# Predicting Swell in Clay-Sand Mixtures Used in Liners
## 4 Discussion
### Prediction of the Swelling Behavior of Clay-Sand Mixtures  
Clay can be found in nature in the form of pure clay or clay intermixed with sand, silt, or other nonclay material (usually discrete inclusions). A clay paste is formed when water in the mixture combines with the clay. The \"clay paste\" can be either too little in volume and not sufficient to fill up the pores between the coarse component or available in large quantities to fill all the available voids. Most of the stresses are taken by the sand or coarse part in the first condition, and are not likely to be of major concern. For the second condition, the stress is shared and the response of the mixture depends on many factors, such as the stress-strain properties of the assemblage of coarse particles, voids within the system, and the type of clay. It is well understood that adding sand to clay improves the shearing strength of the system. Additionally, it contributes indirectly by accelerating the consolidation of the slurry ([PERSON] et al., 1994). It has also been found that the addition of sand to clay material affects the permeability of the mixture and helps with the quicker drainage of water. Artificial clay consisting of 40% bentonite and 60% kaolinite was added to natural sand to form three different clay-sand mixtures. The clay was taken as 20%, 40%, or 80% according to the weight of sand. The clay-sand mixture with 20% clay was tested for the effective stress and clay void ratio relations. The results measured in the laboratory are comparable to the data predicted by the Studds modified method. Table 4 presents how to calculate the final clay void ratio for different stress levels. The third column computes the porosity of the mixture at the given stress and as obtained from a direct test in the laboratory. The clay void ratio was computed and is presented in the fourth column. The stress of clay, which produces the same clay void ratio, is presented in a separate column. The stress exerted on the sand can be obtained by subtracting the stress on the clay from the total stress applied. The clay void ratio for the mixture was computed. Table 4 indicates that sands contribute to taking some of the load from very low stresses. The portion taken by clay reduces upon increasing the applied load. This becomes insignificant for extremely high loads. The clay can fill up the voids of the sand and push the sand grains apart. This action causes the sand porosity to increase. When pressure is exerted on clay, it compresses to a smaller volume, making the sand less porous. The clay-sand mixture with 40% clay by weight tested similarly, and yielded the results presented in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Stress Level (kPa)** & **Clay \%** & **Porosity \(\eta\)** & **Void Ratio \(e_{c}\)** & **In \(\sigma^{\prime}_{v\,\mathrm{clay}}\)** & \(\sigma^{\prime}_{v\,\mathrm{clay}}\)** & **Stress on Sand \(\sigma^{\prime}_{v\,\mathrm{sand}}\)** & \(e_{c}\) **(mix)** \\ \hline
2 & 0.2 & 0.597 & 4.931 & \(-\)0.161186 & 0.851 & 1.1489 & 12.328 \\
4 & 0.2 & 0.586 & 4.659 & 0.248376 & 1.281 & 2.7181 & 11.647 \\
50 & 0.2 & 0.544 & 3.78 & 1.567824 & 4.796 & 45.204 & 9.451 \\
100 & 0.2 & 0.533 & 3.567 & 1.888987 & 6.613 & 93.387 & 8.917 \\
200 & 0.2 & 0.521 & 3.363 & 2.194884 & 8.979 & 191.021 & 8.408 \\
300 & 0.2 & 0.515 & 3.248 & 2.367175 & 10.667 & 289.333 & 8.121 \\
400 & 0.2 & 0.510 & 3.169 & 2.486579 & 12.020 & 387.980 & 7.922 \\
500 & 0.2 & 0.507 & 3.108 & 2.577623 & 13.166 & 486.834 & 7.771 \\
600 & 0.2 & 0.504 & 3.059 & 2.651015 & 14.168 & 585.832 & 7.649 \\
700 & 0.2 & 0.501 & 3.019 & 2.71238 & 15.065 & 684.935 & 7.547 \\
1000 & 0.2 & 0.495 & 2.926 & 2.852011 & 17.323 & 982.677 & 7.314 \\ \hline \end{tabular}
\end{table} 
Table 4: Prediction table: clay-sand ratio of 0.2.