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complex variable solution of Interference Effect of Two Nearby Strip Footings on Layered Soil

INTERNATIONAL JOURNAL OF GEOMECHANICS 2023年第10期23卷 04023161-04023161页

作者： Sha, Xiangyu Lu, Aizhong Zhang, Ning North China Elect Power Univ Sch Water Resources & Hydropower Engn Beijing 102206 Peoples R China North China Elect Power Univ Sch Water Resources & Hydropower Engn Beijing 102206 Peoples R China

This study provides a solution for determining stress and displacement measurements of layered soil under the interaction of two adjacent strip footings by using conformal transformation methods (CTMs) in complex variable functions. Using the CTM, this research maps each layer of soil to a unit circle and calculates two single-valued analytic functions of each layer based on continuous conditions and boundary conditions to obtain the stress and displacement fields of the entire soil. The results were verified after being compared with the numerical solution of the Analysis Systems (ANSYS) finite-element software. In addition, this research uses two layers (as an example) to analyze influences of clear spacing of the footings and shear modulus of the soil on the interaction of two strip footings, as well as the influence of the center spacing of the footings and shear modulus of the bottom layer on differential settlements. The results indicate that an increase in the clear spacing of the footings and shear modulus of the soil sublayer greatly reduces the interaction between the two footings. Moreover, the differential settlement will increase with the center spacing, but will not vary with a changing shear modulus of the sublayer soil.

关键词： Layered soil Interaction of two footings complex variable solution Bedrock Differential settlement

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complex variable solution for Twin Tunneling-Induced Ground Movements Considering Nonuniform Convergence Pattern

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2020年第6期20卷

作者： Zhang, Zhiguo Huang, Maosong Zhang, Chengping Jiang, Kangming Wang, Zhiwei Xi, Xiaoguang Univ Shanghai Sci & Technol Sch Environm & Architecture 516 Jungong Rd Shanghai 200093 Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore Singapore Beijing Jiaotong Univ Minist Educ Key Lab Urban Underground Engn Beijing 100044 Peoples R China China Acad Railway Sci State Key Lab Track Technol High Speed Railway Beijing 100081 Peoples R China Tongji Univ Dept Geotech Engn Shanghai 200092 Peoples R China

The construction of twin tunnels in crowed urban cities requires tunnel excavations in close proximity to one another, in which the interaction between tunnels significantly affects the ground movements generated by tunneling. However, little information was provided for the effects of twin tunnels interaction on the ground movements during tunneling. In this paper, a new analytical approach is introduced to efficiently assess the ground surface settlements induced by twin tunneling in clay, with the nonuniform contraction deformation pattern richly considered at the tunnel opening boundary. Other than simply using linear superpositions of results of a single tunnel, special attention is paid in this literature to the interaction of twin tunnels in various configurations, on the basis of the complex variable theory and Schwartz alternating control method. The analytical presented solution is then verified by comparisons with a total of four centrifuge model tests and two engineering case records, together with the superposition of each single tunnel result. It is revealed that the presented complex variable solution considering the nonuniform contraction deformation model can provide a prediction of soil subsidence in good agreements with the experimental data and field measurements. Finally, a parametric study is performed to investigate the influence of different configurations and spacing of twin tunnels on the interaction degree. The configurations of twin tunnels are of horizontal, vertical, and diagonal arrangements. It is revealed that the twin tunnels interaction contributes to significantly large ground movements when the tunnels are in small spacing and shallow depths, but the interaction progressively decreases as the tunnel spacing increases. The ground settlements induced by twin tunneling are generally same with the results for combined superpositions from two single tunnels at a horizontal tunnel spacing of 10D. The complex variable solution proposed

关键词： Twin tunnels Different configurations Ground settlements Nonuniform contraction deformation model Interaction effect complex variable solution

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complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application*

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Applied Mathematics and Mechanics(English Edition) 2017年第9期38卷 1329-1346页

作者： Hang ZHOU College of Civil Engineering Key Laboratory of New Technology for Construction of Cities in Mountain AreaChongqing UniversityChongqing 400045China State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and TechnologyXuzhou 221116Jiangsu ProvinceChina

A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect （NUDE） of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index （CFI）, and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.

