Distribution Of Active Earth Pressure Research Articles

Simplified Method for Calculating Active Earth Pressure Against Rigid Retaining Walls for Cohesive Backfill

The horizontal slice element method for calculating active earth pressure against rigid retaining walls has been extended to the cohesive backfill. The formula of the nonlinear distribution of active earth pressure is derived satisfying the reciprocal theorem of shear stress. According to the Mohr-Coulomb theory, the lateral active earth pressure coefficient can be determined. In order to check the accuracy of the proposed equation; the predictions from the equation are compared with both existing full-scale test results and values from other studies. The comparisons between calculated and measured values show that the proposed equations provide satisfactory results.

Analytical solution for active earth pressure of c–φ soil considering arching effect

ABSTRACTThe current study was undertaken to study the effect of soil arching on active earth pressure distribution in retaining walls with c–φ backfill. An analytical approach is presented to develop a general solution considering the effects of surcharge, backfill soil cohesion and slip surface inclination. The magnitude and height of the application of lateral active force is also derived. The results from the proposed equation corresponded to the measured results from a full-scale test, shows non-linear pressure distribution with zero pressure at wall base and less pressure in deeper heights compared to Coulomb’s method. According to the results of parametric analysis, the proposed equation predicts the active earth thrust nearly equal to that of the Coulomb’s equation, however, the surcharge-induced soil pressure is obtained approximately 50% greater than the conventional equation. Moreover, the height of application of active thrust is located at the height of 0.4H from the wall base. These indicate that using the Coulomb’s active equation for retaining walls design, is not in the safe side.

Active State Earth Pressure based on Dubrova’s Method of Redistribution of Pressure

Modes and magnitude of wall movement have great influence on the distribution of earth pressure behind retaining wall. For gravity retaining wall exerted by cohesionless soil rotating outward about the base, based on Dubrova’s method of redistribution of pressure and forming mechanism of earth pressure, the distribution pattern of internal friction angle along the wall back was established for different displacements, and then, an improved method of calculating active earth pressure was proposed, which considers the influence of displacement. When the retaining wall is in an at-rest state, the distribution of earth pressure calculated in this paper is defined as initial active state earth pressure, and it is not equal to static earth pressure, because the retaining wall has a tendency of active displacement. As the wall movement develops, the mobilized internal friction angle of the quasi sliding surface increases gradually from the initial internal friction angle to the internal friction angle, and accordingly, the distribution of earth pressure at the intersection of the sliding surface and the wall back decrease gradually from the distribution of initial active state earth pressure in static state to that of Coulomb active earth pressure.

Effect of Soil Amplification on Seismic Earth Pressure Using Pseudo-Dynamic Approach

The study of seismic earth pressure is essential for the design of a retaining wall in the earthquake-prone regions. Pseudo-static and pseudo-dynamic approaches are widely used for cohesionless soil backfill without considering the effect of soil amplification. Soil amplification is a very important factor for the calculation of seismic active earth pressure and should not be ignored in the design in the earthquake-prone regions. In this paper, a generalized formulation has been presented to compute the seismic active earth pressure distribution on the inclined retaining wall back-face. The retaining wall supports the inclined cohesionless soil backfill. A parametric study has been conducted to study the effect of various parameters like soil friction angle, the inclination of wall back-face, the inclination of soil backfill, wall friction angle, soil amplification, horizontal and vertical seismic coefficients. The results of the present study have been compared with the available results of an earlier study. The study highlighted the effect of model parameters on seismic earth pressure.

