Lateral earth pressure of granular backfills on retaining walls with expanded polystyrene geofoam inclusions under limited surcharge loading

Existing studies have focused on the behavior of the retaining wall equipped with expanded polystyrene(EPS)geofoam inclusions under semi-infinite surcharge loading rather than limited surcharge loading.In this paper,the failure mode and the earth pressure acting on the rigid retaining wall with EPS geofoam inclusions and granular backfills(henceforth referred to as EPS-wall),under limited surcharge loading are investigated through two-and three-dimensional model tests.The testing results show that different from the sliding of almost all the backfill in the EPS-wall under semi-infinite surcharge loading,only an approximately triangular backfill slides in the wall under limited surcharge loading.The distribution of the lateral earth pressure on the EPS-wall under limited surcharge loading is non-linear,and the distribution changes from the increase of the wall depth to the decrease with the increase of the limited surcharge loading.An approach based on the force equilibrium of a differential element is developed to predict the lateral earth pressure behind the EPS-wall subjected to limited surcharge loading,and its performance was fully validated by the three-dimensional model tests.

A general method to calculate passive earth pressure on rigid retaining wall for all displacement modes

A general analytical method to calculate the passive rigid retaining wall pressure was deduced considering all displacement modes. First, the general displacement mode function was setup, then the hypotheses were made that the lateral passive pressure is linear to the corresponding horizontal displacement and the soil behind retaining wall is composed of a set of springs and ideal rigid plasticity body, the general analytical method was proposed to calculate the passive rigid retaining wall pressure based on Coulomb theory. The analytical results show that the resultant forces of the passive earth pressure are equal to those of Coulomb＇s theory, but the distribution of the passive pressure and the position of the resultant force depend on the passive displacement mode parameter, and the former is a parabolic function of the soil depth. The analytical results are also in good agreement with the experimental ones.

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.

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 polystyrene inclusions. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Time history of seismic earth pressure response from gravity retaining wall based on energy dissipation

The seismic design of gravity retaining walls is based mostly on the pseudo static method.The seismic earth pressure is assumed to be a constant without considering the wave traveling effect when the seismic wave propagates through the slope.However,under continuous ground motion,the actual earth pressure on the retaining wall varies with time.The present seismic earth pressure calculation method yields results that differ significantly from the actual scenario.Considering this,a slip surface curve was assumed in this study.It is more suitable for engineering practice.In addition,a theoretical calculation model based on energy dissipation was established.The time history of seismic earth pressure response under continuous ground motion was calculated using the equilibrium equation between the external power and the internal energy dissipation power of the sliding soil wedge.It can more effectively reflect the stress scenario of a retaining wall under seismic conditions.To verify the applicability of the proposed approach,a large-scale shaking table test was conducted,and the time history of the seismic earth pressure response obtained from the experiment was compared with the calculation results.The results show that the proposed approach is applicable to the calculation of the time history of seismic earth pressure response of gravity retaining walls.This lays the foundation for the seismic design of retaining structures by using dynamic time history.

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.

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.

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.

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.

A modified logarithmic spiral method for determining passive earth pressure

In this study, a modified logarithmic spiral method is proposed to determine the passive earth pressure and failure surface of cohesionless sloping backfill, with presence of wallesoil interface friction. The proposed method is based on a limit equilibrium analysis wherein the assumed profile of the backfill failure surface is a composite of logarithmic spiral and its tangent. If the wallesoil interface is smooth, a straight line does not need to be assumed for the failure surface. The geometry of the failure surface is determined using the Mohr circle analysis of the soil. The resultant passive earth thrust is computed considering equilibrium of moments. The passive earth pressure coefficients are calculated with varied values of soil internal friction angle and cohesion, wall friction angle and inclination angle, and sloping backfill angle. This method is verified with the finite element method(FEM) by comparing the horizontal passive earth pressure and failure surface. The results agree well with other solutions, particularly with those obtained by the FEM. The implementation of the present method is efficient. The logarithmic spiral theory is rigorous and self-explanatory for the geotechnical engineer.

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.

Calculation of passive earth pressure of cohesive soil based on Culmann's method

Based on the sliding plane hypothesis of Coulumb earth pressure theory, a new method for calculation of the passive earth pressure of cohesive soil was constructed with Culmann＇s graphical construction. The influences of the cohesive force, adhesive force, and the fill surface form were considered in this method. In order to obtain the passive earth pressure and sliding plane angle, a program based on the sliding surface assumption was developed with the VB.NET programming language. The calculated results from this method were basically the same as those from the Rankine theory and Coulumb theory formulas. This method is conceptually clear, and the corresponding formulas given in this paper are simple and convenient for application when the fill surface form is complex.

