Elasto-plastic and hydromechanical models of failure around an infinitely long magma chamber

Geochemistry, Geophysics, Geosystems

Volumn 13, Issue 3, 2012, Pages

  Gerbault, Muriel ^a   Cappa, Frederic ^a   Hassani, Riad ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

eruption mechanisms; volcano monitoring

Indexed keywords

ELASTICITY; ELASTOPLASTICITY; POROSITY; SAILING VESSELS; SURFACE MEASUREMENT; TENSILE STRENGTH;

ANALYTICAL AND NUMERICAL MODELS; BODY FORCES; CHAMBER WALLS; COULOMB FAILURE CRITERIA; EFFECTIVE NORMAL STRESS; ELASTO-PLASTIC; ERUPTION MECHANISMS; FLUID PRESSURES; GRAVITY EFFECTS; HIGH POROSITY; HYDROMECHANICAL MODEL; LOW POROSITY; MAGMA CHAMBER; NUMERICAL CODE; OVERPRESSURE; PATTERNS OF FAILURE; PLANE-STRAIN; PORE FLUID PRESSURE; SHEAR FAILURE; STANDARD SOLUTIONS; STRESS EQUILIBRIUM; SURFACE DISPLACEMENT; TENSILE FAILURES; TUNNELING ENGINEERING; UNDERPRESSURE; UNDRAINED CONDITIONS; VOLCANO MONITORING; VOLUMETRIC STRAIN;

GRAVITATION;

BEDROCK; COULOMB CRITERION; DEFORMATION; ELASTOPLASTICITY; FAILURE MECHANISM; HYDROMECHANICS; MAGMA CHAMBER; NUMERICAL MODEL; OVERPRESSURE; PORE PRESSURE; TENSILE STRENGTH; THRESHOLD; VOLCANIC EARTHQUAKE; VOLCANIC ERUPTION;

EID: 84858671440     PISSN: None     EISSN: 15252027     Source Type: Journal    
DOI: 10.1029/2011GC003917     Document Type: Article

References (90)

