US 12,385,823 B2 · Evaluation method for corrosion damage evolution of underwater concrete structures

Abstract

An evaluation method for corrosion damage evolution of underwater concrete structures includes performing the time reversal test on the concrete beam specimen placed in the water, performing the uniaxial compression test on the concrete cube specimens; immersing the concrete beam specimen and the concrete cube specimens in a hydrochloric acid solution, and performing the time reversal test on the concrete beam specimen on the 10th, 20th and 30th days respectively. At the same time, a concrete cube specimen is taken out to perform the uniaxial compression test on the 10th, 20th and 30th days respectively; and using the above calculation results to evaluate the corrosion evolution process thereof without damaging the underwater concrete structure.

An evaluation method for corrosion damage evolution of underwater concrete structures, comprising:

(a) immersing a concrete beam specimen and a plurality of concrete cube specimens in water to obtain a first immersed concrete beam specimen and a plurality of first immersed concrete cube specimens;
(b) performing a time reversal test on the first immersed concrete beam specimen in the water to obtain a damage index DI0 of a concrete in a water-immersed state, performing a uniaxial compression test on the plurality of first immersed concrete cube specimens to obtain a compressive strength Fcp0 and an elastic modulus Ec0 of the concrete in the water-immersed state;
(c) immersing the first immersed concrete beam specimen and the plurality of first immersed concrete cube specimens in a hydrochloric acid solution to mimic a long-term corrosion damage of the concrete in the water-immersed state to obtain a second immersed concrete beam specimen and a plurality of second immersed concrete cube specimens, performing the time reversal test on the second immersed concrete beam specimen in the hydrochloric acid solution on 10th, 20th, and 30th days respectively to obtain a damage index DI′ of a concrete in a corrosion state, and at the same time, performing the uniaxial compression test on the plurality of second immersed concrete cube specimens on 10th, 20th, and 30th days respectively to obtain a compressive strength Fcp′ and an elastic modulus Ec′ of the concrete in the corrosion state;
(d) calculating a corrosion index CI with formula (1), calculating a concrete compressive strength loss rate LRF with formula (2), calculating a concrete elastic modulus loss rate LRE with formula (3), and
CI
=
DI
′
-
DI
0
(
1
)
LR
F
=
F
c
⁢
p
0
-
F
c
⁢
p
′
F
cp
0
(
2
)
LR
E
=
E
c
0
-
E
c
′
E
c
0
(
3
)
(e) calculating an absolute error δCF between the corrosion index and the concrete compressive strength loss rate with formula (4), and calculating the absolute error δCE between the corrosion index and the concrete elastic modulus loss rate with formula (5) to realize an evaluation of the corrosion damage evolution of the underwater concrete structures;
δCF=CI−LRF (4)
δCE=CI−LRE (5)
wherein a method for obtaining a damage index of a concrete by performing the time reversal test on the concrete beam specimen comprises:
(21) determining an excitation signal VA(t);
(22) inputting the excitation signal VA(t) to a first sensor at position A on the concrete beam specimen, an expression of response signals VB received by a second sensor at position B in a frequency domain is formula (6),
VB(r,ω)=kA(ω)kB(ω)G(r,ω)VA(ω) (6)
an expression of the response signals VB in a time domain is formula (7),
V
B
(
t
)
=
1
2
⁢
π
⁢
∫
-
∞
+
∞
V
B
(
r
,
ω
)
⁢
e
i
⁢
ω
⁢
t
⁢
d
⁢
ω
(
7
)
in the formula, r is a distance from the position A to the position B, kA is an electromechanical coupling coefficient of the first sensor at the position A, kB is an electromechanical coupling coefficient of the second sensor at the position B, and G(r,ω) is a transfer function from the first sensor at the position A to the second sensor at the position B;
