Lie group properties and solutions of the soil consolidation equations

• Main Authors: Ping-Rong Hong, 洪炳榮
• Other Authors: Mr.Lie,Hin-Chi
• Format: Others
• Language: zh-TW
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/73945341664339000789

碩士 === 國立中央大學 === 土木工程研究所 === 82 === The purpose of this research is to apply Lie group theory to get symmetries and solutions of consolidation equations. The two different consolidation equations we study are nonlinear partial differential equations proposed respectively by Raymond in 1966 and by Gibson in 1967. Both differential equations describe the one dimensional consolidation pheomenon of homogenous saturated soil. Symmetry groups and a number of invariant solutions of both consoldation equations are obtained. Knowing the forms of the invariant solutions can help us to understand the important properties of the solutions such as self-similarities and singularities. Ordinary differential equations can be reduced from partial differential equations for the invariant solutions. Comparing symmetry groups of the consolidation equation for a thick soil layer and those for a thin soil layer shows that there is a great difference between the Raymond equation and the Gibson equation. The difference is that the Raymond equation admits scaling groups in both the case of thick soil layer and the case of thin soil laye while the Gibson equation does not admit any scaling group in the case of thick soil layer. The physical meaning of this fact is that if consolidation pheomena of soil layers in different layer sizes can not be related to each other by simple space- time scaling if the consolidation behavior obeys the Gibson equation.