关键词： complex variable solution boundary value problem plane elasticity X-section cast-in-place concrete （XCC） pile deformation mechanism theoretical study

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Generalized complex variable analysis of shallow tunneling through multi-layered ground

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APPLIED MATHEMATICAL MODELLING 2024年第PartB期125卷 230-259页

作者： Sun, Zhenyu Zhang, Dingli Fang, Huangcheng Hong, Xuefei Beijing Jiaotong Univ Key Lab Urban Underground Engn Minist Educ Beijing 100044 Peoples R China

The mechanical analysis of shallow tunnels crossing multiple ground layers is a common problem in urban underground engineering. Since the tunnel boundary intersects multiple ground layers, the challenges of mixed boundary value problem for composite boundary and the conformal mapping of irregular banding computational domain are faced in solving the multi-boundary problem. For this, a new solution strategy regarding the generalized complex variable method to calculate the mechanical responses of the multi-layered ground is proposed. The research object is divided into two independent objects including the complete multi-layered ground without tunnel and the complete tunnel boundary. Firstly, the mechanical responses of the complete multi-layered ground are solved through the superposition of multiple single-boundary contributions. Subsequently, the virtual boundary circle and its corresponding analytic functions are introduced in analyzing the tunnel boundary contribution. Finally, the solution for the stress and displacement field of the multi-layered ground is modified by superimposing the contribution of the virtual boundary circle, so that all the given boundary conditions are satisfied. The selfconsistency and accuracy of the proposed method are validated by several examples. The characteristics of the displacement propagation of typical multi-layered ground patterns are analyzed based on the analytical solution. The proposed method can be used to analyze the mechanical responses of multi-layered ground with arbitrary intersections between the tunnel and ground boundaries.

关键词： Shallow tunneling Mechanical response Multi -layered ground Virtual boundary circle complex variable solution Ground displacement propagation

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Mechanical responses of multi-layered ground due to shallow tunneling with arbitrary ground surface load

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Frontiers of Structural and Civil Engineering 2023年第5期17卷 745-762页

作者： Xuefei HONG Dingli ZHANG Zhenyu SUN Key Laboratory for Urban Underground Engineering of Ministry of Education Beijing Jiaotong UniversityBeijing 100044China

An analytical model based on complex variable theory is proposed to investigate ground responses due to shallow tunneling in multi-layered ground with an arbitrary ground surface *** ground layers are assumed to be linear-elastic with full-stick contact between *** solve the proposed multi-boundary problem,a series of analytic functions is introduced to accurately express the stresses and displacements contributed by different *** on the principle of linear-elastic superposition,the multi-boundary problem is converted into a superposition of multiple single-boundary *** conformal mappings of different boundaries are independent of each other,which allows the stress and displacement fields to be obtained by the sum of components from each *** analytical results are validated based on numerical and in situ monitoring *** present model is superior to the classical model for analyzing ground responses of shallow tunneling in multi-layered ground;thus,it can be used with assurance to estimate the ground movement and surface building safety of shallow tunnel constructions beneath surface ***,the solution for the ground stress distribution can be used to estimate the safety of a single-layer composite ground.

关键词： analytical model mechanical response multi-layered ground shallow tunneling ground surface load complex variable solution

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Time-dependent analyses for ground movement and stress field induced by tunnelling considering rainfall infiltration mechanics

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TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY 2022年第0期122卷 104378-104378页

作者： Zhang, Zhiguo Huang, Maosong Pan, Yutao Li, Zhenbo Ma, Shaokun Zhang, Yangbin Univ Shanghai Sci & Technol Sch Environm & Architecture 516 Jungong Rd Shanghai 200093 Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore Singapore Minist Nat Resources Fujian Key Lab Geohazard Prevent Key Lab Geohazard Prevent Hilly Mt Minist Fuzhou 350002 Fujian Peoples R China Tongji Univ Dept Geotech Engn Shanghai 200092 Peoples R China Norwegian Univ Sci & Technol Fac Engn Trondheim Norway Guangxi Univ Sch Civil Engn & Architecture Nanning 530004 Guangxi Peoples R China

