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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

Damage deterioration mechanism and damage constitutive modelling of red sandstone under cyclic thermal-cooling treatments

Cao Ri-hong, Fang Lei, Qiu Xianyang, Lin Hang, Li Xilong, Li Wenxin

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 4

art. no. e188, 2022

EN

In the process of exploiting mineral and geothermal energy resources, the influence of the cyclic heat effect on the mechanical properties of the surrounding rock becomes increasingly prominent. To further study the damage deterioration mechanism, deformation and failure characteristics of cyclic heating–cooling (H–C) of the rock, cyclic H–C treatment tests and uniaxial compression tests were conducted, acoustic emission (AE) events were monitored, and the mesoscale characteristics of the fracture surface were imaged and analysed. The results show that the number of H–C cycles played an important role in the evolutions of the strength, cumulative damage variables and deformation modulus of the red sandstone. The peak strength of the specimens decreased with the increase in the number of H–C cycles, and the damage variables increased with the number of H–C cycles. The cyclic H–C treatments promoted the development of microcracks and the growth of the stress–strain curve crack closure stage. Both the crack closure stress and crack closure strain increased with the number of H–C cycles. Furthermore, both the number of transgranular microcracks and the microcrack spacing increased during cyclic H–C treatment, which also led to the failure mode of the specimens gradually changing from shear failure to splitting failure. In addition, based on the principle of strain equivalence, a damage constitutive model under the coupling action of cyclic H–C treatment and loading was deduced. The crack closure deformation of specimens treated with different numbers of H–C cycles was well reflected by the proposed model, and the prediction of other mechanical parameters, such as the peak stress, peak strain and tangent modulus of the theoretical curves, was also verified by test data.

4

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.

5

Control Strategy of Parallel Systems with Efficiency Optimisation in Switched Reluctance Generators

Zan Xiaoshu, Lin Hang, Xu Guanqun, Zhao Tiejun, Gong Yi

Power Electronics and Drives

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2021

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Vol. 6 (41)

61--74

EN

To solve motor heating and life shortening of parallel switched reluctance generator (SRG) induced by uneven output currents due to different external characteristics, we generally adopt current sharing control (CSC) to make each parallel generator undertake large load currents on average to improve the reliability of parallel power generation system. However, the method usually causes additional loss of power because it does not consider the efficiency characteristics of each parallel generator. Therefore, with the efficiency expression for the parallel system of SRG established and analysed, the control strategy based on differential evolution (DE) algorithm is proposed as a mechanism by which to enhance generating capacity and reliability of multi-machine power generation from the perspective of efficiency optimisation. We re-adjust the reference current of each parallel generator to transform the working point of each generator and implement the efficiency optimisation of parallel system. The performance of the proposed control method is evaluated in detail by the simulation and experiment, and comparison with traditional CSC is carried out as well.

6

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.

7

Investigation of the correlation between crack propagation process and the peak strength for the specimen containing a single pre-existing flaw made of rock-like material

Yang Hengtao, Lin Hang, Wang Yixian, Cao Rihong, Li Jiangteng, Zhao Yanlin

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 2

458--478

EN

This paper investigated the relationship between the strength of fractured rock and the crack propagation process. A series of uniaxial compression tests were carried out on the rock-like material specimens with single pre-fabricated flaw. Moreover, DIC (digital image correlation) technology was utilized to monitor and analyze the failure process of specimens. The initiation of each crack was defined as a key event, and the relationship between several key events and the axial load of the specimen during the crack propagation was quantitatively analyzed. The time-sequence analysis of crack propagation was also conducted by selecting benchmark points on the both sides of major cracks. It can be found that only the wing crack propagation occurs and there is no obvious shear crack before the peak strength. When the first secondary crack initiated, the specimen reached its peak strength and the wing crack just reached its critical length. Beyond the peak strength, secondary cracks initiated and coalesced rapidly, which leads to the sudden failure of fractured rock. Therefore, the peak strength of the specimen can be assessed by taking the critical length of the steadily propagating wing crack as the condition which determines whether the specimen reaches the peak strength. Furthermore, the discrete element numerical simulation was also implemented to confirm the experimental results.

