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Frontiers of Structural and Civil Engineering

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Front. Struct. Civ. Eng.    2023, Vol. 17 Issue (4) : 503-521    https://doi.org/10.1007/s11709-023-0927-4
RESEARCH ARTICLE
Cohesive zone model-based analyses of localized leakage of segmentally lined tunnels
Jiachong XIE1,2, Xin HUANG1,2(), Zixin ZHANG1,2, Guolong JIN3
1. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
2. Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education, Tongji University, Shanghai 200092, China
3. China Shipbuilding NDRI Engineering Co., Ltd., Shanghai 200063, China
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Abstract

This paper presents a novel approach for simulating the localized leakage behavior of segmentally lined tunnels based on a cohesive zone model. The proposed approach not only simulates localized leakage at the lining segment, but also captures the hydromechanically coupled seepage behavior at the segmental joints. It is first verified via a tunnel drainage experiment, which reveals its merits over the existing local hydraulic conductivity method. Subsequently, a parametric study is conducted to investigate the effects of the aperture size, stratum permeability, and spatial distribution of drainage holes on the leakage behavior, stratum seepage field, and leakage-induced mechanical response of the tunnel lining. The proposed approach yields more accurate results than the classical local hydraulic conductivity method. Moreover, it is both computationally efficient and stable. Localized leakage leads to reduced local ground pressure, which further induces outward deformation near the leakage point and slight inward deformation at its diametrically opposite side. A localized stress arch spanning across the leakage point is observed, which manifests as the rotation of the principal stresses in the adjacent area. The seepage field depends on both the number and location of the leakage zones. Pseudostatic seepage zones, in which the seepage rate is significantly lower than that of the adjacent area, appear when multiple seepage zones are considered. Finally, the importance of employing the hydromechanical coupled mechanism at the segment joints is highlighted by cases of shallowly buried tunnels subjected to surface loading and pressure tunnels while considering internal water pressure.
Keywords segmentally lined tunnel      localized leakage      cohesive element      hydraulic behavior      numerical modeling     
Corresponding Author(s): Xin HUANG   
About author:

