# Effect of Bentonite Content and Hydration Time on Mechanical Properties of Sand-Bentonite Mixture
## 4 Micro-Mechanical Behavior of Sand-Bentonite Mixture
### Simulation Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Sand** & **Bentonite** & **Loading Surface** & **Cylinder Wall** \\ \hline Normal stiffness (N\(\cdot\)m) & \(1\times 10^{8}\) & \(1\times 10^{7}\) & \(1\times 10^{8}\) & \(1\times 10^{6}\) \\ Tangential stiffness (N\(\cdot\)m) & \(1\times 10^{8}\) & \(1\times 10^{7}\) & \(1\times 10^{8}\) & \(1\times 10^{6}\) \\ Density (kg/m\({}^{3}\)) & 2600 & 2000 & - & - \\ Coefficient of friction & 0.5 & - & 0.7 & 0.2 \\ Damping (N\(/\) (m\(/\)s)) & 0.7 & 0.7 & - & - \\ Equivalent elastic modulus (Pa) & \(6\times 10^{9}\) & \(3\times 10^{9}\) & - & - \\ Normal bond strength (Pa) & - & \(1\times 10^{4}\) & - & - \\ Tangential bond strength (Pa) & - & \(1\times 10^{4}\) & - & - \\ \hline \end{tabular}
\end{table} 
Table 3: Mesoscopic parameters of DEM models. Figure 9: Simulated results of the triaxial tests for sand–bentonite mixture specimens under various confining pressures: (**a**) stress–strain results under 200 kPa; (**b**) dilation behavior under 200 kPa; (**c**) stress–strain results under 300 kPa; (**d**) dilation behavior under 300 kPa; (**e**) stress–strain results under 400 kPa; (**f**) dilation behavior under 400 kPa. The particle contact force was further quantified by the probability density function (PDF). Figure 11 was the PDF curves of the normal (\(f_{\rm n}\)) contact force distribution. In this study, the normalized normal contact force less than 0.2 was defined as a minimal normal contact force (\(f_{\rm n,min}\)). The probability of \(f_{\rm n,min}\) under different conditions was calculated and labeled beside the corresponding PDF curves in Figure 11. It can be seen from Figure 11 that \(f_{\rm n}\)/\(<\)\(f_{\rm n}\)\(>\) was mainly concentrated in the range of 0-2.0. In the analysis of the influence of confining pressure and bentonite content, it was found that the distribution of normal contact force changed obviously with the increase in bentonite content. The specific influences of bentonite content are as follows. The normalized normal contact force was bounded by about 0.36. The probability of normal contact force increased with bentonite content when \(f_{\rm n}\)/\(<\)\(f_{\rm n}\)\(>\) was lower than 0.36, and the probability decreased when \(f_{\rm n}\)/\(<\)\(f_{\rm n}\)\(>\) was higher than 0.36. Combined with the nephograms of contact force distribution in Figure 10, it could be inferred that the addition of bentonite changed the force transfer structure of sand particles. The contact force distributed more evenly as bentonite was involved in force transfer because the added bentonite helped to share a part of the load. The main force chain tended to homogenize, and the value shifted to the direction of \(f_{\rm n,min}\). Figure 10: X-shaped distribution of contact force at xoy plane for sand–bentonite mixture specimens with various confining pressures and bentonite contents: (**a**) 200 kPa, 0%; (**b**) 200 kPa, 5%; (**c**) 200 kPa, 10%; (**d**) 300 kPa, 0%; (**e**) 300 kPa, 5%; (**f**) 300 kPa, 10%; (**g**) 400 kPa, 0%; (**h**) 400 kPa, 5%; (**i**) 400 kPa, 10%. Figure 11: _Cont._  
The experimental results showed that bentonite content and hydration time jointly affect the mechanical properties of sand-bentonite mixture. However, the impact analysis based on DEM only considered physical and mechanical mechanisms without the chemical ones (i.e., hydration time). In future studies, further breakthroughs are needed for the DEM simulation by considering the influence of hydration time. Considering that the contact form between sand particles is associated with the hydration of bentonite, future attempts can be made to simulate the hydration effect by modeling the particle contact form.