1. Acocella, V. (2007), Understanding caldera structure and development: An overview of analogue models compared to natural calderas, Earth Sci. Rev., 85, 125-160, doi:10.1016/j.earscirev.2007.08.004. (Pubitemid 350131571)
2. Anderson, E. M. (1936), The dynamics of formation of conesheets, ring-dykes and cauldron subsidences, Proc. R. Soc. Edinburgh, 56, 128-163.
3. Battaglia, M., P. Segall, and C. Roberts (2003), The mechanics of unrest at Long Valley Caldera: 2. Constraining the nature of the source using geodetic and micro-gravity data, J. Volcanol. Geotherm. Res., 127, 219-245, doi:10.1016/ S0377-0273(03)00171-9. (Pubitemid 37241043)
4. Bjornsson, G., L. Kristjansson, and H. Johnsen (1990), Some observations of the Heimaey deep drill hole during the eruption of 1973, Jokull, 26, 52-57.
5. Bonaccorso, A., S. Cianetti, C. Giunchi, E. Trasatti, M. Bonafede, and E. Boschi (2005), Analytical and 3-D numerical modeling of Mt. Etna (Italy) volcano inflation, Geophys. J. Int., 163, 852-862, doi:10.1111/j.1365- 246X.2005.02777.x. (Pubitemid 43922814)
6. Bonafede, M., and C. Ferrari (2009), Analytical models of deformation and residual gravity changes due to a Mogi source in a viscoelastic medium, Tectonophysics, 471, 4-13, doi:10.1016/j.tecto.2008.10.006.
7. Bonafede, M., and M. Mazzanti (1998), Modelling gravity variations consistent with ground deformation in the Campi Flegrei caldera (Italy), J. Volcanol. Geotherm. Res., 81, 137-157. (Pubitemid 28415814)
8. Bower, S. M., and A. W. Woods (1997), control of magma volatile content and chamber depth on the mass erupted during explosive volcanic eruptions, J. Geophys. Res., 102, 10,273-10,290, doi:10.1029/96JB03176.
9. Burov, E., and L. Guillou-Frottier (1999), Thermomechanical behavior of large ash flow calderas, J. Geophys. Res., 104(B10), 23,081-23,109, doi:10.1029/1999JB900227.
10. Burov, E., C. Jaupart, and L. Guillou-Frottier (2003), Ascent and emplacement of buoyant magma bodies in brittle-ductile upper crutst, J. Geophys. Res., 108(B4), 2177, doi:10.1029/ 2002JB001904.
11. Caquot, A., and J. Kerisel (1956), Traité de Mécanique des Sols, Gauthier-Villars, Paris.
12. Cayol, V., and F. H. Cornet (1998), Three-dimensional modeling of the 1983-1984 eruption at piton de la Fournaise volcanoe, Réunion Island, J. Geophys. Res., 103(B8), 18,025-18,037, doi:10.1029/98JB00201.
13. Chéry, J., A. Bonneville, J. P. Villote, and D. Yuen (1991), Numerical modelling of caldera dynamical behaviour, Geophys. J. Int., 105, 365-379, doi:10.1111/j.1365-246X. 1991.tb06719.x.
14. Chéry, J., M. D. Zoback, and R. Hassani (2001), An integrated mechanical model of the San Andreas fault in central and northern California, J. Geophys. Res., 106, 22,051-22,066, doi:10.1029/2001JB000382.
15. Cundall, P. A. (1989), Numerical experiments on localization in frictional materials, Arch. Appl. Mech., 59, 148-159, doi:10.1007/BF00538368.
16. Cundall, P., and M. Board (1988), A microcomputer program for modeling large-strain plasticity problems, in Numerical Methods in Geomechanics, pp. 2101-2108, A. A. Balkema, Rotterdam, Netherlands.
17. d'Escatha, Y., and J. Mandel (1974), Stabilité d'une galerie peu profonde en terrain meuble, Extrait Ind. Miner., Numero Spec., 1974, 45-53.
18. Dieterich J. H., and R. W. Decker (1975), Finite element modeling of surface deformation associated with volcanism, J. Geophys. Res., 80, 4094-4102.
19. Dragoni, M., and C. Magnanensi (1989), Displacements and stress produced by a pressurised spherical magma chamber, surrounded by a viscoelastic shell, Phys. Earth Planet. Inter., 56, 316-328, doi:10.1016/0031-9201(89)90166-0.
