Pseudo-Dynamic Bearing Capacity of Shallow Strip Footing Resting on c-Φ Soil Considering Composite Failure Surface: Bearing Capacity Analysis Using Pseudo-Dynamic Method

Introduction

The seismic bearing capacity problem is one of the greatest challenges to the Civil Engineers and various methods have been extensively applied towards the challenge given by the Geotechnical Earthquake Engineers. Many researchers have investigated the problem of bearing capacity of foundation using different mechanisms. The pioneering works in determining the bearing capacity in static condition were done by Prandtl, 1921; Terzaghi, 1943; Meyerhoff, 1957, 1963; Vesic, 1973; Saran and Agarwal, 1991 and many others. For foundation of structures built in seismic areas, the demands to the sustain load and deformation during an earthquake will probably be the most severe in their design life. Thus the design of foundation in seismic areas needs special considerations compared to the static case. A number of researcher had analysed the seismic bearing capacity of shallow strip footings using pseudo-static approach with the help of different solution techniques such as method of slices, limit equilibrium, method of stress characteristics an upper bound limit analysis. Budhu and Al-karni, 1993; Soubra, 1993, 1997, 1999; Richards et al. 1993; Choudhury and Subha Rao, 2005; Kumar and Ghosh, 2006; and many more had considered the effect of earthquake on the bearing capacity of a surface to a shallow strip footing under pseudo-static method using different approaches. IS 6403:1981 also gives a formulation of ultimate bearing capacity for different types of foundation in different types of soils considering pseudo-static method. However, in the pseudo-static method, the dynamic nature of earthquake loading is considered in a very approximate way without taking any effect of time and phase difference. To overcome this drawback, Steedman and Zeng, 1990; and Choudhury and Nimbalkar, 2005; developed the pseudo-dynamic solutions where the effects of both shear and primary waves as well as the amplification of excitation were considered during the earthquake along with the duration of earthquake and the period of lateral shaking to predict the seismic earth pressure behind the vertical retaining wall. Recently, Ghosh, 2008; gives a solution of pseudo-dynamic bearing capacity of shallow strip footing resting on cohesionless soil using limit analysis method considering the Coulomb failure mechanism. But the solutions which were given for foundation resting on c-Φ soil, three different bearing capacity coefficients are suggested for three different failure mechanism. In Saha and Ghosh (2014), it is tried to take into account the simultaneous resistance of unit weight, surcharge and cohesion considering linear failure surface using limit equilibrium method. Here in this analysis, an attempt is made to solve this problem of pseudo-dynamic bearing capacity of shallow strip footing resting on c-φ soil considering the composite failure mechanism. A composite failure surface involving planar and log spiral surface is considered in the present analysis. To evaluate the bearing capacity under seismic loading condition, the simultaneous resistance of unit weight, surcharge and cohesion is taken into account. Results are presented in both tabular and graphical non-dimensional form including comparison with other available methods. Effects of wide range of variation of parameters like soil friction angle (φ), cohesion factor (2c/γB₀), depth factor (D_f/B₀) and horizontal and vertical seismic accelerations (k_h, k_v) along with primary wave and shear wave velocity on the pseudo-dynamic bearing capacity coefficient (N_γe) have been studied.