The method rests on a striking wave phenomenon. When an ultrasonic pulse is launched from a transmitter on one side of a surface-breaking crack and detected by a receiver on the other side, the phase of the first arriving wave can abruptly flip by 180 degrees as the receiver is moved away from the crack. This reversal happens because the wave diffracted from the crack tip changes its vibration polarity once a critical geometric condition is met among the transmitter, the crack tip, and the receiver. The critical folding angle that governs the flip is tied to the Poisson’s ratio of the material, and for typical concrete values between 0.20 and 0.25 the angle is close to 90 degrees. In that ideal case, the crack depth is simply the geometric mean of the distances from the transmitter and the receiver to the crack, a relationship so clean that it turns a subtle waveform feature into a direct ruler for hidden damage.

What sets the new work apart from earlier numerical studies is its refusal to treat concrete as an idealized, uniform solid. At the mesoscale, concrete is a multiphase composite of randomly distributed coarse and fine aggregates embedded in mortar, and those stiff, irregular inclusions scatter stress waves in complicated ways that could in principle corrupt any measurement based on wave timing and polarity. The researchers, led by Zeyu Li and Hongbing Chen, built two-dimensional finite element models populated with randomly placed aggregates of three distinct shapes: circular, elliptical, and polygonal. Aggregate positions were generated by Monte Carlo sampling with strict non-overlap rules, and the gradation followed an ideal maximum-density curve converted to two dimensions with the Walraven method. Aggregate shapes were synthesized parametrically, with ellipses derived by scaling and rotating base circles and polygons grown by an iterative skeleton-extension algorithm that expands a convex quadrilateral until its area reaches 80 percent of the corresponding circle.

To make these computationally demanding models practical, the team introduced a localized perturbation algorithm for aggregate placement. Instead of discarding a newly generated aggregate the moment it overlaps an existing one, the algorithm attempts up to ten small local repositioning moves before rejecting the candidate. On a representative 100 by 100 millimeter specimen, this simple change cut the average aggregate generation time from 281.61 seconds to 53.93 seconds, a reduction of roughly 80 percent, without sacrificing the randomness of the packing. That kind of efficiency gain matters because wave propagation simulations in heterogeneous media are expensive, and the researchers needed to run many configurations spanning crack depths of 3, 6, and 9 centimeters across all three aggregate shapes.

The baseline simulations used a homogeneous 1000 by 300 millimeter concrete slab with a 1 millimeter mesh and a 0.25 microsecond explicit time step, fine enough to resolve at least ten elements per wavelength of the 50 kilohertz excitation signal. A half-cycle sine pulse was applied at a point fixed at a distance equal to the crack depth from the crack, while receiving points marched away from the crack in 10 millimeter steps. In the intact model, no phase change ever appeared, and the arriving waves carried markedly larger amplitudes. In the cracked models, the reversal occurred exactly where the geometry predicted: the estimated depth ranges bracketed the true depths of 3, 6, and 9 centimeters in every case, with the upper bound landing precisely on the actual depth each time.

The team then confronted two complications that plague field inspections. First, they filled a 6-centimeter-deep, 1-millimeter-wide crack with sand, soil, or water, assigning realistic elastic and acoustic properties to each filler. Because all three materials are low-impedance, low-velocity media relative to concrete, they allow partial stress-wave transmission across the crack, weakening the free-surface constraint at the crack tip and shifting the reversal point slightly toward the crack face. The result was a modest underestimation of depth by about 8.67 percent, and notably the identified depth range was identical for all three fillers, because the filler-induced shift was smaller than the spatial resolution set by the measurement point spacing. Second, they compared the mesoscale models against the homogeneous baseline and found that although aggregates injected local stress fluctuations and complicated the received waveforms, the critical geometric condition for the first phase reversal remained untouched. Every aggregate shape, from smooth circles to jagged polygons, produced the same accurate depth estimates as the uniform model.

The decisive test came in the laboratory. The researchers cast a large C40 concrete specimen measuring 1500 by 1500 by 300 millimeters, embedding reinforcement only in its lower section so the unreinforced top surface could host twelve artificial cracks ranging from 2 to 20 centimeters deep. The cracks were pre-formed with 1-millimeter-thick PVC plates coated in light oil to prevent bonding, and three 10-centimeter cracks were deliberately filled with water, soil, and sand to replicate the infiltration that outdoor and underground structures inevitably suffer. The measurement protocol was straightforward: the excitation point started 2 centimeters from the crack, the receiver stepped away in 2-centimeter increments, and then the excitation itself was advanced, building a grid of transmitter-receiver pairs spanning the crack region until the phase flip revealed itself.

The experimental results vindicated the method across nearly the entire depth range. Cracks from 6 to 16 centimeters and the 20-centimeter crack were all correctly bracketed within their estimated intervals, and accuracy improved as cracks got deeper, exactly as the theory suggests. The failures were instructive rather than fatal. The 2-centimeter and 18-centimeter cracks fell into adjacent intervals, and the 4-centimeter crack could not be reliably estimated at all, because the physical dimensions of the transducers and impact source prevent them from getting close enough to shallow cracks and blur the phase reversal in the recorded waveform. Low first-arrival energy combined with surface roughness further muddied the signal at some receiver positions. For the filled cracks, the outcome mirrored the simulations perfectly: the dry, water-filled, soil-filled, and sand-filled 10-centimeter cracks all yielded the same estimated depth range, from 10.00 to 10.95 centimeters, confirming that common environmental fillers do not defeat the technique.

The broader significance of this work lies in its honesty about real materials and real conditions. Most nondestructive evaluation methods are validated on dry, clean, laboratory-pristine cracks, yet structures in the field are riddled with cracks infiltrated by rainwater, soil, and debris, which can render timing-based ultrasonic readings ambiguous. Thermal methods are hostage to sunlight, wind, and humidity; optical methods see only surfaces; ground-penetrating radar demands elaborate arrays. The phase reversal method, by contrast, needs only a transmitter, a receiver, and a geometric interpretation of the first arriving wave, and it now carries evidence that it tolerates both aggregate heterogeneity and crack filling. The authors are candid about the limits of the current study: their mesoscale model includes only aggregate and mortar, omitting the interfacial transition zone that is known to influence wave behavior, and only vertical surface-breaking cracks were considered. Extending the approach to inclined cracks and adding the interfacial zone are the declared next steps. Even so, the demonstration that a 180-degree flip in a wave’s first arrival can survive jagged aggregates, standing water, and packed soil marks a meaningful step toward crack depth measurements that work where infrastructure actually lives, outside and underground, in the rain.

Subject of Research: Non-destructive ultrasonic detection of surface crack depth in concrete using the initial wave phase reversal method, validated with mesoscale numerical models and experiments

Article Title: Crack depth detection in concrete by initial wave phase reversal method: Mesoscale numerical analysis and experimental validation

Article References: Li, Z., Gokarna, C., Li, Y., & Chen, H. (2026). Crack depth detection in concrete by initial wave phase reversal method: Mesoscale numerical analysis and experimental validation. Case Studies in Construction Materials, 25, Article e06573. https://doi.org/10.1016/j.cscm.2026.e06573

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06573

Keywords: concrete, crack depth, non-destructive testing, ultrasonic testing, phase reversal, mesoscale modeling, finite element analysis, random aggregate model, stress waves, structural health monitoring, crack filling materials, experimental validation