Theoretical and numerical analyses of squeezing rock mass around a spherical opening considering the existence of a damaged zone

Document Type : Research Article

Authors

Department of geotechnical Engineering, Faculty of civil engineering, University of Tabriz, 29 Bahman Blvd, Tabriz, Iran

Abstract

If an underground opening is excavated using the drill and blast method, an excavation damaged zone (EDZ) will appear around the opening in which it's mechanical and creep properties can be very different from the initial rock mass. The existence of such a zone in squeezing rock masses can lead the time-dependent displacements to increase. Therefore, in this paper, a closed-formed analytical solution is proposed to determine the long-term performance of a spherical opening surrounded by an EDZ. To consider the time-dependent behavior, the viscoelastic Burgers model is assigned to the rock mass. After verifying the proposed method, a parametric study is performed and the influence of various factors such as the radii of the opening and EDZ, the shear modulus, and the viscosity of rock mass are investigated. It is found that if the EDZ radius is considered constant, the displacement of the cavity with 7 meters radius, immediately and after 10 years, is respectively 1.42 and 1.57 times greater than the case in which the cavity radius is 4.57 meters. On the other hand, if the cavity radius is equal to 4.57 meters, immediately and after 10 years, the displacement of the cavity wall in which the EDZ radius is 8 meters is respectively 50% and 70% greater than the case in which this radius is equal to 6 meters. When the radii of the cavity and the EDZ are constant, if the Kelvin viscosity becomes one-twentieth, the cavity displacement increases by 115% and 173% after 1 year, respectively. However, if 20 times of the initial Maxwell viscosity of the EDZ is used in the calculations, this displacement decreases by about 14%, after 50 years.

