Study of Reinforced Concrete Corrosion Using Impedance Measurements

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.

The Method

Rc1 Rc2 Rc3

Rc5

Rcm

Rc4

Z Z

A M N B

The Proof of Concept

Cast a large concrete block with different bars

Gold bar

Casting

Block

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)

Test set-up

Results

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.