“…Figure 1 shows the plastic zone, viscoelastic zone and initial stress zone. Figure 1 Stress distribution around the roadway 10 , 20 . …”
Section: Calculation Model Of the Plastic Zone Of A Roadway Considerimentioning
confidence: 99%
“…Additionally, Chen et al 8 established the boundary implicit equation for the plastic zone of a circular roadway. Abdel et al 9 , Leitman and Villaggio 10 considered that the shape of the plastic zone of roadways located in non-uniform stress fields should be elliptical. Guo et al 11 and Wang et al 12 pointed out that the shape of the plastic zone of a roadway could be circular, elliptical or butterfly-shaped under different in situ stress conditions.…”
The plastic zone range is an important parameter in the analysis of damage characteristics and the degree of damage to the rock surrounding a roadway. Based on the establishment of a plastic zone calculation model considering the creep effect, this paper obtains the characteristics of the change in the plastic zone damage range with time by solving the model. Additionally, the validity of the model is verified by field experiments. The research results can provide guidance for gas pressure measurement and gas drainage in coal mines.
“…Figure 1 shows the plastic zone, viscoelastic zone and initial stress zone. Figure 1 Stress distribution around the roadway 10 , 20 . …”
Section: Calculation Model Of the Plastic Zone Of A Roadway Considerimentioning
confidence: 99%
“…Additionally, Chen et al 8 established the boundary implicit equation for the plastic zone of a circular roadway. Abdel et al 9 , Leitman and Villaggio 10 considered that the shape of the plastic zone of roadways located in non-uniform stress fields should be elliptical. Guo et al 11 and Wang et al 12 pointed out that the shape of the plastic zone of a roadway could be circular, elliptical or butterfly-shaped under different in situ stress conditions.…”
The plastic zone range is an important parameter in the analysis of damage characteristics and the degree of damage to the rock surrounding a roadway. Based on the establishment of a plastic zone calculation model considering the creep effect, this paper obtains the characteristics of the change in the plastic zone damage range with time by solving the model. Additionally, the validity of the model is verified by field experiments. The research results can provide guidance for gas pressure measurement and gas drainage in coal mines.
“…Detournay [18][19][20] extended Galin's result to other materials and obtained the boundary of the elastic and plastic zones. Tokar [21], Leitman and Villaggio [22], and Ochensberger et al [23] also presented a series of analytical solutions for a circular wellbore in some certain cases based on Galin's solution.…”
Pore water pressure has an important influence on the stresses and deformation of the surrounding rock of deep tunnels in water-rich areas. In this study, a mechanical model for deep tunnels subjected to a nonuniform stress field in water-rich areas is developed. Considering the pore water pressure, a new unified solution for the stresses, postpeak zone radii, and surface displacement is derived based on a strain-softening model and the Mogi-Coulomb criterion. Through a case study, the effects of pore water pressure, intermediate principal stress, and residual cohesion on the stress distribution, postpeak zone radii, and surface displacement are also discussed. Results show that the tangential stresses are always larger than the radial stress. The radial stress presents a gradually increasing trend, while the tangential stress presents a trend of first increasing and then decreasing, and the maximum tangential stress appears at the interface between the elastic and plastic zones. As the pore water pressure increases, the postpeak zone radii and surface displacement increase. Because of the neglect of the intermediate principal stress in the Mohr-Coulomb criterion, the postpeak zone radii, surface displacement, and maximum tangential stress solved by the Mohr-Coulomb criterion are all larger than those solved by the Mogi-Coulomb criterion. Tunnels surrounded by rock masses with a higher residual cohesion experience lower postpeak zone radii and surface displacement. Data presented in this study provide an important theoretical basis for supporting the tunnels in water-rich areas.
“…The DE algorithm is used as the optimization algorithm in this paper, and the number of design variables R, c k (k = 1, 2, Á Á Á , m), and b 0 is m + 2. Through the later examples, it is found that if the number of the terms m in the conformal mapping function and the number of the terms n in the complex potential functions are large enough, the value of the objective function will be very close to zero, which indicates that the satisfaction for both Equations (30) and (31) is perfect.…”
Section: Solving Methods For the Conformal Mapping Functionmentioning
confidence: 93%
“…The perturbation method was applied to determine an approximate solution by Bykovtsev and Tsvetkov [27] and Lozhkin [28,29]. In addition, Leitman and Villaggio [30] and Chanyshev and Abdulin [31] used the complex variable method to propose an approximate procedure by assuming that the shape of the elastoplastic interface is circular, which is not consistent with fact.…”
Based on the Mohr–Coulomb yield criterion, an analytical method is presented to determine the plastic zone in an infinite plate weakened by a circular hole and subjected to non-hydrostatic stresses at infinity. It is worth noting that this paper considers the more complicated case that the plastic zone cannot completely surround the hole, namely the elastoplastic interface is non-enclosed. Initially, the non-circular elastic zone in the physical plane is mapped onto the outer region of a unit circle in the image plane by the conformal transformation in the complex variable method. Thereby, determining the elastoplastic interface is equivalent to solving the mapping function coefficients. The nonlinear equations for solving the coefficients are established by considering both the stress continuity conditions along the elastoplastic interface and the stress boundary conditions along the elastic part of the hole. Naturally, the problem can be further transformed into an optimization problem, which is ultimately achieved by the differential-evolution algorithm; what is more, an analytical solution with high accuracy is obtained. Based on the programmed computing, the influences of various parameters on the shape and size of the plastic zone are given.
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