Study On The Characterization Method Of Meso-macro Contacts Of The Granular Material And Its Application On DEM

The macroscopic mechanical response of the granular material is derived from the interaction of its internal discrete particles.In this paper,the topological relation between meso-contact and the macroscopic contact is analyzed on the basis of graph theory,and a quantitative characterization method of macro-meso contact is proposed.The distribution equation of contact force on macroscopic contact surface is given.In this paper,we propose a new method for the characterization and visualization of macro-meso cracks and the criterion of the overall failure,especially for the cohesive granular materials(such as rock materials).Finally,a method for determining the slope stability is proposed for the formation of slopes formed by viscous particles.The main contents and innovations of the paper include:This paper points out the physical meaning of pores,mesoscopic contact and macroscopic contact from the mesoscopic scale of granular materials.Based on graph theory,this paper analyzes the distribution of meso-contact in the macroscopic contact surface of granular materials,and reveals the topological and geometric relations between mesoscopic contacts and macroscopic contacts.Two-dimensional macroscopic contact is a meso-contact set that satisfies the constraint condition of one-dimensional manifold with boundary.Three-dimensional macroscopic contact is a meso-contact set that satisfies the constraint condition of two-dimensional manifold with boundary.The characterization method of macro-meso contact of two-dimensional granular materials is proposed.The characterization method has a clear physical basis and is quantifiable in math.On the basis of graph theory,the dual geometric systems(the void cell system and the solid cell system)are abstracted from the particle accumulation.The edge and path of the solid cell system realize the mathematical representation of the macro-meso contacts of the two-dimensional granular material.The topological relations of particles,voids and contacts of three-dimensional granular materials are discussed and the characterization method of macro-meso contact of three-dimensional granular materials is proposed.The mathematical representation of the macro-meso contacts of the three-dimensional granular material is realized by the cycle and the set of cycles satisfying the constraint of two-dimensional manifold with boundary in the solid cell system.Based on the theory of graph theory,the distribution equation of contact force on arbitrary macroscopic contact surfaces of granular material is deduced.For the cohesivetype granular material(such as rock material),combined with the law of " for mesocontact set in the granular material,there is always a subset correspondin to an arbitrary set of cracks",this paper proposed a characterization method of macro-meso cracks to realize the visualization of macro-meso cracks.According to the topological distribution of mesoscopic cracks in macroscopic cracks,the criterion of the overall failure of cohesive granule material is put forward.The characterization method of the contacts proposed in this paper is used to extract the soil contact surface of a typical slope constructed by the discrete element method.By comparing the theoretical results of the comparative model and the calculation method of the contact force of this method,the validity of the proposed model was verified.The calculation of the slope stability of the cohesive particles is deduced from the microscopic point of view,which is based on the characteristic of the bond fracture of the cohesive soil.The result shows good accuracy.