Simplified formulas for the seismic bearing capacity of shallow strip foundations

The seismic bearing capacity of shallow foundations is affected by inertia forces acting both on the structure and in the supporting soil. Even though the former have been recognised to play often the major role, by increasing the horizontal load and the overturning moment transferred to the foundation, both of them must be taken into account in the seismic design of foundations. Using a pseudostatic approach and based on the upper bound theorem of limit analysis, a comprehensive set of formulas is derived for the computation of the seismic bearing capacity of strip footings resting on cohesive-frictional and purely cohesive soils. Results are given in terms of: (i) reduction coefficients for the Terzaghi's equation of the vertical bearing capacity and (ii) ultimate failure envelopes in the space of normalised loading variables. These formulas extend to more general conditions other literature results, allowing to take into account easily the effects of inertia forces acting both on the superstructure (load inclination and eccentricity) and into the foundation soil. The reliability of the proposed equations, suitable for the design practice, is verified through a thorough comparison with other rigorous and approximate solutions.