Distribution Of Active Earth Pressure Research Articles

Rankine Active Earth Pressure of Unsaturated Filling under Earthquake

The pseudo-static method was adopted to expand the application field of classical Rankine soil pressure theory to the circumstance of infinite inclined backfill acting on the retaining wall under earthquakes. The calculation formula of the active earth pressure for unsaturated soil was deduced by combining the shear strength model of unsaturated soil and the unified strength theory. The effects of matric suction, matric-suction-related friction angle and seismic coefficients on the intensity distribution of Rankine active earth pressure were evaluated, and the resultant action position was discussed. This research shows that rising seismic coefficients lead to a growth of the active earth pressure and an upward movement of the resultant action point; on the other hand, an increasing matric suction and its related friction angle causes a reduction of the active earth pressure and a downward movement of the resultant action. Examples indicate that the suggested formulas in this paper are in good agreement with those of the previous literature subjected to certain conditions. However, compared to the classic Rankine theory, the proposed method extends its application range by considering earthquake, unsaturated soil, inclined rough wall back, non-horizontal backfill surface, and the intermediate principal stress.

Calculation of Nonlimit Active Earth Pressure against Rigid Retaining Wall Rotating about Base

A retaining wall with sandy fill was considered as the research object in order to study the nonlimiting active earth pressure under the rotation about the base (RB mode). Rankine’s and Coulomb’s earth pressure theories are no longer applicable to the above conditions (RB mode and nonlimiting active earth pressure). In order to improve the traditional earth pressure calculation methods (Rankine and Coulomb), a calculation method using curvilinear thin layer elements is presented with overall considerations of wall displacement, soil arching effect, and friction angle exertion coefficient to deduce the nonlimit active earth pressure under RB. Additionally, the calculation results were in good agreement with model test data (from Fang and Smita). Moreover, a parametric analysis was carried out. It was revealed that the developed value of the shear strength decreased with the depth, and the active earth pressure distribution curve was linear and nonlinear in the upper and lower halves, respectively.

Active Earth Pressure for Sloping Finite Soil While Accounting for Shear Stress and Curved Slip Surface

Calculating the earth pressure of the sloping soil having finite width behind the retaining wall is difficult for stability calculation. Thus, a novel method to calculate the active pressure of cohesionless sloping finite soil behind a retaining wall was developed to investigate. Taking cohesionless soil as the research object and considering the principal stress rotation of soil, the resultant force for active earth pressure, action point position, and earth pressure distribution of sloping finite soil was obtained based on assumptions of the translational mode of the rigid retaining wall and cycloidal slip surface. The accuracy of the proposed method was verified by model tests. The influence of the slope height ratio l / H and slope angle α on earth pressure was analyzed in this study. The result revealed that the horizontal component of the active earth pressure distribution curve for sloping finite soil was linear in area I and nonlinear with a drum shape in area II. There was a noticeable change at the junction of the two areas. The resultant force of earth pressure and the height of action point of resultant force increased and tended to reach a certain value as the aspect ratio l / H increased. When l / H ≥ 0.4 , the height of the action point of resultant force tended to be two-fifths the height of the wall. The resultant force and the height of the action point decreased linearly as the slope bottom angle increased.

DEM Analysis and Simplified Calculation of Passive Earth Pressure on Retaining Walls Backfilled with Sand Considering Strain-Softening Behavior

Common calculation methods of passive earth pressure, such as the Rankine or Coulomb earth pressure theory, assume that the width of the fill behind the wall is sufficient for the development of the slip surface and that after the passive earth pressure reaches the limit state, its value remains unchanged with the increase of displacement of the retaining wall. Nevertheless, cases with narrow backfill width should be considered when retaining walls must be built close to existing stabilization walls in urban areas or near rock faces in mountainous areas. Furthermore, for sand, especially dense sand, when the displacement of the retaining wall is large, a strain-softening behavior similar to the triaxial test will appear, resulting in a decrease in passive earth pressure. In this regard, a practical model for strain-softening of dense sand is proposed firstly and verified by the discrete element method (DEM) using the Particle Flow Code (PFC-2D) software. Then, based on the sliding surface shape obtained by DEM, a simplified method for determining the passive earth pressure distribution of retaining walls using limit equilibrium analysis was proposed. Finally, the passive earth pressures calculated by the proposed method agree well with those from PFC results, and the effects of the width of the backfill and displacement of retaining wall on the distribution of active earth pressure were discussed.