Comparison of Seismic Design Codes between China and the United States for Reinforced Soil Retaining Walls

Because of its excellent seismic performance, reinforced soil retaining walls are increasingly used in civil engineering. Although many countries have published corresponding design codes, the differences between them are still relatively large. Using the FHWA Code and the Code for Seismic Design of Railway Engineering(CSDRE), stability calculations of reinforced soil retaining walls were carried out and the similarities and differences between these two design codes were analyzed. According to the comparative analysis, the following conclusions are drawn: the inertia force, the earth pressure and the tensile force of reinforcements calculated from the CSDRE are less than those from the FHWA Code, and the safety factor calculated from the former is larger. Although the M-O method is recommended to calculate the dynamic earth pressure, the FHWA Code suggests a higher action point as compared to the CSDRE.

Study on Ultimate Pullout Force of Grouting Anchors of the Anchor-Pull Retaining Wall

Determination of the grouting anchor pullout force is a key step during the design of anchor-pull retaining wall, but it is mostly determined relied on empirical formula at present, and the rationality and the safety cannot be effectively guaranteed. Based on the engineering case of the gravity retaining wall of Qinglin Freeway, the model test was designed, and combined with the results of the ABAQUS finite element numerical analysis, it was analyzed that how the anchor axial pulling force distributes. The results showed that the force of the anchor near the wall bolt was large and which far from the wall was small and the ultimate pullout force was proportional to the length, diameter and shear strength. When the end tension of the anchor was small, the top load played a leading role on the anchor tension. This conclusion confirmed the calculation formula of ultimate pullout force was and provided a theoretical basis for anchor-pull retaining wall design and calculation.

Limit state analysis of rigid retaining structures against seismically induced passive failure in heterogeneous soils

Soils are not necessarily uniform and may present linearly varied or layered characteristics,for example the backfilled soils behind rigid retaining walls.In the presence of large lateral thrust imposed by arch bridge,passive soil failure is possible.A reliable prediction of passive earth pressure for the design of such wall is challenging in complicated soil strata,when adopting the conventional limit analysis method.In order to overcome the challenge for generating a kinematically admissible velocity field and a statically allowable stress field,finite element method is incorporated into limit analysis,forming finiteelement upper-bound(FEUB)and finite-element lower-bound(FELB)methods.Pseudo-static,original and modified pseudo-dynamic approaches are adopted to represent seismic acceleration inputs.After generating feasible velocity and stress fields within discretized elements based on specific criteria,FEUB and FELB formulations of seismic passive earth pressure(coefficient K_(P))can be derived from work rate balance equation and stress equilibrium.Resorting to an interior point algorithm,optimal upper and lower bound solutions are obtained.The proposed FEUB and FELB procedures are well validated by limit equilibrium as well as lower-bound and kinematic analyses.Parametric studies are carried out to investigate the effects of influential factors on seismic K_(P).Notably,true solution of K_(P) is well estimated based on less than 5%difference between FEUB and FELB solutions under such complex scenarios.

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.

强夯作用下回填砂土挡墙墙后土压力分布研究

挡土墙墙后土压力分布是墙体形状及配筋设计的重要依据,为研究强夯作用下挡墙墙后土压力分布规律,开展了自重、堆载及强夯荷载下的挡土墙物理模型试验,通过不同深度的土压力监测,分析了夯击落距和夯击次数对墙后土压力分布的影响,重点分析了强夯冲击松动区的影响,并基于等效静力法修正了强夯作用下墙后土压力理论计算公式。结果表明:单次夯击作用下墙后土压力瞬间增大至极值后逐渐衰减至稳定,随着夯击次数的增多,土体逐渐密实,相应的墙后土压力会逐次增加;浅部土体在强夯作用下会形成冲击松动区,松动区内土体变得松散从而土压力值较小,而松动区下部土压力随深度迅速增大后再减小,呈“鼓肚”状非线性分布;松动区土体重度、松动区厚度尤其是后者对于墙后土压力理论分布曲线影响较大,考虑松动区影响的墙后土压力等效静力法修正理论公式更符合实际情况。

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。