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.

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.

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.

Settlement patterns of mountainous half-filled and half-cut widened subgrade with retaining wall

The settlement of widened highway subgrade in mountainous area is not only affected by the interaction between new and existing subgrade, but also seriously restricted by the external retaining wall. Based on the practical engineering of half-filled and half-cut widened mountainous highway subgrade with external balance weight retaining wall(BWRW), a sophisticated finite element numerical model is established. The evolution law of subgrade settlement is revealed during the whole process of new subgrade filling and BWRW inclination after construction. The settlement component of subgrade is clarified considering whether the existing pavement continues to be used. The results show that the additional settlement caused by the BWRW inclination after construction cannot be ignored in the widening and reconstruction of mountainous highway subgrade. In addition, pursuant to the comprehensive design of subgrade and pavement, the component of subgrade settlement should be determined according to whether the existing pavement continues to be used, while considering the influence of BWRW inclination after construction. When the existing pavement continues to be used, the settlement of the existing subgrade is caused by the new subgrade filling and the BWRW inclination after construction. On the contrary, the settlement is only caused by the BWRW inclination after construction.

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.

Shaking table test of subgrade slope reinforced by gravity retaining wall with geogrids

Gravity retaining wall with geogrids has showed excellent seismic performance from Wenchuan great earthquake.However,seismic damage mechanism of this kind of wall is not sufficiently clear.In view of this,a large shaking table test of the gravity retaining wall with geogrids to reinforce the subgrade slope was carried out,and based on the HilbertHuang transform and the marginal spectrum theory,the energy identification method of the slope dynamic failure mode was studied.The results show that the geogrids can effectively reduce displacement and rotation of the retaining wall,and it can effectively absorb the energy of the ground movement when combined with the surrounding soil.In addition,it also reveals the failure development of the gravity retaining wall with geogrids to reinforce the subgrade slope.The damage started in the deep zone near the geogrids,and then gradually extended to the surface of the subgrade slope and other zones,finally formed a continuous failure surface along the geogrids.The analysis results of the failure mode identified by the Hilbert marginal spectrum are in good consistency with the experimental results,which prove that the Hilbert marginal spectrum can be applied to obtain the seismic damage mechanism of slope.

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.

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.

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.

Mechanical Behaviors and Deformation Properties of Retaining Wall Formed by Grouting Mould-Bag Pile

The simplified mechanical model and finite element model are established on the basis of the measured results and analysis of the grouting pile deformation monitoring,surface horizontal displacement and vertical displacement monitoring,deep horizontal displacement(inclinometer)monitoring,soil pressure monitoring and seepage pressure monitoring in the lower reaches of Wuan River regulation project in Shishi,Fujian Province.The mechanical behavior and deformation performance of mould-bag pile retaining wall formed after controlled cement grouting in the silty stratum of the test section are analyzed and compared.The results show that the use of controlled cement grouting mould-bag pile technology is to strengthen the soft stratum for sealing water and reinforcement,so that it can rock into a retaining wall,which can both retain soil and seal water with excellent effect.The control of cement grouting technology not only makes the soft soil rock in the range of retaining wall of mould-bag pile,but also makes a wide range of soil around the mould-bag pile squeeze and embed to compaction;and its cohesion and internal friction angle increased,so as to achieve the purpose of reducing soil pressure and improving mechanical and deformation properties of retaining wall.

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.

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.

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.

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.

Field Measurements and Pullout Tests of Reinforced Earth Retaining Wall

In this paper, field measurements and pullout tests of a new type of reinforced earth retaining wall, which is reinforced by trapezoid concrete blocks connected by steel bar, are described. Field measurements included settlements of the earth fill, tensile forces in the ties and earth pressures on the facing panels during the construction and at completion. Based on the measurements, the following statements can be made: (1) the tensile forces in the ties increased with the height of backfill above the tie and there is a tensile force crest in most ties; (2) at completion, the measured earth pressures along the wall face were between the values of the active earth pressures and the pressures at rest; (3) larger settlements occurred near the face of the wall where a zone of drainage sand and gravel was not compacted properly and smaller settlements occurred in the well-compacted backfill. The results of field pullout tests indicated that the magnitudes of pullout resistances as well as tensile forces induced in the ties were strongly influenced by the relative displacements between the ties and the backfill, and pullout resistances increased with the height of backfill above the ties and the length of ties.