Study on the Calculation Method of Active Earth Pressure and Critical Width for Finite Soil Behind the Retaining Wall

The method to determine the active earth pressure and critical width for finite soil behind the retaining wall in mountainous areas is one of the concerns of geotechnical engineering. In order to study the active earth pressure distribution of the finite soil against the retaining wall and determine the critical width of the boundary between the finite soil and the semi-infinite soil, this study focuses on investigating a retaining wall with finite cohesionless backfill. The shape of the failure surface is assumed to be a cycloid passing through the heel of the wall in the limit equilibrium state. Considering the deflection of soil principal stress induced by wall–soil friction effect, a calculation method of active earth pressure for finite soil is proposed by using an arc-shaped small principal stress trajectory, and the rationality of this method is verified. On this basis, a calculation formula of the critical width for finite soil is proposed. The influence of the internal friction angle and the wall–soil friction angle on the critical width of finite soil is examined. The results indicate that the active earth pressure of finite soil presents a nonlinear drum distribution along the height of the retaining wall under the failure mode of the cycloidal surface. The maximum value of active earth pressure is close to the bottom of the wall. The critical width of finite soil decreases with the increase of the internal friction angle, and its variation rate decreases gradually. The critical width of finite soil increases with the increase of the wall–soil friction angle, and its variation rate also increases gradually. Under different internal friction angles and wall–soil friction angles, the critical width values of finite soil calculated by the assumption of the cycloidal failure surface are smaller than those calculated by the Coulomb earth pressure calculation method.

Active failure characteristics and earth pressure distribution around deep buried shield tunnel in dry sand stratum

The stability of the tunnel face is a key issue in shield tunnel engineering. In this paper, a series of 1 g model tests were conducted in dry sand for various buried depth ratios H/D = 2, 3, 4, 5, and 6 to study the failure characteristics, earth pressure distribution and the soil arching effect. Each test provided a measurement of the earth pressure with the face withdrawal displacement. And the soil deformation and the failure characteristics were investigated by Particle Image Velocimetry (PIV) system. The development of the failure characteristics was discussed for the buried depth ratios H/D = 3. The relationships between the failure characteristic and buried depth ratios were investigated. The variation of limit support pressure, soil stress distribution at different depths and earth pressure around the tunnel are analyzed. The soil arching effect around the tunnel at deep burial conditions is revealed. With the withdrawal displacement increasing, the tunnel face is in close contact with the support panel at first, and then gradually separated from the support panel. The larger the H/D is, the smaller the increment of horizontal soil stress is. It could be concluded that the increase of tunnel depth directly leads to the soil arching effect.

Study on Seismic Amplification Effect and Active Earth Pressure of Retaining Wall Based on Pseudo-Dynamic Method and Numerical Simulation

Abstract In this paper, the finite element numerical analysis verified that the critical failure surface of the backfill under active conditions was curved, and it was consistent with the composite form of a logarithmic spiral and a straight line assumed by the study based on the pseudo-dynamic method. On the basis of the failure surface of the backfill as a curved surface, the seismic active earth pressure on the retaining wall was calculated by the pseudo-dynamic method and the finite element method respectively. Results showed that in the finite element analysis, the acceleration amplitude of the backfill had an obvious amplification effect along the depth of the retaining wall, and this amplification effect was related to many factors. Under the action of low-frequency seismic load, linear amplification effect occurred, while nonlinear amplification effect occurred under the action of high-frequency seismic load. The amplification factors increased with the increase of retaining wall height. According to the characteristics of the amplification effect, after modifying the input seismic acceleration in the pseudo-dynamic method, the distribution of seismic active earth pressure on the retaining wall was close to that obtained by finite element analysis.

