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Modelling rock fracturing caused by magma intrusion using the smoothed particle hydrodynamics method

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Abstract

In this paper, the applicability of a mesh-free method, called smoothed particle hydrodynamics (SPH), to modelling of geological and mineral system formation is explored, focusing on rock fracture development associated with a magmatic intrusion. A generic geological system that represents a magmatic body intruded into upper-crustal rocks typical of the Yilgarn Craton of Western Australia is modelled using SPH in order to explore patterns of fracture development around such a body. The SPH method is first validated via a uniaxial test problem. A coupled elastic deformation-fluid flow-thermal analysis is conducted to model the fracturing of rocks surrounding the magmatic intrusion, including the effects of pre-tensile and pre-compressive geotechnical strains in the rocks. The SPH method was found to be effective in capturing discrete fracturing processes caused by intruding magma which cannot be easily simulated using the finite element method (FEM). The SPH model predicted fracture patterns in the rocks that were found to compare well with geological structures observed in nature. This study establishes SPH as a useful computational tool to understand the influence of intruding magmas on rock deformation and fracture development that has important implications on fracture and vein formation, magma and fluid flow migration and hence associated mineralisation.

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References

  1. Groves, D.I., Goldfarb, R.J., Knox-Robinson, C.M., Ojala, J., Gardoll, S., Yun, G.Y., Holyland, P.: Late-kinematic timing of orogenic gold deposits and significance for computer-based exploration techniques with emphasis on the Yilgarn Block, Western Australia. Ore Geol. Rev. 17(1–2), 1–38 (2000)

    Article  Google Scholar 

  2. Goldfarb, R.J., Groves, D.I., Gardoll, S.: Orogenic gold and geologic time: a global synthesis. Ore Geol. Rev. 18(1–2), 1–75 (2001)

    Article  Google Scholar 

  3. Henson, P.A., Blewett, R.S., Champion, D.C., Goleby, B.R., Czarnota, K.: How does the 3D architecture of the Yilgarn control hydrothermal fluid focusing? In: Henson, P.A., Blewett, R.S., Champion, D.C., Goleby, B.R., Czarnota, K. (eds.) Kalgoorlie 07 Conference, in WA, pp 57–61. Geoscience Australia (2007)

  4. Blewett, R.S., Czarnota, K., Henson, P.A.: Structural-event framework for the eastern Yilgarn Craton, Western Australia, and its implications for orogenic gold. Precambrian Research 183(2), 203–229 (2010)

    Article  Google Scholar 

  5. Duuring, P., Hagemann, S.G., Groves, D.I.: Structural setting, hydrothermal alteration, and gold mineralisation at the Archaean syenite-hosted Jupiter deposit, Yilgarn Craton, Western Australia. Miner. Deposita 35(5), 402–421 (2000)

    Article  Google Scholar 

  6. Sheldon, H.A.: Simulation of magmatic and metamorphic fluid production coupled with deformation, fluid flow and heat transport. Comput. Geosci. 35, 2275–2281 (2009). Compendex

    Article  Google Scholar 

  7. Schaubs, P.M., Rawling, T.J., Dugdale, L.J., Wilson, C.J.L.: Factors controlling the location of gold mineralisation around basalt domes in the stawell corridor: insights from coupled 3D deformation-fluid flow numerical models. Australian Journal of Earth Sciences: An International Geoscience Journal of the Geological Society of Australia 53(5), 841–862 (2006)

    Article  Google Scholar 

  8. Sorjonen-Ward, P., Zhang, Y., Zhao, C.: Numerical modelling of orogenic processes and gold mineralisation in the southeastern part of the Yilgarn Craton, Western Australia. Aust. J. Earth Sci. 49(6), 935–964 (2002)

    Article  Google Scholar 

  9. Zhang, Y., Sorjonen-Ward, P., Ord, A., Southgate, P.N.: Fluid Flow during deformation associated with structural closure of the Isa Superbasin at 1575 Ma in the Central and Northern Lawn Hill Platform, Northern Australia. Econ. Geol. 101(6), 1293–1312 (2006)

