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Time-dependent analysis of stress components around lined tunnels with circular configuration considering tunnel advancing rate effects

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INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES 2020年 133卷 104422-104422页

作者： Kargar, Ali Reza Haghgouei, Hadi Babanouri, Nima Univ Tehran Coll Engn Sch Min Engn Tehran Iran Hamedan Univ Technol Dept Min Engn Hamadan Hamadan Iran

An analytical solution is recommended in this paper for time-dependent stress analysis of lined tunnels with a circular shape, regarding tunnel advancing rate. In previous works, it was assumed that the tunnel is excavated under an infinite advancing rate such that the progressing rate effect was neglected, the assumption which is not always true. However, this barrier is removed in this paper. The non-hydrostatic stress field is assumed as initial stress within rock mass. The concrete lining, and surrounding mass are supposed as isotropic homogenous materials, following elastic and viscoelastic constitutive models, respectively. The Burgers model is assumed to dominate viscoelastic behavior. The solution benefits from time discretization for both tunnel advancing rate, and rock support interaction, along with employing complex variable method. The solution presents a good agreement with COMSOL finite element software simulation for different advancing rates. It is found that there exist the progressing rate and time limits, which for higher values, the problem could be solved assuming instantaneous excavation of the hole.

关键词： Lined circular tunnels Viscoelastic model complex variable method Tunnel advancing rate

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Analytical solution for an arbitrary-shaped tunnel with full-slip contact lining in anisotropic rock mass

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INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES 2020年 128卷 104276-104276页

作者： Wang, Shaojie Lu, Aizhong Tao, Junye Zeng, Xiangtai Yin, Chonglin North China Elect Power Univ Renewable Energy Sch Inst Hydroelect & Geotech Engn Beijing Peoples R China China Nucl Power Engn Co Ltd Shenzhen Guangdong Peoples R China Beijing Engn Co Ltd Powerchina Beijing Peoples R China Nanchang Univ Sch Civil Engn & Architecture Nanchang Jiangxi Peoples R China

Under the full-slip contact assumption along rock-lining interface, the analytical solution for an arbitrary-shaped lined tunnel that is excavated in anisotropic rock mass and supported by an isotropic lining is presented. The equations and solutions of stresses and displacements in lining and surrounding rock mass are introduced based on the complex variable method. The analytical solutions are validated by the boundary condition checks and compared with the numerical simulation. The results are in very high precision. With the analytical algorithm, the effects caused by the angle of rock layers and the anisotropic elastic modulus are investigated. By comparing with another important contact assumption, pure-bond contact condition, the analytical solutions on excavation boundary and two lining boundaries are discussed.

关键词： Arbitrary-shaped lined tunnel Anisotropic rock mass Full-slip contact condition complex variable method Power series method

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Fractional viscoelastic analytical solution for the ground displacement of a shallow tunnel based on a time-dependent unified displacement function

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COMPUTERS AND GEOTECHNICS 2020年 117卷 103284-000页

作者： Lu, Dechun Kong, Fanchao Du, Xiuli Shen, Chenpeng Su, Cancan Wang, Jun Beijing Univ Technol Key Lab Urban Secur & Disaster Engn Minist Educ Beijing 100124 Peoples R China Wenzhou Univ Key Lab Engn & Technol Soft Fdn & Tideland Reclam Wenzhou 325035 Zhejiang Peoples R China

A time-dependent unified displacement function expressed by a Fourier series is used as the displacement boundary condition of the tunnel cross-section (BCTC). Abel element expressed by the fractional differential is adopted to reflect the rheological behaviours of the surrounding rock. Using Laplace transform and the inverse transformation, the relaxation modulus of the Fractional Generalized Kelvin constitutive model for one-dimensional (1D) is obtained. The effects of the fractional order and viscous material parameters on the relaxation modulus are analysed. The correspondence principle and complex variable method are adopted to develop the elastic analytical solution into the fractional viscoelastic analytical solution of the ground displacement. Two factors are considered to capture the time effect of ground deformation: a time-dependent displacement BCTC and time-dependent mechanical parameters. A parameter study is conducted to investigate the time effect of the ground displacement. The deformation parameters of the tunnel cross-section are first calibrated by a part of the field data for the Longdong tunnel and Gaoqiao tunnel. Based on the calibrated model, the proposed method can well predict ground displacement due to the time effect.