Seismic Active Earth Pressure of Limited Backfill with Curved Slip Surface Considering Intermediate Principal Stress

The traditional method for seismic earth pressure calculation has certain limitations for retaining structures under complex conditions. For example, when the soil width is small, the results obtained by the traditional method will be much larger. Therefore, this paper assumes that the soil slip surface is a logarithmic spiral. Based on the plane strain unified strength theory formula, while also considering the soil arching effects and tension cracks, the analytical solutions of the lateral earth pressure coefficient and the active earth pressure under the earthquake action were deduced. The mechanism and distribution of seismic active earth pressure with limited width were discussed in terms of some relevant parameters. The results indicated that the seismic active earth pressure presented a “convex” nonlinear distribution along the retaining structure. As the contribution of the intermediate principal stress increased, the strength limit of the material was effectively utilized, and the earth pressure was reduced by 22.96%. The resultant force increased as the horizontal seismic coefficient increased. However, this effect was no longer evident when the wall–soil friction angle was close to the internal friction angle. The resultant force action point increased with the wall–soil friction angle, and it should be noted that ha>H/3 was true when δ/φ0>0.55. Finally, by drawing a comparison with previous studies, we verified that the method proposed in this paper is reasonable and can provide a new idea for subsequent 3D seismic earth pressure research.

Effect of arching on active earth pressure distribution against braced wall

ABSTRACT Active earth pressure distribution against the braced wall depends on the mode of wall movement, which may be translational or rotational. The pressure distribution is generally non-linear resulting from arching effects. Here new formulations are proposed for calculation of active earth pressure above and below cut level of braced excavation considering arching effects. Horizontal translation as well as rotation about the top of wall is accounted for above excavation level whereas in case of below cut level it is assumed that the wall is tilting around its lower edge. Expressions for earth pressure coefficient and soil deformation profile are also provided analysing the equilibrium condition of soil within failure zone. In order to find out effects of major soil parameters like soil friction angle ‘ϕ’, wall friction angle ‘δ’ and cohesion ‘c’, parametric studies are carried out. The prposed formulations are validated with existing case studies and found satisfactory results.

Calculation of active earth pressure on retaining walls with line surcharge effect and presentation of design diagrams in cohesive – frictional soils

In this study, a formulation and models have been proposed to calculate the active earth pressure on the wall and to determine the angle of failure wedge with line surcharge effect and taking into account the soil cohesion. The proposed method has the advantage of taking into account soil parameters such as cohesion, the angle of friction between the soil and the wall, the surcharge effect in the elasto-plastic environment, and the range that determines the critical surcharge. This paper presents dimensionless diagrams for different soil specifications and surcharges. According to these diagrams, it is easy to determine the distribution of excess pressure caused by surcharge, the distribution of the total active earth pressure on the wall, the angle of the failure wedge as well as the minimum and maximum active coefficient of the pressure with respect to surcharge distance. Furthermore, all soil parameters, surcharge and the results have been addressed. In general, the results indicated that increasing the angle of internal friction of the soil and cohesion would result to a nonlinear reduction in the active earth pressure coefficient, contrary to the line surcharge, which increases the active earth pressure of the soil and ultimately increases the active earth pressure coefficient. In this research, a diagram has been presented that expresses the surface that the active earth pressure coefficient changes with respect to the surcharge distance. The lower limit of each graph expresses the minimum active earth pressure coefficient (kas (min)) at the minimum surcharge distance, whereas the upper limit indicates the maximum active earth pressure coefficient (kas (max)) at the maximum surcharge distance from the wall. Comparison of the results of the proposed method with previous methods, codes and numerical software shows that in general, the proposed method is able to simplify the analysis of walls with surcharge effect in cohesive-frictional soils. In addition to the formulation and diagrams, a computer program in MATLAB software has been written. Using the results of these codes, the pressure on the wall with the linear surcharge effect, angle of failure wedge and pressure distribution on the wall in the cohesive-frictional soils can be calculated for all scenarios.

Analytical solution for the active earth pressure of cohesionless soil behind an inclined retaining wall based on the curved thin-layer element method

In order to improve the theoretical strictness and expand the applied range of the traditional earth pressure calculation methods, a new analytical solution for the active earth pressure distribution of the cohesionless backfill soil has been established. The curved trajectory of minor principal stress in the backfill is adopted in the proposed analytical solution, which is able to represent the rotation of principal stress resulting from the soil arching effect. The proposed solution is capable of reflecting the effect of the wall back roughness and inclination. The rationality of the proposed solution has been proven by comparisons between the experimental data and other solutions. The solution shows similar active earth pressure distribution with Coulomb solution in the shallow backfill, while better nonlinear results in the deep backfill, which is more consistent with the experimental observations.

