等方性球殻理論による初期応力測定値の分析と考察

Abstract

A general theory of isotropic elastic spherical shell has been presented to evaluate the initial stress field. Extending the original theory of isotropic elastic spherical shell presented by McCutchen, the thermal stress has been analyzed and the influence of the temperature gradient near the surface and the thermal stress has been discussed. The theoretical solution shows that the fundamental relationships realized near the surface are as follows. Namely, the vertical normal stress coincides with the overburden pressure and the horizontal strain is determined by the ratio of the surface subsidence to the radius of the earth. Then, in the general model, the average horizontal stress at a certain depth is given by a function of the elastic constants with stress dependency.To make clear the profile of the average horizontal stress and to investigate the applicability of the general theory, the ratio of the average horizontal stress to the vertical stress has been analyzed and compared to the measurements by means of the stress relieving method in the world. Showing the close agreement between the measurement and the calculation, it has been concluded that the vertical distribution of the Young's modulus, which is deeply depending on the mean normal stress, plays an important role in determining the magnitude of the average horizontal stress. Finally, the expansion of the theory to the anisotropic field has been pointed out to be a future work.