The Plastic Zone of Tunnel Surrounding Rock under Unequal Stress in Two Directions Based on the Unified Strength Theory

Zongshan Zou,Hongyan Liu,Jun Yang,Zhongming Wang,Georgios I Giannopoulos

doi:10.1155/2021/8842153

Abstract

For the deficiencies that the existing calculation theory for the Plastic Zone of Tunnel Surrounding Rock (PZTSR) does not consider the effect of the intermediate principal stress σ2 and interaction between the surrounding rock and support structure on the PZTSR under unequal stress, the Unified Strength Theory (UST) for the rock is adopted to replace the often used Mohr-Coulomb (M-C) strength criterion to consider the effect of σ2 on the PZTSR. Meanwhile, the interaction mechanism between the surrounding rock and support structure is also considered in the proposed model. Finally, the effect of the initial elastic displacement of the surrounding rock, stiffness of the support structure, and the coefficient b of the intermediate principal stress on the plastic zone is discussed. The results show that the PZTSR will increase nonlinearly with increasing the initial elastic displacement of the surrounding rock, and when it increases to a certain value, its increase extent will be much obvious. With increasing the stiffness of the support structure, the PZTSR will gradually decrease nonlinearly, but the decrease extent is not very much. With increasing b, the PZTSR will decrease; namely, σ2 can improve the stress condition of the surrounding rock and reduce the PZTSR.

Highlights

For the deficiencies that the existing calculation theory for the Plastic Zone of Tunnel Surrounding Rock (PZTSR) does not consider the effect of the intermediate principal stress σ2 and interaction between the surrounding rock and support structure on the PZTSR under unequal stress, the Unified Strength eory (UST) for the rock is adopted to replace the often used Mohr-Coulomb (M-C) strength criterion to consider the effect of σ2 on the PZTSR
The effect of the initial elastic displacement of the surrounding rock, stiffness of the support structure, and the coefficient b of the intermediate principal stress on the plastic zone is discussed. e results show that the PZTSR will increase nonlinearly with increasing the initial elastic displacement of the surrounding rock, and when it increases to a certain value, its increase extent will be much obvious
The natural geostress field of the tunnel is often nonhydrostatic, and the horizontal stress is often larger than the vertical one with the increased buried depth of the tunnel and intensive geological tectonic action. erefore, the study on the mechanical behavior of the tunnel under unequal stress in two directions is of more practical significance

Summary

The PZTSR under Unequal Stress in Two Directions Based on the UST

3.1. e eoretical Model. e field test of the ground stress indicates that the horizontal stress is not equal to the vertical one in most cases [27, 28], and so the surrounding rock plastic p0. It can be seen that the surrounding rock relative plastic zone of the circular tunnel under unequal stress in two directions is not a circle anymore, but an oval It indicates that the coefficient λ has much effect on the PZTSR. It can be seen that the surrounding rock relative plastic zones are all oval It indicates that increasing c does not change the shape of the PZTSR and only affects its size. The decrease extent of the PZTSR becomes less and less with increasing c. e effect of rock internal friction angle φ on the PZTSR is shown in Figure 6(b), which is similar to that of the rock cohesion c, and we do not state it again

The PZTSR by considering the Interaction between the Ground and the Support

Findings

Conclusions