Abstract:Particle breakage of granular materials is ubiquitous in nature and engineering practices and often takes place under high stress levels. The phenomenon of particle breakage may not only influence the mechanical response of granular materials, resulting the contraction of the volume of the material and reduction of the shearing strength, but is also closely associated to a variety of engineering problems. The existing research is mainly focused on depicting the evolution of the particle breakage and uses a quantifiable parameter to relate the particle breakage to the subsequent mechanical response. However, little attention has been paid to exploring the underlying physics of the driving force that initiates and attenuates the particle breakage. In this study, we present the formulation of an elastic-breakage model for the isotropic compression of frictionless spheres in the framework of thermodynamics. In the model, both the elastic strain energy and the dissipation due to particle breakage are formulated using the micro-macro averaging procedure, which is often used in micromechanics of granular materials. The evolution path of the particle breakage is determined using the maximum energy dissipation hypothesis. As the modelling does not involve any empirical results, all the model parameters have concrete physical meanings. Comparison of the model prediction with the experimental data in the literature showed that the initial gradation has different effects on the elastic bulk modulus and the breakage stress: the bulk modulus increase initially and then decrease with the fractal dimension of the gradation, which implies that there is a peak bulk modulus for a certain value of the fractal dimension; while the breakage stress increases monotonically with the increase of the fractal dimension. In addition, both the bulk modulus and the breakage stress increase monotonically with the increase of the polydispersity of the particle sizes. The evolution path of the gradation due to particle breakage is found to indeed satisfy the maximum dissipation hypothesis. Both experimental results and model prediction show that the compression curve of granular materials can be divided into three stages: the elastic compression stage under low compressive stress, particle breakage stage and the pseudoelastic compression after sufficiently large amount of particle breakage.