Statistical Damage Model for Whole Deformation and Failure Process of Rock Considering Initial Void Closure
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摘要:
为了建立能够准确模拟岩石变形全过程的本构模型，深入分析了现有统计损伤模型难以描述岩石初始非线性变形阶段的局限性. 综合考虑岩石的变形机理，将岩石抽象为由空隙和骨架组成的材料，分析了岩石变形及空隙与骨架两部分变形之间的关系，提出了空隙应变比
K 的概念；利用岩石三轴试验结果，提出了岩石骨架和空隙两部分应变的计算方法，推导了K 的演化方程；通过引入统计损伤理论，将岩石看作是由众多强度服从Weibull函数分布的微元组成，最终建立了能够反映岩石变形全过程的本构模型，并给出了模型相关参数的确定方法. 现有模型结果和试验结果比较分析表明：本文模型能够较好地模拟荷载作用下岩石变形破坏全过程的5个阶段，相关系数均在0.92以上，很好地解释了围压越大初始空隙压密阶段越短以及弹性模量、峰值强度和峰值应变均越大的力学行为特性.Abstract:In order to establish a constitutive model that can accurately simulate the whole deformation and failure process of rock, a deep analysis is made of the limitations of the existing statistical damage models incapable of well describing the initial nonlinear phase of rock deformation. Considering the deformation mechanism of rock comprehensively, the intact rock is abstracted as a material composed of rock skeleton and voids. Based on the analysis of the deformation relationships among the whole rock, rock skeleton and voids, the concept of rock void strain ratio
K is proposed; the calculation methods of rock skeleton strain and voids strain are presented using triaxial test results to derive the evolution equation ofK . By introducing the statistical damage theory, the rock is regarded as being composed of many micro elements whose strength obeys the distribution of Weibull function. Finally, a new constitutive model is established to describe the whole rock deformation process, and the determination methods of relevant model parameters are given. Compared with other model calculations and test results, this constitutive model can better simulate the five phases of the whole rock deformation and failure process under load, and the correlation coefficients are all larger than 0.92 for different confining test results. It also well explains the mechanical behavior characteristics that the larger the confining pressure, the shorter the initial void closure phase, and the larger the elastic modulus, peak strength and peak strain. -
图 8 不同m值对应的损伤变量D随ε/ε0的变化
Figure 8. Variation of damage variables D with ε/ε0 for different m
图 9 Weibull分布参数ε0与εc的关系
Figure 9. Relationship between peak strain εc and the parameter ε0 of Weibull distribution
图 10 本文模型计算结果与试验曲线之间的比较
Figure 10. Comparison between the proposed constitutive model calculation values and experimental curves
图 11 不同模型计算结果与试验值的比较
Figure 11. Different model calculations versus experimental curve
表 1 岩石三轴试验参数
Table 1. Triaxial test parameters for rocks
σ3
/MPaE
/MPaεa
/%σc
/MPaεc
/%R
/MPa0 13.72 0.487 54.92 0.697 0 10 14.68 0.443 122.38 1.235 57.7 20 16.17 0.425 171.2 1.57 101.5 30 18.12 0.409 201.17 1.762 123.8 40 19.28 0.374 243.36 1.993 154.9 
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表 2 本文岩石统计损伤模型参数
Table 2. Parameters of statistical damage model for rocks
σ3 /MPa a1 a2 ε0/% m ε0－εc/% 0 0.203 6.301 0.782 14.258 0.095 10 0.226 5.965 1.337 7.576 0.102 20 0.252 5.694 1.714 4.735 0.144 30 0.249 5.379 1.827 4.581 0.065 40 0.217 5.283 2.134 4.269 0.141
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