# Settlement Prediction of Footings Using \(V_{s}\)
## 3 Centrifuge Study
### Results and Discussion
#### 3.2.3 Comparisons of Load-Settlement Curves with Predictions  
In Figures 7-9, measured model settlements were compared with the predictions for \(L/B\) ratios of 1.0, 2.5, and 5.0, respectively. Settlement of model footing was normalized using the footing breadth (\(B\)), and the load-settlement curves were presented up to the normalized settlement of 3%. To take into account the foundation load eccentricity, load inclination following step-by-step procedures suggested by [PERSON] [27] was adopted as shown in Figure 7. The straight line part of the 2 nd load-settlement curve was extended to zero pressure, thereby shifting the vertical axis to the value of \(s/B\), where that straight line portion intersects the horizontal axis. The centrifuge test results for 1 st loading in Figures 7-9 showed very soft deformable behavior compared with the two predictions, regardless of the \(L/B\) ratio. It could be reasoned that particle rearrangement, caused by interparticle slip and rotation, governs the deformation behavior rather than the compression of the soil mass related to the modulus for the 1 st loading [28]. Irrecoverable plastic behavior caused by the particle rearrangement started at very small strain region and, then, the elastoplastic behavior of soil emerged after a very small elastic limit. Since modeling of soil behavior utilizing the stiffness is valid until the elastic limit, it is not possible that the developed settlement prediction method using the hyperbolic stress-strain model in this study estimates the soil deformation behavior under the normally-consolidated (NC) stress state governed by relative particle movements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(f\) & \(g\) & \(n\) & **Poisson Ratio, \(\
u\)** & **Friction Angle, \(\sigma\)** & **Bearing Capacity, \(\sigma_{max}\)** \\ \hline
0.96 & 0.09 & 0.5 & 0.2 & 43\({}^{\circ}\) & \(L/B=1.0\), 3439 kPa \\  & & & & & \(L/B=2.5\), 2729 kPa \\  & & & & & \(L/B=5.0\), 2506 kPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Soil parameters for settlement predictions. Figure 6: Determination of model parameters \(f\) and \(g\) from triaxial test (TX) tests. The elastoplastic behavior of soil after the elastic limit (i.e., yield point) can be considered by the plasticity theory; however, this kind of complicated modeling technique is not suitable for settlement prediction in engineering practice using a simple tool such as [PERSON]'s method. On the contrary, the centrifuge test results and two predictions for the 2 nd loading show different tendencies. Unlike the results from the 1 st loading, the predictions for the three cases using \(I_{z}\) from elasticity theory yielded good agreement with centrifuge test results, especially up to the settlements corresponding to the maximum previous loadings (pre-consolidation pressure). Because the yield points of the three model grounds increased due to the maximum previous loading of the 1 st loading cycle, the elastic limit also increased more than that of the original NC stress state ground. Major particle rearrangement occurred and disappeared considerably during the 1 st loading cycle, and this particle rearrangement might readily induce more compact configuration of structures. Consequently, elastic soil deformation, which is represented by the modulus, was generated in the recompression stage i.e., 2 nd loading. As mentioned before, modeling of soil deformation behavior using a nonlinear hyperbolic stress-strain model based on stiffness is possible up to the elastic limit, and thus the developed settlement prediction method correctly evaluates the load-settlement behavior in the enlarged elastic region. After the maximum previous loading in 2 nd loading stage, predictions using \(I_{z}\) from elasticity theory underestimate the settlements of model footing.