# Analysis of Damage and Permeability Evolution of Sandstone under Compression Deformation
## 6 Conclusions  
In this study, a new coupled seepage theory model for sandstone was developed. Drawing on extensive mechanical and permeability tests, the evolution equation for rock damage and permeability under compression was derived based on theoretical analysis and experimental observations. Moreover, the relationship between porosity and permeability in both porous media flow and fractured flow was unified. To solve the coupled seepage equation and verify its validity, the model was implemented in finite element software through programming and applied to the fluid-solid coupling analysis of rocks under triaxial compression.  
Comparisons between the numerical results and experimental data indicated that this model can well describe the entire process of the investigated rock deformation and reproduce the damage and permeability evolution behavior, particularly the phenomenon of damage-induced permeability surge. The numerical results for stress-induced damage, damage-induced permeability, and seepage-induced deformation show strong agreement with the experimental data. The damage-strain curve resembles an \"S-shaped\" curve, characterized by slow growth, accelerated growth, and balance. The permeability-strain curve follows a \"V-shaped\" pattern, initially decreasing and then rapidly increasing. The turning point when the permeability changes from decreasing to increasing is the starting  
Figure 14: The variation curves of pore pressure with flow distance.  
point of rock dilatancy. The permeability surge is mainly concentrated in the stage of rock dilatancy-failure.  
Damage and effective mean stress (\(\sigma_{m}\)-\(\alpha_{b}p\)) play a crucial role in the evolution of rock permeability and porosity. Among these factors, the effective mean stress has a dominant effect on permeability during the compaction stage of the rock, so the permeability shows a decreasing trend. When the effect of damage exceeds the effective mean stress, the permeability begins to turn into an increasing trend. This is the fundamental reason for the evolution of permeability.  
To summarize, damage and permeability evolution exist in actual engineering and cannot be ignored. Seepage pressure not only reduces the strength of rocks but also aggravates the damage and thus induces an increase in permeability. This model reveals the mechanisms behind damage and permeability evolution in rocks and has significant application value in practical engineering fields, such as stability analysis of surrounding rock, leakage analysis in underground energy storage, and shale gas extraction.  
Conceptualization, Y.R., X.C. and C.X.; Methodology, Y.R. and H.D.; Software, Y.S.; Validation, Y.S., H.D. and C.X.; Formal analysis, X.C. and H.D.; Investigation, X.C.; Resources, Y.R. and YS.; Data curation, H.D.; Writing--original draft, Y.R. and H.D.; Writing--review & editing, X.C.; Supervision, Y.S. and C.X.; Project administration, C.X.; Funding acquisition, X.C. and C.X. All authors have read and agreed to the published version of the manuscript.  
The authors would gratefully like to acknowledge the financial support from the National Key R&D Program of China (grant no. 2023 YFC3009400), the National Natural Science Foundation of China (grant nos. 52208342 and 52068033), the Jiangxi Provincial Natural Science Foundation (grant nos. 20242 ACB214008, 20232 BAB204072, and 20232 BCJ23069), and the Foundation of the Department of Transportation of Jiangxi Province (grant no. 2021C0006).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Authors [PERSON] and [PERSON] were employed by the company Jiangxi Transportation Institute Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.