Displacement Dependent Stiffness And Damping Constants Of Pile Groups

Equivalent spring constants for analysis of footings is a function of Young's modulus of pile material (Ep), shear modulus of soil (Gs), and geometry of the footing and/or piles. Shear modulus is strongly strain dependent in soils. Therefore, the spring constants are strain dependent, which is acceptable to the Geotechnical engineers. However, structural engineers prefer to use spring constants as a function of displacement, rather than strain. In order to develop these relationships, appropriate relationships between strain and displacement are needed. Also, modulus degradation with strain needs be built into these relationships. Description of spring constants kx , ky, and kz in x, y, and z direction and k?, k?, k?, about x, y, and z directions are relatively simple. However, description of kxø and ky?, the cross-coupling spring constants depend on 2 - components of displacement and rotation. Thus, there are 8 spring constants and likewise there are 8 damping constants. Approximate strain-displacement relationships on which displacement dependant k's and c's are based are presented with appropriate equations, and a numerical example is included illustrating k's and c's as functions of displacement.