# Pavement models

The basis of any mechanistic pavement design method are the structural pavement models employed. Sound understanding of it’s basic principles and limitations is mandatory.

Pavers ® contains a linear elastic multi layered model, which allows for the assessment and design of flexible pavement. The layers are isotropic except for the bottom layer where anisotropy is addressed by different moduli in the horizontal and vertical direction. The interface between two adjacent layers can be varied between full friction to full slip using the classic BISAR or Van Cauwelaert’s WESLAY definition.

Pavers® uses closed form integral solutions to model a concrete multi slab-on-grade as a classical Westergaard slab on a Pasternak foundation. This model overcomes the classical discrepancy between the Westergaard-Winkler (joints) model and the layered elastic Burmister model (no joints). By using closed formed solutions, it is possible to calculate the response of multiple loads placed at random positions on a slab, thus overcoming the ESWL and pass-to-load repetition ratio concept for rigid pavements.

### Rigid pavement

The rigid pavement is modelled as a slab on-grade system. The Pasternak two-parameter foundation was chosen as an attractive alternative for the classical Winkler (k) foundation. The introduction of a horizontal linkage, Pasternak's shear constant (G), in Winkler's model is a remedy for the discrepancies between Westergaard's theory and the multilayer theory, while the great advantages of Westergaard's model (edge and corner loading) are maintained (for G=0, one obtains a classical Winkler foundation). The model allows for load transfer at the slab edge. The rigid pavement model allows (back-)calculation not only at the interior position, but also on the slab’s edge position. Multiple loads can be placed anywhere on the slab. The closed form mathematical solving technique allows the use of multiple placed at random positions on a slab, overcoming the ESWL concept which can be considered as one of the major drawbacks of the Westergaard model.

The Westergaard model is often used for cemented bases too. This conflicts with Westergaards assumption based on the theory of thin plates: thin against other dimensions means a two-layered structures only (slab on an infinite subgrade). However, McCoullough’s transformation by computing an equivalent k-modulus is often used, but is only valid when the modulus of the layered materials is far smaller than the Young’s modulus of the concrete. This is obviously not the case when using cemented bases. A muli-layered slab model should be used instead. Van Cauwelaert’s multi-slab model is based in equivalency of elasticity and allows partial friction at the interfaces of adjacent layers.

### Flexibele pavement

The flexible multi-layer model in Pavers ® is a classical linear elastic Burmister multi-layered structure. The layers are isotropic except for the bottom layer where anisotropy is addressed by different moduli in the horizontal and vertical direction. The interface between two adjacent layers can be varied between full friction to full slip using the BISAR or WESLAY definition.

### Pavement performance and fatigue

No matter how good the pavement and load models might be, mechanistic-empirical data is still required to tie the life of a pavement to the computed stress or strain response. Pavers ® implements a rigorous rigid and flexible pavement design methodology that incorporates the use of state-of-the–art pavement material properties and performance models. The tool calculates the cumulative damage induced by the whole traffic spectrum comprising any combination of types and configuration. The system includes the ameliorating effect of wander through a user defined standard deviation. The program library contains suggested values.

It is important to carefully calibrate the function so that the predicted distress can match with field applications. The software tool contains a library of state-of-the-art fatigue transfer functions (performance relationships) taken from literature including all popular models. Transfer functions are available for subgrade, base material, cemented and bitumen bound materials. Mechanistic-empirical calibration can be done by using calibrated transfer functions which relate critical stresses and strains in a multi-layered flexible or rigid pavement structure to an allowable number or load repetitions. Implementation of these calibrated transfer functions into modern software tools and pavement design and assessment methodologies will ultimately lead to even better pavement designs and predictions. The tools are available and can assist airport authorities and responsible pavement engineers to make structural pavement condition a practical and managerial pavement parameter.

The PAVERS tools do not dictate a certain design methodology, but allows the pavement engineer to define or use calibrated failure criteria for all pavement materials. If fatigue relationships exist of these materials, then this information can be entered quite smoothly into one of the program’s subroutines. Hence, the effect of different pavement materials, strengths, loads or complex load mixes can quickly be explored.