Calculation Of Active Earth Pressure Research Articles

Active Earth Pressure Calculation of Equilateral Convex Corners in Excavation Engineering

Active Earth Pressure Calculation of Equilateral Convex Corners in Excavation Engineering

Study on active earth pressure of narrow backfill of balance weight retaining wall under translational displacement mode

The balance weight retaining wall is a kind of gravity retaining wall. However, the theoretical results of the earth pressure are relatively few. The failure modes of backfill soil under different factors such as width to depth ratio of fill soil and rock inclination angle were studied by finite element limit analysis. Based on differential element methods and wedge limit equilibrium method, the active earth pressure calculation formula of balance weight retaining wall under translational displacement mode was derived. According to the parameter analysis, the interface friction resistance escalates alongside the rise in the boundary friction angle. The active earth pressure resultant force of the retaining wall increases with the increase of the width to depth ratio of filling, and decreases with the increase of the friction angle of filling. The design of counterweight retaining wall can benefit from the scientific basis and technical reference offered by the research findings.

Calculation of active earth pressure on external corners with equal length on both sides in excavation engineering

Taking the external corner with equal lengths as the research object, two failure modes of the equilateral external corner are established, and the active earth pressure calculation formula of the equilateral external corner in the limit state is further deduced when the external angle is 90°. The comparison between the theoretical calculation results and Midas/GTS simulation results shows that when the ratio of the side length B to the depth H is large, the sliding wedge failure will occur at the external corner, and the active earth pressure of the external corner in the range of wedge-shaped slider will not change with the change of size B. When the ratio of the side length B to the depth H is small, the displaced soil is composed of two parts, and the earth pressure varies with the change of size B. In this paper, the magnitude and distribution law of the active earth pressure obtained by the horizontal micro-layered limit equilibrium analysis method is similar to the three-dimensional simulation value of the Midas/GTS software, which can prove the feasibility and rationality of the theoretical calculation.

Inclined Layer Method-Based Theoretical Calculation of Active Earth Pressure of a Finite-Width Soil for a Rotating-Base Retaining Wall

In this study, we evaluated the active earth pressure on a retaining wall with a narrow cohesive fill under the rotation about the base mode. Under these conditions, Rankine’s and Coulomb’s earth pressure theories are not strictly effective. To improve the traditional earth pressure calculation methods (Rankine and Coulomb methods) and deduce the active earth pressure under the rotation about the base mode, here, we propose a new calculation method that incorporates the effects of wall displacement, soil arching and soil cohesion using inclined thin-layer elements. The calculation results are in good agreement with the model test data. Based on the parameter analysis, a critical aspect ratio of B/H = cotβ is determined along with a detailed elucidation of the various influencing factors (such as aspect ratio, cohesion and friction angle). The paper presents several solutions to improve the stability and lower the costs of retaining walls.

New procedure for active earth pressure calculation in cohesive-frictional soil

New procedure for active earth pressure calculation in cohesive-frictional soil

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.

Estimation of Active Earth Pressure Against Rigid Retaining Walls Considering Soil Arching Effects and Intermediate Principal Stress

Abstract In this study, a novel analytical approach is proposed for the calculation of active earth pressure on rigid retaining walls considering the influence of intermediate principal stress and ...

New Approach for Active Earth Pressure Calculation on Rigid Retaining Walls with Cohesive Backfill

The variational limit equilibrium method is adopted to calculate the active earth pressure with and without tension cracks appearing. According to static equilibrium equations of sliding soil, a functional extreme-value isoperimetric model of cohesive soil is deduced in the general case of an inclined wall, sloping backfill, and uniform surcharge on the backfill surface. The active earth pressure is caculated by a functional extreme-value problem of two unknown functions through introducing two undefined Lagrange multipliers. According to the corresponding Euler equations and the boundary conditions, functions of the sliding surface and the normal stress distribution along the sliding surface, which contain two undefined Lagrange multipliers, are deduced.

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.

Calculation of active earth pressure against retaining walls under translation mode considering soil arching effect in cohesive soil

In this study, the contour of the soil arch is not assumed as a certain curve, and the soil stress analysis is conducted on a differential element with two dimensions. Herein, analytical expressions of the active earth pressure, active earth force are derived based on the static equilibrium of the differential element. Furthermore, the effects of wall-soil friction angle and soil internal friction angle on the active earth pressure are investigated. Eventually, comparisons among the proposed method of this study and the previous measured data and other analytical approaches yield satisfactory results.

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.

Estimation of 3D active earth pressure under nonlinear strength condition

The calculation of active earth pressure behind retaining wall is a typical three-dimensional (3D) problem with spatial effects. With the help of limit analysis, this paper firstly deduces the internal energy dissipation power equations and various external forces power equations of the 3D retaining wall under the nonlinear strength condition, such as to establish the work-energy balance equation. The pseudo-static method is used to consider the effect of earthquake on active earth pressure in horizontal state. The failure mode is a 3D curvilinear cone failure mechanism. For the different width of the retaining wall, the plane strain block is inserted in the symmetric plane. By optimizing all parameters, the maximum value of active earth pressure is calculated. In order to verify the validity of the new expressions obtained by the paper, the solutions are compared with previously published solutions. Agreement shows that the new expressions are effective. The results of different parameters are given in the forms of figures to analysis the influence caused by nonlinear strength parameters.

