Abstract
We present a multiscale investigation on the initiation and development of compaction bands in high-porosity sandstones based on an innovative hierarchical multiscale approach. This approach couples the finite element method and the discrete element method (DEM) to offer direct, rigorous linking of the microscopic origins and mechanisms with complex macroscopic phenomena observed in granular rocks such as strain localization and failure. To simulate compaction band in granular cementitious sandstone, we adopt a bonded contact model with normal and tangential interparticle cohesions in the DEM and propose a dual-porosity structure consisting of macro-pores and interstitial voids for the representative volume element to mimic the typical meso-structure of high-porosity sandstones. In the absence of particle crushing, our multiscale analyses identify debonding and pore collapses as two major contributors to the formation of compaction bands. The critical pressures predicted by our simulations, corresponding to surges of debonding and pore collapse events, agree well with the estimations from field data. The occurrence patterns of compaction band are found closely related to specimen heterogeneity, porosity and confining pressure. Other deformation band patterns, including shear-enhanced compaction bands and compactive shear bands, were also observed under relatively low confining pressure conditions with a rough threshold at \(0.55P^{*}\) (\(P^{*}\) is the critical pressure) on the failure envelop. Key microscopic characteristics attributable to the occurrence of these various deformation patterns, including fabric anisotropy, particle rotation, debonding and pore collapse, are examined. Shear-enhanced compaction bands and pure compaction bands bear many similarities in terms of these microscopic characteristics, whereas both differ substantially from compactive shear bands.
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References
Andrade JE, Avila CF, Hall SA, Lenoir N, Viggiani G (2011) Multiscale modeling and characterization of granular matter: from grain kinematics to continuum mechanics. J Mech Phys Solids 59(2):237–250. doi:10.1016/j.jmps.2010.10.009
Antonellini MA, Aydin A, Pollard DD (1994) Microstructure of deformation bands in porous sandstones at Arches National Park, Utah. J Struct Geol 16(7):941–959. doi:10.1016/0191-8141(94)90077-9
Aydin A (1978) Small faults formed as deformation bands in sandstone. Pure Appl Geophys 116(4–5):913–930. doi:10.1007/BF00876546
Aydin A, Ahmadov R (2009) Bed-parallel compaction bands in aeolian sandstone: their identification, characterization and implications. Tectonophysics 479(3–4):277–284. doi:10.1016/j.tecto.2009.08.033
Aydin A, Borja RI, Eichhubl P (2006) Geological and mathematical framework for failure modes in granular rock. J Struct Geol 28(1):83–98. doi:10.1016/j.jsg.2005.07.008
Baud P, Klein E, Wong TF (2004) Compaction localization in porous sandstones: spatial evolution of damage and acoustic emission activity. J Struct Geol 26(4):603–624. doi:10.1016/j.jsg.2003.09.002
Bernabé Y, Fryer DT, Hayes JA (1992) The effect of cement on the strength of granular rocks. Geophys Res Lett 19(14):1511. doi:10.1029/92GL01288
Bésuelle P (2001) Compacting and dilating shear bands in porous rock: theoretical and experimental conditions. J Geophys Res Solid Earth 106(B7):13435–13442. doi:10.1029/2001JB900011
Bésuelle P, Desrues J, Raynaud S (2000) Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a triaxial cell. Int J Rock Mech Min Sci 37(8):1223–1237. doi:10.1016/S1365-1609(00)00057-5
Challa V, Issen KA (2004) Conditions for compaction band formation in porous rock using a two-yield surface model. J Eng Mech 130(9):1089–1097. doi:10.1061/(ASCE)0733-9399(2004)130:9(1089)
Charalampidou E-M, Hall SA, Stanchits S, Viggiani G, Lewis H (2014) Shear-enhanced compaction band identification at the laboratory scale using acoustic and full-field methods. Int J Rock Mech Min Sci 67:240–252. doi:10.1016/j.ijrmms.2013.05.006
