Ultimate limit state analysis in geotechnical engineering using discrete element method, plasticity and extremum principle

Abstract

Lateral earth pressure, ultimate bearing capacity and slope stability problems are three important and classical geotechnical problems which are well considered by the use of the limit equilibrium method, limit analysis method and method of characteristics in the past. These three classical problems are considered separately in the past, though they are all related to the ultimate limit state of a system. The author views that these problems are governed by similar ultimate requirements, and they can be considered as different views of the ultimate limit state of the system. Therefore, this research focuses on the theoretical analysis of the ultimate limit state in geotechnical engineering using a continuum plasticity as well as discrete element approach. Firstly, classical bearing capacity problem is re-considered using slip-line method, adaptive finite element limit analysis and discrete element analysis. It is considered from the elastic stage, plastic stage to the rupture stage under the ultimate condition. The large scale failure mechanism and movement of soil for a strip footing are studied, and the influences of the micro-parameters on the bearing capacity of soil are also investigated. This work helps to identify the failure mechanism in bearing capacity problem and the assessment of the classical Limit Equilibrium and plasticity Methods for which the constitutive model and initial conditions are neglected. The differences between different methods of analyses are then investigated and discussed. It is found that there are noticeable differences between the continuum and discontinuum analyses, and the well-known log-spiral transition zone is also not apparent in both the discrete element approach as well as the laboratory tests, which is one useful new contribution in this study. Next, discrete element method and slip line method are adopted to analyze the lateral pressure behavior of soil under different boundary conditions and friction angles. The large displacement failure mechanism and movement of soil with the lateral earth pressure of a backfill is further investigated, and the ultimate limit state and the influence of the micro-parameters on the lateral pressure of soil are also observed and compared with the classical plasticity based methods. Moreover, in order to develop the lower bound solution and extremum principle with internal and external variables in limit equilibrium analysis, the well-known slip line solutions is then applied on a bearing capacity problem to determine the interslice force function f(x) and the thrust line for a "horizontal slope". It is found that it is not important that which variables are used in the stability formulation, either external boundary forces or internal forces, if the ultimate state is considered. Furthermore, it is demonstrated that the maximum extremum from the limit equilibrium analysis is equivalent to the slip line solution of the classical bearing capacity problem. Lastly, the author demonstrates the equivalence between the classical lateral earth pressure and bearing capacity problem by the slip line method. The equivalence between the lateral earth pressure problem and slope stability problem is then illustrated by the use of the extremum principle. The three classical geotechnical problems can then be unified by varying f(x) until the maximum resistance of the system is fully mobilized, and the corresponding solution is practically equivalent to the plasticity slip line solution. Such unification is not surprising because the fundamental principles behind the three problems are exactly the same: equilibrium and yield. By using an extremum limit equilibrium slope stability program, the author has also determined the bearing capacity factors and lateral earth pressure coefficients which are exactly the same as those classical plasticity slip line solutions. The classification of a problem is hence just a matter of convenience instead of the difference in the nature of the problem. Through the present works, the three classical geotechnical problems are unified which is an innovative and interesting result in geotechnical engineering and also another new contribution in this study. In conclusion, the innovations in this thesis include the unification of the three classical geotechnical problems by slip line method and extremum principle; the equivalence of external or internal variables formulations of limit equilibrium method and the equivalence of the limit equilibrium method with the plasticity analysis under the ultimate condition and the consideration of the failure mechanism under very soil movement and the corresponding comparisons with the distinct element analysis.