在地应力测量中准确求解最大、最小水平应力问题的探讨

Computing maximum and minimum horizontal stresses in in-situ stress measurements

目前,在地应力测量和应用中,人们常常用近于水平的两个主应力或其在水平面上的投影来代替或估计最大和最小水平应力,这在一般情况下误差不大,但是当应力结构比较特殊时这种代替或近似将带来较大的误差,甚至给工程实践带来危害。以投影近似为例按3种三维应力状态分别讨论了方位误差随应力形因子R与主应力轴倾角的变化和量值误差随R、主应力轴倾角和最大、最小主应力量值之差的变化。并用原地应力测量资料求得了方位和量值误差。理论分析和实例都证明了用近于水平的两个主应力的投影代替两个水平应力的误差可能很大。建议在研究与水平应力相关的问题或与水平方向相关的物理参量时采用本文的计算方法求出准确值。

At present, for the measurements and applications of in-situ stress, people often use the two nearly horizontal principal stresses or their projections on horizontal surface to replace or estimate the maximum and minimum horizontal stresses. Generally, there are no considerable errors. But when the stress structure is special, this replacement or approximation will bring great errors, even harm to engineering practice. To argue for this fact, taking projection approximation as an example, the variations of azimuth and magnitude error with the stress shape factor R and the inclination of the principal stress axis and different magnitudes of the maximum and the minimum principal stresses in three different 3D stress states are discussed. Also, as examples, the errors of azimuth and magnitude are calculated using the in-situ stress measurement data. Theoretical analysis and examples demonstrate that there may be considerable errors in using the projections of two nearly horizontal principal stresses on horizontal plane to approximate the two horizontal stresses. It is suggested that in the study of horizontal stresses or physical quantities related to horizontal direction, the proposed method should be employed.