Analytical solutions for rock stress around square tunnels using complex variable theory

Zhao, Guangpu; Yang, Shengli

doi:10.1016/j.ijrmms.2015.09.018

Cited by 55 publications

(20 citation statements)

References 11 publications

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“…As an example, the boundary condition across the lining-rock interface and tunnel lining inside can be determined by Equations (13)- (15). The boundary conditions at infinity can be expressed through Equations (9) and (10).…”

Section: Comparison Of the New Analytical Solution With That Of The Nmentioning

confidence: 99%

“…Verruijt [8,9] calculated the stress and displacement components around a circular tunnel in an elastic half-plane. Zhao and Yang [10] obtained a general solution for deep square tunnels with different pressure coefficients. Kargar et al [11] made an attempt to study lining stress and deformation in a non-circular deep tunnel using the Cauchy integral formula of complex variable methods.…”

Section: Introductionmentioning

confidence: 99%

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A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification

Chen

2018

MCA

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A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respectively. The new method is validated by FLAC3D finite difference software through an example. Both the new method and the numerical simulation obtained similar results for the stress concentration and the minimum radial displacement occurred at a similar place in the tunnel. It is demonstrated that the new complex variable method is reliable and reasonable. The new method also provides another way to solve non-circular tunnel excavation problems in a faster and more accurate way.

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Section: Comparison Of the New Analytical Solution With That Of The Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification

Chen

2018

MCA

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“…Chen et al [22] studied the working face stability of shallow buried square tunnels in heterogeneous soil. Zhao et al [23] applied the theory of complex variable function to solve the stress of square tunnel surrounding rock in a homogeneous isotropic elastic rock mass. Zhang et al [24] established the friction work calculation model of roadway plastic zone and studied the influence of the relationship between total energy and friction work in roadway impact area on rock burst.…”

Section: Introductionmentioning

confidence: 99%

Sliding Impact Mechanism of Square Roadway Based on Complex Function Theory

Jiang

Wang

et al. 2021

Shock and Vibration

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To clarify the process of stress change and plastic zone evolution of square roadways under high-stress conditions, the rotational square expansion plastic zone evolution model of square roadway was established by theoretical analysis, numerical simulation, and engineering verification. The shear slip impact stress criterion of square roadway based on complex variable function theory was studied, and the law of surrounding rock stress distribution, plastic zone expansion, elastic energy density, local energy release rate (LERR), and total energy release of square roadway were analyzed. The results show that the compressive stress is concentrated in the four corners of the roadway after the roadway excavated and transfers with the change of plastic zone. Main shear failures start from the four corners and develop in a rotating square shape, forming square failure zones I and II. The square failure zone I is connected with the roadway contour and rotated 45°. The square failure zone II is connected with the square failure zone I and rotated 45°. When the original rock stress is low, the surrounding rock tends to be stable after the square shear slip line field formed. When the original rock stress is high, the shear failure of the surrounding rock continues to occur after the square failure zone II formed, showing a spiral slip line. Corners of the square roadway and square failure zones I and II are the main energy accumulation and release areas. The maximum elastic energy density and LERR increase exponentially with the ratio of vertical stress to uniaxial compressive strength (Ic). When square corners of the roof are changed to round corners, the plastic zone of the roof expands to form an arch structure. The maximum elastic energy density decreases by 22%, which reduces the energy level and possibility of rock burst. This study enriches the failure mechanism of roadway sliding impact. It can provide a basic theoretical reference for the design of the new roadway section and support form based on the prevention of rock burst.

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“…The stress and displacement in single tunnel excavation at great depth were studied [6,7]. Analytical solutions for deep rectangular structures and a square tunnel were conducted analytically [8,9]. A correction factor was adopted for improving the accuracy of the CVM [10].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Solution for Stress and Displacement Field for Arbitrarily Positioned Twin-Tunnel Excavation at Great Depth

Lin

Chen

2018

Mathematical Problems in Engineering

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In this study, an analytical solution for the stress and displacement field for arbitrarily positioned twin-tunnel excavation at great depth is proposed. The twin-tunnel is subjected to equivalent loads on the tunnel periphery and uniform loads at infinity. The analytical continuation of the complex variable method is used for stress “stair”, owing to the equivalent loads of the tunnel support. Subsequently, the Schwarz alternating method and Cauchy integral formula are used. The redundant surface forces on the periphery are expanded into Laurent series in the sequence of iterations, and a reasonable series truncation is adopted. Comparing with several existing solutions covering special cases from different perspectives, it is found that the proposed solution meets accuracy requirements for tunnel center distance greater than 2.2 times tunnel radius after 1.5 iterations. The proposed solution is fast and yields reference value to tunnel engineering.

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Analytical solutions for rock stress around square tunnels using complex variable theory

Cited by 55 publications

References 11 publications

A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification

A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification

Sliding Impact Mechanism of Square Roadway Based on Complex Function Theory

An Analytical Solution for Stress and Displacement Field for Arbitrarily Positioned Twin-Tunnel Excavation at Great Depth

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