Stress on the wall surface of levels with cross sections of various shapes

Abstract

INTRODUCTION THE authors have published, previously, the results of investigations on the stress concentration in elastic rock around a level or a shaft, applying the theory of elasticity and photoelastic experiments under the conditions that before the excavation was made, the rock was in a general three-dimensional state of stress, i.e. the rock was subject to compression in all directions, and the directions of principal stresses were not always vertical and horizontal [1]. The stress on the wall of a level or a shaft under such conditions is very complicated. Therefore, in order to understand the relation between the shapes of cross section of levels, and stress concentrations around levels, it will be more convenient to study the latter under somewhat simpler initial conditions. For this reason, the stress concentrations around levels will be treated in this paper with the assumption that one of the smaller principal stresses took the direction of the axis of the level before the level was driven. As a matter of course, the analysis of stress under this condition is easier and needs only three two-dimensional photoelastic experiments for each shape of cross section, while the analysis of stress under general conditions requires five photoelastic experiments, three of them being two-dimensional and the other two three-dimensional. Referring to the results of investigations under the general conditions described above, it is supposed that the stress concentration under this special condition is greater than that under other conditions, so that the analysis of stress under this condition will contribute to the study of earth pressure.