20. Engelder, T., and J. T. Leftwich (1997), A pore-pressure limit in overpressured South Texas oil and gas field, in Seals, Traps, and the Petroleum System, edited by R. C. Surdam, AAPG Mem., 67, 255-267.
21. Fialko, Y., Y. Khazan, and M. Simons (2001), Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy, Geophys. J. Int., 146, 181-190, doi:10.1046/j.1365-246X.2001. 00452.x. (Pubitemid 32608663)
22. Galgana, G. A., P. J. McGovern, and E. B. Grosfils (2011), Evolution of large Venusian volcanoes: Insights from coupled models of lithospheric flexure and magma reservoir pressurization, J. Geophys. Res., 116, E03009, doi:10.1029/ 2010JE003654.
23. Gerbault, M. (2012), Pressure conditions for shear and tensile failure around a circular magma chamber, insight from elasto-plastic modeling, in Faulting, Fracturing and Igneous Intrusion in the Earth's Crust, edited by D. Healy, Geol. Soc. Spec. Publ., in press.
24. Gerbault, M., A. Poliakov, and M. Daignières (1998), Prediction of faulting from the theories of elasticity and plasticity: What are the limits?, J. Struct. Geol., 20, 301-320, doi:10.1016/S0191-8141(97)00089-8. (Pubitemid 28295902)
25. Gray, J. P., and J. J. Monaghan (2004), Numerical modelling of stress fields and fracture around magma chambers, J. Volcanol. Geotherm. Res., 135, 259-283, doi:10.1016/j.jvolgeores.2004. 03.005. (Pubitemid 38774074)
26. Grosfils, E. B. (2007), Magma reservoir failure on the terrestrial planets: Assessing the importance of gravitational loading in simple elastic models, J. Volcanol. Geotherm. Res., 166, 47-75, doi:10.1016/j.jvolgeores.2007. 06.007. (Pubitemid 47440431)
27. Gudmundsson, A. (1988), Effect of tensile stress concentration around magma chambers on intrusion and extrusion frequencies, J. Volcanol. Geotherm. Res., 35, 179-194, doi:10.1016/ 0377-0273(88)90015-7.
28. Gudmundsson, A. (2006), How local stresses control magmachamber ruptures, dyke injections, and eruptions in composite volcanoes, Earth Sci. Rev., 79, 1-31, doi:10.1016/j. earscirev.2006.06.006. (Pubitemid 44734558)
29. Gudmundsson, A., J. Marif, and E. Turon (1997), Stress field generating ring faults in volcanoes, Geophys. Res. Lett., 24, 1559-1562, doi:10.1029/97GL01494.
30. Gudmundsson, A., I. Fjeldskaar, and S. L. Brenner (2002), Propagation pathways and fluid transport of hydrofractures in jointed and layered rocks in geothermal fields, J. Volcanol. Geotherm. Res., 116, 257-278, doi:10.1016/S0377-0273(02) 00225-1. (Pubitemid 34870062)
31. Guillou-Frottier, L., E. B. Burov, and J. P. Milesi (2000), Genetic links between ash flow calderas and associated ore deposits as revealed by large-scale thermo-mechanical modeling, J. Volcanol. Geotherm. Res., 102, 339-361, doi:10.1016/S0377-0273(00)00246-8. (Pubitemid 32166123)
32. Hardy, S. (2008), Structural evolution of calderas: Insights from two-dimensional discrete element formulations?, Geology, 36, 927-930, doi:10.1130/G25133A.1.
33. Hassani, R., D. Jongmans, and J. Chéry (1997), Study of plate deformation and stress in subduction processes using twodimensional numerical models, J. Geophys. Res., 102, 17,951-17,965, doi:10.1029/97JB01354.
34. Heap, M. J., P. Baud, P. G. Meredith, S. Vinciguerra, A. F. Bell, and I. G. Main (2011), Brittle creep in basalt and its application to time-dependent volcano deformation, Earth Planet. Sci. Lett., 307, 71-82, doi:10.1016/j.epsl. 2011.04.035.
35. Henry, C. D., M. J. Kunk, W. R. Muehlberger, and W. C. McIntosh (1997), Igneous evolution of a complex laccolithcaldera, the Solitario, Trans-Pecos Texas: Implications for calderas and subjacent plutons, Geol. Soc. Am. Bull., 109, 1036-1054, doi:10.1130/0016-7606(1997)109<1036:IEOACL> 2.3.CO;2.
