotropic permeability along the vertical and horizontal directions. The extremely unfavourable seepage flow on the back of the retaining wall due to heavy rainfall or other causes will dramatically increase the active earth pressure acting on the retaining walls, increasing the probability of instability. In this paper, an analytical solution to the Laplace differential governing equation is presented for seepage problems considering anisotropic permeability based on Fourier series expansion method. A good correlation is observed between this and the seepage forces along a planar surface generated via finite element analysis. The active earth pressure is calculated using Coulomb's earth pressure theory based on the calculated pore water pressures. The obtained solutions can be degenerated into Coulomb's formula when no seepage exists in the backfill. A parametric study on the influence of the degree of anisotropy in seepage flow on the distribution of active earth pressure behind the wall is conducted by varying ratios of permeability coefficients in the vertical and horizontal directions,showing that anisotropic seepage flow has a prominent impact on active earth pressure distribution. Other factors such as effective internal friction angle of soils and soil/wall friction conditions are also considered.

Limit analysis method for active earth pressure on laggings between stabilizing piles

Stabilizing pile is a kind of earth shoring structure frequently used in slope engineering. When the piles have cantilever segments above the ground,laggings are usually installed to avoid collapse of soil between piles. Evaluating the earth pressure acting on laggings is of great importance in design process.Since laggings are usually less stiff than piles,the lateral pressure on lagging is much closer to active earth pressure. In order to estimate the lateral earth pressure on lagging more accurately,first,a model test of cantilever stabilizing pile and lagging systems was carried out. Then,basing the experimental results a three-dimensional sliding wedge model was established. Last,the calculation process of the total active force on lagging is presented based on the kinematic approach of limit analysis. A comparison is made between the total active force on lagging calculated by the formula presented in this study and the force on a same-size rigid retaining wall obtained from Rankine's theory. It is found that the proposed method fits well with the experimental results.Parametric studies show that the total active force on lagging increases with the growth of the lagging height and the lagging clear span; while decreases asthe soil internal friction angle and soil cohesion increase.

Active earth pressure for subgrade retaining walls in cohesive backfills with tensile strength cut-off subjected to seepage effects

The commonly used Mohr-Coulomb(M-C) failure condition has a limitation that it overestimates the tensile strength of cohesive soils. To overcome this limitation, the tensile strength cut-off was applied where the predicted tensile strength is reduced or eliminated. This work then presented a kinematical approach to evaluate the active earth pressure on subgrade retaining walls in cohesive backfills with saturated seepage effects. An effective rotational failure mechanism was constructed assuming an associative flow rule. The impact of seepage forces, whose distribution is described by a closed-form solution, was incorporated into the analysis. The thrust of active earth pressure was derived from the energy conservation equation, and an optimization program was then coded to obtain the most critical solution. Several sets of charts were produced to perform a parameter analysis. The results show that taking soil cohesion into account has a distinct beneficial influence on the stability of retaining walls, while seepage forces have an adverse effect. The active earth pressure increases when tensile strength cut-off is considered, and this increment is more noticeable under larger cohesion.

Pseudo-dynamic active earth pressure behind retaining wall for cohesive soil backfill

A formula was derived for the computation of seismic active earth pressure behind retaining wall using pseudo-dynamic method.This formula considered the actual dynamic effect with variation of time and propagation of shear and primary wave velocities through the soil backfills.The influence of tension crack in the top portion of the backfill under seismic loading was investigated.The effects of wall friction angle,soil friction angle,horizontal and vertical seismic coefficients on the seismic active force were also explored.The parametric study shows that the total seismic active force increases as horizontal seismic coefficient increases,while it decreases with the increase in vertical seismic coefficient,internal friction angle and unit cohesion.The seismic active force calculated by the proposed method is larger than that calculated by previous theory.

Internal variable gradient model for active earth pressure of rigid retaining wall moving with translation

The instability of retaining wall is a key factor for many geo-hazards,such as landslides.To estimate the stability of retaining wall,the distribution of earth pressure is necessary.The results of in-situ observations and indoor experiments demonstrate that the distribution of earth pressure behind the retaining wall exhibits remarkable nonlinearity.When the results are analyzed in details,the oscillation and quasi-periodicity of the distribution of earth pressure are observed,which has not been given widely concerns and cannot be described by the existing analytical models.Based on the internal variable gradient theory and operator averaging method,a gradientenhanced softening constitutive model is proposed in this paper to describe the oscillation and quasiperiodicity of the distribution of earth pressure acting on the retaining wall,by introducing the high-order gradient terms of the hydrostatic pressure into Mohr-Coulomb yield condition.In order to check the applicability of the proposed formulation,the predictions from the formulations are compared with the full-scale and laboratory-scale test results as well as the existing formulations.It is noted from the comparisons between predicted and measured values that the results of gradient-dependent softening constitutive model provides the comparable approximations for active earth pressure and describes the oscillation and quasi-periodicity very well.This model may enhance the comprehension of soil mechanics and provide a novel view for the design of the retaining wall.

