Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method

Abstract After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function. The expression of the relevant stress component is derived, and the displacement boundary conditions of the surrounding rock of shallow circular tunnel are obtained. Furthermore, the paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel. The simulation is carried out by finite element method. The establishment of complex variable function has a good application value in solving the stress of surrounding rock of shallow tunnel.

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Coefficients Calculation of Laurent Series in the Neighborhood of Complex Variable Function Poles

Tobacco Regulatory Science ◽

10.18001/trs.7.6.108 ◽

2021 ◽

Vol 7 (6) ◽

pp. 6348-6360

Author(s):

Zhijin Zhou

Keyword(s):

Complex Variable ◽

Laurent Series ◽

Function Theory ◽

Complex Function ◽

Research Field ◽

Complex Function Theory ◽

Complex Variable Function ◽

Object A ◽

Order Pole ◽

Variable Function

The theory of complex function is a key part of mathematics, which can solve the complex problems in production and life. It is of great significance to extend the research field of complex function theory. In this paper, taking a complex variable function as the research object, a calculation method of Laurent series coefficient of complex function pole neighborhood expansion was proposed to determine the complex variable function pole, determine the order of complex variable function pole, calculate the residue of high-order pole in complex variable function, thus judging the attribute of complex variable function. In this regard, the coefficient formula was used to calculate the coefficients of Laurent series in the neighborhood of the complex variable function poles.

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Elastoplastic Analysis on Circular Tunnels Surrounding Rock under Asymmetry Load

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.671-674.1098 ◽

2013 ◽

Vol 671-674 ◽

pp. 1098-1101

Author(s):

Yu Zhou ◽

Ai Zhong Lu ◽

Lin Kuang

Keyword(s):

Finite Element ◽

Surrounding Rock ◽

Elastoplastic Analysis ◽

Circular Tunnel ◽

Complex Variable Function ◽

Element Simulation ◽

Variable Function ◽

Simulation Based ◽

Complex Variable Function Method ◽

Tresca Criterion

The analytic solution for circular tunnel under asymmetry load usually uses C-M criterion, and the finite element calculation usually uses D-P criterion. In this paper, the complex variable function method is employed to do an elastoplastic analysis based on Tresca Criterion, obtained the stress and plastic radius in elastoplastic region. The result shows that extent of stress in elastic region is no longer match the Krisch solution. The solution is in good agreement with Sun GZ’s solution and finite element simulation based on ANSYS, which can be used in simple elastoplastic analysis of surrounding rock instead of finite element method.

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