8

Creep damage model of rock mass under multi-level creep load based on spatio-temporal evolution of deformation modulus

Zhang Xing, Lin Hang, Wang Yixian, Zhao Yanlin

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 2

508--523

EN

To study the damage characteristics of rock mass under multi-level creep load, damage variable D was defined based on the spatio-temporal evolution characteristics of deformation modulus E, and the Kachanov damage theory is used to describe the damage evolution, then the damage evolution equation of the rock mass under multi-level creep load is obtained. Combining the damage evolution equation with the Lemaitre strain equivalence principle, the creep damage constitutive model of rock mass under multi-level creep load considering initial damage is obtained. By comparing the results of uniaxial and triaxial tests with the calculated values of the model, the rationality, reliability, application range of the model proposed in this paper is verified. According to the results of parameter inversion, obtain the relationship between damage, stress and time. Results show that time and stress are the important factors influencing the damage of rock mass under multi-level creep loading, the damage increases with time and stress level. However, the influence of time and stress on damage has a significant stress response characteristics: under low stress, the instantaneous damage Dis caused by the instantaneous stress loading is the main reason for the damage. With the increase of the load level, the main cause of the damage gradually changes from the instantaneous loading of the stress to the creep accumulation of the damage, and the greater the initial damage, the higher the time-dependent damage DiT proportion in the global damage.

9

Nonlinear shear constitutive model for peak shear-type joints based on improved Harris damage function

Xie Shijie, Lin Hang, Wang Yixian, Cao Rihong, Yong Rui, Du Shigui, Li Jiangteng

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 3

454--467

EN

The majority of jointed rock mass failures mainly occur along the joints in shear mode, which promotes a wide investigation on the proposal of a reasonable and reliable shear constitutive model of rock joints. In this paper, based on Improved Harris function and laboratory shear tests, a new constitutive model of saw-tooth joints was proposed. Firstly, a series of laboratory direct shear tests were carried out on saw-tooth joint specimens made of rock-like materials (cement mortar) to obtain the shear stress-displacement curves. Subsequently, the test results were divided into sliding failure type and peak shear type according to whether there is a significant stress drop between peak stress and residual stress. It is assumed that rock elements can be divided into undamaged parts and damaged parts during the shearing process. The stress-displacement relation of the undamaged part satisfies Hooke’s law, while the damaged part provides residual stress. Via the comparison with commonly used micro-element failure probability density functions, the Improved Harris distribution function was selected as the standard to characterize the strength of micro rock units. Finally, derived from the theory of damage statistical mechanics, a damage statistical constitutive model was proposed, which can reflect the deformation characteristics of rock joints. Compared with previous models and experimental data, the model proposed in this paper can represent the trend of peak shear curve variation with higher accuracy, the parameters are easy to be solved and have obvious physical significance, which verifies the advantages and applicability of this model.

10

Mechanical behavior around double circular openings in a jointed rock mass under uniaxial compression

Lin Qibin, Cao Ping, Cao Rihong, Lin Hang, Meng Jingjing

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 1

264--281

EN

To better understand the mechanical behavior in a jointed rock mass, a series of uniaxial compression tests were conducted on non-persistently jointed rock specimens with double circular holes. Acoustic emission (AE) and digital image correlation (DIC) techniques were applied to capture micro-crack events and real-time strain field evolution in the specimens. The results indicate that the existence of non-persistent joints has a significant influence on the strength characteristics of the specimens. Specifically, peak strength decreases at first and reaches a minimum at 30° then increases with increase in the joint dip angle. DIC technology has successfully monitored the development of surface strain fields. The fracture evolution process is comprehensively understood. Every sudden change in a strain field is usually accompanied by apparent AE events and stress–strain curves take the form of oscillations. The crack coalescence modes among joints can be summarized as six types and the crack coalescence patterns around holes and joints can be divided into three categories. These results are helpful to understanding further the mechanical properties and fracture mechanism of openings in non-persistently jointed rock masses.