Analytical solutions for the stress of a lined non-circular tunnel under full-slip contact conditions

Lu, Aizhong; Zhang, Ning; Qin, Yuan

doi:10.1016/j.ijrmms.2015.08.008

Cited by 55 publications

(17 citation statements)

References 10 publications

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“…The stress and displacement components can be expressed by two complex variable functions φ( z ) and ψ( z ). The stress and displacement formulas can be described as follows: 27 where σ r , σ θ , and τ r θ are the radial stress, circumferential stress, and shear stress, respectively, at any location; u r and u θ are the radial displacement and circumferential displacement, respectively; z is the coordinate of the complex function; i is the imaginary unit; G is the shear modulus, G = E /[2(1 + μ)]; μ is Poisson’s ratio; κ is the coefficient, the plane strain model takes (3–4μ); and F x and F y are the horizontal force and vertical force, respectively, on the boundary.…”

Section: Solutionmentioning

confidence: 99%

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Analytical Solution of the Grouting Reinforcement Response of a Circular Cavern in Deeply Buried Fractured Surrounding Rock under a Nonuniform Stress Field

Liu

Lyu

et al. 2022

ACS Omega

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Grouting is widely utilized to reinforce fractured surrounding rock. However, presently, the secondary stress distribution of fractured surrounding rock after grouting is not distinct, which hinders the accurate evaluation of the grouting effect. Therefore, a complex variable function solution is provided for the evolution of the stress field and the displacement field around the reinforced fractured surrounding rock subjected to a nonuniform load. By comparing the evolution of the stress and radial displacement fields around the cavern, the reinforcement effect on the fractured surrounding rock is quantitatively confirmed. The results show that grouting has an obvious modification effect on fractured surrounding rock: its radial stress and circumferential stress fields are affected to different degrees, and the circumferential stress is more obvious. Grouting makes the circumferential stress peak transfer from the wall of the cavern to the roof and floor of the cavern, which is beneficial to the stability of the cavern. The radial displacement around the cavern also decreases. The displacement of the wall decreases by approximately 24.0%, and the radial displacement of the roof and floor decreases by approximately 61.8%.

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Section: Solutionmentioning

confidence: 99%

“…Considering the boundary condition of infinite stress, the complex stress function in the grouting wall is expressed by φ 1 ( z ) and ψ 1 ( z ). The complex stress function in the surrounding rock is expressed by φ 2 ( z ) and ψ 2 ( z ), which can be determined as follows: 27 …”

Section: Solutionmentioning

confidence: 99%

Analytical Solution of the Grouting Reinforcement Response of a Circular Cavern in Deeply Buried Fractured Surrounding Rock under a Nonuniform Stress Field

Liu

Lyu

et al. 2022

ACS Omega

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“…In Equation (7), the coefficient of displacement released η is equal to the ratio of the displacement that the surrounding rock has undergone before bolting to the maximum displacement that the surrounding rock can generate [22–24].…”

Section: Principle and Methods For Solving Shear Stresses Along The B...mentioning

confidence: 99%

A theoretical method of mechanical analysis for a circular tunnel reinforced by fully grouted rock bolts

Liu¹,

Zeng

2021

Mathematics and Mechanics of Solids

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Analysis of the mechanical behavior of rock mass reinforced by fully grouted rock bolts is introduced based on the interaction between the rock mass and the bolts. The model is based on the following premises: (1) the elastic behavior of the rock mass and rock bolts; (2) the plane strain condition; (3) a deeply buried circular tunnel; (4) complete contact between the bolts and the surrounding rock, that is, they are bonded together; (5) the loads on the surrounding rock from the fully grouted rock bolts are replaced by innumerable concentrated forces along the longitudinal direction of the bolts. For this, the analytical radial displacement solution for a deeply buried circular tunnel subjected to concentrated forces at arbitrary points in surrounding rock is derived. As long as this displacement solution is integrated along the length direction of the bolt, the effect of the bolt on the surrounding rock can be obtained. According to the complete contact condition at the anchoring interface and the force balance condition of the bolts, under the action of the in situ stress, linear equations made up of shear stresses on the bolts are established, from which the distribution of shear stresses and axial forces along the bolts can be solved. Model simulations confirm the previous findings that each installed bolt has a pick-up length, an anchor length and a neutral point. Besides, the influence of the parameters of the rock bolts and the surrounding rock are discussed. The conclusion is consistent with the results of a practical project without adopting any empirical equations. The results of this method can provide a theoretical basis for the design and layout of rock bolts in underground caverns.

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“…Guan et al [6] and Liu et al [7,8] studied horseshoe-shaped tunnels and compared analytical solutions with FLAC3D and ANSYS numerical results, respectively. For a lined straight wall arch tunnel, Kargar et al [9,10] and Lu et al [11] provided analytical solutions for stress according to the different contact condition between lining and surrounding rock; Lu et al [12] gave analytic solutions for stress and displacement considering support delay. Li and Chen [13] and Liu et al [14] obtained the analytical solutions for stress and displacement of lined horseshoe-shaped tunnels in isotropic and orthotropic surrounding rock, respectively.…”

Section: Introductionmentioning

confidence: 99%

Elastic Stress and Plastic Zone Distributions around a Deeply Buried Tunnel under the Nonhydrostatic Pressure

Liu

Fan

et al. 2022

Geofluids

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The elastic stress and the plastic zone are the important mechanical parameters to determine the tunnel support design. Based on Muskhelishvili’s complex variable function, the analytical solution for the elastic stress around a deeply buried noncircular tunnel under the nonhydrostatic pressure is firstly derived. The shape and size of the plastic zone of the surrounding rock mass are then determined by substituting the elastic stresses into the Drucker-Prager yield criterion. Finally, taking a horseshoe-shaped tunnel as an example, the analytical solutions of elastic stress distribution and plastic zone shape around the tunnel under different lateral pressure coefficients are in good agreement with ANSYS numerical solutions. The calculation results show that if the vertical in situ stress exceeds the critical value, with increasing lateral pressure coefficient, the hoop stress at the roof and floor of the tunnel increases significantly and the shape and size of the plastic zone change obviously.

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Analytical solutions for the stress of a lined non-circular tunnel under full-slip contact conditions

Cited by 55 publications

References 10 publications

Analytical Solution of the Grouting Reinforcement Response of a Circular Cavern in Deeply Buried Fractured Surrounding Rock under a Nonuniform Stress Field

Analytical Solution of the Grouting Reinforcement Response of a Circular Cavern in Deeply Buried Fractured Surrounding Rock under a Nonuniform Stress Field

A theoretical method of mechanical analysis for a circular tunnel reinforced by fully grouted rock bolts

Elastic Stress and Plastic Zone Distributions around a Deeply Buried Tunnel under the Nonhydrostatic Pressure

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