## 2 Calculation Method of Thermal Pore Water Pressure with Different OCR  
[PERSON] and [PERSON] [8] developed a calculation model of thermal pore water pressure in saturated clay during an undrained heating test:  
\[\Delta u_{T}=\frac{n(\alpha_{w}-\alpha_{s})+\alpha_{sT}}{m_{v}}\Delta T \tag{1}\]in which \(\Delta u_{T}\) (kPa) is the change of pore pressure caused by thermal loading, \(n\) is the porosity, \(m_{v}\) (kPa\({}^{-1}\)) is the compressibility of soil skeleton, \(\Delta T\) (\({}^{\circ}\)C) is the change in temperature, \(\alpha_{ST}\) (\({}^{\circ}\)C\({}^{-1}\)) is the physicochemical coefficient of structural volume change, and \(\alpha_{uv}\) (\({}^{\circ}\)C\({}^{-1}\)) and \(\alpha_{s}\) (\({}^{\circ}\)C\({}^{-1}\)) are the volumetric expansion coefficients of pore water and soil particles, respectively. Under undrained heating conditions, saturated soil will expand along the secondary compression curve, and the compressibility of soil skeleton can be estimated by the isotropic recompression curve and written as  
\[m_{v}\approx\left(m_{v}\right)_{r}=\frac{1}{1+e_{0}}\frac{\kappa}{p^{\prime}} \tag{2}\]  
in which \(e_{0}\) is the initial void ratio, \(\kappa\) is the slope of the isotropic recompression line, \(p^{\prime}\) is the mean effective stress, and \((m_{v})_{r}\) is the compressibility of the soil skeleton determined from the recompression curves. Substituting Equation (2) into Equation (1) results in  
\[\Delta u_{T}=\frac{n(\alpha_{uv}-\alpha_{s})+\alpha_{sT}}{\kappa}(1+e_{0})p^{ \prime}\Delta T \tag{3}\]  
For most soils, the values of \(\alpha_{uv}\) and \(\alpha_{s}\) are usually taken as \(1.7\times 10^{-4}\) (\({}^{\circ}\)C\({}^{-1}\)) and \(3.5\times 10^{-5}\) (\({}^{\circ}\)C\({}^{-1}\)), respectively [8; 9; 12; 27]. Since the change of porosity during undrained heating tests is generally negligible and has little effect on the thermal pore water pressure, the porosity (\(n\)) is approximately equal to the initial porosity (\(n_{0}\)) [9; 28]. The physicochemical coefficient \(\alpha_{sT}\) is often used to characterize the volume change caused by soil structural rearrangement under unit thermal loading, which is not straightforward to obtain [8; 9]. In fact, \(\alpha_{sT}\) can be estimated from experimental data of \(\Delta u_{T}\) at a given \(\Delta T\), and the relationship is rearranged as [9]  
\[\alpha_{sT}=[\frac{\Delta u_{T}}{p_{0}^{\prime}}\frac{\kappa}{1+e_{0}}\frac{ 1}{\Delta T}]-n(\alpha_{uv}-\alpha_{s}) \tag{4}\]  
where \(p_{0}^{\prime}\) (kPa) is the initial mean effective stress. Because Equation (4) needs to know the experimental data of \(\Delta u_{T}\), the undrained heating test must be carried out. To avoid complicated heating tests, [PERSON] et al. [9] proposed an empirical expression for the physicochemical coefficient of normally consolidated clay, which can be written as  
\[\alpha_{sT}=1.0\times 10^{-4}e^{-0.014I_{p}} \tag{5}\]  
where \(I_{p}\) is soil plasticity index and \(e\) is the Napierian base. In addition, through undrained heating tests, [PERSON] et al. [26] found that the thermal pore water pressure of normally consolidated and overconsolidated soil meets  
\[\Delta u_{Tocr}=\ln(1+\frac{1.717}{OCR})\Delta u_{T} \tag{6}\]  
where \(\Delta u_{Tocr}\) is the thermal pore water pressure of the overconsolidated soil. Substituting Equation (3) into Equation (6) results in  
\[\Delta u_{Tocr}=\ln(1+\frac{1.717}{OCR})\frac{n(\alpha_{uv}-\alpha_{s})+ \alpha_{sT}}{\kappa}(1+e_{0})p^{\prime}\Delta T \tag{7}\]  
According to Equation (7), it can be seen that \(\kappa\) is a key parameter for estimating thermal pore water pressure. However, compared to the slope of the isotropic recompression line, the slope of the isotropic compression line (\(\Lambda\)) is more commonly adopted in studiesto calculate thermal pore water pressure. Therefore, the value of \(\Lambda\) is used to estimate \(\kappa\).