When an inspecting engineer finds a crack in a concrete column, beam or wall, the first question is not "how many millimeters wide" but "has it reached the reinforcement yet", because depth shows whether the crack is only superficial or has penetrated deep enough to compromise the steel's corrosion protection. This article focuses on estimating crack depth with ultrasonic pulses, building on What Is a UPV Test and Interpreting Low UPV Results.

How does UPV measure crack depth?

The principle is that ultrasonic pulses cannot travel across an air gap. When the transmitter and receiver are placed on the same surface straddling a surface-opening crack, the wave detours around the crack tip instead of traveling straight between the two transducers. As a result, the actual path is longer than the surface distance, and the travel time read by the instrument increases with crack depth.

This transducer arrangement is called indirect transmission (or surface transmission), one of the transducer arrangements specified in BS EN 12504-4:2021 (ASTM C597 mainly covers direct transmission through the concrete). These standards define how to measure pulse velocity, while the formula converting travel time into crack depth comes from BS 1881-203:1986, which has since been superseded by BS EN 12504-4, although the formula is still widely cited and used in technical literature and instrument manuals.

In Thailand, ultrasonic testing of concrete mainly references DPT 1504-51 (Standard for Inspection of Reinforced Concrete Structures by Non-Destructive Testing: Ultrasonic Test Method for Concrete, issued by the Department of Public Works and Town & Country Planning).

Measuring crack depth with indirect UPV, placing transducers across the crack at spacings x and 2x, with the formula and a worked example The left image is a section of concrete with a crack opening from the surface down to depth h, with the crack tip below the surface. In the first reading, transmitter T and receiver R are placed at an equal distance x on each side of the crack; the wave cannot cross the air gap, so it travels around the crack tip, giving time T1. In the second reading the transducers are moved out to 2x on each side, giving time T2. The right side shows the formula: h equals x times the square root of 4T1 squared minus T2 squared, divided by T2 squared minus T1 squared, from BS 1881-203. Example: x equals 150 mm, T1 equals 90 microseconds, T2 equals 158 microseconds, giving h of about 100 mm, with the condition that both readings must be on the same line with equal spacing on both sides. The bottom strip shows the three steps. Crack depth by UPV (two-spacing method) Not to scale Crack tip T R T R x 2x h h = crack depth Orange: x each side → read T₁ Blue: 2x each side → read T₂ Pulse can't cross air gap → detours around tip Formula (BS 1881-203) h = x · √[(4T₁² − T₂²) ÷ (T₂² − T₁²)] Example from article x = 150 mm · T₁ = 90 µs · T₂ = 158 µs 4T₁² = 32,400 · T₂² = 24,964 Num. 7,436 · Den. 16,864 h = 150 × √(0.441) ≈ 99.6 mm → report “approx. 100 mm” No prior velocity needed but same line required and equal spacing both sides Diagram not drawn to scale 1 Straddle crack, x each side Read T₁ 2 Move to 2x each side Read T₂, same line 3 Apply formula → h Report as estimate
Measuring crack depth with indirect UPV — transducers are placed across the crack twice, at spacings x and 2x, and the travel times of the wave detouring around the crack tip are compared

What formula converts wave travel time into crack depth?

Crack depth can be calculated with two formulas used in the field. The first does not require the concrete's pulse velocity to be known beforehand; the second requires the surface velocity to be measured first.

Formula 1 — two-spacing method (no pulse velocity needed)

Place the transducers across the crack at an equal distance x on each side and read time T1. Then move them out to 2x on each side, read time T2, and substitute into the formula.

h = x × √( 4T12 − T22 ) ÷ ( T22 − T12 ) h = crack depth (mm) · x = distance from the crack to each transducer in reading 1 (mm) · T₁ = travel time at spacing x each side (µs) · T₂ = travel time at spacing 2x each side (µs) — source: BS 1881-203:1986

The strength of this formula is that pulse velocity cancels out of the equation, so the velocity of the concrete in that area does not need to be measured first, and it can be used even on structures where the concrete mix is unknown. The key condition, however, is that both readings must be taken on the same line with exactly equal spacing on both sides.