Charalampidou EM, Hall SA, Stanchits S, Lewis H, Viggiani G (2011) Characterization of shear and compaction bands in a porous sandstone deformed under triaxial compression. Tectonophysics 503(1–2):8–17. doi:10.1016/j.tecto.2010.09.032
Cheng Y, Nakata Y, Bolton M (2003) Discrete element simulation of crushable soil. Géotechnique 53(7):633–641. doi:10.1680/geot.2003.53.7.633
Cheung CSN, Baud P, Wong TF (2012) Effect of grain size distribution on the development of compaction localization in porous sandstone. Geophys Res Lett 39(21):6–10. doi:10.1029/2012GL053739
Ciantia MO, Hueckel T (2013) Weathering of submerged stressed calcarenites: chemo-mechanical coupling mechanisms. Géotechnique 63(9):768–785. doi:10.1680/geot.SIP13.P.024
Das A, Nguyen GD, Einav I (2011) Compaction bands due to grain crushing in porous rocks: a theoretical approach based on breakage mechanics. J Geophys Res 116(B8):B08203. doi:10.1029/2011JB008265
Das A, Nguyen GD, Einav I (2013) The propagation of compaction bands in porous rocks based on breakage mechanics. J Geophys Res Solid Earth 118(5):2049–2066. doi:10.1002/jgrb.50193
Dattola G, di Prisco C, Redaelli I, Utili S (2014) A distinct element method numerical investigation of compaction processes in highly porous cemented granular materials. Int J Numer Anal Methods Geomech 38(11):1101–1130. doi:10.1002/nag.2241
Delenne JY, El Youssoufi MS, Cherblanc F, Bénet JC (2004) Mechanical behaviour and failure of cohesive granular materials. Int J Numer Anal Methods Geomech 28(15):1577–1594. doi:10.1002/nag.401
Eichhubl P, Taylor WL, Pollard DD, Aydin A (2004) Paleo-fluid flow and deformation in the Aztec Sandstone at the Valley of Fire, Nevada—evidence for the coupling of hydrogeologic, diagenetic, and tectonic processes. Geol Soc Am Bull 116(9):1120. doi:10.1130/B25446.1
Eichhubl P, Hooker JN, Laubach SE (2010) Pure and shear-enhanced compaction bands in Aztec Sandstone. J Struct Geol 32(12):1873–1886. doi:10.1016/j.jsg.2010.02.004
Fortin J, Stanchits S, Dresen G, Guéguen Y (2006) Acoustic emission and velocities associated with the formation of compaction bands in sandstone. J Geophys Res 111(B10):B10203. doi:10.1029/2005JB003854
Fortin J, Stanchits S, Dresen G, Gueguen Y (2009) Acoustic emissions monitoring during inelastic deformation of porous sandstone: comparison of three modes of deformation. Pure Appl Geophys 166(5–7):823–841. doi:10.1007/s00024-009-0479-0
Fossen H, Schultz RA, Shipton ZK, Mair K (2007) Deformation bands in sandstone: a review. J Geol Soc Lond 164(4):1–15. doi:10.1144/0016-76492006-036
Fossen H, Schultz RA, Torabi A (2011) Conditions and implications for compaction band formation in the Navajo Sandstone, Utah. J Struct Geol 33(10):1477–1490. doi:10.1016/j.jsg.2011.08.001
Gao Z, Zhao J (2013) Strain localization and fabric evolution in sand. Int J Solids Struct 50(22–23):3634–3648. doi:10.1016/j.ijsolstr.2013.07.005
Guo N, Zhao J (2014) A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. Int J Numer Methods Eng 99(11):789–818. doi:10.1002/nme.4702
Guo N, Zhao J (2016) 3D multiscale modeling of strain localization in granular media. Comput Geotech 80:360–372. doi:10.1016/j.compgeo.2016.01.020
Guo N, Zhao J (2016) Multiscale insights into classical geomechanics problems. Int J Numer Anal Methods Geomech 40(3):367–390. doi:10.1002/nag.2406
Guo N, Zhao J (2016) Parallel hierarchical multiscale modelling of hydro-mechanical problems for saturated granular soils. Comput Methods Appl Mech Eng 305:37–61. doi:10.1016/j.cma.2016.03.004
Guo N, Zhao J, Sun WC (2016) Multiscale analysis of shear failure of thick-walled hollow cylinder in dry sand. Géotech Lett 6(1):77–82. doi:10.1680/jgele.15.00149
Hazzard JF, Young RP, Maxwell SC (2000) Micromechanical modeling of cracking and failure in brittle rocks. J Geophys Res 105:16683–16697. doi:10.1029/2000JB900085
Hill RE (1989) Analysis of deformation bands in the Aztec Sandstone. University of Nevada, Reno
