Calculations of Bearing Capacity Factor N Using Numerical Limit Analyses

This paper presents numerical upper- and lower-bound solutions for the well-known bearing capacity factor N 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 N 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 N (average of upper and lower bounds) obtained from the current numerical limit analyses. Other well-known analytical solutions and numerical calculations appear to overestimate N for rough footings. Comparisons of predicted upper-bound failure mechanisms and lower-bound contact pressures help to explain similarities and differences among these solutions.