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References

[1] H.N. Wang, G.H. Nie, Analytical expressions for stress and displacement fields in viscoelastic axisymmetric plane problem involving time-dependent boundary regions, Acta Mechanica, 210(3) (2010) 315-330.
[2] A. Fahimifar, F.M. Tehrani, A. Hedayat, A. Vakilzadeh, Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field, Tunnelling and Underground Space Technology, 25(4) (2010) 297-304.
[3] P. Nomikos, R. Rahmannejad, A. Sofianos, Supported Axisymmetric Tunnels Within Linear Viscoelastic Burgers Rocks, Rock Mechanics and Rock Engineering, 44(5) (2011) 553-564.
[4] Z. Chu, Z. Wu, B. Liu, Q. Liu, Coupled analytical solutions for deep-buried circular lined tunnels considering tunnel face advancement and soft rock rheology effects, Tunnelling and Underground Space Technology, 94 (2019) 103111.
[5] Z. Chu, Z. Wu, Q. Liu, B. Liu, Analytical Solutions for Deep-Buried Lined Tunnels Considering Longitudinal Discontinuous Excavation in Rheological Rock Mass, Journal of Engineering Mechanics, 146(6) (2020) 04020047.
[6] M.R. Zareifard, A. Fahimifar, Rock-lining interaction calculations for tunnels excavated in Hoek-Brown rock mass considering excavation damaged zone, Amirkabir Journal of Civil Engineering, 51(5) (2019) 865-884, [in Persian].
[7] M. Zaheri, M. Ranjbarnia, Ground reaction curve of a circular tunnel considering the effects of the altered zone and the self-weight of the plastic zones, European Journal of Environmental and Civil Engineering, (2021) 1-24.
[8] M.R. Zareifard, A new semi-numerical method for elastoplastic analysis of a circular tunnel excavated in a Hoek–Brown strain-softening rock mass considering the blast-induced damaged zone, Computers and Geotechnics, 122 (2020) 103476.
[9] M.R. Zareifard, A. Fahimifar, Analytical solutions for the stresses and deformations of deep tunnels in an elastic-brittle-plastic rock mass considering the damaged zone, Tunnelling and Underground Space Technology, 58 (2016) 186-196.
[10] J. Zuo, J. Shen, The Blast Damage Factor D, in: J. Zuo, J. Shen (Eds.) The Hoek-Brown Failure criterion—From theory to application, Springer Singapore, Singapore, 2020, pp. 105-115.
[11] E. Hoek, C. Carranza-Torres, B. Corkum, Hoek-Brown failure criterion-2002 edition, Proceedings of NARMS-Tac, 1 (2002) 267-273.
[12] E. Hoek, P. Marinos, Predicting tunnel squeezing problems in weak heterogeneous rock masses, Tunnels and tunnelling international, 32(11) (2000) 45-51.
[13] R. Osgoui, E. Unal, Characterization of Weak Rock Masses Using GSI-Index and the Estimation of Support-Pressure, in: Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS), 2005.
[14] R.R. Osgoui, E. Ünal, An empirical method for design of grouted bolts in rock tunnels based on the Geological Strength Index (GSI), Engineering Geology, 107(3) (2009) 154-166.
[15] M. Giordanella, M. Ranjbarnia, P. Oreste, M. Zaheri, Study of the systematic fully grouted rock bolts performance in tunnels considering installation condition of bolt head, Geomechanics and Geoengineering, (2021) 1-17.
[16] M. Ranjbarnia, M. Zaheri, D. Dias, Three-dimensional finite difference analysis of shallow sprayed concrete tunnels crossing a reverse fault or a normal fault: A parametric study, Frontiers of Structural and Civil Engineering, 14(4) (2020) 998-1011.
[17] M. Zaheri, M. Ranjbarnia, A New Procedure for Calculation of Ground Response Curve of a Circular Tunnel Considering the Influence of Young’s Modulus Variation and the Plastic Weight Loading, Geotechnical and Geological Engineering, 39(2) (2021) 1079-1099.
[18] M. Zaheri, M. Ranjbarnia, D. Dias, 3D numerical investigation of segmental tunnels performance crossing a dip-slip fault, Geomechanics and Engineering, 23(4) (2020) 351-364.
[19] M. Zaheri, M. Ranjbarnia, D. Dias, P. Oreste, Performance of segmental and shotcrete linings in shallow tunnels crossing a transverse strike-slip faulting, Transportation Geotechnics, 23 (2020) 100333.
[20] M. Zaheri, M. Ranjbarnia, P. Oreste, Performance of systematic fully grouted rockbolts and shotcreted layer in circular tunnel under the hydrostatic conditions using 3D finite difference approach, Geomechanics and Geoengineering, 16(3) (2021) 198-211.
[21] C. Carranza-Torres, C. Fairhurst, The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek–Brown failure criterion, International Journal of Rock Mechanics and Mining Sciences, 36(6) (1999) 777-809.
[22] C. Carranza-Torres, C. Fairhurst, On the stability of tunnels under gravity loading, with post-peak softening of the ground, International Journal of Rock Mechanics and Mining Sciences, 34(3) (1997) 75.e71-75.e18.
