Back Issues 11-20

GOVERNING EQUATIONS AND COMPLETE MATHEMATICAL PROOFS FOR COULOMB’S THEORY OF EARTH PRESSURE

Tse-Shan Hsu

President, Institute of Mitigation for Earthquake Shear Banding Disasters

Professor, Department of Civil Engineering, Feng-Chia University, Taiwan, R.O.C.

This email address is being protected from spambots. You need JavaScript enabled to view it.

Yi-Ju Chen

Ph.D. Student, Ph.D. Program of Mechanical and Aeronautical Engineering, 

Feng-Chia University, Taiwan, R.O.C.

Zong-Lin Wu   Tzu-Che Chao   Ding-Yu Wei

Directors, Institute of Mitigation for Earthquake Shear Banding Disasters

Taiwan, R.O.C.

Jiann-Cherng Yang   Yi-Min Huang

Associate and Assistant Professors, Feng-Chia University, Respectively,

Taiwan, R.O.C.

Abstract

Coulomb’s theory of earth pressure, proposed in 1776, has been widely used by engineers to design retaining walls for 245 years. However, because the earth pressure functions are very complicated, there is still no study providing governing equations and complete mathematical proofs. Therefore, this paper provides governing equations for solving Coulomb’s theory of earth pressure using the first-order differential equations of Coulomb’s earth pressure functions. Furthermore, the second-order differential equations of Coulomb’s earth pressure functions are used to mathematically prove that the active earth pressure is the maximum value and the passive earth pressure is the minimum value. This not only completes the mathematical proofs for Coulomb’s theory of earth pressures, but also enhances the physical understanding and mathematical basis of the calculation of Coulomb’s earth pressures.

Keywords: Coulomb’s theory, active and passive earth pressures, governing equation.

Attachments:

1146 Final.pdf

[ ]

800 kB