## 4 Engineering Application
### Influence of the Tunnel Diameter on the Tunnel Surrounding Rock  
According to Code for risk management of underground works in urban rail transit (GB50652-2011) [28], when the probability value of the risk is greater than 10%, the occurrence probability of the risk is classified as level 1. And when the probability value of the risk is between 1% and 10%, the occurrence probability of the risk is classified as level 2. With a view to analysing the influence of the tunnel diameter on the instability probability of the tunnel's surrounding rock under the PH\(-\)1 failure model and the PH\(-\)2 failure model, as shown in Figure 6a, when the tunnel diameter is 3 m and the tunnel is boring in slightly weathered dolomite strata, the instability probability of the M\(-\)1 region in the PH\(-\)1 failure mode and the instability probability of the P\(-\)1 zone and the P\(-\)2 zone in the PH\(-\)2 failure mode is 5.5% and 2.86%, respectively. And the difference in the instability probability calculated for the two damage modes is 2.6%. When the tunnel diameter is 8 m and the tunnel is boring in moderately weathered dolomite strata, the instability probability of the M\(-\)1 region in the PH\(-\)1 failure mode and the instability probability of the P\(-\)1 zone and the P\(-\)2 failure mode is 7.76% and 7.8%, respectively. And the difference in the instability probability calculated for the two damage modes is 0.04%. When the tunnel diameter is 15 m and the tunnel is boring in the hard plastic red clay strata, the instability probability of the M\(-\)1 region in the PH\(-\)1 failure mode and the instability probability of the P\(-\)1 zone and the P\(-\)2 zone in the PH\(-\)2 failure mode is 37.59% and 21.95%, respectively. And the difference in the instability probability calculated for the two damage modes is 15.64%. This investigation shows that when the tunnel passes through the moderately weathered dolomite strata and slightly weathered dolomite strata, there is not much difference between the results of the PH\(-\)1 failure mode and the PH\(-\)2 failure mode. However, the instability probability calculated from the PH\(-\)1 failure model and the instability probability calculated from the PH\(-\)2 failure model differ considerably when tunnelling in hard plastic red clay strata. This is owing to the good stratigraphic integrity of the moderately weathered dolomite strata and slightly weathered dolomite strata and the high self-supporting capacity of the tunnel surrounding rock. Nevertheless, the cohesion of the hard plastic red clay is relatively weak, and the self-supporting capacity of the tunnel surrounding rock is also relatively weak. Hence, both the PH\(-\)1 failure mode and the PH\(-\)2 failure mode are appropriate for analysing the instability probability in tunnel construction in moderately weathered dolomite and slightly weathered dolomite formations. However, the PH\(-\)1 failure model is not suitable for analysing the probability of instability in tunnel construction in hard plastic red clay strata, while the PH\(-\)2 failure model is appropriate for analysing the probability of instability in tunnel construction in hard plastic red clay strata.