Electrical Resistance Tomography (ERT)

Introduction � It is an imaging modality used to estimate the internal conductivity distribution.

� The current is injected into an object and voltage measurements are then acquired from the object boundary.

Comparison to X-ray tomography

ERT is considered a diffusive modality because if a current is injected into the target volume between any two points, the electric current (density) spreads into the whole volume

Comparison to X-ray tomography

The reconstruction of the image is more complicated than, for example, when using X-ray tomography, because X-rays travel in straight line, and one measurement carries information from a very restricted subset of the target

Measurements

K. Karhunen, A. Seppänen, A. Lehikoinen, P.J.M. Monteiro, J. P. Kaipio, Electrical Resistance Tomography Imaging of Concrete, Cement and Concrete Research, Volume: 40 Pages: 137-145, 2010

A bit of math (see details in the textbook or in the papers)

The complete electrode model follows the Poisson equation

∇⋅(σ∇u) = 0, r ∈Ω

Boundary conditions

σ ∂u∂neℓ

∫ dS = Iℓ, r ∈eℓ, ℓ = 1,…,L

σ ∂u∂n

= 0, r ∈∂Ω \ ∪ℓ=1L eℓ

u + zℓσ

∂u∂n

=Uℓ, r ∈eℓ, ℓ = 1,…,L

�  Finding heterogeneity (reinforcing bar)

K. Karhunen, A. Seppänen, A. Lehikoinen, P.J.M. Monteiro, J. P. Kaipio, Electrical Resistance Tomography Imaging of Concrete, Cement and Concrete Research, Volume: 40 Pages: 137-145, 2010

�  Finding heterogeneity (plastic plate)

K. Karhunen, A. Seppänen, A. Lehikoinen, P.J.M. Monteiro, J. P. Kaipio, Electrical Resistance Tomography Imaging of Concrete, Cement and Concrete Research, Volume: 40 Pages: 137-145, 2010

More challenging cases:

� In the previous examples the sensors surrounded the sample. This is unrealistic in field conditions.

� More sophisticated tests were done by placing the sensors just in one planar surface of the concrete

Surface measurements

Slabs

Beams

Finite Element Modeling

Slabs

Beams

� Crack detection after bending test

surface plots of the reconstructed conductivity distribution of the specimen

K. Karhunen, A. Seppänen, A. Lehikoinen, J. Blunt, J. P. Kaipio, and P. J. M. Monteiro, Electrical Resistance Tomography for Assessment of Cracks in Concrete, ACI Materials Journal, V. 107, No. 5, September-October 2010