* These authors contributed equally to this work.
Just Accepted Date: 14 February 2023   Online First Date: 09 May 2023    Issue Date: 25 June 2023
 Cite this article:   
Jiachong XIE,Xin HUANG,Zixin ZHANG, et al. Cohesive zone model-based analyses of localized leakage of segmentally lined tunnels[J]. Front. Struct. Civ. Eng., 2023, 17(4): 503-521.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-023-0927-4
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I4/503
Fig.1  Existing numerical modeling methods for groundwater infiltration: (a) equivalent hydraulic conductivity method; (b) partial hydraulic conductivity method; (c) local hydraulic conductivity method embedded with localized leakage area; (d) local hydraulic conductivity method embedded with localized leakage area and discrete spring elements; (e) local hydraulic conductivity method embedded with one-dimensional leakage elements; (f) inflow rate method.
modeling methodsreferencesoftwarestrengthsimperfections
Fig.1(a): equivalent hydraulic conductivity method[25]ICFEP (Imperial College Finite Element Program)It assumes that the entire tunnel drainage is uniform, with a single parameter representing the lining permeability.It disregards the difference in the local leakage behavior of joints, handholes, and segments. The lining permeability is difficult to calibrate. The ground movement and pore pressure may be inaccurate when applied to a shallowly buried tunnel [4].
[26,27]PLAXIS 2D
[28]ABAQUS
Fig.1(b): partial hydraulic conductivity method[29]ABAQUSIt considers the variation in leakage behaviors throughout the lining structure based on field survey data of leakage [6].It is similar to the equivalent hydraulic conductivity method and does not offer a refined simulation of local leakage.
[6]ABAQUS
[30]FLAC
Fig.1(c)–1(e): local hydraulic conductivity method[21]ICFEPThe local leakage behavior can be explicitly simulated.The permeability coefficient and the width of the leakage area cannot be determined easily. Moreover, the coupling between the hydraulic and mechanical behaviors at the leakage area is not considered.
[4,31]ABAQUS
[32]FLAC
Fig.1(f): inflow rate method[22]not mentionedThe leakage rate is applied directly on the soil near the tunnel extrados; thus, the hydraulic conductivity need not be specified to the lining.The accuracy of seepage field relies on the prescribed leakage rate or the implemented hydromechanical leakage behavior.
[23,24]ABAQUS
Tab.1  Summary and comparison of different methods for modeling lining permeability
Fig.2  Schematic illustration of hydraulic and mechanical coupling cycle of gap flow in stratum-structure model.
Fig.3  Cohesive elements with initial aperture.
Fig.4  Change in aperture due to external loads: (a) closed state; (b) opening state with constant aperture; (c) opening state under uniaxial compression; (d) opening state under uniaxial tension; (e) opening state subject to bending (g0 represents initial aperture, ?g represents the increment of gap separation due to external loads, dmax and dmin are the maximum and minimum opening sizes along the cohesive element, respectively).
Fig.5  Correlations among effective aperture, hydraulic conductivity, and leakage rate in different scenarios (?p was set at 0.5 MPa/m for illustration).
Fig.6  Meshes for the 2D numerical models: (a) lining model derived from CZM; (b) lining model partitioned via local hydraulic conductivity method (where kl and kj refer to the permeability coefficient of the lining and leakage area, respectively).
materialdensity (kg/m3)elasticity modulus (GPa)Poisson’s ratiovoid ratio
stratum20001.50.350.2
lining250035.00.200.1
Tab.2  Input physical and mechanical parameters of stratum and lining [13]
Fig.7  Seepage rate of water infiltration (values have been converted to prototype values).
Fig.8  Time history of localized seepage stabilization.
Fig.9  Seepage fields near tunnel varying with permeability of stratum ks: (a) numerical results using CZM method; (b) numerical results using local hydraulic conductivity method.
Fig.10  Hydraulic behavior and mechanical response of stratum at external periphery of lining: (a) pore pressure (kPa); (b) seepage velocity (m/s); (c) ground loading (kPa).
Fig.11  Mechanical response of tunnel lining: (a) additional bending moments (kN·m); (b) additional axial force (kN); (c) additional radial displacements (mm).
Fig.12  Effect on seepage rate of single leakage gap.
Fig.13  Effect of stratum permeability on hydraulic behavior and mechanical response of stratum at external periphery of lining: (a) pore pressure (kPa); (b) seepage velocity (m/s); (c) ground loading (kPa).
Fig.14  Mechanical response (effective stress) of stratum induced by leakage when ks = 1 × 10?8 m/s: (a) vertical stress distribution of non-gap case; (b) vertical stress distribution with g0 = 0.05 mm at #1; (c) minor principal stress distribution of non-gap case; (d) minor principal stress distribution when g0 = 0.05 mm at #1; (e) deviation of principal stress along survey line.
Fig.15  Seepage velocity for different combinations of leakage gaps: (a) #1; (b) #1 + #2; (c) #1 + #6; (d) #1 + #7; (e) #1 + #2 + #7; (f) #1 + #3 + #6; (g) #1 + #2 + #3 + #6 + #7; (h) #1–#7.
Fig.16  Influence region of three leakage gaps: #1 + #3 + #6.
Fig.17  Seepage rate at single leakage gap under different combinations of gap locations.
Fig.18  Seepage fields with different Enn of hydraulically deteriorated joint: (a) Enn = 1 × 1010 N·m–2; (b) Enn = 2 × 1010 N·m–2; (c) Enn = 10 × 1010 N·m–2; (d) Enn = 200 × 1010 N·m–2.
Fig.19  Seepage rate vs. Enn of hydraulically deteriorated joint.
Fig.20  Seepage field, lining response, and hydraulic opening of shallowly and deeply buried cases: (a) shallowly buried case with surface overloading; (b) deeply buried case with high water pressure.
Fig.21  Effect of hydromechanical coupling on seepage velocity distribution: (a) shallowly buried case; (b) deeply buried case.
Fig.22  Effect of IWP on seepage direction and induced response of localized leakage (d represents the final aperture size): (a) seepage fields when IWP = 0 MPa; (b) seepage fields when IWP = 1 MPa; (c) seepage fields when IWP = 2 MPa; (d) effect of IWP on additional radial displacements.
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