The paper proposes a three-scale binary medium-based constitutive model on the basis of the meso structures and micro components to describe the elasto-plastic mechanical behavior of mudstone samples. Based on the breakage mechanism of geomaterials, mudstone samples are considered as two different materials(bonded and frictional elements) at mesoscales. From micro to meso scales, given the similar but different mineralogy composition and porosity of the bonded and frictional elements at microscale, as well as their separate mechanical characteristics, different homogenization methods are adopted to obtain their respective meso mechanical properties. At the mesoscale, in view of the unique meso structures and the continuous material transformation, the extended self-consistent scheme(SCS)is improved to be adaptable to elasto-plastic composites with varying meso components. With the consideration of the evolution form of the breakage ratio under the external loading being given based on the assumed strength distribution of the meso bonded elements, the mechanical relations between meso and macro scales are established. Finally, on the basis of the mean-field method and combined with the critical mechanical connections between different scales, the micro-meso-macro constitutive model for mudstone samples are proposed. The model validation shows that, with a few model parameters, the proposed model can well reflect the stress and deformation features of mudstone samples with complex micro-components.

supportedbythefundingofHighwayPlanning,SurveyandDesignResearchInstitute,SichuanProvincialTransportDepartment(No.2020-WX-15)；theNationalNaturalScienceFoundationofChina(NSFC)(No.U22A20596)；

1. Introduction
2. The idea of three-scale constitutive model for rock
3. Mechanical connections between micro and meso scales
3.1. Mechanical properties of the bonded elements
3.2. Elastoplastic behavior of the frictional elements
4. Modelling meso to macro scales
4.1. Mechanical relations from macro to meso scales
4.2. Evolution of the breakage ratio
4.3. Relations of stress (resp.strain) connections between the local and average phases at meso scales
4.4. Determining approaches for model parameter
5. Application to mudstone samples
5.1. General situation of mudstone samples
5.2. Determination of model parameters and model validation of mudstone samples at different depths
5.3. Model validation of mudstone samples at different confining pressures
6. Conclusions
Appendices A and B.Supplementary material

Di Yu,Enlong Liu,Bo Xiang,Yunyong He,Fei Luo,Chuan He.A micro–macro constitutive model for rock considering breakage effects[J].International Journal of Mining Science and Technology,2023,33(02):173-184.