Some Aspects Of The Wave Behavior In Piles

Guideci wave propagatjon in an infinitely long cylindrical pile embedded in soil is developed from dynamic equations ot?elasticity. Considering axisymmetric motion in the pile, the frequency equation for longitudinal modes is derived herein. The frequency equation represents a transcendental relationship between the non梔imensional frequency, Q, and non梔imensional wave number, Ja .The solution of the frequency equation is satisfied by an infinite number of modes that form branches in Q梸a plane. The first five branches of the longitudinal family of modes in a concrete pile embedded in sottjloose and hard dense soils were numerically evaluated respectively. Sensitivity analyses show that the real branches in the Q梸tplane are essentially independent of the shear modulus and density of the surrounding soil, and correspond closely to the branches of longitudinal modes in a free梥tanding?pile. However, the imaginary components of the branches in the Q梸~ plane are higher for soils with increased shear modulus and density. The attenuation of the longitudinal guided wave modes is represented directly by the imaginary part of the wave number, in nepers per length. The phase and group velocities vary with the frequency or wave number, contrary to the assumptions made in the theory of the one梔imensional approach. The power and displacement profiles of a given guided wave mode generally become more oscillatory as the order o~ the branch increases and as the frequency increases. For non梔imensional frequencies less than 2, the L (0, 1) modes display the lowest attenuation and are easily induced in a pile, as evidenced by the popularity of the impulse response test in practice. Modes on the L(0,2)hranch have the least attenuation compared to all other modes for non梔imensional frequencies above 12, and their relative simple mode shapes suggest that they are likely to be induced in practice.