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.

Time-History Dynamic Characteristics of Reinforced Soil-Retaining Walls

Given the complexities of reinforced soil materials’constitutive relationships,this paper compares reinforced soil composite materials to a sliding structure between steel bars and soil and proposes a reinforced soil constitutive model that takes this sliding into account.A finite element dynamic time history calculation software for composite response analysis was created using the Fortran programming language,and time history analysis was performed on reinforced soil retaining walls and gravity retaining walls.The vibration time histories of reinforced soil retaining walls and gravity retaining walls were computed,and the dynamic reactions of the two types of retaining walls to vibration were compared and studied.The dynamic performance of reinforced earth retaining walls was evaluated.

Protective effect of retaining wall on rock avalanche:A case study of Nayong rock avalanche in China

Rock avalanches are generally difficult to prevent and control due to their high velocities and the extensive destruction they cause.However,barrier structures constructed along the path of a rock avalanche can partially mitigate the magnitudes and consequences of such catastrophic events.We selected a rock avalanche in Nayong County,Guizhou Province,China as a case to study the effect of the location and height of a retaining wall on the dynamic characteristics of rock avalanche by using both actual terrain-based laboratory-model tests and coupled PFC3D-FLAC3D numerical simulations.Our findings demonstrate that a retaining wall can largely block a rock avalanche and its protective efficacy is significantly influenced by the integrity of the retaining wall.Coupled numerical simulation can serve as a powerful tool for analyzing the interaction between a rock avalanche and a retaining wall,facilitating precise observations of its deformation and destruction.The impact-curve characteristics of the retaining wall depend upon whether or not the rock avalanche-induced destruction is taken into account.The location of the retaining wall exerts a greater influence on the outcome compared to the height and materials of the retaining wall,while implementing a stepped retaining-wall pattern in accordance with the terrain demonstrates optimal efficacy in controlling rock avalanche.

Analytical and Numerical Study of the Hydro-Mechanical Behavior of a Cantilever Retaining Wall in Upward Seepage Conditions

Poor design of ground water evacuation mechanisms is often blocked and leads to the rise of ground water behind the wall. As a result, free water behind the wall that is not quickly evacuated, increases the lateral pressure and thus favors overturning failure. The resolution of the overturning problem in cantilever retaining walls caused by hydro-mechanical interaction was studied. An analytical and numerical method was used to study this type of wall-floor interaction. Then Coulomb’s design criterion against overturning to develop a mathematical model that compute analytical factor of safety against overturning in different water conditions and heel lengths was used. The modeling and simulation of this system in the Cast3m software which took into account a wide variety of floor and wall properties were performed. The numerical factor of safety against rollover was obtained, and the graphs for the factor of safety versus heel length and immersion depth for both methods were plotted. From (0 ≤ Hw ≤ H/3), water effect is not dangerous to wall stability against overturning and from (H/3 Hw ≤ H), water effect is very dangerous to wall stability against overturning. For analytical and numerical methods, the heel can be predimensioned against overturning as: Lc: [0.27H 0.38H], [0.29H 0.43H] for 0 ≤Hw ≤ H/3;[0.33H 0.45H], [0.39H 0.53H] for H/3 Hw ≤ 2H/3;[0.5H 0.6H], [0.50H 0.67H] for 2H/3 Hw≤ H. The numerical method guaranteeing more safety than the analytical method, Cantilever retaining walls can thus be pre-dimensioned considering Clayey-Sand soil in hydro-mechanical conditions.

Pseudo-static analysis of cantilever retaining walls using upper bound limit analysis approach

Given the extensive utilization of cantilever retaining walls in construction and development projects,their optimal design and analysis with proper attention to seismic loads is a typical engineering problem.This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method.The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism.One of the main features of this algorithm is its ability to determine the critical condition of failure wedges,the minimum safety factor and maximum force acting on the wall,as well as the minimum weight of the wall,simultaneously,by effectively using the multi-objective optimization.The results obtained by the proposed failure mechanisms show that,while using the upper bound limit analysis approach,the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel.The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient.The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability.The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis.The critical failure mechanisms were determined via optimization with genetic algorithm.

