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Plastic zone characteristics and rapid stability evaluation indexes of circular tunnels subjected to non-hydrostatic stress: A novel complex variable solution incorporating 3D rock mass strength

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TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY 2024年 151卷

作者： Ma, Yaocai Cai, Wuqiang Zhu, Hehua Su, Chenlong Wei, Xiangyang Tongji Univ Coll Civil Engn Dept Geotech Engn Shanghai 200092 Peoples R China Tongji Univ State Key Lab Disaster Reduct Civil Engn Shanghai 200092 Peoples R China Chinese Acad Sci Inst Rock & Soil Mech State Key Lab Geomech & Geotech Engn Beijing Peoples R China

The morphological characteristics and distribution range of the plastic zone around tunnels, influenced by the true three-dimensional high geostress environment in deep engineering, constitute fundamental reference data for both tunnel design and the control of surrounding rock stability. Based on the GZZ three-dimensional rock mass strength criteria and the complex variable method, a novel semi-analytical method for solving the plastic zone of a circular tunnel subjected to non-hydrostatic stress is presented. The conformal mapping is employed to intricately transform the complex boundaries of plastic zones characterized by diverse shapes onto the unit circle boundary within the image plane. This framework proves invaluable for the precise analytical process of the complex plastic zone morphology and the plastic influence range within the surrounding rock under complex stress conditions. In contrast to traditional analytical methods, the efficacy and versatility of our proposed approach are substantiated. Notably, it demonstrates unique advantages, particularly in the context of nonhydrostatic stress fields and varied rock mass parameters, with respect to predicting both surrounding rock stability and plastic zone morphology. Through the analysis of numerous cases, the study reveals the systematic patterns of influence that in-situ stress and surrounding rock characteristic parameters have on the shape and maximum depth of the plastic zone. The results indicate that (1) there are notable disparities in the morphology and extent of the plastic zone between the GZZ and GHB criteria;(2) the transition of the plastic zone in surrounding rock from U-shaped to V-shaped is significantly influenced by the geostress-to-strength ratio K sigma;(3) there is a notable linear correlation observed between the maximum plastic zone thickness rmax and both K sigma and the stress concentration factor KSCF, importantly, this correlation is independent of far-field stress and the britt

关键词： Deep tunnel Non-hydrostatic stress Localized failure Plastic zone characteristics complex variable method

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Elliptic Rigid Inclusion in Soft Materials of Harmonic Type

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JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 2024年第7期91卷 071004-071004页

作者： Miao, Kui Dai, Ming Gao, Cun-Fa Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Aerosp Struct Nanjing 210016 Peoples R China

We investigate finite plane deformations of an elliptic rigid inclusion embedded in a soft matrix that is made of a particular class of harmonic-type hyperelastic materials. The inclusion is assumed to be perfectly bonded to the matrix, which is subjected to a constant remote in-plane loading. Utilizing the Cauchy integral techniques associated with conformal mappings, we derive closed-form solutions for the full-field deformation, Piola stress, and Cauchy stress in the entire matrix. Numerical examples are presented to illustrate the current solutions in comparison with those established from linear elasticity theory. We find that in terms of the Cauchy stress around the inclusion, the maximum normal stress component always appears at the endpoints of the major axis of the inclusion, irrespective of the magnitude of the remote loading, while the maximum hoop stress component occurs not exactly at the above-mentioned endpoints when the remote loading exceeds a certain value. In particular, we identify an exact explicit formula for determining the relative rotation of the inclusion during deformation induced by a remote uniaxial loading of arbitrarily given magnitude and direction.

关键词： finite deformation harmonic material rigid inclusion complex variable method mechanical properties of materials stress analysis

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Discussion on the conformal mapping of a half-plane onto a unit disk in anisotropic elasticity and related applications

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MATHEMATICS AND MECHANICS OF SOLIDS 2021年第1期26卷 110-117页

作者： Dai, Ming Hua, Jian Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China

The conformal mapping, which transforms a half-plane into a unit disk, has been used widely in studies involving an isotropic elastic half-plane under anti-plane shear or plane deformation. However, very little attention has been paid to the possibility of utilizing this mapping in the study of an anisotropic elastic half-plane under the same deformation. In this paper, we discuss a general case of an arbitrarily located anisotropic elastic half-plane that corresponds to several affine counterparts (resulting from corresponding complex variable formalism). We show that this mapping is indeed applicable to each of the affine half-planes if and only if the key parameters in the mapping satisfy simple geometrical conditions. In addition, we introduce the application of this mapping with the corresponding geometrical conditions to the related study of anisotropic thin films under two-dimensional deformation.

