As depicted in Fig.
1, MC-based constitutive material models are used in a two-dimensional plane–strain linear elastic [Eq. (
1)] model (henceforth referred to as the
elastic model) to provide shrinkage-induced strain (
), modulus (
), and strength (
) for a specific MC level via Eqs. (
2), (
4), and (
5), respectively. The elastic model simulates and compares maximum shrinkage stresses (
) to predicted strength (
); if
, then MC is further reduced to simulate the subgrade drying process. The process is repeated until the threshold is reached. The locations of the top 50 most critical stress points and critical MC thresholds for crack initiation (
) are identified. The elastic model was developed in
MATLAB and linked to the
ExSPRS program. Mesh generation and optimization were automated so that pavement engineers would not have to spend time on FEA modeling details but rather focus on analyzing the results. Once a crack starts in a subgrade (
), a more sophisticated nonlinear plastic–elastic model (referred to as a
fracture model) developed in commercial FEA software is used to further study crack propagation within pavement layers. [Wanyan et al. (
2008a) provides FEA developmental details.] The fracture toughness (
) and the stress intensity factor (
) for Mode I fracture (
Griffith 1921;
Irwin 1957) are used as crack propagation criteria to further examine whether the initial shrinkage crack is stable or whether it will propagate through the pavement structure by
where
= dimensionless parameter also referred to as a
geometric factor. As its name implies,
depends on the geometries of both the specimen and the crack. Parameter
is the through-thickness crack length;
is the (remotely, not on crack tip) applied stress. Parameters
and
can be compared using the same Eq. (
6) but different applied linear tensile stresses (
versus
) and different geometry factors (semi-infinite subgrade vs. four point bending test dimensions) respectively. When
, the crack is stable and will not grow. The controlled parameter MC is then further reduced. On the other hand, however, when
, the crack will start to propagate upward. The progression of the initial shrinkage crack is critical to the development of the surface longitudinal crack. The fracture model identifies the other threshold (
) at which the cracks will grow through pavement layers and appear at the surface. The final outputs of the LSC model include the two moisture thresholds
and
and the coordinates of the critical locations for longitudinal cracking.
The two FEA models were set up using the same geometry to present typical low-volume pavement sections consisting of a HMA layer over a flexible base, an optional subbase, and a subgrade. Because of the symmetry, a half-width 3.66-m (12-ft) wide pavement with a 1.22-m (4-ft) wide shoulder was studied to reduce calculation efforts. The pavement shoulder was modeled as a uniform block fully bounded at the pavement interface. As few as three layers and as many as five layers can be introduced into the FEA models. Pavement layers were assumed to be homogeneous and isotropic.