| Summary: | Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1998. Includes bibliographical references. This thesis describes the development and application of numerical limit analyses for planar, undrained stability problems in geotechnical engineering. The proposed analyses formulate upper and lower bound theorems for perfectly plastic, cohesivefrictional soils as linear programming problems, with spatial variations of the unknown velocities and stresses approximated by standard finite element interpolation functions. The thesis includes three substantial modifications of the pre-existing software: l) inclusion of structural beam and joint elements, that enable the program to model failure in combined bending, shear and axial loading; 2) implementation of functions to represent the undrained strength anisotropy of soft clays; and 3) representation of pore water pressures and effective stress strength parameters for stability analyses that include free draining soil layers. In all of the examples presented in this thesis, the proposed numerical limit analyses are able to bracket the true collapse load within ±5%. The stability of surface footings under combined effects of vertical, horizontal and moment (V, H, M) loading is solved in the form of three-dimensional failure envelopes, that include effects of underbase suction and non-homogeneous undrained strength profiles. Existing empirical bearing capacity factors for inclined, eccentric loading are shown to be conservative, often underestimating the exact collapse solutions for footings on homogeneous clay by more than 25%. However, the same correction factors can become completely unreliable when there is a significant undrained strength gradient. The numerically-derived failure envelope for footings on homogeneous clay is described approximately by curve fitting techniques using relatively simple functions that can be used to update the existing bearing capacity factors. The undrained (short-term) pullout capacity of a single caisson cell in clay is initially investigated as a planar problem. Limit analyses show that the capacity can be presented as a normalized function of the undrained strength gradient in the clay, and interior surface area of the caisson. The results show that there are significant errors in limit equilibrium calculations which assume mechanisms of reverse end-bearing. Pullout predictions are compared with measured data from 1) small scale laboratory element tests on miniature caissons, 2) centrifuge models and 3) field tests on a four-cell caisson unit. These comparisons introduce approximations in the scaling of the planar solutions to axisymmetric cell geometries, and inclined loading cases. Good agreement is obtained with all three sets of experiments, and confirms that the proposed limit analyses are at least comparable in predictive capability to the limit equilibrium calculations currently used in practice. The limit analyses represent the undrained strength anisotropy of soft clays using a yield function originally proposed by Davis and Christian ( 1970). Undrained strength anisotropy is found to have a major influence on the stability and failure mechanisms for unbraced vertical cuts in clay. In contrast, there is minimal effect on the failure mechanisms for kinematically constrained problems such as the lateral load capacity of deeply embedded pile or pipe sections. Applications of limit analyses for braced excavations show important errors in existing calculations of basal stability. The analyses also provide the first theoretical solutions that quantify effects of wall embedment and bending strength on the stability of well-braced cuts. The results have also been compared with previous displacement-based finite element calculations based on the anisotropic MIT-E3 soil model. Good matching is obtained using the limit analyses together with anisotropic strength parameters mobilized at shear strains, y = 0.6 - 1.0%, corresponding to failure conditions in the finite element solutions. Limit analyses have been used to re-assess the stability of tied-back walls at Bird Island Flats in East Boston. Detailed analyses were carried out for two cases l) estimated excavation and support geometry at an unstable section; and 2) at final excavated grade after placement of a remedial buttress constructed by deep soil-mixing and jet grouting. Reliability analyses show that uncertainties in the undrained strength profile represent the major factor affecting predictions of stability. Successful performance of the improved cross-section is not consistently explained by strength parameters derived from the unstable cross-section. Additional calculations compare the stabilizing effects of different designs for the wall, tiebacks and remedial buttress. The failure of an offshore breakwater in Brazil was analyzed extensively using conventional slope stability methods in a recent Ph.D thesis by Lee ( 1995). Limit analyses, using the same soil parameters, shows similar mechanisms of failure controlled by the undrained shear strength of the underlying Sergipe clay. However, the factors of safety computed by Spencer's method are shown to be unrealistically low due to the assumed directions of interslice forces in the overlying sand and rockfill layers. by Boonchai Ukritchon. Sc.D.
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