Modeling of abrasion and crushing of unbound granular materials during compaction

Unbound compacted granular materials are commonly used in engineering structures as layers in road pavements, railroad beds, highway embankments, and foundations. These structures are generally subjected to dynamic loading by construction operations, traffic and wheel loads. These repeated or cyclic loads cause abrasion and crushing of the granular materials. Abrasion changes a particle's shape, and crushing divides the particle into a mixture of many small particles of varying sizes. Particle breakage is important because the mechanical and hydraulic properties of these materials depend upon their grain size distribution. Therefore, it is important to evaluate the evolution of the grain size distribution of these materials. In this paper an analytical model for unbound granular materials is proposed in order to evaluate particle crushing of gravels and soils subjected to cyclic loads. The model is based on a Markov chain which describes the development of grading changes in the material as a function of stress levels. In the model proposed, each particle size is a state in the system, and the evolution of the material is the movement of particles from one state to another in n steps. Each step is a load cycle, and movement between states is possible with a transition probability. The crushing of particles depends on the mechanical properties of each grain and the packing density of the granular material. The transition probability was calculated using both the survival probability defined by Weibull and the compressible packing model developed by De Larrard. Material mechanical properties are considered using the Weibull probability theory. The size and shape of the grains, as well as the method of processing the packing density are considered using De Larrard's model. Results of the proposed analytical model show a good agreement with the experimental tests carried out using the gyratory compaction test.