Calculation of Active Earth Pressure for Narrow Backfill with a Curved Slip Surface

A method was proposed to calculate the earth pressure from a cohesionless backfill with a high aspect ratio (ratio of height to width of retaining wall). An exponential equation of slip surface was proposed first. The proposed nonlinear slip surface equation can be obtained once the width and height of the backfill as well as the internal friction angle of the backfill were given. The failure surface from the proposed formula agreed well with the experimental slip surface. Then, the earth pressure was calculated using a simplified equilibrium equation based on the proposed slip surface. It is assumed that the minor principal stress of the backfill near the wall and at its corresponding slip surface where the depth is the same is the same. Thus, based on the vertical force balance of the horizontal backfill strip, assuming the wall‐soil interface and the slip surface is in the limit equilibrium state, defined by the Mohr–Coulomb criterion, the differential equilibrium equation was obtained and numerically solved. The calculated results agreed well with the test data from the published literature.

Active earth pressure for soils with tension cracks under steady unsaturated flow conditions

The calculation of active earth pressure has commonly been performed under dry or saturated conditions. However, in practice soils are usually unsaturated. With the aim of estimating active earth pressure under steady unsaturated flow conditions, this paper describes a new method within the framework of the kinematic approach of limit analysis. A closed-form formula is adopted to estimate the suction stress of unsaturated soils subjected to vertical steady flow. A rotational failure mechanism composed of a log-spiral curve and a vertical crack is presented for calculations of the external work rate and internal energy dissipation rate. Pre-existing cracks as well as cracks that form as part of the failure mechanism are considered in the present work. The maximum depth of cracks is determined by requiring the vertical crack boundary to be stable. Explicit expressions about the thrust of active earth pressure for different crack types are derived from the work–energy balance equation, and the most critical solutions are obtained by optimizing the variables from the failure mechanism. Numerical results for different parameters are calculated and given in the form of graphs for practical use. A parametric study is performed to investigate the impact of different parameters on the active earth pressure.

Calculation of earth pressure on rigid retaining walls with considerations to the seismic load and soil stress-deflection

At present, the calculation of active earth pressure behind retaining walls is mainly based on the hypothesis that the fracture surface of rolling earth behind retaining walls is straight-running through wall heels. However, most experiments have proven that this hypothesis is false. In this study, active earth pressure behind retaining walls under seismic loading was discussed from the perspective of stress deflection. Stress on soil layer behind the vertical retaining wall was analyzed by quasi-static method. Then, the expression of seismic angle of rupture was proposed by referring to the balance of horizontal forces and changes with wall height. On this basis, the calculation formulas of active earth pressure, seismic active earth force, total moment at the wall and the point of application of active thrust from the base of wall were acquired by solving this balance equation. Calculated results were compared with test data and results of other methods. The rationality of the proposed method was verified. Thus, the proposed method is applicable to multi-layered filling behind the retaining wall.

Upper bound analysis of 3D static and seismic active earth pressure

This paper adopts a three-dimensional (3D) rotational failure mechanism to calculate the static and seismic active earth pressure acting on rigid retaining walls within the framework of the kinematic approach of limit analysis. The failure mechanism can be generated through rotating a varying circle defined by two log-spirals, and a plane strain block is inserted into the mechanism for consideration of retaining walls with different widths. Quasi-static representation using the seismic coefficient concept is applied to consider horizontal earthquake effects for the seismic active earth pressure calculation. Two cases with the different points of action of resultant earth pressure are included in this study. In the realm of soil plasticity, the new expressions about 3D active earth pressure are educed from the work-energy balance equation. The critical solution is obtained from an optimization scheme where the maximum of active earth pressure is obtained. Numerical results for different parameters are calculated and presented in the forms of graphs and tables, which may serve as a useful tool for practical application. Compared with existing 2D and 3D solutions, the validity of the proposed method is shown. A parametric study is conducted to investigate the effects of different parameters on the static and seismic active earth pressure under 3D conditions.

Active earth pressure of retaining wall considering wall movement

The coulomb’s limit equilibrium theory is employed for the active earth pressure calculation of retaining wall considering translational wall movement. It is considered that the earth pressure against the back of the wall is due to the thrust exerted by a wedge of soil between the wall and a plane passing through the heel of the wall. The soil–wall friction angle and internal soil friction angle are obtained via the simulation of the unloading triaxial test. The basic equations are established by considering the force equilibrium of a partial soil wedge. The lateral earth pressure coefficient is achieved through the moment equilibrium of the whole soil wedge. Comparisons illustrating the accuracy of the proposed approach are made with solutions available in the literature.

Lateral Earth Pressure behind Walls Rotating about Base considering Arching Effects

In field, the earth pressure on a retaining wall is the common effect of kinds of factors. To figure out how key factors act, it has taken into account the arching effects together with the contribution from the mode of displacement of a wall to calculate earth pressure in the proposed method. Based on Mohr circle, a conversion factor is introduced to determine the shear stresses between artificial slices in soil mass. In the light of this basis, a modified differential slices solution is presented for calculation of active earth pressure on a retaining wall. Comparisons show that the result of proposed method is identical to observations from model tests in prediction of lateral pressures for walls rotating about the base.

Method for Calculating Active Earth Pressure of Retaining Wall Based on Energy Theory

Calculation methods for active earth pressure of retaining wall are analyzed and discussed, and then based on energy conservation principle, one formula about calculation of active earth pressure was deduced which was illustrated with two engineering examples. The results suggest: compared with other limit equilibrium method, this method is closer to practical action and relatively simple, and is applicable to any case calculation for active earth pressure of wall retaining, so has high promotion value.