Reliability analysis of retaining walls with multiple failure modes

In order to reduce the errors of the reliability of the retaining wall structure in the establishment of function, in the estimation of parameter and algorithm, firstly, two new reliability and stability models of anti-slipping and anti-overturning based on the upper-bound theory of limit analysis were established, and two kinds of failure modes were regarded as a series of systems with multiple correlated failure modes. Then, statistical characteristics of parameters of the retaining wall structure were inferred by maximal entropy principle. At last, the structural reliabilities of single failure mode and multiple failure modes were calculated by Monte Carlo method in MATLAB and the results were compared and analyzed on the sensitivity. It indicates that this method, with a high precision, is not only easy to program and quick in calculation, but also without the limit of nonlinear functions and non-normal random variables. And the results calculated by this method which applies both the limit analysis theory, maximal entropy principle and Monte Carlo method into analyzing the reliability of the retaining wall structures is more scientific, accurate and reliable, in comparison with those calculated by traditional method.

Influence factors on the seismic behavior and deformation modes of gravity retaining walls

This study investigated the influence factors on the seismic response and deformation modes of retaining walls using large-scale model shaking table tests. Experimental results showed that the distribution of peak seismic earth pressures along the height of a wall was a single peak value curve. The seismic earth pressures on a gravel soil retaining wall were larger than the pressures on the weathered granite and quartz retaining walls. Also, the peak seismic earth pressure increased with increases in the peak ground acceleration and the wall height. The measured seismic active earth pressures on a rock foundation retaining wall were larger than the calculated values, and the action position of resultant seismic pressure was higher than 0.33 H. In the soil foundation retaining wall, the measured seismic earth pressures were much smaller than the calculated values, while the action position was slightly higher than 0.33 H. The soil foundation retaining wall suffered base sliding and overturning under earthquake conditions, while overturning was the main failure mode for the rock foundation retaining walls.

Dynamic earth pressure on rigid retaining walls induced by a neighboring machine foundation,by the meshless local Petrov-Galerkin method

Dynamic earth pressure induced by machine foundations on a neighboring retaining wall is analyzed with emphasis on factors which control the intensity and location of the design forces. The meshless local Petrov-Galerkin (MLPG) method is used to analyze the problem for a variety of retaining wall and machine foundation geometries. The soil medium is assumed to be homogeneous and visco-elastic. The machine foundation is idealized as a harmonic sinusoidal dynamic force often encountered in practice. A number of analyses have been made to reveal the effect of the loading frequency, the location and size of the foundation and the soil shear wave velocity on the distribution and magnitude of the dynamic earth pressure. Results indicate that there is a critical frequency and a critical location for which the passive pressure takes the maxima in the entire duration of the dynamic load.

Development of a monitoring and warning system based on optical fiber sensing technology for masonry retaining walls and trees

Hong Kong has a long history of applying masonry retaining walls to provide horizontal platforms and stabilize man-made slopes.Due to the sub-tropical climate,some masonry retaining walls are colonized by trees.Extreme weather,such as typhoons and heavy rains,may cause rupture or root failure of those trees,thus resulting in instability of the retaining walls.A monitoring and warning system for the movement of masonry retaining walls and sway of trees has been designed with the application of fiber Bragg grating(FBG)sensing technology.The monitoring system is also equipped with a solar power system and 4G data transmission devices.The key functions of the proposed monitoring system include remote sensing and data access,early warning,and real-time data visualization.The setups and working principles of the monitoring systems and related transducers are introduced.The feasibility,accuracy,serviceability and reliability of this monitoring system have been checked by in-site calibration tests and four-month monitoring.Besides,a two-level interface has been developed for data visualization.The monitoring results show that the monitored masonry retaining wall had a reversible movement up to 2.5 mm during the monitoring period.Besides,it is found that the locations of the maximum strain on trees depend on the crown spread of trees.

Upper bound seismic rotational stability analysis of gravity retaining walls considering embedment depth

Stability analysis of gravity retaining wall was currently based on the assumption that the wall had no embedment depth. The effect of earth berm was usually neglected. The present work highlighted the importance of embedment depth when assessing the seismic stability of gravity retaining walls with the pattern of pure rotation. In the framework of upper bound theorem of limit analysis, pseudo-static method was applied into two groups of parallel rigid soil slices methods in order to account for the effect of embedment depth on evaluating the critical acceleration of wall-soil system. The present analytical solution is identical to the results obtained from using limit equilibrium method, and the two methods are based on different theory backgrounds. Parameter analysis indicates that the critical acceleration increases slowly when the ratio of the embedment depth to the total height of the wall is from 0 to 0.15 and increases drastically when the ratio exceeds 0.15.

