UPV surface crack depth

An air-filled, surface-breaking crack is an almost perfect barrier to ultrasound: the pulse cannot cross the air gap, so a compression wave sent along the surface must dive under the crack and diffract around its tip to reach a receiver on the far side. The extra path costs time, and that extra time carries the depth of the crack. The classic two-spacing arrangement from BS 1881-203 exploits it: place the transmitter and receiver on the surface an equal distance x either side of the crack mouth and record transit time t₁, then move both out to 2x and record t₂.

The diffracted path is 2·√(x² + h²) at the first spacing and 2·√(4x² + h²) at the second, for a crack of depth h. Taking the ratio of the two times eliminates the velocity entirely, leaving h = x·√((4t₁² − t₂²)/(t₂² − t₁²)). That self-calibration is the whole appeal of the method: indirect surface velocity is the least reliable number in concrete UPV, and here it cancels. On uncracked concrete both paths are straight along the surface, so t₂ = 2·t₁ and the depth comes out as zero — any measured ratio between 1 and 2 maps to a finite depth. The velocity implied by the result, 2·√(x² + h²)/t₁, is a built-in cross-check: it should agree with a direct-transmission reading on the same concrete, and a mismatch flags a bad timing or a bridged crack.

Three things break the method. Water in the crack transmits the pulse across the faces, so the first arrival no longer travels via the tip and the depth reads shallow — dry the area, or treat the answer as a lower bound. Reinforcement crossing the crack short-circuits the path in exactly the same way; keep the measurement line clear of bars. And the geometry assumes a crack roughly perpendicular to the surface with the transducers centred on it: an inclined crack reads the slant projection, not the vertical depth. The spacing should be of the same order as the expected depth — much smaller and the two times sit so close to the no-crack ratio of 2 that timing error dominates; much larger and the diffracted-path difference disappears into the noise.

The technique appears in BS 1881-203, the indirect arrangement is covered in BS EN 12504-4, and ACI 228.2R lists it among the crack-characterisation methods. The result is an estimate of the depth to the effective acoustic tip: a crack that tapers to a tight, touching tip reads shallow of the true structural depth, so core to confirm wherever a repair decision hangs on the number.

t₁ at spacing ±x about the crack;  t₂ at ±2x
h = x · √( (4·t₁² − t₂²) / (t₂² − t₁²) )
implied velocity v = 2 · √(x² + h²) / t₁
uncracked concrete: t₂ = 2·t₁  (h = 0)