Upper Bound of Seismic Active Earth Pressure on Gravity Retaining Wall with Limited Backfill Width

The failure mechanisms of backfill with limited width that is subjected to a co-application of earthquake force and surcharge formed by single and double wedges, respectively, were introduced to address the active earth pressure acting on gravity walls. An analytic model that is applicable to general cases of tilt walls with frictional backs and inclined ground surfaces was established by incorporating the quasi-static Mononobe-Okabe method and upper bound limit analysis. The reasonability and effectiveness of this technique were verified and supported by a comparison with results from reported laboratory model tests. A sample case analysis revealed a nonlinear distribution of active earth pressure on a gravity wall with limited backfill width. Coulomb's solution and three other published methods tended to overestimate the earth pressure measured in the laboratory more significantly than the proposed method did when the width of the backfill was reduced to a critical threshold. The superiority of this suggested technique increased with the shrinkage of backfill width. Moreover, the ascending horizon seismic coefficient k and surcharge q mobilized an increasing active thrust on the wall while easing and enlarging the crack angle of the slip surface, respectively.

Investigation of three-dimensional active earth pressure and load transfer according to aspect ratio

ABSTRACTAlthough there is a noticeable difference between two-dimensional and three-dimensional earth pressures, most researchers have suggested various earth pressure theories under the two-dimensional condition. Only a few studies have been conducted on the three-dimensional load transfer to the adjacent ground, whereas most studies in literature on the three-dimensional active earth pressure have been conducted by focusing on the stability of active wall. For accurate prediction of the three-dimensional active earth pressure, it is required to study not only the three-dimensional earth pressure distribution but also the three-dimensional load transfer to the adjacent ground. In this paper, size and distribution of the three-dimensional active earth pressure as well as the load transfer according to aspect ratio of retaining wall are investigated through a series of model tests. As a results, the three-dimensional active earth pressure distribution showed the highest value at the wall height of 0.5–0.55h when the aspect ratio of equal to 1.2 or higher. The load transfer showed higher values in vertical direction than horizontal direction. The load transfer distribution can be evaluated by applying the size and effect range of the loads transferred to the adjacent soil of the retaining wall.

A Computational Method of Active Earth Pressure from Finite Soil Body

Nowadays, Coulomb and Rankine earth pressure theories have been widely applied to solve the earth pressure on a retaining structure. However, both of the theories established on the basis of the semi-infinite space assumption are not suitable for calculating the earth pressure from finite soil body. Therefore, this paper focuses on a theoretical study about the active earth pressure from finite soil body. Firstly, a common calculation model of finite soil body is established according to the results of previous studies. And then, based on Coulomb’s theory and the wedge element method, an analytical solution of the unit active earth pressure from finite soil body is deduced without an assumption of its linear distribution in advance. Meanwhile, formulas of the active earth pressure strength coefficient and the application point of the resultant force are also deduced. Finally, the influence of parameters such as the frictional angle between the retaining wall back and backfill, slope angle of backfill, dip angle of the retaining wall back, the frictional angle between backfill and rock slope, and uniformly applied load on the backfill surface on the distribution of the unit active earth pressure and the application point of the resultant force is analyzed in detail.

Redistribution Principle Approach for Evaluation of Seismic Active Earth Pressure Behind Retaining Wall

The knowledge of seismic active earth pressure behind the rigid retaining wall is very essential in the design of retaining wall in earthquake prone regions. Commonly used Mononobe–Okabe (MO) method considers pseudo-static approach. Recently there are many pseudo-dynamic methods used to evaluate the seismic earth pressure. However, available pseudo-static and pseudo-dynamic methods do not incorporate the effect of wall movement on the earth pressure distribution. Dubrova (Interaction between soils and structures, Rechnoi Transport, Moscow, 1963) was the first, who considered such effect and till date, it is used for cohesionless soil, without considering the effect of seismicity. In this paper, Dubrova’s model based on redistribution principle, considering the seismic effect has been developed. It is further used to compute the distribution of seismic active earth pressure, in a more realistic manner, by considering the effect of wall movement on the earth pressure, as it is displacement based method. The effects of a wide range of parameters like soil friction angle (ϕ), wall friction angle (δ), horizontal and vertical seismic acceleration coefficients (kh and kv); on seismic active earth pressure (Kae) have been studied. Results are presented for comparison of pseudo-static and pseudo-dynamic methods, to highlight the realistic, non-linearity of seismic active earth pressure distribution. The current study results in the variation of Kae with kh in the same manner as that of MO method and Choudhury and Nimbalkar (Geotech Geol Eng 24(5):1103–1113, 2006) study. To increase in ϕ, there is a reduction in static as well as seismic earth pressure. Also, by keeping constant ϕ value, as kh increases from 0 to 0.3, earth pressure increases; whereas as δ increases, active earth pressure decreases. The seismic active earth pressure coefficient (Kae) obtained from the present study is approximately same as that obtained by previous researchers. Though seismic earth pressure obtained by pseudo-dynamic approach and seismic earth pressure obtained by redistribution principle have different background of formulation, the final earth pressure distribution is approximately same.

