Determination of bearing capacity of shallow foundations without using superposition approximation

The Terzaghi superposition assumption has been widely used to determine the bearing capacity of shallow footings. Although this assumption always errs on the safe side, a rigorous procedure to calculate the bearing capacity is still of engineering value. This paper presents such a procedure that is free from errors as a result of the superposition assumption. It demonstrates that the ultimate bearing capacity can be precisely expressed by the Terzaghi equation, except that the bearing capacity factor Nγ is dependent upon the surcharge ratio. A recently developed numerical method, i.e., the critical slip field method, is used to calculate the modification coefficient for modifying Nγ. It is found that this modification coefficient increases with the surcharge ratio at small values of surcharge ratio and then remains constant for large values of surcharge ratio. However, the errors invoked by the superposition assumption do not exceed 10%. On the basis of numerical calculations, a simple closed-form expression of the modification coefficient is proposed that yields the theoretically rigorous ultimate bearing capacity. In the later part of the paper, errors in bearing capacity calculations owing to the use of conventional procedures are analyzed. It is concluded that the continued use of conventional procedures is justified, but the inherent errors should not be neglected in assessing the performance of shallow foundations.Key words: shallow foundation, strip footing, ultimate bearing capacity, critical slip field.