Research on Surrounding Rock Stress Distributions for Circular Tunnels Based on the Schwarz-Christoffel Transformation

CUI Jianbin; JI Anzhao; XIONG Guiming

doi:10.21656/1000-0887.390326

Volume 40 Issue 10

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CUI Jianbin, JI Anzhao, XIONG Guiming. Research on Surrounding Rock Stress Distributions for Circular Tunnels Based on the Schwarz-Christoffel Transformation[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1089-1098. doi: 10.21656/1000-0887.390326

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Research on Surrounding Rock Stress Distributions for Circular Tunnels Based on the Schwarz-Christoffel Transformation

doi: 10.21656/1000-0887.390326

¹School of Mathematics and Statistics, Longdong University, QingYang, GanSu 745000, P.R.China;²School of Energy Engineering, Longdong University, QingYang, GanSu 745000, P.R.China;³College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, P.R.China

Received Date: 2018-11-26
Rev Recd Date: 2019-03-13
Publish Date: 2019-10-01

Abstract

Abstract

The transformation method with which the surrounding rock stress was mapped to an actual area, has been more and more widely applied to engineering practice, which is of practical guiding significance to the stress calculation method and the study on stability of tunnel surrounding rock. A mechanical model was established for circular tunnels in rock mass, with a mapping function obtained from a unit circle to a polygonal rock mass in the complex plane through the Schwarz-Christoffel transformation method based on the complex variable function theory. Then the solution of the stress distribution in the polygonal rock mass was studied in the complex function field, and subsequently the formulas of complex stress functions Φ(ξ) and φ(ξ) for circular tunnels in irregular rock masses were derived based on the elasticity theory. Finally, the analytical formulas of stress components σ^ρ and σ^θ for any point in the surrounding rock mass were obtained. Analysis of examples indicates that the shape of the rock mass has large influence on the stability of circular tunnels. Here is the maximum stress distribution law for 4 shapes of rock masses: the maximum stresses in the roof and floor of the hexagon, the pentagon, the quadrilateral and the circle decrease in order; otherwise, those in the sidewalls of the circle, the quadrilateral, the pentagon and the hexagon decrease successively.
- polygonal surrounding rock tunnel,
- Schwarz-Christoffel transformation,
- plane stress,
- stress distribution of surrounding rock

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References(18)

References

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