Relationship between the Seismic Coefficient and the Unfactored Geosynthetic Force in Reinforced Earth Structures

This paper presents an integrated analytical method for calculating the resultant unfactored geosynthetic force in reinforced earth structures under seismic loading conditions. The method utilizes a pseudostatic limit equilibrium approach for assessing the internal stability of a reinforced earth structure, assuming a potential rotational failure along a log spiral trace. A closed-form solution is presented for determining the sum of all horizontal forces mobilized in the geosynthetic reinforcement along their intersection with the critical log spiral surface. This mobilized sum is then redistributed among the individual layers to determine the unfactored reinforcement forces that are needed to resist the applied seismic acceleration. Parametric studies were utilized, and the results are presented in a series of design charts for different conditions. Such charts can be used to determine the required tensile strength of the reinforcement for a given seismic coefficient. Alternatively, for a given reinforcement strength, the formulation can also be used to determine the yield acceleration that is required for calculating seismic displacements. An advantage of the proposed methodology is that it determines the yield acceleration caused by rotation of the reinforced mass (internal stability), which allows for a rational, yet simple, assessment of the displacement related to the internal movement of the reinforced mass. The design charts illustrate the effect of earth structure backslope and the vertical seismic coefficient. The results also show the impact of the assumed location of the resultant reinforcement force under seismic loading conditions. Variations in the location of this force over a reasonable range have little impact on the results. The inclination of the backslope has a significant effect for earth structures with smaller batters and/or larger horizontal seismic coefficients. Additionally, vertical seismic coefficients with a downward direction increase the mobilized force in the geosynthetic reinforcement. DOI:10.1061/(ASCE)GT.1943-5606.0000701. (C) 2012 American Society of Civil Engineers.