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.

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.

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.

Non-limit passive soil pressure on rigid retaining walls

This paper aims to reveal the depth distribution law of non-limit passive soil pressure on rigid retaining wall that rotates about the top of the wall(rotation around the top(RT) model). Based on Coulomb theory, the disturbance degree theory, as well as the spring-element model, by setting the rotation angle of the wall as the disturbance parameter, we establish both a depth distribution function for sand and a nonlinear depth distribution calculation method for the non-limit passive soil pressure on a rigid retaining wall under the RT model, which is then compared with experiment. The results suggest that under the RT model: the non-limit soil pressure has a nonlinear distribution; the backfill disturbance degree and the lateral soil pressure increase with an increase in the wall rotation angle; and, the points where the resultant lateral soil pressure acts on the retaining wall are less than 2/3 of the height of the wall. The soil pressure predicted by the theoretical calculation put forward in this paper are quite similar to those obtained by the model experiment, which verifies the theoretical value, and the engineering guidance provided by the calculations are of significance.

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 Distribution and Sand Deformation Around Modified Suction Caissons(MSCs) Under Monotonic Lateral Loading

The modified suction caisson(MSC) is a novel type of foundation for ocean engineering, consisting of a short external closed-top cylinder-shaped structure surrounding the upper part of the regular suction caisson(RSC). The MSC can provide larger lateral bearing capacity and limit the deflection compared with the RSC. Therefore, the MSC can be much more appropriate to use as an offshore wind turbine foundation. Model tests on the MSC in saturated sand subjected to monotonic lateral loading were carried out to investigate the effects of external structure sizes on the sand surface deformation and the earth pressure distribution along the embedded depth. Test results show that the deformation range of the sand surface increases with the increasing width and length of the external structure. The magnitude of sand upheaval around the MSC is smaller than that of the RSC and the sand upheaval value around the MSC in the loading direction decreases with the increasing external structure dimensions. The net earth pressure in the loading direction acting on the internal compartment of the MSC is smaller than that of the RSC at the same embedded depth. The maximum net earth pressure acting on the external structure outer wall in the loading direction is larger than that of the internal compartment, indicating that a considerable amount of the lateral load and moment is resisted by the external skirt structure.

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.

Development of High-Pressure Multigrain X-Ray Diffraction for Exploring the Earth’s Interior

The lower mantle makes up more than a half of our planet’s volume. Mineralogical and petrological experiments on realistic bulk compositions under high pressure–temperature (P–T) conditions are essential for understanding deep mantle processes. Such high P–T experiments are commonly conducted in a laser-heated diamond anvil cell, producing a multiphase assemblage consisting of 100 nm to submicron crystallite grains. The structures of these lower mantle phases often cannot be preserved upon pressure quenching;thus, in situ characterization is needed. The X-ray diffraction (XRD) pattern of such a multiphase assemblage usually displays a mixture of diffraction spots and rings as a result of the coarse grain size relative to the small X-ray beam size (3–5 lm) available at the synchrotron facilities. Severe peak overlapping from multiple phases renders the powder XRD method inadequate for indexing new phases and minor phases. Consequently, structure determination of new phases in a high P–T multiphase assemblage has been extremely difficult using conventional XRD techniques. Our recent development of multigrain XRD in high-pressure research has enabled the indexation of hundreds of individual crystallite grains simultaneously through the determination of crystallographic orientations for these individual grains. Once indexation is achieved, each grain can be treated as a single crystal. The combined crystallographic information from individual grains can be used to determine the crystal structures of new phases and minor phases simultaneously in a multiphase system. With this new development, we have opened up a new area of crystallography under the high P–T conditions of the deep lower mantle. This paper explains key challenges in studying multiphase systems and demonstrates the unique capabilities of high-pressure multigrain XRD through successful examples of its applications.

New Formulas of Earth Pressure on Large Successive Cylinders

The retaining wall made of large successive cylinders is a kind of structure which draws much attention in coastal engineering of China. The earth pressure on the arched back of large successive cylinders is different from that on the plane back of a general wall. On the basis of equilibrium of forces on the strip element taken from the soil between two cylinders, the differential equation is established and the analytic solution to the equation is obtained. The formulas of earth pressure on large successive cylinders are given in this paper. The distribution of earth pressure around the circle given by the present formulas is different from that given by the formulas commonly used at present, but it is identical with that measured in the model test.

A modified logarithmic spiral method for determining passive earth pressure

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

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.

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.

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.

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.

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 K0 to avoid some accidents.

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

Exact calculations of the static earth pressure from a thick alluvium require accurate K0 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-mechanics 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 defined 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.

Study on the Test Method of Static Earth Pressure Coefficient of Deep Soils

The static earth pressure coefficient of soils is,approximately,considered to be a constant in the view of clas-sical soil mechanics. This is supported by many research results. The high pressure experimental research and analysis of remolding deep soil described herein indicate that the static earth pressure of thick overburden has a notable non lin-ear characteristic. It also appears larger than that of superficial soils. It is necessary for deep coal mine design and con-struction to consider this particularity of soil pressure so as to avoid engineering accidents and heavy loss of life and property.

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.