Experimental and numerical investigation of Weibullian behavior of grain crushing strength

The Weibullian behavior of single grain crushing strength was investigated experimentally and numerically with the aim of enhancing the understanding of rock grain breakage.The morphologies of pebble grains were obtained using white light 3D laser scanning and image processing.A grain shape library was constructed for grain shape analysis with different shape descriptors.The use of the shape library and grain stability analysis is discussed for a suggested procedure to rotate a grain to its most stable configuration.Single grain crushing tests were performed for 30 pebbles to obtain force-displacement curves and fracture patterns.Each grain was compressed diametrically between flat platens.As expected,the values of the stress at bulk fracture follow a Weibull distribution.A procedure for generating crushable agglomerates with realistic particle shapes was demonstrated,which was accomplished in the discrete element modeling(DEM)of the single grain crushing test.The work presented here is novel in that both the heterogeneous micro-structures and randomly distributed flaws are considered.The DEM results demonstrate that the proposed modeling approach and calibrated parameters are reliable and can reflect the crushing behavior of rock pebbles.Finally,three parametric studies were presented evaluating the effects of micro-crack density,micro-crack disorder,and grain morphology on the Weibullian behavior of the crushing strength,none of which has previously been thoroughly considered.These three studies provide a deeper insight into the origin of the Weibullian behavior of single grain crushing strength.

Grain crushing in geoscience materials-Key issues on crushing response,measurement and modeling:Review and preface

Grain crushing is commonly encountered in deep foundation engineering,high rockfill dam engineering,railway engineering,mining engineering,coastal engineering,petroleum engineering,and other geoscience application.Grain crushing is affected by fundamental soil characteristics,such as their mineral strength,grain size and distribution,grain shape,density and specimen size,and also by external factors including stress magnitude and path,loading rate and duration,degree of saturation,temperature and geochemical environment.Crushable material becomes a series of different materials with the change in its grading during grain crushing,resulting in a decrease in strength and dilatancy and an increase in compressibility.Effects of grain crushing on strength,dilatancy,deformation and failure mechanisms have been extensively investigated through laboratory testing,discrete element method(DEM)modelling,Weibull statistics,and constitutive modelling within the framework of the extended crushing-dependent critical state theory or the energy-based theory.Eleven papers summarized in this review article for this special issue addressed the above issues in grain crushing through the advanced testing and modelling.

A combined method to model grain crushing with DEM

This paper presents a combined method to model grain crushing effects with discrete element method.This method combines the two most commonly used concepts to model grain crushing in DEM,i.e.the replacement method and the agglomerate method,so that it is both accurate and efficient.The method can be easily implemented.The performance is shown by several DEM simulations of biaxial tests.Particles with different crush-abilities are modeled.DEM simulation results with and without grain crushing are compared and discussed.The change of grain size distribution due to grain crushing is also investigated.

Investigation on relations between grain crushing amount and void ratio change of granular materials in one-dimensional compression and creep tests

Grain crushing plays an important role in one-dimensional (1D) compression and creep behaviors of granular materials under high stress. It is clear that the macro-properties of granular materials are closely related to the micro-fracture properties of grains in 1D compression and creep tests. In this paper, a series of 1D compression and creep tests were performed on Ottawa sand to investigate the deformation and grain crushing properties of granular materials, and it shows that the void ratio is correlated to the grain crushing amount (the quantity of crushed grains) for granular materials subjected to grain crushing. The test results, combining with the existing test data related to grain crushing of granular materials, were used to verify the relation. Moreover, the implications of these relations on the yield of granular material, and the equivalent effect of stress and time in changing soil fabric are presented.

Generalized plasticity model considering grain crushing and anisotropy for rockfill materials

Rockfill materials have been widely used in the construction of rockfill dam,railway and highway subgrade due to its high filling density,good compaction performance,strong water permeability,small settlement deformation and high bearing capacity.A reasonable constitutive model for rockfill materials is very important for engineering computation and analysis,and has a great development space.Based on the crushing stress and spatial mobilized plane(SMP),a state parameter that can comprehensively reflect the anisotropy and grain crushing is proposed.This state parameter is used to improve the MPZ model(a modifed ZienkiewiczⅢmodel),so that a generalized plastic model is constructed to describe the stress and deformation characteristics of rockfill materials in engineering.The validity of the developed model is verified by a series of conventional triaxial tests with different inclination angles of the compaction plane.The variation trend of the constructed anisotropy indexωcan reflect the non monotonic variation of the deformation and strength of rockfill with the direction angle of large principal stress,so the model can reflect the obvious difference caused by the initial anisotropy of rockfill on the mechanical properties.

