Page 84 - SAPEM-Chapter-10-2nd-edition-2014

South African Pavement Engineering Manual
Chapter 10: Pavement Design

Discussion of Complexities of Response Models
The continuum mechanics model used for pavement materials is the homogenous, isotropic, linear-elastic model.
See Chapter 2, 3 and 4.2 for a description of this model and further discussion.

The system response for continuum mechanics models is done using integral transformation or finite element
techniques.
• Integral transformation techniques are based on closed form integral solutions of the displacement,
strain and stress of layered systems. These solutions are derived from classic elasticity theory for layered
systems of simple geometry and basic load types.
• Finite element solutions model the pavement system as a number of separate but interconnected
elements. Finite element solutions can accommodate more complex geometry, including pre-defined cracks
in the pavement system, as well as non-linear material models.

Both solutions consider conditions of equilibrium and compatibility as well as the boundary conditions of the
problem, to solve the internal displacement, strain and stress for a given external load. These system models
are also based on static or dynamic response analyses, although static response models are much more
common.

Static response analysis assumes that the load is applied to the system for such a long period that the response
of the system comes to rest. Although there are internal displacements in the system and therefore
displacement at the boundaries of the system, these displacements are constant and the velocity and
acceleration of all points within the system are zero. The external load, is therefore, only resisted by the
stiffness of the system.

Dynamic response analysis incorporates the effects of load magnitude variation, movement of the point of load
application and the dynamic response of the system to the changing load conditions. The load characteristics
therefore change continuously, and the system reacts dynamically and has not come to rest. The damping and
inertia of the system therefore needs to be included in the response, in addition to the system stiffness.

The best known, and most often used, response model is the integral transformation solution for the static
analysis of a homogenous, isotropic multi-layered, linear-elastic system subjected to a circular load of uniform
contact pressure. This solution is available in the pavement engineering industry in a number of software
packages, the most common being the older BISAR, ELSYM5, CHEV15 and WESLEA and the more recent Cyrano
200, ME-Pads, and Rubicon Toolbox (see Section 7.10).

Section 6: Structural Capacity Estimation
Page 73