## 3 Experimental and Numerical Procedures  
### Soil Samples  
In order to obtain various PIs, a fine sand was mixed with bentonite (montmorillonite) at various ratios of 0, 20, 40, 60, 80 and 100% bentonite, and labeled as B0, B20, B40, B60, B80 and B100, respectively. The bentonite powder was a commercial product, which is mainly used as drilling mud for geotechnical construction. The commercial bentonite powder was purchased from Geomechanical Service Co., Ltd., Bangkok, Thailand. The grain size distribution of bentonite powder was investigated by laser diffraction grain size analyzer. The bentonite consisted of 98% clay and 2% silt. The liquid limit (LL) and plastic limit (PL) of bentonite obtained from the Casagrande's and rolling thread methods, according to ASTM-D4318, were 347% and 33%, respectively.  
The fine sand was air-dried and passed through a 2.00 mm sieve (No.10). The tested sand (B0) consisted of 98% sand and 2% silt, as shown in Figure 1a. Its average grain size, D50 was 0.5 mm. The bentonite and sand had specific gravity values of 2.35 and 2.80, respectively, and they were classified as a high plasticity clay (CH) and poorly graded sand (SP), respectively, according to the Unified Soil Classification System (USCS).  
Figure 1a also shows the grain size distribution curves of the sand-bentonite mixtures. Figure 1b shows the relationships between clay fraction content (<0.002 mm) and LL, PL and PI. The LL significantly increased from 49 to 347% with the increased clay fraction content from 19 to 98% due to the increase in water holding capacity of bentonite. The linear increase of PL, LL and PI with the increased bentonite content (clay fraction) is in agreement with the previous researches [41; 42]. The slope of the relationship between PI and clay content, defined as activity [43], was equal to 3.61 and, therefore, classified as active soil. Table 1 summarizes the optimum water content and maximum dry unit weight of these mixtures under the standard Proctor energy (ASTM-D698 [44]).  
The dried sand-bentonite mixtures were mixed with water by spraying water droplets to attain their optimum water content (obtained from laboratory compaction tests). The soil preparation and direct shear test details can be referenced to [PERSON] et al. [19]. The values of cohesion and internal friction angle were obtained from a 65 mm in diameter of a direct shear device at a constant shearing rate of 0.5 mm/min.  
Figure 2 shows the internal friction angle and cohesion versus clay fraction relationship. The cohesion linearly increased, while the internal friction angle decreased in a polynomial manner as the clay fraction increased. For clay fraction < 60% (B0, B20, B40 and B60), the internal friction angle significantly decreased with increasing the clay content. Previous researchers [45; 46; 47] reported that the \(\phi\) value decreased, as the clay fraction content increased, due to increased lubrication from the clay paste filling the void spaces between sand. The rate of reduction in value was relatively low when clay fraction > 60% (B80 and B100). The highest cohesion of 33 kPa and lowest friction angle of 0 were found at B100. Table 1 summarizes the physical and engineering properties of tested soils.