|
|
Quantitatively assessing the pre-grouting effect on the stability of tunnels excavated in fault zones with discontinuity layout optimization: A case study |
Xiao YAN1, Zizheng SUN2,3(), Shucai LI3, Rentai LIU3, Qingsong ZHANG3, Yiming ZHANG2() |
1. State Key Laboratory for Geo-mechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China 2. School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China 3. Geotechnical & Structural Engineering Research Center, Shandong University, Jinan 250061, China |
|
|
Abstract Pre-grouting is a popular ground treatment strategy utilized to enhance the strength and stability of strata during the excavation of a tunnel through a fault zone. Two important questions need to be answered during such an excavation. First, how should the grouting size be determined? Second, when should excavation begin after grouting? These two questions are conventionally addressed through empirical experience and standard criteria because a reliable quantitative approach, which would be preferable, has not yet been developed. To address these questions, we apply a recently proposed numerical approach known as discontinuity layout optimization, an efficient node-based upper bound limit analysis method. A case study is provided utilizing a tunnel located in a stratum characterized by complicated geological conditions, including soft soil and a fault zone. The factor of safety is used to quantitatively assess the stability of the tunnel section. The influences of the grouted zone thickness and the time-dependent material properties of the grouted zone on the stability of the tunnel section are evaluated, thereby assisting designers by quantitatively assessing the effects of pre-grouting.
|
Keywords
pre-grouting
stability analysis
factor of safety
discontinuity layout optimization
|
Corresponding Author(s):
Zizheng SUN,Yiming ZHANG
|
Just Accepted Date: 21 August 2019
Online First Date: 22 October 2019
Issue Date: 21 November 2019
|
|
1 |
Y Hao, R Azzam. The plastic zones and displacements around underground openings in rock masses containing a fault. Tunnelling and Underground Space Technology, 2005, 20(1): 49–61
https://doi.org/10.1016/j.tust.2004.05.003
|
2 |
C A Anagnostopoulos. Laboratory study of an injected granular soil with polymer grouts. Tunnelling and Underground Space Technology, 2005, 20(6): 525–533
https://doi.org/10.1016/j.tust.2005.04.005
|
3 |
Å Fransson. Characterisation of a fractured rock mass for a grouting field test. Tunnelling and Underground Space Technology, 2001, 16(4): 331–339
https://doi.org/10.1016/S0886-7798(01)00060-8
|
4 |
M Yesilnacar. Grouting applications in the Sanliurfa tunnels of GAP, turkey. Tunnelling and Underground Space Technology, 2003, 18(4): 321–330
https://doi.org/10.1016/S0886-7798(02)00103-7
|
5 |
J Funehag. Sealing of narrow fractures in hard rock – A case study in hallandsås, sweden. Tunnelling and Underground Space Technology, 2004, 19: 1–8
|
6 |
J Funehag, G Gustafson. Design of grouting with silica sol in hard rock – New design criteria tested in the field, part ii. Tunnelling and Underground Space Technology, 2008, 23(1): 9–17
https://doi.org/10.1016/j.tust.2006.12.004
|
7 |
L Faramarzi, A Rasti, S M Abtahi. An experimental study of the effect of cement and chemical grouting on the improvement of the mechanical and hydraulic properties of alluvial formations. Construction & Building Materials, 2016, 126: 32–43
https://doi.org/10.1016/j.conbuildmat.2016.09.006
|
8 |
Z Sun, X Yan, R Liu, Z Xu, S Li, Y Zhang. Transient analysis of grout penetration with time-dependent viscosity inside 3d fractured rock mass by unified pipe-network method. Water, 2018, 10: 1122
