The Solution Of Elasticity Theory With Different Modulus In Tension And Compression And Settlement Calculation Of Piles

Such engineering materials as soil,rock and porcelain,they present different properties in tension and compression. Not only their strengths but also elastic moduli are not equal. These properties are beyond the research of classic theory of elasticity. The errors may be not allowable if theory of elasticity is employed in the problems concerning these materials. The study on theory with different properties in tension and compression is important to engineering practice.Vertical concentrated load acting into semi-infinite elastic body is a basic problem in theory of elasticity. Mindlin's solution is used broadly to solve engineering problems. This paper focuses on the problem of semi-infinite elastic body filled with the material which behaves differently in tension and compression. The contents include:(1) The solution of elasticity theory for the material incapable in tension is established by introducing Heaviside function;(2) The solution of elasticity theory with different modulus in tension and compression is established based on the solution of elasticity theory for the material incapable in tension and Mindlin's solution;(3) The solution of elasticity theory with different modulus in tension and compression is employed to analyze the stress of pile foundation;(4) The solution of elasticity theory with different modulus in tension and compression is employed to analyze the settlement of pile foundation.The applications in analysis of pile foundation show that the method based on the solution of elasticity theory with different modulus in tension and compression gives reasonable results and the method can explain the questions of some methods in existence logically. It can be concluded that difference between tensile modulus and compressive modulus is an important property of soil and the solution of elasticity theory with different modulus in tension and compression is necessary and reasonable. The method based on the solution of elasticity theory with different modulus in tension and compression not only solves the problem of settlement calculation of pile foundation,but also can play an important role in other engineering field.