Determinationof the foundations bearing capacity and maximum applicable load to the soil mass are important aspects of geotechnical engineering. More exact solutions of the soil mechanics problems such as bearing capacity of foundations, can be obtained when elasto plastic behavior of the soil mass, equilibrium equations, compatibility conditions, and stress–strain relations are considered simultaneously. Complication in achieving the actual ultimate load, become an incentive for researchers to develop methods that solve problems without need to regard all of the conditions and constraints (complete solution). Limit analysis is one of the prevalent methods that simplifies stability calculations. Use of soil plasticity theory with neglecting equilibrium equations and compatibility conditions can lead to upper and lower bound of limit analysis respectively. earing capacity of shallow strip footings are mostly presented for homogenous soil but soil strength profiles especially for normally consolidated and slightly over consolidated clays are non-homogenous. To estimate bearing capacity of non-homogenous soils, average strength, empirical methods, as well as numerical methods such as upper bound limit analysis, finite element method and finite element upper bound limit analysis have been recommended. Therefore selecting of these methods depended on the required accuracy. Present study focuses on bearing capacity of foundations on clay under undrained condition which cohesion varying linearly with depth by using upper bound limit analysis. Both upper bound multi rigid blocks with genetic algorithm and finite element limit analysis methods are applied to obtain the results. In this study, results of upper bound multi rigid blocks based on Prandtl mechanism lead to accepted bearing capacity coefficient compared to results in the literature. By the way, the obtained results are in good agreement with results of finite element upper bound. Finally, a simple relation is proposed which can easily considers the varying in depth cohesion of clay soil. Keyword: Upper bound limit analysis, Upper bound finite element, Failure mechanism, nonhomogeneous clay, Numerical optimization, Genetic algorithm
