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Frontiers of Structural and Civil Engineering

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Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (4) : 998-1011    https://doi.org/10.1007/s11709-020-0621-8
RESEARCH ARTICLE
Three-dimensional finite difference analysis of shallow sprayed concrete tunnels crossing a reverse fault or a normal fault: A parametric study
Masoud RANJBARNIA1(), Milad ZAHERI1, Daniel DIAS2,3
1. Department of Geotechnical Engineering, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran
2. School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009, China
3. Université Grenoble Alpes, Grenoble F-38000, France
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Abstract

Urban tunnels crossing faults are always at the risk of severe damages. In this paper, the effects of a reverse and a normal fault movement on a transversely crossing shallow shotcreted tunnel are investigated by 3D finite difference analysis. After verifying the accuracy of the numerical simulation predictions with the centrifuge physical model results, a parametric study is then conducted. That is, the effects of various parameters such as the sprayed concrete thickness, the geo-mechanical properties of soil, the tunnel depth, and the fault plane dip angle are studied on the displacements of the ground surface and the tunnel structure, and on the plastic strains of the soil mass around tunnel. The results of each case of reverse and normal faulting are independently discussed and then compared with each other. It is obtained that deeper tunnels show greater displacements for both types of faulting.
Keywords urban tunnel      sprayed concrete      reverse fault      normal fault      finite difference analysis     
Corresponding Author(s): Masoud RANJBARNIA   
Just Accepted Date: 07 May 2020   Online First Date: 10 July 2020    Issue Date: 27 August 2020
 Cite this article:   
Masoud RANJBARNIA,Milad ZAHERI,Daniel DIAS. Three-dimensional finite difference analysis of shallow sprayed concrete tunnels crossing a reverse fault or a normal fault: A parametric study[J]. Front. Struct. Civ. Eng., 2020, 14(4): 998-1011.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0621-8
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I4/998
Fig.1  Hanging wall and foot wall: (a) in the reverse fault; (b) in the normal fault.
Fig.2  Definition of W parameter.
parameter unit value
elastic modulus of soil MPa 20
friction angle of soil - 37
soil density kg/m3 1630
Poisson’s ratio of soil - 0.3
cohesion of soil kN/m2 0
segment density kg/m3 2600
Poisson’s ratio of segment - 0.28
elastic modulus of segment GPa 20
Tab.1  Properties of the soil and of the tunnel in the centrifuge test level [16]
fault type fault angle height of overburden of soil (m) the length of the tunnel affected by normal fault movement (m) maximum displacement of tunnel (m)
reverse 60° 4.42 - 0.550
reverse 75° 4.42 - 0.256
normal 60° 4.42 9.44 2.500
normal 75° 5.90 11.5 2.500
Tab.2  The displacement of tunnel obtained by the centrifuge physical test model level [16]
Fig.3  Effect of mesh sizes on the tunnel deflection values (the first and second numbers in the legend of figure represent the number of meshes in the Y and Z directions, respectively).
Fig.4  Perspective view of the model and its meshes: (a) general model; (b) half of model along the tunnel axis.
Fig.5  (a) Friction and (b) dilation angle parameters versus plastic shear strain used for the dense soil.
parameter unit dense soil loose soil
elastic modulus MPa 34 15
peak friction angle - 34 30
peak dilation angle - 4 a 0
residual friction angle - 30 30
residual dilation angle - 0 a 0
density kg/m3 1800 b 1500 b
Poisson’s ratio - 0.3 0.3
cohesion kN/m2 0 0
Tab.3  Properties of the soil [51,52]
parameter unit value
density kg/m3 2600
Poisson’s ratio - 0.28
thickness m 0.3
elastic modulus GPa 34
Tab.4  Properties of the shotcrete
Fig.6  Effect of the tunnel shotcrete thickness on the deformed mesh due to the reverse faulting (the properties of the dense soil are mentioned in Table 3). (a) Shotcrete thickness= 0.30 m; (b) shotcrete thickness= 0.35 m.
Fig.7  Effect of the tunnel shotcrete thickness on the deformed mesh due to the normal faulting (the properties of the dense soil are mentioned in Table 3). (a) Shotcrete thickness= 0.30 m; (b) shotcrete thickness= 0.35 m.
Fig.8  Effect of shotcrete thickness on the settlement profile along the tunnel crossing a reverse fault or a normal fault.
