Abstract
A barrier function method based on the fmincon optimization function in MATLAB was used to determine the function to map a tunnel boundary to the unit circle in the complex plane, and a structural failure criterion of the mapping convergence was established based on the reliability theory of underground engineering. The joints were approximated as cracks around the tunnel, the anisotropy of the stress intensity factor due to the crack inclination and position changes was studied, and the modified scoring parameter of the layered joints around the tunnel for the rock geomechanics classification (RMR) was proposed and used at points around the tunnel. The calculation method for the supporting stress was required to balance the bias load. The results showed the following: (1) When taking the structural failure criterion as the convergence condition of the mapping function, the mapping function converged when the mapping accuracy was δ ≥ 31.74 % . (2) The crack with an inclination angle of β = 45 ° was the dominant structural plane of the jointed rock mass around the tunnel. The anisotropy of the stress intensity factor K II at the tip of the mode II crack indicated that the corresponding cracks at the various points around the tunnel had inconsistent influences on the tunnel. The position had the greatest influence, followed by the straight wall area, and then by the top and floor areas. (3) When the crack inclination β was equal to the inclination angle β 0 of the dominant joint plane, the secondary crack was parallel to the unloading surface of the corresponding tunnel. (4) The bias load formed by the layered joints around the tunnel reduced the stress threshold of the failure of the rib spalling.
Highlights
(3) When the crack inclination β was equal to the inclination angle β0 of the dominant joint plane, the secondary crack was parallel to the unloading surface of the corresponding tunnel. (4) e bias load formed by the layered joints around the tunnel reduced the stress threshold of the failure of the rib spalling
A layered jointed rock mass is a sedimentary rock with a layered structure composed of an array of parallel joint planes. e anisotropy of the mechanical behavior of the rock strata and the low-strength characteristics of the joint planes make the stability of the surrounding rock complicated for underground engineering [1]
Zhou et al [7, 8], Li and Zhu [9], and Liu et al [10] approximated joints as cracks around tunnels, and they used different finite element analysis software programs to simulate the stability of the tunnelsurrounding cracks to the surrounding rock of straight wall arch tunnels. ese simulations were combined with model tests to study the damage and destruction behaviors under confining pressure. e results showed that the cracks at the shoulder and foot of the tunnel were weaker locations of the Mathematical Problems in Engineering tunnel-surrounding rock damage
Summary
A layered jointed rock mass is a sedimentary rock with a layered structure composed of an array of parallel joint planes. e anisotropy of the mechanical behavior of the rock strata and the low-strength characteristics of the joint planes make the stability of the surrounding rock complicated for underground engineering [1]. Many results have been obtained using numerical simulation and model test methods to study the mechanical characteristics of the surrounding rock with different rock inclination angles. Using conformal mapping theory of complex analysis can provide a method to study the surrounding rock stress in underground engineering to obtain a closed solution via mathematical mechanics, i.e., using a complex analytical method. The complex analysis method has seldom been used to study the mechanical behaviors of tunnel-surrounding rock in a layered jointed rock mass. According to Muskhelishvili’s complex function method [21], the stress analysis of the surrounding rock of a deep underground tunnel can be classified as the problem of excavation in an infinite plane. Equations (8) and (10) together form a complex function for assessing the stability of the layered joint plane at any point around the tunnel
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