## 4 Application Example
### Case for Impact Loading
#### 4.2.1 Laboratory Drop Weight Impact
In the laboratory drop weight test, the upper soil layers were compacted and reinforced with geocell material, which would enhance the strength of the soil, and the lower layer has no reinforcement. Hence, in the numerical model, it is necessary to consider the function of the geocell material. From the laboratory test on the geocell-encased sand [26], it is observed that the geocell confinement did not change the friction angle of soil while significant cohesion occurred in the granular soil, which indicated that for the geocell-reinforced sand layer, the strength and stiffness behaviour of the soil would be enhanced. However, in the numerical model, it is difficult to model and mesh the geocell material due to its complex geometry. Hence, it would be preferable to use the composite model to consider the enhancement of the shear strength and stiffness of the geocell-reinforced sand layer. [PERSON] et al. [27] purposed an empirical equation to calculate Young's modulus of the geocell-reinforced sand using the secant tensile modulus of the geocell material and Young's modulus parameter of the unreinforced sand, which could be expressed as:  
\[E_{r}=4(\sigma_{3})^{0.7}\left(K_{u}+200M^{0.16}\right) \tag{21}\]  
in which \(E_{r}\) is the [PERSON]'s modulus of the geocell-reinforced sand, \(M\) is the secant modulus of the geocell material at axial strain 2.5% in \(\mathrm{kN/m}\) and \(\sigma_{3}\) is the confining pressure from the geocell in kPa. \(k_{u}\) is the dimensionless modulus parameter of the unreinforced sand, which is a modulus number in the hyperbolic model developed by [PERSON] and [PERSON] [28]. The confining pressure \(\sigma_{3}\) could be calculated as:  
\[\sigma_{3}=\frac{2M}{D_{0}}\left(\frac{1-\sqrt{1-\varepsilon_{a}}}{1- \varepsilon_{a}}\right) \tag{22}\]  
where \(D_{0}\) is the initial diameter of the geocell and \(\varepsilon_{a}\) is the axial strain of the geocell at failure; the induced cohesion in the geocell-reinforced sand is then related to the increase in the confining pressure \(\sigma_{3}\):  
\[c_{r}=\frac{\sigma_{3}}{2}\sqrt{K_{p}} \tag{23}\]  
in which \(c_{r}\) is the enhanced cohesion and \(k_{p}\) is the coefficient of passive earth pressure. In the current study, the geocell MC-100 from Polyfelt is used. The geocell dimension is a rhombus with two diagonal lengths of 203 mm and 244 mm. Thus, the equivalent diameter is calculated as about 177.5 mm. The secant modulus \(M\) for the geocell is obtained as 278 \(\mathrm{kN/m}\) from the tensile test [20]. Additionally, the value of \(\varepsilon_{a}\) is taken as 4.8%. The modulus parameter \(k_{u}\) for unreinforced sand in the current study is taken as 727 MPa according to the curve fitting from the triaxial test, and hence, the confining pressure, enhanced cohesion and Young's modulus for geocell-reinforced sand could be calculated based on Equations (21)-(23). The parameters for the unreinforced sand and geocell reinforced sand are summarized in Table 10.  
During the impact test, the deformation of the drop weight head was negligible compared to the deformation of the pavement slab. Hence, the drop weight head is modelled with a rigid body in the current study. For the configuration of the drop weight head, the simple cylindrical shape is modelled instead of modelling the head with weight mass (as shown in Figure 15). The simple cylindrical head \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Reinforced Sand Layer** & **Unreinforced Sand Layer** \\ \hline Density, \(\rho\) (\(\mathrm{kg/m^{3}}\)) & 1600 & 1600 \\ Young’s modulus \(E\) (MPa) & 103.5 & 40 \\ Shear modulus, \(G\) (MPa) & 39.8 & 15.4 \\ Poisson’s ratio, \(\
u\) & 0.3 & 0.3 \\ Cohesion, \(c\) (MPa) & 0.089 & 0.001 \\ Friction angle, \(\phi\) (\({}^{\circ}\)) & 40 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Material properties of the foundation soil. For the 1.5-m drop weight impact, the drop weight head is assigned with 5.02 m/s for the first impact.