# Predicting Swell in Clay-Sand Mixtures Used in Liners
## 4 Discussion
### Prediction of the Swelling Behavior of Clay-Sand Mixtures
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Stress Level** & **Clay \%** & **Porosity \(\eta\)** & **Void Ratio \(e_{c}\)** & **In \(\sigma^{\prime}_{v\,\mathrm{clay}}\)** & **Stress on Sand \(\sigma^{\prime}_{v\,\mathrm{sand}}\)** & \(e_{c}\) **(mix)** \\ \hline
2 & 0.4 & 0.7062 & 2.606 & 3.332896 & 28.019 & \(-\)26 & 6.514 \\
4 & 0.4 & 0.6924 & 2.377 & 3.676886 & 39.523 & \(-\)35.5 & 5.942 \\
50 & 0.4 & 0.6422 & 1.692 & 4.705966 & 110.610 & \(-\)60.6 & 4.229 \\
100 & 0.4 & 0.6284 &It can be noted from Table 5 that the clay carried all the low stresses. The model shows that the stresses acting on the sand were negative. This results from the use of the clay profile equation over the full range. The points showing negative values reflect the theoretical figures so that all assumptions hold. This method can show when the sand starts to contribute to taking up stresses. This point is defined by [PERSON] as the threshold point. It can be graphically determined if the void ratio versus the effective stress profile of the clay-sand mixture intersects the profile of clay. The clay-sand mixture with 80% clay was entirely governed by the behavior of the clay. The results of the measured clay void ratio were found to coincide with those of the clay alone (40% bentonite). For this case, the prediction model used the equation for the clay. This finding has been reported by many authors, including [PERSON] [8] and [PERSON] [11]. [PERSON] and [PERSON] [20] found that, for a clay content above 35%, the clay matrix alone controlled the mechanical behavior of the mixture. This value is for a clay-gravel mixture and for a particular clay material, which is kaolinite. However, when investigating the dry powder effect on the porosity of the coarse material, it can be observed that the shift in the porosity line is large compared with that in the original line of the coarse material only. Pure bentonite clay tested by [PERSON] [8] showed that a clay content as small as 10% could control the behavior of a mixture until a certain point of stress. This is the threshold point mentioned above. The clay content at which the entire mechanical behavior is controlled by the fine part depends on the type of clay, the porosity of the coarse material, and the stress level. The authors of reference [21] regarded the sand as an inert filler and the clay phase as determining the swelling of clay-sand mixes. This is not necessarily true; the coarse material also has a role in the way clay can expand. The porosity and geometry of sand grains can influence the quantitative behavior of the clay paste. Studies conducted to investigate the characteristics and shear strength behavior of clay-sand mixtures, in general, include the works in references [22; 23; 24]. In reference [25], it is stated that the clay content in clayey sand has a significant influence on the stress-strain profile of the soil mass. As the fine content increased, the dilatant behavior of the clayey sand decreased and the response gradually became similar to that of clay-like material at about 40% fine content. The authors of reference [26] experimentally studied the behavior of clay-sand mixtures under compression and extension triaxial loading paths. Reference [23] reports that the shear strength properties and the stress-strain characteristics of mixtures of sand-kaolin showed a significant change at a kaolin content of 20%. In a study in reference [27], the authors performed a series of unconsolidated, undrained triaxial tests to evaluate the effects of some factors on the compacted bentonite-sand mixtures. These included the moisture, the energy of compaction, and the confining pressure in addition to the clay content. [PERSON] and [PERSON] [28] claim that the liquid limit and the plastic limits cannot represent the plasticity limits and they do not correspond to stress-free reference states. They suggested three characteristic water contents, namely the free swell limit, the settling limit, and the shrinkage limit.