Active earth pressure acting on retaining wall considering anisotropic seepage effect

This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of cohesionless and fully saturated sand with anisotropic permeability along the vertical and horizontal directions. The extremely unfavourable seepage flow on the back of the retaining wall due to heavy rainfall or other causes will dramatically increase the active earth pressure acting on the retaining walls, increasing the probability of instability. In this paper, an analytical solution to the Laplace differential governing equation is presented for seepage problems considering anisotropic permeability based on Fourier series expansion method. A good correlation is observed between this and the seepage forces along a planar surface generated via finite element analysis. The active earth pressure is calculated using Coulomb’s earth pressure theory based on the calculated pore water pressures. The obtained solutions can be degenerated into Coulomb’s formula when no seepage exists in the backfill. A parametric study on the influence of the degree of anisotropy in seepage flow on the distribution of active earth pressure behind the wall is conducted by varying ratios of permeability coefficients in the vertical and horizontal directions, showing that anisotropic seepage flow has a prominent impact on active earth pressure distribution. Other factors such as effective internal friction angle of soils and soil/wall friction conditions are also considered.

Experimental investigation of three-dimensional earth pressure according to aspect ratio of retaining wall

ABSTRACTThe purpose of this study is to investigate the scale and load distribution of three-dimensional active earth pressure and the load transferred to the adjacent soil by changing the aspect ratio of a retaining wall through a series of model tests. In this research, 42 earth pressure plates of different heights and widths were installed to evaluate the earth pressures by considering the wall aspect ratio and the change of earth pressure. The test results showed that the active earth pressures were uniformly converged when the percentage of limit displacement against wall height was 0.12%. The distribution of active earth pressure on the wall showed a parabola shape for most aspect ratios while the wedge shape identified by the model test was similar to the shell-shaped model. In this paper, two diagrams were proposed regarding the active earth pressure according to the aspect ratio of a retaining wall; (1) a diagram of earth pressure conversion against the aspect ratio based on evaluated three-dimensional active earth pressures with traditional two-dimensional earth pressures, (2) a load transfer diagram based on the horizontal distance by analyzing the horizontal and vertical load transfer ranges with the relevant increasing rates.

Active earth pressure on translating rigid retaining structures considering soil arching effect

Accurate determination of active earth pressure distribution on rigid retaining wall including the magnitude and height of application of its resultant is of immense importance for designing the earth retaining structures. In this paper, an analytical solution based on the soil arching effect is presented. According to Mohr’s stress circle, a new relationship between active earth pressure and normal stress on failure surface at any depth from backfill surface is obtained. By analysing parabolic arch of minor principal stresses, a new coefficient of active lateral earth pressure is proposed. The problems that the vertical static equilibrium equation of differential flat element considering soil arching effect is not reasonable are analysed. Then, based on the limit equilibrium of differential flat element, new formulas relevant to the distribution of active earth pressure, the magnitude and height of application of its resultant are derived. The effects of backfill internal friction angle, wall–soil friction angle, wall height, surcharge load and backfill unit weight on those formulas are investigated in detail. In addition, the comparisons of the predictions by proposed equations with available test data as well as existing solutions are carried out, which implies adequate accuracy of the proposed solutions for all ratios of wall–soil friction angle to internal friction angle.