Lateral Earth Pressure Coefficient and Lateral Earth Pressure against Retaining Walls

According the Coulomb earth pressure theory,it is obtained that,for normally consolidated soils,the lateral pressure coefficient of a soil at rest is equal to 1,and it is independent of the soil type,either granular or cohesive;or that the material is in a loose or compact state;hard or a soft cohesive soil.Also,a methodology to calculate the earth pressure for intermediate states between at rest condition and the active pressure is presented.In addition,a methodology to calculate the earth pressure for intermediate states between at rest condition and the passive pressure is presented.Two practical examples are presented:one for a frictionless wall;and another for a coarse wall.Practical recommendations are given for the use of the lateral earth pressure coefficient for different applications.

Earth Pressure of Retaining Structure Induced by Subgrade under Rainfall

This article selects the retaining wall as the research object, introducing the rainfall infiltration model, considering the infiltration of rainwater into the groundwater recharge, analysizing the variation of earth pressure in the subgrade retaining wall. On this occasion, the back of retaining wall produces stable seepage water and compares with the non drainage water body. The results show that, with the infiltration of rainwater into the groundwater recharge, the greater the active earth pressure under the condition of rainfall appears, more quickly the active earth pressure of the retaining wall with the drainage body increases. The matrix suction of unsaturated soils, which is infiltrated into soil of subgrade, has a positive effect on the shear strength of the earth pressure.

General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach,a general closed-form solution to seismic and static active earth pressure on the walls,which considers shear and tension failure of the retained soil,is put forward using a variational calculus method.The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls.In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure,the proposed method can be performed easily via an implicit strategy.There are 13 basic factors related to the retained soils,walls,and external loads to be involved in the proposed method.The tension crack segment of the slip surface is obviously influenced by these parameters,apart from vertical seismic coefficient and geometric bounds of the surcharge,but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters.Noticeably,the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall.

绕墙底转动模式下装配式挡土墙土压力研究

墙背土压力分布及大小是装配式挡土墙设计的关键依据。设计并开展新型装配式混凝土挡土墙现场试验,研究挡土墙在加载条件下的位移模式和土压力分布规律。以现场试验为原型,建立无黏性填土、墙背倾斜且粗糙的挡土墙理论计算模型,同时考虑挡土墙位移模式与大小、土拱效应和土层间剪应力的影响,采用水平层分析法推导了绕墙底转动(RB)模式下挡土墙的土压力计算公式。结果表明:①该装配式挡土墙整体性能良好,绕墙底刚性转动。在RB模式下,墙顶处土体最先达到主动极限状态,土体从上至下逐渐达到极限状态;任意深度处的土体位移S_(c)达到7 mm时将达到极限状态,即S_(c)=0.16%H(H为墙高)。②本文理论解与试验值吻合较好,计算公式可用于求解挡土墙绕墙底转动过程中的土压力分布及大小。③随着挡土墙转动幅度的增大,土压力分布曲线凹向逐渐明显,土压力合力作用点高度呈现先降低后回升的现象;挡土墙转动角度η=0.007 rad为挡土墙达到主动状态的临界值。

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.

General axisymmetric active earth pressure obtained by the characteristics method based on circumferential geometric condition

Existing solutions for axisymmetric active earth pressure are based on certain hypotheses of the circumferential stress, lacking of strict basis. This article presents a technique for deriving the actual circumferential stress according to the circumferential geometric condition, the Drucker-Prager criterion and incremental theory. Based on the actual circumferential stress, a new characteristics method for determining the axisymmetric active earth pressure in plastic flow is developed in this article. In this new method, the inclined angle of boundaries, interface friction of contact interface, dilatation effect and flow velocity of soil are considered at the same time. The validity of the new method is confirmed using several sets of experimental data from the literature. The pressure coefficients are investigated individually in detail, and some different conclusions are found. Finally, a practical formula for calculating axisymmetric active earth pressure is presented based on the linear superposition principle, and related tables of coefficients are also provided for engineering application.

