## 3 Solution and Analysis of Longitudinal Deformation Curve of Surrounding Rock
### Numerical Simulation and Verification Analysis  
To further verify the rationality and practicality of the optimization and improvement theory, FLAC3D is used to establish a numerical model, in which the model size is 42 m wide, 35 m high, 84 m long, with a total of 23,531 grid units and 21,902 nodes. The model adopts the M-C constitutive equation and the bottom and both sides are fixed constraints. According to the in situ stress at the location of the section, the buried depth of the Class-III surrounding rock is about 150 m, with 3.5 Mpa applied on the top, and the buried depth of the Class-IV surrounding rock is about 120 m, with 2.4 Mpa applied on the top. The model is shown in Figure 8.  
FLAC3D is used to simulate the whole excavation process of the Class-III and -IV surrounding rocks. The footage of each excavation is 3.5 m. The whole process is excavated 24 times in a cycle and the radial displacement of the vault at the section is monitored. The displacement and stress changes of different monitoring sections are shown in Figure 9.  
The monitoring results show that: (1) when the excavation surface is five times the tunnel radius from the monitoring surface, the monitoring points on the monitoring section begin to have radial displacement, but the displacement value is very small; (2) with the gradual advance of the excavation surface, the displacement of the surrounding rock at the monitoring point on the monitoring section increases rapidly, and then gradually tends to be stable; (3) the stress of the monitoring section is \"8-shaped\" and the stress of the arch crown and bottom is larger than that of the arch waist; (4) by analyzing the Class-III surrounding rock, the final settlement of the vault of the sections YK30+960 and YK30+911 measured when the long step method was used for excavation was 15.8 mm and 17.2 mm, respectively; (5) the final settlement of the vault of sections YK31+645 and YK31+422, measured when the reserved core soil method was used for the excavation of the Class-IV surrounding rock, was 18.3 mm and 20.2 mm, respectively. The above simulation results are close to the actual monitoring data, which confirms the effectiveness of the on-site tunnel excavation process.  
Figure 8: Schematic diagram of tunnel model and monitoring section.  
By comparing and analyzing the simulation data with the monitoring data and theoretical calculation data, the displacement release coefficient deformation curves at different sections are obtained, as shown in Figure 10.  
The simulation curve in Figure 10 is fitted with theoretical Equation (8) and theoretical Equation (10), and the correlation coefficients of each fitting curve are shown in Table 4:  
Figure 10: Simulation, theory, monitoring fitting diagram of vault displacement release coefficient: (**a**) Class—III surrounding rock; (**b**) Class—IV surrounding rock.  
Figure 9: Nephogram of displacement and stress changes of different monitoring sections: (**a**) displacement nephogram; (**b**) stress nephogram.  
Through the comparative analysis of the fitting parameters in Tables 2-4, it is not difficult to see that the modified Formula (10) can better match the actual monitoring data and simulation data (its R-square reaches about 0.95), and its curve change form has also been improved, meaning it can be more truly applied to practical projects. It is further confirmed that the variation law of the displacement release coefficient of the surrounding rock is not only related to Poisson's ratio, but also related to the elastic-plastic modulus, internal friction angle, cohesion and blasting parameters.