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One-dimensional stress wave theory is widely used to analyze quantitatively the reflections in low-strain integrity testing of piles. However, a point or disk loading produces body and Rayleigh waves near the pile top. The multireflections of these waves from the lateral surface of a pile are present in the wave field near the pile top. Effects of three-dimensional waves on the near field responses are obvious. These effects can be interpreted erroneously by an inexperienced user as 'noises' or 'pile anomalies.' To investigate wave propagation in the longitudinal direction, the behavior of the waves in the far field (some distance below the pile top) is studied by theoretical analysis of the longitudinal modes in free cylinders and numerical simulations. The wave pattern at the pile top is analyzed based on the response of an elastic half-space to a harmonic disk loading. The results show that when the ratio of the characteristic length of an impact pulse to the cylinder radius is large enough, the components of Rayleigh waves in the wave field at the pile top are diminished; the waves in the far field behave approximately as plane waves; the responses at positions between 1/2R and 3/4R from the pile axis are less affected by the multireflections. The results from numerical simulations support the practical recommendation to use a ratio of characteristic wavelength to pile radius larger than four. Under this condition, the reflections from the far field (say deeper than two pile diameters) can be analyzed from the responses at receiver positions about 0.6R from the pile axis based on one-dimensional stress wave theory. DOI: 10.1061/(ASCE)GT.1943-5606.0000272 CE Database subject headings: Rayleigh waves; Dispersion; Piles; Tests; Wave propagation. Author keywords: Longitudinal mode; Rayleigh waves; Dispersion; Low-strain integrity testing of piles; Pulse echo method.

ABSTRACT In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half-spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back-analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non-planar. The geometric discrepancy could result in Rayleigh waves manifesting distance-dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc-like surface sources using the thin-layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms. [ABSTRACT FROM AUTHOR]