<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Department of Information Technology, Faculty of Computing and Information Technology

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential...

Key location	Dome	Left arch waist	Right arch waist	Left arch	Right arch	Left wall	Right wall	Left wall foot	Right wall foot	Inverted arch

Axial force/kN	−137.5	−316.3	−238.1	−403.4	−489.4	−425.8	−537.1	−371.7	−407.6	−205.6
Moment/kN·m	11.87	−9.035	10.386	5.5608	15.619	−1.833	11.876	38.058	−36.01	−22.84
Safety factor	8.06	7.69	8.8	7.16	4.8	7.71	4.86	3.66	2.6	2.99

Support scheme	Vault settlement	Left arch horizontal displacement	Right arch horizontal displacement	Retaining wall foundation settlement

No retaining wall without crowded pile	4.72	4.4	1.7	–
Retaining wall + pipe shed	1.86	1.73	1.38	2.96

Material	Density/kg/m³	Elastic Modulus/MPa	Poisson's ratio	Cohesion/kPa	Internal friction angle/°
Expansive Soil	2000	50	0.3	35	23
Sandy loess	2000	50	0.3	28	45
Leading support	2000	60	0.3	33	53
Bolt reinforcement ring	2000	60	0.3	42	28
Initial support	2500	29.5E3	0.2	——	——
Retaining wall	2500	29.5E3	0.2	——	——
Lime-soil pile	2000	150	0.3	33.8	48

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

Online veröffentlicht: 15. Dez. 2021

Seitenbereich: 629 - 640

Eingereicht: 16. Juni 2021

Akzeptiert: 24. Sept. 2021

DOI: https://doi.org/10.2478/amns.2021.1.00050

Schlüsselwörter
complex variable function, shallow-buried circular tunnel surrounding rock, deformation analysis, stress finite element analysis

© 2021 Guizhen Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

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Fig. 9

Fig. 10

Typical section safety factor of initial support structure

Summary of displacement calculation of key points of different supporting schemes (cm)

Model calculation of mechanical parameters

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

Online veröffentlicht: 15. Dez. 2021

Seitenbereich: 629 - 640

Eingereicht: 16. Juni 2021

Akzeptiert: 24. Sept. 2021

DOI: https://doi.org/10.2478/amns.2021.1.00050

Schlüsselwörtercomplex variable function, shallow-buried circular tunnel surrounding rock, deformation analysis, stress finite element analysis

© 2021 Guizhen Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Typical section safety factor of initial support structure

Summary of displacement calculation of key points of different supporting schemes (cm)

Model calculation of mechanical parameters

Schlüsselwörter
complex variable function, shallow-buried circular tunnel surrounding rock, deformation analysis, stress finite element analysis