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.

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.

At-rest lateral earth pressure of compacted expansive soils:Experimental investigations and prediction approach

This paper presents experimental studies on a compacted expansive soil,from Nanyang,China for investigating the at-rest lateral earth pressureσL of expansive soils.The key studies include(i)relationships between theσL and the vertical stressσV during soaking and consolidation,(ii)the influences of initial dry densityρd0 and moisture content w 0 on the vertical and lateral swelling pressures at no swelling strain(i.e.σV0 andσL0),and(iii)evolution of theσL during five long-term wetting-drying cycles.Experimental results demonstrated that the post-soakingσL-σV relationships are piecewise linear and their slopes in the passive state(σL>σV)and active state(σL<σV)are similar to that of the consolidationσL-σV relationships in the normal-and over-consolidated states,respectively.The soakingσL-σV relationships converge to the consolidationσL-σV relationships at a thresholdσV where the interparticle swelling is restrained.TheσL0 andσV0 increase monotonically withρd0;however,they show increasing-then-decreasing trends with the w 0.The extent of compaction-induced swelling anisotropy,which is evaluated byσL0/σV0,reduces with an increase in the compaction energy and molding water content.TheσL reduces over moisture cycles and the stress relaxation in theσL during soaking is observed.An approach was developed to predict the at-rest soakingσL-σV relationships,which requires conventional consolidation and shear strength properties and one measurement of theσL-σV relationships during soaking.The proposed approach was validated using the results of three different expansive soils available in the literature.

A fiber Bragg grating based earth and water pressures transducer with three-dimensional fused deposition modeling for soil mass

A novel fiber Bragg grating(FBG)sensor with three-dimensional(3D)fused deposition modeling(FDM)approach is proposed for effective stress measurement in soil mass.The three-diaphragm structure design is developed to measure earth and water pressures simultaneously.The proposed transducer has advantages of small size,high sensitivity,low cost,immunity to electromagnetic interference and rapid prototyping.The working principle,design parameters,and manufacturing details are discussed.The proposed transducer was calibrated for earth and water pressures measurement by using weights and a specially designed pressure chamber,respectively.The calibration results showed that the wavelength of the transducer was proportional to the applied pressure.The sensitivity coefficients of the earth and water pressures were 12.633 nm/MPa and 6.282 nm/MPa,respectively.Repeated tests and error analysis demonstrated the excellent stability and accuracy of the earth and water pressure measurements.The performance of the proposed transducer was further verified by a model experimental test and numerical analysis,which indicated that the proposed transducer has great potential for practical applications.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

Evaluation and prediction of earth pressure balance shield performance in complex rock strata:A case study in Dalian,China

This research explores the potential for the evaluation and prediction of earth pressure balance shield performance based on a gray system model.The research focuses on a shield tunnel excavated for Metro Line 2 in Dalian,China.Due to the large error between the initial geological exploration data and real strata,the project construction is extremely difficult.In view of the current situation regarding the project,a quantitative method for evaluating the tunneling efficiency was proposed using cutterhead rotation(R),advance speed(S),total thrust(F)and torque(T).A total of 80 datasets with three input parameters and one output variable(F or T)were collected from this project,and a prediction framework based gray system model was established.Based on the prediction model,five prediction schemes were set up.Through error analysis,the optimal prediction scheme was obtained from the five schemes.The parametric investigation performed indicates that the relationships between F and the three input variables in the gray system model harmonize with the theoretical explanation.The case shows that the shield tunneling performance and efficiency are improved by the tunneling parameter prediction model based on the gray system model.

Supporting Earth Pressures for Foundation Excavation Considering Suction Stress of Soil

The infiltration,evaporation and variation of the groundwater table have significant effects on the suction stress of the soils and the supporting earth pressures of the foundation excavation.The distribution of the suction stresses above the ground water table is derived under different fluxes at the ground surface,according to the soil-water characteristic parameters and the effective degree of saturation.In consideration of the cohesive stress formed from the soil suction stress and the relevant anti sliding effect,the calculation model of supporting earth pressures for foundation excavation is established by the variational limit equilibrium method under the steady flow condition.The evolution of the supporting earth pressures is studied in detail for foundation excavation under different fluxes at the ground surface.The effects of the soil-water characteristic parameters,the ground water table and the internal friction angle on the supporting earth pressures are discussed.The results show that the suction stress is reduced because of the infiltration,and thus the supporting earth pressure increases.The larger the air-entry pressures and the pore size are,the smaller the supporting earth pressures are.The higher the ground water table is,the larger the supporting earth pressures are.In order to reduce the construction risk,the effects of the suction stress and the evolution of the potential critical sliding surface should be considered during the calculation of the supporting earth pressures.