Grain crushing and its effects on rheological behavior of weathered granular soil

To disclose the grain crushing effects on the weathered granular soil rheological behavior,a series of rheological tests (odometer compression and triaxial shearing) were carried out.At the same time,the sieving analysis tests of these specimens were also executed before and after tests,and the grain crushing degree,Br and n5,were collectively adopted to estimate the grain crushing.The grain crushing degree depends on the stress path,stress level,and load time,especially,the longer load time and more intensive gradient shearing path will increase the grain crushing quantity.The Hardin crushing degrees Br are 0.191,0.118 and 0.085 in the ordinary compression,rheological compression and triaxial rheological shearing,respectively;The grain crushing degrees n5 are 1.9,1.4 and 1.32,respectively.The strain softening phase indicates the grain crushing and diffusive collapse,and the strain hardening phase indicates the rearrangement of these crushed grains and formation of new bearing soil skeleton.The rheological deformation of granular soil can be attributed to the coarse grain crushing and the filling external porosity with crushed fragments.

Bounding surface plasticity model for stress-strain and grain-crushing behaviors of rockfill materials

Crushing of grains can greatly influence the strength,dilatancy,and stress-strain relationship of rockfill materials.The critical state line(CSL)in the void ratio versus mean effective stress plane was extended to the breakage critical state plane(BCSP).A state void-ratio-pressure index that incorporated the effect of grain crushing was proposed according to the BCSP.Rowe’s stress-dilatancy equation was modified by adding the breakage voidratio-pressure index,which was also incorporated into the formulations of the bounding stress ratio and plastic modulus.A BCSP-based bounding surface plasticity model was proposed to describe the state-dependent stressstrain behaviors and the evolution of grain crushing during shearing process of rockfill materials,and was shown to sufficiently capture the breakage phenomenon.

Effects of particle size on crushing and deformation behaviors of rockfill materials

Strength and deformation behaviors of rockfill materials,key factors for determining the stability of dams,pertain strongly to the grain crushing characteristics.In this study,single-particle crushing tests were carried out on rockfill materials with nominal particle diameters of 2.5 mm,5 mm and 10 mm to investigate the particle size effect on the single-particle strength and the relationship between the characteristic stress and probability of non-failure.Test data were found to be described by the Weibull distribution with the Weibull modulus of 3.24.Assemblies with uniform nominal grains were then subjected to one-dimensional compression tests at eight levels of vertical stress with a maximum of 100 MPa.The yield stress in one-dimensional compression tests increased with decreasing the particle size,which could be estimated from the single-particle crushing tests.The void ratio-vertical stress curve could be predicted by an exponential function.The particle size distribution curve increased obviously with applied stresses less than 16 MPa and gradually reached the ultimate fractal grading.The relative breakage index became constant with stress up to 64 MPa and was obtained from the ultimate grading at the fractal dimension(a?2:7).A hyperbolical function was also found useful for describing the relationship between the relative breakage index and input work during one-dimensional compression tests.

Modeling the effect of wetting on the mechanical behavior of crushable granular materials

It is well known that the compressibility of crushable granular materials increases with the moisture content,due to the decrease of particle strength in a humid environment.An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work.But how the material humidity can affect this relationship is not clear,and experimental evidence is quite scarce.Based on compression tests on dry and saturated crushable sand recently reported by the present authors,a new non-linear relationship is proposed between the amount of particle breakage and the plastic work.The expression contains two parameters:(1)a material constant dependent on the grain characteristics and(2)a constant depending on the wetting condition(in this study,dry or saturated).A key finding is that the relationship does not depend on the stress path and,for a given wetting condition,only one set of parameters is necessary to reproduce the results of isotropic,oedometric,and triaxial compression tests.The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression.The breakage ratio is introduced into the expression of the elastic stiffness,the critical state line and the hardening compression pressure.Incremental stress-strain computations with the model allow the plastic work to be calculated and,therefore,the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations.Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained.