# Analysis of Damage and Permeability Evolution of Sandstone under Compression Deformation
## 4 Model Validation and Results Analysis
### Damage Evolution Analysis  
A series of model parameter analyses and conventional triaxial compression tests were investigated. The comparison results of the stress-strain curves between the theoretical analysis and experimental data are shown in Figure 9. It can be seen that the numerical results are in good agreement with the experimental data, especially the elastic and plastic deformation, strain softening, and residual strength. However, the numerical results of this model in the crack compaction stage of rock have some deviations from the tests when the confining pressure is equal to 10, 20, and 30 MPa because the elastoplastic damage constitutive model has some shortcomings in describing the compaction behavior of rock cracks and pores [35]. Therefore, the proposed model is more suitable for rocks with a short compaction stage and a low confining pressure, such as granite, limestone, and dense sandstone. Figure 10 shows the stress-strain curves of sandstone under the fluid-solid coupling conditions with a confining pressure of 5 MPa and different inlet seepage pressures. Seepage pressure weakens rock strength and accelerates rock failure. Both the peak and residual strength of the rock decrease with the increase in the seepage pressure, which conforms to the Mohr-Coulomb strength criterion considering the effective stress.  
Figure 11 shows the numerical results of the damage evolution of sandstone under the fluid-solid coupling conditions with a confining pressure of 5 MPa and different inlet seepage pressures. One can see that the damage evolution trend obtained from the analytical simulation and experimental tests is basically consistent, especially in the slow growth and early accelerated growth stages. There is a deviation between the theoretical prediction results and the experimental data in the later accelerated growth and balance stages, with a maximum error of about 10.13%. The main reason for this deviation is that the current theory is temporarily unable to consider the cumulative effect of primary cracks and initial damage on rock failure. But it is certain that this effect is positive; that is, the existence of primary cracks and initial damage is conducive to rock failure. Therefore, the theoretical prediction results are lower than the experimental data.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Density of sandstone, \(\rho\) (kg/m\({}^{3}\)) & 2650.00 \\ Young’s modulus of sandstone, \(E\) (GPa) & 4.75 \\ Poisson’s ratio of sandstone, \(\
u\) (1) & 0.28 \\ Cohesion of sandstone, \(c\) (MPa) & 10.88 \\ Angle of internal friction of sandstone, \(\varphi\) (\({}^{\circ}\)) & 31.56 \\ Initial porosity of sandstone, \(\varphi_{0}\) (\(\%\)) & 7.76 \\ Initial permeability of sandstone, \(k_{0}\) (m\({}^{2}\)) & 3.99 \(\times\) 10\({}^{-16}\) \\ Dynamic viscosity of nitrogen, \(\mu\) (Pa-s) & 1.76 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Property parameters of selected sandstone and nitrogen.  
It is also noticed that under the same boundary and deformation conditions, the higher the seepage pressure, the larger the rock damage. In other words, the seepage pressure aggravates the damage and failure of rocks. The influence degree decreases with the increase in the seepage pressure. If the influence of fluid-solid coupling on the strength and damage of rock is ignored in practical engineering, its stability and safety will be misjudged, which may lead to engineering accidents, especially in tunnel engineering and underground engineering.  
Figure 10: Stress–strain curves of sandstone specimen with different inlet seepage pressures \(p_{in}\).  
Figure 9: Comparison results of stress–strain curves obtained by experimental data and theoretical analysis under different confining pressures.