the interior of the solid as spherical wavefronts, while
the R-wave radiates outward along the surface of the
solid. The propagation modes of the three types of
stress waves are shown in Figure 1.
Figure 1: Finite element simulation of impact on a plate
(Carino, 2001).
When a stress wave propagates through a material
and encounters an interface with a different material,
a portion of the incident wave is reflected. The
amplitude of this reflected wave is dependent on the
angle of incidence, achieving its maximum at 90°
(normal incidence). Different types of stress waves
can be clearly distinguished from one another,
providing valuable information about the material
properties. For instance, when the S-wave reaches the
boundary at the bottom of the concrete slab, the
reflected P-wave may have already arrived at the
midpoint of the slab, highlighting the differing
velocities of these wave types. As these waves
interact with interfaces that possess varying acoustic
impedances, they undergo complex phenomena such
as reflection, refraction, and diffraction. These
processes are critical for understanding the internal
structure of the material being tested. Once the waves
are captured by sensors, they undergo thorough
analysis using spectrum analysis techniques. This
involves transforming the time-domain signals into
the frequency domain, which allows for the
assessment of the relationship between the received
signals and the quality of the concrete, thereby
achieving the goal of NDE.
2.2 The Principle of IE Method
The principle of the IE method is that a brief
mechanical impact, such as the strike of a small steel
sphere on a concrete surface, generates low-
frequency stress waves that travel through the
structure and reflect off internal voids and external
boundaries. The transducer near the impact point
captures surface displacements from reflected waves.
The recorded time-domain signals are transformed
into the frequency domain to generate amplitude
versus frequency spectra. When stress waves interact
with the impact surface, voids, and external surfaces,
they cause multiple reflections that result in transient
resonances detectable in these spectra. These
resonances are used to assess the structural integrity
or locate voids within the structure. The principle of
the IE method is illustrated (see Figure 2).
The IE method is capable of detecting voids in
grouted prestressed ducts in various under a majority
of circumstances. However, its performance is
contingent upon several critical factors, including the
geometric configuration of the structure, the
dimensions and morphology of the voids, and the
positioning and arrangement of the prestressed ducts.
Furthermore, external environmental conditions, such
as temperature fluctuations and humidity levels, can
significantly influence the propagation characteristics
of the stress waves and the accuracy of detection
(Losanno et al., 2024; Dethof and Kessler, 2024;
Tang, 2021).
Figure 2: Principle diagram of IE method.
Similar to other defect types, voids within
prestressed ducts may be positioned too deep in a
structure to be detected. The IE signals recorded from
intact concrete, completely grouted ducts, and
partially grouted ducts will exhibit distinct patterns
(JGJ/T 411-2017) (see Figure 3).
2.2.1 Normal Concrete
The principle is similar to that employed in the
Impact-Echo method for detecting the thickness of
concrete slabs. The tests produce distinctive
waveforms and spectra, in which the prominent
characteristics—especially the quantity and
distribution of peaks—are clearly identifiable, as
illustrated in Figure 3 (a). The relationship among the
frequency peak (F
T
), the compression wave velocity
(V
P
) and the echo depth (T) is expressed in the
following equation:
/2
Tsp
FVT
α
=⋅
(1)