Skip to main content
Erschienen in: Rock Mechanics and Rock Engineering 6/2013

01.11.2013 | Original Paper

Dynamic Study on Fracture Problems in Viscoelastic Sedimentary Rocks Using the Numerical Manifold Method

verfasst von: Zhijun Wu, Louis Ngai Yuen Wong, Lifeng Fan

Erschienen in: Rock Mechanics and Rock Engineering | Ausgabe 6/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The viscoelastic deformation behavior of a sedimentary rock under different loading rates is numerically modeled and investigated by the numerical manifold method (NMM). By incorporating a modified 3-element viscoelastic constitutive mode in the NMM, crack initiation and propagation criteria, and crack identification and evolution techniques, the effects of the loading rates on the cracking behavior of a sedimentary rock, such as crack open displacement, crack sliding displacement, crack initiation, crack propagation and final failure mode, are successfully modeled. The numerical results reveal that under a high loading rate (>1,000 MPa/s), due to the viscoelastic property of the sedimentary rock, not only the structural behavior deviates from that of elastic model, but also different cracking processes and final failure modes are obtained.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Abraham FF, Broughton JQ (1998) Large-scale simulations of brittle and ductile failure in fcc crystals. Comput Mater Sci 10(1–4):1–9CrossRef Abraham FF, Broughton JQ (1998) Large-scale simulations of brittle and ductile failure in fcc crystals. Comput Mater Sci 10(1–4):1–9CrossRef
Zurück zum Zitat Abraham FF, Brodbeck D, Rafey RA, Rudge WE (1994) Instability dynamic of fracture-A computer-simulation investigation. Phys Rev Lett 73(2):272–275CrossRef Abraham FF, Brodbeck D, Rafey RA, Rudge WE (1994) Instability dynamic of fracture-A computer-simulation investigation. Phys Rev Lett 73(2):272–275CrossRef
Zurück zum Zitat An XM (2010) Extended numerical manifold method for engineering failure analysis PhD Thesis, Nanyang Technology University Singapore An XM (2010) Extended numerical manifold method for engineering failure analysis PhD Thesis, Nanyang Technology University Singapore
Zurück zum Zitat Banthia NP, Mindess S, Bentur A (1987) Impact behavior of concrete beams. Mater Struct/Materiaus et Constructions 20:293–302 Banthia NP, Mindess S, Bentur A (1987) Impact behavior of concrete beams. Mater Struct/Materiaus et Constructions 20:293–302
Zurück zum Zitat Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45(5):601–620CrossRef Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45(5):601–620CrossRef
Zurück zum Zitat Belytschko T, Chen H, Xu JX, Zi G (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Meth Eng 58(12):1873–1905CrossRef Belytschko T, Chen H, Xu JX, Zi G (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Meth Eng 58(12):1873–1905CrossRef
Zurück zum Zitat Blanton TL (1981) Effect of strain rates from 10 to 2 to 10-sec-1 in triaxial compression tests on rocks. Int J Rock Mech Min Sci 18(1):47–62CrossRef Blanton TL (1981) Effect of strain rates from 10 to 2 to 10-sec-1 in triaxial compression tests on rocks. Int J Rock Mech Min Sci 18(1):47–62CrossRef
Zurück zum Zitat Brady BHG, Brown ET, Chapama&Hall (1993) Rock mechanics for underground mining, 2nd edn. London, UK Brady BHG, Brown ET, Chapama&Hall (1993) Rock mechanics for underground mining, 2nd edn. London, UK
Zurück zum Zitat Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20–22):2899–2938CrossRef Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20–22):2899–2938CrossRef
Zurück zum Zitat Chen PW, Huang T, Yang J, Zhang GX (2006) Numerical simulation of rock fracture under dynamic loading using Manifold method. Paper presented at the fracture and damage mechanics V, Pts 1 and 2 Chen PW, Huang T, Yang J, Zhang GX (2006) Numerical simulation of rock fracture under dynamic loading using Manifold method. Paper presented at the fracture and damage mechanics V, Pts 1 and 2
Zurück zum Zitat Christensen RM (1982) Theory of viscoelasticity: an introduction. Academic Press, New York Christensen RM (1982) Theory of viscoelasticity: an introduction. Academic Press, New York
