Abstract
Based on the Hertzian granular contact mechanics model, the paper built up a Macroscopic Young’s Elastic Modulus of particle/granular packing rock layers, and built up a ties to connecting Young’s Elastic Modulus of sand particle in Meso and the Macroscopic Young’s Modulus of granular packing rock layers. The Macroscopic Young’s Modulus of granular packing rock layers is far less than the Young’s Modulus of sand particle. The Macroscopic Young’s Modulus of granular packing rock layers is proportioned to the powers of 1/3 of the vertical contact force of sand particles. The Macroscopic Young’s Modulus is inversely proportional to particle diameter. The paper calculated the vertical contact force of five types aligning mode of the particles. When equal stress, the increased of the coordination number lead to the decrease of the contact force fn, this lead to the coordination number is an inverse proportion to Macroscopic Young’s Modulus. But the larger coordination number change only means very little Macroscopic Young’s Modulus change.
Highlights
Young’s Modulus of rocks or soil is the important parameters in calculating seismic velocity, liquefaction of sand-soil, seismic exploration and hydrocarbon prediction, earthquake engineering, tunnel excavating, deformation of sand body, dynamic diagenesis of sandstone
The increased of the coordination number lead to the decrease of the contact force fn, this lead to the coordination number is an inverse proportion to Macroscopic Young’s Modulus
Scholars always study the macroscopic structure of porous media used the relation of wave velocity and density of material experientially
Summary
Young’s Modulus of rocks or soil is the important parameters in calculating seismic velocity, liquefaction of sand-soil, seismic exploration and hydrocarbon prediction, earthquake engineering, tunnel excavating, deformation of sand body, dynamic diagenesis of sandstone. (1992) [3] set up the relationship between fabric tensor and contact density distribution functions, and the relationship between fabric tensor and stress tensor are analyzed Those model on stress tensor and arrangements of particle is too fussy to used on geologic and macroscopic mechanics of rocks and soils. The paper effort to set up a ties model between the macroscopic elastic parameter of granular packing rock layers and the elastic parameter of those sand particles. Effort to make out a series of simple theoretical logics and catch hold of those dominant factors of those logics Maybe this can help those investigators and engineers to qualitatively and semi-quantitatively grasp the macroscopic elastic parameter of unconsolidated sandstone
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