Analytical approach for circular‐jointed shield tunnel lining based on the state space method

Wang, Jinchang; Huang, Weiming; Xu, Riqing; Yang, Z. X.; Xu, Rongqiao

doi:10.1002/nag.3012

Cited by 29 publications

(7 citation statements)

References 33 publications

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“…According to the modified routine method, it is stipulated that the positive and negative signs of internal forces are as follows. The bending moment is positive when the inner side is tension; the axial force is positive when this is compression; the shear force is positive with the counterclockwise direction around the isolator [10,14]. The unit bending moment diagrams M 1 and M 2 are shown in Figure 3.…”

Section: Internal Force Calculation Of Liningmentioning

confidence: 99%

“…The elastic center method and superposition principle are adopted to deduce the calculation formula of lining internal force with the discontinuous joint. Wang et al [10] introduced a new analytical solution to calculate the internal force and deformation of the circular tunnel lining by using the curved Euler beam theory and the principle of minimum potential energy. This method can consider joints and loads with arbitrary distribution and has remarkable advantages in rigid body displacement treatment and soil reaction calculation.…”

Section: Introductionmentioning

confidence: 99%

“…This paper refers to internal force positive and negative sign provisions in the modified routine method. The general formula for calculating the internal force of lining under different water levels and water conveyance pressures is derived by using the mechanical analysis method [10,14]. The internal force generated by the lining structure of the tunnel under the external load can be calculated by the modified routine method or other methods [15].…”

Section: Introductionmentioning

confidence: 99%

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Study on the Influence of Internal Water Pressure on the Internal Force of Circular Hydraulic Tunnel Lining

Zhu

Cheng

2022

Applied Sciences

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The internal water pressure condition influences the internal force of the circular hydraulic tunnel lining. However, calculating the lining’s internal force of this type of tunnel still lacks practical theory. Based on the modified routine method and the theory of structural mechanics, the internal stress model of the tunnel section is established in this paper. The general calculation formula of lining internal force is deduced by considering arbitrary water level height and different water conveyance pressures. The formula is used to calculate the internal force of the lining under the action of internal water pressure and the influence laws of water level height and water conveyance pressure are explored, respectively. In addition, case analysis was carried out for several typical projects. The results show that the maximum internal force of the lining increases with the increase of water pressure and inner radius and the maximum internal force is in a fixed special position when the water is conveyed under pressure. When the water is conveyed without pressure, the internal force of the lining will increase with the increased water level. However, the maximum bending moment and axial force will reduce at the special water level. This calculation theory considering different working conditions of internal water pressure solves the calculation problem of the internal force of a circular hydraulic tunnel. It improves the design theory of tunnel structure and provides a theoretical basis for this type of tunnel’s structural design and safe operation.

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Section: Internal Force Calculation Of Liningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Study on the Influence of Internal Water Pressure on the Internal Force of Circular Hydraulic Tunnel Lining

Zhu

Cheng

2022

Applied Sciences

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“…Lee et al adopted the force method to predict internal forces and displacements of a jointed circular segmental tunnel lining by treating the longitudinal joints as a set of linear rotational springs [27]. Wang et al presented an analytical solution for circular segmental tunnel lining based on the state space method [28]. e curved Euler beam theory and the principle of minimum potential energy were adopted during the derivation of governing equations.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for the Mechanical Responses of Shallow Double‐Arched Tunnel Subjected to Symmetric Loads

Yang

Dai²,

Ai³

et al. 2021

Advances in Civil Engineering

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Double-arched tunnel is a special kind of tunnel structure which is widely adopted for shallow rock tunnels. The internal forces within a double-arched tunnel are difficult to be determined due to its special geometry and complex interactions with surrounding rock masses. This paper presents a set of analytical solutions for determining the internal forces within the lining structure of shallow double-arched tunnel subjected to symmetric external loads. The double-arched tunnel is decomposed into three main parts, i.e., the arch rings, the side walls, and the middle wall. The force method and the elastic foundation beam model are employed for the arch rings and the side walls, respectively, while the middle wall is treated as a cantilever beam fixed at the bottom. Analytical solutions for the internal forces of the three parts are derived separately, which are continuous at the conjunctions of different parts. The derived analytical solutions are verified by comparing with the FEM simulation results. Finally, parametric studies are performed to investigate the influences of burial depth, elastic resistance coefficient, opening angle, and tunnel span on the internal forces based on which some recommendations are provided for the construction and design of the double-arched tunnels. The derived analytical solutions provide fast estimations for the internal forces and deformation of the double-arched lining structures, which will be a useful tool for design optimization.

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“…By virtue of the strong adaptability to surrounding rock, little impact on environment, mechanized operation, high construction speed and low labor intensity, the fabricated lining is widely used in the underground rail transit, the water conveyance system and the river‐crossing tunnel, for instance, the circular subway tunnel in Figure 1 and the rectangular underground passage in Figure 2 1–5 . With the rapid development of the urban infrastructure construction, the burial depth, diameter and load of the fabricated lining all present an increasing trend, which brings enormous challenges to the design 6–8 .…”

Section: Introductionmentioning

confidence: 99%

Independent cover isogeometric Reissner‐Mindlin shell model for the simulation of the fabricated lining

Cai

Chen

2021

Num Anal Meth Geomechanics

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The fabricated lining is widely used in the underground rail transit, water conveyance system and river‐crossing tunnel. It is generally composed of the precast concrete segments, joints, bolts and reinforcements. Compression and separation often coexist in a single joint, which brings great challenges to the modeling and calculation of the fabricated lining. In this paper, an independent cover isogeometric Reissner‐Mindlin shell model (denoted as the ICI‐R shell model) is proposed for the simulation of the fabricated lining. In the ICI‐R shell model, each segment is regarded as an independent cover, whose geometry is described with the nonuniform rational B‐splines (NURBS) surface, and an isogeometric displacement function is defined based on the Reissner‐Mindlin shell deformation theory. The adjacent segments are connected with the fictitious thin layers, of which the normal and tangential deformations and stresses can be correctly calculated. Within this framework, the difficulties in the continuity‐discontinuity coupling analysis occurring when using the existing shell models are well solved, and the fabricated lining can be simulated expediently. The ICI‐R shell model has the advantages of clear physical meaning, concise formulas and convenient implementation. Benefiting from the strong capability of representing geometries of NURBS and the simplicity of the formulation of the ICI‐R shell model, the parameterized modeling and automatic calculation of the fabricated lining can be easily achieved for simplifying the analysis process and reducing user cost for geotechnical engineers. The successful application in the benchmark tests and engineering example shows the versatility, efficiency and robustness of the ICI‐R shell model.

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Analytical approach for circular‐jointed shield tunnel lining based on the state space method

Cited by 29 publications

References 33 publications

Study on the Influence of Internal Water Pressure on the Internal Force of Circular Hydraulic Tunnel Lining

Study on the Influence of Internal Water Pressure on the Internal Force of Circular Hydraulic Tunnel Lining

Analytical Solutions for the Mechanical Responses of Shallow Double‐Arched Tunnel Subjected to Symmetric Loads

Independent cover isogeometric Reissner‐Mindlin shell model for the simulation of the fabricated lining

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