Modeling The Influence Of The Particle Size Distribution On The Critical State Mechanical Behavior Of Granular Material

Grading changing in geotechnical engineering will significantly influence the bearing capacity of granular material at critical state, which probably leads to large deformation or even collapsibility of the related structures.Combined laboratory test and numerical test, this study aims to investigate the effects of initial grading on the mechanical response of granular materials. A relationship between grading state of granular material and its critical state mechanical behavior is established, and embedded into an elasto-plasticity constitutive model to simulate the mechanical problem due to grading changing.(1) Experimental investigations on glass ball and Hostun sand were carried out to study grading dependent stress-strain response and obtain the relationship between critical state of granular and its grading. Test results show that, with a same initial relative density, the undrained shear strength and phase transformation shear stress ratio of the material decrease as the coefficient of uniformity increases and tend to be stable as Cu surpasses 10. Analysis of the second-order work demonstrate a significant influence of the grading on the instability of granular materials: increasing the coefficient of uniformity heightens the potential of static liquefaction and the materials become more unstable. Nonlinear relationships between critical state parameters and the grading index Cu are established. With grading broadening, the critical state line shifts down in the e-p’ plane as well as its slope reduce, and both tend to be stable as Cu surpasses 10. In the q-p’ plane, the critical state line becomes a straight line, regardless of gradings.(2) Numerical experiments extend the stress-strain response study of laboratory tests with more stress paths. The results revealed that with the same initial loading conditions, granular materials with a wider particle distribution display more contractive behavior and also strain hardening upon shearing. With the same initial condition, the undrained shear strength decreases as grading broadens. Test results further confirm the nonlinear relationship between critical state parameters and the grading index Cu,regardless of drain condition and shear modes(compression and extension). Critical state line in the e-p’ plane for a material is unique and shifts down as grading broadening; in the q-p’ plane it becomes a line with its slope differs from shear modes, regardless of grading.(3) Micro-mechanical analysis further elaborates the internal mechanism of the shifting down of critical state line in the e-p’ plane and its linear feature in the q-p’ plane. From the evolution of the mechanical coordination number, it is indicated that granular material has a higher instability under undrained shear condition than under drained shear condition. At critical state, the relationship between the average coordination number and mean effective stress is unique and shifts down as grading broadens. By stress–fabric–contact force analysis, it is concluded that the contribution of each micro fabric anisotropy variables to the micro stress ratio is the same for granular material regardless of gradings and confining pressure, which explains the macro finding that the critical state line in the q-p’ plane is unique and grading independent.(4) Constitutive modelling study embeds the grading dependent critical state mechanical behavior, to analyze the mechanical behavior of granular material with any grading. The nonlinear relationship of critical state line and grading index is implanted into an elasto-plasticity constitutive model. The model can predict drained and undrained triaxial tests of granular material with any gradings. By comparison with an existing grading dependent constitutive model, the main reasons for the different predictions between the two models are pointed out as the relation between critical state parameters and the selected grading index used. Numerical tests were performed to find out that the existing grading index(Cu or IG) can not accurately describe the grading dependent mechanical behavior of granular material. Thus a new index including the merits from Cu and IG is introduced to improve the former constitutive model. Test verifications show that the improved constitutive model can well predict the mechanical behavior of granular material with any grading curve.(5) Secondary development of the constitutive model into finite element method program is performed, which is used to study the bearing capacity of footing on the breakable subsoil. The constitutive model is compiled into a UMAT subroutine and applied to Abaqus. Simulation of the bearing capacity of footing are carried out. The results show that particle breakage reduces the bearing capacity of the subsoil; as the initial grading broadens, the breakage decreases as well as the trend of bearing capacity reduction.Over all, this study provides a reference for the constitutive research and micro-mechanics analysis for sandy soils. Resolving Geotechnical problems caused by the grading change can also benefit from this study.