Research On The Constitutive Model Of Crushable Granular Materials Considering The Effect Of Particle Shape

In the construction of dams in water conservancy projects,earth-rock dams with granular materials as the main body of the project are one of the main forms.Therefore,understanding the mechanical properties of granular materials has become a key point in evaluating the stability of dam engineering.Meanwhile,particle shape and particle breakage have a greater impact on the mechanical properties of granular materials.In this context,it is urgent to carry out research on the deformation and strength characteristics of granular materials on particle shape and particle breakage.In view of this,the particle shape quantification parameterspherical modulus GM is established,then the conventional triaxial compression test(CD)of particle-shaped granular material specimens with different particle shapes is carried out.The influence law of particle shape on deformation and strength characteristics is studied,and the local particle breakage law during deformation process is deeply analyzed.Based on the binary media theory,an elastoplastic constitutive model and strength criterion that can reflect this factor are proposed,and the experimental data is finally reasonably predicted.The main research results are introduced as follows:(1)The experimental rules of particle shape on compression deformation and strength characteristics were studied.Firstly,the quantitative parameter describing particle shapespherical modulus GM and the quantitative parameter describing the shape of granular material aggregates composed of several particles-average spherical modulus GM are established respectively,and the calculation method is given.Secondly,a method for artificially prepared crushable granular materials was developed.The artificially prepared homogeneous and crushable granular materials(Granules and Flakes)were prepared into five different GM(0.777、0.701、0.668、0.625、0.573)granular material samples by adjusting the incorporation ratio of flake particles.Lastly,the triaxial compression tests were carried out under different confining pressures(200、300、400、500、600kPa).In the triaxial shear test,the crushable granular material exhibits the hardening and shrinkage deformation characteristics.With the decrease of the average spherical modulus GM,the nonlinear property of the strength law of the granular material is more obvious;with the increase of GM,the Mohr circle of stress under low confining pressure first increases and then decreases,and it increases gradually under higher stress.Further analysis,the granular material rotates and slides under low confining pressure,butthe granular material does not have time to rotate and slide under high confining pressure,,and particle breakage occurs directly.(2)The local crushing law of particles in the deformation process of granular materials was studied.By sieving the samples before and after the triaxial test,the change of the particle size distribution curve was determined,and the relationship between the particle breakage rate and the particle shape and confining pressure was obtained,and the calculation model of the particle breakage rate was established.At the same time,the q-p’ curves and e-logp’curves of granular materials with different shapes was given,and the critical state of granular materials was analyzed,then a calculation model for the critical void ratio of granular materials was established that considered the particle shape and particle breakage.(3)A binary medium elastoplastic constitutive model that reflects particle breakage was derived.Based on the binary medium theory,the granular material samples that have not been deformed and particles are crushed are regarded as bonded elements,and the aggregate of granular materials reaching the ultimate crushing state is regarded as a frictional elements.The broken of bonded elements is transformed into frictional elements.Meanwhile,in order to improve the calculation accuracy,the concept of friction-like elements is proposed to describe the remodeling specimen after crushing containing a small amount of cement elements,and the weakening coefficient of frictional elements is introduced to eliminate the influence of a small number of bonded elements on the calculation.By giving the volume breakage ratio considering the particle shape and particle crushing,a binary medium constitutive model was derived,and the experimental data was successfully predicted,which indicatied the rationality of the constitutive model.(4)A binary medium strength criterion considering particle shape was established.The strength envelope of the granular material and the remodeled specimen after crushing showed obvious nonlinearity.Based on the binary media model theory,the shear strength component weakening coefficient of the friction element affected by the shape of the particle was introduced,and a criterion for considering the strength of the particle damage and shape binary medium was established.By comparing theoretical predictions and experimental results,the rationality of this strength criterion is demonstrated.