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This paper deals with optimum cost (objective function) design of geosynthetic reinforced earth retaining walls subjected to static and dynamic loading. The design restrictions are imposed as design constraints in the analysis. Choice of the initial designed length and strength of the reinforcement, which are the elements of the design vectors are made in a way that it forms an initial feasible design vector. Thus the problem is one of mathematical programming. The constraints and the objective function being nonlinear in nature, the Sequential Unconstrained Minimization Technique (SUMT) has been used in conjunction with conjugate direction and quadratic fit methods for multidimensional and unidirectional minimization to arrive at the optimal (minimum) cost of the reinforced earth wall. Optimal cost tables are presented for different combinations of the loading and the developed procedure is validated by taking up an example problem. It has been found from the typical example problem that saving of the order of 7-8% can be made over the conventional design of mechanically stabilized earth (MSE) walls with the aid of design charts.

The ultimate bearing capacity of foundation placed on a slope is significantly affected by its vicinity to the slope face, which offers substantially lesser passive resistance as compared to a footing resting on a semi-infinite medium. Conventional bearing capacity theories fail to address the behavior of such foundations. Few existing theories predict the bearing capacity of foundations on slopes considering stress-based failure approach. However, deformation along the slope plays a major role in governing the failure of such foundations, thus requiring a coupled stress-deformation based failure analysis. With the aid of 3-D finite element modelling, employing coupled stressdeformation analysis, this study addresses the failure mechanism and the bearing capacity (q u ) of a square footing located on a dry cohesionless slope. The effect of various parameters, namely the angle of internal friction of soil, setback distance, slope inclination, footing width and the depth of embedment of the footing, have been investigated. Variations parameters are found to noticeably alter the bearing capacity estimate and the observed failure mechanism. A critical setback distance is obtained [(b/B) critical = 3] beyond which the failure mechanism resembles the same obtained for a footing resting on horizontal ground. The unit weight and modulus of elasticity of the soil material is found to have negligible effect on the bearing capacity.

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