Exercise set

Civil Infrastructure Inspection and Condition Assessment Exercises

Solved civil infrastructure inspection exercises for records, corrosion, load rating, movement, NDT, condition index, IRI, culverts and service gates.

Branch: Civil and Construction Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises focus on civil infrastructure inspection and condition assessment: records, photographs, corrosion loss, load utilization, bridge rating, movement, deflection, NDT sampling, monitoring reliability, condition scoring, pavement roughness, culvert capacity and service gates. Rehabilitation funding and portfolio prioritization are handled in a separate specialist exercise set.

Use these calculations as screening tools. Real service decisions require drawings, inspection procedures, material evidence, access notes, load history, environmental exposure, governing codes, uncertainty review and responsible engineering approval.

Release Evidence Notes

Inspection evidence should identify the asset, element, date, method, access limitation, calibration basis, defect location, mechanism, consequence, threshold and reviewer. A photo, scan or sensor reading is not enough unless it can be tied to a decision about service, restriction, monitoring, repair or further investigation.

Engineering Boundary Notes

The simplified calculations below do not replace bridge load rating, structural assessment, pavement design, hydraulic modelling or formal NDT qualification. They teach how to move from field evidence to a defensible screening decision.

Common Release Mistakes

Common mistakes include treating missing records as harmless, averaging away high-consequence defects, mixing visible condition with structural capacity, ignoring NDT coverage, using corrosion rates outside the exposure basis, and closing an inspection without stating the next action.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Records and traceability	1, 2, 16	Completeness, tagged evidence and usable monitoring data	Decide whether the evidence base is sufficient.
Deterioration and capacity	3, 4, 5, 6, 7, 8, 15, 18	Section loss, load utilization, rating factor, movement and fatigue	Continue service, restrict, inspect sooner or escalate.
Field methods and condition metrics	9, 10, 11, 12, 13, 14, 17	NDT coverage, reliability, condition score, IRI and freeboard	Accept the inspection result or require more evidence.

Exercise 1: Inspection Record Completeness

A bridge inventory has 128 critical elements. Current inspection records exist for 112 elements. Find the record completeness.

Solution

C=\dfrac{112}{128}\times 100=87.5\%

Engineering Comment

Completeness below 100 percent should trigger a list of missing high-consequence elements, not just a portfolio average.

Plausibility Check

Because 112 is close to but less than 128, a result slightly below 90 percent is reasonable.

Exercise 2: Tagged Photo Traceability

Of the same 128 elements, 96 have correctly tagged photographs. Find the photo traceability and the gap relative to inspection records.

Solution

C_p=\dfrac{96}{128}\times100=75.0\%, \qquad \Delta C=87.5-75.0=12.5\%

Engineering Comment

The record may exist, but comparison over time becomes weak if photographs cannot be matched to element IDs.

Plausibility Check

The photo traceability is lower than record completeness, so the positive gap is expected.

Exercise 3: Corrosion Section Loss

A steel plate is 200 mm wide. Original thickness was 12.0 mm and measured remaining thickness is 10.8 mm. Find area loss.

Solution

A_o=200(12.0)=2400\ \text{mm}^2,\quad A_r=200(10.8)=2160\ \text{mm}^2

\text{loss}=\dfrac{2400-2160}{2400}\times100=10.0\%

Engineering Comment

The result is a section-loss screen. It does not prove residual member capacity without load path and demand checks.

Plausibility Check

The thickness loss is 1.2 mm out of 12.0 mm, so 10 percent is consistent.

Exercise 4: Corrosion Projection Gate

If the plate in Exercise 3 lost 1.2 mm over 15 years, estimate years until remaining thickness reaches 9.6 mm.

Solution

r=\dfrac{1.2}{15}=0.08\ \text{mm/yr}

t=\dfrac{10.8-9.6}{0.08}=15\ \text{yr}

Engineering Comment

Projection assumes exposure is unchanged. A drainage or coating failure can make the historical rate non-conservative.

Plausibility Check

The next loss is also 1.2 mm, so the time equals the previous 15-year period.

Exercise 5: Load Utilization Screen

A member demand is 820 kN and screening resistance is 1000 kN. Find utilization.

Solution

U=\dfrac{820}{1000}=0.82

Engineering Comment

A utilization of 0.82 may support continued service only if resistance, demand and deterioration evidence are credible.

Plausibility Check

Demand is lower than resistance, so utilization must be below 1.

Exercise 6: Bridge Rating Factor

For a rating check, capacity is 1250 kN, dead-load effect is 430 kN and live-load effect is 760 kN. Compute the simple rating factor.

Solution

RF=\dfrac{1250-430}{760}=1.08

Engineering Comment

The screen suggests the live load can be carried, but posting decisions require the governing code format and condition modifiers.

Plausibility Check

Available capacity above dead load is slightly larger than live-load effect, so RF is slightly above 1.

Exercise 7: Deflection Trend

Midspan deflection readings increased from 14.0 mm to 17.5 mm over 5 years. Find the average trend.

Solution

\dot{\delta}=\dfrac{17.5-14.0}{5}=0.70\ \text{mm/yr}

Engineering Comment

Trend matters more than one isolated reading when creep, settlement or bearing restraint is suspected.

Plausibility Check

A 3.5 mm change over five years gives less than 1 mm per year.

