# Three-Dimensional Theoretical Model for Soil Arching with Inclined Slip Surfaces
## 5 Comparison with Experimental Tests  
Experiment tests results are compared with the results from the proposed 3D solution with inclined slip surface. [PERSON] et al. [24] conducted three groups of trapdoor tests with buried depth ratios \(H/B\) equal to 1, 2, and 4, respectively. The width and length of the trapdoor in the tests were 0.25 m and 0.5 m, respectively. The internal friction angle of well-graded sands was 31.6\({}^{\circ}\). According to the image of test results, the angle of the slip surfaces is considered as 85\({}^{\circ}\) in the following calculation. The comparison is shown in Figure 13 It can be seen from the comparison that the calculation results from this paper considering 3D conditions are slightly less than that of [PERSON]'s solution. The results by 3D solution in this paper is closer to the test results when the buried depth ratio is small. The results by [PERSON]'s solution is closer to the test results when the buried depth ratio is large. This is because the front wall of the model test chamber is made by toughened glass plate and the other steel walls of the model test chamber are attached with thin Teflon films. The toughened glass plate and thin Teflon films can be regarded as smooth enough  
Figure 12: Earth pressure versus aspect ratio of loose area under earth different pressure coefficients.  
to mitigate the effect of friction. In the case of a large buried depth ratio, the 3D solution in this paper treat the front and back wall of the test chamber as slip surface equivalent to the left and right sides, which leads to the smaller results of the calculated earth pressure.  
[PERSON] et al. [19] developed and performed 3D Trapdoor experiments to clarify the mechanical behavior in tunnel excavations. In the test, a series of adjacent trapdoors gradually lowered down, one-by-one to simulate the soil loosening during shield tunneling. For all trapdoors, the width of the cross-section is 150 mm. For trapdoors numbers 1 and 6, the lengths were 200 mm, while they were 150 mm for trapdoors numbers 2, 3, 4 and 5. The loads applied to the Trapdoors are measured by load cells. The tests results and calculated results by presented solution and [PERSON]'s solution for difference buried depth ratio are shown in Figures 14-16, respectively. It can be found from results that the earth pressure ratio increases with the increase of the aspect ratio of the loose zone with the test process. The traditional 2D Terzaghi solution can not reflect this trend, but the 3D solution in this paper can reflect this trend. When part of the trapdoors were lowered down, such as when the aspect ratio of the loose zone \(L/B\) was 1.33, the earth pressure ratio obtained by [PERSON]'s solution were very different to the test results, and the results obtained by the solution in this paper were closer to the tests results. When all of the trapdoors were lowered down, such as when the aspect ratio of the loose zone \(L/B\) was 6.67, the earth pressure ratio obtained by [PERSON]'s solution and the solution in this paper were both close to the test results. The comparison between the solution in this paper and the test results shows that the solution in this paper is more accurate than the traditional 2D solution for calculating loose-earth pressure, especially in 3D conditions.  
Figure 13: Comparison of tests results ([PERSON] et al. [24]) and 3D solution.  
Figure 14: Comparison of tests results ([PERSON] et al. [19]) and 3D solution under \(H/\)B = 1.  
Figure 15: Comparison of tests results ([PERSON] et al. [19]) and 3D solution under \(H/\)B = 2.