Fig.9  Effect of the shotcrete thickness on the maximum vertical displacement of a tunnel crossing a reverse fault or a normal fault.
peak friction angle
(°)		 peak dilation angle
(°)		 soil density (kg/m3) elastic modulus of soil (MPa) maximum vertical tunnel displacement for reverse faulting (m) maximum vertical tunnel displacement for normal faulting (m)
34 4 1800 34 1.14 2.16
36 6 1800 34 1.17 2.16
38 8 1800 34 1.19 2.16
30 - 1500 15 0.62 2.18
28 - 1500 15 0.59 2.18
24 - 1500 15 0.54 2.18
Tab.5  Effect of the soil geo-mechanical properties on the maximum tunnel vertical displacement in the reverse and normal faulting
Fig.10  Effect of the soil mechanical properties on the deformed mesh due to the reverse faulting. (a) φ= 38°, ψ= 8°, soil density= 1800 kg/m3, elastic modulus of soil=24 MPa; (b) φ= 30°, ψ= 0°, soil density= 1500 kg/m3, elastic modulus of soil=15 MPa.
Fig.11  Effect of the soil mechanical properties on the deformed mesh due to the normal faulting. a) φ= 38°, ψ= 8°, soil density= 1800 kg/m3, elastic modulus of soil=24 MPa; (b) φ= 30°, ψ= 0°, soil density= 1500 kg/m3, elastic modulus of soil=15 MPa.
Fig.12  Effect of the soil geo-mechanical properties on the settlement profile along the tunnel crossing a reverse fault or a normal fault.
Fig.13  Effect of the tunnel depth on the deformed mesh due to the reverse faulting. (a) Tunnel depth= 7.4 m; (b) tunnel depth= 14 m.
Fig.14  Effect of the tunnel depth on the deformed mesh due to the normal faulting. (a) Tunnel depth= 7.4 m; (b) tunnel depth= 14 m.
Fig.15  Effect of the tunnel depth on the settlement profile along the tunnel crossing a reverse fault or a normal fault.
Fig.16  Effect of the tunnel depth on the maximum displacement of a tunnel crossing a reverse fault or a normal fault.
Fig.17  Effect of the reverse fault dip angle on the deformed mesh. (a) Fault dip angle= 75°; (b) fault dip angle= 90°.
Fig.18  Effect of the normal fault dip angle on the deformed mesh. (a) Fault dip angle= 75°; (b) fault dip angle= 90°.
Fig.19  Effect of the fault dip angle on the settlement profile along the tunnel crossing a reverse fault or a normal fault.
Fig.20  Effect of the fault dip angle on the maximum displacement of a tunnel crossing a reverse fault or a normal fault.
the cases point of the maximum gradient in the reverse fault (m) Y maximum gradient in the reverse fault point of the maximum gradient in the normal fault (m) Y maximum gradient in the normal fault
the base example case ?8 −0.09 ?−9 0.10
shotcrete thickness= 0.25 m ?8 −0.1? ?−9 0.10
shotcrete thickness= 0.35 m ?8 −0.09 ?−9 0.10
dense sand, φ = 36°, Es = 24 MPa ?8 −0.11 −10 0.11
dense sand, φ = 38°, Es = 24 MPa 10 −0.14 −12 0.12
loose sand, φ = 30°, Es = 15 MPa 10 −0.07 ??11 0.12
loose sand, φ = 28°, Es = 15 MPa ?7 ?−0.065 ??11 0.12
loose sand, φ = 24°, Es = 15 MPa 10 −0.06 ??11 0.12
tunnel depth= 7.4 m −15?? −0.10 −28 0.16
tunnel depth= 14 m ?5 −0.14 ???8 0.18
fault dip angle= 75° ?2 −0.09 ???5 0.09
fault dip angle= 90° −2? −0.09 ???0 0.06
Tab.6  The maximum gradient of settlement and corresponding location for the different cases (reverse and normal faults)
the cases tunnel deformation in the horizontal direction (%) tunnel deformation in the vertical direction (%)
the base example case 1.64 1.66
shotcrete thickness= 0.25 m 2.91 2.96
shotcrete thickness= 0.35 m 0.86 0.91
dense sand, φ = 36°, Es = 24 MPa 1.56 1.59
dense sand, φ = 38°, Es = 24 MPa 1.50 1.54
loose sand, φ = 30°, Es = 15 MPa 1.40 1.44
loose sand, φ = 28°, Es = 15 MPa 1.33 1.35
loose sand, φ = 24°, Es = 15 MPa 1.18 1.18
tunnel depth= 7.4 m 1.74 1.74
tunnel depth= 14 m 1.79 1.88
fault dip angle= 75° 2.20 2.20
fault dip angle= 90° 2.40 2.44
Tab.7  Tunnel deformation in the horizontal and vertical directions in the reverse fault movement
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[1] Mehdi SABAGH, Abbas GHALANDARZADEH. Centrifuge experiments for shallow tunnels at active reverse fault intersection[J]. Front. Struct. Civ. Eng., 2020, 14(3): 731-745.
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