Page - 861 - in Book of Full Papers - Symposium Hydro Engineering

of uncertainty and acceptable risk. Reliability analysis can be considered as an alternative to the definitive methods and makes engineering judgment easier [1]. 2. EFFECT OF FLOW RULE ON THE BEARING CAPACITY COEFFICIENTS Bearing capacity of the soil is the maximum load pressure that soil can tolerate at the moment of the failure. The most common methods used to determine the bearing capacity of foundations are limit methods so that these methods can be divided into three basic types of limit equilibrium method, method of stress characteristic and limit analysis. Limit analysis method determines the upper and lower collapse load by theory of plasticity. In this method if the upper and lower limit give the same result, then it will be the exact solution of the problem. Researchers investigate foundation bearing capacity using different methods in the literature. One of the famous theories is known as Terzaghi bearing capacity theory. Terzaghi defines ultimate bearing capacity of foundation according to Eq. 1 [2]. [1] Qu = CNc + qNq + 0.5BγNγ where Nc,Nq,Nγ are bearing capacity factors which are dimensionless and can be computed by friction angle, φ.B is the foundation width, and γ is unit weight. Also in this equation q is surcharge pressure and C is soil cohesion. Michalowski (1997) [3] estimated to calculate bearing capacity of a foundation using the upper bound approach which is applied to determine bearing capacity of a dam foundation on granular soil without surcharge pressure (C = 0 , q = 0). In Michalowski estimation, the substantial influence of the dilatancy angle on limit load was also considered. It is worthy to note that limit theorems are based on rigid-perfectly-plastic behavior that follow the associated flow rule. It should be noted that the soil used in this paper is coarse; the soil cohesion, therefore, is set zero. Furthermore, surcharge pressure has not been taken into account, i.e. the third term of the bearing capacity equation, qNq, becomes zero. Accordingly, the bearing capacity equation of Michalowski can be written as below: [2] Qu = 0.5BγNγ Concerning associated flow rule, the yield function is equal to the potential function [28]. Assuming Mohr-Coulomb yield criterion and associativity, the aforementioned statement renders the equality of yield surface. Although the associated flow rule leads the limit theorems , the theorems based on which limit analysis of stability problems can be well carried out to be developed [29], granular soils often dilates under deviatoric loads in an angle much less than the friction angle. Therefore, it seems to be more or less inaccurate assuming associativity, and non-associated flow rule, instead, should be considered in order to increase the accuracy of the assumptions. 861