考虑岩石微缺陷影响的损伤本构模型

doi:10.11872/j.issn.1005-2518.2023.03.164

摘要/Abstract

摘要：

为准确描述岩石应力—应变曲线非线性过程，提出了考虑岩石微缺陷影响的损伤本构模型。首先对含微缺陷岩石进行分析，把含微缺陷岩石抽象成不含微缺陷的岩石骨架部分和微缺陷部分。岩石微缺陷包括初始空隙和岩石受载新增的微裂纹，微缺陷只能产生应变，不能承受应力。初始空隙产生的应变反映压密阶段的非线性特征，新增的微裂纹产生的应变反映岩石峰后阶段应变软化，用修正系数b来表示新增微缺陷的影响，假设岩石骨架部分的损伤符合Weibull概率分布，最后推导出基于微裂纹的损伤本构模型，并给出参数V_m 、n、F₀、m和b的确定方法，对模型参数进行讨论。用砂岩和苏长岩试验数据进行验证，结果显示试验数据与理论结果相吻合。

关键词: 含微缺陷岩石, 本构模型, 微缺陷, 压密阶段, 应变软化, 修正系数

Abstract:

In order to accurately describe the whole process of rock stress-strain curve，a statistical damage contitutive model considering the effect of rock microdefects was proposed.Firstly，rocks containing microdefects are analysed and abstracted into a rock skeleton part and a defective part without microdefects.The rock microdefects include initial microdefects and new microdefects added to the rock by loading，which can only generate strain but not stress.The strain generated by the initial microdefects is negatively exponential to the stress during the compression-density stage，and the model parameters n and V_m are obtained by fitting the experimental curve of closed strain-stress for the microdefects.After the compression-density stage，the initial micro-defects are completely closed and the resulting strain is a constant.As additional micro-defects are mainly generated in large numbers in the post-peak stage，the effect of additional micro-defects on the post-peak stage is mainly considered.A variable b in the range of 0 to 1 is used to represent the weakening effect of the strain formed by the additional micro-defects on the strain generated in the rock.Different values of b can reflect the degree of strain softening in the rock，and a method for determining the value of b is given to obtain the value of b under different stress states for different rocks.The deformation of the rock skeletal part without micro-defects and whose damage conforms to the Weibull probability distribution，the deformation of the rock skeletal part and the micro-defective part make up the deformation of the rock，which leads to the derivation of the damage constitutive model of the rock，and the specific determination method of the parameters m and F₀ of this damage constitutive model is given.The parameters of the model are discussed.The smaller the value of b，the greater the strain generated by the new microcracks in the rock and the more obvious the strain softening is.The damage variables of the rock are analysed for different values of b.The smaller the value of b，the faster the damage value of the rock reaches 1 and the faster the skeletal part of the rock is damaged.The damage costitutive model in this paper takes into account the compression-density phase，the strain-softening phase，the effect of residual strain，and can characterise all phases of the rock stress-strain curve，and the model parameters are small and the method of determination is clear.Finally，the model is validated with sandstone and saprolite test data，and the test data agree with the theoretical results，indicating the reasonableness of the model.

Key words: rocks with microdefects, constitutive model, microdefects, compression-density stage, strain softening, correction factor

中图分类号:

TD853

刘志祥,晏孟洋,张双侠,熊帅,王凯. 考虑岩石微缺陷影响的损伤本构模型[J]. 黄金科学技术, 2023, 31(3): 507-515.

Zhixiang LIU,Mengyang YAN,Shuangxia ZHANG,Shuai XIONG,Kai WANG. Damage Constitutive Model Considering the Effect of Rock Microdefects[J]. Gold Science and Technology, 2023, 31(3): 507-515.

图/表 11

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图2

图3

图4

表1

图5

表2

砂岩和苏长岩损伤演化方程参数"

岩石类型	σ₃₃ /MPa	σ $11 r$ /MPa	ε $11 p$ /%	σ $11 p$ /MPa	b=b（MSE_min）	F₀/%	m
砂岩	3	25.1474	0.74	107.1221	0.70	0.5271	8.7655
	5	37.2000	0.85	132.1709	0.74	0.6660	7.5065
	8	62.9458	0.98	156.6792	0.85	0.9274	3.4272
苏长岩	3	56.8732	0.44	249.1216	0.90	0.4307	6.8780
	5	69.0954	0.50	274.0948	0.85	0.4707	6.8579
	8	101.7840	0.58	306.4413	0.80	0.5192	6.6992

表2

图6

图7

图8

图9

参考文献 0

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岩石种类	E/GPa	ε_cc/‰	V_m/‰	n	R²（拟合系数）
砂岩	28	1.37	1.43	4.64	0.9468
苏长岩	85	0.67	0.68	14.71	0.9924

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