Rock Mechanics - Photoelastic Analysis of A Composite Model

In this paper, a new technique developed to analyze two-dimensional nonhomogeneous models is described. A simple three-layered medium with a circular hole centrally located in the intermediate layer is considered. The layered sheet is loaded uniaxially perpendicular to the stratification. The Young's modulus of the intermediate layer is lower than that of the outer layers. The stress distribution around the circular hole in a stratified medium is significantly different when compared to the case of a continuous homogeneous medium. The distribution depends upon the ratio of the height of the intermediate layer and the hole diameter. A comparison of stress distribution and procedures for preparation and testing of the model are given. The potential of the technique is outlined. In the process of applying the techniques of stress analysis to problems of rock mechanics, the recent discernible trend has been to postulate highly idealized models of physical situations. As new techniques have been developed, more complicated models have been conceived to simulate mote accurately the physical environment to which the analysis results are eventually applied. In this investigation, a new technique is developed to analyze two-dimensional nonhomogeneous models. The technique is used to determine the stress concentration around a circular hole in a soft material overlain and underlain by a hard material. In mining practice, such situations arise commonly in coal deposits and frequently in bedded or vein-type metallic mineral deposits. DEFINITION OF THE PROBLEM A plate, consisting of three layers with a circular hole in the intermediate layer, is loaded uniaxially, Fig. 1. The variable in the experimental investigation is the height of the intermediate layer, H. The diameter of the hole, D, is kept constant. The stress concentration factors around the periphery of the hole, for various values of H/D, are evaluated using the technique of photoelasticity, Table I. TECHNIQUE OF EXPLORATION Photoelastic analyses of composite models have hitherto been limited to the study of lap and butt joints between glued metals and dissimilar materials.1-3 In mining, Haber and Oudenhoven used composite models to study the stress distribution around a circular hole in two-layered media and the behavior of elastic liners in shallow underground openings.4-5 They used the stress freezing technique devised by Dally et a1.6 The procedure used in this investigation is outlined below: Casting of Layer A: Flat sheets of plastic were cast in a silicon-coated mold using Araldite 502 with hardener 951 in the ratio of 100:8 by weight. After