# Field Test Study on Vertical Bearing Characteristics of Coal Rock
## 4 Discussion  
As shown in Figure 4, the position of the plate load test points PLT1 and PLT2 are close to the test piles TP1 and TP2. Figure 17 is the pressure-settlement curve of PLT1 and PLT2 and the unit tip resistance-displacement curve of TP1 and TP2. The test points PLT1 and PLT2 fall in the first half of the unit tip resistance curves of TP1 and TP2. The average value of the ultimate unit tip resistance of TP1 and TP2 is 3458 kPa, the average value of the ultimate bearing capacity of PLT1 and PLT2 is 1890 kPa, and the ratio of the two is 1.83. The ultimate bearing capacity of the pile is significantly higher than that of the plate load test. As to the testing conditions, the plate load test is carried out on the surface without surrounding rock constraints, and the pile tip resistance test is conducted at depths of 7.5 m and 7.7 m, which are constrained by surrounding rocks. This means the bearing capacity of the coal rock increases with the burial depth, and it has been significantly improved by the surrounding rock constraints. When the bearing capacity of the upper pile and the lower pile are obtained by the bi-directional load test, the load-settlement curve of the pile top loading can be obtained  
Figure 16: Relationship between unit side resistance and displacement: (**a**) TP1; (**b**) TP2. Figure 17: Comparison of plate load test results and pile tip resistance test results. by certain equivalent conversion methods [20; 21; 27; 29]. The commonly used method is as follows [27]:  
\[Q_{\rm e}=\frac{Q_{\rm u}-W_{\rm u}}{\gamma}+Q_{\rm d} \tag{12}\]  
\[s_{\rm e}=s_{\rm d}+\frac{\frac{Q_{\rm u}-W_{\rm u}}{\gamma}+2Q_{\rm d}}{2E_{\rm p }A_{\rm p}}L_{\rm u} \tag{13}\]  
where \(Q_{\rm e}\) is the equivalent pile top load (kN); \(Q_{\rm u}\) is the corresponding load of the upper pile when the displacement value is \(s_{\rm d}\) (kN); \(W_{\rm u}\) is the weight of the upper pile (kN); \(\gamma\) is the side resistance conversion coefficient, for rock \(\gamma=1.0\); \(Q_{\rm d}\) is the corresponding load of the lower pile when the displacement value is \(s_{\rm d}\) (kN); \(s_{\rm e}\) is the equivalent settlement of the pile top (mm); \(s_{\rm d}\) is the downward displacement at the load cell (mm); \(E_{\rm p}\) is the elastic modulus of the pile (kPa); \(A_{\rm p}\) is the pile cross-sectional area (m\({}^{2}\)); \(L_{\rm u}\) is the length of the upper pile (m). In this paper, the unit tip resistance and unit side resistance of the pile in coal rock are obtained, and the mathematical functions are given in Equations (5) and (11). On this basis, the equivalent pile top load-settlement curve can be calculated:  
\[Q_{\rm e}=q\frac{\pi}{4}d_{\rm l}^{2}+\tau\pi D_{\rm w}h_{\rm w} \tag{14}\]  
\[s=s_{\rm d}+\frac{\tau\pi D_{\rm w}h_{\rm w}+2q\frac{\pi}{4}d_{\rm l}^{2}}{2E_ {\rm p}A_{\rm p}}L_{\rm u} \tag{15}\]  
The equivalent conversion curves calculated according to the bi-directional load test method and this paper's method are shown in Figure 18, and the two curves are in good agreement. The distribution of the equivalent conversion points of the bi-directional load test method depends on the distribution of test points, and the data in the front section of the equivalent conversion curve are often missing, as shown in Figure 18a. This paper's method overcomes that shortcoming. In the middle section of the equivalent conversion curve, this paper's method agrees well with the bi-directional load test method. At the end of the equivalent conversion curve, the curve of this paper's method has a steep drop, which is caused by the tip resistance reaching the limit value in Equation (5), and the side resistance is close to the limit value in Equation (11). Field test results based on the piles in soil and rock show that there is a size effect on the unit tip resistance and the unit side resistance, i.e., the unit resistance decreases when  
Figure 18: Equivalent conversion curves of pile top load–settlement: (**a**) TP1; (**b**) TP2. the pile diameter increases [30,31].