关键词： Fractional Generalized Kelvin constitutive model Time-dependent unified displacement function complex variable method Fractional viscoelastie analytical solution Analyses of the time effect of ground displacement field

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Stress field around rectangular hole in functionally graded plate

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2018年 136卷 360-370页

作者： Dave, Jatin M. Sharma, Dharmendra S. Nirma Univ Inst Technol Mech Engn Dept Ahmadabad Gujarat India Maharaja Sayajirao Univ Baroda Fac Engn & Technol Vadodara India

In this paper, functionally graded plate having rectangular cut-out/hole at the center is considered. The plate thickness is discretized into large number of thin orthotropic lamina such that continuous variation/gradation of moduli of elasticity and Poisson's ratio along the thickness can be obtained. The power law is used to have linear, quadratic and cubic gradation of these material properties. Using complex variable method, the stress functions are obtained for stress and moment resultants for rectangular hole. The influence of parameters like moduli of elasticity and Poisson's ratio, variation of these material properties, shape of the hole and applied loading on the orientation of material axes and stress field around the hole is presented. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Rectangular hole Functionally graded plate complex variable method Through thickness variation Stresses and moments around hole

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The stress state around an elliptical borehole in anisotropy medium

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2018年 166卷 313-323页

作者： Qi, Dexuan Li, Lijuan Jiao, Yongshu Hebei Univ Technol Sch Mech Engn Tianjin 300401 Peoples R China CNHTC Jinan Truck Co Ltd Dept Technol Jinan Shandong Peoples R China

Under the assumption of generalized plane strain condition, this paper presents an analytical solution for stresses near an inclined elliptical wellbore drilled in anisotropic formation based on the linear theory of anisotropic elasticity and complex variable method. The solution is suitable for calculating the stresses around an elliptical borehole drilled with any inclination and orientation angles in a linear elastic, continuous, homogeneous and general anisotropic medium. The solution for the stresses can also show the effects of the liquid pressure exerted by drilling mud, the ratio and the direction of the in-situ stresses. For engineering utilization the transformation of compliance matrix for the transversely isotropic medium is formulated. An example is calculated and shown by contours of stress components around an inclined elliptical wellbore in a transversely isotropic formation. The stress contours can be utilized to some extent to predict the location, the range, the depth and even the outlines of fractured or collapsed well wall. Then a range of parametric analysis is carried out on the impacts of borehole inclination, orientation and ellipticity on the first principal stress and maximum shearing stress. The results indicate that for various boreholes with different degree of formation anisotropy the algebraic values of the first principal stress and maximum shearing stress go down gradually with the increase of borehole inclination, and these two stresses vary in the pattern of half a sinusoidal wave with the variation of orientation angles. Furthermore, the stresses go up with the increase of ellipticity. The solution presented in this paper might supply a more realistic technique for assessing the stability of borehole and optimizing the well path in anisotropic medium.

关键词： Borehole stability Elliptical borehole Stress state Anisotropic elasticity complex variable method Analytical solution

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UNIFORM STRESS RESULTANTS INSIDE TWO NONELLIPTICAL INHOMOGENEITIES IN ISOTROPIC LAMINATED PLATES

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JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES 2018年第4期13卷 531-541页

作者： Wang, Xu Chen, Liang Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn Shanghai Peoples R China Univ Alberta Dept Mech Engn Edmonton AB Canada

We use complex variable methods to establish two sets of specific conditions which ensure the existence of uniform and hydrostatic internal membrane stress resultants and bending moments inside two through-thickness nonelliptical elastic inhomogeneities embedded in an infinite isotropic laminated Kirchhoff plate subjected to uniform remote membrane stress resultants and bending moments. These conditions can be interpreted as restrictions on the remote membrane stress resultants and bending moments for the given material and geometric parameters. We show that when these conditions are met, explicit expressions are available for the uniform stress resultants inside the two inhomogeneities and the constant hoop stress resultants on the matrix side along the two interfaces.