    Article  Google Scholar 

  10. Zhang, Y., Lin, G., Roberts, P., Ord, A.: Numerical modelling of deformation and fluid flow in the Shuikoushan district, Hunan Province, South China. Ore Geol. Rev. 31(1–4), 261–278 (2007)

    Article  Google Scholar 

  11. Das, R., Cleary, P.W.: Modelling brittle fracture and fragmentation of a column during projectile impact using a mesh-free method. In: 6th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries in Trondheim, Norway (2008)

  12. Das, R., Cleary, P.W.: Modelling 3D fracture and fragmentation in a thin plate under high velocity projectile impact using SPH. In 3rd SPHERIC workshop, in Lausanne, Switzerland (2008)

  13. Larsson, R., Fagerstrom, M.: A framework for fracture modelling based on the material forces concept with XFEM kinematics. Int. J. Numer. Methods Eng. 62, 1763–1788 (2005). Compendex

    Article  Google Scholar 

  14. Gray, J.P., Monaghan, J.J.: Numerical modelling of stress fields and fracture around magma chambers. J. Volcanol. Geotherm. Res. 135, 259–283 (2004)

    Article  Google Scholar 

  15. Cleary, P., Ha, J., Alguine, V., Nguyen, T.: Flow modelling in casting processes. Appl. Math. Model. 26(2), 171–190 (2002)

    Article  Google Scholar 

  16. Cleary, P.W., Prakash, M., Ha, J., Stokes, N., Scott, C.: Smooth particle hydrodynamics: status and future potential. Progress in Computational Fluid Dynamics 7(2–4), 70–90 (2007)

    Article  Google Scholar 

  17. Monaghan, J.J.: Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys. 30, 543–574 (1992)

    Article  Google Scholar 

  18. Monaghan, J.J.: Simulating free surface flows with SPH. J. Computat. Phys. 110, 399–406 (1994)

    Article  Google Scholar 

  19. Kulasegaram, S., Bonet, J., Lewis, R.W., Profit, M.: High pressure die casting simulation using a Lagrangian particle method. Commun. Numer. Methods Eng. 19(9), 679–687 (2003)

    Article  Google Scholar 

  20. Cedric, T., Janssen, L.P.B.M., Pep, E.: Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations. Physical Review E (Statistical Nonlinear, and Soft Matter Physics) 72(1), 016713 (2005)

    Article  Google Scholar 

  21. Cleary, P.W., Ha, J., Prakash, M., Nguyen, T.: 3D SPH flow predictions and validation for high pressure die casting of automotive components. Appl. Math. Model. 30(11), 1406–1427 (2006)

    Article  Google Scholar 

  22. Fang, J., Owens, R.G., Tacher, L., Parriaux, A.: A numerical study of the SPH method for simulating transient viscoelastic free surface flows. J. Non-Newtonian Fluid Mech. 139(1–2), 68–84 (2006)

    Article  Google Scholar 

  23. Imaeda, Y., Inutsuka, S.-i.: Shear flows in smoothed particle hydrodynamics. The Astrophysical Journal 569(1), 501–518 (2002)

    Article  Google Scholar 

  24. Cleary, P.W., Sinnott, M., Morrison, R.: Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media. Miner. Eng. 19(15), 1517–1527 (2006)

    Article  Google Scholar 

  25. Cleary, P.W., Ha, J.: Three-dimensional smoothed particle hydrodynamics simulation of high pressure die casting of light metal components. J. Light. Met. 2(3 SPEC.), 169–183 (2002)

    Article  Google Scholar 

  26. Cleary, P.W.: Modelling confined multi-material heat and mass flows using SPH. Appl. Math. Model. 22(12), 981–993 (1998)

    Article  Google Scholar 

  27. Cleary, P.W., Monaghan, J.J.: Conduction modelling using smoothed particle hydrodynamics. J. Comput. Phys. 148(1), 227–264 (1999)

    Article  Google Scholar 

  28. Cleary, P.W., Prakash, M., Ha, J.: Novel applications of smoothed particle hydrodynamics (SPH) in metal forming. J. Mater. Process. Technol. 177(1–3), 41–48 (2006)

