Dilation angle variations in plastic zone around tunnels in rocks-constant or variable dilation parameter

Abstract

Dilation angle is a significant parameter needed for numerical simulation of tunnels. Even though dilation parameter is physically variable and dependent on confinement and experienced shear plastic strain based on the existing dilation models, numerical simulations of tunnels and underground openings with constant dilation parameter usually lead to satisfactory results in practical use. This study aims to find out why constant dilation angle is enough under practical conditions to simulate numerically tunnels and underground excavations in spite of the fact that dilation angle is variable in laboratory and experimental scale. With this aim, this work studies how mobilized dilation angle varies in a plastic zone surrounding a tunnel. For the circular tunnel under uniform in situ stress field, the stepwise finite difference approximation analytical solution considering strain softening rock mass behavior with mobilized dilation angle was used to study how mobilized dilation angle varies in plastic zone around tunnel under very different conditions. In practical conditions determined in this study, dilative behavior of all over the plastic zone around the tunnel can be approximated to constant dilation angle in the middle region of the plastic zone. Moreover, the plastic zone displacements for mobilized and constant dilation angle models are compared with each other. Further investigation under more general non-uniform in situ stress conditions and non-circular tunnels is performed by using the commercial finite difference software to numerically simulate the Mine-by experimental tunnel of AECL (Atomic Energy of Canada Limited) and the arched tunnel. Although the Mine-by and arched tunnels were numerically simulated based on the mobilized dilation angle model, the variability associated with dilation angle around the simulated Mine-by and arched tunnels is insignificant, and dilation angle is approximately constant in the plastic zone.

Keywords

dilation / post-peak behavior / plastic zone / strain softening

References

[1] ZhaoX G, CaiM. Influence of plastic shear strain and confinement-dependent rock dilation on rock failure and Displacement near an excavation boundary [J]. International Journal of Rock Mechanics and Mining Sciences, 2010, 47: 723-738

[2] KaiserP K, MccreathD R, TannantD DCanadian rockburst support handbook [M], 1996, Sudbury, Geomechanics Research Centre/MIRARCO

[3] BiJ, ZhouX P, XuX M. Numerical simulation of failure process of rock-like materials subjected to impact loads [J]. Int Geomech J, 2017, 17(3): 04016073

[4] BiJ, ZhouX P, QianQ H. The 3D numerical simulation for the propagation process of multiple pre-existing flaws in rock-like materials subjected to biaxial compressive loads [J]. Rock Mech Rock Eng, 2016, 4951611-1627

[5] ZhouX P, BiJ, QianQ H. Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws [J]. Rock Mech Rock Eng, 2015, 48(3): 1097-1114

[6] ZhouX P, ZhaoY, QianQ H. A novel meshless numerical method for modeling progressive failure processes of slopes [J]. Engineering Geology, 2015, 192: 139-153

[7] SillingS A. Reformulation of elasticity theory for discontinuities and long-range forces [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175-209

[8] ZhouX P, GuX B, WangY T. Numerical simulations of propagation, bifurcation and coalescence of cracks in rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2015, 80: 241-254

[9] DetournayE. Elastoplastic model of a deep tunnel for a rock with variable dilatancy [J]. Rock Mech Rock Eng, 1986, 19: 99-108

[10] AlejanoL R, AlonsoE. Considerations of the dilation angle in rocks and rock masses [J]. International Journal of Rock Mechanics & Mining Sciences, 2005, 42: 481-507

[11] ZhaoX G, CaiM. A mobilized dilation angle model for rocks [J]. International Journal of Rock Mechanics & Mining Sciences, 2010, 47: 368-384

[12] WaltonGImproving continuum models for excavations in rock masses under high stress through an enhanced understanding of post-yield dilatancy [D], 2014, Canada, Queen’s University

[13] SalehniaF, CollinF, CharlierR. On the variable dilatancy angle in rocks around underground galleries [J]. Rock Mech Rock Eng, 2016115

