Analytic Method of Stress Analysis for an Orthotropic Rock Mass with an Arbitrary-Shaped Tunnel

Lu, Aizhong; Zhang, Ning; Zhang, Xiaoli; Lu, Donghai; Li, Weisheng

doi:10.1061/(asce)gm.1943-5622.0000408

Cited by 31 publications

(18 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Transversely Isotropic Rocks. In anisotropic elastic mechanics, the cross section no longer remains flat after deformation due to the presence of positive shear and shear coupling [29]. To solve this problem, three mapping functions z � ω(ζ), z 1 � ω 1 (ζ 1 ), and z 2 � ω 2 (ζ 2 ) are introduced to transform the outer regions of the circular hole in the z-, z 1 -, and z 2 -planes into the outer regions of the unit circle in the ζ-, ζ 1 -, and ζ 2 -planes, respectively.…”

Section: Mapping Function For the Elastic Mechanic Analysis Ofmentioning

confidence: 99%

See 1 more Smart Citation

An Analytical Solution for the Frost Heaving Force considering the Freeze‐Thaw Damage and Transversely Isotropic Characteristics of the Surrounding Rock in Cold‐Region Tunnels

Zhang

et al. 2020

Advances in Civil Engineering

View full text Add to dashboard Cite

Frost damage is a frequent occurrence in cold regions and can threaten the normal use and structural stability of tunnel engineering projects. To accurately determine the frost heaving force and effectively evaluate the frost damage in cold-region tunnels, an analytical solution for the frost heaving force considering the freeze-thaw (F-T) damage and transversely isotropic characteristics of surrounding rock is presented based on complex variable theory and the power series method. The calculation results indicate that the frost heaving force acts on the lining considering that the transversely isotropic characteristics of surrounding rock are significantly greater than those when assuming the surrounding rock is homogeneous isotropic media. This demonstrates that the transversely isotropic characteristics of surrounding rock have a considerable impact on the frost heaving force and should be considered. The frost heaving force continuously increases as the bedding angle increases from 0° to 90°, and the maximum frost heaving force in the Guanjiao tunnel (the rock mass bedding angle is 30°) of the Xining-Geermu Railway in China is approximately 1.04 MPa. In addition, the influence of F-T cycles on the frost heaving force in cold-region tunnels is investigated based on the analytical solution of the frost heaving force proposed in this paper. The frost heaving force acting on the lining decreases with an increasing number of F-T cycles due to the deterioration of the mechanical parameters of the surrounding rock.

show abstract

Section: Mapping Function For the Elastic Mechanic Analysis Ofmentioning

confidence: 99%

“…where ω(ζ) is an analytical function of ζ. However, its conjugate, ω(ζ), is not an analytical function of ζ [29].…”

Section: Mapping Function For the Elastic Mechanic Analysis Ofmentioning

confidence: 99%

An Analytical Solution for the Frost Heaving Force considering the Freeze‐Thaw Damage and Transversely Isotropic Characteristics of the Surrounding Rock in Cold‐Region Tunnels

Zhang

et al. 2020

Advances in Civil Engineering

View full text Add to dashboard Cite

show abstract

“…(2.6) can then be obtained. The three mapping functions are expressed by z = ω(ζ), z 1 = ω 1 (ζ 1 ) and z 2 = ω 2 (ζ 2 ), respectively (Lu et al, 2015)…”

Section: The Affine Transformation and Mappingmentioning

confidence: 99%

“…(2.13)-(2.15) by using the power-series method. Then, the stress components σ x , σ y and τ xy in the Cartesian coordinates can be determined by the following equations (Lu et al, 2015)…”

Section: Calculation Of the Analytical Solution Of Stressmentioning

confidence: 99%

“…Lekhnitskii (1968Lekhnitskii ( , 1981 used the complex function method, developed by Muskhelishvili (1963), to determine the stress in an anisotropic plate, and gave an accurate solution of stress around an elliptic hole under in-plane loading at infinity. Some researchers have obtained analytical solutions for other non-elliptic holes (Romeo, Lu et al (2015) found an accurate analytic solution of stress for plates with an arbitrarily shaped hole using the power-series method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimum design of fiber angle and hole orientation of an orthotropic plate

Zhang

Wang

et al. 2018

jtam

Self Cite

View full text Add to dashboard Cite

With the goal of decreasing the stress concentration along the hole boundary in an orthotropic plate under inequi-biaxial loadings, an optimum design of the fiber angle and hole orientation is presented. The maximum absolute tangential stress along the hole boundary is taken as the objective function, and the fiber orientation angle and the hole orientation angle are considered as design variables. The conformal transformation method of a complex function and the Differential Evolution (DE) algorithm are used. Two non-circular shapes, ellipse and hexagon are taken as examples to analyze the problem. Based on the results, we can conclude that the major axis of elliptical holes should be designed in the direction of the maximum external loading for a perforated structure in an orthotropic plate. However, the principal direction that has the larger Young's modulus should be inclined to the direction of the minimum loading, especially for a significantly orthotropic plate.

show abstract

Stress analysis of elliptical tunnels in an orthogonally anisotropic elastic full‐space under non‐uniform in‐situ stress

Ai,

Ye,

Huang

et al. 2023

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Non‐uniformly distributed in‐situ stress around the tunnel is a significant factor inducing various geohazards during tunnel excavation in the rock mass, and the anisotropy of the rock mass would further differentiate the in‐situ stress state around the tunnel. To ensure the safety of tunnel construction and operation, it is necessary to deeply analyze the stress distribution law and mechanical mechanism of the orthogonally anisotropic elastic media the around tunnel. This paper presents a complex variable function method for the elliptical tunnel in an orthogonally anisotropic elastic full‐space under non‐uniform in‐situ stress. To obtain the analytical solution, the affine transform and conformal mapping are applied to consider the orthogonal anisotropy of material and the ellipticity of the tunnel. A numerical series fitting method is introduced to describe the non‐uniformly distributed load, and then the stress solution around tunnel is further obtained. The comparisons with the existing literature, numerical solutions and model tests are provided to verify the correctness of the proposed method. Finally, the convergence study and the numerical analysis on the stress distribution are given graphically.

show abstract

Analytic Method of Stress Analysis for an Orthotropic Rock Mass with an Arbitrary-Shaped Tunnel

Cited by 31 publications

References 16 publications

An Analytical Solution for the Frost Heaving Force considering the Freeze‐Thaw Damage and Transversely Isotropic Characteristics of the Surrounding Rock in Cold‐Region Tunnels

An Analytical Solution for the Frost Heaving Force considering the Freeze‐Thaw Damage and Transversely Isotropic Characteristics of the Surrounding Rock in Cold‐Region Tunnels

Optimum design of fiber angle and hole orientation of an orthotropic plate

Stress analysis of elliptical tunnels in an orthogonally anisotropic elastic full‐space under non‐uniform in‐situ stress

Contact Info

Product

Resources

About