    Article  Google Scholar 

  29. Gray, J.P., Monaghan, J.J., Swift, R.P.: SPH elastic dynamics. Comput. Methods Appl. Mech. Eng. 190(49–50), 6641–6662 (2001)

    Article  Google Scholar 

  30. Libersky, L.D., Petschek, A.G.: Smooth particle hydrodynamics with strength of materials. In: Trease, H.E., Crowley, W.P. (eds.) Advances in the free-lagrange method. Springer, Berlin (1990)

    Google Scholar 

  31. Liu, Z.S., Swaddiwudhipong, S., Koh, C.G.: High velocity impact dynamic response of structures using SPH method. Int. J. Comput. Eng. Sci. 5(2), 315–326 (2004)

    Article  Google Scholar 

  32. Strength modeling in SPHC. Wingate, C.A., and Fisher, H.N., 1993. Los Alamos National Laboratory, Report No. LA-UR-93-3942

  33. Cleary, P.W., Prakash, M., Sinnott, M.D., Rudman, M., Das, R.: Large scale simulation of industrial, engineering and geophysical flows using particle methodsmethods. In: Onate, R.O.A.E. (ed.) Particle methods (Selected papers from Proceedings of Particles 2009 conference). Springer (2010)

  34. Cleary, P.W.: Elastoplastic deformation during projectile-wall collision. Appl. Math. Model. 34(2), 266–283 (2010)

    Article  Google Scholar 

  35. Tunsakul, J., Jongpradist, P., Soparat, P., Kongkitkul, W., Nanakorn, P.: Analysis of fracture propagation in a rock mass surrounding a tunnel under high internal pressure by the element-free Galerkin method. Comput. Geotech. 55, 78–90 (2014)

    Article  Google Scholar 

  36. Das, R., Cleary, P.W.: The potential for SPH modelling of solid deformation and fracturefracture. In: Reddy, D. (ed.) IUTAM Proceedings Book Series Volume on Theoretical, Computational and Modelling Aspects of Inelastic Media. Springer, Capetown (2008)

    Google Scholar 

  37. Das, R., Cleary, P.W.: Effect of rock shapes on brittle fracture using smoothed particle hydrodynamics. Theor. Appl. Fract. Mech. 53, 47–60 (2010)

    Article  Google Scholar 

  38. Karekal, S., Das, R., Mosse, L., Cleary, P.W.: Application of a mesh-free continuum method for simulation of rock caving processes. International Journal of Rock Mechanics and Mining Sciences 48(5), 703–711 (2011)

    Article  Google Scholar 

  39. Balmforth, N.J., Burbidge, A.S., aster, R.V., Salzig, J., Shen, A.: Visco-plastic models of isothermal lava domes. J. Fluid Mech. 403, 37–65 (2000)

    Article  Google Scholar 

  40. Herschel, W.H., Bulkley, R.: Uber die viskositat und Elastizitat von Solen. American Society of Testing Materials 26, 621–633 (1923)

    Google Scholar 

  41. Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759 (2005)

    Article  Google Scholar 

  42. Cocchetti, G., Pagani, M., Perego, U.: Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements. Comput. Struct. 127(0), 39–52 (2013)

    Article  Google Scholar 

  43. Olovsson, L., Simonsson, K., Unosson, M.: Selective mass scaling for explicit finite element analyses. Int. J. Numer. Methods Eng. 63(10), 1436–1445 (2005)

    Article  Google Scholar 

  44. Grady, D.E., Kipp, M.E.: Continuum modelling of explosive fracture in oil shale. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 17(3), 147–157 (1980)

    Article  Google Scholar 

  45. Melosh, H.J., Ryan, E.V., Asphaug, E.: Dynamic fragmentation in impacts: hydrocode simulation of laboratory impacts. J. Geophys. Res. 97, 14735–14759 (1992)

    Article  Google Scholar 

  46. Grady, D.E., Kipp, M.E., Smith, C.S.: Explosive fracture studies on oil shale. Soc. Pet. Eng. J. 5, 349–356 (1980)

    Article  Google Scholar 

  47. Das, R., Cleary, P.W.: A mesh-free approach for fracture modelling of gravity dams under earthquake. Int. J. Fract. 179(1–2), 9–33 (2013)

