Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination

Abstract

Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a statistical damage evolution equation was established based on the property that strength of micro-cells is consistent with normal distribution function, through discussing the characteristics of random distributions for strength of micro-cells, then a statistical damage constitutive model that can simulate the full process of rock strain softening under specific confining pressure was set up. Secondly, a new method to determine the model parameters which can be applied to the situations under different confining pressures was proposed, by deeply studying the relations between the model parameters and characteristic parameters of the full stress-strain curve under different confining pressures. Therefore, a unified statistical damage constitutive model for rock softening which can reflect the effect of different confining pressures was set up. This model makes the physical property of model parameters explicit, contains only conventional mechanical parameters, and leads its application more convenient. Finally, the rationality of this model and its parameters-determining method were identified via comparative analyses between theoretical and experimental curves.

Keywords

constitutive model / rock / damage / strain softening / normal distribution

References

[1] KrajcinovicD., FonsekaG. U.. The continuous damage theory of brittle materials (Part I, II)[J]. Journal of Applied Mechanics, 1981, 48: 809-824

[2] KrajcinovicD., SilvaM. A. G.. Statistical aspects of the continuous damage theory[J]. Int J Solids Structures, 1982, 18(7): 551-562

[3] TangC.-an.Catastrophe in Rock Unstable Failure[M], 1993, Beijing, The Coal Industry Publication Company

[4] CaoW.-g., FangZ.-l., TangX.-jun.. A study of statistical constitutive model for softening and damage rocks[J]. Chinese Journal of Rock Mechanics and Engineering, 1998, 17(6): 628-633

[5] CaoW.-g., ZhaoM.-h., LiuC.-xue.. Study on the model and its modifying method for rock softening and damage based on Weibull random distribution[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(19): 3223-3231

[6] YangM.-h., ZhaoM.-h., CaoW.-gui.. Method for determining the parameters of statistical damage softening constitutive model for rock[J]. Journal of Hydraulic Engineering, 2005, 36(3): 345-349

[7] LemaitreJ.. How to use damage mechanics[J]. Nuclear Engineering and Design, 1984, 80(3): 233-245

[8] LemaitreJ.. A continuous damage mechanics model for ductile fracture[J]. Journal of Engineering Materials and Technology, 1985, 107(1): 83-89

[9] PanC.-l., ZhuF.-c., CaoP., et al.. Characteristics of acoustic emission of bursting-intended rocks under uniaxial compression[J]. Journal of Central South University of Technology: Natural Science, 2001, 32(4): 336-338

[10] HuL.-q., LiX.-bing.. Damage and fragmentation of rock under experiencing impact load[J]. Journal of Central South University of Technology, 2006, 13(4): 432-437

[11] ZhouW.-y., WuP., YangR.-qiong.The Damage Model of Rock[M], 1989, Shenyang, Northeast College of Engineering: 37-53

[12] KawamotoT.. Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J]. Int J Num Anal Methods Geomech, 1988, 12: 1-30

[13] ZengY.-w., ZhaoZ.-y., ZhuY.-wen.. Bifurcation analysis on failure forms of rock material[J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(7): 948-952

[14] LinZ.-y., WuY.-s., GuanL.-li.. Research on the brittle-ductile transition property of rocks under triaxial compression[J]. Rock and Soil Mechanics, 1992, 13(2/3): 45-51

[15] YE Jin-han. The stress-strain curve and testing techniques of rock[J]. Journal of Hydraulic Engineering, 1984(9): 43–48. (in Chinese)

[16] LuY.-d., GeX.-r., JiangY., et al.. Study on conventional triaxial compression test of complete process for marble and its constitutive equation[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(15): 2489-2493

[17] YouM.-qin.. Effect of confining pressure on the Young’s modulus of rock specimen[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(1): 53-60

[18] SuC.-d., ZhaiX.-x., LiY.-m., et al.. Study on deformation and strength of coal samples in triaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(S1): 2963-2968