Static and seismic active lateral earth pressure coefficients for c-ϕ soils

In this paper, the active lateral earth pressure is evaluated using the stress characteristics or slip line method. The lateral earth pressure is expressed as the lateral earth pressure coefficients due to the surcharge, the unit weight and cohesion of the backfill soil. Seismic horizontal and vertical pseudo-static coefficients are used to consider the seismic effects. The equilibrium equations along the characteristics lines are solved by the finite difference method. The slope of the ground surface, the wall angle and the adhesion and friction angle of the soil-wall interface are also considered in the analysis. A computer code is provided for the analysis. The code is capable of solving the characteristics network, determining active lateral earth pressure distribution and calculating active lateral earth pressure coefficients. Closed-form solutions are provided for the lateral earth pressure coefficients due to the surcharge and cohesion. The results of this study have a good agreement with other reported results. The effects of the geometry of the retaining wall, the soil and soil-wall interface parameters are evaluated. Non-dimensional graphs are presented for the active lateral earth pressure coefficients.

A Numerical Study of the Active Earth Pressure on a Rigid Retaining Wall for Various Modes of Movements

The magnitude and the application point of the resultant active earth pressure are two key problems in the design of a variety of civil engineering structures. Experimental results indicate that these parameters are affected by the wall movements. In this paper, series of two- dimensional finite difference analyses have been carried out using the code FLAC (Fast Lagrangian Analyses of Continua) to study the active earth pressure distribution behind a retaining wall under horizontal translation, rotation about the bottom, and rotation about the top modes of wall displacements. The computation results show remarkable similarity to experimental results available in the literature indicating that the active earth pressure distribution is nonlinear due to the arching effect. It is found that, for a wall under translational and base rotation modes, the active earth pressure is substantially hydrostatic except at the wall base where curvature was observed. These two wall modes are in good agreement with classical solutions. However, the earth pressure distribution due to rotation about the top is found far from the hydrostatic distribution and is highly affected by the arching effect.

Seismic active earth pressure of cohesive-frictional soil on retaining wall based on a slice analysis method

The M–O (Mononobe–Okabe) theory is used as a standard method to determine the seismic earth pressure. However, the M–O theory does not consider the influence of soil cohesion, and it cannot determine the nonlinear distribution of the seismic earth pressure. This paper presents a general solution for the nonlinear distribution of the seismic active earth pressure of cohesive-frictional soil using the slice analysis method. A new method is proposed to determine the critical failure angle of the backfill wedge under complex conditions, and an iterative calculation method is presented to determine the tension crack depth of the seismic active earth pressure. The considered parameters in the proposed method include the horizontal and vertical seismic coefficients, wall inclination angle, backfill inclination angle, soil friction angle, wall friction angle, soil cohesion, wall adhesion and uniform surcharge. The classical methods of the M–O and Rankine theories can be regarded as special cases of the proposed method. Furthermore, the proposed method is compared with the test results and previously existing solutions to validate the correctness of the results. Additionally, the parameters׳ effect on the critical failure angle, the resultant force, the application-point position, the tension crack depth and the nonlinear distribution of seismic active earth pressure are studied in graphical form.

Comparative study of different theories on active earth pressure

Determination of distribution and magnitude of active earth pressure is crucial in retaining wall designs. A number of analytical theories on active earth pressure were presented. Yet, there are limited studies on comparison between the theories. In this work, comparison between the theories with finite element analysis is done using the PLAXIS software. The comparative results show that in terms of distribution and magnitude of active earth pressure, RANKINE’s theory possesses the highest match to the PLAXIS analysis. Parametric studies were also done to study the responses of active earth pressure distribution to varying parameters. Increasing soil friction angle and wall friction causes decrease in active earth pressure. In contrast, active earth pressure increases with increasing soil unit weight and height of wall. RANKINE’s theory has the highest compatibility to finite element analysis among all theories, and utilization of this theory leads to proficient retaining wall design.

