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.