The evaluation of influence of heavy rainfall on tunnel structural construction is a problem being faced by engineers around the world. Current analytical solutions on the tunnelling-induced ground movements are generally based on the normal sunny weather and provide little attention on the rainfall intensity and duration risk. In this paper, a time-dependent complex variable approach is proposed to estimate the deformation and stress of surrounding soils caused by tunnelling considering the rainfall infiltration mechanisms. The modified Green-Ampt model under the assumption of stratification is used to simulate the rainfall infiltration process and the complex function theory is employed to calculate the subregion mapping for the saturated, transitional, and natural layers. The non-uniform convergence deformation boundary is adopted at the tunnel structure opening so as to consider the displacement controlled excavation effects due to tunnelling. The analytical presented solution is then verified by comparisons with a total of three engineering case records. It is revealed that the presented complex variable solution considering the rainfall infiltration mechanism can provide a prediction of surface settlement, soil subsidence and horizontal displacement in good agreements with the field measurements. Finally, the parameters that affect the ground deformation and stress induced by tunneling in rainy day, including the rainfall intensity, saturated permeability, matric suction, initial water content, are studied. The paper contributes to provides a relatively quick and easy way of accurately evaluating the time-dependent feedback in tunnel-soil interaction system involving heavy rainfall as a potential risk in the preliminary design of tunnel structures considering the adverse weather condition.

关键词： Tunnelling Rainfall Ground movement Green-Ampt model complex variable solution

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complex variable solutions for Soil and Liner Deformation due to Tunneling in Clays

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2018年第7期18卷

作者： Zhang, Zhiguo Huang, Maosong Xi, Xiaoguang Yang, Xuan Univ Shanghai Sci & Technol Sch Environm & Architecture 516 Jungong Rd Shanghai 200093 Peoples R China Tongji Univ Dept Geotech Engn Shanghai 200092 Peoples R China China Univ Min & Technol State Key Lab Geomech & Deep Underground Engn Xuzhou 221116 Peoples R China

Current research to predict the soil deformation due to tunneling pays little attention to the impact of soil-liner interaction. Moreover, the conventional solution for the stress function method has an inherent physical defect that leads to a nonzero ground displacement at infinity. To overcome these disadvantages, an analytical solution by the complex variable method is presented for problems in evaluating the liner and disturbed surrounding soil deformation due to tunneling in clays. The interaction mechanism between tunnel liners and surrounding soils is considered in this study, and the deterministic nonuniform convergence boundary model is composed as the displacement controlled condition on tunnel opening. The applicability of the proposed method is observed based on the existing analytical solutions and a series of field cases. It has been demonstrated that the proposed complex variable solution for the estimation of soil displacements considering the soil-liner interaction and nonuniform convergence model agrees well with the observation data. The impacts of key parameters on the tunneling-induced soil deformation are also assessed, including the tunneling gap, the soil and liner physical characteristics, and the buried depth liner thickness for the tunnel. In addition, the effects of the liner thickness and buried depth on the circular expression of liner deformation, including the radial and tangential displacements, are investigated by the parametric analyses considering the soil-liner interaction mechanism. To consider the liner stiffness influence and the nonuniform convergence boundary condition, the complex variable solution in this study can be regarded as an effective approach to conservatively predict the soil and liner deformation. (C) 2018 American Society of Civil Engineers.