|
9 |
L Hernqvist, Å Fransson, G Gustafson, A Emmelin, M Eriksson, H. Stille Analyses of the grouting results for a section of the APSE tunnel at Äspö Hard Rock Laboratory. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(3): 439–449
https://doi.org/10.1016/j.ijrmms.2008.02.003
|
10 |
H Lisa, B Christian, F Åsa, G Gunnar, F Johan. A hard rock tunnel case study: Characterization of the water-bearing fracture system for tunnel grouting. Tunnelling and Underground Space Technology, 2012, 30: 132–144
https://doi.org/10.1016/j.tust.2012.02.014
|
11 |
H Lisa, G Gunnar, F Åsa, N Tommy. A statistical grouting decision method based on water pressure tests for the tunnel construction stage – A case study. Tunnelling and Underground Space Technology, 2013, 33: 54–62
https://doi.org/10.1016/j.tust.2012.08.004
|
12 |
H Huang, G Ye, C Qian, E Schlangen. Self-healingin cementitious materials: materials, methods and service conditions. Materials & Design, 2016, 92: 499–511
https://doi.org/10.1016/j.matdes.2015.12.091
|
13 |
Y Song, D Huang, B Zeng. Gpu-based parallel computation for discontinuous deformation analysis (DDA) method and its application to modelling earthquake-induced landslide. Computers and Geotechnics, 2017, 86: 80–94
https://doi.org/10.1016/j.compgeo.2017.01.001
|
14 |
J Y Wu, V P Nguyen. A length scale insensitive phase-field damage model for brittle fracture. Journal of the Mechanics and Physics of Solids, 2018, 119: 20–42
https://doi.org/10.1016/j.jmps.2018.06.006
|
15 |
J Y Wu. Robust numerical implementation of non-standard phase-field damage models for failure in solids article. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 767–797
https://doi.org/10.1016/j.cma.2018.06.007
|
16 |
J Wu, C McAuliffe, H Waisman, G Deodatis. Stochastic analysis of polymer composites rupture at large deformations modeled by a phase field method. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 596–634 doi:10.1016/j.cma.2016.06.010
|
17 |
J Y Wu. A unified phase-field theory for the mechanics of damage and quasi-brittle failure. Journal of the Mechanics and Physics of Solids, 2017, 103: 72–99 doi:10.1016/j.jmps.2017.03.015
|
18 |
S Zhou, X Zhuang, T Rabczuk. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203
https://doi.org/10.1016/j.enggeo.2018.04.008
|
19 |
S Zhou, X Zhuang, H Zhu, T Rabczuk. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192 doi:10.1016/j.tafmec.2018.04.011
|
20 |
J Wu, Y Cai. A partition of unity formulation referring to the NMM for multiple intersecting crack analysis. Theoretical and Applied Fracture Mechanics, 2014, 72: 28–36
https://doi.org/10.1016/j.tafmec.2014.07.001
|
21 |
H Zheng, F Liu, X Du. Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method. Computer Methods in Applied Mechanics and Engineering, 2015, 295: 150–171
https://doi.org/10.1016/j.cma.2015.07.001
|
22 |
H Zheng, D Xu. New strategies for some issues of numerical manifold method in simulation of crack propagation. International Journal for Numerical Methods in Engineering, 2014, 97(13): 986–1010
https://doi.org/10.1002/nme.4620
|
23 |
S Saloustros, M Cervera, L Pelà. Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures. Archives of Computational Methods in Engineering, 2018 (in press)
https://doi.org/10.1007/s11831-018-9274-3
|
24 |
S Saloustros, L Pelà, M Cervera, P Roca. Finite element modelling of internal and multiple localized cracks. Computational Mechanics, 2017, 59(2): 299–316
https://doi.org/10.1007/s00466-016-1351-6
|
25 |