关键词： Half-plane conformal mapping anisotropic material thin film complex variable method

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Semi-analytical solution for stress and displacement of lined circular tunnel at shallow depths

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APPLIED MATHEMATICAL MODELLING 2021年 100卷 263-281页

作者： Cai, Hui Lu, Ai-zhong Ma, Yao-cai Yin, Chong-lin North China Elect Power Univ Renewable Energy Sch Inst Hydroelect & Geotech Engn 2 Beinong Rd Beijing 102206 Peoples R China

In this study, a new approach is presented to determine the stress and displacement field of a shallow buried circular tunnel subject to gravity and arbitrary lateral stress based on the complex variable method. The soil mass and lining are conformally mapped onto two ring regions. A more effective method than the power series method is used to solve the undetermined coefficients of complex potential functions. The interaction mechanism between the lining and the soil mass is fully considered. The boundary conditions along the inner boundary of the lining and the ground surface and the stress and displacement continuity conditions along the excavation line are used in the analytical derivation. In the verification, the stress and displacement distributions obtained in the semi-analytical solution agree with the numerical results and satisfy the boundary and continuity condi-tions. Using examples, the stress distributions along the inner boundary of the lining and interface are presented to examine the influence of key parameters including the Young's modulus and buried depth. The effect of the lining in reducing stress concentration and restricting tunnel convergence is quantitatively analyzed. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Shallow buried tunnel Lining complex variable method Stress and displacement

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A complex variable solution for a non-circular tunnel in an elastic half-plane

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL methodS IN GEOMECHANICS 2021年第12期45卷 1833-1853页

作者： Lu, Ai-zhong Zeng, Gui-sen Zhang, Ning North China Elect Power Univ Inst Hydroelect & Geotech Engn 2 Beinong Rd Huilongguan Beijing 102206 Peoples R China Guizhou Power Grid Co Ltd Elect Res Inst Guiyang Guizhou Peoples R China

An analytical solution for a non-circular tunnel excavated in an elastic homogeneous half-plane is obtained, which considers gravity and different lateral pressure coefficients. The solution is deduced using the complex variable method, mapping the region containing a non-circular tunnel onto a circular ring. The basic equations for the analytic functions are established using the stress boundary conditions at the ground surface and the edges of the tunnel and the analytical functions are solved by the power series method. In the process of solving, the Fourier series was used. To elaborate the solution process clearly and verify the correctness of the solution, a shallow quasi-ellipse tunnel was analyzed as a computational example, and the results obtained using the presented analytical method are compared with that obtained by the numerical software ANSYS.

关键词： analytical solution complex variable method conformal transformation half‐ plane non‐ circular tunnel

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A modified Laurent series for hole/inclusion problems in plane elasticity

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2021年第3期72卷 1-10页

作者： Li, Chao Huang, Cheng Wang, Shuang Cai, Deng'an Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China Nanjing Fiberglass Res & Design Inst Nanjing 210012 Peoples R China Changzhou Inst Technol Sch Aviat & Mech Engn Changzhou 213032 Peoples R China Peking Univ Coll Engn Dept Mech & Engn Sci BIC ESATState Key Lab Turbulence & Complex Syst Beijing 100871 Peoples R China

We propose a modified Laurent series for investigating the elastic field around holes/inclusions under plane deformation by dividing the classical Laurent series over the first derivative of the conformal mapping, which is justified from a mathematical point of view. Through a group of numerical examples concerning the stress concentration around holes of common shapes, the accuracy of the modified Laurent series is verified. It is also demonstrated that the use of the modified Laurent series as compared with the classical one generally leads to significantly more accurate results with even much fewer terms of the series. Utilizing the modified Laurent series, we revisit the stress field around an irregularly shaped elastic inclusion embedded in an infinite matrix and effectively eliminate the severe interfacial stress fluctuation reported earlier in the literature. More importantly, the modified Laurent series may be very useful for a highly accurate prediction of the physical field in particulate composites with densely packed inclusions.

关键词： Plane elasticity complex variable method Laurent series Convergence speed Stress fluctuation

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Effects of bi-stable grounded nonlinear energy sink on energy dissipation of the system

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART K-JOURNAL OF MULTI-BODY DYNAMICS 2021年第4期235卷 668-682页

作者： Khalatbari, Arash Jalali, Amir Ahmadi, Habib Foroutan, Kamran Shahrood Univ Technol Dept Mech & Mechatron Engn Shahrood Iran Ryerson Univ Dept Mech & Ind Engn Toronto ON Canada Politecn Torino Dept Mech & Aerosp Engn MUL2 Grp Turin Italy

In this paper, one of the most efficient passive absorbers, called nonlinear energy sink (NES), is analytically studied. A two-degree-of-freedom system is considered which consists of a linear oscillator (LO) with a base excitation and an NES, called grounded NES (GNES), which is connected to the ground with a nonlinear spring. In this study, we proposed a new arrangement of potential elements in GNES and studied invariant manifolds of the system, as well as the energy absorption performance of the NES. The system is considered in the vicinity of 1:1 resonance to investigate the strongly modulated response (SMR). To this end, after obtaining the equations of motion, the Manevitch complex variable and multiple scale method are applied to solve the equations, analytically. Then, the slow invariant manifold (SIM) is obtained. Also, the energy dissipation ratio of the NES and the percentage of the instantaneous total energy stored in the NES are calculated via the time-amplitude diagram. The results show that when the nonlinear effect decreases, the occurrence of energy pumping is less probable. Also, when the excitation amplitude decreases, the percentage of the instantaneous total energy stored in the NES increases as well as the amount of energy dissipation.