VB(t) is the response signals received by the sensor at the position B in the time domain;
(23) applying a rectangular window, as shown in formula (8), to a response signal VB to remove a crosstalk, and then performing a time reversal to obtain the reversed signal {circumflex over (V)}B,
w
⁡
(
t
)
=
{
1
,
0
≤
t
≤
T
0
,
else
(
8
)
an expression of a reversed signal {circumflex over (V)}B in the frequency domain is formula (9),
{circumflex over (V)}B(r,ω)=kA*(ω)kB*(ω)G*(r,ω)VA*(ω)ejωT (9)
an expression of a reversed signal {circumflex over (V)}B in the time domain is formula (10),
V
B
(
-
t
)
=
1
2
⁢
π
⁢
∫
-
∞
+
∞
V
B
*
(
r
,
ω
)
⁢
e
i
⁢
ω
⁢
T
⁢
e
i
⁢
ω
⁢
t
⁢
d
⁢
ω
(
10
)
in the formulas, VB* is a phase conjugation of VB, * is a complex conjugation operator, T is a sampling duration;
(24) inputting the reversed signal {circumflex over (V)}B to the second sensor at the position B, then the first sensor at the position A receives a focused signal {circumflex over (V)}A, an expression of the focused signal {circumflex over (V)}A in the frequency domain is formula (11), and
{circumflex over (V)}A(r,ω)=kA(ω)kA*(ω)kB(ω)kB*(ω)G(r,ω)G*(r,ω)VA*(ω)eiωT (11)
an expression of the focused signal {circumflex over (V)}A in the time domain is formula (12);
V
^
A
(
t
)
=
1
2
⁢
π
⁢
∫
-
∞
+
∞
V
^
A
(
r
,
ω
)
⁢
e
i
⁢
ω
⁢
T
⁢
d
⁢
ω
=
1
2
⁢
π
⁢
∫
-
∞
+
∞
k
A
(
ω
)
⁢
k
A
*
(
ω
)
⁢
k
B
(
ω
)
⁢
k
B
*
(
12
)
(
ω
)
⁢
G
⁡
(
r
,
ω
)
⁢
G
*
(
r
,
ω
)
⁢
V
A
*
(
ω
)
⁢
e
i
⁢
ω
⁢
T
⁢
e
i
⁢
ω
⁢
t
⁢
d
⁢
ω
(25) performing a time reversal reconstruction on a focused signal {circumflex over (V)}A to obtain a reconstructed signal {tilde over (V)}A, and an expression of the reconstructed signal {tilde over (V)}A in the frequency domain is formula (13),
{tilde over (V)}A(r,ω)={circumflex over (V)}A*(r,ω)eiωT (13)
in the formula, {circumflex over (V)}A* is a phase conjugation of {circumflex over (V)}A, and * is the complex conjugation operator;
and
an expression of a reconstructed signal {tilde over (V)}A in the time domain is formula (14);
V
~
A
(
t
)
=
1
2
⁢
π
⁢
∫
-
∞
+
∞
V
^
A
*
(
r
,
ω
)
⁢
e
i
⁢
ω
⁢
T
⁢
e
i
⁢
ω
⁢
t
⁢
d
⁢
ω
=
1
2
⁢
π
⁢
∫
-
∞
+
∞
k
A
(
ω
)
⁢
k
B
(
ω
)
⁢
k
A
*
(
ω
)
⁢
k
B
*
(
14
)
(
ω
)
⁢
G
⁡
(
r
,
ω
)
⁢
G
*
(
r
,
ω
)
⁢
V
A
(
ω
)
⁢
e
i
⁢
ω
⁢
T
⁢
d
⁢
ω
(26) performing a normalization on the excitation signal VA(t) and the reconstructed signal {tilde over (V)}A with formula (15),
NA(t)=VA(t)/max(VA(t)) (15)
in the formulas, NA is a normalized excitation signal, and ÑA is a normalized reconstructed signal;
and
(27) substituting the normalized excitation signal NA(t) and the normalized reconstructed signal ÑA(t) into formula (16) to calculate a damage index DI;
DI
=
1
-
[
∫
t
0
t
1
N
A
(
t
)
⁢
N
~
A
(
t
)
⁢
d
⁢
t
]
2
/
∫
t
0
t
1
[
N
A
(
t
)
]
2
⁢
d
⁢
t
⁢
∫
t
0
t
1
[
N
~
A
(
t
)
]
2
⁢
dt
×
100
⁢
%
(
16
)
in the formula, t0 and t1 are a start time and an end time of a signal comparison interval separately;
wherein a method for determining the excitation signal VA(t) comprises:
an expression of a 5-cycle sine function modulated by a Hanning window is formula (17),
x
⁡
(
t
)
=
sin
⁢
(
2
⁢
π
⁢
f
c
⁢
t
)
[
1
-
cos
⁢
2
⁢
π
⁢
f
c
t
5
]
(
17
)
in the formula, fc is a central frequency of modulated signals;
a method for determining the central frequency fc of the modulated signals is as follows:
modulating modulated signals with different central frequencies from 0-10 MHz at an interval of 10 kHz, inputting the modulated signals with different central frequencies to the first sensor at the position A on the concrete beam specimen separately, response signals are received by the second sensor at the position B, comparing the response signals and selecting a modulated signal with a largest amplitude of the response signals as the excitation signal VA(t).

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Evaluation method for corrosion damage evolution of underwater concrete structures

Life of this patent

Evaluation method for corrosion damage evolution of underwater concrete structures

Life of this patent

Abstract

Claims3