关键词： Tunneling Soil movement Liner deformation Nonuniform convergence model Soil-liner interaction complex variable solution

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Displacement analytical prediction of shallow tunnel based on unified displacement function under slope boundary

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2019年第1期43卷 183-211页

作者： Kong, Fanchao Lu, Dechun Du, Xiuli Shen, Chenpeng Beijing Univ Technol Key Lab Urban Secur & Disaster Engn Minist Educ Beijing 100124 Peoples R China

For slope condition of ground surface, the asymmetrical deformation about the vertical center line and the horizontal center line of the tunnel cross section can be formed. A unified displacement function expressed by the Fourier series is presented to express the asymmetrical deformation of the tunnel cross section. Five basic deformation modes corresponding to the expansion order 2 are a complete deformation mode to reflect deformation behaviors of the tunnel cross section under slope boundary. Such this complete displacement mode is implemented into the complex variable solution for analytically predicting tunneling-induced ground deformation under slope boundary. All of these analytical solutions are verified by good agreements of the comparison between the analytical solutions and finite element method results. A parameter study is carried out to investigate the influence of deformation modes of the tunnel cross section, geometrical conditions of the tunnel and the slope angle, and "Buoyancy effect" on the displacement field. Finally, the proposed method is consistent with measured data of the Hejie tunnel in China qualitatively. The presented solution can provide a simplified indication for evaluating the ground deformation under slope condition of ground surface.

关键词： asymmetrical deformation modes complex variable solution elastic analytical solution of ground displacement slope condition of ground surface unified displacement function

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A unified displacement function to analytically predict ground deformation of shallow tunnel

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TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY 2019年 88卷 129-143页

作者： Lu, Dechun Kong, Fanchao Du, Xiuli Shen, Chenpeng Gong, Qiuming Li, Pengfei Beijing Univ Technol Minist Educ Key Lab Urban Secur & Disaster Engn Beijing 100124 Peoples R China

A unified displacement function of the cross-section of a circular shallow tunnel, expressed by the Fourier series, is proposed. The unified displacement function can reflect main deformation behaviors of the tunnel cross-section. Five basic deformation modes corresponding to the expansion order n = 2 show the horizontal and vertical asymmetrical deformation, which is a complete deformation mode. This complete displacement mode is implemented into the complex variable solution for analytically predicting the tunnelling-induced ground deformation. The effects of the tunnel cross-section deforming parameters and the "Buoyancy effect" on the displacement field are discussed. Case studies from the section MS-5 of the Docklands Light Railway Lewisham Extension are used to verify the capacity and applicability of the proposed solution. The presented solution provides a simplified indication for evaluating the tunnel deformation under complex geological and construction conditions.

关键词： Shallow tunnel Unified displacement function Asymmetrical deformation modes complex variable solution Ground deformation

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Upper-Bound Limit Analysis of Shield Tunnel Stability in Undrained Clays Using complex variable solutions for Different Ground-Loss Scenarios

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2017年第9期17卷 04017057-04017057页

作者： Xiang, Yanyong Song, Wenjie Beijing Jiaotong Univ Sch Civil Engn Beijing 100044 Peoples R China

Continuum upper-bound limit analyses in existing literature are based on empirical formulas or singular analytical solutions for a uniform-convergence type of tunnel boundary condition. This paper presents an upper-bound limit analysis of shield tunnel stability in undrained clays using complex variable displacement fields for four different ground-loss scenarios. The upper-bound theorem was applied on a prescribed perfect plastic Tresca kinematic zone with a slip line boundary to seek the supremum (minimal upper bound) of the tunnel stability number, which should not be exceeded to avoid collapse. For an imposed identical volume of ground loss, the maximum ground surface settlement was found to be the smallest for ground-loss Scenario A (circular convergence), larger for Scenario B (downward oval convergence), and much larger for Scenario C (halved oval convergence), which is slightly smaller than Scenario D (mixed oval convergence);the opposite is true for comparisons of the widths of the settlement troughs. Ground-loss Scenario A presents the worst case in terms of tunnel stability, with the smallest allowable stability number and the widest spread of the least favorable slip line boundary, while Scenario D is the second worst case with the second-smallest allowable stability number. Similar results were found, in sequential order, for Scenarios B and C. The presented approach, because of the complex variable solutions used, may extend upper-bound limit analyses to more complicated tunnel boundary conditions. (C) 2017 American Society of Civil Engineers.

关键词： Tunnel stability Undrained clays Ground loss complex variable solution Supremum Upper-bound theorem Limit analysis

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