study of reinforced concrete corrosion using impedance...
TRANSCRIPT
To develop a new non-destructive method that uses a multielectrode electrical resistivity array to measure the complex impedance along the surface of a concrete structure in order to determine the position of the reinforcing bars and their corrosion state
Objective
Challenges 1) It should be able to locate the reinforcing bar, and be able to localize the measurement to identify the location of a bar undergoing corrosion .
2) It must make the measurement from the surface of concrete
3) It must measure the electrical resistivity of the concrete itself.
4) It must measure the properties of the interface.
5) It must be simple to use and require a minimum of data processing.
Rebars were located and their surface identified
1e-03 1e-02 1e-01 1e+00 1e+01 1e+02 1e+03-5
0
5
10
15
20Rebar No.1, As recieved No.2, Clean No.3, Painted No.4, Gold-coated
Frequency(Hz)
Results (2)
1e-03 1e-02 1e-01 1e+00 1e+01 1e+02 1e+03 1e+040
10
20
30
Frequency(Hz)
Specimen A2Pseudosection location ρ2,1
Free corrosion 0.05 µA/cm2 1.0 µA/cm2 5.0 µA/cm2 10 µA/cm2
Results
10 20 30 40 50 60 700
5
10
15
20
25
Real (Ω.m)
Free corrosion 0.05 µA/cm2 1.0 µA/cm2 5.0 µA/cm2 10 µA/cm2
0.01Hz
0.1Hz
Looks good but life is never that easy...
… to become quantitative needs to solve the inverse problem
Model
y
x
y
Rebar, ρ0
Concrete,ρ1
Interface,zinterface
Input I I
xz
z
Plane yz for x = 0 Plane xy for z = 0
Prospecting of V
Drθ
a
2r0
Fundamental equations
1r∂∂r(∂V(r)
∂r) + 1r2
∂2V(r)∂θ2
+∂ 2V(r)∂z2
=I4π
ρ1δ(r − rs )
V0(r,z) =I2π2
Am(u)Im (ur)cos(uz)du0
∞
∫[ ]m= 0
∞
∑ cos(m(θ − θ0 ))
V1 (r,z) = Vp(r,z) + I2π2
Bm (u)Km (ur)cos(uz)du0
∞
∫[ ]m= 0
∞
∑ cos(m(θ − θ0 ))
Poisson equation:
Solutions in the concrete (V1) and in the rebar (V0) are:
Coefficients
Bm (u) =
σ0
σ 1
2 − δ 0m( )Km (urs )Im (ur0 )[ ] u × Im−1(ur0 ) −m × Im(ur0 )
r0
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
Im(ur0 )+ Zinterfaceσ 1 (uIm−1(ur0 ) −m × Im(ur0 )
r0
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
− 2 − δ 0m( )Km (urs ) uIm−1 (ur0 ) −m × Im(ur0 )
r⎡ ⎣ ⎢
⎤ ⎦ ⎥ uKm− 1(ur0 ) −
mKm(ur0 )r0
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
uKm− 1(ur0 ) −mKm(ur0 )
r0
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ −
σ0
σ1
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ Km(ur0 ) u × Im− 1(ur0 ) −
m × Im (ur0 )r
⎡ ⎣ ⎢
⎤ ⎦ ⎥
Im(ur0 )+ Zinterfaceσ1 (uIm−1(ur0 ) −m × Im(ur0 )
r0
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Am(u) =2 − δ 0m( )Km (urs )Im (ur0 ) + Bm (u)Km(ur0 )
Im (ur0 ) + Zinterfaceσ1 (uIm− 1(ur0 )−m × Im (ur0 )
r0
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Yes, it does get more complicated than this because we need to solve for the half-space (please see paper for details)
Once model is done we can run simulations
Rp
ReCd
0 5 10 15 20 250
5
10
15
Real (Ω.m2)
0.0398 Hz
0.4 Hz
Interface impedance simulated by
the simple electrical circuit
Re=0.0005 Ω.m2
Cd=0.15F/m2
Rp=2.5 Ω.m2
Rp=25 Ω.m2
1. Geometry effect
0 1 2 3 4 5 6 740
50
60
70
80
90
100
Electrode distance na / the concrete cover D (na/D)
Concrete cover D / rebar radius r0 D/r0 =3 D/r0 =2 D/r0 =1
r0=0.0127 m (1/2 in.)ρ1 =100 Ω.m (concrete)ρ0=0.01 Ω.m (rebar)
Electrode array: Wenner
2. Apparent resistivity response with corrosion rate
10 15 20 25 30 35 40 45 50 550
5
10
15
20
Real (Ω.m)
Concrete, rebar, and geometric properties
ρconcrete =50 Ω.m ρrebar =10- 6 Ω.m
D=0.0254 m (1 in.)