36. Hillis, R. R. (2003), Pore pressure/stress coupling and its implications for rock failure, Geol. Soc. Spec. Publ., 216, 359-368, doi:10.1144/GSL.SP.2003. 216.01.23. (Pubitemid 38070189)
37. Hubbert, M. K., and W. W. Rubey (1959), Role of fluid pressure in mechanics of overthrust faulting, Geol. Soc. Am. Bull., 70, 115-166, doi:10.1130/0016-7606(1959)70[115: ROFPIM]2.0.CO;2.
38. Huppert, H., and A. W. Woods (2002), The role of volatiles in magma chamber dynamics, Nature, 420, 493-495, doi:10.1038/nature01211. (Pubitemid 35477038)
39. Hurwitz, S., L. B. Christiansen, and P. A. Hsieh (2007), Hydrothermal fluid flow and deformation in large calderas: Inferences from numerical simulations, J. Geophys. Res., 112, B02206, doi:10.1029/2006JB004689. (Pubitemid 46993076)
40. Hutnak, M., S. Hurwitz, S. E. Ingebritsen, and P. A. Hsieh (2009), Numerical models of caldera formation: Effects of multiphase and multicomponent hydrothermal fluid flow, J. Geophys. Res., 114, B04411, doi:10.1029/ 2008JB006151.
41. Itasca Consulting Group (2006), FLAC3D, Fast Lagrangian Analysis of Continua in 3 Dimensions, version 3.0, user manual, Minneapolis, Minn.
42. Jeffery, J. B. (1921), Plane stress and plane strain in bi-polar coordinates, Philos. Trans. R. Soc. London A, 221, 265-293, doi:10.1098/rsta. 1921.0009.
43. Jellinek, A. M., and D. J. De Paolo (2003), A model for the origin of large silicic magma chambers: Precursors of calderaforming eruptions, Bull. Volcanol., 65, 363-381. (Pubitemid 36947308)
44. Johnson, D. J., F. Sigmundsson, and P. T. Delaney (2000), Comment on "Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea volcano" by P. T. Delaney and D. F. McTigue, Bull. Volcanol., 61, 491-493. (Pubitemid 30144693)
45. Karlstrom, L., J. Dufek, and M. Manga (2010), Magma chamber stability in arc and continental crust, J. Volcanol. Geotherm. Res., 190(3-4), 249-270, doi:10.1016/j.jvolgeores. 2009.10.003.
46. Kaus, B. (2010), Factors that control the angle of shear bands in geodynamic numerical models of brittle deformation, Tectonophysics, 484, 36-47, doi:10.1016/j.tecto.2009. 08.042.
47. Kumagai, H., P. Placios, M. Ruiz, H. Yepes, and T. Kozono (2011), Ascending seismic source during an explosive eruptionat Tunguruhua volcano, Ecuador, Geophys. Res. Lett., 38, L01306, doi:10.1029/2010GL045944.
48. Kusumoto, S., and K. Takemura (2003), Numerical simulation of caldera formation due to collapse of a magma chamber, Geophys. Res. Lett., 30(24), 2278, doi:10.1029/2003GL018380.
49. Lavier, L., W. Buck, and A. Poliakov (2000), Factors controlling normal fault in an ideal brittle layer, J. Geophys. Res., 105, 23,431-23,442, doi:10.1029/2000JB900108.
50. Lister, J. R., and R. C. Kerr (1991), Fluid-mechanical models of crack propagation and their application to magma transport in dykes, J. Geophys. Res., 96, 10,049-10,077, doi:10.1029/91JB00600.
51. Long, S. M., and E. B. Grosfils (2009), Modeling the effect of layered volcanic material on magma reservoir failure and associated deformation, with application to Long Valley caldera, California, J. Volcanol. Geotherm. Res., 186, 349-360, doi:10.1016/j.jvolgeores.2009.05.021.
52. Marti, J., A. Geyer, A. Folch, and J. Gottsmann (2008), A review of collapse caldera modelling, in Caldera Volcanism: Analysis, Modelling and Response, Dev. Volcanol., vol. 10, pp. 233-283, Elsevier, Amsterdam, doi:10.1016/S1871- 644X(07)00006-X.
53. Masek, J. G., and C. C. Duncan (1998), Minimum-work mountain building, J. Geophys. Res., 103, 907-917, doi:10.1029/ 97JB03213.
