Laboratory Validation of an Integrated Ground Penetrating Radar and Electrical Resistivity Tomography Framework for Reinforced Concrete Condition Assessment

1. Introduction

Reinforced concrete (RC) infrastructure deterioration represents one of the most pressing challenges confronting the global civil engineering profession. Chloride-induced reinforcement corrosion, carbonation-driven depassivation, crack propagation, moisture ingress, and void formation progressively degrade both the protective concrete cover and embedded steel reinforcement in bridges, tunnels, coastal sea walls, and building frames [1,2]. The economic consequences are substantial — estimated annual repair expenditure exceeds £40 billion across European member states — and the safety implications have been demonstrated by events such as the 2018 Genoa Ponte Morandi collapse and the 2021 Surfside condominium failure [3,4].

Conventional inspection methods — visual survey, cover-meter measurement, half-cell potential (HCP) mapping, and rebound hammer testing — are collectively limited by their inability to provide spatially continuous, depth-resolved images of subsurface deterioration [5,6]. This limitation directly motivates the application of geophysical non-destructive evaluation (NDE) methods to RC assessment.

Ground Penetrating Radar (GPR) and Electrical Resistivity Tomography (ERT) sense distinct and complementary physical properties of the concrete matrix. GPR responds to dielectric permittivity contrasts at material boundaries — void surfaces, crack faces, moisture fronts, and rebar positions — and has been extensively applied to RC bridge deck inspection [7,8,9], cover depth measurement [10], and corrosion-related amplitude attenuation [11,12]. ERT responds to ionic pore fluid conductivity, providing sensitivity to moisture saturation gradients, chloride contamination, and active corrosion zones [13,14,15]. Poupard et al. [16] provided critical ground-truth validation by demonstrating that ERT resistivity below approximately 30 Ω·m at rebar depth consistently associates with active corrosion in a 40-year marine RC beam. Villain et al. [17] applied both methods to a marine RC structure, demonstrating method complementarity but stopping short of a structured integration framework.

Despite growing recognition of method complementarity, a physically grounded, laboratory-validated integration framework with explicit failure mode analysis remains absent from the published literature. Existing multi-method studies are either qualitative comparisons [17] or empirical regression models [18,19], and no published study has systematically characterised the conditions under which integration fails. The present study addresses these gaps through a controlled laboratory experiment with known ground truth, providing: (i) calibrated ERT and GPR signatures for four deterioration states; (ii) a four-stage integrated interpretation framework; (iii) explicit failure mode and threshold robustness analysis; and (iv) quantitative comparison with the published literature.

2. Materials and Experimental Programme

2.1. RC Beam Specimen

A single RC beam specimen with nominal dimensions of 3000 × 300 × 200 mm was cast from a C30/37 mix design (CEM I 42.5N Portland cement, 360 kg/m³; water/cement ratio 0.50; 20 mm maximum aggregate size; total aggregate content 1750 kg/m³). The primary reinforcement comprised three T12 bars (ø12 mm, B500B) at 35 mm soffit cover, two T10 hanger bars at 25 mm top cover, and R8 mild steel stirrups at 150 mm centres. The beam was cured for seven days under wet hessian and subsequently stored air-dried at 20 °C and 65% relative humidity. The active survey length was 924 mm, corresponding to the central section between end supports. Table 1 summarises the specimen properties.

The single-specimen sequential conditioning design — all four conditions applied to the same beam — eliminates inter-specimen material variability as a confounding factor in the comparative analysis. The key caveat is that the calibrated reference resistivity ρ₀ = 558 Ω·m reflects air-dried laboratory conditions and is not directly transferable to field-cured concrete without local recalibration.

