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

01.11.2013 | Original Paper

Kinetic Energy Dissipation and Convergence Criterion of Discontinuous Deformations Analysis (DDA) for Geotechnical Engineering

verfasst von: Qinghui Jiang, Yifeng Chen, Chuangbing Zhou, Man-chu Ronald Yeung

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 discontinuous deformation analysis (DDA) is a numerical method for modeling discontinuous deformation behaviour of jointed rocks. In this paper, two basic problems are discussed related to kinetic energy dissipation and the convergence criterion for the DDA method when it is applied to geotechnical engineering. In view of the fact that the deformation and progressive failure can be treated as a quasi-static process with low kinetic energy dissipation rates, this paper introduces a viscous damping component to absorb discrete blocks’ kinetic energy, establishes the global equations of motion of the discrete block system that take damping effects into account, investigates the energy dissipation mechanism when solving a static or quasi-static problem, and defines the convergence criteria of displacement, kinetic energy and unbalanced force for DDA solutions when the system arrives at a stable state.

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 Bao HR, Hatzor YH, Huang X (2012) A new viscous boundary condition in the two-dimensional discontinuous deformation analysis method for wave propagation Problems. Rock Mech Rock Eng 45:919–928 Bao HR, Hatzor YH, Huang X (2012) A new viscous boundary condition in the two-dimensional discontinuous deformation analysis method for wave propagation Problems. Rock Mech Rock Eng 45:919–928
Zurück zum Zitat Beyabanaki SAR, Mikola RG, Hatami K (2008) Three-dimensional deformation analysis (3-D DDA) using a new contact resolution algorithm. Comput Geotech 35:346–356CrossRef Beyabanaki SAR, Mikola RG, Hatami K (2008) Three-dimensional deformation analysis (3-D DDA) using a new contact resolution algorithm. Comput Geotech 35:346–356CrossRef
Zurück zum Zitat Beyabanaki SAR, Jafari A, Biabanaki SOR, Yeung MR (2009) Nodal-based three-dimensional deformation analysis (3-D DDA). Comput Geotech 36:359–372CrossRef Beyabanaki SAR, Jafari A, Biabanaki SOR, Yeung MR (2009) Nodal-based three-dimensional deformation analysis (3-D DDA). Comput Geotech 36:359–372CrossRef
Zurück zum Zitat Cai YE, Liang GP, Shi GH, Cook NGW (1996) Studying impact problem by using LDDA method. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 288–294 Cai YE, Liang GP, Shi GH, Cook NGW (1996) Studying impact problem by using LDDA method. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 288–294
Zurück zum Zitat Chen GQ, Miki S, Ohnishi Y (1997) Development of the interactive visualization system for DDA. In: Proceedings of the 9th international conference on computer methods and advances in geomechanics, Wuhan, pp 495–500 Chen GQ, Miki S, Ohnishi Y (1997) Development of the interactive visualization system for DDA. In: Proceedings of the 9th international conference on computer methods and advances in geomechanics, Wuhan, pp 495–500
Zurück zum Zitat Cheng YM, Zhang YH (2000) Rigid body rotation and block internal discretization in DDA analysis. Int J Numer Anal Methods Geomech 24:567–578CrossRef Cheng YM, Zhang YH (2000) Rigid body rotation and block internal discretization in DDA analysis. Int J Numer Anal Methods Geomech 24:567–578CrossRef
Zurück zum Zitat Chern JC, Koo CY, Chen S (1990) Development of second order displacement function for DDA and manifold method. In: Working forum on the manifold method of material analysis, Vicksburg, pp 183–202 Chern JC, Koo CY, Chen S (1990) Development of second order displacement function for DDA and manifold method. In: Working forum on the manifold method of material analysis, Vicksburg, pp 183–202