[23] L. Alejano, E. Alonso, A. Rodriguez-Dono, G. Fernandez-Manin, Application of the convergence-confinement method to tunnels in rock masses exhibiting Hoek–Brown strain-softening behaviour, International Journal of Rock Mechanics and Mining Sciences, 1(47) (2010) 150-160.
[24] L.R. Alejano, A. Rodriguez-Dono, E. Alonso, G. Fdez.-Manín, Ground reaction curves for tunnels excavated in different quality rock masses showing several types of post-failure behaviour, Tunnelling and Underground Space Technology, 24(6) (2009) 689-705.
[25] E. Alonso, L.R. Alejano, F. Varas, G. Fdez-Manin, C. Carranza-Torres, Ground response curves for rock masses exhibiting strain-softening behaviour, International Journal for Numerical and Analytical Methods in Geomechanics, 27(13) (2003) 1153-1185.
[26] E.T. Brown, J.W. Bray, B. Ladanyi, E. Hoek, Ground Response Curves for Rock Tunnels, Journal of Geotechnical Engineering, 109(1) (1983) 15-39.
[27] N.A. Do, D. Dias, A comparison of 2D and 3D numerical simulations of tunnelling in soft soils, Environmental Earth Sciences, 76(3) (2017) 102.
[28] N.A. Do, D. Dias, P. Oreste, Numerical investigation of segmental tunnel linings-comparison between the hyperstatic reaction method and a 3D numerical model, Geomechanics and Engineering, 14(3) (2018) 293-299.
[29] N.A. Do, D. Dias, P. Oreste, I. Djeran-Maigre, 2D numerical investigations of twin tunnel interaction, Geomech. Eng., Int. J, 6(3) (2014) 263-275.
[30] N.A. Do, D. Dias, P. Oreste, I. Djeran-Maigre, The behaviour of the segmental tunnel lining studied by the hyperstatic reaction method, European Journal of Environmental and Civil Engineering, 18(4) (2014) 489-510.
[31] N.-A. Do, D. Dias, P. Oreste, 3D numerical investigation on the interaction between mechanized twin tunnels in soft ground, Environmental Earth Sciences, 73(5) (2015) 2101-2113.
[32] N.-A. Do, D. Dias, P. Oreste, I. Djeran-Maigre, 2D numerical investigation of segmental tunnel lining behavior, Tunnelling and Underground Space Technology, 37 (2013) 115-127.
[33] N.-A. Do, D. Dias, P. Oreste, I. Djeran-Maigre, 2D tunnel numerical investigation: the influence of the simplified excavation method on tunnel behaviour, Geotechnical and Geological Engineering, 32(1) (2014) 43-58.
[34] N.-A. Do, D. Dias, P. Oreste, I. Djeran-Maigre, Three-dimensional numerical simulation for mechanized tunnelling in soft ground: the influence of the joint pattern, Acta Geotechnica, 9(4) (2014) 673-694.
[35] N.-A. Do, D. Dias, P. Oreste, I. Djeran-Maigre, Three-dimensional numerical simulation of a mechanized twin tunnels in soft ground, Tunnelling and Underground Space Technology, 42 (2014) 40-51.
[36] A.R. Kargar, An analytical solution for circular tunnels excavated in rock masses exhibiting viscous elastic-plastic behavior, International Journal of Rock Mechanics and Mining Sciences, 124 (2019) 104128.
[37] M. Zaheri, M. Ranjbarnia, M. Goudarzy, Analytical and Numerical Simulations to Predict the Long-Term Behavior of Lined Tunnels Considering Excavation-Induced Damaged Zone, Rock Mechanics and Rock Engineering,  (2022).
[38] S. Keawsawasvong, B. Ukritchon, Undrained stability of a spherical cavity in cohesive soils using finite element limit analysis, Journal of Rock Mechanics and Geotechnical Engineering, 11(6) (2019) 1274-1285.
[39] H.-S. Yu, Cavity expansion methods in geomechanics, Springer Science & Business Media, Springer Netherlands, 2000.
[40] J. Zhao, G. Wang, Unloading and reverse yielding of a finite cavity in a bounded cohesive–frictional medium, Computers and Geotechnics, 37(1) (2010) 239-245.
[41] F. Huang, X.L. Yang, T.H. Ling, Prediction of Collapsing Region Above Deep Spherical Cavity Roof Under Axis-Symmetrical Conditions, Rock Mechanics and Rock Engineering, 47(4) (2014) 1511-1516.
[42] K.H. Park, Similarity solution for a spherical or circular opening in elastic-strain softening rock mass, International Journal of Rock Mechanics and Mining Sciences, 71 (2014) 151-159.
[43] K.H. Park, Large strain similarity solution for a spherical or circular opening excavated in elastic-perfectly plastic media, International Journal for Numerical and Analytical Methods in Geomechanics, 39(7) (2015) 724-737.
[44] P. Oreste, Face stabilization of deep tunnels using longitudinal fibreglass dowels, International Journal of Rock Mechanics and Mining Sciences, 58 (2013) 127-140.
[45] S. Ottosen, Behaviour of viscoelastic-viscoplastic spheres and cylinders—Partly plastic vessel walls, International Journal of Solids and Structures, 21(6) (1985) 573-595.
[46] A.D. Polyanin, A.V. Manzhirov, Handbook of integral equations, 2nd Edition ed., Chapman and Hall/CRC, New York, 2008.
Amirkabir Journal of Civil Engineering
Volume 54, Issue 11
February 2023
Pages 4215-4238

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