    Article  Google Scholar 

  48. Grady, D.E., Kipp, M.E.: Oil shale fracture and fragmentation at higher rates of loading. U.S. Symposium on Rock Mechanics, 403–406 (1979)

  49. Thorne, B.J., Hommert, P.J., Brown, B.: Experimental and computational investigation of the fundamental mechanisms of cratering. In: 3rd International Symposium on Rock Fragmentation by Blasting, in Brisbane, pp. 117–124 (1990)

  50. Aliabadi, M.H., Rooke, D.P.: Numerical fracture mechanics. Computational Mechanics Publications and Kluwer Academic Publishers, Boston (1991)

    Book  Google Scholar 

  51. Fernandez-Mendez, S., Bonet, J., Huerta, A.: Continuous blending of SPH with finite elements. Comput. Struct. 83, 1448–1458 (2005)

    Article  Google Scholar 

  52. Bradley, G.L., Chang, P.C., McKenna, G.B.: Rubber modeling using uniaxial test data. J. Appl. Polym. Sci. 81(4), 837–848 (2001)

    Article  Google Scholar 

  53. Nawrocki, P.A., Dusseault, M.B., Bratli, R.K.: Use of uniaxial compression test results in stress modelling around openings in nonlinear geomaterials. J. Pet. Sci. Eng. 21(1–2), 79–94 (1998)

    Article  Google Scholar 

  54. Kahraman, S., Alber, M.: Estimating unconfined compressive strength and elastic modulus of a fault breccia mixture of weak blocks and strong matrix. International Journal of Rock Mechanics and Mining Sciences 43(8), 1277–1287 (2006)

    Article  Google Scholar 

  55. Wu, B., Tan, C.P.: Sand production prediction of gas field: methodology and laboratory verification. In: SPE Asia Pacific Oil & Gas Conference and Exhibition, in Melbourne (2002)

  56. Turcotte, D.L., Schubert, G.: Geodynamics: applications of continuum physics to geological problems. Wiley, New York (1982)

    Google Scholar 

  57. Leitch, A.M., Weinberg, R.F.: Modelling granite migration by mesoscale pervasive flow. Earth Planet. Sci. Lett. 200(1–2), 131–146 (2002)

    Article  Google Scholar 

  58. Büttner, R., Zimanowski, B., Blumm, J., Hagemann, L.: Thermal conductivity of a volcanic rock material (olivine-melilitite) in the temperature range between 288 and 1470 K. J. Volcanol. Geotherm. Res. 80(3–4), 293–302 (1998)

    Article  Google Scholar 

  59. Cardoso, S.S.S., Woods, A.W.: On convection in a volatile-saturated magma. Earth Planet. Sci. Lett. 168(3–4), 301–310 (1999)

    Article  Google Scholar 

  60. Goode, A.D.T.: Sedimentary structures and magma current velocities in the Kalka Layered Intrusion, Central Australia. J. Petrology 17(4), 546–558 (1976)

    Article  Google Scholar 

  61. Pinkerton, H., Stevenson, R.: Methods of determining the rheological properties of magmas at sub-liquidus temperatures. J. Volcanol. Geotherm. Res. 53(1), 47–66 (1992)

    Article  Google Scholar 

  62. Williams, D.A., Kerr, R.C., Lesher, C.M., Barnes, S.J.: Analytical/numerical modeling of komatiite lava emplacement and thermal erosion at Perseverance, Western Australia. J. Volcanol. Geotherm. Res. 110(1–2), 27–55 (2001)

    Article  Google Scholar 

  63. Anderson, T.L.: Fracture mechanics: fundamentals and applications. CRC, Boca Raton (1991)

    Google Scholar 

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Das, R., Zhang, Y., Schaubs, P. et al. Modelling rock fracturing caused by magma intrusion using the smoothed particle hydrodynamics method. Comput Geosci 18, 927–947 (2014). https://doi.org/10.1007/s10596-014-9437-8

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