双组份裂缝岩石非线性有效应力模型研究

为认识黏土矿物和裂缝对岩石有效应力的影响，提出了双组份裂缝岩石椭圆模型.同时，将双组份裂缝岩石椭圆模型等效为共聚焦的椭圆岩石环与椭圆黏土环的叠加；基于复变函数和保角变换，分别得到了黏土环内椭圆长半轴和短半轴与压力间的关系式.进而结合椭圆孔渗透率计算式和岩石有效应力表达式，计算与分析了岩石孔隙度、黏土矿物含量、硬度比以及椭圆孔截面纵横比等参数对有效应力系数的影响.结果表明，当岩石中不含黏土矿物时，有效应力系数随纵横比的减小而增大，且小于1.0，这与Bernabé的观点一致.当岩石中含有易于压缩的黏土矿物，且纵横比为1.0（孔隙截面为圆形）时，有效应力系数随硬度比和黏土矿物含量的增大而增大，甚至远大于1.0，这与Al-Wardy等的研究结论一致；当纵横比小于1.0时，有效应力系数表现出了明显的非线性特征，随硬度比的增大而增大——甚至远大于1.0，而随黏土矿物含量的增大而减小，纵横比对有效应力系数的影响受黏土矿物含量大小的影响.易于压缩组分和裂缝的存在使得岩石有效应力系数变化特征更为复杂.

Theoretical study on non-linear effective pressure in two-constitute fractured rock

To obtain the effect of clay minerals and fractures on the effective stress law, we proposed a two-constitute elliptical-fracture model, which was divided into confocal elliptical rock ring and elliptical clay ring. Meanwhile, based on complex function theory and conformal transformation method, we deduced the calculation expressions between the two semi-axis (semimajor axis and semiminor axis) of elliptical clay ring and stresses. Then together with the permeability calculation equation and the effective stress law, we analyzed the impact of porosity, clay content, stiffness ratio, pore aspect ratio on the effective stress coefficient. The results show that when clay content equals to zero, effective stress coefficients increase with the decrease of aspect ratio, and are less than 1.0, agreeing with Bernabe's viewpoint. When some highly compressible clay minerals exist and pore aspect ratio equals to 1.0 (i.e., cylinder pore), the effective stress coefficients increase with the increase of stiffness ratio and clay content, and even far exceed 1.0, which is in accord with Al-Wardy. When pore aspect ratio is less than 1.0, the effective stress coefficients display obvious nonlinear characteristics and increase with the increase of stiffness ratio, and are also much greater than 1.0, but decrease with the increase of clay mineral content, and the effect of aspect ratio on the effective stress coefficient is impacted by the amount of clay content. The existences of highly compressible components and fractures make the characteristics of effective stress coefficient more complex.