🧮 Worked example (Formula 1)

Measuring a crack on a concrete column with x = 150 mm gives T1 = 90 µs, and moving out to 2x = 300 mm gives T2 = 158 µs.

4T12 = 4 × 8,100 = 32,400 · T22 = 24,964
Numerator = 32,400 − 24,964 = 7,436 · Denominator = 24,964 − 8,100 = 16,864
h = 150 × √(7,436 ÷ 16,864) = 150 × 0.664 ≈ 99.6 mm

Report it as "approximately 100 mm deep", not 99.6 mm, because the method's resolution does not extend to decimals.

Formula 2 — from a previously measured surface velocity

If the pulse velocity on an uncracked area of the concrete surface (Vs) has already been measured, a single reading across the crack is enough.

h = √( Vs × T ÷ 2 )2 − x2 Vs = pulse velocity on uncracked concrete surface (mm/µs) · T = travel time with transducers across the crack at x each side (µs)
🧮 Worked example (Formula 2)

The surface velocity measured on an uncracked area is Vs = 4.0 km/s (equal to 4.0 mm/µs). Measuring across the crack at x = 150 mm gives T = 90 µs.

Half the actual travel path = 4.0 × 90 ÷ 2 = 180 mm
h = √(1802 − 1502) = √(32,400 − 22,500) = √9,900 ≈ 99.5 mm

The result matches Formula 1 for the same example. Calculating with both methods and comparing them is a good way to check the result when the crack is critical to the decision.

Which formula should you use?

Both formulas give the same answer when site conditions match the assumptions; they differ in what information is needed before measuring.

TopicFormula 1 (two spacings)Formula 2 (surface velocity)
Pulse velocity needed beforehand?Not requiredMust measure Vs on uncracked concrete in the same area
Readings across the crack2, at spacings x and 2x1, at spacing x
Best whenThe concrete mix is unknown, or there is no sound surface to measure velocitySpace is limited and transducers cannot be placed at 2x, or to cross-check Formula 1
Watch out forBoth readings on the same line, equal spacing on both sidesThe measured surface velocity must be from the same concrete

What are the steps for measuring crack depth on site?

A sequence that gives stable results has 8 steps. Most of the errors we encounter come from steps 1 to 4, not from the instrument.

  1. Always scan for reinforcement first — use GPR concrete scanning to locate bars in the area to be measured, then choose a measuring line with no bars crossing the crack.
  2. Expose the concrete — remove plaster or paint only at the transducer positions and grind smooth. Plaster lengthens the travel time for reasons unrelated to the crack.
  3. Check that the crack is dry and free of debris — blow dust and water out of the crack. If water is trapped, wait for it to dry first.
  4. Mark spacings x and 2x on a line perpendicular to the crack — typical spacings are 150 mm and 300 mm, measured with a tape, not estimated by eye.
  5. Apply couplant and press the transducers firmly — insufficient couplant causes the wave onset time to be misread, which directly affects the result because the formula is based on time.
  6. Measure T₁ then T₂ on the same line — do not shift the line between the two readings, because the formula assumes the crack depth is the same for both.
  7. Repeat at least 3 readings per point — if the scatter exceeds about 5%, reapply couplant and re-measure before calculating.
  8. Measure at several locations along the crack — cracks are rarely equally deep along their length. Measuring one point and drawing conclusions for the whole crack is the most common mistake.

Raw travel times in microseconds (µs) must be recorded in the report for every point, not just the calculated depth, so that if the spacing x later turns out to be wrong, depth can be recalculated from the raw data.

Water-filled cracks give values far below the true depth

Water conducts ultrasonic pulses better than air. If the crack holds water, the pulse short-cuts across the crack instead of traveling around the tip, so the travel time shortens and the calculated depth is significantly shallower than the true depth. This case is especially dangerous because the result looks safer than reality.

