Analytical Models

A few material models have been proposed for the development of plastic strains in unbound granular materials in a pavement structure. Lashine et al. (1971), and Barksdale (1972) tested unbound granular material in a repeated load triaxial test for 100 000 cycles. They found that the permanent axial deformation, єpb at different

stress states is proportional to number of load cycles, N (Fig. 9.4). Since 1971, many analytical models have been developed and most of them are listed by Lekarp and Dawson (1998).

However, these models have never been used with finite element (FE) calcula­tions except the Hornych model (Hornych et al., 1993) which has been used with a simplified finite element calculation by de Buhan (Abdelkrim et al., 2003) for a railway track construction and by Hornych et al. (2007) for a full scale flexible pavement.

The mechanical processes that form the basis of a flexible pavement’s perfor­mance and of a flexible pavement’s deterioration can be separated into two cate­gories, namely:

(i) short-term mechanical processes; and

(ii) long-term mechanical processes.

The first category concerns the instantaneous behaviour of a flexible pavement, as activated during the passage of a vehicle, thus the flexible pavement behaviour can be studied by means of (visco)elastic models. de Buhan (Abdelkrim et al., 2003) and Hornych et al. (2007) use, respectively, linear moduli with a Boussinesq stress analysis and the modified Boyce models with a simple FE analysis for the short term behaviour. The second category concerns the mechanical processes, typically characterized by a quasi-static time-dependency, such as long-term settlements un­der a large number of vehicle axle passages. Together, the approach requires the following parameters:

• Elastic behaviour: E, v or Ka, Ga, у and n.

• Plastic behaviour:

о Rupture (i. e. shear failure) parameters: m, s.

p0

о Plasticity parameters: e B and n.

The Hornych model is another formulation of the Paute model (Paute et al., 1988) which was adopted also in an European norm — EN 13268-7 (CEN, 2000). Some other alternatives were suggested in Lekarp and Dawson (1998), but no overall framework has been established yet to explain completely the behaviour of unbound granular materials under complex repeated loading.