## 1 Introduction  
As a potential host medium for the deep geological disposal of radioactive nuclear waste, claystone is found under highly complex hydro-mechanical (HM) conditions [1]. Therefore, studying the stress-strain laws of claystone under HM conditions is essential for the stability analysis of radioactive waste disposal repositories. Because of its important role in the stress-strain laws of a geomaterial, the effective stress principle of claystone was studied in this paper. Effective stress was first proposed by [PERSON] [2], who considered that pore pressure could counteract total stress. The effective stress principle satisfies the following form:  
\[\sigma_{e}=\sigma-\sigma_{p} \tag{1}\]  
where \(\sigma_{e}\) is the effective stress, \(\sigma\) is the total stress, and \(\sigma_{p}\) is the pore pressure. However, [PERSON] [3] found that [PERSON]'s effective stress principle was unsuitable for porous media with low permeability and believed that pore pressure could not offset the total pressure in a 1:1 ratio. A modified effective stress principle was proposed as follows [3]:  
\[\sigma_{e}=\sigma-\eta\sigma_{p} \tag{2}\]where \(\eta\) is the effective stress coefficient of a geomaterial. Since [PERSON] [3] modified the effective stress principle, numerous studies have investigated it in different soils and rocks [4; 5; 6; 7; 8]. Table 1 presents a summary of the various equations used in the literature for the effective stress principle. \begin{table}
\begin{tabular}{c c c} \hline \hline
**References** & **Effective Stress** & **Related Research Work** \\ \hline \multirow{2}{*}{[PERSON] and [PERSON] [9]} & **Saturated:**\(\eta=1-(K/K_{s})\) & The rock strain was quantified based on this effective stress principle, and its validity was verified via compression test results of sandstone and granite. \\  & \(K\) is the bulk moduli of rock; \(K_{s}\) is the bulk moduli of grain. & The phenomenon that pore pressure has a greater impact on permeability than confining pressure was found according to the permeability test results of sandstone under different confining and pore pressures. \\ \hline \multirow{4}{*}{[PERSON] and [PERSON] [10]} & **Saturated:**\(\eta=\frac{K}{K^{(1)}-K^{(2)}}\left(\eta^{(1)}-\eta^{(2)}\right)+\theta\); & The effective stress coefficients of a two-component porous medium are deduced based on the existing research work, and \(\eta^{(1)}\) and \(\eta^{(2)}\) are the effective stress coefficient of porous constituents (1) and (2); \(\theta\) is the effective change in the effective stress coefficient for a two-component porous medium. \\ \hline \multirow{4}{*}{[PERSON] and [PERSON] [10]} & **Saturated:**\(\sigma_{t}=\sigma-\eta_{1}\sigma_{t}^{\prime}-\eta_{2}\sigma_{t}^{\prime}\eta_{1}= \frac{(1-\sigma)K_{s}}{K_{s}^{\prime}}-\frac{1}{\gamma_{t2}}=\frac{K_{s}}{K_{ s}}-\frac{(1-\sigma)K_{s}}{K_{s}^{\prime}}\); \\  & \(\eta_{1}\) is the effective stress coefficient for the fractures; \(\eta_{2}\) is the effective stress coefficient for the pores; \(\sigma_{t}^{\prime}\) is the pore pressure in the fractures; \(\sigma_{t}^{\prime}\) is the pore pressure in the pores; \(\alpha\) is the volume fraction of the fractures; \(K_{s}\) is the bulk moduli of grain; \(K_{s}^{\prime}\) is the drained bulk modulus of the fractured porous medium; \(K_{s}^{\prime}\) is the drained bulk modulus of the nonfractured porous medium. \\ \hline \multirow{4}{*}{[PERSON] and [PERSON] [13]} & **Saturated:**\(\eta=0.71\); & A series of loading-unloading (both total stress and pore pressure) cycles applied by gas pressure were performed on the cool specimen, and the effective stress coefficient was obtained. \\ \hline \multirow{2}{*}{[PERSON] et al. [14]} & **Saturated:**\(\eta=-\frac{\alpha\log(\alpha/\alpha_{\rm{H}})}{\alpha\log(\alpha/\alpha_{\rm{H}})}\); & The effective stress coefficient of illite-rich shale was determined according to the transient pulse test results of saturated samples. \\  & \(k\) is the permeability.