基于分形与损伤理论的岩石声-应力相关性理论模型研究

建立单一微裂纹在单轴压缩荷载作用下的力学模型,采用宏观复合型断裂理论中的最大周向应力理论,求出单一微裂纹达到稳定时的形态尺寸.利用分形损伤理论,求出不同荷载阶段的分形维数;由分形维数的定义导出了不同荷载阶段的裂纹个数的变化情况;结合单一微裂纹的形态尺寸,求出不同荷载阶段中岩石孔隙率与荷载值之间的关系;利用目前被广泛采用的超声波纵波速度与孔隙率的关系式,最终导出单轴压缩荷载作用下岩石超声波纵波速度与应力的理论关系式.进行岩石声-应力的试验测试,根据试验成果作出声-应力曲线,并与理论声-应力曲线进行比对,结果表明,理论模型比较适合于反映岩石受载全过程中的后半部分的声-应力关系.

Theoretical model research on relationship between ultrasonic and stress of rock based on fractals and damage theory

The mechanical model of single microcrack under uniaxial compression loading is established; then maximum circumferential stress theory ( criterion ) is adopted among macroscopic multiple fracture theories to calculate the stability size of single microcrack. According to the fractal damage theory, fractal dimension is calculated in different loading stages; the amount of microcracks is derived based on the definition of fractal dimension; combining the form and size of single microcrack, the relationship between rock porosity and loading value in different loading stages is obtained; according to the formula about p-wave velocity and porosity which has been adopted extensively now, the theoretical formula about p-wave velocity and stress of rock under uniaxial compression loading is obtained. Test on the relationship between ultrasonic and stress of rock is made; then the curve of ultrasonic and stress is drawn. Compared with theoretical curve of ultrasonic and stress, the result shows that this theoretical model is suitable to describe the latter half part relationship between ultrasonic and stress in the whole loading process of rock.