Zurück zum Zitat Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 16:155–169CrossRef Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 16:155–169CrossRef
Zurück zum Zitat Curran DR (1975) Dynamic failure of solids. Bull Am Phys Soc 20(12):1497 Curran DR (1975) Dynamic failure of solids. Bull Am Phys Soc 20(12):1497
Zurück zum Zitat Erdogan F, Sih SC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng ASME 85:519–525CrossRef Erdogan F, Sih SC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng ASME 85:519–525CrossRef
Zurück zum Zitat Falk ML, Needleman A, Rice JR (2001) A critical evaluation of cohesive zone models of dynamic fracture. J Phys IV 11:43–50 Falk ML, Needleman A, Rice JR (2001) A critical evaluation of cohesive zone models of dynamic fracture. J Phys IV 11:43–50
Zurück zum Zitat Fan LF, Ren F, Ma GW (2012) Experimental study on viscoelastic property of sedimentary rock. Rock Mech Rock Eng 45(3):433–438 Fan LF, Ren F, Ma GW (2012) Experimental study on viscoelastic property of sedimentary rock. Rock Mech Rock Eng 45(3):433–438
Zurück zum Zitat Green S, Perkins R (1968) Stiffness and maximum stress of five rocks at strain rates to 1000/s. Trans Am Geophys Union 49(4):756–770 Green S, Perkins R (1968) Stiffness and maximum stress of five rocks at strain rates to 1000/s. Trans Am Geophys Union 49(4):756–770
Zurück zum Zitat Hussian MA, Pu SL, Underwood J (1974) Strain energy release rate for a crack under combined mode I and mode II. Fract Anal ASTM STP 560:2–28 Hussian MA, Pu SL, Underwood J (1974) Strain energy release rate for a crack under combined mode I and mode II. Fract Anal ASTM STP 560:2–28
Zurück zum Zitat Khan AS, Irani FK (1982) Dynamic tensile fracture strength of rocks. Exp Mech 22(5):N43–N43 Khan AS, Irani FK (1982) Dynamic tensile fracture strength of rocks. Exp Mech 22(5):N43–N43
Zurück zum Zitat Khan SMA, Khraisheh MK (2000) Analysis of mixed mode crack initiation angles under various loading conditions. Eng Fract Mech 67(5):397–419CrossRef Khan SMA, Khraisheh MK (2000) Analysis of mixed mode crack initiation angles under various loading conditions. Eng Fract Mech 67(5):397–419CrossRef
Zurück zum Zitat Kolsky H (1963) Stress waves in solids. Dover, New York Kolsky H (1963) Stress waves in solids. Dover, New York
Zurück zum Zitat Kumar A (1968) Effects of stress rate and temperature on strength of basalt and granite. Geophysics 33(3):501–510CrossRef Kumar A (1968) Effects of stress rate and temperature on strength of basalt and granite. Geophysics 33(3):501–510CrossRef
Zurück zum Zitat Ladeveze P (1992) A damage computational method for composite structure. Comput Struct 44(1–2):79–87CrossRef Ladeveze P (1992) A damage computational method for composite structure. Comput Struct 44(1–2):79–87CrossRef
Zurück zum Zitat Li SC, Cheng YM (2005) Enriched mesh less manifold method for two-dimensional crack modeling. Theoret Appl Fract Mech 44(3):234–248CrossRef Li SC, Cheng YM (2005) Enriched mesh less manifold method for two-dimensional crack modeling. Theoret Appl Fract Mech 44(3):234–248CrossRef
Zurück zum Zitat Li SC, Cheng YM (2006) Meshless manifold method for dynamic fracture mechanics. Acta Physica Sinica 55(9):4760–4766 Li SC, Cheng YM (2006) Meshless manifold method for dynamic fracture mechanics. Acta Physica Sinica 55(9):4760–4766
Zurück zum Zitat Li HB, Li TJ, Zhao J, Gao JG, Jiang JG (2000) Study on strength of rock material under dynamic triaxial compressive loads based on sliding crack model. In: Hwang W, Han KS (eds) Fracture and strength of solids, Pts 1 and 2, vol 183–1. Key Engineering Materials, pp 67–72 Li HB, Li TJ, Zhao J, Gao JG, Jiang JG (2000) Study on strength of rock material under dynamic triaxial compressive loads based on sliding crack model. In: Hwang W, Han KS (eds) Fracture and strength of solids, Pts 1 and 2, vol 183–1. Key Engineering Materials, pp 67–72
Zurück zum Zitat Li HB, Zhao J, Li JR, Liu YQ, Zhou QC (2004) Experimental studies on the strength of different rock types under dynamic compression. Int J Rock Mech Min Sci 41(3):365CrossRef Li HB, Zhao J, Li JR, Liu YQ, Zhou QC (2004) Experimental studies on the strength of different rock types under dynamic compression. Int J Rock Mech Min Sci 41(3):365CrossRef
