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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Influence of groundwater level changes on the seismic response of geosynthetic-reinforced soil retaining walls

Geosynthetic-reinforced soil retaining walls(GSRWs)have been widely used in civil engineering projects.However,as the climate changes,extreme weather conditions and natural hazards are likely to become more frequent or intense,posing a huge threat to the stability of GSRWs.In this paper,the effect of groundwater level fluctuations on the seismic response of GSRWs is investigated.First,a dynamic numerical model was established and validated through centrifugal shaking-table test results.Using the established numerical model,the seismic response of GSRWs under four different groundwater level conditions was then investigated,i.e.,an earthquake occurring at a low groundwater level(Case LW),an earthquake occurring when the groundwater level rises(Case RW),an earthquake occurring at a high groundwater level(Case HW),and an earthquake occurring when the groundwater level drops(Case DW).The results show that the GSRW in Case DW has the worst seismic stability because of the drag forces generated by the water flowing to the outside of the GSRW.For Case RW,deformation of the GSRW under earthquake forces was prevented by the drag forces generated by the water flowing to the inside of the GSRW and the water pressure acting on the outside of the facing,giving the GSRW the best seismic stability in this case.Compared with Case LW,the seismic stability of a GSRW in Case HW is worse,because the high groundwater level will generate excess pore-water pressure during an earthquake.On this basis,we provide engineering design suggestions to be considered by practitioners.

Self-centring segmental retaining walls—A new construction system for retaining walls

This paper reports on an experimental study on a new self-centring retaining wall system.Four post-tensioned segmental retaining walls(PSRWs)were experimentally tested.Each of the walls was constructed using seven T-shaped concrete segments with a dry stack.The walls were tested under incrementally increasing cyclic lateral load.The effect of the wall height,levels of post-tensioning(PT)force,and bonded versus unbonded condition of PT reinforcement on the structural behavior of the PSRWs was investigated.The results showed that such PSRWs are structurally adequate for water retaining structures.According to the results,increasing the wall height decreases initial strength but increases the deformation capacity of the wall.The larger deformation capacity and ductility of PSRW make it a suitable structural system for fluctuating loads or deformation,e.g.,seawall.It was also found that increasing the PT force increases the wall’s stiffness;however,reduces its ductility.The residual drift and the extent of damage of the unbonded PSRWs were significantly smaller than those of the bonded ones.Results suggest that this newly developed self-centring retaining wall can be a suitable structural system to retain lateral loads.Due to its unique deformation capacity and self-centring behavior,it can potentially be used for seawall application.

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.

Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.

Study on the FEM design of reinforced earth retaining wall with geogrid

At present,limit equilibrium method is often adopted in the design of reinforced earth retaining wall. Geotechnical engineers home and abroad have done a lot of work to improve the traditional calculation methods in recent years,while there are lots of defects. This paper first identifies the location of failure surface and safety factor through the finite element program of PLAXIS and then analyses the influencing factors of the stability of reinforced earth retaining wall with geogrid. The authors adopt strength reduction FEM (finite element method)in the design and stability analysis of reinforced earth retaining wall and have achieved some satisfying results. Without any assumptions,the new design method can automatically judge the failure mode of reinforced earth retaining wall,consider the influence of axial tensile stiffness of the reinforcement stripe on the stability of retaining wall,identify reasonable distance and length of the reinforcement stripe,and choose suitable parameters of reinforcement stripe,including strength,stiffness and pseudo-friction coefficient which makes the design optimal. It is proved through the calculation examples that this method is more reasonable,reliable and economical in the design of reinforced earth retaining wall.

Optimum Design of Tied Back Retaining Wall

This paper presents an optimization algorithm for the design of tied back retaining wall which is comprised of the same three basic elements: stem, toe and heel, where the stem is hinged to the base and tied to the heel by multiple tie rods at intervals along the wall. The aim of this study is to find the values of design variables for this suggested type of tied back retaining walls which minimize the cost function subjected to constraints of the problem. The optimum design of such structure is conducted by using one of the nontraditional optimization methods, genetic algorithm (GA). The formulation of the problem is based on the elastic analysis and the ultimate strength method of design as per ACI-318-2011 code. The built-in genetic algorithm optimtool of Matlab program is utilized to optimize the cost function of the wall. The cost of concrete, reinforcing steel, tie steel, formwork, excavation, and backfilling works are included. The considered design variables are the geometric dimensions and the amounts of reinforcement for the base slab and stem slab, as well as the amount of tie steel. The developed program is utilized to perform an extensive parametric study regarding the height of wall, backfill soil properties, and materials properties including concrete, reinforcing steel, and tie steel. The backfill properties are represented by a pressure coefficient, which is a function of the unit weight and the angle of internal friction. Average expressions are calculated for the total cost and optimum dimensions as ratios of the wall height H2 which may be useful for the practical design of walls.