Abstract: Rankine’s theory of earth pressure can not be directly employed to the case of cohesive backfill with an inclined surface .For this practical case ,it seems that no analytical solution is available .In this paper ,a theoretical solution of active and passive earth pressures of cohesive backfill with an inclined surface under surcharge was developed on the basis of the lower-bound theorem of limit analysis .First ,a statically-balanced stress field of the slope ground consisting of cohesive soils was construed from elasticity theory .Then it was enforced to not violate the Mohr-Coulomb yield condition .According to the lower-bound theorem of limit analysis ,two extreme values of lateral stress which respectively correspond to active and passive earth pressures were to be found and expressed in the superposition from .Based on the a number of numerical computations conducted for different combinations of the key parameters related to the problem ,the computed results useful for engineering practice were given in tabular and graphical forms .The effects of the main parameters on comprehensive coefficients of active and passive were discussed .

Key words: earth pressure , limit equilibrium ;limit analysis , lower-bound theorem ;cohesive soil