2.2. ERT Acquisition and Processing

Five ERT datasets were acquired across four beam conditions and two electrode spacings using a Wenner-Schlumberger array. The fundamental ERT measurement is the apparent resistivity ρₐ = K·ΔV/I, where K = πn(n+1)a is the geometric factor for the Wenner-Schlumberger configuration, ΔV is the measured potential difference, I is the injected current, a is the unit electrode spacing, and n is the separation level. The primary dataset (mlab, a = 44 mm, 22 electrodes, 71 data points) was acquired in October 2024; a confirmatory dataset (muf6, a = 30 mm) was acquired 16 months earlier in July 2023. The Model D (corroded) dataset employed a finer spacing of a = 24 mm (257 data points) to improve sensitivity at rebar depth. Inversion was performed using RES2DINV (Geotomo Software, Malaysia) with L1-norm robust regularisation, minimising the objective function Φ = ‖Wd(d_obs − d_cal)‖ + λ‖Wm m‖. Table 2 summarises the acquisition programme.

2.3. GPR Acquisition and Processing

Three 800 MHz profiles were acquired using a MALA RAMAC system for Models A, B, and C/D respectively. The 800 MHz frequency provides λ/4 ≈ 30 mm vertical resolution in concrete (v = 0.096 m/ns, ε_r = 9.8). Processing applied a uniform five-step chain to all profiles: (i) dewow high-pass temporal filter; (ii) time-zero correction aligned to the air–concrete interface using median first-break (samples 65–67); (iii) spatial median background removal; (iv) time-varying gain (TVG) for geometric spreading compensation; (v) hyperbola fitting for velocity calibration. The identical processing chain ensures that amplitude differences between conditions reflect genuine subsurface property changes rather than processing artefacts.

3. ERT Results

3.1. Model A — Intact Dry Beam: Reference Baseline

The muf6 measured apparent resistivity pseudosection (a = 30 mm) shows pervasive high resistivity throughout the section body (ρₐ > 2000 Ω·m) with a systematic near-surface gradient (120–460 Ω·m at n = 1–2) attributable to surface carbonation and atmospheric moisture adsorption. No spatially localised anomaly is present at any horizontal position, confirming the intact reference state. The mlab inverted section (a = 44 mm; 16 months later) recovers a median ρ = 558 Ω·m (Figure 1a), substantially above published values for field-cured concrete (150–300 Ω·m; [20]) but fully consistent with the published range for air-dried Portland cement concrete (300–10,000 Ω·m; [20,21]). The reproducibility of the two independent datasets 16 months apart confirms measurement stability. The Stage 2 conductive detection threshold for this dataset is ρ < 0.60 × 558 = 335 Ω·m.

3.2. Model B — Water-Filled Crack

The laB inverted section (Figure 1b) reveals a pronounced localised conductive anomaly at x ≈ 418–638 mm against a high-resistivity background (median ρ = 481 Ω·m). The minimum inverted resistivity within the anomaly zone reaches ρ_min = 1.46 Ω·m, representing a 382-fold reduction from the intact background and substantially below the Stage 2 threshold of 335 Ω·m. The background resistivity (481 Ω·m) is consistent with the intact reference, confirming that the anomaly is genuinely localised rather than a global change in beam moisture state. The ERT detects the moisture halo surrounding the crack (~20–50 mm extent) rather than the crack aperture itself (~0.5 mm), which falls far below the minimum resolvable feature size (~1.8 × a = 79 mm). The amplitude under-recovery implicit in the inversion smoothness constraint means the true fluid resistivity (~0.1–1.2 Ω·m) is not fully recovered [22].

3.3. Models C and D — Saturated and Corroded Conditions

Both the labmuftah (Model C; Figure 1c) and lab01102024 (Model D; Figure 1d) inverted sections show pervasive low-resistivity distributions, with median values of 9.2 Ω·m and 10.6 Ω·m respectively — well below the 50 Ω·m threshold for high chloride/corrosion risk [16]. The critical discriminating feature is the spatial distribution of the lowest-resistivity blocks: in Model C, the low-ρ distribution is spatially uniform throughout the section (55/58 blocks < 50 Ω·m); in Model D, the lowest-ρ values (ρ < 10 Ω·m) are preferentially concentrated at rebar depth z ≈ 24–48 mm, reflecting ionic accumulation at the active electrochemical cell. ERT difference sections (log₁₀(ρ_condition/ρ_intact)) confirm that this depth-preferential distribution constitutes the primary — though not definitive — discrimination criterion between moisture saturation and active corrosion.