Zurück zum Zitat Lindholm US, Yeakley LM, Nagy A (1974) Dynamic strength and fracture properties of dresser basalt. Int J Rock Mech Min Sci 11(5):181–191CrossRef Lindholm US, Yeakley LM, Nagy A (1974) Dynamic strength and fracture properties of dresser basalt. Int J Rock Mech Min Sci 11(5):181–191CrossRef
Zurück zum Zitat Ling DS, Xu X (2004) Nonlinear finite element method and programming. Zhejiang University Press, Hangzhou. (In Chinese) Ling DS, Xu X (2004) Nonlinear finite element method and programming. Zhejiang University Press, Hangzhou. (In Chinese)
Zurück zum Zitat Lipkin J, Grady DE (1977) Dynamic flow and fracture of rock in pure shear. In: Proceedings of 18th US symposium rock mechanics, Keystone, Colorado: Colorado School of Mines Press (3B2-1) Lipkin J, Grady DE (1977) Dynamic flow and fracture of rock in pure shear. In: Proceedings of 18th US symposium rock mechanics, Keystone, Colorado: Colorado School of Mines Press (3B2-1)
Zurück zum Zitat Liu ZL, Menouillard T, Belytschko T (2011) An XFEM/spectral element method for dynamic crack propagation. Int J Fract 169(2):183–198CrossRef Liu ZL, Menouillard T, Belytschko T (2011) An XFEM/spectral element method for dynamic crack propagation. Int J Fract 169(2):183–198CrossRef
Zurück zum Zitat Ma GW, An XM, Zhang HH, Li LX (2009) Modeling complex crack problems using the numerical manifold method. Int J Fract 156(1):21–35CrossRef Ma GW, An XM, Zhang HH, Li LX (2009) Modeling complex crack problems using the numerical manifold method. Int J Fract 156(1):21–35CrossRef
Zurück zum Zitat Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1–4):289–314CrossRef Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1–4):289–314CrossRef
Zurück zum Zitat Menouillard T, Song JH, Duan QL, Belytschko T (2010) Time dependent crack tip enrichment for dynamic crack propagation. Int J Fract 162(1–2):33–49CrossRef Menouillard T, Song JH, Duan QL, Belytschko T (2010) Time dependent crack tip enrichment for dynamic crack propagation. Int J Fract 162(1–2):33–49CrossRef
Zurück zum Zitat Ning YJ, An XM, Ma GW (2011) Footwall slope stability analysis with the numerical manifold method. Int J Rock Mech Min Sci 48(6):964–975CrossRef Ning YJ, An XM, Ma GW (2011) Footwall slope stability analysis with the numerical manifold method. Int J Rock Mech Min Sci 48(6):964–975CrossRef
Zurück zum Zitat Olsson WA (1991) The compressive strength of tuff as a function of strain rate from 10–6 to 103/s. Int J Rock Mech Min Sci Geomech Abstr 28(1):115–118CrossRef Olsson WA (1991) The compressive strength of tuff as a function of strain rate from 10–6 to 103/s. Int J Rock Mech Min Sci Geomech Abstr 28(1):115–118CrossRef
Zurück zum Zitat Rabczuk T, Song JH, Belytschko T (2009) Simulations of instability in dynamic fracture by the cracking particles method. Eng Fract Mech 76(6):730–741CrossRef Rabczuk T, Song JH, Belytschko T (2009) Simulations of instability in dynamic fracture by the cracking particles method. Eng Fract Mech 76(6):730–741CrossRef
Zurück zum Zitat Resende R, Lamas LN, Lemos JV, Calcada R (2010) Micromechanical modelling of stress waves in rock and rock fractures. Rock Mech Rock Eng 43(6):741–761CrossRef Resende R, Lamas LN, Lemos JV, Calcada R (2010) Micromechanical modelling of stress waves in rock and rock fractures. Rock Mech Rock Eng 43(6):741–761CrossRef
Zurück zum Zitat Rinehart JS (1965) Dynamic fracture strength of rocks. In: Proceedings of 7th US symposium rock mechanics, 1, New York. Society of Mining, Metallurgical and Petroleum Engineering Rinehart JS (1965) Dynamic fracture strength of rocks. In: Proceedings of 7th US symposium rock mechanics, 1, New York. Society of Mining, Metallurgical and Petroleum Engineering
Zurück zum Zitat Shi GH (1991) Manifold method of material analysis. Paper presented at the Trans 9th Army conference on applied mathematics and computing, Minneaplolis: Minesota Shi GH (1991) Manifold method of material analysis. Paper presented at the Trans 9th Army conference on applied mathematics and computing, Minneaplolis: Minesota