54. Massinas, S. A., and M. G. Sakellariou (2009), Closed-form solution for a plastic zone formation around a circular tunnel in half-space obeying Mohr-Coulomb criterion, Geotechnique, 59(8), 691-701, doi:101680/geot8.069.
55. Masterlark, T. (2007), Magma intrusion and deformation predictions: Sensitivities to the Mogi assumptions, J. Geophys. Res., 112, B06419, doi:10.1029/2006JB004860. (Pubitemid 47364492)
56. McLeod, P., and S. Tait (1999), The growth of dyke from magma chambers, J. Volcanol. Geotherm. Res., 92, 231-245, doi:10.1016/S0377-0273(99)00053-0. (Pubitemid 30061893)
57. McTigue, D. F. (1987), Elastic stress and deformation near a finite spherical magma body: Resolution of a point source paradox, J. Geophys. Res., 92, 12,931-12,940, doi:10.1029/ JB092iB12p12931.
58. Mogi, K. (1958), Relations between the eruption of various volcanoes and the deformation of the ground surfaces around them, Bull. Earthquake Res. Inst. Univ. Tokyo, 36, 99-134.
59. Nadai, A. (1950), The Theory of Flow and Fracture of Solids, 402 pp., Mc-Graw Hill, New York.
60. Parfitt, E. A., L. Wilson, and J. W. Head (1993), Basaltic magma reservoirs: Factors controlling their rupture characteristics and evolution, J. Volcanol. Geotherm. Res., 55, 1-14, doi:10.1016/0377-0273(93)90086-7. (Pubitemid 23390101)
61. Pinel, V., and C. Jaupart (2003), Magma chamber behavior beneath a volcanic edifice, J. Geophys. Res., 108(B2), 2072, doi:10.1029/2002JB001751.
62. Pinel, V., and C. Jaupart (2005), Caldera formation by magma withdrawal from a reservoir beneath a volcanic edifice, Earth Planet. Sci. Lett., 230, 273-287, doi:10.1016/j.epsl.2004. 11.016.
63. Podladchikov, Y., A. N. B. Poliakov, and P. Cundall (1993), An explicit inertial method for the simulation of visco-elastic flow: An evaluation of elastic effects on diapiric flow in twoand three-layers models, in Flow and Creep in the Solar System: Observation, Modelling and Theory, NATO Sci. Ser., Ser. C, vol. 391, pp. 175-195, Kluwer Acad., Dordrecht, Netherlands. (Pubitemid 23391329)
64. Poliakov, A., and Y. Podladchikov (1992), Diapirism and topography, Geophys. J. Int., 109, 553-564, doi:10.1111/ j.1365-246X.1992.tb00117.x.
65. Poliakov, A. N. B., Y. Podladchikov, and C. Talbot (1993), Initiation of salt diapirs with frictional overburdens: Numerical experiments, Tectonophysics, 228, 199-210. (Pubitemid 24423221)
66. Prevost, J. H., and B. Loret (1990), Dynamic strain localization in elasto-(visco-)plastic solids, part 2. Plane Strain examples, Comput. Methods Appl. Mech. Eng., 83, 275-294, doi:10.1016/0045-7825(90)90074-V.
67. Pritchard, M. E., and M. Simons (2004), An InSAR-based survey of volcanic deformation in the central Andes, Geochem. Geophys. Geosyst., 5, Q02002, doi:10.1029/2003GC000610.
68. Reid, M. E. (2004), Massive collapse of volcano edifices triggered by hydrothermal pressurization, Geology, 32(5), 373-376, doi:10.1130/G20300.1. (Pubitemid 38616688)
69. Rivalta, E., and P. Segall (2008), Magma compressibility and the missing source for some dike intrusions, Geophys. Res. Lett., 35, L04306, doi:10.1029/2007GL032521. (Pubitemid 351721406)
70. Roche, O., and T. H. Druitt (2001), Onset of caldera collapse during ignimbrite eruptions, Earth Planet. Sci. Lett., 191, 191-202, doi:10.1016/S0012-821X(01)00428-9. (Pubitemid 32974625)
71. Rozhko, A. Y., Y. Y. Podladchikov, and F. Renard (2007), Failure patterns caused by localized rise in pore-fluid overpressure and effective strength of rocks, Geophys. Res. Lett., 34, L22304, doi:10.1029/2007GL031696. (Pubitemid 351222786)
