| Zhengzhou Institute of Multipurpose Utilization of Mineral Resources, Chinese Academy of Geological Sciences | Host |
| Citation: |
ZHAO Wenhuan, LONG Gan, LI Jinhua. Analysis of Stress Distribution Law of Surrounding Rock of Rectangular Roadway with Different Specifications Based on Complex Variable Function[J]. Conservation and Utilization of Mineral Resources, 2024, 44(4): 111-123. doi: 10.13779/j.cnki.issn1001-0076.2024.04.013
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Analysis of Stress Distribution Law of Surrounding Rock of Rectangular Roadway with Different Specifications Based on Complex Variable Function
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Abstract
Given the widespread use of rectangular tunnels, in order to deeply analyze the degree and pattern of the influence of factors such as the size and lateral pressure coefficient of rectangular tunnels on the stress of the surrounding rock of the tunnels. This article regards the solution of the surrounding rock of a rectangular roadway as an elastic mechanics orifice problem, and uses the theory of complex variables and Schwartz Chistoffel mapping function, combined with conformal transformation for analysis ζ Complex plane unit circle ζ Analysis function of φ0(ζ)、ψ0(ζ), After expanding the Laurent series, obtain the complex potential function φ(ζ)、ψ(ζ). After further deduction, the analytical solution for the circumferential stress of the surrounding rock of the rectangular tunnel was finally determined. Based on this, the polar coordinate expression of the circumferential stress was used to deeply analyze the stress variation law and degree of influence of the surrounding rock of the rectangular tunnel under the changes in the size and lateral pressure coefficient of the rectangular tunnel. The results showed that taking the first three calculations of the mapping function, the mapping roadway section had approached the theoretical section, which could ensure the accuracy requirements; with the increase of the width−height ratio of the roadway, the peak stress around the surrounding rock of the roadway increased first and then decreased with the width−height ratio of 1 as the dividing point. The stress of surrounding rock of roadway side decreased with the increase of width−height ratio, and the stress of surrounding rock of roadway roof and floor increased with the increase of width−height ratio. The larger the lateral pressure coefficient was, the larger the peak stress of the surrounding rock was, and the smaller the peak stress of the roof and floor was. The stress of side wall surrounding rock increased with the increase of lateral pressure, and the two were positively correlated. The stress of roof and floor decreased with the increase of lateral pressure, and the two were negatively correlated.
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References
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ZHAO Wenhuan, LONG Gan, LI Jinhua. Analysis of Stress Distribution Law of Surrounding Rock of Rectangular Roadway with Different Specifications Based on Complex Variable Function[J]. Conservation and Utilization of Mineral Resources, 2024, 44(4): 111-123. doi: 10.13779/j.cnki.issn1001-0076.2024.04.013
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Figure 1.
Mechanical model for stress analysis of rectangular tunnels
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Figure 2.
Z−plane rectangle to ζ map of unit circle in complex plane
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Figure 3.
Conformal mapping to rectangular roadway contour under rectangular coordinates at different aspect ratios
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Figure 4.
Circumferential stress distribution of surrounding rock with different w values in polar coordinates when λ = 0.8
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Figure 5.
Stress distribution map of surrounding rock under different aspect ratios (a—lateral pressure coefficient of 0.6; b—lateral pressure coefficient of 1.0; c—lateral pressure coefficient of 1.4; d—lateral pressure coefficient of 1.8; e—lateral pressure coefficient of 2.2)
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Figure 6.
Circumferential stress distribution of surrounding rock with different λ values in polar coordinates when w = 1.0
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Figure 7.
Stress distribution map of surrounding rock under different lateral pressure coefficients (a—aspect ratio of 0.6; b—aspect ratio of 1.0; c—aspect ratio of 1.4; d—aspect ratio of 1.8; e—aspect ratio of 2.2)
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Figure 8.
Variation law of the maximum stress concentration coefficient Kc with lateral pressure coefficient(a) and aspect ratio(b)
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Figure 9.
Numerical calculation model
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Figure 10.
Stress cloud maps under different lateral pressure coefficients when the aspect ratio of 1 (a—lateral pressure coefficient is 0.8; b—lateral pressure coefficient is 1.0); c—side pressure coefficient is 1.4)
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Figure 11.
Stress cloud maps under different aspect ratios with a lateral pressure coefficient of 1 (a—aspect ratio of 0.6; b—aspect ratio of 1.0); c—aspect ratio of 1.4)