# Numerical Analysis for Ground Subsidence Caused by Extraction Holes of Removed Piles
## 2 Analysis and Target Ground
### Material Parameters of Target Ground  
Table 1 shows the parameters of the surrounding ground used for the analysis. The pile foundation parameters are shown in Table 2, and the joint element parameters are shown in Table 3. It is most desirable to use the parameters of the surrounding ground  
Figure 1: Analysis of cross-section on ground with extraction holes of removed piles; (**a**) case with one extraction hole of removed pile; (**b**) case with two extraction holes of removed piles; (**c**) case with three extraction holes of removed piles.  
Figure 2: Process of pulling out existing piles.  
obtained from triaxial compression test results. In this study, however, the parameters were selected from the \(N\)-value in order to obtain the generally required strength of the filler. The other parameters are typical values [25; 26]. The elastic modulus (\(E\)) of the clay layer was calculated by Equation (1), and the elastic modulus (\(E\)) of the gravel layer was calculated by Equation (2).  
\[E=500N+6900 \tag{1}\]  
\[E=2800N \tag{2}\]  
The internal friction angle (\(\phi\)) of the gravel layer was calculated by Equation (3) (the internal friction angle of the clay layer was 0).  
\[\phi=\sqrt{20N}+15 \tag{3}\]  
The uniaxial compressive strength (\(q_{u}\)) and the adhesive strength (\(c\)) of the clay layer were calculated by Equation (4) (the adhesive strength of the gravel layer was 0).  
\[q_{u}=40+2N \tag{4}\]  
where \(\gamma_{t}\) is the unit volume weight (\(\rm{kN/m^{3}}\)), \(\gamma_{sat}\) is the saturation unit volume weight (\(\rm{kN/m^{3}}\)), \(E\) is the elastic modulus (\(\rm{kN/m^{2}}\)), \(\
u\) is Poisson's ratio (-), \(c\) is the adhesive force (\(\rm{kN/m^{2}}\)), \(\phi\) is the internal friction angle (\({}^{\circ}\)), \(q_{u}\) is the uniaxial compressive strength (\(\rm{kN/m^{2}}\)), \(k\) is the hydraulic conductivity (\(\rm{m/s}\)), \(K_{u}\) is the normal stiffness (\(\rm{kN/m^{3}}\)), and \(K_{t}\) is the shear stiffness (\(\rm{kN/m^{3}}\)).  
The parameters of the pile foundation were selected with reference to the previous literature [27; 28]. For the joint elements of pile foundations, values that are 100 times the small values of the elastic modulus and shear stiffness of the adjacent elements are generally applied [29]. Thus, in this analysis, a value 100 times the shear stiffness of the clay layer was applied to the joint element of the pile foundation.  
\begin{table}
\begin{tabular}{c c c c} \hline  & & **Clay Layer** & **Gravel Layer** \\ \hline \(\gamma_{t}\) & (\(\rm{kN/m^{3}}\)) & 15 & 21 \\ \(\gamma_{sat}\) & (\(\rm{kN/m^{3}}\)) & 16 & 21 \\ \(E\) & (\(\rm{kN/m^{3}}\)) & \(7.9\times 10^{3}\) & \(1.4\times 10^{5}\) \\ \(\
u\) & (-) & 0.45 & 0.3 \\ \(c\) & (\(\rm{kN/m^{2}}\)) & 25.0 & 0 \\ \(\varphi\) & (\({}^{\circ}\In addition, the Mohr-Coulomb model [30; 31], which is widely used as a failure criterion for clayey soil, was applied to the clay and gravel layers. Although there are certainly more advanced failure criterion models, especially developed for clay and granular materials [32], the Mohr-Coulomb model is known to be the simplest and easiest to use model. When its own weight or external force is applied, shear stress is generated inside the ground, and as this stress increases, the strain increases. With this progression, it slides along a specific surface. Such failure is called the shear failure and the limit value for this is called the shear strength. The soil shear strength (\(\tau\)) represented by this model is shown in Equation (5).  
\[\tau=c+\tan\phi \tag{5}\]  
where \(c\) is the adhesive force (\(\mathrm{kN/m^{2}}\)) and \(\phi\) is the internal friction angle (\({}^{\circ}\)).