## 1 Introduction  
The interplay between rock porosity and mechanical behavior remains a pivotal research frontier in geomechanics. Natural rock formations inherently contain multiscale, irregular pore networks and different layered states that profoundly govern their physico-mechanical responses, with critical implications for geotechnical applications ranging from slope stabilization to underground excavation engineering [1, 2, 3, 4, 5, 6]. While empirical correlations between porosity and macroscopic mechanical properties have been established, the inherent complexity of pore geometry coupled with methodological constraints in conventional experimental approaches has hindered the development of rigorous theoretical frameworks. Notably, conventional laboratory techniques face inherent limitations in isolating porosity as an independent variable during mechanical characterization. For porous materials such as rocks, porosity is considered to be an important parameter affecting the physical properties of porous materials [7]. In general, the compressive strength and Young's modulus of rocks are mainly affected by porosity and less affected by other parameters such as pore diameter, pore connectivity, and pore surface roughness. Consequently, scholars from various research fields have conducted extensive studies on the relationship between pore characteristics in rocks and their physical and mechanical properties from various perspectives. Multidisciplinary investigations employing integrated experimental and numerical approaches have systematically quantified porosity-property relationships, yielding critical insights for energy resource development and geotechnical engineering applications. Contemporary methodologies combining high-resolution microstructural characterization with multiscale modeling are progressively elucidating the mechanistic connections between void space architecture and macroscopic rock performance. Recent advances in digital rock physics have enabled novel approaches through numerical reconstruction of pore architectures. This methodology permits systematic investigation of porosity-dependent mechanical responses by controlling pore volume fraction as a singular variable. Numerous scholars have contributed to this evolving field through innovative methodologies: [PERSON] et al. developed a modified Vipulanandan failure criterion for predicting shear strength characteristics while [PERSON] et al. conducted comprehensive analyses of tuff mechanical behavior with particular emphasis on pore geometry effects [8; 9]. Computational approaches have seen significant development, exemplified by [PERSON] et al. [10], who integrated extreme gradient boosting with Firefly algorithms (XGBoost-FA hybrid model) for elastic modulus prediction, and [PERSON] and [PERSON] implemented application of boosted regression tree ensembles for brittleness index estimation [11]. Parallel developments in microstructural reconstruction techniques continue to enhance pore-scale modeling capabilities. [PERSON] and [PERSON] pioneered geometric reconstruction methods correlating fractal pore dimensions with mechanical properties in Chongqing sandstone [12]. [PERSON] et al. devised adaptive phase-recovery algorithms enabling accurate 3D porous media reconstruction from 2D imaging data [13], while [PERSON] et al. implemented deep learning architectures for 3D pore network restoration from limited tomographic slices [14]. Despite these advancements, a critical knowledge gap persists in establishing quantitative mathematical relationships between reconstructed pore architecture parameters and macroscopic mechanical properties. This study addresses this scientific gap through an integrated experimental-numerical framework. Utilizing Sichuan white sandstone as a representative lithology, we combine high-resolution X-ray micro-computed tomography (\(\upmu\)CT) with mechanical testing to establish baseline parameters.