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1

New constitutive model based on disturbed state concept for shear deformation of rock joints

Xie Shijie, Lin Hang, Chen Yifan

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e26, 2023

EN

The mechanical behavior and constitutive relation of rock joints have caught more and more attention in the field of geotechnical engineering. The disturbed state concept (DSC) theory offers a powerful tool for building a constitutive model to interpret the mechanical response of geomaterials. In this paper, a new constitutive model for joint shear deformation was developed based on the DSC theory. The characteristics of quasi-elastic phase, pre-peak hardening phase, peak shear strength, post-peak softening phase and residual strength during the whole process of joint shear deformation are considered in this model. In the framework of this shear constitutive model, the rock material was assumed to consist of two kinds of micro-units with different mechanical responses, namely the relatively intact unit and the fully adjusted unit. Subsequently, the DSC theory was used to connect the mechanical behavior of micro-units with the macroscopic joint shear deformation characteristics, and a disturbance factor was introduced to reveal the disturbed state evolution process inside the rock. In addition, the proposed DSC model was simple in form, less in parameters and reasonable in physical meaning. The model was cross-validated by experimental data of different kinds of natural joints and artificial joint replicas. Finally, the model is compared with existing models, and the model effectiveness is quantitatively evaluated through statistical indicators. The values of R2 are greater than 0.9, and the AAREP and RMSE of the proposed DSC model are closer to 0 than those of other models. The research results can provide a valuable reference for further understanding of shear deformation mechanism.

2

Shear expression derivation and parameter evaluation of Hoek-Brown criterion

Chen Yifan, Lin Hang, Li Su, Cao Rihong, Yong Weixun, Wang Yixian, Zhao Yanlin

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e77, 1--9

EN

Hoek-Brown criterion is one of the most widely used strength criteria in the field of rock engineering, which can reflect the nonlinear empirical relationship between the ultimate principal stresses in rock failure, while the determination of Hoek-Brown parameters is still controversial. The evaluation of Hoek-Brown parameters according to geological strength index (GSI) classification of rock mass involves engineering experiences and subjectivity, and the fitting method of Hoek-Brown parameters based on laboratory triaxial experimental results of multiple fractured rocks is also not going to be easy. Besides, the majority of previous studies were still carried out through the triaxial tests of intact rocks. In this study, the shear expression of Hoek-Brown criterion was derived, and an approximate method for determining Hoek-Brown parameters basedon shear tests was established. Primarily, Hoek-Brown criterion was briefly reviewed and the variations of Hoek-Brown parameters with the change of GSI was analyzed. When GSI decreases from 100 to 50, the reduction of a is only 0.006.While s shows almost no change and approximates to 0 when GSI decreases from 50 to 0. On this basis, the existing shear expression of Hoek-Brown criterion for intact rock (GSI = 100) was extended to the fractured rock mass with 50 < GSI < 100. In addition, the approximate shear expression of Hoek-Brown criterion for fractured rock mass in the range of 0 < GSI < 50 was deduced by assuming s = 0. Then, Hoek-Brown parameters can be calculated through shear tests and MATLAB programing. Finally, based on the structural plane occurrence information of Tangdan copper mine, a random fracture network was generated by Monte Carlo method to prepare random fractured rock mass samples for compression-shear experiments, which were employed to verify the proposed method.

3

Constitutive modeling of rock materials considering the void compaction characteristics

Xie Shijie, Han Zhenyu, Chen Yifan, Wang Yixian, Zhao Yanling, Lin Hang

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e60, 1--15

EN

The study of constitutive model is of great significance to engineering safety evaluation and geological disaster prevention. In this paper, rock materials were regarded as a composite geological material composed of voids and rock matrix, and then a piecewise constitutive model bounded by the yield point was proposed. It can reflect the complete stress–strain curves of rocks, including the compaction stage, the elastic stage, the plastic yield stage and the post-peak stage. Primarily, an objective method to determine the yield point based on the stress difference was proposed. For the rock deformation before yielding, the relationship between the strain of rock materials and the strains of voids and rock matrix was analyzed to establish the corresponding constitutive model. Subsequently, based on the modified Weibull distribution, a damage statistical constitutive model of rocks was established to describe the nonlinear deformation after the yield point. Meanwhile, the determining method of model parameters was given. Finally, the uniaxial and triaxial compression test data of different types of rocks were used to verify the proposed model. The results indicate that the model curves are in good agreement with the experimental results. Hence, it is feasible and reasonable to divide the macroscopic strain of rocks into the strains of voids and rock matrix. Additionally, there is a power function attenuation relationship between the deformation ratio of voids to rock matrix and the axial stress.

4

Statistical damage constitutive model based on the Hoek-Brown criterion

Chen Yifan, Lin Hang, Wang Yixian, Xie Shijie, Zhao Yanlin, Yong Weixun

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

556--564

EN

The constitutive models of rock are essentially the general depictions of the mechanical responses of rock mass under complex geological environments. Statistical distribution-based constitutive models are of great efficacy in reflecting the rock failure process and the stress–strain relation from the perspective of damage, while most of which were achieved by adopting Drucker–Prager criterion or Mohr–Coulomb criterion to characterize microelement failure. In this study, underpinned by Hoek–Brown strength criterion and damage theory, a new statistical damage constitutive model, which is simple in terms of model expression and capable of reflecting the strain softening characteristics of rock in post-peak stage, was established. First, the rock in the failure process was divided into infinite microelements including elastic part satisfying Hooke’s law and damaged part retaining residual strength. Based on strain equivalence hypothesis, the relation between rock microelement strength and damage variable was derived. By assuming the statistical law of microelement strength obeying Weibull distribution and the microelement failure conforming to Hoek–Brown criterion, the new statistical damage constitutive model based on Hoek–Brown criterion was, therefore, gained. The mathematical expressions of the corresponding model parameters were subsequently deduced in accordance with the geometric characteristics of the deviatoric stress–strain curve. Last, the existing conventional triaxial compression test data of representative rock samples under different confining stresses were employed to compare with the theoretical curves by proposed model, the consistency between which was quantified by utilizing the correlation factor evaluation method. The result indicated that the proposed model could well describe the entire stress–strain relationship of rock failure process and manifest the characteristics of rock residual strength. It is of great significance to the researches on rock damage and softening issues and rock reinforcement treatments.