Holcomb D, Rudnicki JW, Issen KA, Sternlof K (2007) Compaction localization in the Earth and the laboratory: state of the research and research directions. Acta Geotech 2(1):1–15. doi:10.1007/s11440-007-0027-y
Holcomb DJ, Olsson WA (2003) Compaction localization and fluid flow. J Geophys Res 108(B6):2290–2302. doi:10.1029/2001JB000813
Issen KA, Rudnicki JW (2000) Conditions for compaction bands in porous rock. J Geophys Res 105(B9):21529–21536. doi:10.1029/2000JB900185
Katsman R, Aharonov E (2006) A study of compaction bands originating from cracks, notches, and compacted defects. J Struct Geol 28(3):508–518. doi:10.1016/j.jsg.2005.12.007
Katsman R, Aharonov E, Haimson BC (2009) Compaction bands induced by borehole drilling. Acta Geotech 4(3):151–162. doi:10.1007/s11440-009-0086-3
Kim SY, Sasaki Y (2013) Simulation of crack formation in an anisotropic coke using discrete element method. Fuel 106:357–364. doi:10.1016/j.fuel.2012.10.070
Klein E, Baud P, Reuschlé T, Wong TF (2001) Mechanical behaviour and failure mode of Bentheim sandstone under triaxial compression. Phys Chem Earth Part A Solid Earth Geodyn 26(1–2):21–25. doi:10.1016/S1464-1895(01)00017-5
Liu C, Pollard DD, Gu K, Shi B (2015) Mechanism of formation of wiggly compaction bands in porous sandstone: 2. Numerical simulation using discrete element method. J Geophys Res Solid Earth 120(12):8153–8168. doi:10.1002/2015JB012374
Liu Y, Sun W, Yuan Z, Fish J (2016) A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials. Int J Numer Methods Eng 106(2):129–160. doi:10.1002/nme.5139
Ma X, Haimson BC (2016) Failure characteristics of two porous sandstones subjected to true triaxial stresses. J Geophys Res Solid Earth 121(9):6477–6498. doi:10.1002/2016JB012979
Marketos G, Bolton MD (2005) Compaction bands as observed in DEM simulations In: Proceedings of the 5th international conference on micromechanics of granular media, powders and grains, pp 1405–1408
Marketos G, Bolton MD (2007) A DEM study of compaction band formation. In: Bifurcations, instabilities, degradation in geomechanics. Springer, Berlin, pp 155–171
Marketos G, Bolton MD (2009) Compaction bands simulated in discrete element models. J Struct Geol 31(5):479–490. doi:10.1016/j.jsg.2009.03.002
Meier HA, Steinmann P, Kuhl E (2008) Towards multiscale computation of confined granular media-Contact forces, stresses and tangent operators. Tech Mech 16(1):77–88
Miehe C, Dettmar J, Zäh D (2010) Homogenization and two-scale simulations of granular materials for different microstructural constraints. Int J Numer Methods Eng 83(8–9):1206–1236. doi:10.1002/nme.2875
Mollema PN, Antonellini MA (1996) Compaction bands: a structural analog for anti-mode I cracks in aeolian sandstone. Tectonophysics 267(1–4):209–228. doi:10.1016/S0040-1951(96)00098-4
Nguyen TK, Combe G, Caillerie D, Desrues J (2014) FEM x DEM modelling of cohesive granular materials: numerical homogenisation and multi-scale simulation. Acta Geophys 62(3):1–18. doi:10.2478/s11600-013-00
Nitka M, Combe G, Dascalu C, Desrues J (2011) Two-scale modeling of granular materials: a DEM–FEM approach. Granul Matter 13(3):277–281. doi:10.1007/s10035-011-0255-6
Oda M (1982) Fabric tensor for discontinuous geological materials. Soils Found 22(4):96–108. doi:10.3208/sandf1972.22.4_96
Oka F, Kimoto S, Higo Y, Ohta H, Sanagawa T, Kodaka T (2011) An elasto-viscoplastic model for diatomaceous mudstone and numerical simulation of compaction bands. Int J Numer Anal Methods Geomech 35(2):244–263. doi:10.1002/nag.987
Olsson WA (1999) Theoretical and experimental investigation of compaction bands in porous rock. J Geophys Res 104(B4):7219–7228. doi:10.1029/1998JB900120
Olsson WA (2001) Quasistatic propagation of compaction fronts in porous rock. Mech Mater 33(11):659–668. doi:10.1016/S0167-6636(01)00078-3
Olsson WA, Holcomb DJ (2000) Compaction localization in porous rock. Geophys Res Lett 27(21):3537–3540. doi:10.1029/2000GL011723
Olsson WA, Holcomb DJ, Rudnicki JW (2002) Compaction localization in porous sandstone: implications for reservoir mechanics. Oil Gas Sci Technol 57(5):591–599. doi:10.2516/ogst:2002040
