Stress Analysis of Infinite Plate with Elliptical Hole

Soni, Sandeep; Saindane, Udaykumar V.

doi:10.1007/978-981-13-6469-3_50

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…σ hmin = 0.8 + 0.0329H (28) where σ v is the vertical stress, σ hmax and σ hmin are the maximum and minimum horizontal stresses, H is the burial depth, respectively. The initial ground stresses at burial depths of 500 m, 650 m, and 800 m are listed in Table 2.…”

Section: Test Materials and Methodsmentioning

confidence: 99%

“…It has been reported that spalling failure mostly occurs in the direction parallel to the maximum principal stress [20][21][22], by analyzing the surrounding rock stress when the tunnel spalling or rockburst occurs, these underground disasters can be further guided and controlled. Stress analysis of the surrounding rock of tunnels containing holes has been systematically studied by scholars [24][25][26][27][28][29][30]. For example, in terms of arch tunnels, Wu et al [31] analyzed the shape and size effect caused by the variation of geometric parameters of straight-walled three-centered arch tunnels on the surrounding rock stresses based on the analytical solutions obtained from the conformal mapping.…”

Section: Introductionmentioning

confidence: 99%

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Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel

Peng

Luo

et al. 2023

Applied Sciences

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To study the stress distribution characteristics of surrounding rock and the spalling mechanism of deep hard rock tunnels with different arch heights, the complex variable function and angle-preserving transformation method in elasticity theory were applied to the analytic solution of tangential stress distribution of arch tunnels during stress adjustment. In addition, true triaxial tests were conducted on granite cube specimens (100 mm × 100 mm × 100 mm) containing holes with three arch heights (including the 25 mm semi-circular arch, 16.7 mm three-centered arch, 12.5 mm three-centered arch) to simulate the spalling process under different initial ground stresses. The stress distribution solution and experimental results show that the initial failure stress of arch holes is 0.39–0.48 times the uniaxial compressive strength (UCS) of the rock. The initial failure location occurs at the arch foot, where tangential stress maximizes. When the lateral pressure coefficient is in the range of 0.38–0.50, the tangential stress is 3.2–3.5 times the UCS. The rock debris of the hole wall are in thin flake shapes. Symmetrical V-shaped or curved failure zones occurred on hole sidewalls. The stress distribution resolution of the surrounding rock of tunnels with different arch heights shows that with the increasing burial depth, the bearing performance of the semi-circular arch tunnel is optimal. In addition, the maximum tangential stress increases as the height of the arch decreases or the lateral stress increases, making it easier for the initial failure to occur at the foot of the arch.

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Section: Test Materials and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel

Peng

Luo

et al. 2023

Applied Sciences

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“…Utilizing the Cauchy integral method, Chen [8] successfully mapped regions with complex boundary shapes to the unit circle domain to solve complex strain functions. SONI et al [9] proposed a methodology for calculating the stress around elliptical holes in isotropic plates.…”

Section: Introductionmentioning

confidence: 99%

Analytical expression of displacement of circular double tunnels in transversely isotropic rock mass in unstable rock zone of southwest mountainous area

Wei,

Zhang

2023

Preprint

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Due to the instability of the underground rock structure in the southwest mountain area, the influence of different pore shapes on the rock mechanics performance and fracture characteristics under uniaxial compression changes. The analysis and research on the displacement of double circular tunnels in layered rock mass lay an essential foundation for back-analyzing the displacement of anisotropic double caverns. Researchers can derive the displacement analytical solution for two circular tunnels in a transverse isotropy rock mass using the complex function and Schwarz alternating methods. This analytic solution can simplify the analytical solution of displacement within an isotropic rock mass and the displacement analytical solution for a single circular tunnel in a transversely isotropy rock mass. The solution demonstrates that even when the tunnel cross-section is presumed to be parallel to the isotropic plane during derivation, the displacement of the surrounding rock is influenced by the elastic modulus and the Poisson ratio in both the isotropic plane and the plane perpendicular to it. Hence, in the displacement back-analysis of two tunnels in transversely isotropic rock mass viewed in cross-section, it is necessary to determine six parameters that meet discernible conditions and use the corresponding sensitivity coefficients to invert the uniqueness of the parameters. By comparing the analytic solution with the numerical solution, it was found that the trends of both solutions were mainly consistent. Moreover, the error between the analytic and numerical solutions was relatively small within the 90 to 105 degrees data, which indicates that the analytical solution can effectively reflect the actual deformation pattern of circular tunnels. This finding is pivotal for back analysis of tunnel excavation displacement in layered rock masses.

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Stress Distribution and Mechanical Behaviour of Rock Mass Containing Two Openings Underground: Analytical and Numerical Studies

et al. 2021

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In this study, stress solution for rock mass containing two rectangular openings was calculated based on the Schwarz alternating method to investigate the stress distribution in rock mass around openings with different layouts. In addition, large-scale numerical models were further established for the two-opening system by means of the PFC-FLAC coupling method, in which the stress evolution, failure patterns, and acoustic emission (AE) events were presented. With the combination of analytical and numerical solutions, the interaction mechanism between two openings under different layouts was discussed from the perspective of stress and failure. The result shows that the confining stress within a certain range contributes to relieving tensile stress concentration around openings. The stress condition within the connecting area and coalescence pattern between two adjacent openings is dominated by their layout. Compared with small-size rock specimens in laboratory tests, the failure patterns around openings show a better agreement with the stress concentration characteristics determined by analytical stress solutions.

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Stress Analysis of Infinite Plate with Elliptical Hole

Cited by 4 publications

References 3 publications

Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel

Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel

Analytical expression of displacement of circular double tunnels in transversely isotropic rock mass in unstable rock zone of southwest mountainous area

Stress Distribution and Mechanical Behaviour of Rock Mass Containing Two Openings Underground: Analytical and Numerical Studies

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