Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress

Lu, Aizhong; Zeng, Xiangtai; Xu, Zhen

doi:10.1016/j.ijrmms.2016.08.004

Cited by 55 publications

(26 citation statements)

References 8 publications

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“…When β = 0, F x = 0 and F y = (1 − w t )πγr 0 2 , which is the same as the results of the flat ground surface. 27,37,39,40 The region R in the z-plane is conformally mapped onto an annular region γ 1 in the ζ − plane, as shown in Figure 4. The conformal transformation function is…”

Section: General Methods Of Complex Variablementioning

confidence: 99%

“…11 There are four methods to obtain the elastic analytical solution: Airy stress function solution [12][13][14] ; the bipolar coordinate method [15][16][17] ; virtual image technique method [18][19][20][21] ; and complex variable solution. [22][23][24][25][26][27][28] The complex variable method can determine displacements and stresses simultaneously throughout the entire half-plane by an infinite power series in the complex plane. In recent years, the complex variable method has been widely used to solve the linear elastic problems in the semi-infinite domain.…”

Section: Introductionmentioning

confidence: 99%

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

Kong

et al. 2018

Num Anal Meth Geomechanics

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Summary 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.

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Section: General Methods Of Complex Variablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kong

et al. 2018

Num Anal Meth Geomechanics

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“…In view of the hazards of stratum cavities to the safety of subway tunnel construction, more and more scholars have studied this issue [7][8][9][10][11]. Abdulla and Goodings [12] studied the instability mechanism of the soil on the cavity structure by means of centrifugal model tests in the laboratory.…”

Section: Introductionmentioning

confidence: 99%

Instability Mechanism of Cavity‐Bearing Formation under Tunnel Excavation Disturbance

Liu

Wang

et al. 2020

Advances in Civil Engineering

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Urban subway construction inevitably causes disturbances to the rock strata. It can even cause ground collapse accidents when construction encounters a bad geological body in the stratum. To verify the influence of cavities on surface settlement and the mechanism of formation instability, the instability mechanism of cavity-bearing strata under tunnel excavation disturbance was herein studied by tests using self-designed indoor models and numerical simulations. This study was based on the concrete project case of Qingdao Metro. Two groups of experiments (with and without cavities) were designed to simulate the four-step excavation by staged unloading of an airbag. The results show that the settlement value in the cavity state was about twice as much as that in the nonvoid state at the same stage. Besides the first step of excavation, in the numerical simulation, the settlement value of the same stage is about 1.3 times that of the model test. Simulating the deformation process of the surrounding rock in model tests shows that, in the excavation of the tunnel, the collapse surface of the tunnel arch roof will be connected with the sliding surface of the formation cavity. The cavity will gradually change from a regular circle to an ellipse or may even close, resulting in a sudden increase in land subsidence or even ground collapse. This indicates that disturbance during tunnel excavation would cause greater instability in a stratum when bad geological bodies, such as cavities, exist in the stratum.

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“…The complex variable method is a common method to solve elastic problems. Since Verruijt (1997;1998) creatively obtained the elastic analytical solution of the shallow tunnel by the boundary conditions and the convergence of the series, the complex variable method (Wang et al, 2009;Fu et al, 2015aFu et al, , 2015bFang et al, 2015;Lu et al, 2016;Zhang et al, 2018) is in a quite wide use solving the elastic analytical solution of shallow tunnel in recent years. A reasonable boundary condition is the key to obtaining an elastic solution.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic analytical solution for shallow tunnel considering time-dependent displacement boundary

Shen

Kong

et al. 2020

JGS Special Publication

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A time-dependent unified displacement function is proposed to capture main deformation responses of the tunnel cross-section. When the expansion order n equals 2, this complete displacement mode is used as displacement boundary condition (DBC) of the tunnel cross-section. Complex variable method is adopted in order to obtain an elastic analytical solution. Considering the time effect of ground mechanical parameters and tunnel cross-section deformation, a viscoelastic analytical solution of ground displacement is obtained. By parametric analyses, time effects of settlement trough curve, ground displacement and the settlement at the center point of ground surface are analyzed.

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Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress

Cited by 55 publications

References 8 publications

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

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

Instability Mechanism of Cavity‐Bearing Formation under Tunnel Excavation Disturbance

Viscoelastic analytical solution for shallow tunnel considering time-dependent displacement boundary

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