Author:  Wang, Yujie 
Title:  Stability analysis of slopes and footings considering different dilationangles of geomaterial 
Degree:  Ph.D. 
Year:  2001 
Subject:  Slopes (Stability) Hong Kong Polytechnic University  Dissertations 
Department:  Dept. of Civil and Structural Engineering 
Pages:  xxvii, 263 leaves : ill. ; 30 cm 
Language:  English 
InnoPac Record:  http://library.polyu.edu.hk/record=b1566404 
URI:  http://theses.lib.polyu.edu.hk/handle/200/705 
Abstract:  The upper bound approach has been successfully applied to the analysis of twodimensional (2D) slopes (Donald and Chen, 1997), although some limitations on this approach still exist. The associated flow rule, on which the upper bound approach relies, to a certain extent, overestimates the dilation of soils or rocks. The randomsearch simplex method employed in the upper bound approach sometimes suffers a premature termination in the search for the global minimum. In spite of these limitations, the potential for extending the upper bound approach to analysis of 2D bearing capacity, wedge stability, and threedimensional (3D) slope stability is highly promising. The improvements of the upper bound approach presented in this thesis are conducted based on the understanding of the limitations. Chapter 1 of the thesis gives a statement of the stability problems in geotechnical engineering, objectives and organization of the thesis. Literature review in the subject area is presented in Chapter 2. The review includes the most relevant work done in the past on 2D and 3D slope stability analysis, 2D bearing capacity analysis, wedge stability analysis, and optimization techniques for finding the most critical failure mechanism. As an extension of the upper bound approach to 2D slope stability analysis, in Chapter 3 of the thesis, a limit method is proposed and presented for analysis of 2D slopes consisting of soils following an associated or a nonassociated flow rule. In other words, various dilations of the soils, from zero (dilation angle y=0) to full dilation (ps=f, where f is friction angle), can be considered in the proposed limit method. When the associated flow rule is used or full dilation is considered, the limit method becomes an upper bound method. Similar to the upper bound method, by constructing a kinematically admissible velocity field, the limit method establishes a work energy balance equation, in which the factor of safety as the only unknown is included and determined iteratively. The minimum of the factor of safety F is found by using an optimization technique among all kinematically admissible failure mechanisms. The investigation into the influence of the dilatancy angle on the factor of safety of 2D slopes is then performed using the limit analysis method. Results are presented and compared to values obtained using other methods. In Chapter 4, the limit method has been extended to study 2D bearing capacity problems. Using this method, a particular equation for calculating the bearing capacity of a strip footing is derived considering various dilatancy angles of the soil. The equation has been used to investigate the joined influence of the cohesion c, the friction angle f, the unit weight y of soils, and the surcharge load q, on the bearing capacity pressure qu of a strip footing. The influence of the dilatancy angle on the three bearing capacity factors is investigated, in a way similar to that in the 2D slope stability analysis. Results using the limit method are presented, compared to other solutions and discussed. Wedge failure is a typical threedimensional (3D) slope stability problem. In Chapter 5, four different methods are presented for the stability analysis of 3D wedge problems. The four methods are the traditional limit equilibrium (TLE) method (Hoek and Bray, 1977), the general limit equilibrium (GLE) method, the upper bound (UB) method extended from 2D slope stability analysis, and a newly proposed limit method considering the dilatancy of slip surfaces (called DD method). Among the four methods, the formulation of the GLE method is, for the first time, derived by the author, based on the Maximum Principle proposed by Pan (1980). The UB method is newly extended in this thesis. The DD method is a new method for 3D wedge stability analysis considering various dilatancy angles of the discontinuity planes. A nonsymmetric wedge (Hoek and Bray, 1977) and a symmetric wedge are studied using the TLE, GLE, UB and DD methods. Results obtained using the four methods are compared and discussed. A typical wedge at the location of a ship lock of the Three Gorges Dam in China is studied using both TLE and UB methods. It is found that when the dilatancy angle is equal to the friction angle, the DD method gives the same upper bound value of factor of safety (F) as that obtained using GLE and UB methods. When the dilatancy angle is zero, the DD method gives the same lower bound Fvalue as that obtained using the TLE method. The DD method gives the factor of safety, which varies from the minimum to the maximum value depending on the dilatancy angle. The relationship among the four methods is discussed. In order to investigate the wedge failure mechanism further and to validate the methods in Chapter 5, a threedimensional (3D) finiteelement (FE) model is established using the commercial software ABAQUS (1998). The 3D FE model is used to study the same wedge problems as in Chapter 4. FE results are compared to results obtained using the GLE and UB methods. The comparison shows that the FE model for dilatancy angle ps=f gives almost the same maximum Fvalue as that obtained using both GLE and UB methods. The Fvalue from the TLE method is considered to give the minimum Fvalue. It is noted that when ps=f, the DD method gives the same upper bound Fvalue as that using both GLE and UB methods. To a certain extent, the FE results support the results obtained by both GLE and UB methods (or the DD method for ps=f. In Chapter 7, a new upper bound (EMU3D) approach (for ps=f) to threedimensional slope stability analysis is presented. This EMU3D approach adopts multiprism blocks with inclined sides to represent a potential sliding mass in three dimensions. A work energy balance equation established in this discretization mode is derived. This equation includes only one unknown  the factor of safety F and is used to determine F iteratively. This approach avoids the complicated spatial force vector analysis exhibited in the conventional 3D limit equilibrium methods. The EMU3D method is used to study a simple 3D purely cohesive soil slope with a spherical failure surface (as Example 1). The factor of safety obtained using the EMU3D method is compared to results obtained using the other three methods including a "closedform" solution. As Example 2, a 3D slope of cohesivefrictional soil with an elliptical failure surface is studied using the EMU3D method. The Fvalue obtained is comparable to that obtained by Zhang (1988). The new EMU3D method has been successfully applied to two real projects. One is the stability analysis of a slope at the site of the Power Plant of the Tianshengqiao n Project in China (as Example 3). The another one is the stability analysis of an abutment of the Xiaowan Arch Dam in China (as Example 4). The influence of the dilatancy angle on the factor of safety has not been studied in this thesis due to time limitation. The consideration of the dilatancy angle can be incorporated into the EMU3D approach by using the nonassociated flow rule in the same way as that in Chapter 3 and Chapter 4 for 2D problems. The optimization techniques are a very important tool used in almost all limit analysis methods, especially the proposed limit methods for 2D and 3D analyses. Chapter 8 presents two optimization methods. The first one is a randomsearch simplex method. The second one is a simulated annealing method. The focus is on the simulated annealing method and its application to slope stability analysis. Steps of the application of the method is presented and discussed. Three examples are used to demonstrate the use of the simulated annealing method for searching for the most critical failure surface of slopes for the minimum Fvalue. Comparison of the two optimization methods is presented and discussed. The overall summary of the work done in the thesis project and major conclusions are presented in Chapter 9. Due to time limitation, some work done so far is preliminary and needs further study, for example the EMU3D method for 3D slope analysis and further examination and applications of the simulated annealing optimization method. Further research work is suggested in the final chapter. 
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