72. Rubin, A. M. (1993), Dikes vs. Diapirs in viscoleastic rock, Earth Planet. Sci. Lett., 119, 641-659, doi:10.1016/0012- 821X(93)90069-L.
73. Rubin, A. M. (1995), Propagation of magma-filled cracks, Annu. Rev. Earth Planet. Sci., 23, 287-336, doi:10.1146/ annurev.ea.23.050195.001443.
74. Rubin, A. M., and D. D. Pollard (1987), Origins of blade-like dikes in volcanic rift zones, U.S. Geol. Surv. Prof. Pap., 1350, 1449-1470.
75. Sammis, C. G., and B. R. Julian (1987), Fracture instabilities accompanying dike intrusions, J. Geophys. Res., 92, 2597-2605, doi:10.1029/JB092iB03p02597.
76. Sartoris, G., J. P. Pozzi, C. Philippe, and J. L. le Mouel (1990), Mechanical instability of shallow magma chambers, J. Geophys. Res., 95, 5141-5151, doi:10.1029/JB095iB04p05141.
77. Segall, P. (2009), Earthquake and Volcano Deformation, 432 pp., Princeton Univ. Press, Princeton, N. J.
78. Sturkell, E., F. Sigmundsson, and R. Slunga (2006), 1983- 2003 decaying rate of deflation at Askja caldera: Pressure decrease in an extensive magma plumbing system at a spreading plate boundary, Bull. Volcanol., 68, 727-735, doi:10.1007/s00445-005-0046-1. (Pubitemid 43880701)
79. Tait, S., C. Jaupart, and S. Vergniolle (1989), Pressure, gas content and eruption periodicity of a shallow, crystallizing magma chamber, Earth Planet. Sci. Lett., 92, 107-123, doi:10.1016/0012-821X(89)90025-3.
80. Timoshenko, S., and J. N. Goodier (1970), Theory of Elasticity, 2nd ed., 608 pp., McGraw-Hill, New York.
81. Townend, J., and M. D. Zoback (2000), How faulting keeps the crust strong, Geology, 28, 399-402, doi:10.1130/0091- 7613(2000)28<399:HFKTCS>2. 0.CO;2. (Pubitemid 32836050)
82. Trasatti, E., C. Giunchu, and M. Bonafede (2005), Structural and rheological constraints on source depth and overpressure estimates at the Campi Flegrei caldera, Italy, J. Volcanol. Geotherm. Res., 144, 105-118, doi:10.1016/j.jvolgeores. 2004.11.019. (Pubitemid 40876211)
83. Turcotte, D., and G. Schubert (1982), Geodynamics, Applications of Continuum Physics to Geological Problems, 450 pp., Wiley, New York.
84. Vermeer, P. A., and R. de Borst (1984), Non-associated plasticity for soils, concrete and rocks, Heron, 29, 1-75.
85. Verruijt, A. (1998), Deformations of an elastic half plane with a circular cavity, Int. J. Solids Struct., 35(21), 2795-2804, doi:10.1016/S0020- 7683(97)00194-7. (Pubitemid 128368523)
86. Watanabe, H. (1983), Changes in water level and their implications to the 1977-1978 activity of Usu volcano, in Arc Volcanism: Physics and Tectonics, edited by D. Shimozuru and I. Yokoyama, pp. 81-93, Terra Sci., Tokyo.
87. Wegler, U., B.-G. Lühr, R. Snieder, and A. Ratdomopurbo (2006), Increase of shear wave velocity before the 1998 eruption of Merapi volcano (Indonesia), Geophys. Res. Lett., 33, L09303, doi:10.1029/2006GL025928. (Pubitemid 43997530)
88. White, B. G., M. K. Larson, and S. R. Iverson (2004), Origin of mining-induced fractures through macro-scale distortion, in Gulf Rocks 2004: Rock Mechanics Across Borders and Disciplines, Proceedings of the Sixth North American Rock Mechanics Conference, Houston, Texas, pp. 1-8, Am. Rock Mech. Assoc., Alexandria, Va.
89. White, R. S., J. Drew, H. R. Martens, J. Key, H. Soosalu, and S. S. Jakobsdottir (2011), Dynamics of dyke intrusion in the mid-crust of Iceland, Earth Planet. Sci. Lett., 304, 300-312, doi:10.1016/j.epsl.2011.02.038.
90. Woodcock, N. H., and R. J. Underhill (1987), Emplacementrelated fault patterns around the Northern granite, Arran, Scotland, Geol. Soc. Am. Bull., 98, 515-527, doi:10.1130/ 0016-7606(1987)98<515:EFPATN>2.0.CO;2.