# Study of Gravelly Soil Core Material Using a Large-Scale Triaxial Wetting Test
## 4 Constitutive Modeling for Wetting  
### Calculation of Wetting Deformation  
The continuous evolution of the strain direction during wetting has posed challenges to establishing constitutive models. In the practice of engineering, [PERSON]'s wetting model [24] is usually used to characterize wetting deformation. In this model, the wetting volumetric  
Figure 7: The model of wetting deformation: (**a**) sample before wetting; (**b**) sample after wetting.  
strain, \(\triangle\varepsilon_{v}\), is kept constant while the wetting shear strain, \(\triangle\varepsilon_{s}\), is considered to satisfy a hyperbolic relationship with the stress level, \(S_{l}\).  
\[\triangle\varepsilon_{s}=d_{w}\frac{S_{1}}{1-S_{1}}, \tag{1}\]  
\[\triangle\varepsilon_{v}=c_{w}, \tag{2}\]  
where \(\triangle\varepsilon_{v}\) is the total wetting volumetric strain, \(\triangle\varepsilon_{s}\) is the total wetting shear strain, and \(d_{w}\) and \(c_{w}\) are parameters.  
The wetting shear strain data can be fitted well with Equation (1). Figure 8 shows the wetting test data and fitting curve of this study. This equation can effectively fit the shear strain, as the wetting shear strain increases with an increasing stress level. When the stress level approaches 1, the shear strain tends towards infinity.  
However, the wetting volumetric strain cannot be described by Equation (2), and the results given by scholars are also significantly different. The wetting volumetric strain is not constant and exhibits different behaviors in different experiments. Some researchers believe that the wetting volumetric strain is influenced by the confining pressure [33; 34], while others suggest that it is influenced by both the confining pressure and stress level [35].  
Figure 9 shows the relationship between the wetting strain ratio, \(\triangle\varepsilon_{v}/\triangle\varepsilon_{1}\), and the stress level, \(S_{1}\). According to Figure 9, the wetting strain ratio gradually declines as the stress level increases, and it exhibits a nonlinear relationship with the stress level. It has been found that the wetting strain ratio, \(\triangle\varepsilon_{v}/\triangle\varepsilon_{1}\), has an exponential function relationship with the stress level, \(S_{1}\):  
\[\frac{\triangle\varepsilon_{v}}{\triangle\varepsilon_{1}}=a_{w}\exp(-b_{w}S_{ 1}), \tag{3}\]  
where \(\triangle\varepsilon_{1}\) is the total wetting axial strain, and \(a_{w}\) and \(b_{w}\) are parameters that can be determined via the test.  
Under the conventional triaxial conditions,  
\[\triangle\varepsilon_{s}=\triangle\varepsilon_{1}-\frac{1}{3}\triangle \varepsilon_{v} \tag{4}\]  
Substituting Equation (4) into Equation (3) yields  
\[\frac{\triangle\varepsilon_{s}}{\triangle\varepsilon_{v}}=\frac{3-a_{w}\exp(- b_{w}S_{1})}{3\cdot a_{w}\exp(-b_{w}S_{1})} \tag{5}\]  
Figure 8: Test data of wetting shear strain and the fitted curves.  
Then, according to Equations (1) and (5), \(\triangle\varepsilon_{v}\) can be obtained as follows:  
\[\triangle\varepsilon_{v}=d_{w}\frac{3\cdot a_{w}\exp(-b_{w}S_{1})}{3-a_{w}\exp (-b_{w}S_{1})}\cdot\frac{S_{1}}{1-S_{1}} \tag{6}\]  
Equation (6) is the final calculation model for the wetting volumetric strain. The model includes the three parameters of \(d_{w}\), \(a_{w}\), and \(b_{w}\).  
The model parameters are determined by a set of experimental data with different confining pressure and stress levels. The wetting shear strain parameter, \(d_{w}\), was determined using Equation (1), and the results are shown in Figure 8. The wetting shear strain parameters, \(a_{w}\) and \(b_{w}\), were determined using Equation (3), and the results are shown in Figure 9.