Abstract:
A mathematical technique is hereby advanced for investigating the bearing capacity and associated normal stress distribution at failure of soil foundations.The stability equations are obtained using the limit Equilibrium(LE)conditions. The conditions of vertical, horizontal and rotational equilibria are transformed mathematically with respect to the soil shearing strength, leading to the derivation of the equation of the functional Q, and two integral constraints. Generally, no constitutive law beyond the coulomb's yield criterion is incorporated in the formulation. Consequently, no constraints are placed on the character of the the critical s except the overall equilibrium of failing soil section. The critical normal stress distribution,Ómin, and consequently the load, Ómin, determine as a result of the minimization of the functional are the smallest stress and load parameters that can cause failure. In other words, for a soil with strength parameters of c, ø, r, and footing with geometry I, II, when stress б<бmin (c, ø, r, I, H) and load Q < Qmin (c, ø, r, I, H) foundation is stable. Otherwise the stability would depend on the constitutive character of the foundation soil. In the mathematical method employed, the stability analysis is transcribed as a minimization problem in the calculus of variations. The result of the analysis shows, among others, that the Terzagh’s superposition approach can be derived using the technique of variational calculus, and consequently the representation of the bearing capacity by the three factors N q’ N ᴄ ’ and N ᵣ is appropriately possible. Also the classical relationship between N c and Nq is again found by the limit equilibrium and therefore independent of the constitutive law the soil medium. Finally, the computer implementation of the entire analytical procedure has been successfully carried out and hereby incorporated, leading to the advancement of a new foundation design technique.
