Re: impact-echo : Recently I read a new paper by Sansalone, Lin and Streett
: in the ACI Materials Journal Nov-Dec 97 where 'a procedure
: for determining p-wave speed in concrete ...' is decribed.
: At one point, a difference between the p-wave speed, and
: a so-called "impact-echo p-wave speed" of about 4 % is
: mentioned and a recent paper of Lin and Sansalone is
: cited for explanation. Since this paper is not available,
: I re-read a paper of 86 by Carino, Sansalone and Hsu (flaw
: detection in concrete ...) where they find a difference
: of about 10 % between the two velocities, but cannot
: find an explanation for that.
: My question is, what is the reason for this phenomenon,
: what is the physical effect standing behind this differnce?
: Who can give an explanation?
Mr. Weiler has asked about confusing statements in the impact-echo
literature about the 4% difference between the true P-wave speed in
concrete and what is sometimes called the 'apparent P-wave speed in a plate'.
If one considers multiple P-wave reflections in a simple plate, the
expected relationship between the wave speed Cp, the thickness T and the
frequency f is: f = Cp/(2 T). This is a simple statement that the period
of wave reflections is twice the thickness divided by the wave speed. In
the early work on impact-echo it was assumed that this relationship
explains the impact-echo response of a plate structure. However, in
studies of the time-domain waveforms from early impact-echo tests, it was
observed that successive P-wave arrivals were slightly delayed, and as a
result the frequency of multiple reflections is slightly lower than that
calculated by the equation above.
It was not until after extensive computer simulations of stress wave
propagation and reflection in a variety of geometric shapes were carried
that the developers of impact-echo realized that multiple P-wave
reflections excite certain transient modes of vibration, and that the
correct relation between the wave speed, the frequency of the first mode,
and a characteristic dimension A is f = bCp/(2A), where b is a "shape
factor". For plates the mode of vibration is a thickness mode, the
characteristic dimension is the thickness T, and the shape factor b = 0.96.
The frequency of the first mode of thickness vibration in a plate is 4%
lower than the frequency of multiple P-wave reflections predicted by the
simple equation f = Cp/(2T).
The values of b for different geometric shapes have been calculated from
computer simulations using a 3-D, dynamic, finite element simulation
method, and they have been verified by repeated tests both in the
laboratory and in the field. (The finite element codes used in the
simulations are the DYNA3D and related programs developed at the Lawrence
Livermore Laboratories in California by G. Goudreau, J. Hallquist and
others.) For more information see references [39, 40, 41] in
See also Chapters 4, 21 and 22 of the book by Sansalone and Streett:
If one measures the P-wave speed using two transducers on the surface of a
concrete structure, the true P-wave speed, Cp, is obtained. If one observes
the thickness frequency of a solid plate of thickness T, and calculates the
wave speed from the simple equation Cp = 2fT, the result is what we now
call "the apparent P-wave speed in a plate". It is equal to 0.96 times the
true P-wave speed.
In impact-echo tests on beams and columns, the same equation f = bCp/(2A)
applies. In this case A is a characteristic cross-sectional dimension, and
the value of b depends on the cross-sectional shape. For circular columns,
for example, A is the diameter and b = 0.92. For a square column, A is the
length of the square, and b = 0.87. For a rectangular column, A is the
dimension in the direction of the impact, and the value of b is a function
of the aspect ratioof the cross section, and its value ranges from about
0.75 to 0.96. The latter value is the limiting value as the shape
approaches that of a plate (lateral dimensions at least 5 times the
There is indeed some confusion on this matter in the published papers on
impact-echo, because it was not fully understood until after the early
papers were published. In addition to the explanation in the book on
impact-echo, an explanation can be found in a recent paper by M. J.
Sansalone, entitled, 'Impact-Echo: The Complete Story', in the
November/December 1997 issue of the ACI Structural Journal, pp. 777-786.
Prof./Dr. William B. Streett
12 February 1998