[14] WaltonG, DiedrichsM S. A new model for the dilation of brittle rocks based on laboratory compression test data with separate treatment of dilatancy mobilization and decay [J]. Geotechnical Geology Engineering, 2015, 33: 661-679

[15] WaltonG, DiederichsM S. Dilation and post-peak behaviour inputs for practical engineering analysis [J]. Geotechnical Geology Engineering, 2015, 33: 15-34

[16] VermeeP A D, BorstR. Non-associated plasticity for soils, concrete and rock [J]. Heron, 1984, 29(3): 1-64

[17] BradyB H G, BrownE TRock Mechanics for Underground Mining [M], 1993, London, Chapman & Hall

[18] EdwinT, BrownM, JohnW, BrankoB, LadanyiF, HoekE. Ground response curves for rock tunnels [J]. Journal of Geotechnical Engineering, 1983, 109: 15-39

[19] AlejanoL R, AlonsoE, Rodriguez-DonoA, Fernandez-ManinG. Application of the Convergenceconfinement Method to Tunnels in Rock Masses Exhibiting Hoek–Brown Strain-softening Behaviour [J]. International Journal of Rock Mechanics And Mining Sciences, 2010, 47: 150-160

[20] LeeY K, PietruszczakS. A new numerical procedure for elasto-plastic analysis of acircular opening excavated in astrain-softening rock mass [J]. Tunnelling and Underground Space Technology, 2008, 23: 588-599

[21] KatebianE, MolladavoodiH. Practical ground response curve considering post peak rock mass behavior [J]. European Journal of Environmental and Civil Engineering, 2017, 21(1): 1-23

[22] FarrokhE, RostamiJ. Correlation of tunnel convergence with TBM operational parameters and chip size in the Ghomroud tunnel, Iran [J]. Tunnelingand Underground Space Technology, 2008, 23: 700-710

[23] EdelbroC. Different approaches for simulating brittle failure in two hard rock mass cases: A parametric study [J]. Rock Mech Rock Eng, 2010, 43: 151-165

[24] MartinC DStrength of massive Lac du Bonnet granite around underground openings [D], 1993, Winnipeg, University of Manitoba

[25] MartinC D, ReadR S. AECL’s Mine-by experiment: A test tunnel in brittle rock [C]. Proceedings of the 2nd North American Rock Mechanics, 1997, Montreal, A. A. Balkema

[26] ZhaoX G, CaimC M. Considerations of rock dilation on modeling failure and deformation of hard rocks—A case study of the mine-by test tunnel in Canada [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2010, 2(4): 338-349

[27] HajiabdolmajidV, KaiserP K, MartinC D. Modelling brittle failure of rock [J]. International Journal of Rock Mechanics & Mining Sciences, 2002, 39: 731-741

[28] EdelbroC. Numerical modelling of observed fallouts in hard rock masses usingan instantaneous cohesion-softening friction-hardening model [J]. Tunneling and Underground Space Technology, 2010, 24: 398-409

[29] DE BorstR. Bifurcations in finite element models with a non-associated flow law [J]. International Journal of Numerical and Analytical Methods in Geomechanics, 1988, 12: 99-116

[30] VardoulakisI. Shear band inclination and shear modulus of sand in biaxial tests [J]. International Journal of Numerical and Analytical Methods in Geomechanics, 1980, 4: 103-119

[31] HobbsB E, OrdA. Numerical simulation of shear band formation in a frictional-dilatational material [J]. Ingenieur-Archiv, 1989, 59: 209-220

[32] KirkebϕSA numerical study of excavations in low permeable soils [D], 1994, Trondheim, University of Trondheim

[33] BernierF, LiX, BastiaensW, OrtizL, VAN GeetM, WoutersL, FriegB, Blu MlingP, DesruesJ, ViaggianiGFracturesand self-healing within the excavation disturbed zone in clays (selfrac) [R], 2007