Biaxial capacity envelopes for the capacity design of biaxially loaded shallow foundations

Earthquakes cause bi-directional horizontal actions on structures. While Eurocode 8 recognizes this fact and mandates that the horizontal components of the design seismic action shall be taken as acting simultaneously, neither Eurocode 8 nor the existing literature provide the interaction behaviour of biaxially loaded shallow foundations. Further, it is to be noted that, in a real structure, the horizontal force and moment acting on a foundation, are inter-related through the effective height of the supported column. The present study considers the inter-relation between horizontal force and moment to generate the normalised vertical load-biaxial horizontal load (V-Hx-Hy) capacity envelopes, which can also be used to directly obtain the V-H-M and V-Mx-My capacity envelopes, considering the effective height of the structure. To develop the V-Hx-Hy capacity envelopes, three-dimensional (3D) finite element limit analyses are performed on surface as well as embedded square and rectangular footings, resting on dry sand. The main factors affecting the capacity of a biaxially loaded shallow foundation are discussed. The effect of ground acceleration on the capacity envelope is highlighted. Limitations of the current design procedures for the design of biaxially loaded foundations are demonstrated, through a case study. Finally, a procedure for the capacity design of biaxially loaded shallow foundations, using capacity envelopes, is proposed.