Problems on Yield Criterion and Dilatancy of Limit Analysis Finite Elements to Bearing Capacity of Geomaterials

Wei-Xue Kong*, 1, 2, Ying-Ren Zheng3, Lu-Hui Yan2
1 Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road & Traffic Safety (Changsha University of Science & Technology), Ministry of Education, Changsha 410004, China
2 School of Basic Education for Commanding Officers, National University of Defense Technology, Changsha 410072, China
3 Department of Architecture and Civil Engineering, Logistical Engineering University, Chongqing 401311, China

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© 2013 Kong et al;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road & Traffic Safety, Changsha University of Science & Technology, Ministry of Education, Changsha 410004, China; Tel: (86) 731-85258786; E-mail:


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.

Keywords: Limit analysis finite elements, Geomaterials, Dilatancy angle, Yield criterion, Slip line field, Ultimate Bearing ca-pacity of foundation, Collapse mechanism.