Non-destructive concrete stress evaluation
A system of monitoring diffuse waves over a concrete beam under different loads. Ultrasound transmitters and receivers are placed over the concrete beam to emit sound waves and collect diffuse waves under different loads. The waveform variations are observed to quantify a decorrelation coefficient (DC) indicating global structural changes and crack position. An inversion of the correlations is applied to estimate distribution density at each localized position following the sensitivity kernel and inversion algorithms. Then, three-dimensional imaging comprised of density values at each localized position are generated to indicate number, position, and depth of multiple cracks.
1. A testing system for concrete structures comprising:
a load sensor positionable to measure a load on the concrete structure to distinguish between at least two different load values;
a plurality of transmitters positionable on the structure and configured to independently transmit acoustic excitation waves into the structure;
a plurality of receivers positioned positionable on the structure and configured to receive diffuse waves of the excitation waves from the plurality of transmitters; and
an electronic computer executing a program stored in a non-transitory medium to:
receive the diffuse waves from the plurality of receivers;
calculate a decorrelation coefficient based on the diffuse waves and a wave speed of the diffuse waves for at least two different load values;
calculate a sensitivity kernel based on the diffuse waves; and
apply an inversion algorithm to estimate a distribution density based on the decorrelation coefficient and the sensitivity kernel and indicating a presence of defects within the concrete structure.
2. The system of claim 1 wherein the defects are cracks.
3. The system of claim 1 wherein the electronic computer further executes the program stored in the non-transitory medium to:
receive a plurality of diffuse waves at multiple times at each load value; and
calculate a mean diffuse wave from the plurality of diffuse wave.
4. The system of claim 1 wherein the electronic computer further executes the program stored in the non-transitory medium to:
output an image of the distribution density as a function of beam location.
5. The system of claim 1 wherein the electronic computer further executes the program stored in the non-transitory medium to:
calculate at least one depth of the defects within the beam.
6. The system of claim 1 wherein the excitation waves are transmitted at a frequency between 60 kHz and 400 kHz.
7. The system of claim 6 wherein the excitation waves are transmitted at a frequency between 100 kHz and 200 kHz.
8. The system of claim 7 wherein the excitation waves are transmitted at a frequency of 150 kHz.
9. The system of claim 1 wherein the excitation waves are driven by a voltage ranging between 3 V to 9 V.
10. The system of claim 9 wherein the excitation waves are driven by a voltage centered on 5.7 V.
11. The system of claim 1 wherein the load sensor is a strain gauge.
12. The system of claim 1 wherein the load sensor is a load jack applying a known load.
13. The system of claim 1 wherein the plurality of transmitters are positioned along a horizontal centerline of the beam, the centerline extending along an axis of the beam and centered between a width of the beam.
14. The system of claim 13 wherein the plurality of receivers are positioned along the axis of the beam and flank the centerline of the beam to surround the plurality of the transmitters.
15. The system of claim 14 wherein a second plurality of receivers are positioned on a perpendicular surface to the plurality of receivers.
16. The system of claim 1 wherein the decorrelation coefficient is estimated using nonlinear least-squares or genetic algorithms.
17. The system of claim 16 wherein the decorrelation coefficient is calculated using:
DC
l
(
t
,
ε
,
r
i
,
j
)
=
1
-
∫
0
t
〈
E
l
[
r
i
,
j
,
t
′
(
1
-
ε
)
]
〉
〈
E
l
-
1
[
r
i
,
j
,
t
′
〉
dt
′
∫
0
t
〈
E
l
[
r
i
,
j
,
t
′
(
1
-
ε
)
]
〉
2
dt
′
∫
0
t
〈
E
l
-
1
(
r
i
,
j
,
t
′
)
〉
2
dt
′
where t indicates a wave propagation time, r i , r and r j represent central positions of the associated elementary cells of the beam, l denotes a loading step, E represents a reference diffuse wave, ε is a relative velocity variations between two diffuse waves.
18. The system of claim 1 wherein the sensitivity kernel is calculated using:
K
l
(
r
i
,
r
,
r
j
,
t
)
=
❘
"\[LeftBracketingBar]"
r
i
-
r
❘
"\[RightBracketingBar]"
+
❘
"\[LeftBracketingBar]"
r
j
-
r
❘
"\[RightBracketingBar]"
4
π
D
l
(
r
i
,
j
)
❘
"\[RightBracketingBar]"
r
i
-
r
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
r
j
-
r
❘
"\[RightBracketingBar]"
exp
[
(
r
ij
)
2
-
(
❘
"\[LeftBracketingBar]"
r
i
-
r
❘
"\[RightBracketingBar]"
+
❘
"\[LeftBracketingBar]"
r
j
-
r
❘
"\[RightBracketingBar]"
)
2
4
D
l
(
r
i
,
j
)
t
]
where t indicates a wave propagation time, r i , r and r j represent central positions of the associated elementary cells of the beam, D denotes a diffusion coefficient.