A Study Of Macro And Micro Mechanical Behavior Of Granular Materials From A Micro-mechanics Approach

Granular materials are defined as materials consisting of discrete particles and most of its unique mechanical behavior is linked to its discrete nature. Of all approaches that describe its behavior, micro mechanical approach is established on the thought that precise mechanical behavior can be obtained through the accurate depicting of contact behavior and configuration of particles. Thus this discrete-based approach is thought to be more dependable. Based on fully verified discrete equations relating macroscopic quantities with microscopic quantities, this thesis proposes some state tensors which are used to characterize those distribution functions of microscopic quantities and inspects mechanical behavior. The following conclusions can be drawn:(1) Macroscopic quantities of granular materials are connected to statistic distribution functions of microscopic quantities, i.e. macroscopic behavior is not influenced by a specified microscopic quantity, but by statistic feature. Based on discrete equations of macroscopic quantities and microscopic quantities derived by numerous researches, this thesis develops the relation of stress and strain with distribution functions of microscopic quantities.(2) This thesis originates a method of calculating the distribution functions based on Laplace harmonic series and demonstrates that approximation with first terms suits distribution functions well. Thus, the feature of every microscopic quantity can be characterized a state tensor. What's more, these state tensors have profound physical meanings.(3) This thesis deduces the relation of macroscopic quantities with state tensors and verifies the equation of stress with contact density, contact tensor, contact force tensor and orientation tensor by DEM simulation.(4) Based on contact model of single contact, a contact model expressed by state tensors was derived, which is the relation of contact force tensor and relative displacement tensor. It is also concluded that it is impossible to obtain contact force tensor from relative displacement tensor without slip probability function. On the other hand, it is impossible to achieve relative displacement tensor from contact force tensor without difference of slip displacement.(5) A scheme of investigating mechanical behavior of granular materials with state tensors is given and microscopic parameters are classified into three types. The first type is contact density characterizing degree of compaction; the second type includes contact force tensor which is the microscopic corresponding of stress and relative displacement tensor which is the microscopic corresponding of strain; the last type comprises contact tensor, orientation tensor and void tensor, all of which are characteristic of fabric of granular materials. All these parameters are connected by relations originated from this thesis.(6) The evolution of micro parameters under conventional triaxial stress path and their values at critical state are investigated by DEM simulation. Furthermore, the mechanism of shear resistance of granular materials is revealed as changing of microscopic quantities. At last, the unique of stress ratio at critical state is verified by microscopic state tensors.