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.

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

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.

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

Currently, knowledge of the failure mechanisms of narrow backfills with retaining walls rotating about the top (RT mode) is still lacking which leads to inaccurate estimations of the earth pressure. Numerical simulations using finite element limit analysis find that under the effects of backfill geometries, interface strengths, and soil properties, the upper soil layer supported by soil arching retains its integrity and the lower soil layer is sheared by multiple curved sliding surfaces in the limit state. Based on the failure mechanisms of narrow backfills, a calculation model is established which considers the soil arching effect, curved sliding surface, and cohesive soils. Analytical solutions for the earth pressure of narrow cohesive backfills with retaining walls rotating about the top are derived by using the limit equilibrium horizontal slice method. Compared with previous studies, the present method predicts the earth pressure distribution with higher accuracy. Several extensive parametric studies have also been conducted. Thus, decreasing the aspect ratio of backfills, increasing the inclined angle of natural slopes, interface strengths, and soil cohesion are beneficial for maintaining backfill integrity and reducing earth pressure against retaining walls.

Analytical solutions for the earth pressure of narrow cohesive backfill with retaining walls rotating about the top

Based on limit equilibrium principles, this study presents a theoretical derivation of a new analytical formulation for estimating magnitude and lateral earth pressure distribution on a retaining wall subjected to seismic loads. The proposed solution accounts for failure wedge inclination, unit weight and friction angle of backfill soil, wall roughness, and horizontal and vertical seismic ground accelerations. The current analysis predicts a nonlinear lateral earth pressure variation along the wall with and without seismic loads. A parametric study is conducted to examine the influence of various parameters on lateral earth pressure distribution. Findings reveal that lateral earth pressure increases with the increase of horizontal ground acceleration while it decreases with the increase of vertical ground acceleration. Compared to classical theory, the position of resultant lateral earth force is located at a higher distance from wall base which in turn has a direct impact on wall stability and economy. A numerical example is presented to illustrate the computations of lateral earth pressure distribution based on the suggested analytical method.

Seismic lateral earth pressure analysis of retaining walls

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.

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

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 τ, 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.

Tang Zhao-ping

Papers

Distribution of active earth pressure of retaining wall with wall movement of rotation about top