Evaluating the <i>N_&#x3b3;</i> Coefficient for Shallow Strip Footings on Sloping Ground by the Method of Stress Characteristics

Abstract

This study presents a new solution algorithm to calculate the bearing capacity coefficient Nγ for a fully rough strip footing located on an infinite slope considering different soil friction angles φ and ground slopes β° using the stress characteristics method. The results showed that Nγ coefficients decreased with an increase in slope inclination, and roughness contribution prevented further reduction, particularly for higher φ values. The higher contribution of the upside-sloping ground for footing laid on the infinite slope led to a lower reduction of the Nγ coefficients compared with the footing placed at the slope vicinity in terms of a larger area affected by the stress field, and a larger plastic region of the downface slope. The reduction value was more eminent for steeper slopes β ≥ 20° due to the tendency for nonsymmetrical failure pattern, especially for higher φ values. The findings of the current research and those described in the literature were in good agreement, so much so that the lower-bound limit analysis and the current solution technique virtually reflect the same trend. The load inclination values for footings located adjacent to the slope with β ≤ 30° were not meaningful, whereas for footing resting on an infinite slope with β ≥ 25° it exceeds 15°, which reflects the fact that its effect should not be neglected, especially for ground slopes greater than 20°. By increasing β°, the maximum values of plastic length and plastic depth on the left and right sides of the footing decrease and increase, respectively. The maximum depth of the plastic region for β ≥ 20° from around the right side of the footing shifts toward the downward-sloping face. The maximum width of the elastic wedge gradually reduces, and the intersection point of the left and right plastic regions slowly shifts to the left and upside of the footing.