考虑土拱效应的多层土体墙后主动土压力模式研究

土拱效应已经被广泛证明存在于岩土工程中,然而关于土拱效应的土压力研究目前常局限于单层土体,对于多层土体墙后主动土压力的分布规律尚不清楚。基于土拱效应理论,提出了多层土体挡土墙后非线性主动土压力求解公式,并通过两种典型地层研究了土体内摩擦角和墙土摩擦角对主动土压力分布规律的影响。结果表明:所提出的计算公式能够很好地描述多层土体墙后主动土压力分布规律,计算结果与数值模拟结果基本一致;当上、下土层参数一致时,该公式可以退化成单一土层土压力计算模型;当墙土摩擦角充分发挥时,上层土体墙后土压力受土体内摩擦角影响明显,而当墙土摩擦角部分发挥时,下层土体墙后土压力受墙土摩擦角影响更大。

基于离散元模拟的不同挡土墙位移模式下非极限主动土压力

针对刚性挡土墙主动位移过程中砂土非极限主动土压力问题,利用PFC 2D分别对挡土墙绕墙顶转动(RB)模式、绕墙顶转动(RT)模式和平动(T)模式下砂土主动破坏过程进行模拟分析。分析结果表明,不同位移模式下土体内摩擦角及墙土摩擦角调动规律存在差异。挡土墙主动位移过程中,RB模式下土体破坏从墙顶开始,向墙脚发展,土楔体内部只有靠近墙背侧区域出现主应力偏转现象,并且土楔体中内摩擦角调动值均能达到极限值。RT模式下,土体破坏沿着墙背和滑裂面从墙脚开始,向土体表面发展,墙后土楔体中上部区域主应力偏转角度较大,形成了大主应力拱,与此对应的是该区域内摩擦角调动值相对初始内摩擦角减小。T模式下,土体破坏分别沿着墙背从墙顶向墙脚发展以及沿着滑裂面从墙脚向土体表面发展,墙后土楔体内部会出现小主应力拱,且内摩擦角调动值从初始内摩擦角增加,但达不到极限值。

拼装式土工格室挡墙受力变形测试分析

以四川成宜高速连接线某试验段变截面土工格室挡墙为工程依托,首先对新型拼装式土工格室挡墙的施工方法进行介绍,采用新型玻璃钢轻质面板有效解决了挡墙线形不美观并容易破损的不足;其次,通过现场监测对该挡墙的支护效果进行分析,现场监测结果表明:该挡墙不同部位的土压力沿墙高呈非线性分布,底部大,顶部小,局部会出现土压力减小的现象;挡墙同一水平高度处墙背和墙中部土压力较大,而墙面处较小,说明土压力从墙中部到墙面范围内的衰减程度较大;对墙身水平位移的监测结果表明:水平位移曲线为“S”形,存在2个位移分界点,水平位移在截面形状改变处变化明显,挡墙顶部和底部的水平位移为最大值和最小值,分别为30 mm和3 mm;对挡墙的沉降监测结果表明:该挡墙填筑施工期沉降量较大,占总沉降量的70%~90%,工后沉降很小,墙体最大沉降发生在挡墙顶部,沉降最大值仅为23 mm。最后,结合土压力计算理论分析该台阶式截面挡墙的土压力分布和墙身变形规律,结果表明该挡墙变形符合“转动+平动+绕墙底转动”模式,采用该文计算方法得到的墙背土压力与实测值较为接近,用于挡墙设计时结果更偏安全。

非饱和边坡中锚托板锚固尺寸的新算法

锚托板支护结构因为其安全稳定、经济和安装简便等优点在填方加固边坡中得到推广应用。然而目前在锚托板支护结构设计过程中,锚托板尺寸仍没有成熟的计算方法,设计过于保守。利用对数螺旋线滑移面结合极限平衡法计算得到非饱和土的主动土压力。根据土体内部平衡求出每层锚托板所需承担的拉力,得到了锚托板尺寸的计算方法,根据滑移面的位置得到了锚托板自由段拉杆的最小设计长度。将主动土压力计算结果与现有的经典文献进行了对比分析,发现主动土压力系数变化趋势与现有结论一致。分析了降雨工况和地震工况对锚托板尺寸的影响,结果表明,在降雨强度较小时对锚托板锚固尺寸的影响可以忽略,但在同时考虑强降雨和地震时,会显著增加所需的锚托板锚固尺寸,最大增大幅度可达136.71%。分析结果可为锚托板锚固尺寸的设计提供参考。