The figures below summarize the principle and steps above: a 2D section showing the two-spacing measurement at x and 2x across the crack, both calculation formulas and three cases that give wrong values, and a 3D model of measuring at several locations along the crack after scanning for reinforcement.

2D model (section) of crack depth measurement by UPV using two spacings x and 2x, with calculation formulas and cases that give wrong values Section through a concrete member perpendicular to a surface-opening crack of depth h. Transmitter T and receiver R are placed across the crack at an equal distance x on each side, giving time T1, then moved out to 2x on each side on the same line, giving time T2. The pulse cannot pass through the crack's air gap, so it must detour around the crack tip as two straight segments. At transducer positions, plaster or paint must be removed down to the concrete. The right box shows Formula 1, the two-spacing method, which needs no pulse velocity: example x 150 mm, T1 90 microseconds, T2 158 microseconds, giving a depth of about 100 mm; and Formula 2, which uses a previously measured surface velocity. The bottom row shows three cases that give wrong values: water in the crack and reinforcement crossing the crack, which make the value shallower than the true depth, and plaster not yet removed, which makes it deeper than the true depth. Side section (2D) Not to scale T R T R x x 2x 2x h Read 1: x/side → T₁ Read 2: 2x/side → T₂ (same line) Crack tip Pulse bends here: two straight legs Crack dry, no debris Bars parallel, not crossing line Formula 1 · two spacings h = x · 4T₁² − T₂² T₂² − T₁² No concrete pulse velocity needed x 150 mm · T₁ 90 µs · T₂ 158 µs h = 150 × √(7,436 ÷ 16,864) ≈ 100 mm Formula 2 · known surface Vs h = √[ (Vs·T ÷ 2)² − x² ] Vs 4.0 mm/µs · T 90 µs · x 150 h = √(180² − 150²) ≈ 100 mm Source: BS 1881-203:1986 Record raw times (µs) for every point ✕ Water in crack Pulse short-cuts across Far shallower than true ✕ Bars crossing crack Pulse short-cuts via steel Too shallow · GPR scan first ✕ Plaster/paint not removed Coating adds travel time Too deep · expose test spots
2D model (side section) — the pulse cannot pass through the crack's air gap, so it detours around the crack tip as two straight segments. Reading 1 at x on each side gives T₁; moving to 2x on each side on the same line gives T₂. The example in the right box gives a depth of about 100 mm from both formulas. Bottom row: trapped water and crossing bars make the value shallower than true, while unremoved plaster makes it deeper than true. (Figure: SPN Soil Engineering)
3D model of crack depth measurement at several locations along a crack after scanning for reinforcement with GPR 3D view of a concrete slab with a crack running across its top surface. Behind it, a GPR unit has scanned for reinforcement and marked the bar lines as dashed lines on the surface. Four measuring lines, S1 to S4, are set perpendicular to the crack in the gaps between bars, each marked with spacings x and 2x on both sides of the crack. At line S2 the transmitter and receiver are in place. The crack plane is shown transparent to reveal that its depth varies along its length. The right box is a chart of the measured depth at each line compared with the reinforcement level, with practice notes: measure at several locations, repeat at least 3 readings per point, accuracy about plus or minus 15 percent, and confirm with a core when load capacity is affected. Values in the figure are hypothetical. 3D model Not to scale S1 S2 S3 S4 T R GPR scan for bars first Mark bar lines on surface Lines ⟂ to crack Between bars, no bar crossing Crack plane (transparent) Depth varies along crack Probes on line S2 Orange = x · Blue = 2x Rebar at cover depth Depth per line S1 45 S2 95 S3 130 S4 80 h (mm) · dashed = bar level Orange = reaches bars Hypothetical values 1 Several lines along crack Don't judge crack from 1 point 2 Repeat ≥ 3 readings/point Scatter > ~5%: re-measure 3 Accuracy approx. ±15% Enough to rank severity 4 Affects load capacity? Confirm with Core Test
3D model — scan with GPR for reinforcement first, then set measuring lines S1–S4 perpendicular to the crack in the gaps between bars. The transparent crack plane varies in depth along its length, so several locations must be measured. The chart on the right compares the depth at each line with the reinforcement level; values are hypothetical. UPV results have an error of about ±15% and are used to rank severity, not to calculate strength directly. (Figure: SPN Soil Engineering)

How accurate is UPV crack depth?

