Infrastructure Engineering - Theses
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ItemStress distribution in discontinuous media( 1967)The determination of the stress distribution within a semi infinite medium, which in fact is an infinitely redundant structure, becomes complex when all the relevant factors such as material characteristics, discontinuity patterns, loading conditions and boundary restraints are considered. This complexity is further accentuated when the material has a non-linear stress-strain relationship and a condition of residual stresses associated with the insitu state. Hence as an initial study the blocks making up the semi infinite medium are considered as homogeneous, isotropic and linear elastic. In this particular study, boundary tractions represented in the form of model foundations are applied to a semi infinite medium of uniform characteristics. That is Young's modulus and Poisson's ratio are constant and the discontinuities are controlled in a horizontal and vertical direction. The stresses within the models are determined by applying photoelastic techniques. Analytical and numerical solutions are developed so as to compare results with those obtained experimentally and subsequently define behaviour patterns. Stress distributions at the contact zone between the foundation and subgrade are also studied. The subgrade is initially studied with no side restraint, however in the latter models a side restraint is applied. Studies on an opening in a discontinuous semi infinite subgrade with surface loading are also made. The relatively low stress fields set up in the subgrade require a much more sensitive photoelastic material than is generally encountered. This sensitivity however, should not be acquired at the expense of reducing Young’s modulus. A material meeting this requirement is Araldite D, with an appropriate hardener. The use of this material however requires the development of careful and precise casting techniques. These techniques are fully covered in the thesis presented. To corroborate the experimental findings with an analytical theory which to date is incompletely defined, a review of the fundamentals controlling the stress distribution is essential. The usual requirement of satisfying compatability of strain at the interface is not always satisfied. This appears to affect the stress-strain relationship, in both a micro and macro scale, and hence the stress distribution and redistribution. Four numerical methods of obtaining an approximate solution to a required degree of accuracy are presented and compared with the experimental work. 1) Finite difference approach. 2) Finite element method. 3) Boundary Singular Integral solution. 4) Energy principle approach. It is concluded that the energy principle offers the most promising approach of determining the stress distribution in a nonlinear elastic-plastic semi infinite discontinuous subgrade. Finally the possibilities of failure conditions within the rock being initiated by environmental changes such as surface loads, excavations and tunnelling are considered.