WEBVTT

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Testing competing stiffness hypotheses. Reference half-space E = 200 MPa; candidates 100–400 MPa.

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

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Reference vector: five modelled sensor readings, generated at E = 200 MPa. Candidate E varies from 100 to 400 MPa; radius, load and ν remain fixed.

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INPUT · synthetic reference readings · read the axis units and the numerical values.

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E = 100 MPa; RMSE = 348.36 μm relative to the synthetic reference.

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E = 150 MPa; RMSE = 116.12 μm relative to the synthetic reference.

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E = 200 MPa; RMSE = 0.00 μm relative to the synthetic reference.

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E = 300 MPa; RMSE = 116.12 μm relative to the synthetic reference.

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E = 400 MPa; RMSE = 174.18 μm relative to the synthetic reference.

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E = 200 MPa; RMSE = 0.00 μm relative to the synthetic reference.

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OUTPUT · residual versus candidate modulus · read the axis units and the numerical values.

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RMSE is zero at the generating modulus of 200 MPa. This checks numerical consistency; real measurements can have model mismatch.

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

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Reference generation: wref = w(E = 200 MPa) five synthetic μm readings

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Candidate scaling: w(100 MPa) = 2 wref same load and geometry

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Residual vector: ri = wi(E) − wi,ref μm

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Objective: RMSE = √(Σri² / 5) μm; zero at 200 MPa

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

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E = 100 MPa: 348.361 μm RMSE. Reference generated at 200 MPa; vary one candidate modulus.

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E = 150 MPa: 116.12 μm RMSE. Reference generated at 200 MPa; vary one candidate modulus.

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E = 200 MPa: 0 μm RMSE. Reference generated at 200 MPa; vary one candidate modulus.

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E = 300 MPa: 116.12 μm RMSE. Reference generated at 200 MPa; vary one candidate modulus.

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E = 400 MPa: 174.18 μm RMSE. Reference generated at 200 MPa; vary one candidate modulus.

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Check: Plot signed residuals by sensor offset as well as RMSE. Perturb the assumed load and test whether the fitted modulus follows it. Keep synthetic recovery tests separate from validation against independent field measurements.

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ONE ROW · If two different input pairs draw the same bowl, which pavement have you identified?

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PARAMETER MAP · 6161 evaluated cells. The colour limits stay fixed across every row.

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The reference bowl uses 200 MPa and 40 kN at offsets 0, 0.3, 0.6, 0.9 and 1.2 m. Linear elasticity scales every displacement with P/E. Evaluate 6,161 input pairs and a low-error

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valley follows P/E = 0.2 kN/MPa. A measured load removes one source of ambiguity; letting both load and stiffness float creates it.

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VALUE LANDSCAPE · Height and colour encode Bowl RMSE (μm). This is a graph over the two input axes, not automatically a physical pavement shape.

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One homogeneous elastic parameter, noise-free synthetic reference and fixed radius/Poisson ratio. This is an identifiability demonstration, not multilayer backcalculation or proof that actual field loads are unknown.

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Recovering a synthetic modulus does not identify the layers of a real pavement.