Figure 2. ERT difference sections: log₁₀(ρ_condition / ρ_intact). Blue = lower than intact (conductive); red = higher. Left: Model B — localised anomaly at crack position. Centre: Model C — pervasive uniform conductivity increase. Right: Model D — pervasive, with strongest signal at rebar depth z ≈ 24–48 mm, providing partial discrimination between active corrosion and moisture saturation.

Figure 2. ERT difference sections: log₁₀(ρ_condition / ρ_intact). Blue = lower than intact (conductive); red = higher. Left: Model B — localised anomaly at crack position. Centre: Model C — pervasive uniform conductivity increase. Right: Model D — pervasive, with strongest signal at rebar depth z ≈ 24–48 mm, providing partial discrimination between active corrosion and moisture saturation.

Table 3. ERT calibration thresholds with literature comparison and critical assessment.

Condition	Median ρ (Ω·m)	Literature Range	Interpretation and Caveat
Model A — Intact dry	558	300–10,000 Ω·m [20]	Reference ρ₀. Elevated vs field concrete due to air-dried condition. Local recalibration required for field application.
Model B — Crack	481 (bkgd); 1.46 (min)	2–10 Ω·m [21]	Localised low-ρ from moisture halo. Dry crack = no anomaly (critical failure mode).
Model C — Saturated	9.2	5–80 Ω·m [17]	Pervasive uniform low ρ. Cannot distinguish from Model D on bulk value alone.
Model D — Corroded	10.6	2–50 Ω·m [16]	Depth-preferential distribution at rebar depth. Primary discrimination criterion from Model C.

Table 3. ERT calibration thresholds with literature comparison and critical assessment.

Condition	Median ρ (Ω·m)	Literature Range	Interpretation and Caveat
Model A — Intact dry	558	300–10,000 Ω·m [20]	Reference ρ₀. Elevated vs field concrete due to air-dried condition. Local recalibration required for field application.
Model B — Crack	481 (bkgd); 1.46 (min)	2–10 Ω·m [21]	Localised low-ρ from moisture halo. Dry crack = no anomaly (critical failure mode).
Model C — Saturated	9.2	5–80 Ω·m [17]	Pervasive uniform low ρ. Cannot distinguish from Model D on bulk value alone.
Model D — Corroded	10.6	2–50 Ω·m [16]	Depth-preferential distribution at rebar depth. Primary discrimination criterion from Model C.

4. GPR Results

4.1. Model A — Intact Beam: Reference Profile

The processed Model A radargram (DAT_1024) shows clean rebar hyperbolas at t₀ ≈ 0.73 ns, corresponding to the three T12 bars at 35 mm cover depth. Hyperbola fitting yields a best-fit wave velocity of v = 0.095 ± 0.008 m/ns (ε_r = 9.8 ± 0.9), consistent with the published range for air-dried Portland cement concrete [23,24]. No anomalous reflections are present at any position, confirming the intact reference state. The natural amplitude variability of ±15–20% in the intact profile establishes the practical detection noise floor for anomaly identification.

4.2. Model B — Water-Filled Crack

The Model B radargram (DAT_1025) shows a localised negative-polarity diffraction at the crack tip position (x ≈ 520 mm), consistent with the theoretical reflection coefficient R = (√9.8 − √80)/(√9.8 + √80) = −0.68 for a concrete–water interface. The negative polarity confirms the water-filled state of the crack; a dry crack would produce positive polarity or no detectable signature — a fundamental diagnostic limitation. Rebar-level amplitude analysis shows a localised 25–35% reduction at the crack position relative to A₀, while maintaining near-reference amplitudes elsewhere. The hyperbola continuity is disrupted at the crack position, with the tip diffraction creating an apparent bifurcation of the rebar signal.

