Real-time porosity inversion of rock based on the ultrasonic velocity and its compression-damage coupled model under triaxial compression

It is of great significance to evaluate the stress state and mechanical properties of deep rock engineering, by inverting the real-time porosity of rocks. In this study, the triaxial compression tests and real-time ultrasonic velocity tests were conducted on siltstone under different confining pressures. Firstly, a nonlinear model for the evolution of rock ultrasonic velocity with axial strain was proposed, based on the characteristic that the ultrasonic velocity rapidly increases and tends to stabilize. Secondly, a correction coefficient for the ultrasonic velocity of the rock matrix was proposed and the Raymer model was modified. The real-time porosity during triaxial compression of rocks was inverted according to the modified Raymer model and the ultrasonic velocity model. Subsequently, the effective compression coefficient of rocks was calculated based on real-time porosity, and a compaction coefficient was established to describe the compaction effect of cracks and pores. Finally, a new compressive-damage coupled constitutive model for rocks was established, by combining the statistical damage theory and compaction effect.