## 1 Introduction
[19] reported consistent increases in \(\sigma_{\text{cd}}\) and \(\sigma_{\text{p}}\) for granite with  
Figure 1: Classification of loading techniques and engineering fields over a wide range of strain rates [2,3]. the increase in strain rate, a result corroborated by [PERSON] et al. [20] using the grain-based finite-discrete element method. Experimental studies on uniaxial and triaxial conditions have also explored strain rate effects on \(\sigma_{\text{ci}}\) for various rock types [21; 22]. While existing studies have analyzed the strain rate effects on characteristic stresses, the effects of the strain rate and confinement in quasi-static compression across varying strain rates have not been fully understood. In addition, the evolutionary patterns of characteristic stresses and their underlying mechanisms under combined strain rate and confining pressure conditions have not been systematically investigated. Rock strength criteria establish functional relationships between principal stresses at failure. Over 100 static criteria have been proposed to date, with widely adopted formulations including the Mohr-Coulomb and Hoek-Brown criteria [23]. Recent research has prioritized adapting these classical frameworks for dynamic loading scenarios. [PERSON] et al. [24] revealed a logarithmic growth of cohesion (c) with the strain rate, while the internal friction angle (\(\varphi\)) remained rate-independent when applying the Mohr-Coulomb criterion to dynamic rock failure. The numerical simulations [25] verified the Mohr-Coulomb framework's applicability across dynamic loading regimes. [PERSON] et al. [26] and [PERSON] et al. [27] extended applications to dynamic tensile and punching shear failure. [PERSON] et al. [28] demonstrated that the m-value in the Hoek-Brown criterion remains unaffected by the strain rate, established a correlation between parameter a and strain rate, and proposed a generalized Hoek-Brown dynamic strength criterion. Although the mechanical response of rocks under dynamic loading conditions has been extensively characterized, the development of strength criteria within quasi-static loading regimes has received comparatively limited attention. Furthermore, existing criteria for quasi-static conditions often exhibit excessive mathematical complexity, highlighting the need for simplified criteria applicable to the quasi-static loading regime. After reviewing the literature, existing studies exhibit three main limitations: (1) the variation trends of \(\sigma_{\text{ci}}\) and \(\sigma_{\text{cd}}\) under combined confining pressure and strain rates have not been clearly defined; (2) the underlying mechanisms governing confining pressure's influence on strain rate effects of different characteristic stresses have not been fully explained; (3) practical dynamic strength criteria for rock under quasi-static loading are still lacking. Based on this, triaxial compression tests on granite specimens were conducted over a wide range of strain rates (\(10^{-6}\) to \(10^{-2}\) s\({}^{-1}\)) and confining pressures (0-40 MPa) to characterize quasi-static mechanical behaviors. Stress-strain curves, characteristic stresses, and macro-fracture patterns were analyzed, with a dynamic strength criterion established based on the Mohr-Coulomb failure theory. The values, ratios, and correlations of characteristic stresses were systematically investigated in relation to the strain rate and confining pressure. Finally, strain rate dependence discrepancies between \(\sigma_{\text{ci}}\) and \(\sigma_{\text{cd}}\) under varying confinement were discussed in detail, accompanied by proposed governing mechanisms.