4.3. Models C/D — Saturated and Corroded Conditions

The Model C/D radargram (DAT_1026) shows pervasive 50–65% amplitude attenuation throughout the full 924 mm profile, accompanied by a velocity pull-down (Δt ≈ 0.05–0.10 ns rightward shift of rebar peak travel time) confirming elevated ε_r from moisture and chloride ingress. A partial signal shadow zone develops below rebar level. The GPR amplitude alone cannot discriminate Model C from Model D — both moisture saturation and active corrosion produce similar 50–65% attenuation through related physical mechanisms (increased ε_i from ionic conductivity in both cases). Table 4 summarises the calibrated GPR thresholds.

Figure 3. Laboratory beam GPR amplitude analysis and corresponding ERT inverse model section. Upper panels: rebar-level amplitude profiles for Model A (intact, blue), Model B (crack, amber), and Models C/D (wet/corroded, red), showing progressive attenuation. Dashed line: 0.70 × A₀ Stage 2 threshold. Lower panel: ERT inverted resistivity section. The GPR amplitude alone cannot discriminate Model C from Model D — ERT spatial analysis (Figure 2) is required.

Figure 3. Laboratory beam GPR amplitude analysis and corresponding ERT inverse model section. Upper panels: rebar-level amplitude profiles for Model A (intact, blue), Model B (crack, amber), and Models C/D (wet/corroded, red), showing progressive attenuation. Dashed line: 0.70 × A₀ Stage 2 threshold. Lower panel: ERT inverted resistivity section. The GPR amplitude alone cannot discriminate Model C from Model D — ERT spatial analysis (Figure 2) is required.

Figure 4. Hyperbola fitting and GPR amplitude analysis. (a) Theoretical hyperbola fits (red dashed, v = 0.096 m/ns) at three T12 rebar positions on the intact beam (DAT_1024). (b) Central trace amplitude comparison for all three conditions: progressive reduction from intact (A₀) through crack (Model B, ∼30% at crack position) to wet/corroded (Models C/D, ∼57% throughout). Cyan dashed: rebar two-way travel time (t = 0.73 ns).

Figure 4. Hyperbola fitting and GPR amplitude analysis. (a) Theoretical hyperbola fits (red dashed, v = 0.096 m/ns) at three T12 rebar positions on the intact beam (DAT_1024). (b) Central trace amplitude comparison for all three conditions: progressive reduction from intact (A₀) through crack (Model B, ∼30% at crack position) to wet/corroded (Models C/D, ∼57% throughout). Cyan dashed: rebar two-way travel time (t = 0.73 ns).

5. Integrated GPR–ERT Analysis and Framework Validation

5.1. Four-Stage Integrated Interpretation Framework

The four-stage framework translates co-located GPR and ERT anomaly observations into risk categories suitable for maintenance decision-making. Stage 1 (Baseline establishment): local reference parameters ρ₀ and A₀ are established from anomaly-free reference zones of the same structure under investigation. Stage 2 (Anomaly identification): ERT blocks exceeding the conductive threshold (ρ < 0.60 × ρ₀) or the resistive threshold (ρ > 1.25 × ρ₀), and GPR traces exceeding the attenuation threshold (amplitude < 0.70 × A₀), are flagged for further investigation. Stage 3 (Cross-validation): spatial co-location (within ±half-electrode-spacing) of ERT and GPR anomalies is assessed, and the combined signature is matched against the diagnostic reference table (Table 5). Stage 4 (Risk classification): the integrated evidence is assigned to Risk Categories 1–4 (Negligible to High).