Zurück zum Zitat Clatworthy D, Scheele F (1999) A method of sub-meshing in discontinuous deformation. In: Proceedings of the third international conference on analysis of discontinuous deformation from theory to practice, Colorado, pp 85–94 Clatworthy D, Scheele F (1999) A method of sub-meshing in discontinuous deformation. In: Proceedings of the third international conference on analysis of discontinuous deformation from theory to practice, Colorado, pp 85–94
Zurück zum Zitat Clough RW, Penzien J (2003) Dynamics of structures, 3rd edn. Computers and Structures, Inc., Berkeley Clough RW, Penzien J (2003) Dynamics of structures, 3rd edn. Computers and Structures, Inc., Berkeley
Zurück zum Zitat Doolin DM, Sitar N (2001) DDAML-discontinuous deformation analysis markup language. Int J Rock Mech Min Sci 38:467–474CrossRef Doolin DM, Sitar N (2001) DDAML-discontinuous deformation analysis markup language. Int J Rock Mech Min Sci 38:467–474CrossRef
Zurück zum Zitat Doolin DM, Sitar N (2004) Time integration in discontinuous deformation analysis. ASCE J Eng Mech 130:249–258CrossRef Doolin DM, Sitar N (2004) Time integration in discontinuous deformation analysis. ASCE J Eng Mech 130:249–258CrossRef
Zurück zum Zitat Grayeli R, Mortazavi A (2006) Discontinuous deformation analysis with second-order finite element meshed block. Int J Numer Anal Methods Geomech 30:1545–1561CrossRef Grayeli R, Mortazavi A (2006) Discontinuous deformation analysis with second-order finite element meshed block. Int J Numer Anal Methods Geomech 30:1545–1561CrossRef
Zurück zum Zitat Hatzor YH, Arzi AA, Zaslavsky Y, Shapira A (2004) Dynamic stability analysis of jointed rock slopes using DDA method: King Herod’s Palace, Masada, Israel. Int J Rock Mech Min Sci 41:813–832CrossRef Hatzor YH, Arzi AA, Zaslavsky Y, Shapira A (2004) Dynamic stability analysis of jointed rock slopes using DDA method: King Herod’s Palace, Masada, Israel. Int J Rock Mech Min Sci 41:813–832CrossRef
Zurück zum Zitat Hsiung SM (2001) Discontinuous deformation analysis (DDA) with nth order polynomial displacement functions. In: Proceedings of the 38th US rock mechanics symposium, Washington DC, pp 1437–1444 Hsiung SM (2001) Discontinuous deformation analysis (DDA) with nth order polynomial displacement functions. In: Proceedings of the 38th US rock mechanics symposium, Washington DC, pp 1437–1444
Zurück zum Zitat Jiang QH, Yeung MR (2004) A model of point-to-face contact for three-dimensional discontinuous deformation analysis. Rock Mech Rock Eng 37:95–116CrossRef Jiang QH, Yeung MR (2004) A model of point-to-face contact for three-dimensional discontinuous deformation analysis. Rock Mech Rock Eng 37:95–116CrossRef
Zurück zum Zitat Jiao YY, Zhang XL, Zhao J, Liu QS (2007) Viscous boundary of DDA for modeling stress wave propagation in jointed rock. Int J Rock Mech Min Sci 44:1070–1076CrossRef Jiao YY, Zhang XL, Zhao J, Liu QS (2007) Viscous boundary of DDA for modeling stress wave propagation in jointed rock. Int J Rock Mech Min Sci 44:1070–1076CrossRef
Zurück zum Zitat Jiao YY, Zhang XL, Zhao J (2012) Two-dimensional DDA constitutive model for simulating rock fragmentation. ASCE J Eng Mech 138(2):199–209CrossRef Jiao YY, Zhang XL, Zhao J (2012) Two-dimensional DDA constitutive model for simulating rock fragmentation. ASCE J Eng Mech 138(2):199–209CrossRef
Zurück zum Zitat Jing LR (1998) Formulation of discontinuous deformation analysis (DDA)—an implicit discrete element model for block systems. Eng Geol 49:371–381CrossRef Jing LR (1998) Formulation of discontinuous deformation analysis (DDA)—an implicit discrete element model for block systems. Eng Geol 49:371–381CrossRef
Zurück zum Zitat Jing LR, Ma Y, Fang Z (2001) Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. Int J Rock Mech Min Sci 38:343–355CrossRef Jing LR, Ma Y, Fang Z (2001) Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. Int J Rock Mech Min Sci 38:343–355CrossRef
