# Study on Characteristic Strength and Constitutive Model of Red Sandstone under Hydraulic Coupling
###### Abstract  
The newly built shaft in the western region needs to pass through the deep Cretaceous stratum, where the pores and fissures are developed, the cementation ability is poor, and the surrounding rock is rich in water. Under the coupling effect of the stress field and seepage field, the surrounding rock is easy to deteriorate and loses stability. The hydraulic coupling test of Cretaceous red sandstone was carried out by using the TAW-2000 rock mechanics testing system, and the characteristic strength evolution law of red sandstone was analyzed; Mohr's circle and strength envelope were obtained by the M-C criterion, and the influence mechanism seepage pressure on red sandstone was explored; and combined with the effective stress principle and M-C strength criterion, a constitutive model under hydraulic coupling was established. Confining pressure limits the development of cracks and strengthens the mechanical properties. The results revealed that red sandstone has the characteristics of low less clay, loose particles, and weak cementation capacity; under the action of water pressure, the cement between particles disintegrates and loses the cementation strength, resulting in a significant decrease in cohesion, and the loss of cementation strength is the internal reason for the softening of red sandstone. The constitutive model based on the effective principle and M-C criterion can better reflect the mechanical behavior of red sandstone under hydraulic coupling. This paper provides a research basis for understanding the microscopic characteristics and hydraulic coupling characteristics of Cretaceous weakly cemented sandstone. pore water pressure has effects on the final failure mode. [PERSON] et al. [18] studied the failure characteristics of sandstone and explored the crack initiation and fracture mechanism under hydraulic-mechanical coupling. [PERSON] et al. [19] found that the failure mode of sandstone under the action of seepage pressure became complex. [PERSON] et al. [20] found that the shear cracks of a rock formed during the failure process will increase under water pressure. [PERSON] et al. [21] conducted the consolidation test of hard rock tailings under the action of pore water pressure, and obtained the influence of pore water pressure on the compression parameters. [PERSON] et al. [22] simulated the coupling effect of hydraulic fracture and primary fracture, which was verified by the Brazil test. In the process of loading, the damage accumulates continuously and finally leads to failure [23; 24; 25; 26]. In terms of a constitutive model, many scholars combine damage mechanics with statistics to form a mesostatistical damage theory. [PERSON] et al. [27], based on shear failure and creep, proposed a constitutive model that can reflect the loading rate of chalk. For a high-porosity rock, [PERSON] et al. [28] proposed a constitutive model considering hydrostatic unloading response and plastic volumetric strain. [PERSON] et al. [29; 30] established a hydraulic fracturing model considering the strain rate and pore water pressure. [PERSON] et al. [31] considered the process of degradation; a constitutive model under hydrological conditions was established. [PERSON] et al. [32] considered the influence of the compression stage; a damage constitutive model considered a weak water effect was established. [PERSON] et al. [33], combined with the composite power function, established the constitutive model reflecting the osmotic pressure. [PERSON] et al. [34] used strain as a damage factor to describe the damage caused by crack generation and propagation; a stress seepage damage constitutive model was established, but it could not reflect the impact of seepage pressure on damage.