Fractal Theory Of Single Particle Crushing Strength And Compression Deformation Of Coarse Granular Materials

Coarse grained soils,as very common materials in nature and engineering,have been widely studied in academic and engineering fields.Coarse grained soils are mixture of stone and soil with a particle content more than 50%and particle size within 0.075⁶0mm.Due to its characteristics of low compressibility,high shearing strength,high large density,hydraulic permeability and quick consolidation speed,the coarse grained soils are widely used as filling materials in foundation,water conservancy,transportation and other engineerings.The coarse grained soils are prone to crushing leading to the change of particle sizes,gradation distributions,compactness of coarse grained soil and finally affecting their subsequent stress-strain behaviors.Based on the impact crushing tests and the single particle crushing test of coarse grained soils,the fractal model of particle crushing successfully revealed the size effect of particle crushing strength and the energy balance equation of particle crushing process was proposed.According to the one-dimensional compression test,the relationship between compression deformation and particle crushing was revealed.Besides,the compressive theory of coarse grained soils was proposed based on the fractal model of particle crushing.By simulating the single particle compression crushing process and the compression process of coarse grained soils in discrete element method,the particle crushing model was explained from the view of the microscopic mechanism and the crushing strength and compression theories of coarse grained soils were verified.The main contents of this paper are as follows:?1?Established the particle crushing fractal model and proposed the calculation method of fractal dimension.According to fractal theory,the particle mass distribution M?d?/M_T is approximately a straight line with the particle size d in the double logarithmic coordinate system with the slope being 3-D,where D is the fractal dimension after particle crushing.The three kinds of experimental materials,marble coarse particles?MCP?,municipal solid waste incinerator bottom ash?MSWIBA?and biomass waste incinerator bottom ash?BWIBA?were selected in the impact crushing test to analyze the fractal model of the particles after crushing.The test results shows that the fractal dimension of the particles is different at different impact energy.As the impact energy increases,the fractal dimension of the particles increases until tends to a constant value and the relationship between the probability of particle crushing and the fractal dimension is revealed by theoretical derivation.It points out that the fractal dimension increases with the crushing probability and the fractal dimension has a limit.The increase of particle crushing energy will lead to the increase of particle crushing probability and the increase of the particle crushing fractal dimension.?2?Established the single particle crushing strength theory and the Weibull correction theory.The size effect of single particle crushing strength was revealed and the energy balance equation of particle crushing was derived.According to the single particle crushing tests,the force-displacement curves of single particle compression test are divided into three types,which are connected with the shape of particles.Based on the fractal model of single particle crushing,the single particle crushing strength?_f is deduced to be the D-3 power of particle size d.After modifying the Weibull theory,it points out that the Weibull modulus m expressed in fractal dimensions of particles should be D/?3-D?.According to the fractal theory and Griffith fracture mechanics theory,it is possible to establish an energy balance equation that considers elastic strain energy E_k which generated from the particles deformed and crushing energy E_s which generated from the new surface area.?3?The one-dimensional compression deformation theory of coarse grained soils considering particle crushing has been established.In the compression test,the deformation of the particles is initially due to the compression of the pores of the particles.Then,with the particles crushing intensified,the deformation increases and the compressive deformation of coarse grained soil is closely related to the particle crushing.The parameter of one-dimensional compression deformation of coarse grained soil is the explicit function of particle crushing fractal dimension D,loge=loge₀-?log?,where?=D/?6D-18?.The results of laboratory compression test and numerical compression test of coarse-grained soil have verified the one-dimensional compression theory of coarse-grained soil.?4?By simulating the crushing process and the crushing mode of the both single particle and coarse grained soils crushing one-dimensional compression tests with DEM,an algorithm for calculating the number of particles after crushing has been developed.The mechanism of single particle crushing has also been revealed and the fractal theories of single particle crushing strength and one-dimensional compression have been verified.DEM has compensated the shortage of laboratory tests.The processes of movement,fracture and crushing of particles are simulated by transferring the contact force and changing the number of bonds.And then the calculation methods of crushing probability,crushing strength and compression deformation of particles are derived.The simulated results are compared with the experimental results.