3.2 Damage and destruction of holes
The failure modes of the specimens can be divided into three types: hole
wall collapse, crack initiation and propagation, and surface peeling
off. The degree of hole wall collapse is found to be different under
different support conditions of the specimens (Figure 3); among them,
the rough hole with a bedding angle of 90° has the most serious collapse
(M2–3), and there is no hole wall collapse in the specimens supported
by the bolts, concrete, and steel arches (BCG2–3). The walls of the
holes under the bolt support (B1–3, B2–3, P1–3, and P2–1) still show
different degrees of collapse and peeling, but the overall damage degree
of these holes has been significantly improved as compared to that of
the rough holes (M1–1 and M2–1). Under the support of bolts and
concrete, the hole walls of the specimens do not peel off, and the holes
of some specimens are compressed, thus resulting in lateral deformation
(BC1–3 and BC2–3). It is foreseeable that without the support and the
bonding effect of the simulated concrete layer, the integrity of the
holes will be difficult to maintain. In addition, the test used the
epoxy resin to simulate the concrete layer, which shows a high plastic
deformation ability, so that the holes can maintain their integrity
after a certain amount of lateral deformation. The concrete used in the
actual engineering is composed of cement, sand, and stones in a certain
mix ratio, and the plastic deformation ability is poor. Therefore, the
deformation of the tunnel often leads to the concrete layer cracking and
flaking off. This means that the development of shotcrete materials with
high strength and high plastic deformation ability is considered to be
beneficial in order to maintain the integrity of the tunnels with large
deformation or dynamic disasters such as high ground stress, deep, soft
rock, and rock burst.
The more severely damaged parts of the holes are located on both sides
of the hole, irrespective of specimens with a bedding angle of 0° or
90°, which is the result of the compressive stress concentration areas
formed on both sides of the hole under the action of the vertical load.
For the plane elasticity problems, the stress distribution around the
hole can be expressed by using Kirsch’s analytical solution as follows:
where is the radial stress at any point around the hole, is the
tangential stress at any point around the hole, is the shear stress at
any point around the hole, is the vertical stress, is the horizontal
stress coefficient, is the radius of the hole, is the radial distance
between the calculated point and the center of the hole, and is the
angle between the line between the calculation point and the center
point of the hole and the horizontal direction.
The lateral and vertical stress distributions along the hole are shown
in Figure 4. In the uniaxial compression test, , and when and on both
sides of the hole, then and , thus resulting in a large compressive
stress concentration on both sides of the hole. At the top and bottom of
the hole, when and , then and , thus, resulting in a tensile stress
concentration at the top and bottom of the hole.