Zurück zum Zitat Ke TC (1996) Artificial joint-based DDA. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 326–333 Ke TC (1996) Artificial joint-based DDA. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 326–333
Zurück zum Zitat Kim YI, Amadei B, Pan E (1999) Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis. Int J Rock Mech Min Sci 36:949–970CrossRef Kim YI, Amadei B, Pan E (1999) Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis. Int J Rock Mech Min Sci 36:949–970CrossRef
Zurück zum Zitat Koo CY, Chern JC (1998) Modification of the DDA method for rigid block problems. Int J Rock Mech Min Sci 35:683–693CrossRef Koo CY, Chern JC (1998) Modification of the DDA method for rigid block problems. Int J Rock Mech Min Sci 35:683–693CrossRef
Zurück zum Zitat Liang GP, Wang CG (1996) LDDA on the high speed catenary-pantograph system dynamics. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 350–356 Liang GP, Wang CG (1996) LDDA on the high speed catenary-pantograph system dynamics. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 350–356
Zurück zum Zitat Lin CT, Amadei B, Jung J, Dwyer J (1996) Extensions of discontinuous deformation analysis for jointed rock masses. Int J Rock Mech Min Sci 33:671–694CrossRef Lin CT, Amadei B, Jung J, Dwyer J (1996) Extensions of discontinuous deformation analysis for jointed rock masses. Int J Rock Mech Min Sci 33:671–694CrossRef
Zurück zum Zitat Ma MY, Zaman M, Zhou JH (1996) Discontinuous deformation analysis using the third order displacement function. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 383–394 Ma MY, Zaman M, Zhou JH (1996) Discontinuous deformation analysis using the third order displacement function. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 383–394
Zurück zum Zitat MacLaughlin MM, Doolin DM (2006) Review of validation of the discontinuous deformation analysis (DDA) method. Int J Numer Anal Methods Geomech 30:271–305CrossRef MacLaughlin MM, Doolin DM (2006) Review of validation of the discontinuous deformation analysis (DDA) method. Int J Numer Anal Methods Geomech 30:271–305CrossRef
Zurück zum Zitat Mortazavi A, Katsabanis PD (2001) Modelling burden size and strata dip effects on the surface blasting process. Int J Rock Mech Min Sci 38:481–498CrossRef Mortazavi A, Katsabanis PD (2001) Modelling burden size and strata dip effects on the surface blasting process. Int J Rock Mech Min Sci 38:481–498CrossRef
Zurück zum Zitat Ning YJ, Yang J, Ma GW, Chen PW (2011) Modelling rock blasting considering explosion gas penetration using discontinuous deformation analysis. Rock Mech Rock Eng 44:483–490CrossRef Ning YJ, Yang J, Ma GW, Chen PW (2011) Modelling rock blasting considering explosion gas penetration using discontinuous deformation analysis. Rock Mech Rock Eng 44:483–490CrossRef
Zurück zum Zitat Ohnishi Y, Yamamukai K, Chen GH (1996) Application of DDA in rock-fall analysis, In: Proceedings of the 2nd North American rock mechanics symposium, Quebec, pp 2031–2037 Ohnishi Y, Yamamukai K, Chen GH (1996) Application of DDA in rock-fall analysis, In: Proceedings of the 2nd North American rock mechanics symposium, Quebec, pp 2031–2037
Zurück zum Zitat Ohnishi Y, Nishiyama S, Sasaki T (2006) Development and application of discontinuous deformation analysis. In: The 4th Asian rock mechanics symposium, Singapore, pp 59–70 Ohnishi Y, Nishiyama S, Sasaki T (2006) Development and application of discontinuous deformation analysis. In: The 4th Asian rock mechanics symposium, Singapore, pp 59–70
Zurück zum Zitat Pearce CJ, Thavalingam A, Liao Z, Bicanic N (2000) Computational aspects of the discontinuous deformation analysis framework for modelling concrete fracture. Eng Fract Mech 65:283–298CrossRef Pearce CJ, Thavalingam A, Liao Z, Bicanic N (2000) Computational aspects of the discontinuous deformation analysis framework for modelling concrete fracture. Eng Fract Mech 65:283–298CrossRef