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.

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.

Stability Analysis of Landfills Contained by Retaining Walls Using Continuous Stress Method

An analytical method for determining the stresses and deformations of landfills contained by retaining walls is proposed in this paper.In the proposedmethod,the sliding resisting normal and tangential stresses of the retaining wall and the stress field of the sliding body are obtained considering the differential stress equilibrium equations,boundary conditions,and macroscopic forces and moments applied to the system,assuming continuous stresses at the interface between the sliding body and the retaining wall.The solutions to determine stresses and deformations of landfills contained by retaining walls are obtained using the Duncan-Chang and Hooke constitutive models.A case study of a landfill in the Hubei Province in China is used to validate the proposed method.The theoretical stress results for a slope with a retaining wall are compared with FEMresults,and the proposed theoreticalmethod is found appropriate for calculating the stress field of a slope with a retaining wall.

Dynamic Behavior of Gravity Retaining Walls with Coral Sand Backfill Under Earthquakes:Shaking Table Tests

The retaining walls in coral sand sites are inevitably threatened by earthquakes. A series of shaking table tests were carried out to study the seismic stability of gravity retaining walls with coral sand backfill. Parallel tests with quartz sand were performed to compare and discuss the special dynamic properties of coral sand sites. The results show that the acceleration difference between the retaining wall and the coral sand backfill is 76%-92% that of the quartz sand,which corresponds to the larger liquefaction resistance of coral sand compared with the quartz sand. However, the horizontal displacement of the retaining walls with coral sand backfill reaches 79% of its own width under 0.4g vibration intensity. The risk of instability and damage of the retaining walls with coral sand backfill under strong earthquakes needs attention.

Seismic analysis of cantilever earth retaining walls embedded in dry sand by simplified approaches and finite element method

In engineering practice simplified methods are essential to the seismic design of embedded earth retaining walls,as fullydynamic numerical analyses are costly,time-consuming and require specific expertise.Recently developed pseudostatic methods provide earth stresses and internal forces,even in those cases in which the strength of the soil surrounding the structure is not entirely mobilised.Semiempirical correlations or Newmark sliding block method provide an estimate of earthquake-induced permanent displacements.However,the use of these methods is hindered by uncertainties in the evaluation of a few input parameters,affecting the reliability of the methods.This study uses 1 D site response analyses and 2 D fully-dynamic finite element analyses to show that simplified methods can provide a reasonable estimate of the maximum bending moment and permanent displacements for stiff cantilever walls embedded in uniform sand,providing that a few input parameters are evaluated through semiempirical correlations and a simple 1 D site response analysis.

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.

Lateral Displacement of Retaining Walls

When Rankine or Coulomb theories to design of retaining wall are used, it is accepted beforehand that the retaining wall will experience a lateral displacement. This displacement is normally not calculated when a retaining wall is designed. This paper describes a method to estimate the lateral displacement of retaining walls. A practical example in the lateral displacement of a gravity retaining wall is presented.

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.

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.

Seismic responses of the steel-strip reinforced soil retaining wall with full-height rigid facing from shaking table test

To investigate the seismic response of the steel-strip reinforced soil retaining wall with fullheight rigid facing in terms of the acceleration in the backfill, dynamic earth pressure in the backfill, the displacements on the facing and the dynamic reinforcement strain distribution under different peak acceleration, a large 1-g shaking table test was performed on a reduced-scale reinforced-earth retaining wall model. It was observed that the acceleration response in non-strip region is greater than that in potential fracture region which is similar with the stability region under small earthquake,while the acceleration response in potential fracture region is greater than that in stability region in middle-upper of the wall under moderately strong earthquakes. The potential failure model of the rigid wall is rotating around the wall toe. It also was discovered that the Fourier spectra produced by the inputting white noises after seismic wave presents double peaks, rather than original single peak, and the frequency of the second peak trends to increase with increasing the PGA(peak ground amplitude) of the excitation which is greater than 0.4 g. Additionally,the non-liner distribution of strip strain along the strips was observed, and the distribution trend was not constant in different row. Soil pressure peak value in stability region is larger than that in potential fracture region. The wall was effective under 0.1 g-0.3 g seismic wave according to the analyses of the facing displacement and relative density. Also, it was discovered that the potential failure surface is corresponds to that in design code, but the area is larger. The results from the study can provide guidance for a more rational design of reinforced earth retaining walls with full-height rigid facing in the earthquake zone.