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.

CALCULATION METHOD FOR EARTH PRESSURE CONSIDERING DISPLACEMENT

The calculation of earth pressure is a difficult problem in the pit foundation design. Aiming at the problem, the earth pressure calculation formulas considering the displacement are proposed. A method for determining the limit displacement is given and it is convenient for use. The result indicates that the earth pressure calculated by the formulas is between the earth pressure at rest and the Rankine earth pressure, the formulas can reflect the change rules of active and passive earth pressures along with the displacement. Moreover, the calculation result using the formulas is approximate to the monitoring result. It confirms the validity of the formula deduction and the rationality of the calculation results. As for the passive earth pressure, the calculation method is theoretically feasible.

Experimental study on workability and permeability of sandy soils conditioned with thickened foam

Water spewing and muck plugging often occur during earth pressure balance(EPB)shield machines tunnelling in water-rich sandy strata,even though the conventional foam has been employed to condition sandy soils.In this study,a novel thickened foaming agent suitable for EPB shield tunnelling in water-rich sandy strata is developed.In contrast to conventional foam-conditioned sands,the thickened foam-conditioned sand has a low permeability due to the consistent filling of soil pores with the thickened foam,and the initial permeability coefficient decreases by approximately two orders of magnitude.It also exhibits a suitable workability,which is attributed to the enhanced capability of the thickened foam to condition sandy soils.In addition,the effect of concentration on the stability of the foam is explained by the Gibbs-Marangoni effect,and conditioning mechanisms for the thickened foam on sands are discussed from the evolution of foam bubbles.

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.

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

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

Discrete element simulation of mechanical characteristic of conditioned sands in earth pressure balance shield tunneling

The discrete element method (DEM) was used to simulate the flow characteristic and strength characteristic of the conditioned sands in the earth pressure balance (EPB) tunneling. In the laboratory the conditioned sands were reproduced and the slump test and the direct shear test of the conditioned sands were implemented. A DEM equivalent model that can simulate the macro mechanical characteristic of the conditioned sands was proposed,and the corresponding numerical models of the slump test and the shear test were established. By selecting proper DEM model parameters,the errors of the slump values between the simulation results and the test results are in the range of 10.3%-14.3%,and the error of the curves between the shear displacement and the shear stress calculated with the DEM simulation is 4.68%-16.5% compared with that of the laboratory direct shear test. This illustrates that the proposed DEM equivalent model can approximately simulate the mechanical characteristics of the conditioned sands,which provides the basis for further simulation of the interaction between the conditioned soil and the chamber pressure system of the EPB machine.

Centrifuge modeling of dynamic behavior of pile-reinforced slopes during earthquakes

A series of centrifuge model tests of sandy slopes were conducted to study the dynamic behavior of pile-reinforced slopes subjected to various motions.Time histories of accelerations,bending moments and pile earth pressures were obtained during excitation of the adjusted El Centro earthquake and a cyclic motion.Under a realistic earthquake,the overall response of the pile-reinforced slope is lower than that of the non-reinforced slope.The histories of bending moments and dynamic earth pressures reach their maximums soon after shaking started and then remain roughly stable until the end of shaking.Maximum moments occur at the height of 3.5 m,which is the deeper section of the pile,indicating the interface between the active loading and passive resistance regions.The dynamic earth pressures above the slope base steadily increase with the increase of height of pile.For the model under cyclic input motion,response amplitudes at different locations in the slope are almost the same,indicating no significant response amplification.Both the bending moment and earth pressure increase gradually over a long period.

Coefficient of earth pressure at rest for normal,consolidated soils

In this study consecutive consolidated isotropically drained triaxial tests for the coefficient of earth pressure at rest(K_0) were carried out to investigate its rules of evolution as well as its strength characteristics for normal,consolidated saturated silt under high pressure.The tests results indicate that:1) for normal,consolidated saturated silt,K_0 values increase as the consolidation stress increases at high pressure levels,while the nonlinear characteristics of K_0 are inconspicuous compared to cohesive soils;2) the Jaky and Roscoe equations,used to calculate K_0,are only suitable for certain soils,but cannot represent these values for normal, consolidated saturated silt due to the variation in bilinear strength at high pressure;and 3) there are close relations between the nonlinear characteristics of K_0 and the void ratio,measured in the tests.Both share the same functional form while under pressure. Based on our experimental results,we developed an empirical linear model to interpret the rules of nonlinear variation for the coefficient of earth pressure at rest.