A novel method of calculating active earth pressure on laggings between piles considering the soil arching effect

For the sake of economic design and safety requirement, the prediction of active earth pressure on laggings between stabilising piles is of great significance. However, the nonlinear distribution of active earth pressure on laggings between piles cannot be accurately predicted by using the classical theory. In this study, a novel method of calculating active earth pressure on laggings between piles is proposed based on the differential flat element method. For validation, calculations of the active earth pressure by using the novel method as well as other methods have been compared against the experimental results, indicating that the proposed method considering soil arching effect can well predict the active earth pressure on laggings. Furthermore, parametric analyses are conducted to examine of the most effective means of the piles and lagging system. It is concluded that the decrease rate of total active force flattens out when internal friction angle is larger than a certain degree and the lagging clear span suggests to be 1.5 to 1.7 times of pile diameter to meet economic requirements. This method can provide a reasonable estimation of the active earth pressure on laggings in the design of supporting structures.

Improved method for determining active earth pressure considering arching effect and actual slip surface

To determine the distribution of active earth pressure on retaining walls, a series of model tests with the horizontally translating rigid walls are designed. Particle image velocimetry is used to study the movement and shear strain during the active failure of soil with height H and friction angle ϕ. The test results show that there are 3 stages of soil deformation under retaining wall translation: the initial stage, the expansion stage and the stability stage. The stable sliding surface in the model tests can be considered to be composed of two parts. Within the height range of 0.82H–1.0H, it is a plane at an angle of π/4+ϕ/2 to the horizontal plane. In the height range of 0–0.82H, it is a curve between a logarithmic spiral and a plane at an angle of π/4+ϕ/2 to the horizontal. A new method applicable to any sliding surface is proposed for active earth pressure with the consideration of arching effect. The active earth pressure is computed with the actual shape of the slip surface and compared with model test data and with predictions obtained by existing methods. The comparison shows that predictions from the newly proposed method are more consistent with the measured data than the predictions from the other methods.

Evaluation of required connection load in GRS-IBS structures under service loads

This study presents an evaluation of the connection load (To) and stress-strain conditions right behind the facing of a Geosynthetic Reinforced Soil – Integrated Bridge Structure (GRS-IBS) based on field instrumentation data obtained from an abutment constructed in Virginia. The observations from this site are compared against other projects in Delaware and Louisiana. The lateral stress distribution obtained from the field was observed to be lower than the active lateral earth pressure distribution but higher than predicted using the bin pressure method. The results from all sites showed that the reinforcement strains measured in the field were below the maximum geosynthetic strains allowed in the design of GRS-IBS. The distributions of both lateral stresses and reinforcement strains with depth were found to be approximately uniform. The To values for the Virginia structure were obtained based both on reinforcement strain and lateral stress data, which agreed well with each other. All sites indicated the existence of lateral stresses behind the facing, which contributed to the development of To. The normalized To values for all GRS-IBS projects evaluated in this study showed that the theoretical tributary area approach outlined in MSE design can be conservatively adopted to predict To in the design of GRS-IBS.

Analytical solution for active pressure of narrow backfills considering arching effect

PurposeThe purpose of this paper is to study the distribution of active earth pressure in retaining walls with narrow cohesion less backfill considering arching effects.Design/methodology/approachTo this end, the approach of principal stresses rotation was used to consider the arching effects.FindingsAccording to the presented formulation, the active soil pressure distribution is nonlinear with zero value at the wall base. The proposed formulation implies that by increasing the frictional forces at both sides of the backfill, the arching effect is increased and so, the lateral earth pressure on the retaining wall is decreased. Also, by narrowing the backfill space, the lateral earth pressure is extremely decreased.Originality/valueA comprehensive analytical solution for the active earth pressure of narrow backfills is presented, such that the effects of the surcharge and the characteristics of the stable back surface are considered. The magnitude and height of the application of lateral active force are also derived.

