WEBVTT

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Penetration as a measured profile. Cumulative blows 0, 10, 25, 55, 100; depth 0–800 mm.

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

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z: cumulative depth (mm); N: cumulative blows. Use differences, not z/N at every point. Intervals: 10, 15, 30 and 45 blows produce 100, 100, 200 and 400 mm.

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INPUT · blow increments · read the axis units and the numerical values.

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Interval 1: (100 − 0) / (10 − 0) = 10.00 mm/blow.

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Interval 2: (200 − 100) / (25 − 10) = 6.67 mm/blow.

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Interval 3: (400 − 200) / (55 − 25) = 6.67 mm/blow.

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Interval 4: (800 − 400) / (100 − 55) = 8.89 mm/blow.

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OUTPUT · incremental penetration rates · read the axis units and the numerical values.

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The last interval gives 8.89 mm/blow. The overall 800/100 = 8.00 conceals the changes between intervals.

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

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Depth increments: 100, 100, 200, 400 mm

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Blow increments: 10, 15, 30, 45 blows

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Interval rates: 10, 6.6667, 6.6667, 8.8889 mm/blow

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Weighted identity: Σ(DNj × ΔNj) / ΣΔNj = 800 / 100 = 8 mm/blow

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

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40 last blows: 10 mm/blow last interval. Last 400 mm divided by 40 blows; other intervals unchanged.

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45 last blows: 8.88889 mm/blow last interval. Reference last interval, 400 mm over 45 blows.

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50 last blows: 8 mm/blow last interval. Last 400 mm divided by 50 blows.

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Check: Require increasing cumulative blows and nondecreasing penetration. A zero blow increment cannot be divided into a rate; flag it for review. Retain refusal and missing intervals explicitly instead of replacing them with zero penetration resistance.

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ONE ROW · One penetration number is convenient. A depth record is more interesting.

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

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Begin with the interval penetration values from the worked record, then prescribe a 15% spatial modulation along a 2 km corridor. DN₀ is 10 from the surface to less than 200 mm,

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6.6666667 from 200 to below 400 mm, and 8.8888889 from 400 mm onward. Read each column as a depth profile. Bands are prescribed layers in the teaching dataset, not detected field

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interfaces.

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

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This synthetic response field does not convert DN to CBR, capacity or DSN800. A real sounding has discrete blows, depth resolution and possible refusal; smooth chainage variation is an imposed assumption.

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This replays an assumed record; it does not predict cone resistance or CBR.