2.3.3.2 Direct Solutions. Presently, there are no direct analy-
tical solutions that can uniquely determine the elastic moduli for a
multilayered pavement system using surface deflection measurements
alone. The so-called direct solutions have been developed for only two-
layer systems which usually involve graphical solutions, nomographs, or
in most cases only provide estimates for the subgrade modulus.
Scrivner et al. (102) presented an analytical technique for using
pavement deflections to determine the elastic moduli of the pavement and
subgrade assuming the structure is composed of two elastic layers.
Based upon the same assumption, Swift (113) presented a simple graphical
technique for determining the same two elastic moduli. Vaswani (124)
used Dynaflect basin parameters to develop charts for the structural
evaluation of the subgrade and its overlying layers for flexible pave-
ments in Virginia (see Table 2.1). The methods by Majidzadeh (64) and
Sharpe et al. (107), among others, employ similar basin parameters from
the Dynaflect or Road Rater to estimate the subgrade modulus and develop
charts to assess the overlying layers.
Jimenez (51) described a method for evaluating pavement-layer
modular ratios from Dynaflect deflections. The pavements were
considered to be three-layer systems, and the deflection data were used
to estimate ratios of the elastic moduli of the adjacent layers. The
ratios reduce the system from three values of elastic modulus to two
values of modular ratio. The major limitation of this method is that
the elastic modulus of the asphalt concrete layer must be known.
Wiseman (129) and Wiseman et al. (131) have, respectively, applied
the Hertz Theory of Plates and the Hogg Model to evaluate two-layered
flexible pavements using surface deflection basins. The Hertz theory is