5.2. Framework Validation Against Known Ground Truth

The framework is applied to all four beam conditions and evaluated against known ground-truth states. Model A (intact dry): both ERT (median ρ = 558 Ω·m; no blocks below threshold) and GPR (amplitude within ±18% of A₀) classify correctly as Risk Category 1 (Negligible). Model B (water-filled crack): Stage 3 co-location of the ERT conductive anomaly (x ≈ 418–638 mm; ρ_min = 1.46 Ω·m) and the GPR negative-polarity diffraction (x ≈ 520 mm; 30% attenuation) provides both-method confirmation, correctly assigned Risk Category 2–3. Models C/D: the pervasive low-ρ ERT sections combined with pervasive GPR attenuation correctly indicate severe deterioration (Risk Category 3–4), with the ERT depth-preferential distribution in Model D providing the additional discriminating evidence for active corrosion. All four laboratory conditions are correctly classified against known ground truth, validating the four-stage framework at laboratory scale.

Figure 5. GPR–ERT cross-validation grid. Top row: GPR B-scans (800 MHz). Bottom row: ERT inverted sections (RES2DINV, L1). Left: Model A (intact) — both methods confirm anomaly-free baseline. Centre: Model B (crack) — Stage 3 co-location confirmed: GPR negative-polarity diffraction (x ≈ 520 mm) co-located with ERT localised low-ρ (x ≈ 418–638 mm). Right: Models C/D (wet/corroded) — both methods detect pervasive deterioration; ERT depth-preferential distribution in Model D partially discriminates active corrosion from moisture saturation. Cyan dashed: rebar depth.

Figure 5. GPR–ERT cross-validation grid. Top row: GPR B-scans (800 MHz). Bottom row: ERT inverted sections (RES2DINV, L1). Left: Model A (intact) — both methods confirm anomaly-free baseline. Centre: Model B (crack) — Stage 3 co-location confirmed: GPR negative-polarity diffraction (x ≈ 520 mm) co-located with ERT localised low-ρ (x ≈ 418–638 mm). Right: Models C/D (wet/corroded) — both methods detect pervasive deterioration; ERT depth-preferential distribution in Model D partially discriminates active corrosion from moisture saturation. Cyan dashed: rebar depth.

Figure 6. Four-stage integrated interpretation framework applied to the laboratory beam against known ground truth. Stage 1 (baseline): ρ₀ = 558 Ω·m and A₀ established from Model A. Stage 2 (anomaly identification): threshold criteria applied to ERT and GPR datasets. Stage 3 (cross-validation): spatial co-location of anomaly zones assessed. Stage 4 (risk classification): Risk Categories 1 (Negligible) through 4 (High) assigned. All four conditions correctly classified.

Figure 6. Four-stage integrated interpretation framework applied to the laboratory beam against known ground truth. Stage 1 (baseline): ρ₀ = 558 Ω·m and A₀ established from Model A. Stage 2 (anomaly identification): threshold criteria applied to ERT and GPR datasets. Stage 3 (cross-validation): spatial co-location of anomaly zones assessed. Stage 4 (risk classification): Risk Categories 1 (Negligible) through 4 (High) assigned. All four conditions correctly classified.

5.3. Failure Mode Analysis

Six conditions under which the framework is unreliable are identified. (i) Dry crack: below the ERT detection threshold (no moisture halo) and produces a weak or absent GPR signature; re-survey after rain is recommended. (ii) Early-stage corrosion (pre-cracking): resistivity may not yet have fallen below the Stage 2 threshold; supplementary HCP measurement is required. (iii) Moisture–corrosion ambiguity: ERT depth-preferential distribution is a partial but not definitive discriminator; HCP is required for mechanistic confirmation. (iv) Heterogeneous background: elevated ERT inversion RMS (> 15%) limits quantitative resistivity interpretation. (v) Heavily carbonated or very dry concrete: ρ₀ may exceed 5000 Ω·m, compressing the threshold sensitivity. (vi) Chloride contamination without active corrosion: low resistivity may be present without an active electrochemical cell; threshold crossed but mechanism different from active corrosion.