S Saloustros, M Cervera, L Pelà. Tracking multi-directional intersecting cracks in numerical modelling of masonry shear walls under cyclic loading. Meccanica, 2017, 53(7): 1757–1776 doi:10.1007/s11012-017-0712-3
|
26 |
D Dias-da-Costa, J Alfaiate, L Sluys, P Areias, E Júlio. An embedded formulation with conforming finite elements to capture strong discontinuities. International Journal for Numerical Methods in Engineering, 2013, 93(2): 224–244
https://doi.org/10.1002/nme.4393
|
27 |
D Dias-da-Costa, V Cervenka, R Graça-e-Costa. Model uncertainty in discrete and smeared crack prediction in RC beams under flexural loads. Engineering Fracture Mechanics, 2018, 199: 532–543
https://doi.org/10.1016/j.engfracmech.2018.06.006
|
28 |
M Nikolić, X N Do, A Ibrahimbegovic, Ž Nikolić. Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 480–499
https://doi.org/10.1016/j.cma.2018.06.012
|
29 |
Y Zhang, X Zhuang. Cracking elements method for dynamic brittle fracture. Theoretical and Applied Fracture Mechanics, 2019, 102: 1–9 doi:10.1016/j.tafmec.2018.09.015
|
30 |
Y Zhang, R Lackner, M Zeiml, H Mang. Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 335–366
https://doi.org/10.1016/j.cma.2015.02.001
|
31 |
Y Zhang, X Zhuang. Cracking elements: a self-propagating strong discontinuity embedded approach for quasi-brittle fracture. Finite Elements in Analysis and Design, 2018, 144: 84–100
https://doi.org/10.1016/j.finel.2017.10.007
|
32 |
T Rabczuk, T Belytschko. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
https://doi.org/10.1002/nme.1151
|
33 |
T Rabczuk, T Belytschko. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
https://doi.org/10.1016/j.cma.2006.06.020
|
34 |
T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
https://doi.org/10.1016/j.cma.2010.03.031
|
35 |
T Rabczuk, T Belytschko. Adaptivity for structured meshfree particle methods in 2D and 3D. International Journal for Numerical Methods in Engineering, 2005, 63(11): 1559–1582
https://doi.org/10.1002/nme.1326
|
36 |
X Zhuang, C Augarde, K Mathisen. Fracture modeling using meshless methods and level sets in 3D: Framework and modeling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998
https://doi.org/10.1002/nme.4365
|
37 |
X Zhuang, C Augarde, S Bordas. Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling. International Journal for Numerical Methods in Engineering, 2011, 86(2): 249–268
https://doi.org/10.1002/nme.3063
|
38 |
S Silling. Reformulation of elasticity theory for discontinuities and long-range force. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209
https://doi.org/10.1016/S0022-5096(99)00029-0
|
39 |
H Ren, X Zhuang, Y Cai, T Rabczuk. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
https://doi.org/10.1002/nme.5257
|
40 |
H Ren, X Zhuang, T Rabczuk. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
https://doi.org/10.1016/j.cma.2016.12.031
|
41 |
F Han, G Lubineau, Y Azdoud, A Askari. A morphing approach to couple state-based peridynamics with classical continuum mechanics. Computer Methods in Applied Mechanics and Engineering, 2016, 301: 336–358
https://doi.org/10.1016/j.cma.2015.12.024
|
42 |
F Han, G Lubineau, Y Azdoud. Adaptive coupling between damage mechanics and peridynamics: A route for objective simulation of material degradation up to complete failure. Journal of the Mechanics and Physics of Solids, 2016, 94: 453–472
https://doi.org/10.1016/j.jmps.2016.05.017
|
43 |
S W Sloan. Upper bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13(3): 263–282
https://doi.org/10.1002/nag.1610130304
|
44 |
S W Sloan. Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(1): 61–77
https://doi.org/10.1002/nag.1610120105
|
45 |
R De Borst, P Vermeer. Possibilities and limitations of finite elements for limit analysis. Geotechnique, 1984, 34(2): 199–210
