# Numerical Analysis of the Settlement Behavior of Soft Soil Improved with Stone Columns
## 4 Comparison of FE Analysis and the [PERSON] (1995) Design Method Calculated Results  
One of the most popular design methods to assess the settlement performance of a footing on top of an infinite grid of stone columns is proposed by [37]. In this method, a  
Figure 17: Influence of column diameter upon footing settlement in drained conditions—Footing 4.  
Figure 18: Influence of column strength upon footing settlement in drained conditions–Footing 4.  
settlement improvement factor, \(n\), is calculated as a function of the area replacement ratio, \(A_{o}\)/\(A_{C}\), and the stone angle of internal friction:  
\[n=\frac{settlement\;of\;untreated\;footing}{settlement\;of\;treated\;footing} \tag{7}\]  
The compressibility of the column material can be considered in the settlement reduction factor by reducing the basic improvement factor. The Priebe design method also accounts for the effect of increasing the overburden stress where the columns are better supported laterally, thus providing more bearing capacity [37]. It is important to note that the Priebe design method does not consider the influence of sensitive clay disturbance during stone column installation and does not account for the presence of a stiff layer at shallow depth.  
The authors evaluated the settlement performance of the Bothkennar field trials using the Priebe method to compare with the settlement behavior captured by PLAXIS 3D and the measured settlement by [36]. The predicted settlement of the untreated soft soil (pre-treatment) and the settlement of the improved soil with stone columns (post-treatment) for the first load increment (\(\approx\)33 kPa) and the second load increment (\(\approx\)70 kPa) are presented in Tables 7 and 8, respectively. A post-treatment settlement ranging from 4.2 mm to 7.6 mm and 12.2 mm to 19.0 mm was calculated using the Priebe method. It is evident that the Priebe method underestimates the settlement performance of the field trials at the Bothkennar site. In addition, the design method by [37] underestimates the settlement values predicted by the FE analysis. This may be attributed to the installation effect of the stone columns and the sensitivity of the Bothkennar soft clay. Moreover, the Priebe method is mostly applicable to wide-spread loads (e.g., rafts and embankments) where the column behavior is stiffer due to greater confinement of the adjacent columns compared to a single column beneath narrow footings.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Trial** \\ **Footing** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **1 st Load** \\ **Increment** \\ **(kPa)** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **\(A_{o}\)** \\ **(m2)** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Measured** \\ **Settlement** \\ **(mm)** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Settlement** \\ **Drained** \\ **(mm)** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Settlement** \\ **Drained** \\ **(mm)** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Priebe Method (1995)** \\ **Treatment** \\ **Settlement** \\ **(mm)** \\ \end{tabular} } \\ \hline
1 & 35.5 & 1.125 & 2.56 & 27.5 & 16.5 & 15.0 & 16.2 & 6.6 & 2.5 \\
2 & 32.9 & 1.500 & 3.41 & 25.0 & 18.0 & 16.0 & 15.9 & 6.9 & 2.3 \\
3 & 33.1 & 1.125 & 2.56 & 17.5 & 14.0 & 13.0 & 13.3 & 5.7 & 2.3 \\
4 & 34.9