Determination of Value and Point of Application of Seismic Total Thrust on Rigid Retaining Walls with Layered Backfill

1. The estimation of lateral earth pressures on retaining walls has been an earliest subject in geotechnical engineering. The earliest lateral earth pressure theories were suggested by Coulomb (1776) and then by Rankine (1857) and remain the basis for the present earth pressure calculation. In fact, Coulomb’s procedure can determine the static lateral total thrust on the wall rather than the distribution of earth pressures. However, the subject has been extensively expanded for better determination of lateral earth pressures on retaining structures. In the present study, a hybrid approach for estimating the total thrust and height of its application is presented. For this purpose, Kotter’s equation [1] of characteristic method is used to determine the governing equations of the failure surface. Then, on the basis of limit equilibrium approach and pseudo static methods by using global equation of forces acting on the wedge, the magnitude and position of application application point of total thrust are determined. The present study considers the inertia effect of the stable soil medium on the failure wedge. Using an analytical procedure, a closed form solution for computing the angle between the failure surface and the horizontal direction is developed. In addition, the height of the application point of total thrust has also been calculated and compared with those obtained from earlier research work. In addition, the method is expanded for layered backfill.2. The present method applies limit equilibrium approach similar to the Mononobe-Okabe (MO) method and first finds seismic reaction pressures on the failed wedge. For this purpose, the retained soil is assumed to be cohesionless, homogeneous, isotropic, semi-infinite and dry. Also for the backfill soil, no effect of strain softening or liquefaction is considered in analyses. Given the global equilibrium equations of forces,, which contain three unknowns (, and), another equation is necessary for rendering the problem statically determined. This equation can be obtained by using the condition. It is useful to choose the angle such that it maximizes the active thrust, as employed in Coulomb’s method, or uses one of Kotter’s equations on the slip surface, as done by Dewaikar and Halkude [1] and also used in the present study.By using Kotter’s equations on the slip surface, this paper can be considered as a simplified approach with respect to the method of characteristics. It assumes a slip surface of arbitrary form (planar), while in the method of characteristics, the form of the slip surface is part of the solution. Moreover, only one of the equations of Kotter is considered, but the problem is governed by a system of four differential equations in the method of characteristics.3. It is well known that in the retaining wall design for overturning stability, the application point of the total thrust is important. The main strong point of the approach of present method is the possibility of determining the position of the point of application of the total thrust. It has been shown that there is no difference for total thrusts determined from the present method and that computed from both Coulomb’s and MO methods. This position is obtained from moment equilibrium. As mentioned before, results of many experiments generally suggest that the application point of the resultant thrust be located higher than one third of the height of the wall and should be located at mid-height of the wall (Sherif and Ishibashi [2], Bolton and Steedman [3], Steedman [4]).The height of the total active thrust application predicted by the present method is similar to that obtained from tests carried out by Sherif and Ishibashi [1]. In addition, it is quite close to that given by Seed and Whitman [5]. It is noted that Al Atik [6] believes that the application point of seismic total active thrust predicted by the MO method is assumed to be at 0.33H from the wall bottom. 4. This paper has presented a theoretical solution for determining the magnitude and height of application of total active and passive thrust exerted on rigid retaining walls. The pressure distribution on the backfill failure surface has been determined using Kotter’s equations. For both active and passive seismic conditions, the angle of failure surface with the horizontal direction, total lateral thrust, soil reaction on the failed wedge and the point of application have been determined. The results of present study can be summarized as follows: The active and passive thrusts and angles of failure plane with respect to the horizontal direction are identical in the present method and both the Coulomb and MO methods. The height of the point of application of seismic total thrust determined using the developed method is in agreement with experimental results obtained in earlier research works. The developed closed-form of the solution enables the designer to determine total active\passive lateral thrusts, point of application of total thrust, and estimation of overturning moment on retaining walls.It has been found that the seismic soil reaction from the stable soil on the backfill failed wedge can not be ignored, since such ignorance would result in overestimation of seismic passive force, underestimation of seismic active force, and under-prediction of the application point of seismic active force. All these may lead to the unsafe design of retaining walls.