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.

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.

Modified particle swarm optimization for optimum design of spread footing and retaining wall

This paper deals with the economically optimized design and sensitivity of two of the most widely used systems in geotechnical engineering: spread footing and retaining wall. Several recent advanced optimization methods have been developed, but very few of these methods have been applied to geotechnical problems. The current research develops a modified particle swarm optimization (MPSO) approach to obtain the optimum design of spread footing and retaining wall. The algorithm handles the problem-specific constraints using a penalty function approach. The optimization procedure controls all geotechnical and structural design constraints while reducing the overall cost of the structures. To verify the effectiveness and robustness of the proposed algorithm, three case studies of spread footing and retaining wall are illustrated. Comparison of the results of the present method, standard PSO, and other selected methods employed in previous studies shows the reliability and accuracy of the algorithm. Moreover, the parametric performance is investigated in order to examine the effect of relevant variables on the optimum design of the footing and the retaining structure utilizing the proposed method.

Seismic analysis of semi-gravity RC cantilever retaining wall with TDA backfill

The seismic behavior of Tire Derived Aggregate （TDA） used as backfill material of 6.10 m high retaining walls was investigated based on nonlinear time-history Finite Element Analysis （FEA）. The retaining walls were semi- gravity reinforced concrete cantilever type. In the backfill, a 2.74 m thick conventional soil layer was placed over a 3.06 m thick TDA layer. For comparison purpose, a conventional all soil-backfill model was also developed, and the analysis results from the two models under the Northridge and Takatori earthquakes were compared. The FEA results showed that both models did not experience major damage in the backfill under the Northridge earthquake. However, under the Takatori earthquake, the TDA-backfiU model developed substantially large displacement in the retaining walls and in the backfill compared with the soil-backfill model. Regions of large plastic strain were mainly formed in the TDA layer, and the soil over the TDA layer did not experience such large plastic strain, suggesting less damage than the soil-backfill model. In addition, the acceleration on the backfill surface of the TDA-backfill model decreased substantially compared with the soil-backfill model. If an acceleration sensitive structure is placed on the surface of the backfill, the TDA backfill may induce less damage to it.

Shaking table tests on a cantilever retaining wall with reinforced and unreinforced backfill

Physical modelling of cantilever retaining walls with and without backfill reinforcement was conducted on a 1g shaking table to evaluate the mitigation effect of reinforcement on system dynamics(g denotes the acceleration of gravity).The model wall has a height of 1.5 m with a scale ratio of 1/4 and retains dry sand throughout.The input motions are amplified to three levels of input peak base acceleration,0.11g,0.24g,and 0.39g,corresponding to minor,moderate,and major earthquakes,respectively.Investigation of the seismic response of the retaining walls focuses on acceleration and lateral displacement of the wall and backfill,dynamic earth pressures,and tensile load in the reinforcements(modeled by phosphor-bronze strips welded into a mesh).The inclusion of reinforcement has been observed to improve the integrity of the wall-soil system,mitigate vibration-related damage,and reduce the fundamental frequency of a reinforced system.Propagation of acceleration from the base to the upper portion is accompanied by time delay and nonlinear amplification.A reinforced system with a lower acceleration amplification factor than the unreinforced one indicates that reinforcement can reduce the amplification effect of input motion.Under minor and moderate earthquake loadings,reinforcement allows the inertia force and seismic earth pressure to be asynchronous and decreases the seismic earth pressure when inertia forces peak.During major earthquake loading,the wall is displaced horizontally less than the backfill,with soil pushing the wall substantially;the effect of backfill reinforcement has not been fully mobilized.The dynamic earth pressure is large at the top and diminishes toward the bottom.