Page - 862 - in Book of Full Papers - Symposium Hydro Engineering

[3] T = σtanφ + C Mohr-Coulomb criteria can be modified for non-associated problems as follows [3] [4] T = σtanφ∗ + C∗ where: [5] tanφ∗ = sinφcosψ 1− sinψsinφ To make a rational and proper judgment to calculate the third term in Eq.1, limit analysis is employed. The advantage of this approach is that a clear distribution weight of the components of the soil, cohesion, and surcharge in bearing capacity formula is considered. 𝑁 ᵧ factor for non-associated flow rule is obtained from the perspective of the limit analysis. 𝑁 ᵧ factor values are shown in the following table for smooth and rough foundations and for different dilation angles as the part of the friction angle. It is worth re-mentioning that by the use of limit analysis, it is possible to obtain numerically estimated 𝑁 ᵧ values, tabled below as the results of Michalovski (1997); the most reasonable curve fits would be achieved in the next step, required for the reliability analysis. Table 1 𝑁 𝛾 for smooth foundation (non-associated flow rule) 𝑁 𝛾 (𝜑 ∗°) 𝜓 = 0 𝜓 = 0.25° 𝜓 = 0.5𝜑 ∗ 0 0 0 0 0.18 0.18 0.18 5 0.683 0.693 0.7 10 1.773 1.842 1.894 15 3.734 4.028 4.261 20 7.058 8.064 8.931 25 12.457 15.442 18.309 30 20.849 28.798 37.606 35 33.306 52.772 78.649 40 50.924 95.428 169.436 45 74.614 170.386 379.868 50 Table2 𝑁 𝛾 for rough foundation (non-associated flow rule) 𝑁 𝛾 (𝜑 ∗°) 𝜓 = 0 𝜓 = 0.25° 𝜓 = 0.5𝜑 ∗ 0 0 0 0 0.126 0.127 0.127 5 862