When evaluating backcalculation procedures it is important to be aware of the simplifications made in modeling the pavement structure.
Most of the procedures presently used are based on the following assumptions:
- the loading is static
- the materials are continuous and homogeneous
- the relationship between strain and stress follows Hooke's law, i.e. linear elastic
The Royal Dutch/Shell Laboratory in Amsterdam began studying pavement dynamics using a Road Vibration Machine in 1951.
Both dynamic deflections and wave propagation was used to determine the stiffness of different pavement layers 9,10).
The work of Lamb 11) was used by the Laboratoire Central des Ponts et Chaussées (LCPC) in France 12) and more recently the work of Kausel 13) has been used by several researchers 6,14,15).
Finite Element methods have also been used for dynamic analysis of road structures 16,17).
In spite of all the effort put into dynamic analysis it is not widely used at the present time. One of the reasons for this is the computational capacity required. Dynamic Finite Element analysis, for example, requires a main-frame computer. More importantly, however, are the additional parameters needed to characterize the materials. In a dynamic analysis the viscous and visco-elastic properties of the material ought to be considered, Poisson's ratio becomes more critical when using wave propagation, and the density of the different materials must also be known.
This leads to the second assumption, that the materials are continuous or compatible. All of the above mentioned methods are based on continuum mechanics, but few pavement materials are continuous. Most pavement materials are particulate in nature and even in asphalt at normal temperature the deformations due to elastic compression of the grains are negligible compared to the deformations due to sliding of the grains.
In well compacted granular materials volume expansion (dilation) often occurs under loading.
In a paper on plasticity in soils 18) Scott concludes:
"There has been a good deal of debate about unstable behavior that develops in association with volume expansions. Loading of such a soil is accompanied by local inhomogenities in the form of slip lines, shear bands, or "bifurcations", as they are now commonly called... It occurs in real soils in nature very frequently, is the source of many soil engineering problems, and so far is not represented by a single soil model.
At present, it is also difficult to see how a suitable model could be implemented in a finite element code, since each individual element must have the opportunity of developing shear bands as the loading progresses. Their position cannot be predicted in advance".
Since then more widespread use has been made of the Distinct Element Method or micromechanical modeling based on the work of Cundall and Strack 19,20).
This, however, puts an even larger strain on computing capacity and also requires knowledge of the grain to grain contact characteristics and on the influence of water or bitumen.
Even though the Distinct Element Method cannot be used for backcalculation in the foreseeable future, it may still be used to study the distribution of stresses and stains in granular materials, and possibly to modify methods based on continuum mechanics.
From the above it is already clear that the use of Hooke's law for pavement materials is very much a simplification of reality, and even that the development of other constitutive equations considering viscosity, non-linearity, or anisotropy may not be of much help.
In addition to the above it may be recalled that the pavement response also depends on the distance from the pavement edge (or a joint) and on the degree of cohesion or friction between pavement layers.
The materials characteristics and layer thicknesses also vary along the length and width of the pavement and with the depth in the subgrade, as well as with the climatic conditions (temperature, temperature gradient, moisture content and distribution, frost, etc.).
Even with all the shortcomings listed above it is still necessary to use backcalculation procedures.
The deterioration of pavements depends on the stresses and strains in the layers and in order to determine the critical stresses or strains the stiffnesses of the layers must be known.
Laboratory testing may be used for some materials, but are often expensive and not very reliable.
What is needed is a validation (and modification) of existing backcalculation procedures.
Some validation can be done by comparing moduli derived from backcalculation to moduli determined by laboratory testing, but only for a few bitumen or cement bound materials.
A thorough validation must be based on a comparison of stresses and strains derived from backcalculation to stresses and strains measured in the pavement layers.
Validation through comparison of measured and calculated stresses and strains (or deflections at multiple depths) is not a simple matter.
It has been attempted over a number of years at a number of locations, using a variety of instruments for measuring the in situ stresses and strains.
In some cases, such as that reported by Lenngren 21), very good correlation has been found.
A very interesting international experiment on measuring strain in bituminous layers was carried out at Nardo in Italy, under the sponsorship of the OECD 22).
With the renewed interest in full scale testing of instrumented pavements similar international experiments could prove very useful.
