## 1 Introduction
& A theoretical relationship between the acoustic velocity and mean effective stress of the Nankai accretionary prism was calculated using DEM (Differential Effective Medium) theory and the aspect ratio spectrum of pore space, and [PERSON]’s effective stress principle was introduced to analyze the pore pressure distribution of Nankai trough. \\ \hline \multirow{4}{*}{[PERSON] et al. [16]} & **Unsaturated:** & \(\sigma_{t}=\sigma\) \\  & \(-\alpha_{m}|x_{m}u_{m}u_{m}+(1-\chi_{m})u_{m}|I\) & \\  & \(-\alpha_{m}|X_{m}u_{m}u_{m}+(1-\chi_{m})u_{m}|I\) & \\  & \(\chi_{m}=\left\{ \begin{array}{cc}\frac{\sigma_{m}(\alpha)}{\alpha_{m}-\alpha_{ m}}\\ 1\quad for\quad S_{m}\leq S_{m(\alpha)}\end{array} \right.\) & ; \\  & \(1\quad for\quad S_{m}\leq S_{m(\alpha)}\) & \\ \(X_{M}=\left\{ \begin{array}{cc}\frac{\sigma_{m}(\alpha)}{\alpha_{m}-\alpha_{ m}}\\ 1\quad for\quad S_{M}\leq S_{M(\alpha)}\end{array} \right.\) & \( \begin{array}{cc}\text{Drying and one-dimensional consolidation tests are performed}\\ \text{on initially saturated samples of the kaolin (double-porosity compacted soil) at different net stresses, and the test results were accurately predicted using the new effective stress principle. \\ \end{array} \right.\) \\  & \(u_{m}\), \(u_{m}\), \(u_{M}\), and \(u_{m}\) are the micropore water, micropore air, macro pore water, and macro pore air pressures; \(\alpha_{m}\) and \(\alpha_{M}\) are the conventional effective stress coefficients of saturated double-porous media; \(S_{m(\alpha)}\) is the suction value separating saturated from unsaturated conditions in the micropores; \(S_{M(\alpha)}\) is the matrix suction value separating saturated from unsaturated conditions in the macro pores; \(\Omega\) is the material parameter. \\ \hline \multirow{4}{*}{[PERSON] et al. [2]} & **Saturated:**\(\eta=c\sigma_{t}+d\); & The effective stress law for the permeability of limestone is studied by drained hydrostatic compression and constant-head permeability tests, and the results show that the effective stress coefficient was linearly related to differential stress. \\ \cline{1-1}  & \(c\) and \(d\) are the fitting parameters; \(\sigma_{t}\) is the differential stress. \\ \cline{1-1}  & \(c\) and \(d\) are the fitting parameters; \(\sigma_{t}\) is the differential stress. The theoretical derivation and empirical formula are the two main expressions of the effective stress principle. The advantage of the theoretical derivation is that an equation that is more consistent with the physical principles can be obtained, but the disadvantage is that some physical quantities in the equation are difficult to measure. The accuracy of the empirical formula is related to the measured physical parameter (the permeability coefficient is favored), which is related to the effective stress coefficient. The adverse effects caused by water pressure changes (the permeability test requires a head difference between the upstream and downstream of the sample) in the permeability test are difficult to evaluate. In this study, the CD tests were conducted to measure the effective stress coefficient of claystone. The samples were firstly saturated under an in situ stress state for about one month. Then the effective stress coefficients were checked by changing the confining pressure and pore pressure in specific increments (the deformations of the samples were recorded during the whole process). Different increments of pore pressure and confining pressure were tried during the effective stress coefficient checking procedures, and an accurate conclusion was obtained through a back analysis (the effective stress coefficient was 0.991 for sample one and 0.995 for sample two). At last, some factors potentially influencing the effective stress principle of claystone were tested and discussed.