## 1 Introduction  
According to conventional fracture mechanics, cracks typically form when the stress intensity factor approaches or surpasses a critical stress intensity factor, \(K_{c}\). However, crack formation in structures which have been loaded over time do not adhere to conventional fracture mechanics, and may propagate at a stress intensity factors significantly lower than the critical value, commonly referred to as subcritical crack growth. Scholars have proposed various potential mechanisms explaining the phenomenon of subcritical crack growth: stress corrosion, dissolution, diffusion, ion change, and microplasticity [1, 2]. All of these mechanisms involve the influence of an environmental agent's chemical activity at the tip of a crack in rocks. The fundamental mechanism for subcritical crack growth of rocks is known as stress corrosion [1]. The interaction of strained bonds with pore water at a crack tip leads to a degraded condition in which the bonds may be separated at lower stresses than the substantial bonds [1]. The hydrolysis of strong Si-O bonds for silicate rocks results in weaker H-bonded hydroxyl groups connecting the Si atoms [3, 4, 5, 6]. The following chemical reaction explains this process. H-O-H + [=Si-O-Si=] \(\leftrightarrow\) 2[=Si-OH] (1)Figure 1 provides a diagram for the crack velocity and normalised stress intensity factor of subcritical crack growth in rocks [2,7]. The rate of stress corrosion at crack tips affects the crack growth velocity in region 1, i.e., the interval \(0.2K_{c}\leq K\leq 0.8K_{c}\)[2,7]. Region 2 is found in certain glasses and ceramics but rarely in rocks [2,7,8]. Crack growth is mainly driven by mechanical rupture in region 3. The empirical power law relationship can describe the subcritical crack growth as follows [2,7]:  
\[v=A\Big{(}\frac{K}{K_{c}}\Big{)}^{n} \tag{2}\]  
where \(v\) indicates the crack velocity, \(A\) and \(n\) are the parameters of subcritical crack growth, \(K\) is the stress intensity factor, and \(K_{c}\) refers to fracture toughness. The parameter \(n\) in the equation is referred to as the stress corrosion index. Rock fractures in geological conditions are caused not only by applied stress, but also by stress corrosion. Stress corrosion is an environmentally activated chemical process associated with the fluid-assisted crack growth. Crack growth caused by stress corrosion is related to the time-dependent behaviours of rocks and is a crucial factor in determining the stability of underground structures over a long period of time. [PERSON] et al. [9] reported that the influence of stress rate on the uniaxial compressive strength can be expressed as the 1/(\(n\)+1)th power of the loading rate. Similarly, according to the subcritical crack growth theory [10], the fracture strength is directly proportionate to the 1/(\(n\)+1)th power of the loading rate, where the parameter \(n\) represents the stress corrosion index, which is related to the time dependence of rocks. Many researchers have reported that the strength of rocks increases slightly when the loading rate increases under static and quasi-static loading [11, 12, 13, 14, 15, 16]. [PERSON] and [PERSON] [17] reported that the rock strength increases significantly after the loading rate is above a critical value under dynamic loading. The degradation of the rock strength on the loading rate under static and quasi-static loading is related to subcritical crack growth caused by stress corrosion. Under static loading, the strength of rock decreases when the rock has a relatively low value of the stress corrosion index for a given loading rate [9]. [PERSON] [18] developed a time-dependent model of rock joint cohesion degradation. At a higher value of the stress corrosion index, it was shown to have a higher value of cohesion and a longer lifetime. Figure 1: Diagram of crack velocity/normalised stress intensity factor for subcritical crack growth in rocks; K\({}_{\text{o}}\) represents the stress corrosion limit.