5 THE ANCHORING MECHANISM OF THE SUPPORT STRUCTURE ON THE SPECIMEN
The support structures show a significant influence on the strength characteristics, deformation characteristics, and the laws of the crack propagation of the specimens. The stress distribution around the holes without the support structures can be solved by formulas (1)–(3). The mechanical model of the anchoring hole with the anchoring effect of bolts is shown in Figure 12.
According to the literature 37, the analytical solution of the stress in the anchored zone and the non-anchored zone can be obtained as follows:
The radial stress in the anchored area is determined by
The tangential stress is calculated as The radial displacement is obtained by where Its first derivative is given by
The radial stress in the non-anchored zone is determined by
The tangential stress is calculated as The radial displacement is obtained by The radial stress at the interface between the anchored zone and the non-anchored zone is measured as follows:
The internal support pressure of the hole is shown in Equations (4)–(12). For other symbolic meanings and solutions, refer to the literature. 37
Therefore, the support of bolts changes the stress and displacement response of the surrounding rock. In addition, some scholars have observed that bolts can effectively improve the mechanical parameters of the rock mass and increase the peak strength and the residual strength of the rock mass, thus reduce the range of the plastic zone of the surrounding rock mass of the tunnel and the displacement of the tunnel surface and maintain the stability of the surrounding rock,38,39 which is found to be consistent with the test results obtained in this paper.
The concrete and steel arches induce internal support pressure on the tunnel, which is related to the material and support parameters of the concrete and steel arches. In calculations, the concrete and steel arches are often considered as a one-layer support structure, and the supporting stiffness 40 is evaluated as follows:
where and are the concrete elastic modulus and Poisson’s ratio, is the thickness of the layer of concrete and steel arches, and is the tunnel radius. The support pressure inside the tunnel is obtained as follows:
where is the hole wall displacement. The tangential stress of the concrete layer is evaluated as follows:
When the tangential stress exceeds the ultimate strength value of the concrete layer, the cracks occur in the concrete layer and gradually develop and the peeling and flaking off of the concrete layer also occur. By substituting formula (14) into formulas (4)–(12), the mechanical response of the tunnel on the surrounding rock under the support of bolts, concrete and steel arches can be obtained.