APSDS 4:
Overview of improvement to damage calculation at layer interfaces
[First released in Version 4.0i (17 September 2001)].
Background
Until this version was released, previous releases of APSDS Version 4 (and all releases of Version 3) did not use the exact z-value when calculating critical strains and damage factors at a layer interface. Instead 0.1 mm was added or subtracted to the z-value. At the time this method of calculation was first introduced it was believed that this would give results that were within engineering tolerances of the values at the interface.
It has recently come to our attention that in some circumstances (usually only associated with the top layer), this method can give rise to numerical errors.
APSDS 4.0i now uses the exact z-values corresponding to layer interfaces, ensuring that results are more accurate.
As a consequence, critical strains and damage factors calculated by APSDS 4.0i (or later) will in many cases be different from values calculated by earlier releases of Version 4 (and all releases of Version 3).
Our testing to date shows that significantly different values will be obtained for the top layer, in particularly relatively thin or very thick layers.
The gross numerical instability (see Example 1 below) that was displayed for a very thick surface layer could lead to the Automatic Thickness Design capability giving spurious thicknesses.
Examples
These examples have been chosen to give existing APSDS users an indication of the order of the differences given by the new version.
Example 1: Asphalt on unbound base and subbase.
The pavement structure is (variable thickness of) Asphalt (Modulus=1400 MPa) on 150 mm base on 500 mm subbase on subgrade (Modulus=60 MPa). Traffic = 1e4 movements of B767 (140 tonnes). Taxiway wander (SD=780 mm).
|
Asphalt Thickness |
Asphalt Damage Factor |
|
|
Version 4.0i |
earlier versions of |
|
| 75 | 3.47 e-3 | 3.19 e-3 |
| 100 | 1.52 e-3 | 1.50 e-3 |
| 125 | 2.46 e-2 | 2.43 e-2 |
| 150 | 2.73 e-2 | 2.62 e-2 |
| 200 | 1.90 e-2 | 1.77 e-2 |
| 500 | 3.89 e-4 | 4.12 e-4 |
| 1000 | 1.76 e-5 | 1.76 e-5 |
| 1200 | 8.10 e-6 | 8.08 e-6 |
| 1400 | 4.16 e-6 | 4.10 e-6 |
| 1600 | 2.16 e-6 | 2.65 e-6 * |
| 1800 | 1.15 e-6 | 9.03 e-5 * |
| 2000 | 6.22 e-7 | 1.07 * |
| 3000 | 4.10 e-8 | 1.34 e+7 * |
| 4000 | 4.42 e-9 | 9.53 e+8 * |
* Note: In previous versions, the results marked * demonstrate the gross numerical instability that was displayed for a very thick surface layer (e.g. thickness > 1500 mm).
Example 2: Asphalt on cement treated base (with unbound subbase).
The pavement structure is 75 mm of Asphalt (Modulus=1400 MPa) on variable thickness cement treated base on 500 mm subbase on subgrade (Modulus=60 MPa). Traffic = 1e4 movements of B767 (140 tonnes). Taxiway wander (SD=780 mm).
|
Cement-Treated Base Thickness |
Cement-Treated Damage Factor |
|
|
Version 4.0i |
earlier versions of |
|
| 200 | 1.02 e10 | 1.00 e10 |
| 500 | 2.37 e2 | 2.35 e2 |
| 1000 | 4.19 e-4 | 4.18 e-4 |
| 2000 | 2.15 e-10 | 2.14 e-10 |
| 3000 | 3.69 e-15 | 3.68 e-15 |
| 4000 | 6.45 e-19 | 6.44 e-19 |
The results for this example show small differences, not the gross numerical instability shown in Example 1 for a very thick surface layer given by earlier versions of APSDS 3/4.
Conclusion
This change to the method of calculating damage at layer interfaces generally does not have a significant impact on resulting design thicknesses.
But with earlier versions a spurious thickness could be obtained using the Automatic Thickness Design capability if trial thicknesses showed gross numerical instability (see Example 1 above).
Click here to download the latest version of APSDS 4.
revised October 03, 2005
