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

Abstract

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

CLC Number:

TD853

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.

Figures/Tables 11

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Fig.5

Table 2

Parameters of the damage evolution equation for sandstone and saprolite"

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

Table 2

Fig.6

Fig.7

Fig.8

Fig.9

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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

Damage Constitutive Model Considering the Effect of Rock Microdefects

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