关键词： Nonlinear energy sinks strongly modulated response slow invariant manifold complex variable method energy dissipation ratio instantaneous total energy stored in the NES

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Analytical model for measurement of stresses using two-hole drilling

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INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2023年第1期206卷

作者： Liu, Huan Han, Dayong Deng, Lu Cao, Ran Hunan Univ Coll Civil Engn Changsha 410082 Hunan Peoples R China Powerchina Rd Bridge Grp Co Ltd Zhongshan 528403 Peoples R China Hunan Univ Hunan Prov Key Lab Damage Diag Engn Struct Changsha 410082 Hunan Peoples R China

Residual stresses have a significant effect on the strength, deformation, plasticity, and fatigue properties of materials. In general, tensile residual stresses are adverse to material performance and component life, while compressive residual stresses can improve material fatigue strength. In this study, an analytical model employing two-hole drilling (THD) is proposed for the measurement of interior stresses. Firstly, the analytical solution for the distortion of the reference hole induced by drilling an adjacent hole is derived using the complex variable method. Based on the analytical solution, the reverse procedure is established to determine the original stress state. Then, the comparative validations of the THD method with the deep hole drilling (DHD) method are performed in conjunction with the finite element (FE) simulations for the beam subjected to bending, the unloaded elastoplastic beam, and the shrink fitted assembly. Finally, parametric analysis is conducted and the results show that: the influence of drilling an adjacent hole on the reference hole rises with the increase of the hole diameters or the decrease of the hole spacing;the THD method is able to give good estimations for the stresses with linear, parabolic, and sinusoidal distributions, although the accuracy is reduced for the prediction of the longitudinal residual stress in the cold-formed section;the uncertainties in evaluated stresses ascend linearly with the increase of the measurement error in the diameter of the reference hole. Relative to the DHD method, the THD method has the merits of less damage and less equipment required and can provide an effective approach for the measurement of stresses inside materials.

关键词： Analytical model Stress measurement Hole drilling complex variable method Strain relief

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A novel complex variable solution for the stress and displacement fields around a shallow non-circular tunnel

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COMPUTERS AND GEOTECHNICS 2023年 164卷

作者： Ye, Zi Kun Ai, Zhi Yong Tongji Univ Dept Geotech Engn Minist Educ Key Lab Geotech & Underground Engn Shanghai Peoples R China

A novel complex variable solution is derived in this paper for the stress and displacement fields around a shallow non-circular tunnel. The proposed method allows explicit computations in matrix form and has advantages of considerable efficiency and high accuracy. Firstly, the stress and displacement boundary conditions for the shallow non-circular tunnel are obtained using the generalized complex variable theory and conformal mapping technique. Then, the fast Fourier transform algorithm is employed to effectively perform the Fourier series fitting for these boundary conditions, and matrix equations for the potential functions in the frequency domain are established. Later, a matrix solution for the potential functions is formulated to determine the stress and displacement fields around the shallow non-circular tunnel. Finally, select numerical analyses are conducted to verify the proposed method, discuss the key parameters in the algorithm, and reveal the effect of the acceleration strategy using FFT as well as the effect of non-circular geometries on the stress and displacement fields.

关键词： complex variable method Shallow non-circular tunnel Matrix form solution Fourier series fitting Stress and displacement fields

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Influence of fiber hollowness on the local thermo-electro-elastic field in a thermoelectric composite

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FRONTIERS IN ENERGY RESEARCH 2023年 11卷

作者： Yu, Chuanbin Liu, Haoxin Du, Chaofan Xing, Shichao Yangzhou Univ Coll Architectural Sci & Engn Yangzhou Jiangsu Peoples R China Tongling Univ Sch Mech Engn Tongling Anhui Peoples R China Tongling Univ Key Lab Construct Hydraul Robots Anhui Higher Educ Inst Tongling Anhui Peoples R China Tongling Univ Key Lab Addit Mfg Tongling City Tongling Anhui Peoples R China

The fiber geometry is one of the important parameters in the effective conversion performance and local strength of thermoelectric composites. In this study, the plane problem of a hollow fiber embedded within a non-linear thermoelectric medium in the presence of a uniform remote in-plane electric current and a uniform remote energy flux is investigated based on the complex variable method. Closed-form expressions for all the potential functions characterizing the thermoelectric field and the associated thermal stress field in both the matrix and fiber are obtained by solving the corresponding boundary value problem. Numerical examples are presented to illustrate the effect of hollowness ratio of the fiber on the local energy conversion efficiency and interfacial thermal stress concentration. It is found that a higher conversion efficiency and a lower amount of thermal stress concentration around a hollow fiber than that around a solid fiber could be achieved simultaneously by appropriate selection of the hollowness ratio of the fiber. The results can be directly used for performance optimization and reliability evaluation in design of thermoelectric composites in engineering.

关键词： thermoelectric materials complex variable method hollow fiber conversion efficiency thermal stress

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