6. Discussion

The principal finding of this study is the confirmation that GPR and ERT are physically non-redundant when applied to RC condition assessment: each method resolves ambiguities that the other cannot, and their combination provides diagnostic capability unavailable from either method applied independently. GPR responds to dielectric contrasts at geometric interfaces, resolving crack geometry, rebar position, and void boundaries; ERT responds to ionic pore fluid conductivity, resolving electrochemical state and moisture distribution. The two methods are sensitive to different but related physical consequences of the same deterioration chain.

The laboratory-calibrated resistivity thresholds are broadly consistent with published values. The intact reference value ρ₀ = 558 Ω·m is elevated relative to field-cured concrete (150–300 Ω·m; [20]) but fully consistent with air-dried Portland cement concrete [20,21], a physically expected difference that is accommodated by the Stage 1 local baseline recalibration procedure. The saturated (9.2 Ω·m) and corroded (10.6 Ω·m) values are consistent with the ranges reported by Villain et al. [17] (5–80 Ω·m) and Poupard et al. [16] (2–50 Ω·m) respectively. The crack minimum (1.46 Ω·m) is consistent with water-saturated crack fluid resistivity reported by McCarter et al. [21].

The GPR amplitude calibration is also consistent with published values. The 25–35% crack-position attenuation is at the upper end of the published range [11,12], attributable to the specific crack aperture and moisture fill of the laboratory specimen. The pervasive 50–65% attenuation for saturated/corroded conditions is consistent with Hugenschmidt [7] and Tarussov et al. [25]. The wave velocity v = 0.096 ± 0.008 m/ns is within the expected range for air-dried concrete [23].

The principal limitation of this laboratory study is the single mix design (C30/37, w/c = 0.50, CEM I 42.5N), which limits the direct transferability of the calibrated ρ₀ and A₀ thresholds to other concrete compositions without local recalibration. The Stage 1 local baseline procedure is specifically designed to accommodate this limitation. Additionally, the two-dimensional ERT survey cannot resolve three-dimensional heterogeneity, and the absence of independent corrosion monitoring (mass loss measurement, electrochemical polarisation) means that the Model D corrosion level cannot be independently quantified beyond the chloride threshold confirmation.

7. Conclusions

This study has presented a laboratory-validated integrated GPR-ERT assessment framework for RC structures, calibrated against four controlled deterioration states with known ground truth. The following conclusions are drawn:

(1) ERT: four beam conditions produce systematically distinct resistivity signatures spanning three orders of magnitude (558 → 10 Ω·m). The depth-preferential low-resistivity distribution at rebar depth (ρ < 10 Ω·m; z ≈ 24–48 mm) provides partial discrimination between active corrosion and bulk moisture saturation.

(2) GPR: three conditions produce distinct amplitude and polarity signatures at 800 MHz. Negative polarity at the crack position (R = −0.68) confirms water-fill. Pervasive 50–65% attenuation characterises both saturated and corroded conditions, with GPR alone unable to discriminate between them.

(3) Integration: GPR and ERT are physically non-redundant — each resolves ambiguities the other cannot. The co-location of ERT conductive anomaly and GPR negative-polarity diffraction at the crack position provides both-method Stage 3 confirmation with higher confidence than either method individually.

(4) Framework validation: the four-stage framework correctly classifies all four beam conditions against known ground truth, validating the detection thresholds and the diagnostic reference table.

(5) Failure modes: six conditions under which the framework is unreliable are explicitly identified and quantified, most critically the invisibility of dry cracks and the moisture–corrosion ambiguity requiring supplementary HCP for definitive mechanistic diagnosis.

These results establish the empirical and physical basis for the integrated GPR-ERT framework and define the epistemic boundaries for its responsible application to field structures.