Comparison of the Accuracy of 2D versus 3D FDTDAir-Coupled GPR Modeling of Bridge Deck Deterioration

Kimberly Belli, Graduate Research Assistant (MIE, Northeastern)Sophia He Zhan, Postdoctoral Research Associate (CEE, Northeastern)

Sara Wadia-Fascetti, Associate Professor of Civil & Environmental Engineering (Northeastern) Carey Rappaport, Professor of Electrical & Computer Engineering (Northeastern)

Abstract: Deterioration in reinforced concrete systems, such as bridge decks, is hidden in the subsurface until the damage progresses to the surface to a condition requiring significant rehabilitation or replacement. Knowledgeabout the condition of the subsurface can provide valuable information for consideration in the management of bridge planning and maintenance. The ability to simulate a subsurface investigation via a forward model providesinsight into the response from and interaction among bridge deck elements and changes in the response due to the presence and relative position of an anomaly. Forward modeling also plays a major role in physics-based

Simulation Information

inversion techniques for reconstruction, and therefore in condition assessment. This work examines the degree of accuracy of an air-coupled Ground Penetrating Radar (GPR) 2D Finite Difference TimeDomain (FDTD) model of a bridge deck evaluated by comparison to a full 3D model. Simulations of healthy and delaminated bridge decks are examined and the accuracy and trade-offs between the twomodels discussed. To compensate for wave propagation differences in 2D and 3D, the 3D FDTD excitation is filtered to produce the same response over the surface of the deck as the 2D response. Tocompare the effect of an anomaly in GPR data, the healthy bridge deck responses are removed from the delaminated bridge deck responses. The response of 2D healthy deck is removed from the 3Ddelaminated case to consider the validity of using 2D simulation results to evaluate 3D data (analogous to field collected data).

Simulation Results

Relevant Publications

AcknowledgementsThis work was supported in part by Gordon-CenSSIS, TheBernard M. Gordon Center for Subsurface Sensing and ImagingSystems, under the Engineering Research Centers Program ofthe National Science Foundation (Award Number EEC-9986821).This work supports research in the fusion of GPR signals underNSF grant CMMI-0600578.

K. Belli, H. Zhan, S. Wadia-Fascetti, C. Rappaport, “Comparisonof the Accuracy of 2D versus 3D FDTD Air-Coupled GPRModeling of Bridge Deck Deterioration,” Journal article inpreparation.aa

dielectric constant=9, conductivity=0, relativepermeability=1

Concrete ElectromagneticProperties:

Cylindrical air void with a 0.6cm thickness and30.0cm diameter

Air Void:

diameter=1.2cm (approximately a #4 rebar)spacing=20.4cm on center, concretecover=6.6cm

Longitudinal Rebar:

diameter=1.8cm (approximately a #5 rebar)spacing=12.6cm on center, concretecover=4.8cm

Transverse Rebar:

18.0cmConcrete Thickness:

dielectric constant=5, conductivity=0, relativepermeability=1

Asphalt ElectromagneticProperties:

2.4cmAsphalt Thickness:

1 trace recorded every 1.2cmB-Scan Rate

Modulated Gaussian pulse with 1.0GHz centerfrequency and bandwidth

Excitation Signal:3.0cm in X-direction, no separation in Y- or Z-directionBi-static Separation:30.6cm above the deckT/R Height:5.0ps (satisfies Courant condition)Temporal Resolution:

0.6cm (satisfies 10 points per wavelength in concreteusing center frequency plus half of bandwidth)

Spatial Resolution:

Notes about 2D geometry due to invariance in the Y-dir:

1. Longitudinal rebar is not modeled in 2D because it would be representedas an infinitely long (Y-direction) and wide (X-direction) metal plate and thewaves would not penetrate. Comparisons of Cases C through F assume arebar mesh in 3D and transverse rebar only in 2D.

2. In 2D, the cylindrical air void representation is analogous to an infinitelylong (Y-direction) rectangular void with a constant width (X-direction) equalto the diameter of the cylinder (because the 2D slice occurs at the centerof the air void).

Healthy Deck Removal ComparisonThe condition assessment of reinforced concrete systems relies on identification of subsurfaceanomalies. The effect of anomalies in the GPR response can be seen after the response of thehealthy deck is removed.

Start (x) & Stop (+) Locations for Air-coupled Transmitter Path

Excitation Filtering ProcessIn 3D, the wave generated by a point source is spherical and the propagationis proportional to the inverse of the radial distance (≈ 1/r). In 2D, the wavegenerated by a point source is cylindrical and the propagation is proportionalto the inverse of the square root of the radial distance (≈ 1/ ). Filtering the3D FDTD excitation signal can account for propagation variation at the decksurface.

Defect 3D - Healthy 2DIn order to consider using 2D simulated data inthe analysis of field collected data, the 2Dhealthy deck response is removed from the 3Ddelaminated response. Using 2D data toidentify anomalies in 3D data has significantpotential.

Potential technology transfer opportunities include extraction of additionalinformation from GPR data and improved identification and quantification ofsubsurface anomalies. The work presented here may be of interest tocompanies such as Geophysical Survey Systems, TransTech Systems andInfrasense who are focused on products and services associated withnondestructive testing of civil infrastructure as well as companies using 2Dsimulations to improve analysis and understanding of 3D data.

Technology Transfer

=-

Comparison of 2D and 3DBackground Removed Images=3D 2D

Case F - Case CDelamination Below

Rebar Mesh

Delaminated Deck Response with Healthy Deck Response Removed

-

Case D - Case CDelamination at Asphalt

& Concrete Interface

Case E - Case CDelamination Above

Rebar Mesh

2D FDTDsystem

h2(t)

3D FDTDsystem

h3(t)

y2(t)

y3(t)

x(t)

2D FDTDsystem

h2(t)

3D FDTDsystem

h3(t)

x(t)

x’(t)

y2(t)

f(t)y2(t)

F(f) = Y2(f)/Y3(f)x’(t) = ifft(Y2(f)/Y3(f))*X(F))

X(f) H2(f) = Y2(f)X(f) H3(f) = Y3(f)X(f) F(f) H3(f) = Y2(f)

Typical Response from Case A

Asphalt & Concrete Only(Case A)

Addition of TransverseRebar (Case B)

Addition of LongitudinalRebar (Case C)

Delamination at Asphalt &Concrete Interface

(Case D)

Delamination Above RebarLayer (Case E)

Delamination Under RebarLayer (Case F)

2D Model B-Scan Simulation Results

Root Mean Square Deviation of 2D and 3D B-Scans

3D Physical Model

2D Physical Model & Detail

3D Model B-Scan Simulation Results

Case D (3D) - Case B (2D)Delamination at

asphalt/concrete interface

Case F (3D) - Case B (2D)Delamination below

rebar mesh

Case E (3D) - Case B (2D)Delamination above

Rebar mesh

These images are comparable.