Park JW, Song JJ (2009) Numerical simulation of a direct shear test on a rock joint using a bonded-particle model. Int J Rock Mech Min Sci 46(8):1315–1328. doi:10.1016/j.ijrmms.2009.03.007
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8 SPEC.ISS.):1329–1364. doi:10.1016/j.ijrmms.2004.09.011
Rudnicki JW (2004) Shear and compaction band formation on an elliptic yield cap. J Geophys Res 109(B3):1–10. doi:10.1029/2003JB002633
Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394. doi:10.1016/0022-5096(75)90001-0
Schultz RA, Okubo CH, Fossen H (2010) Porosity and grain size controls on compaction band formation in Jurassic Navajo Sandstone. Geophys Res Lett 37(22):1–5. doi:10.1029/2010GL044909
Sternlof KR, Rudnicki JW, Pollard DD (2005) Anticrack inclusion model for compaction bands in sandstone. J Geophys Res 110(B11):B11403. doi:10.1029/2005JB003764
Tembe S, Vajdova V, Wong T, Zhu W (2006) Initiation and propagation of strain localization in circumferentially notched samples of two porous sandstones. J Geophys Res 111(B2):B02409. doi:10.1029/2005JB003611
Tembe S, Baud P, Wong T (2008) Stress conditions for the propagation of discrete compaction bands in porous sandstone. J Geophys Res 113(B9):B09409. doi:10.1029/2007JB005439
Townend E, Thompson BD, Benson PM, Meredith PG, Baud P, Young RP (2008) Imaging compaction band propagation in Diemelstadt sandstone using acoustic emission locations. Geophys Res Lett 35(15):1–5. doi:10.1029/2008GL034723
Vajdova V, Wong TF (2003) Incremental propagation of discrete compaction bands: acoustic emission and microstructural observations on circumferentially notched samples of Bentheim. Geophys Res Lett 30(14):1775–1778. doi:10.1029/2003GL017750
Wang B, Chen Y, Wong T (2008) A discrete element model for the development of compaction localization in granular rock. J Geophys Res 113(B3):B03202. doi:10.1029/2006JB004501
Wang K, Sun W (2016) A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain. Comput Methods Appl Mech Eng. doi:10.1016/j.cma.2016.02.020
Wang Y-H, Leung S-C (2008) A particulate-scale investigation of cemented sand behavior. Can Geotech J 45(1):29–44. doi:10.1139/T07-070
Wong T, Szeto H, Zhang J (1992) Effect of loading path and porosity on the failure mode of porous rocks. Appl Mech Rev 45(8):281–293. doi:10.1115/1.3119759
Wong T-F, David C, Zhu W (1997) The transition from brittle faulting to cataclasic flow in porous sandstones: mechanical deformation. J Geophys Res 102(B2):3009–3025
Wong TF, Baud P (1999) Mechanical compaction of porous sandstone. Oil Gas Sci Technol 54(6):715–727. doi:10.2516/ogst:1999061
Wong TF, Baud P, Klein E (2001) Localized failure modes in a compactant porous rock. Geophys Res Lett 28(13):2521–2524. doi:10.1029/2001GL012960
Zhang J, Wong T-F, Davis DM (1990) Micromechanics of pressure-induced grain crushing in porous rocks. J Geophys Res 95(B1):341. doi:10.1029/JB095iB01p00341
Zhao J, Guo N (2015) The interplay between anisotropy and strain localisation in granular soils: a multiscale insight. Géotechnique 65(8):642–656. doi:10.1680/geot.14.P.184
Zheng Z, Sun WC, Fish J (2016) Micropolar effect on the cataclastic flow and brittle–ductile transition in high-porosity rocks. J Geophys Res B Solid Earth 121(3):1425–1440. doi:10.1002/2015JB012179
Acknowledgements
This work was partially supported by Research Grants Council of Hong Kong through a Theme-based Research Project (No. T22-603/15N) and a Collaborative Research Fund project (Grant No. C6012-15G) and by Natural Science Foundation of China under Project No. 51679207. The authors are also grateful for Prof. Teng-fong Wong of CUHK and Dr. WaiChing Sun of Columbia University for useful discussion on this topic.
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Wu, H., Guo, N. & Zhao, J. Multiscale modeling and analysis of compaction bands in high-porosity sandstones. Acta Geotech. 13, 575–599 (2018). https://doi.org/10.1007/s11440-017-0560-2
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DOI: https://doi.org/10.1007/s11440-017-0560-2