https://doi.org/10.1680/geot.1984.34.2.199
|
46 |
C V Le, H Nguyen-Xuan, H Nguyen-Dang. Upper and lower bound limit analysis of plates using FEM and second-order cone programming. Computers & Structures, 2010, 88(1–2): 65–73
https://doi.org/10.1016/j.compstruc.2009.08.011
|
47 |
E Leca, L Dormieux. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Geotechnique, 1990, 40(4): 581–606
https://doi.org/10.1680/geot.1990.40.4.581
|
48 |
G Mollon, D Dias, A H Soubra. Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield. International Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35(12): 1363–1388
https://doi.org/10.1002/nag.962
|
49 |
C Zhang, K Han, D Zhang. Face stability analysis of shallow circular tunnels in cohesive frictional soils. Tunnelling and Underground Space Technology, 2015, 50: 345–357
https://doi.org/10.1016/j.tust.2015.08.007
|
50 |
G Anagnostou, P Perazzelli. Analysis method and design charts for bolt reinforcement of the tunnel face in cohesive-frictional soils. Tunnelling and Underground Space Technology, 2015, 47: 162–181
https://doi.org/10.1016/j.tust.2014.10.007
|
51 |
K Han, C Zhang, D Zhang. Upper-bound solutions for the face stability of a shield tunnel in multilayered cohesive-frictional soils. Computers and Geotechnics, 2016, 79: 1–9
https://doi.org/10.1016/j.compgeo.2016.05.018
|
52 |
Z Chen, G Hofstetter, H Mang. A Galerkin-type BE-FE formulation for elasto-acoustic coupling. Computer Methods in Applied Mechanics and Engineering, 1998, 152(1–2): 147–155
https://doi.org/10.1016/S0045-7825(97)00187-4
|
53 |
H Dang, M A Meguid. An efficient finite discrete element method for quasi-static nonlinear soil-structure interaction problems. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(2): 130–149 doi:10.1002/nag.1089
|
54 |
C C Smith, M Gilbert. Application of discontinuity layout optimization to plane plasticity problems. Proceedings: Mathematical, Physical and Engineering Sciences, 2007, 463(2086): 2461–2484
https://doi.org/10.1098/rspa.2006.1788
|
55 |
C C Smith, M Gilbert. Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimisation. Geotechnique, 2013, 63(14): 1194–1208
https://doi.org/10.1680/geot.12.P.082
|
56 |
M Gilbert, C Casapulla, H Ahmed. Limit analysis of masonry block structures with non-associative frictional joints using linear programming. Computers & Structures, 2006, 84(13–14): 873–887
https://doi.org/10.1016/j.compstruc.2006.02.005
|
57 |
S Hawksbee, C C Smith, M Gilbert. Application of discontinuity layout optimization to three-dimensional plasticity problems. Proceedings of The Royal Society A, 2013, 469(2155): 20130009
|
58 |
S Lin, Y Xie, Q Li, X Huang, S Zhou. On the shape transformation of cone scales. Soft Matter, 2016, 12(48): 9797–9802
https://doi.org/10.1039/C6SM01805J
|
59 |
S Nanthakumar, T Lahmer, X Zhuang, H S Park, T Rabczuk. Topology optimization of piezoelectric nanostructures. Journal of the Mechanics and Physics of Solids, 2016, 94: 316–335
https://doi.org/10.1016/j.jmps.2016.03.027
|
60 |
H Ghasemi, H S Park, T Rabczuk. A multi-material level set-based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 332: 47–62
https://doi.org/10.1016/j.cma.2017.12.005
|
61 |
C C Smith, M Cubrinovski. Pseudo-staticlimit analysis by discontinuity layout optimization: Application to seismic analysis of retaining walls. Soil Dynamics and Earthquake Engineering, 2011, 31(10): 1311–1323
https://doi.org/10.1016/j.soildyn.2011.03.014
|
62 |
S D Clarke, C C Smith, M Gilbert. Modelling discrete soil reinforcement in numerical limit analysis. Canadian Geotechnical Journal, 2013, 50(7): 705–715
