## 3 Experimental and Numerical Procedures
### Numerical Modeling  
The numerical simulation was conducted using a finite element program, PLAXIS 2D (Figure 5). The bottom boundary of the model was fixed against movement in all directions, while the vertical boundaries were free to move in the vertical direction but restricted in the horizontal direction. The soil elements were modeled using 15-noded triangular elements. Very fine meshes were used around the geometry line of footing and reinforcements to minimize the mesh size effect. The linear-elastic perfectly plastic Mohr-Coulomb (MC) model was utilized for soil and interface elements. Five basic parameters for MC-model, Young's modulus (E), Poisson's ratio (\(\
u\)), cohesion (c), internal friction angle (\(\phi\)), and dilation angle (\(\psi\)), were obtained from conventional laboratory tests. The coefficient of earth pressure at rest, K\({}_{0}\) was calculated from (1\(-\)sin\(\phi\)). Table 3 summarizes the numerical soil parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Soil** & \multirow{2}{*}{**E (kN/m\({}^{2}\))**} & \multirow{2}{*}{\(\
u\)} & \(\phi\) & \multirow{2}{*}{\(c\) (kPa)} & \(\psi\) & \multirow{2}{*}{\(\mathbf{R_{inter}}\)} \\
**Mixtures** & & & **(Degree)** & & & \\ \hline B0 & 20,000 & 0.3 & 40 & 2 & 10 & 0.66 \\ B20 & 17,000 & 0.3 & 30 & 9 & 0 & 0.59 \\ B40 & 15,000 & 0.35 & 12 & 18 & 0 & 0.54 \\ B60 & 13,000 & 0.4 & 9 & 20 & 0 & 0.48 \\ B80 & 8000 & 0.4 & 5 & 25 & 0 & 0.45 \\ B100 & 5000 & 0.4 & 0 & 33 & 0 & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The soil parameters used in numerical analysis. The geotextile material was modeled using a geogrid element (line elements), which is generally used to model geosynthetics reinforcement in the PLAXIS program. The geotextile was assumed as slender structures with a nonzero value of normal stiffness and zero bending stiffness, since it can only sustain tensile force, but not compression forces [50]. The elastic axial stiffness (EA) of geotextile material was equal to 200 kN/m obtained from the tensile strength test according to ASTM-D4595 [51]. The layout configuration of the geotextile reinforcement (Figure 4 and Table 2) and the material properties (Table 3) were simulated. The interaction parameter (R\({}_{\text{inter}}\)) was simulated with the interface elements that were located between the geotextile reinforcement and surrounding soils. The R\({}_{\text{inter}}\) values for different configurations of geotextile reinforcement were summarized in Table 3.  
The load was applied on the footing using the prescribed displacement method. The calculation was terminated when the final settlement reached 15 mm. The pressure (stress point; Sig-yy) and vertical settlement (displacement node; U\({}_{y}\)) values under the center of strip footing were compared with the measured results. The bearing capacity ratio (\(q_{b}/q_{b0}\)) at the S/B ratio of 15% was used to illustrate the bearing capacity improvement due to the geotextile reinforcement, where \(q_{b}\) = bearing capacity of RSF and \(q_{b0}\) = the bearing capacity of unreinforced soil. Table 2 summarizes the conditions of experimental model tests and numerical simulations. approximately equal to 5%, and then gradually decreased. For B20, B40, B60, B80 and B100, the \(q\) gradually increased with increasing the S/B ratio. After S/B \(>\) 10%, the \(q\) was almost constant without peak. The \(q_{b0}\) decreased as the bentonite content increased i.e., \(q_{b0}\) of B100 was the lowest, while \(q_{b0}\) of B0 was the highest. In other words, the \(q_{b0}\) decreased with the increase of PI. The soil surface on both sides of the foundation noticeably heated, indicating the general shear failure, which is the common failure mode for a shallow foundation on the dense sand and stiff cohesive soils [4]. Figure 7 shows the relationship between \(q_{b0}\) and PI at S/B = 15%. The measured \(q_{b0}\) was compared with the calculated bearing capacity using Equations (1)-(5).