Abstract
In this study, the triangle interpolation method for the calculation of mapping functions of plates containing an opening with arbitrary shapes is investigated with an improved method for point adjudgment during iterations. Afterwards, four kinds of openings with typical shapes are considered and the mapping functions for them are calculated, based on which the influence of calculation parameters such as iteration time and the number of terms on the accuracy of mapping function is discussed. Finally, the stress around an inverted U-shaped opening and around an arched opening under different far-field stress conditions is calculated and the effect of opening shape and lateral pressure coefficient on stress distribution and rock mechanical behaviors is further analyzed combined with the discrete element method (DEM) numerical simulation. The result shows that the stability and failure pattern of the rock mass is correlated with the stress around the opening, which is affected by the opening shape. The existence of opening also greatly reduces the enhancing influence of confining stress on rock specimen.
Highlights
Take the numerical specimen containing an arched opening for example, its peak axial stress under uniaxial compression condition is 30.94 MPa, which is 79.76% of that of the intact specimen
The stress solution for plates containing an opening was studied based on conformal mapping
The stress distribution and failure patterns of rock mass containing an opening under different confining stress conditions were further analyzed with the combination of analytical stress solutions and numerical simulations
Summary
The mechanical behavior of underground engineering structures is usually studied via experiments on rock specimens containing one or more openings or joints under different stress conditions [6,7,8]. Wu et al [11] processed rock specimens containing an opening with five presentive shapes and investigated the influence of an opening shape on the mechanical properties and fracture characteristics of rock specimens under uniaxial loading These studies show that maniacal properties and fracturing behavior of rock specimens are tightly correlated with the loading condition and opening shape. The initial failure tends to appear at the top and bottom of the opening and dominated cracks always develop from opening corners These influences of openings may be attributed to stress distribution. The failure pattern of the specimen is transformed from vertical failure to horizontal failure with the increase in confining stress and is dominated by shear cracks under high confining stress conditions
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