https://doi.org/10.1139/cgj-2012-0387
|
63 |
S D Clarke, C C Smith, M Gilbert. Analysis of the stability of sheet pile walls using Discontinuity Layout Optimization. In: Benz T, Nordal S., eds. Numerical Methods in Geotechnical Engineering-Proceedings of the 7th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2010). CRC Press, 2010, 163–168
|
64 |
M Gilbert, C C Smith, I Haslam, T J Pritchard. Application of discontinuity layout optimization to geotechnical limit analysis problems. In: Benz T, Nordal S., eds. Numerical Methods in Geotechnical Engineering-Proceedings of the 7th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2010). CRC Press, 2010, 169–174
|
65 |
Y Zhang, X Zhuang, R Lackner. Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42(11): 1199–1216
https://doi.org/10.1002/nag.2775
|
66 |
M Gilbert, C C Smith, T J Pritchard. Masonry arch analysis using discontinuity layout optimisation. Proceedings of the Institution of Civil Engineers-Engineering and Computational Mechanics, 2010, 163(3): 155–166
https://doi.org/10.1680/eacm.2010.163.3.155
|
67 |
L He, M Gilbert. Automatic rationalization of yield-line patterns identified using discontinuity layout optimization. International Journal of Solids and Structures, 2016, 84: 27–39
https://doi.org/10.1016/j.ijsolstr.2015.12.014
|
68 |
L He, M Gilbert, M Shepherd. Automatic yield-line analysis of practical slab configurations via discontinuity layout optimization. Journal of Structural Engineering, 2017, 143(7): 04017036 doi:10.1061/(ASCE)ST.1943-541X.0001700
|
69 |
Y Zhang. Multi-slicing strategy for the three-dimensional discontinuity layout optimization (3D DLO). International Journal for Numerical and Analytical Methods in Geomechanics, 2017, 41(4): 488–507
https://doi.org/10.1002/nag.2566
|
70 |
H Zheng, L Tham, D Liu. On two definitions of the factor of safety commonly used in the finite element slope stability analysis. Computers and Geotechnics, 2006, 33(3): 188–195
https://doi.org/10.1016/j.compgeo.2006.03.007
|
71 |
M Farias, D Naylor. Safety analysis using finite elements. Computers and Geotechnics, 1998, 22(2): 165–181
https://doi.org/10.1016/S0266-352X(98)00005-6
|
72 |
M Gilbert, C Smith. Evaluating Displacements at Discontinuities within a Body. UK Patent GB 2442496, 2008
|
73 |
LimitState Ltd. Limitstate: Analysis and Design Software for Engineers. Sheffield: The Innovation Centre, 2019
|
74 |
Y Zhang, C Pichler, Y Yuan, M Zeiml, R Lackner. Micromechanics-based multifield framework for early-age concrete. Engineering Structures, 2013, 47: 16–24
https://doi.org/10.1016/j.engstruct.2012.08.015
|
75 |
Y Zhang, M Zeiml, C Pichler, R Lackner. Model-based risk assessment of concrete spalling in tunnel linings under fire loading. Engineering Structures, 2014, 77: 207–215
https://doi.org/10.1016/j.engstruct.2014.02.033
|
76 |
Y Zhang, M Zeiml, M Maier, Y Yuan, R Lackner. Fast assessing spalling risk of tunnel linings under RABT fire: From a coupled thermo-hydro-chemo-mechanical model towards an estimation method. Engineering Structures, 2017, 142: 1–19
https://doi.org/10.1016/j.engstruct.2017.03.068
|
77 |
Y Zhang, X Zhuang. A softening-healing law for self-healing quasi-brittle materials: Analyzing with strong discontinuity embedded approach. Engineering Fracture Mechanics, 2018, 192: 290–306
https://doi.org/10.1016/j.engfracmech.2017.12.018
|
78 |
Z Sun, S Li, L Rentai, G Bo, Q Zhang, Z Lewen. Quantitative research on grouting reinforcement of soft fluid-plastic stratum. Chinese Journal of Rock Mechanics and Engineering, 2016, 35: 3385–3393 (in Chinese)
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|