Under suitable conditions, meaning the crack is dry, perpendicular to the surface, not crossed by reinforcement and roughly 50 to 300 mm deep, results typically have an error of about ±15% compared with direct verification by coring. This means a crack calculated at 100 mm may actually be roughly 85 to 115 mm deep.

This accuracy is enough to rank crack severity, decide which locations to repair first and plan the repair method, but it is not enough to use the figure directly in calculating the load capacity of the section. If crack depth affects the strength assessment, it must be confirmed with a Concrete Core Test per ASTM C42 or another method that provides direct evidence.

The practice of combining several non-destructive methods to confirm results before concluding is set out in the guidance document ACI PRC-228.2 (Report on Nondestructive Test Methods for Evaluation of Concrete in Structures), which stresses that NDT gives indications, not verdicts.

When can UPV not measure crack depth?

Both formulas assume the pulse travels around the crack tip as two straight segments through homogeneous concrete. When this assumption does not hold, the result will be wrong without any warning from the instrument. The table below lists common site cases.

Site conditionEffect on measured valueRecommended option
Crack contains water or is saturatedFar shallower than trueWait until fully dry or blow out water before re-measuring
Crack filled with mortar debris, dust or sedimentShallower than trueClean out the crack before measuring
Reinforcement crosses the crack on the measuring lineShallower than trueGPR scan, then move the measuring line away from the bars
Crack is inclined, not perpendicular to the surfaceCan be wrong either wayAlso measure from the opposite face, or confirm by another method
Branched or map crackingCannot be interpretedAssess the pattern and find the cause rather than measuring depth
Internal crack not open to the surfaceMethod not applicableImpact Echo per ASTM C1383 or direct transmission
Surface still plastered or paintedDeeper than trueRemove the coating at measuring points down to the concrete
Crack previously repaired with epoxy injectionShallower than trueUse it to check injection quality instead, not to measure original depth
Crack deeper than the transducers can reachWeak signal, unclear onset timeIncrease spacing x and use lower-frequency transducers

The two most common cases are water in the crack and reinforcement crossing it. Both make the result shallower than the true depth, which is the dangerous direction because severity is underestimated. Scanning for reinforcement and checking moisture first are therefore not steps that can be skipped.

Crack depth measured: what next?

Depth on the day of measurement is a single snapshot in time. What the engineer needs to know next is whether the crack is stable or still growing, which requires crack monitoring through repeated measurements over time, not a single measurement.

  • Stable crack, not reaching reinforcement — usually handled by sealing the surface against water and moisture ingress, with a scheduled monitoring interval.
  • Stable crack, but reaching reinforcement level — assess the corrosion risk and consider injection repair with a suitable material.
  • Crack still growing — find the structural cause before repairing, because repairing without addressing the cause will let the crack return.
  • Effect on load capacity — must be confirmed with a Core Test or another direct method, with conclusions drawn by a licensed civil engineer (COE).

For choosing between confirming with another NDT method or taking actual samples, the pros and cons are compared in NDT vs. Core Test: What's the Difference.

SPN provides UPV crack depth measurement, always scanning for reinforcement with GPR beforehand, and issues reports certified by a licensed civil engineer (COE) with signature and registration number for submission to the relevant authorities. See all services at Non-Destructive Structural Testing (NDE). The fee depends on the number of measuring points and site conditions. Request a free quotation within 24 hours. Prices do not include travel and equipment transport, which are charged extra according to the distance to site.