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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

2020

Vol. 20, no. 3

454--467

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.

Research on E.C. Bingham constitutive model of rock under impact load for deep well

Zhao G. M., Xie L. X., Meng X. R.

AGH Journal of Mining and Geoengineering

2012

Vol. 36, no. 3

489-500

The soft rock materials have special dynamic properties in deep mining. Their dynamic compression tests are performed with experimental system of Split Hopkinson Pressure Bar (SHPB). The results of experiment indicate that the dynamic stress-strain curves of rock materials are of distinct plastic yield characteristics. Based on modified excess stress model, according to the function relationship between strain, strain rate and, to simplify constitutive equation of modified excess stress model with dimensionless analysis, the simplified constitutive equation of modified excess stress model is obtained; And then, continuum damage theory and statistical damage theory are incorporated into the simplified constitutive equation of modified excess stress model account for the influence of damage to dynamic strength, the simplified constitutive equation of damage excess stress model is built up. The simplified constitutive functions are fitted out respectively on the basis of the experimental data. There is a good coherence between the fitting stress-strain curves and the experimental stress-strain curves.

Miękkie materiały skalne w kopalniach głębokich posiadają specyficzne właściwości dynamiczne. Wykonano testy kompresji dynamicznej przy zastosowaniu urządzenie kompresyjnego Hopkinsona (Split Hopkinson Pressure Bar SHPB). Wyniki przeprowadzonych badań wykazały, krzywe wykresu rozciągania skał mają charakterystykę typową dla materiałów upłynnionych. W oparciu o model rozkładu naprężeń, zgodnie z funkcją zależności pomiędzy typem odkształcenia a jego szybkością, celem uproszczenia równania odkształcenia zmodyfikowanego przy pomocy analizy bezwymiarowej, otrzymano równanie opisujące model naprężeń zmodyfikowanych. Następnie wykorzystano teorię ciągłego kontinuum oraz teorię statystyki odkształceń w równaniu odkształcenia zmodyfikowanego celem ustalenia zależności z badanym modelem. Uproszczone w ten sposób funkcje skorelowano na podstawie otrzymanych danych doświadczalnych. Ustalono wysoką spójność pomiędzy krzywymi teoretycznymi i doświadczalnymi.