## 3 Compared with Centrifugal Test Results
### Comparative Analysis of Results  
The comparative analysis of the results is shown in Figure 7; the vertical displacement contours of 37.5 mm and 30 mm in the central part show good consistency and regularity. In general, the centrifugal test results are nearly straight-line contours, while the theoretical calculation results are arc contours, which also leads to a large difference between 22.5 mm, 15 mm, and 7.5 mm contours, and shows a trend of increasing the difference from the center to the edge.  
As for vertical displacement, the numerical value is relatively small, and its regularity is not obvious. This can also be seen from the poor symmetry of the left and right halves of the horizontal displacement in the centrifugal test nephogram. The shape and distribution position of centrifugal contours and theoretical contours are similar, especially the upper 4 mm curve and the central 2 mm curve. However, the difference between theoretical contours and centrifugal contours also shows an increasing trend from the center to the edge, the whole lines shift to the right a little, and the theoretical contour has a wider range. This is consistent with the law that the settlement trough of sand is narrower and deeper than that of clay [76].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **Unit Weight (kN/m\({}^{3}\))** & **Typical D\({}_{50}\)** & **Maximum/Minimum** & **Relative** & **Poisson’s** & **Elastic Modules** \\  & **(km)** & **Void Ratios** & **Density** & **Ratio** & **(MPa)** \\ \hline Dry Leighton & & & & & & \\ Buzzard Fraction & 26.7 & 122 & 0.97/0.64 & 90\% & 0.4 & 20 \\ E silica sand, UK. & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical parameters of soil samples.  
Figure 7: Contour comparison of [PERSON]’s solution, theorical calculation of this paper, and centrifugal test results (2.5% volume loss): (**a**) Horizontal displacement contours for Greenfield; (**b**) vertical displacement contours for Greenfield.  
Due to sand soil being chosen as the test soil sample in centrifugal test, [PERSON]'s solution is applicable to sand soil, but another important part of our theoretical formula, [PERSON]'s solution, is only applicable to clay soil. Be aware of the exponential function of [PERSON]' solution modify the formation loss coefficient by fitting the clay soil data, although the soil parameters substituted in Equation (12) are sand soil's, which cannot eliminate the difference between the [PERSON]'s \(\varepsilon_{x,z}\) and the properties of sand. This leads to the fact that in the vertical displacement contours, the centrifugal contours are linear and the theoretical contours arc, which is similar to the difference between the two on the slip fracture surface of soil. Generally, clay soil has a complex composition, elastic-plastic deformation occurs easily, deformation has a time-delay property, and many other disturbing factors, all of which are very unfavorable to the test analysis. However, sand soil has a single material, of which properties are easier to control in the test, and the drainage or non-drainage conditions need not be considered. Therefore, the current centrifugal tests are mostly based on sand. We regret that we have not found a suitable clay centrifugal test as a reference. However, considering the inevitable errors in centrifugal test and theoretical calculations, the comparison results are still acceptable.