Prandtl_China Uni - A Revised Failure Mechanism of Strip...

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A Revised Failure Mechanism of Strip Footings for Upper Bound Solution F. Yang and J. S. Yang School of Civil Engineering and Architecture Central South University, Changsha 41007, China ABSTRACT The bearing capacity factor N γ of rough strip footing is investigated using rigid block upper bound limit analysis with a revised failure mechanism of subsoil. The velocity discontinues are assumed to occur in both radial and tangent directions, and the velocity values can vary in radial direction in this failure mechanism. Increasing the number of rigid blocks, the velocity discontinues gradually become curved lines in the radial shear zone. Calculating formula of upper bound solution for bearing capacity factor N γ are deduced based on the proposed failure mechanism, and a corresponding procedure is compiled. Compared with other solutions of rigid block upper bound limit analysis, the obtained results in this study can give better values of N γ , which are closer to the exact values, provided by Martin using the method of characteristics. And it is shown that the proposed revised failure mechanism of subsoil is reasonable for determination of bearing capacity factor N γ of strip footings. KEYWORDS: Bearing capacity Failure mechanism Strip footing Upper bound method Limit analysis
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Vol. 13, Bund. F 2 INTRODUCTION The ultimate bearing capacity of strip footings can be determined using the method proposed by Terzaghi (1943): 1 2 ucq q cN qN BN γ =++ (1) Where q u = ultimate bearing capacity, c = soil cohesion, q = surcharge, γ = soil unit weight, B = width of strip footing. N c , N q and N γ = bearing capacity factors which depend only on friction angle of soil, φ . Several methods have been proposed to calculate the bearing capacity factors of N c , N q and N γ . The exact values of N q were obtained by Prandtl (1921) for strip footing on weightless subsoil, from which N c can be derived. However, exact values of N γ have not been obtained for quite a long time; numerical solutions have been obtained by many researchers including recently by Martin (2005) using the method of characteristics. There are several quite different methods for determination of ultimate bearing capacity, i.e. limit equilibrium, slip line method, finite element method, finite difference method and limit analysis. By using these methods, several results of bearing capacity factor N γ have been investigated. Sokolovskii (1965), Booker (1969), Hansen (1970), Bolton and Lau (1993) and Kumar (2003) have obtained N γ using slip line method. Griffiths (1982), Frydman and Burd (1997) obtained N γ using finite element method and finite difference method. Chen (1975), Michalowski (1997), Soubra (1999) and Zhu (2000) obtained N γ using rigid block upper bound limit analysis. Zhu et al (2001) employed slice method of limit equilibrium to calculate N γ . Recently, upper bound finite element analysis, combined with optimization procedure, provided a rigorous numerical solution to ultimate bearing capacity problem (Sloan, 1989).
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This note was uploaded on 04/19/2010 for the course CIVL 306455301 taught by Professor Mudiliu during the Three '09 term at University of Sydney.

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Prandtl_China Uni - A Revised Failure Mechanism of Strip...

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