Seismic Active Earth Pressure on the Back of Battered Retaining Wall Supporting Inclined Backfill

Knowledge of seismic active earth pressure behind a rigid retaining wall and its point of application are very important to the design of retaining walls in earthquake-prone regions. This paper presents a detailed study on the seismic active earth pressure and its point of application behind a nonvertical, rigid retaining wall supporting inclined, cohesionless backfill, using pseudo-dynamic analysis that is more realistic to representing the time and phase difference within the backfill. A planar failure surface is considered in the analysis. The effects of soil and wall friction angle, wall and backfill surface inclination, and horizontal and vertical earthquake acceleration on the active earth pressure have been explored. Results are presented in both tabular and graphical nondimensional form, including comparison with other available methods to highlight the realistic nonlinearity of seismic active earth pressure distribution.

협소한 뒤채움을 갖는 옹벽에 작용하는 토압에 대한 연구

협소한 뒤채움을 갖는 옹벽에 대하여 옹벽 배면에 작용하는 주동토압분포를 알아보고자 수치해석을 수행하였다. 수치해석시 협소한 뒤채움은 벽체 바닥 뒷굽에서부터 지표면에서의 뒤채움 끝단까지 연결한 선이 수평면과 이루는 각도인 <TEX>${\beta}$</TEX> 값을 변화시켜가며 모사하였다. <TEX>${\beta}$</TEX> 값은 <TEX>$60^{\circ}$</TEX>에서부터 <TEX>$5^{\circ}$</TEX> 씩 증가시켜 <TEX>$80^{\circ}$</TEX>까지 변화시켜가며 수치해석을 수행하였는데 <TEX>${\beta}$</TEX> 값이 <TEX>$60^{\circ}$</TEX>인 경우는 해석대상 지반에 대해 통상적인 Coulomb 주동토압론을 적용할 수 있는 뒤채움폭에 대응하게 된다. 해석결과에 따르면 <TEX>${\beta}$</TEX> 값, <TEX>$60^{\circ}$</TEX>를 기준으로 볼 때 <TEX>${\beta}$</TEX> 값이 <TEX>$65^{\circ}$</TEX>인 경우의 전체 토압력은 <TEX>$60^{\circ}$</TEX>인 경우에 비해 큰 차이가 없었으며 <TEX>${\beta}$</TEX> 값이 증가함에 따라 전체 토압력은 감소하여 <TEX>${\beta}$</TEX> 값이 <TEX>$80^{\circ}$</TEX>인 경우는 <TEX>$60^{\circ}$</TEX>인 경우에 비해 0.89배로서 11% 감소된 값을 나타내었다. 전체 토압력의 작용위치는 <TEX>${\beta}$</TEX>가 증가함에 따라 감소하는 양상을 보여주는데 <TEX>${\beta}$</TEX> 값이 <TEX>$60^{\circ}$</TEX>일 때 전체 토압력의 작용위치는 벽체 높이의 0.38배 되는 위치이며 <TEX>${\beta}$</TEX> 값이 <TEX>$80^{\circ}$</TEX>일 때 횡방향 토압력의 작용위치는 벽체 높이의 0.35배 이었다. Numerical analysis was carried out in order to find out the distribution of active earth pressure acting on the rigid wall with narrow backfill. The analysis was executed by varying value which was defined as the angle between the horizontal line and the line which connects the heel of the wall to the end point of ground surface of the backfill. The <TEX>${\beta}$</TEX> values considered in numerical analysis were <TEX>$60^{\circ}$</TEX>, <TEX>$65^{\circ}$</TEX>, <TEX>$70^{\circ}$</TEX>, <TEX>$75^{\circ}$</TEX> and <TEX>$80^{\circ}$</TEX>. The value of lateral thrust corresponding to the <TEX>${\beta}$</TEX> value of <TEX>$80^{\circ}$</TEX> was 11 percent lower than the value calculated for the backfill with large backfill. Furthermore, the height of the resultant force for the lateral thrust decreased as the <TEX>${\beta}$</TEX> value increased. The locations of the resultant forces correspond to the <TEX>${\beta}$</TEX> values of <TEX>$60^{\circ}$</TEX> and <TEX>$80^{\circ}$</TEX> were 0.38 and 0.35 times lower than the wall height respectively.

