A new theory for determining large deformation area of roof at intersection and verification analysis

Abstract

The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway, and determining the subsidence hidden danger area of the roof is the key to its stability control. However, applying traditional maximum equivalent span beam (MESB) theory to determine deformation range, peak point, and angle influence poses a challenge. Considering the overall structure of the intersection roof, the maximum equivalent triangular plate (METP) theory is proposed, and its geometric parameter calculation formula and deflection calculation formula are obtained. The application of the two theories in 18 models with different intersection angles, roadway types, and surrounding rock lithology is verified by numerical analysis. The results show that: 1) The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone; 2) The area comparison method of the METP theory can be reasonably explained: ① The roof subsidence of the intersection decreases with the increase of the intersection angle; ② The roof subsidence at the intersection of different roadway types has a rectangular type > arch type > circular type; ③ The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock. According to the application results of the two theories, the four advantages of the METP theory are compared and clarified in the basic assumptions, mechanical models, main viewpoints, and mechanism analysis. The large deformation inducement of the intersection roof is then explored. The J₂ peak area of the roof drives the large deformation of the area, the peak point of which is consistent with the center of gravity position of the METP. Furthermore, the change in the range of this peak is consistent with the change law of the METP’s area. Hence, this theory clarifies the large deformation area of the intersection roof, which provides a clear guiding basis for its initial support design, mid-term monitoring, and late local reinforcement.

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