Simulated TSD and FWD results based on an elastostatic layered half-space model.
<p dir="ltr">One million pavement configurations were simulated using a mechanistic model to generate synthetic FWD and corresponding TSD slopes. The ELLEA1 code (Ver. 0.96) served as the underlying computational kernel for all cases [Levenberg, E., ELLEA1: Isotropic Layered Elasticity in Excel: Pavement analysis tool for students and engineers (ver. 0.96), 2016]. This program numerically solves the classical quasi-static formulation for a layered half-space loaded at the surface by a circular stress patch; it considers five fully bonded linear elastic layers, numbered sequentially from Layer#1 at the top down to Layer#5 at the bottom (with semi-infinite thickness).</p><p dir="ltr">A total of one million cases were simulated, where each case represents a specific combination of layer thicknesses and elastic properties. In all cases, the model layering was associated with (top to bottom): asphalt concrete, base, subbase, upper subgrade, and lower subgrade. A range of thicknesses and a fixed Poisson ratio were chosen to represent each pavement layer. Ultimately, distinct layered models were generated by randomly selecting a set of layer thicknesses and moduli such that they reside within the extreme values.</p><p dir="ltr">Poisson ratios: ν1=0.30; ν2=0.35; ν3=0.35; ν4=0.40; and ν5=0.50. Modulus range for Layer #1 (E1) [MPa]: 1000 – 25000; Thickness range for Layer #1 [mm]: 40 – 450. Modulus range for Layer #2 (E2) [MPa]: 100 – 8000; Thickness range for Layer #2 [mm]: 150 – 300. Modulus range for Layer #3 (E3) [MPa]: 80 – 600; Thickness range for Layer #3 [mm]: 150 – 600. Modulus range for Layer #4 (E4) [MPa]: 20 – 500; Thickness range for Layer #4 [mm]: 0 – 500. Modulus range for Layer #5 (E5) [MPa]: 15 – 150.</p><p dir="ltr">The FWD deflections (in μm units) were calculated for a 50 kN force, distributed evenly over a circular area with a diameter of 300 mm. The FWD geophone spacings [mm]: 0, 200, 300, 450, 600, 900, 1200, 1500, and 1800.</p><p dir="ltr">The TSD-reported slopes (in μm/m units) were calculated by reproducing the tire configuration, wheel loads, and laser spacings of MESAS (Multifunktionales Erfassungssystem zur Substanzbewertung und zum Aufbau von Straßen), the TSD device owned and operated by the German Federal Highway and Transport Research Institute (BASt). MESAS has 11 lasers, with the laser at offset 3010 mm serving as a reference; the laser spacings were [mm]: -450, -300, -200, 110, 210, 310, 460, 610, 910, and 1510.</p><p dir="ltr">Under the truck’s ten-wheel loading, surface slopes were calculated for every model-pavement configuration. This was done with a central difference formula applied to deflections calculated five millimeters before and after each of the laser locations. Lastly, the calculated slope at the reference laser was subtracted from the others to generate synthetic TSD-reported slopes.</p>