The Research of Seismic Active Earth Pressure with Mode of Translation by Horizontal Slices Analysis Method and Shaking Table Tests

In order to get the seismic active earth pressure with the mode of translation, adopting some related assumptions of the M-O theory, this paper establishes the first-order differential equation of the Seismic active earth pressure by horizontal slices analysis method and gets the solution of the seismic active earth pressure by boundary conditions. This formula can solve the distribution of the seismic active earth pressure is nonlinear along the wall, the point of application of the dynamic active thrust which is the advantage of this formula and announces the decreasing process of the filling’s rupture angle with the increase of the horizontal peak ground acceleration (PGA) , as well. The rationality and validity of the formula is confirmed by the comparison between the results of the shaking table tests and the formula, respectively. If the retaining wall takes place the mode of translation, the point of application of the seismic active thrust ranges between 0.4 and 0.5 times wall’s height at the horizontal seismic peak ground acceleration (PGA)&lt;0.4g.At the same time, the computational accuracy of the dynamic active thrust, their points of application and the angle of rupture increases with the increase of the horizontal peak ground acceleration at the horizontal PGA&lt;1.0g, as the astigmatic of the retaining wall in highly seismic intensity region supplying the valuable reference.

New analytical procedure for seismic analysis of reinforced retaining wall with cohesive-frictional backfill

ABSTRACT: A simple analytical method is proposed for analysis of reinforced retaining walls with cohesive-frictional backfill under pseudo-dynamic loadings. The suggested formulation for n layers (slices), including 5n equations and 5n unknowns for analysis of each retaining wall, is presented based on limit equilibrium principles and the horizontal slices method. The angle of the critical failure wedge, the tensile force in the reinforcements and distribution of active earth pressure along the height of wall can all be determined in each moment of loading using this method. The results of the analysis indicate that seismic active earth pressure has a nonlinear distribution in cohesive-frictional soils. Also, the results reveal that the period of seismic load is of considerable influence on the tensile force in the reinforcements. Moreover, comparison of results reported by other researchers with those of the suggested method shows a small difference between them in most cases. Finally, it has been concluded that the proposed analytical procedure reliably calculates the resultant seismic earth pressure and its distribution, the tensile forces in the reinforcements, and the angle of failure wedge for unreinforced and reinforced walls in cohesive-frictional soil.

Pseudo-static lateral earth pressures on broken-back retaining walls

Displacement of retaining walls during earthquakes causes damage to the structures founded on their backfill. The displacement of the wall can be reduced by decreasing the lateral earth pressure applied on its back. This can be achieved in a broken-back wall as the size of the failure wedge formed behind the wall is reduced; therefore, the calculation of lateral earth pressures is essential in assessing the safety of and designing broken-back retaining walls. In this study, a series of reduced-scale shaking table model experiments were performed on broken-back quay walls composed of concrete blocks with two different rear-face shapes. In comparison with a vertical-back wall, earth pressures increased at the upper forward (i.e., seaward) leaning rear-face segments of the wall, whereas they decreased at lower backward (i.e., landward) leaning elevations. Because of the wide application of the pseudo-static method of Mononobe–Okabe in engineering practice and design codes, lateral earth pressures have also been estimated using this approach. The comparison between the measured lateral earth pressures and those calculated using the Mononobe–Okabe method shows fairly good agreement in predicting the overall distribution of lateral active earth pressure during and after the shaking.