Calculations of Bearing Capacity Factor N[sub γ] Using Numerical Limit Analyses

Abstract

This paper presents numerical upper- and lower-bound solutions for the well-known bearing capacity factor Nγ of a surface strip footing on a frictional soil. The analyses use linear programming and finite-element spatial discretization to solve limit analysis of perfect plasticity, assuming a linear Mohr-Coulomb failure envelope with associated flow within the soil and along the soil-footing interface. The current analyses are to bound the exact value of Nγ within ±5% increasing to ±30% as the internal friction angle increases from 5° to 45° for both smooth and rough interface conditions. Previous solutions by Hansen and Christensen in 1969 and Booker in 1969 are in excellent agreement with the best estimate of Nγ (average of upper and lower bounds) obtained from the current numerical limit analyses. Other well-known analytical solutions and numerical calculations appear to overestimate Nγ for rough footings. Comparisons of predicted upper-bound failure mechanisms and lower-bound contact pressures help to explain similarities and differences among these solutions.