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Material loss and replacement volume. 1,000 m × 5 m; prescribed loss increases from 0 to 40 mm.

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MATHEMATICS · define the relationship and the meaning of each symbol before calculating.

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L = 1,000 m; b = 5 m; h is prescribed loss in metres. Each 1 mm loss represents 5 m³ across this area; no wear-rate law is inferred.

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INPUT · loss scenarios · read the axis units and the numerical values.

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1,000 m × 5 m; prescribed loss increases from 0 to 40 mm.

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40 mm = 0.040 m; 1,000 × 5 × 0.040 = 200 m³. Surface movement is exaggerated.

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OUTPUT · missing material · read the axis units and the numerical values.

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A 40 mm loss gives 200 m³. This is in-place geometry; loose haul volume additionally requires density and compaction factors.

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CALCULATION · substitute the defined inputs; keep units through each intermediate step.

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Area: 1000 × 5 = 5000 m²

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Thickness conversion: 40 / 1000 = 0.04 m

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In-place volume: 5000 × 0.04 = 200 m³

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Sensitivity: dV/dh = 5000; 1 mm corresponds to 5 m³ per mm

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SENSITIVITY · change one declared input · read the axis units and the numerical values.

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Loss 35 mm: 175 m³ in-place volume. Uniform prescribed loss over 1000 m by 5 m; no wear law assumed.

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Loss 40 mm: 200 m³ in-place volume. Uniform prescribed loss over 1000 m by 5 m; no wear law assumed.

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Loss 45 mm: 225 m³ in-place volume. Uniform prescribed loss over 1000 m by 5 m; no wear law assumed.

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Check: Check metre conversions and reconstruct a nonuniform case section by section. Keep in-place, compacted and loose quantities labelled separately. Do not multiply by a bulking factor without its source and material-state definition.

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ONE ROW · A uniform forty-millimetre allowance hides the places where the surface has lost much more.

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PARAMETER MAP · 12261 evaluated cells. The colour limits stay fixed across every row.

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This 1 km by 5 m synthetic loss field varies from 25 to 55 mm. Integrate thickness over area after converting millimetres to metres: V = ∫∫h/1000 db dx. Four complete longitudinal

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sine cycles cancel the signed fluctuation, leaving exactly 200 m³. Equal total volume therefore coexists with substantial local variation.

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VALUE LANDSCAPE · Height and colour encode Prescribed thickness loss (mm). This is a graph over the two input axes, not automatically a physical pavement shape.

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Prescribed loss geometry, not an erosion model or a measured change survey. Bulk density, compaction and loose supply volume are separate quantities.

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Loss is prescribed; density, compaction and haul factors are not included.