1-D wave propagation techniques in foundation engineering

The guided wave approach to wave propagation in cylindrical concrete piles and drilled shafts to show the limits of conventional interpretations of surface reflection methods. The solutions to the dispersion equation for both longitudinal and flexural wave propagation and their implications are presented. Theoretical results concerning propagation velocity, attenuation, and displacements are presented. The results show that relatively constant propagation velocities of longitudinal waves in sonic echo and impulse response tests are limited to relatively low frequencies as a function of the diameter of a pile or shaft. On the other hand, flexural waves are dispersive at low frequencies and only become constant at relatively high frequencies. Implications of these results are illustrated for deep foundations and bender element tests. Comparisons are made between the geometric attenuation of longitudinal and flexural stress waves in concrete piles and shafts. Additional limitations of surface reflection tests arise from the stiffness of the soil adjacent to the pile, soil stratigraphy, variability in propagation velocity, and the presence of any intervening structure between the impact and the deep foundation element.