Abstract
The theoretical basis of classic geotechnical engineering stability problems is limit analyis thereom. Incremen-tal loading finite elements and strength reduction finite elements were put forward by Zienkiewicz in 1975 and the meth-ods are called by the authors Limit Analysis Finite Elements (abbreviation LAFE for short). It has been successfully ap-plied to slope engineering, and used to bearing capacity problems foundations. The LAFE method is still in initial stage, with problems in engineering practice. Key problems on yield criterion and dilatancy angle were also discussed in detail. The paper proved again that same ultimate bearing capacity and slip line are obtained in slip line field theory under asso-ciated and nonassociated flow rule, with the only difference of velocity vector direction. Meanwhile, the dilatancy angle should be φ/2 when nonassociated flow rule is employed under plane strain, and corresponding volumetric strain is zero. Thus the correctness of the theoretical solution in literature [19] is proved, and LAFE method is also proved a very prom-ising approach in solving bearing capacity problems of foundations. Rigorous theoretical basis is available for finite ele-ments incremental loading to solve the bearing capacity problems of foundations, and the approach is simple to use. In the numerical simulation process, not only the ultimate bearing capacity and load-displacement curve are obtained, but also the failure mechanism proved same as the one by traditional limit analysis approach is achieved. Only the yield criterion matched with practical engineering problems can generate a precise result. Under plane strain the results by Mohr-Coulomb inscribed circle yield criterion (DP3) for associated flow rule, and Mohr-Coulomb match yield criterion (DP5) for nonassociated flow rule are close to the accurate theoretical solution by Prandtl. The achievements can be applied in practical geotechnical engineering purposes.
Highlights
Classic geotechnical engineering stability problems include slope stability, bearing capacity of foundations and earth pressure problems, and limit analyis thereom [1,2] is their theoretical basis
Problems on Yield Criterion and Dilatancy of Limit Analysis Finite tion of strength reduction finite elements will be discussed in another paper
Finite elements incremental loading was employed in calculation of the ultimate bearing capacity of the foundation with the mesh shown in Fig. (9)
Summary
Classic geotechnical engineering stability problems include slope stability, bearing capacity of foundations and earth pressure problems, and limit analyis thereom [1,2] is their theoretical basis. After 100 years’ development, limit analysis method has gradually become mature It demonstrated good practica-ility in engineering practice, and solved some problems in engineering design, especially strength and stability problems. Due to difficulties in solving traditional limit analysis equations, discrete methods, such as slip line field finite difference, upper and lower bound finite elements etc, were applied to limit analysis theorem. Two alternatives are available for geomaterials to reach limit equilibrium state through finite elements method. Problems on Yield Criterion and Dilatancy of Limit Analysis Finite tion of strength reduction finite elements will be discussed in another paper. In finite elements analysis under limit equilibrium state, slip line, and velocity vector direction, and ultimate load can be obtained automatically. The essence of LAFE is that geomaterials reach failure state through reducing strength indexes or increasing applied load. Key problems on yield criterion and dilatancy angle were discussed in detail in this paper
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