Optimization Of The Gradation Of Rockfill Materials Based On Fractal Theory

Rockfill materials are discontinuous granular materials,usually consisting of sand and gravel,gravel,stones and other particles mixed,has been widely used in geotechnical engineering,such as dam,highway subgrade construction,coastal engineering,building foundation.The rapid development of the high rockfill dam project puts forward higher requirements for the macro and micro mechanical properties of the main rockfill materials.The macro mechanical properties of rockfill materials,such as nonlinear,elastic-plastic,dilatancy and anisotropy of the external loads,sliding friction between micro particles,motion and crushing results,are closely related to the distribution characteristics of rockfill materials.The mechanical properties result from the particle interaction,particle interlocking and particle breakage.The numerical simulation methods based on continuum mechanics have difficulty in revealing the evolution of microscopic structure of rockfill materials.In order to realize the simulation of crushing of rockfill particles,the random simulation technique is adopted base on the combined finite-discrete method(FDEM)in this paper.A three-dimensional particle crushing model is put forward to simulate the particle crushing explicitly.At the same time,the fractal model of particle size distribution of rockfill is established to describe the gradation characteristics of rockfill.The effect of aggregate gradation on the macro and micro mechanical properties of rockfill materials is also studied through single particle crushing test and triaxial shear test with numerical simulation.In order to carry out the simulation of particle crushing for rockfill,the cohesive zone model is adopted,which simulate rockfill particle crack,expansion and failure of the whole process and the explicit representation of rockfill particle crushing process in the condition of the rockfill particles for discrete element and interface element of zero thickness,solid element occurs only elastic deformation,damage and fracture occurred in the interface element.Single particle crushing tests are carried out on 40 sphere particles which are generated by the particle random generation algorithm.Weibull statistical model is used to analyze crushing strengths of single particle crushing tests and its results indicate that crushing strengths can satisfy the Weibull distribution except the small strength deviation range.Therefore the applicability of the particle crushing model proposed in this paper gets verified.Fractal geometry theory can describe the fractal characteristics of nonlinear system quantitatively and the local inhomogeneity of the system.Based on the fractal geometry,a fractal model for the rockfill particle-size distribution is employed and the range of fractal dimension is estimated through fitting the gradation curves of 35 rockfill materials from different rockfill dams,23 coarse grain materials from laboratory tests and 11 single particles from single particle crushing tests.Fractal behavior of rockfill materials is analyzed to find the geometric parameters that can reflect the filling structure of rockfill.The gradation of rock materials possesses good fractal behavior,so that the fractal dimension can be used as a new index to describe the gradation characteristics of rockfill materials from three levels of large-scale system,laboratory-scale system and single particle.Six sets of gradation curves for cushion layers of Gushui rockfill dam are designed based on the fractal model for the rockfill particle-size distribution.The relative density test and the conventional triaxial numerical shear tests are carried out to study the effects of fractal dimension on compaction capacity and the macroscopic and mesoscopic mechanical properties of rockfill materials.With the change of the fractal dimension D from 2.0 to 2.8,the void ratio decreases first and then increases,the material achieves its maximum compaction at the value of D of 2.7.The degree of inhomogeneity of force chains increases with the increasing of fractal dimension,which comes to the maximum at the value of D of 2.8.Synthesizes compaction capacity and inhomogeneity of force chains,the gradation corresponding to the value of D of 2.7 is identified as the optimized gradation.As fractal dimension varies from 2.0 to 2.8,the anisotropy of contact force increases and the degree of heterogeneity of contact force is more obvious.Besides,the average friction excitation index is higher,then the force chain network is attains the maximum at D= 2.8.By considering both the compaction capacity and the force chain heterogeneity,it is found that the gradation at D= 2.7 is the optimum gradation.Comparing the uncertainty of the non-uniformity coefficient Cu and the curvature coefficient Cc in describing the gradation,the fractal dimension D can be considered as a new index to represent the gradation of rockfill materials.