Active Earth Pressure of Limited C-φ Soil Based on Improved Soil Arching Effect

For c-φ soil formation (cohesive soil) of limited width with ground surface overload behind a deep retaining structure, a modified active earth pressure calculation model is established in this study. And three key issues are addressed through improved soil arching effect. First, the soil-wall interaction mechanism is determined by considering the soil arching effect. The slip surface of a limited soil is proved to be a double-fold line passing through the retaining wall toe and intersecting the side wall of the existing underground structure until it reaches the ground surface along the existing side wall. Second, the limited width boundary is explicated. And third, the variation in the active earth pressure from parameters of limited c-φ soil is determined. The lateral active earth pressure coefficient is nonlinear distributed based on the improved soil arching effect of the symmetric catenary curve. Furthermore, the active earth pressure distribution, the tension crack at the top of the retaining wall and the resultant force and its action point were obtained. By comparing with the existing analytical methods, such as the Rankine method, it demonstrates that the model proposed in this study is much closer to the measured and numerical results. Ignoring the influence of soil cohesion and the limited width will exponentially reduce the overall stability of the retaining structure and increase the risk of accidents.

A Pseudodynamic Approach of Seismic Active Pressure on Retaining Walls Based on a Curved Rupture Surface

Reasonable determination of the magnitude and distribution of dynamic earth pressure is one of the major challenges in the seismic design of retaining walls. Based on the principles of pseudodynamic method, the present study assumed that the critical rupture surface of backfill soil was a composite curved surface which was in combination with a logarithmic spiral and straight line. The equations for the calculation of seismic total active thrusts on retaining walls were derived using limit equilibrium theory, and earth pressure distribution was obtained by differentiating total active thrusts. The effects of initial phase, amplification factor, and soil friction angle on the distribution of seismic active earth pressure have also been discussed. Compared to pseudostatic and pseudodynamic methods for the determination of planar failure surface forms, the proposed method receives a bit lower value of seismic active earth pressures.

Calculation of Active Earth Pressure in the Non-Limit State Based on Wedge Unit Method

Based on the wedge unit method, the active earth pressure against a retaining wall in the non-limit state is studied. According to the relationship between the displacement of the retaining wall and the mobilized internal frictional angle of filling in the non-limit state obtained by earlier researchers, the influences of the internal frictional angle and the displacement ratio of the wall on the unit active earth pressure coefficient, the distribution of the active earth pressure, and the application point of the active earth pressure in the non-limit state are discussed. Finally, through comparison with experimental data, the distribution of the active earth pressure calculated by the method proposed is shown to agree well with experimental results. Therefore, the method proposed in this paper has theoretical significance and engineering value.

Stability Assessment of Earth Retaining Structures under Static and Seismic Conditions

An accurate estimation of static and seismic earth pressures is extremely important in geotechnical design. The conventional Coulomb’s approach and Mononobe-Okabe’s approach have been widely used in engineering practice. However, the latter approach provides the linear distribution of seismic earth pressure behind a retaining wall in an approximate way. Therefore, the pseudo-dynamic method can be used to compute the distribution of seismic active earth pressure in a more realistic manner. The effect of wall and soil inertia must be considered for the design of a retaining wall under seismic conditions. The method proposed considers the propagation of shear and primary waves through the backfill soil and the retaining wall due to seismic excitation. The crude estimate of finding the approximate seismic acceleration makes the pseudo-static approach often unreliable to adopt in the stability assessment of retaining walls. The predictions of the active earth pressure using Coulomb theory are not consistent with the laboratory results to the development of arching in the backfill soil. A new method is proposed to compute the active earth pressure acting on the backface of a rigid retaining wall undergoing horizontal translation. The predictions of the proposed method are verified against results of laboratory tests as well as the results from other methods proposed in the past.

Simplified Method for Calculating the Active Earth Pressure on Retaining Walls of Narrow Backfill Width Based on DEM Analysis

Spaces for backfills are often constrained and narrowed when retaining walls must be built close to existing stable walls in urban areas or near rock faces in mountainous areas. The discrete element method (DEM), using Particle Flow Code (PFC‐2D) software, was employed to simulate the behavior of cohesionless soil with narrow width behind a rigid retaining wall when the wall translation moved away from the soils. The simulations focused on the failure model of the soil when the movement of the wall reaches the value where active earth pressure occurs, and the shape of the sliding surface was captured. Then, based on the limit equilibrium method with the obtained slip surfaces in PFC‐2D, a simplified analytical method is presented to obtain a solution of the active earth pressure acting on rigid retaining with narrow backfill width. The point of application of the active earth pressure is also obtained. The calculated values agree well with those from physical tests in the previous literature. Furthermore, the effects of the width of the backfill, internal friction angle of soil, and wall‐soil friction angle on the distribution of active earth pressure are discussed.