基于球壳模型的地壳应力与深度关系研究

随着矿产资源的开发逐步进入地壳深部，对深部地应力场的变化趋势的探究愈发重要。近些年的研究更新了许多地应力数据，有必要基于最新数据对现有估算方法做出改进。本文根据弹性力学基本理论和球壳模型，研究随深度变化的万有引力体积力和内压的作用，得到宏观的应力分布理论公式；引用广泛分布的实测数据，对理论公式中的地壳物理参数进行拟合，得出垂直地应力和平均水平地应力随深度变化的拟合公式。结果表明:在地球的宏观尺度上，地壳应力随深度的分布不再是线性关系，但在当前人类活动范围内，地应力均值随深度基本呈线性变化，与金尼克假说在γ=22 kN/m3、λ=0.9时的结果最为接近；随着深度增加，平均侧应力系数逐渐趋近于1，比Brown和Hoek提出的包络线更接近实测数据；地壳内部的高压会引起水平拉应力，但自重引起的压应力更高，使得整个地壳内的垂直地应力和水平地应力都为压应力。研究结果可为地壳应力分布趋势的预测特别是深部区域的预测提供参考。

A study on relationships between measured crustal stresses and depth based on spherical shell model

Due to the exploitation of mineral resources in the deep underground space, it is more and more important to study the variation trend of deep in-situ stress field. In recent years the researches have updated many in-situ stress data. It is necessary to improve the existing estimation methods on this account. Based on the basic theory of elasticity and spherical shell model, this paper studied the effect of gravitational body force varying with depth and internal pressure, and obtained the theoretical formula of macro in-situ stress distribution; Employing the latest and widely distributed measured data, this paper fitted the crustal physical parameters in the theoretical formula, and obtained the fitting formula of vertical in-situ stress and average horizontal in-situ stress varying with depth. The results show that: the distribution of crustal stresses with depth is no longer linear on the macroscopic scale of the Earth; however, within the current depth range of human activities, basically the average in-situ stresses vary linearly with depth, which is closest to the results of the Dinnick hypothesis at γ=22 kN/m3 and λ=0.9; with the increase of depth, the average lateral pressure coefficient gradually approaches 1, which is closer to the measured data than the envelope proposed by Brown and Hoek; the high pressure in the crust will cause horizontal tensile stress, but the compressive stress generated by gravity is higher and therefore the vertical and horizontal in-situ stress in the whole crust are compressive stress. The research results provide a theoretical prediction model for the estimation of crustal stress distribution trend, especially in deep underground space.