# Settlement Prediction of Footings Using \(V_{s}\)
## 3 Centrifuge Study
### Experimental Description  
A large rigid box with a length, width, and height of 1000, 1000, and 477 mm, respectively, was utilized as a centrifuge model box. Model footing with breadth equal to 60 mm was considered to avoid the arching effect caused by side wall friction of the model box. Figure 2 shows the model footings placed inside the model box. Stress distribution in the soil mass caused by the footing load was approximated using a simple approximate method (i.e., the 2:1 method), as presented by the dotted lines. The bottom areas estimated by the approximate method were expressed with respect to the \(L/B\) ratio of the model footing as shown in Figure 2b. It is expected that when the breadth of the model footing is 60 mm, the deformation behavior would not be affected by the wall friction of the model box, even in the case where the \(L/B\) ratio equals 5.0. Dry silica sand was used for model ground construction and its basic properties are presented in Table 1. Before constructing the model ground, bender elements (BE) were installed in the model box for the measurement of the \(V_{S}\) of model ground while accelerating the model in a centrifuge [22]. A total of 15 pairs of bender elements arrays were installed on aluminum rods and the rods were attached on the bottom of the model box, as presented in Figure 2a. The bender elements were equipped vertically on the rods to generate and measure \(V_{S,HH}\), for which directions of propagating and particle motion are horizontal. Source bender elements were made in parallel, whereas receiver bender elements were made in series to enhance sending and receiving of the shear wave. The bender element arrays cover depths up to 5 \(B\) beneath the model footing, and the tip-to-tip distance between source and receiver bender elements was 300 mm. This distance of 300 mm between the bender pair minimizes the effect of the supporting rods and bender elements on the soil mass beneath footings. The soil mass is not affected by these anomalies up to a depth of 4 \(B\) based on the 2 to 1 method, as presented in Figure 2a. After installing the rods, the model ground was constructed by a dry compaction method, and this procedure was repeated 3 times for each test. The final relative density (\(Dr\)) of the prepared model ground was 85%, and the height of the prepared soil model was 460 mm, which is 7 times larger than the footing breadth. Figure 2: Model configuration: (**a**) Cross Section; (**b**) Top View. The model footings were made of aluminum having same width and height of 60 \(\times\) 20 mm for the three different models. The length of the model footings was 60 mm, 150 mm, and 300 mm for \(L/B\) ratios of 1.0, 2.5, and 5.0, respectively. The model footings were placed at a height of 430 mm from the bottom of the soil deposit, and they were laid in a perpendicular direction to the shear wave ray path, as presented in Figure 2b. In order to minimize the bedding error during vertical loading, model footings were embedded into the soil. An embedding depth of 30 mm was used for considering the equivalent soil weight with model footing to remove the overburden pressure before vertical loading. Acryl resin was attached on the top of model footing's perimeter to prevent the collapse of soil into the footing, as shown in Figure 2a. The experiments were conducted in a 5 m platform radius geotechnical centrifuge having a 240 g-ton capacity [23]. A target centrifugal acceleration level of 40 g was adopted, and thus model footings with a prototype length of 2.4 m, 6.0 m, and 12.0 m were simulated according to the centrifuge scaling law. Vertical loading equipment was used to apply a vertical load, and the loading condition was controlled with a constant velocity of 0.075 mm/s. After the 1 st loading, the load was completely removed, and the 2 nd loading was then applied with a larger load than that of the 1 st loading. The vertical load and the settlement of the foundation were measured by load cell and the linear variable differential transformer (LVDT), respectively.