# Numerical Analysis of the Settlement Behavior of Soft Soil Improved with Stone Columns
## 2 Numerical Analysis of Field Trials at Bothkennar Site
### Validation of Bothkennar Soil Profile  
A field trial of pad footings at the Bothkennar site by [41] was simulated by [29] using PLAXIS 3D in order to validate the parameters shown in Table 3. A 2.2 m square pad footing and 0.8 m thick was loaded to failure over a period of three days. The load-settlement curve recorded by [41] is presented in Figure 3 along with the calculation using PLAXIS 3D [29]. It is evident that the agreement of the two curves is good; thus, the selection of the material properties and the soil profile is verified.  
Settlement values were recorded in the field trials at Bothkennar by [36] after five months of placing each of the first and second load increments. Pieometers were installed at different depths and continued to measure pore water pressure due to installation of the stone columns in excess of pre-treatment values for up to four months. In this work, the predicted long-term settlement using PLAXIS 3D is compared with the measured settlement monitored by [36] at the end of the five-month period for the two load increments, as shown in Table 4. PLAXIS 3D allows the modeling of the long-term behavior of soft soil in two ways. The first method is drained analysis, and the second method is undrained analysis followed by consolidation. It is more realistic but more time consuming to perform undrained analysis to simulate the settlement performance of stone columns. Table 4 presents settlement predictions using both methods which calculate similar settlement values.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Crust** & **Carse Clay** & **Stone Backfill** \\ \hline Depth (m) & 0.0–1.2 & 1.2–14.5 & - \\ Unit weight, \(\gamma\) (kN/m\({}^{3}\)) & 18 & 16.5 & 19 \\ Friction angle, \(\varphi\)’ (degrees) & 34 & 34 & 45 \\ Cohesion, \(c\)’ (kPa) & 3 & 1 & 1 \\ Dilatancy angle, \(\psi\) (degrees) & 0 & 0 & 15 \\ Secant stiffness in standard triaxial test, & 1068 & 231 & 70,000 \\ E\({}_{50}^{\rm erf}\) (kPa) & 1068 & 231 & 70,000 \\ Tangent stiffness for primary oedometer & 1068 & 231 & 70,000 \\ test, E\({}_{\rm oed}^{\rm erf}\) (kPa) & 5382 & 1164 & 210,000 \\ Unloading/reloading stiffness, E\({}_{\rm ur}^{\rm erf}\) (kPa) & 5382 & 1164 & 210,000 \\ Overconsolidation ratio, OCR & 1 & 1.5 & - \\ Preoverburden stress (kPa) & 15 & 0 & - \\ Power for stress level dependency of & 1 & 1 & 0.3 \\ stiffness, m & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Material parameters [28].  
Table 4 shows that PLAXIS 3D predicts well the settlement values for most of the trial footings after the application of the second load increment. However, FE analysis slightly overpredicts the stiffness response of the field trials after the first load increment. This may be attributed to the thin shell layer at the base of the crust (Figure 1) which is not modeled in PLAXIS 3D. In addition, the HS model parameters are derived from laboratory tests at high levels of strain; thus, the numerical analysis may produce a relatively stiffer footing response at the first load increment.