关键词： isotropic laminated plate uniform stress resultants complex variable method conformal mapping

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Closed-Form Solution for the Stresses in Brazilian Disc Tests Under Vertical Uniform Loads

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ROCK MECHANICS AND ROCK ENGINEERING 2018年第11期51卷 3489-3503页

作者： Lu, Aizhong Wang, Shaojie Cai, Hui North China Elect Power Univ Inst Hydroelect & Geotech Engn Renewable Energy Sch 2 Beinong Rd Beijing 102206 Peoples R China

Loading arcs, which create a definite contact range and have a radius equal to the test specimen, have been recently introduced into Brazilian disc tests, which are common indirect tensile strength tests. Inspired by the testing apparatus, a new kind of loading pattern acting on the disc is assumed: the vertical uniform load. This load can be resolved into radial and tangential surface forces on the loaded rims of the specimen. Under the assumptions of isotropic, linear-elastic, and homogenous disc materials, the explicit closed-form expressions for the full-field stresses in the disc are derived by the complex variable method. The analytical solutions satisfy the stress boundary condition, and the analytical results are in good agreement with the numerical simulations. Based on the closed-form solutions, it is analytically proven that the maximum tensile stress occurs at the disc center. Then, the suggested formula for the tensile strength, which is related to the contact range, the external load, and the size of specimen, is provided.

关键词： Brazilian disc test Loading arcs Vertical uniform load Closed-form stress expressions complex variable method

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Analytical solution for the electric field in Hall plates

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2018年第4期69卷 1-7页

作者： Homentcovschi, Dorel Bercia, Romeo SUNY Binghamton Binghamton NY USA Univ Politehn Bucuresti Dept Appl Math Bucharest 060042 Romania

The paper provides a closed-form expression (the General Formula) for the electric field in a Hall plate. The parameters entering in this formula are the images of the contacts extremities in the conformal map into the upper half-plane (canonical domain) and also a number of real unknown constants equal to the number of contacts. The paper gives also formulas for computing the voltages and currents at contacts of the Hall plate. Since the unknown constants are connected in a linear manner with the terminal voltages and the currents, the General Formula can be used for modeling a large variety of Hall devices. Finally, the explicit calculations require the quadrature of some analytic functions having integrable singularities.

关键词： complex variable method Boundary-value problem in the complex half-plane Closed-form solution Hall plates

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Effect of uniform heat flux on stress distribution around a triangular hole in anisotropic infinite plates

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JOURNAL OF THERMAL STRESSES 2018年第6期41卷 726-747页

作者： Jafari, Mohammad Jafari, Mohammad Shahrood Univ Technol Dept Mech Engn Shahrood Iran

The presence of a hole in an anisotropic plate under uniform heat flux causes thermal stress around the hole. In this study, on the basis of two-dimensional thermoelastic theory and using Lekhnitskii's complex variable technique, the stress analysis of an anisotropic infinite plate with a circular hole under a uniform heat flux is developed to the plate containing a triangular hole. For this purpose, an infinite plate containing a triangular hole is mapped to the outside of a unit circle using a conformal mapping function. Stress and displacement distributions around the triangular holes in an anisotropic infinite plate are investigated in thermal steady-state condition. The plate is under uniform heat flux at infinity and Neumann boundary conditions and thermal-insulated condition on the hole boundary are considered. The rotation angle of the hole, fiber angle, the angle of heat flux, bluntness, and the aspect ratio of hole size are investigated in the present study. The accuracy of the analytical results is also confirmed by finite element analysis.

关键词： complex variable method conformal mapping function infinite anisotropic plate triangular hole

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Electro-elastic fields in an elliptic piezoelectric plane with an elliptic hole or a crack of arbitrary location

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MECCANICA 2018年第1-2期53卷 347-357页

作者： Li, Min Gao, Cun-Fa Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Jiangsu Peoples R China

Electro-elastic fields in an elliptic piezoelectric plane with an elliptic hole or a crack of arbitrary location are studied based on the complex variable method and the assumption that the elliptic hole or the crack is impermeable to an electric field. The novel feature of the present work is to construct the complex potentials in a finite piezoelectric body with Faber series containing unknown coefficients. Using the given boundary conditions, the coefficients can be solved, and then the electro-elastic fields in the plane can be calculated. Finally, numerical examples are given for the electro-elastic fields in the plane and the electro-elastic intensity factors at the crack tips when the hole degenerates into a crack. It is found that the sizes of the elliptic plane and the elliptic hole (or the crack) have a great influence on electro-elastic fields (or the intensity factors of the crack).

关键词： Finite piezoelectric body Electromechanical coupling complex variable method Crack Arbitrary location

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