Zurück zum Zitat Shi GH (1992) Modeling rock joints and blocks by manifold method. In: Proceedings of the 33th US rock mechanics symposium, New Mexico: SanTa Fe Shi GH (1992) Modeling rock joints and blocks by manifold method. In: Proceedings of the 33th US rock mechanics symposium, New Mexico: SanTa Fe
Zurück zum Zitat Sih GC (1974) Strain-energy-density factor applied to mixed crack problems. Int J Fract 10:305–321CrossRef Sih GC (1974) Strain-energy-density factor applied to mixed crack problems. Int J Fract 10:305–321CrossRef
Zurück zum Zitat Song JH, Wang HW, Belytschko T (2008) A comparative study on finite element methods for dynamic fracture. Comput Mech 42(2):239–250CrossRef Song JH, Wang HW, Belytschko T (2008) A comparative study on finite element methods for dynamic fracture. Comput Mech 42(2):239–250CrossRef
Zurück zum Zitat Tang CA, Kou SQ (1998) Crack propagation and coalescence in brittle materials under compression. Eng Fract Mech 61(3–4):311–324CrossRef Tang CA, Kou SQ (1998) Crack propagation and coalescence in brittle materials under compression. Eng Fract Mech 61(3–4):311–324CrossRef
Zurück zum Zitat Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws–Part II: numerical approach. Int J Rock Mech Min Sci 38(7):925–939CrossRef Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws–Part II: numerical approach. Int J Rock Mech Min Sci 38(7):925–939CrossRef
Zurück zum Zitat Thiagarajan G (2007) Dynamic fracture simulation of concrete using a virtual internal bond model. J Eng Mech Asce 133(5):514–522CrossRef Thiagarajan G (2007) Dynamic fracture simulation of concrete using a virtual internal bond model. J Eng Mech Asce 133(5):514–522CrossRef
Zurück zum Zitat Wang LL (1985) The foundation of stress wave. National Defence Industry Press, Beijing (in Chinese) Wang LL (1985) The foundation of stress wave. National Defence Industry Press, Beijing (in Chinese)
Zurück zum Zitat Wang QZ, Li W, Song XL (2006) A method for testing dynamic tensile strength and elastic modulus of rock materials using SHPB. Pure Appl Geophys 163(5–6):1091–1100CrossRef Wang QZ, Li W, Song XL (2006) A method for testing dynamic tensile strength and elastic modulus of rock materials using SHPB. Pure Appl Geophys 163(5–6):1091–1100CrossRef
Zurück zum Zitat Wu ZJ, Wong LNY (2012a) Frictonal crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53CrossRef Wu ZJ, Wong LNY (2012a) Frictonal crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53CrossRef
Zurück zum Zitat Xu XP, Needleman A (1994) Numerical simulation of fast crack-growth in brittle solids. J Mech Phys Solids 42(9):1397–1434CrossRef Xu XP, Needleman A (1994) Numerical simulation of fast crack-growth in brittle solids. J Mech Phys Solids 42(9):1397–1434CrossRef
Zurück zum Zitat Zhang CY (2006) Viscoelastic fracture mechanics. Science Press, Beijing Zhang CY (2006) Viscoelastic fracture mechanics. Science Press, Beijing
Zurück zum Zitat Zhang HH, Li LX (2009) Modeling inclusion problems in viscoelastic materials with the extended finite element method. Finite Elem Anal Des 45(10):721–729CrossRef Zhang HH, Li LX (2009) Modeling inclusion problems in viscoelastic materials with the extended finite element method. Finite Elem Anal Des 45(10):721–729CrossRef
Zurück zum Zitat Zhang HH, Rong G, Li LX (2010) Numerical study on deformations in a cracked viscoelastic body with the extended finite element method. Eng Anal Bound Elem 34(6):619–624CrossRef Zhang HH, Rong G, Li LX (2010) Numerical study on deformations in a cracked viscoelastic body with the extended finite element method. Eng Anal Bound Elem 34(6):619–624CrossRef
Metadaten
Titel
Dynamic Study on Fracture Problems in Viscoelastic Sedimentary Rocks Using the Numerical Manifold Method
verfasst von
Zhijun Wu
Louis Ngai Yuen Wong
Lifeng Fan
Publikationsdatum
01.11.2013
Verlag
Springer Vienna
Erschienen in
Rock Mechanics and Rock Engineering / Ausgabe 6/2013
Print ISSN: 0723-2632
Elektronische ISSN: 1434-453X
DOI
https://doi.org/10.1007/s00603-012-0349-4

Weitere Artikel der Ausgabe 6/2013

Rock Mechanics and Rock Engineering 6/2013 Zur Ausgabe