Macroscopic Young’s Elastic Modulus Model of Particle Packing Rock Layers

Author(s)
Cheng-Yao Guan^{*},
Jia-Fu Qi,
Nan-Sheng Qiu,
Guo-Chun Zhao,
Qiao Yang,
Xiang-Dong Bai,
Chao Wang

Affiliation(s)

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China.

The College of Geosciences and Resources, China University of Geosciences, Beijing, China.

Institute of Disaster Prevention, Sanhe, China.

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China.

The College of Geosciences and Resources, China University of Geosciences, Beijing, China.

Institute of Disaster Prevention, Sanhe, China.

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.

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.

Cite this paper

C. Guan, J. Qi, N. Qiu, G. Zhao, Q. Yang, X. Bai and C. Wang, "Macroscopic Young’s Elastic Modulus Model of Particle Packing Rock Layers,"*Open Journal of Geology*, Vol. 2 No. 3, 2012, pp. 198-202. doi: 10.4236/ojg.2012.23020.

C. Guan, J. Qi, N. Qiu, G. Zhao, Q. Yang, X. Bai and C. Wang, "Macroscopic Young’s Elastic Modulus Model of Particle Packing Rock Layers,"

References

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[2] T.-D. Xia, Y. Liu, M. Wu, et al., “Shear Wave Velocity in Deep Buried Sand Based on Spheres-Contact Theory,” Journal of Harbin Institute of Technology, Vol. 43, 2011, pp. 99-103.

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[9] J.-N. Tian and H.-L. Shi, “Comparison and Experimental Study of Dynamic Elastic Modulus and Tatic Modulus,” Journal of Hydro Electric Power, Vol. 4, 1988, pp. 21-27.

[10] A. S. Elnashai and L. D. Sarno, “Fundamentals of Earthquake Engineering,” Wiley, Hoboken, 2008, pp. 28-29.

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[1] X. Liu, “Elastic Parameters and Velocity Calculation in Multi-Phase Materials,” Ph.D. Thesis, Institute of Geophysics, Beijing, 2002, pp. 1-78.

[2] T.-D. Xia, Y. Liu, M. Wu, et al., “Shear Wave Velocity in Deep Buried Sand Based on Spheres-Contact Theory,” Journal of Harbin Institute of Technology, Vol. 43, 2011, pp. 99-103.

[3] X.-X. Zhong and J.-X. Yuan, “Microfabrics and Constitutive Relations of Granular Materials,” Chinese Journal of Geotechnical Engineering, Vol. 14, 1992, pp. 39-48.

[4] K. L. Johnson, “Contact Mechanics,” Cambridge University Press, Cambridge, 1985, pp. 91-104.

[5] M. Oda and K. Iwashita, “Mechanics of Granular of Granular Materials: An Introduction,” A. A. Balkema, Rotterdam, 1999, pp. 207-209.

[6] Q.-C. Sun, M.-Y. Hou, F. Jin, et al., “The Physical and Mechanical of Granular Materials,” Science Press, Beijing, 2011, pp. 191-193.

[7] Y. Liu, “Research on Sand Shear Wave Velocity Based on Particle Contact Model,” Ph.D. Thesis, Zhejiang University, Hangzhou, 2010, pp. 1-127.

[8] F. Zeng, et al., “Particle Technology of Mineral Processing,” China University of Mining Press, Xuzhou, 2001, pp. 92-93.

[9] J.-N. Tian and H.-L. Shi, “Comparison and Experimental Study of Dynamic Elastic Modulus and Tatic Modulus,” Journal of Hydro Electric Power, Vol. 4, 1988, pp. 21-27.

[10] A. S. Elnashai and L. D. Sarno, “Fundamentals of Earthquake Engineering,” Wiley, Hoboken, 2008, pp. 28-29.

[11] An-Ou, “Tectonic Stress Field,” Earthquake Publishing House, Beijing, 1992, pp. 1-60.