## 5 Results and Discussion
### Bearing Capacity of the Shaft lining Model  
Table 3 summarizes the failure loads for the specimens of the shaft lining model. The thin specimens of the steel-plate-confined high-performance composite concrete shaft lining model each had a high bearing capacity and therefore provided reasonable support for the large-diameter drill shaft.  
To analyze the strength improvement coefficient of this type of composite shaft lining structure, based on the limit equilibrium conditions and the concrete strength theory, an equation for calculating the ultimate bearing capacity (\(P_{b}\)) was established:  
\[P_{b}=[m\cdot R_{a}\cdot(h-h_{gn}-h_{gw})+R_{e}\cdot(h_{gn}+h_{gw})]/b \tag{6}\]  
where \(m\) is the compressive strength improvement coefficient of the concrete, \(R_{a}\) is the axial compressive strength of the concrete, \(R_{e}\) is the lower yield point strength of the steel plates, \(b\) is the outer radius of the shaft lining, \(h\) is the thickness of the shaft lining, and \(h_{gn}\) and \(h_{gw}\) are the thicknesses of the inner and outer steel plates, respectively.  
Table 3 summarizes the compressive strength improvement coefficients of the concrete in the composite shaft lining structure calculated using Equation (4) based on the test values of the bearing capacity. As demonstrated in Table 3, due to the constraints exerted by the inner and outer steel plates, the concrete layer in this shaft lining structure was under triaxial compression and, consequently, its compressive strength increased significantly by a factor of 1.97-2.52. This result is consistent with the results reported by researchers in China and elsewhere on the improvement of the compressive strength of concrete under compressive stresses [31; 32; 33; 34]. In addition, the values of the improvement coefficient also meet the requirements for the compressive strength improvement coefficient of concrete in the current standard of China [24], which suggests that this parameter should be taken into consideration in design calculations of this type of shaft lining structure to allow the structure to reflect its actual reliability.  
Based on testing and theoretical analyses, factors affecting the compressive strength improvement coefficient (\(m\)) of concrete in this type of thin, high-performance shaft lining structure include the thickness of the shaft lining, the lower point yield strength and thickness of the steel plates (\(h_{g}\) represents the sum of the thicknesses of the inner and outer steel plates), the inner diameter of the shaft lining (\(2a\)), and the compressive strength of the concrete layer (\(R_{a}\)). The expression of \"\(m\)\" can thus be determined by a dimensional analysis method using the data in Table 3 [35]:  
\[m=10.20\cdot(h/a)^{0.57}\cdot(R_{a}/R_{e})^{-0.05}\cdot(h_{g}/h)^{0.18}. \tag{7}\]  
The correlation coefficient of Formula (7) was represented by \(R^{2}\) (\(R^{2}=0.942\)) and satisfied the requirement of relevance.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & **Shaft lining** & \multicolumn{2}{c}{**Steel Plate Thickness (mm)**} & **Concrete** & **Bearing** & **Improvement** \\
**Number** & **Thickness (mm)** & **Inner Steel Plate** & **Outer Steel Plate** & **Strength (MPa)** & **Capacity (MPa)** & **Coefficient \(m\)** \\ \hline ZJ1 & \(56.1\) & \(0.93\) & \(0.93\) & \(61.7\) & \(12.8\) & \(1.97\) \\ ZJ2 & \(56.1\) & \(1.50\) & \(0.93\) & \(66.3\) & \(14.3\) & \(2.03\) \\ ZJ3 & \(56.1\) & \(1.86\) & \(1.50\) & \(70.8\) & \(16.5\) & \(2.17\) \\ ZJ4 & \(65.4\) & \(1.86\) & \(1.50\) & \(60.2\) & \(17.0\) & \(2.24\) \\ ZJ5 & \(65.4\) & \(0.93\) & \(0.93\) & \(67.1\) & \(16.5\) & \(2.05\) \\ ZJ6 & \(65.4\) & \(1.50\) & \(0.93\) & \(70.6\) & \(18.5\) & \(2.17\) \\ ZJ7 & \(74.8\) & \(1.50\) & \(0.93\) & \(61.4\) & \(20.2\) & \(2.39\) \\ ZJ8 & \(74.8\) & \(1.86\) & \(1.50\) & \(65.8\) & \(23.0\) & \(2.52\) \\ ZJ9 & \(74.8\) & \(0.93\) & \(0.93\) & \(71.2\) & \(21.0\) & \(2.18\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model specimen loading results.