Harichandran, R. S., Mahmood, T., Raab, A., and Baladi, G. Y. (1993). "A
modified Newton algorithm for backcalculation of pavement layer
properties." Transportation Research Record, 1384, 15-22.
Abstract
An efficient algorithm for the backcalculation of pavement layer moduli
from measured surface deflections is presented. The algorithm is an
iterative one and can use any mechanistic analysis program for forward
calculations (presently an extended precision CHEVRON program is used
for this purpose). Most mechanistic-based backcalculation methods
attempt to find the layer moduli that minimize the weighted sum of the
relative or absolute errors between measured and predicted surface
deflections. Using a search techniques to achieve such a minimization
sometimes requires hundreds of calls to a mechanistic analysis program,
and some programs try to speed this up by using a previously created
database. The algorithm presented here is different in that it uses a
modified Newton method to obtain the least-squares solution of an
over-determined set of equations. This gives the proposed algorithm a
robustness that some other approaches appear to lack. For example, the
predicted moduli are not too sensitive to the initially assumed seed
moduli or the location of the stiff layers (e.g., CRAM section,
composite pavements, shallow or deep bedrock, etc.). Further, a set of
auxiliary equations that are totally independent of those used in the
modified Newton method, and which relate surface deflections to the
compressions in each pavement layer, are used to improve the speed of
convergence. The algorithm is also extended to improve incorrectly
specified layer thicknesses. This algorithm is being implemented in a
new backcalculation program nameMICHBACK.