Zurück zum Zitat Shi GH (1988) Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block system. PhD thesis, University of California, Berkeley Shi GH (1988) Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block system. PhD thesis, University of California, Berkeley
Zurück zum Zitat Shi GH (2001) Theory and examples of three dimensional discontinuous deformation analysis. In: Proceedings of the 2nd Asian rock mechanics symposium, Beijing, pp 27–32 Shi GH (2001) Theory and examples of three dimensional discontinuous deformation analysis. In: Proceedings of the 2nd Asian rock mechanics symposium, Beijing, pp 27–32
Zurück zum Zitat Shi GH, Goodman RE (1989) Generalization of two-dimensional discontinuous deformation analysis for forward modelling. Int J Numer Anal Methods Geomech 13:359–380CrossRef Shi GH, Goodman RE (1989) Generalization of two-dimensional discontinuous deformation analysis for forward modelling. Int J Numer Anal Methods Geomech 13:359–380CrossRef
Zurück zum Zitat Thomas PA, Bray JD (1999) Capturing nonspherical shape of granular media with disk clusters. ASCE J Geotech Geoenviron Eng 125:169–178CrossRef Thomas PA, Bray JD (1999) Capturing nonspherical shape of granular media with disk clusters. ASCE J Geotech Geoenviron Eng 125:169–178CrossRef
Zurück zum Zitat Tsesarsky M, Hatzor YH, Sitar N (2005) Dynamic displacement of a block on an inclined plane: analytical, experimental and DDA results. Rock Mech Rock Eng 38(2):153–167CrossRef Tsesarsky M, Hatzor YH, Sitar N (2005) Dynamic displacement of a block on an inclined plane: analytical, experimental and DDA results. Rock Mech Rock Eng 38(2):153–167CrossRef
Zurück zum Zitat Wang CY, Chuang CC, Sheng J (1996) Time integration theories for the DDA method with finite element meshes. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 263–287 Wang CY, Chuang CC, Sheng J (1996) Time integration theories for the DDA method with finite element meshes. In: Proceedings of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, Berkeley, pp 263–287
Zurück zum Zitat Wartman J, Bray JD, Seed RB (2003) Inclined plane studies of the Newmark sliding block procedures. J Geotech Geoenviron Eng ASCE 129(8):673–684CrossRef Wartman J, Bray JD, Seed RB (2003) Inclined plane studies of the Newmark sliding block procedures. J Geotech Geoenviron Eng ASCE 129(8):673–684CrossRef
Zurück zum Zitat Wu JH, Juang CH, Lin HM (2005) Vertex-to-face contact searching algorithm for three-dimensional frictionless contact problems. Int J Numer Methods Eng 63:876–897CrossRef Wu JH, Juang CH, Lin HM (2005) Vertex-to-face contact searching algorithm for three-dimensional frictionless contact problems. Int J Numer Methods Eng 63:876–897CrossRef
Zurück zum Zitat Yeung MR, Jiang QH, Sun N (2007) A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis. Comput Geotech 34:175–186CrossRef Yeung MR, Jiang QH, Sun N (2007) A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis. Comput Geotech 34:175–186CrossRef
Zurück zum Zitat Zhang YJ (2006) Equivalent model and numerical analysis and laboratory test for jointed rock masses. Chin J Geotech Eng 28:29–32 Zhang YJ (2006) Equivalent model and numerical analysis and laboratory test for jointed rock masses. Chin J Geotech Eng 28:29–32
Zurück zum Zitat Zheng H, Jiang W (2009) Discontinuous deformation analysis based on complementary theory. Sci China Ser E Technol Sci 52:2547–2554CrossRef Zheng H, Jiang W (2009) Discontinuous deformation analysis based on complementary theory. Sci China Ser E Technol Sci 52:2547–2554CrossRef
Metadaten
Titel
Kinetic Energy Dissipation and Convergence Criterion of Discontinuous Deformations Analysis (DDA) for Geotechnical Engineering
verfasst von
Qinghui Jiang
Yifeng Chen
Chuangbing Zhou
Man-chu Ronald Yeung
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/s00603-012-0356-5

Weitere Artikel der Ausgabe 6/2013

Rock Mechanics and Rock Engineering 6/2013 Zur Ausgabe