Exercise 8: Expansion Joint Movement Deficit

A bridge joint should accommodate 42 mm of thermal movement. Field measurement shows only 25 mm. Find the unavailable movement percentage.

Solution

\text{deficit}=\dfrac{42-25}{42}\times100=40.5\%

Engineering Comment

A large movement deficit can transfer thermal force into bearings, substructure and deck elements.

Plausibility Check

The missing movement is 17 mm, a little over two-fifths of 42 mm.

Exercise 9: NDT Sample Defect Estimate

Ultrasonic testing samples 60 locations and flags 9 above the defect threshold. Estimate the sample defect rate.

Solution

p=\dfrac{9}{60}\times100=15.0\%

Engineering Comment

The number is a sample rate, not a whole-asset defect rate unless the sample plan is representative.

Plausibility Check

Nine is 3 out of every 20 locations, which is 15 percent.

Exercise 10: NDT Coverage Gap

A planned inspection required 240 m of ultrasonic scan coverage. The crew completed 204 m. Find completed coverage and missing length.

Solution

C=\dfrac{204}{240}\times100=85.0\%,\qquad L_m=240-204=36\ \text{m}

Engineering Comment

An 85 percent scan may still be unacceptable if the missing 36 m covers the most critical zones.

Plausibility Check

The missing length is 15 percent of 240 m, matching the coverage result.

Exercise 11: Inspection Network Reliability

Three independent sensors must all be available for a movement decision. Their availabilities are 0.98, 0.96 and 0.95. Find combined availability.

Solution

R=0.98(0.96)(0.95)=0.894

Engineering Comment

Even reliable individual sensors can produce a lower system availability when all are required.

Plausibility Check

The product of three numbers below 1 must be below the smallest individual availability.

Exercise 12: Weighted Condition Index

Deck, joint and drainage scores are 72, 55 and 40 with weights 0.50, 0.30 and 0.20. Compute the weighted condition index.

Solution

CI=0.50(72)+0.30(55)+0.20(40)=60.5

Engineering Comment

The drainage score is low, but its weight limits the index impact. A critical failure mode may still override the weighted average.

Plausibility Check

The result lies between the lowest and highest component scores.

Exercise 13: Pavement IRI Trigger

Measured IRI is 3.6 m/km and the intervention trigger is 3.2 m/km. Find the exceedance percentage.

Solution

E=\dfrac{3.6-3.2}{3.2}\times100=12.5\%

Engineering Comment

The trigger exceedance supports treatment review, but traffic class and distress type still affect the selected treatment.

Plausibility Check

The excess is 0.4 on a 3.2 basis, which is one eighth.

Exercise 14: Culvert Freeboard Release

A culvert passes a design flow with computed headwater elevation 101.35 m. Road crest elevation is 102.00 m and required freeboard is 0.50 m. Check freeboard.

Solution

F=102.00-101.35=0.65\ \text{m}

\text{margin}=0.65-0.50=0.15\ \text{m}

Engineering Comment

The hydraulic screen passes, but debris blockage, outlet erosion and survey datum should still be checked.

Plausibility Check

The headwater is below the road crest, so freeboard is positive.

Exercise 15: Heavy-Traffic Fatigue Exposure

An inspection interval has 210,000 heavy-truck crossings. The screening threshold is 250,000 crossings. Find the consumed fraction.

Solution

f=\dfrac{210000}{250000}=0.84

Engineering Comment

The exposure is below the threshold, but crack-prone details may still require targeted inspection.

Plausibility Check

210,000 is 84 percent of 250,000, so the fraction is below 1.

Exercise 16: Crack-Width Growth Rate

A concrete crack increased from 0.22 mm to 0.34 mm in 18 months. Find growth per year.

Solution

g=\dfrac{0.34-0.22}{1.5}=0.08\ \text{mm/yr}

Engineering Comment

Growth rate helps distinguish dormant shrinkage cracking from active movement or corrosion-related deterioration.

Plausibility Check

The increase is 0.12 mm over one and a half years, giving less than 0.1 mm per year.

Exercise 17: Monitoring Data Completeness

A monitoring system should log one reading every hour for 30 days. It recorded 654 readings. Find data completeness.

Solution

N=30(24)=720,\qquad C=\dfrac{654}{720}\times100=90.8\%

Engineering Comment

Completeness may be sufficient for slow trends but weak for short-duration overload or flood events.

Plausibility Check

The missing count is 66 readings, so completeness just above 90 percent is plausible.

Exercise 18: Inspection Service Gate

A service gate requires record completeness at least 90 percent, NDT coverage at least 80 percent and rating factor at least 1.00. Results are 87.5 percent, 85 percent and 1.08. Decide the gate.

Solution

87.5\%<90\%,\qquad 85\%\ge80\%,\qquad 1.08\ge1.00

The gate fails because the record-completeness requirement is not met.

Engineering Comment

One failed evidence criterion can block release even when capacity and NDT coverage appear acceptable.

Plausibility Check

The failed item is visible directly from the three comparisons, so the decision should be a hold.

Validation Package Checklist

asset boundary, element IDs and inspection date are recorded;
missing records and missing scan zones are listed explicitly;
deterioration mechanism is linked to each defect;
load, movement, hydraulic and pavement triggers are checked against thresholds;
NDT and sensor evidence include coverage, calibration and uncertainty limits;
the final service decision states continue, restrict, monitor, inspect, repair or hold.

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