r0=0.00635(1/4 in.)
Rp=2.5 Ω.m2
Rp=25 Ω.m2
1 Hz
1.584 Hz
0 5 10 15 20 250
5
10
15
Real (Ω.m2)
0.0398 Hz
0.4 Hz
Interface impedance simulated by
the simple electrical circuit
Re=0.0005 Ω.m2
Cd=0.15F/m2
Rp=2.5 Ω.m2
Rp=25 Ω.m2
0.04
0.4
1 Hz
1.6 Hz
3. Geometry effect on corrosion measurement
1e-04 1e-03 1e-02 1e-01 1e+00 1e+01 1e+02 1e+03 1e+040
5
10
15
20Concrete, rebar, and geometric properties
ρconcrete =50 Ω.m ρrebar =10- 6 Ω.mInterface impedance
Rp=2.5 Ω.m2, Cd=0.15F /m2
r0=0.00635 m(0.25 in.) D=0.0254 m (1 in.)
D=0.0381m (1.5 in.)
Frequency (Hz)
Conclusions � The Surface Measurement Method
accurately detects the different corrosion states of embedded reinforcing bars in concrete structures. This method is applied on the structure surface, with no need to connect with the reinforcement. In addition, it localizes the measurement to a confined segment of the rebar beneath the electrode array.
Conclusions � The measured resistivity spectra
distinguish various corrosion rates and various corrosion extents. The decreased resistivity modulus and peak phase angle can be used to characterize how rapidly the reinforcing bar is corroding, and the peak phase angle shift to a smaller frequency indicates to what extent the reinforcing bar has corroded.
Conclusions � The analytical solution is obtained to the
surface-based measurement of rebar corrosion in concrete.
� Both the analytical and experimental study confirmed the capability and feasibility of the new method as a prospective quick, convenient, and quantitative solution to corrosion detection.
References � Paulo Monteiro and Frank Morrison “Non-Destructive Method of Determining the Position and
Condition of Reinforcing Steel in Concrete”, US Patent 5,855,721 (1999).
� Monteiro, P.J.M., Morrison, F., and Frangos, W., "Non-Destructive Measurement of Corrosion State of Reinforcing Steel in Concrete," ACI Materials Journal, Vol. 95, No. 6, pp. 704-709, Nov-Dec. 1998.
� Zhang, J., P.J.M. Monteiro and F. Morrison, “Non-invasive surface measurement of the corrosion impedance of rebar in concrete. Part I: experimental results, ACI Materials Journal, V98 (N2): 116-125, Mar-Apr 2001.
� Zhang, J. and P.J.M. Monteiro, “Validation of Resistivity spectra from reinforced concrete corrosion by Kramers-Kronig transformations,” Cement and Concrete Research, V31, 603-607, 2001.
� Zhang, J., P.J.M. Monteiro, and F. Morrison, “Non Invasive surface measurement of the corrosion impedance of rebar in concrete. Part II: forward modeling,” ACI Materials Journal, V99 (N3):242-249, May-June 2002.
� J. Zhang, P. J. M. Monteiro, and F. Morrison, M. Mancio, Non Invasive Surface Measurement of the Corrosion Impedance of Rebar in Concrete. Part III: Effect of Geometry and Material Properties, ACI materials journal, Vol 101, No. 4, 273, 2004.