## 4 In-Situ Monitoring
### Strain of Steel Tube
#### 4.1.2 Relationship between Stress and Jacking Distance  
Based on the monitoring results, the strain of steel tube is elastic in the jacking stage. So the relationship between the stress and strain is defined in the elasticity stage based on the Hooke law, as shown in Formula (2) [31].  
\[\begin{array}{rcl}\varepsilon_{x}&=&\frac{1}{E}[\sigma_{x}-\
u(\sigma_{y}+ \sigma_{z})]\\ \varepsilon_{y}&=&\frac{1}{E}[\sigma_{y}-\
u(\sigma_{x}+\sigma_{z})]\\ \varepsilon_{z}&=&\frac{1}{E}[\sigma_{z}-\
u(\sigma_{x}+\sigma_{y})]\\ \end{array} \tag{2}\]  
However, the force mechanism is attributed to plane stress problem, \(\sigma_{z}=0\), as shown in Formula (3) [31].  
\[\begin{array}{rcl}\varepsilon_{x}&=&\frac{1}{E}(\sigma_{x}-\
u\sigma_{y})\\ \varepsilon_{y}&=&\frac{1}{E}(\sigma_{y}-\
u\sigma_{x})\\ \end{array} \tag{3}\]  
The formula can be transformed into another form, as shown in Formula (4)  
\[\begin{array}{rcl}\sigma_{x}&=&\frac{1}{1-\
u^{2}}(\varepsilon_{x}+\mu \varepsilon_{y})\\ \sigma_{y}&=&\frac{1}{1-\
u^{2}}(\varepsilon_{y}+\mu\varepsilon_{x})\\ \end{array} \tag{4}\]  
where, \(E\) is the elasticity modulus of steel tube; vis the poisson ratio; \(\sigma_{x}\), \(\sigma_{y}\) and \(\sigma_{z}\) are the longitudinal strain, the circumferential strain and the radius strain, respectively.  
Based on the in-situ monitoring data, the longitudinal and circumferential stain (\(\varepsilon_{x}\) and \(\varepsilon_{y}\)) is obtained, and the stress values with the two direction are required using Formula (4).  
The longitudinal and circumferential stress are shown in Figures 12 and 13, along with the increase of the jacking distance in the construction stage. Based on the monitoring results, the stress trend of section A is similar to section B. The results are thus analyzed according to section A. As point 3 is damaged in the construction stage, it is not analyzed.  
Longitudinal Stress of Steel Tube at Section A  
The longitudinal stress is shown in Figure 12. From the figure, the left and right side is the compressive stress, and the inner side is larger than the outer side because the steel tube turns right, which leads to compressive stress concentration at right side. Although the bottom of the steel tube performs the tensile strain, but the final longitudinal stress is tensile stress, this is because it is less than the circumferential stress and affected by Poisson effect. Therefore, the longitudinal stress is controlled by the lacking of force in the horizontal direction.  
Circumferential Stress of Steel Tube at Section A  
The circumferential stress is shown in Figure 13. As it is indicated that the bottom of the steel tube reflects the tensile stress, the left and right side is the compressive stress. Moreover, the value of the left and right side is less than the bottom, and the inner side is larger the outer side. This is because the circumferential tensile strain is larger than the longitudinal compressive strain, which decrease the influences of longitudinal compressive deformation. As for the inner stress is larger than the outer side, this is because the outer resistance of soil is usually larger than the inner side, and the right pressure decreases the compression deformation, which lead to the decrease of the compressive stress.