New Approach for Active Earth Pressure Calculation on Rigid Retaining Walls with Cohesive Backfill
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SOIL MECHANICS NEW APPROACH FOR ACTIVE EARTH PRESSURE CALCULATION ON RIGID RETAINING WALLS WITH COHESIVE BACKFILL
UDC 624.131.531.1 Yi Tang* and Jiangong Chen Department of Civil Engineering, National Joint Engineering Research Center of Geohazards Prevention in Reservoir Areas, Chongqing University, Chongqing, China, *Corresponding author Email: [email protected].
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.
Introduction Problems of calculating the active earth pressure on a retaining wall are of great interest in geotechnical engineering and have been theoretically studied by many researchers [1-5]. The Coulomb theory [1] and the Rankine theory [2] are the most well-known classical theories. However, these theories are established on two assumptions: 1) that the sliding surface is a plane, and 2) that the distribution of earth pressure on the retaining wall is linear. Furthermore, since a corresponding moment equilibrium equation is not taken into consideration for these two theories, the point of application of the resultant earth pressure, which is assumed to act at one-third of the wall height according to the linear distribution of earth pressure, may not be accurately determined using the moment equation and may also not be exact. To avoid the restrictions of these assumptions and their imperfections, this paper proposes a more mathematically rigorous approach called the variational limit equilibrium method to solve this problem. The variational limit equilibrium method was first proposed by Kopacsy [6-8]. The method was subsequently widely used to evaluate the slope stability problem [9-12]. However, a few scholars have adopted this method to study the active earth pressure on retaining walls. Soubra et al. [13, 14] applied the variational method to study the passive earth pressure problem, taking into consideration the seepage flow, but the effective passive pressures was assumed to act at the bottom third of the penetration depth. Considering the corresponding moment equilibrium equation, this paper adopts the variational limit equilibrium method to discuss the active earth pressure problem of cohesive soil in the general case without the above assumptions. The presented method can be used for obtaining functions of the sliding surface and the normal stress distribution along the sliding surface
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