Coefficients of earth pressure at rest in thick and deep soils

The effect of test methods and stress paths on the experimental value of the coefficient of earth pressure at rest, K0, was investigated under high pressures. The results indicate that the rigid pressure chamber and flexible lateral confining pressure medium method gives a stress ratio at the initial stage that is not the real K0. Moreover, K0 increases during the loading process becoming greater at high pressures. In the unloading process, however, K0 increases only at the initial stage but decreases thereafter. In addition, the incremental magnitude definition, K0=dσ3/dσ1, gives higher values than the total magnitude definition, K0=σ3/σ1, under loading. This is also true during initial stages of unloading. The experiment results also indicate that earth pressure at rest in deep and thick soils can be estimated by a power function of axial and confining pressures. It is necessary to choose the appropriate Kn to avoid some accidents.

Calculation of earth pressure based on disturbed state concept theory

The theoretical formulations of Coulomb and Rankine still remain as the fundamental approaches to the analysis of most gravity-type retaining wall,with the assumption that sufficient lateral yield will occur to mobilize fully limited conditions behind the wall.The effects of the magnitude of wall movements and different wall-movement modes are not taken into consideration.The disturbance of backfill is considered to be related to the wall movement under translation mode.On the basis of disturbed state concept(DSC),a general disturbance function was proposed which ranged from-1 to 1.The disturbance variables could be determined from the measured wall movements.A novel approach that related to disturbed degree and the mobilized internal frictional angle of the backfill was also derived.A calculation method benefited from Rankine's theory and the proposed approach was established to predict the magnitude and distribution of earth pressure from the cohesionless backfill under translation mode.The predicted results,including the magnitude and distribution of earth pressure,show good agreement with those of the model test and the finite element method.In addition,the disturbance parameter b was also discussed.

Feasibility study of tar sands conditioning for earth pressure balance tunnelling

This paper presents the results of laboratory test on the feasibility of soil conditioning for earth pressurebalance （EPB） excavation in a tar sand, which is a natural material never studied in this respect. Thelaboratory test performed is based on a procedure and methods used in previous studies with differenttypes of soils, but for this special complex material, additional tests are also conducted to verify particularproperties of the tar sands, such as the tilt test and vane shear test usually used in cohesive materials, anda direct shear test. The laboratory test proves that the test procedure is applicable also to this type of soiland the conditioned material can be considered suitable for EPB excavations, although it is necessary touse a certain percentage of fine elements （filler） to create a material suitable to be mixed with foam. Thetest results show that the conditioned material fulfils the required standard for an EPB application.

Optimal arrangement for pressure measurement points in working chamber of earth pressure balance shield

In order to exactly provide scientific basis for pressure dynamic balance control of working chamber of earth pressure balance shield (EPBS),study on optimal arrangement of pressure measurement points in working chamber was conducted. Based on mathematical description of optimal arrangement for pressure measurement points,fuzzy clustering analysis and discriminant analysis were used to divide pressure regions of nodes on bulkhead. Finally,the selection method of optimal measurement points was proposed,and by selecting d6.28 m EPBS as study object,the case study was conducted. By contrast,based on optimal arrangement scheme of pressure measurement points,through adopting weighted algorithm,the absolute error mean of equivalent pressure of working chamber is the smallest. In addition,pressure curve of optimal arrangement points presents parabola,and it can show the state of pressure distribution on bulkhead truly. It is concluded that the optimal arrangement method of pressure measurement points in working chamber is effective and feasible,and the method can provide basis for realizing high precision pressure control of EPBS.

"Nonlinear" characteristics of the static earth pressure coefficient in thick alluvium

Exact calculations of the static earth pressure from a thick alluvium require accurate/Co values. These calculations influence the sinking cost and the safety of the freezing method. The static earth pressure coefficient （K0） of thick and deep soil was analyzed using laboratory tests. The results show that the static earth pressure coefficient of thick and deep soils is nonlinear and different from that of superficial soils. The constant of superficial soils is usually invariant and the total stress or incremental stress definitions used in traditional geo-meehanics give the same value. The influence of load increments when calculating for superficial soil is ignored. The difference in values of K0 for thick alluvium defimed by the total stress or the incremental stress methods is over 10%. The effects of the thick alluvium on K0 should be considered during the design of frozen shaft projects. Such things as the frozen shaft thickness and the excavated section height should be chosen to assure the rationality of the design and to avoid potential faults and accidents.