Mechanics is the science of motion and the action of forces on bodies.  Thus, a mechanistic approach seeks to explain phenomena only by reference to physical causes.  In pavement design, the phenomena are the stresses, strains and deflections within a pavement structure, and the physical causes are the loads and material properties of the pavement structure.  The relationship between these phenomena and their physical causes is typically described using a mathematical model.  Various mathematical models can be (and are) used; the most common is a layered elastic model.

Along with this mechanistic approach, empirical elements are used when defining what value of the calculated stresses, strains and deflections result in pavement failure.  The relationship between physical phenomena and pavement failure is described by empirically derived equations that compute the number of loading cycles to failure.

The basic advantages of a mechanistic-empirical pavement design method over a purely empirical one are:

The benefit of a mechanistic-empirical approach is its ability to accurately characterize in situ material (including subgrade and existing pavement structures).  This is typically done by using a portable device (like a FWD) to make actual field deflection measurements on a pavement structure to be overlaid.  These measurements can then be input into equations to determine existing pavement structural support (often called "backcalculation") and the approximate remaining pavement life. This allows for a more realistic design for the given conditions.

This section describes the basics behind flexible pavement mechanistic-empirical design to include:

4.1 Mechanistic Model

Mechanistic models are used to mathematically model pavement physics.  There are a number of different types of models available today (e.g., dynamic, viscoelastic models) but this section will present two, the layered elastic model and the finite elements model (FEM), as examples of the types of models typically used.  Both of these models can easily be run on personal computers and only require data that can be realistically obtained.

4.1.1 Layered Elastic Model

A layered elastic model can compute stresses, strains and deflections at any point in a pavement structure resulting from the application of a surface load.  Layered elastic models assume that each pavement structural layer is homogeneous, isotropic, and linearly elastic.  In other words, it is the same everywhere and will rebound to its original form once the load is removed.  The origin of layered elastic theory is credited to V.J. Boussinesq who published his classic work in 1885.  Today, Boussinesq influence charts are still widely used in soil mechanics and foundation design.  This section covers the basic assumptions, inputs and outputs from a typical layered elastic model.

4.1.1.1 Assumptions

The layered elastic approach works with relatively simple mathematical models and thus, requires some basic assumptions.  These assumptions are:

4.1.1.2 Inputs

A layered elastic model requires a minimum number of inputs to adequately characterize a pavement structure and its response to loading. These inputs are:

Figure 6.4 shows how these inputs relate to a layered elastic model of a pavement system.

4.1.1.3 Output

The outputs of a layered elastic model are the stresses, strains, and deflections in the pavement:

The use of a layered elastic analysis computer program will allow one to calculate the theoretical stresses, strains, and deflections anywhere in a pavement structure.  However, there are a few critical locations that are often used in pavement analysis (see Table 6.1 and Figure 6.5).

Table 6.1: Critical Analysis Locations in a Pavement Structure

Figure 6.5: Critical Analysis Locations in a Pavement Structure

4.1.2 Finite Elements Model

The finite element method (FEM) is a numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems.  Although originally developed to study stresses in complex airframe structures, it has since been extended and applied to the broad field of continuum mechanics (Huebner et al., 2001).  In a continuum problem (e.g., one that involves a continuous surface or volume) the variables of interest generally possess infinitely many values because they are functions of each generic point in the continuum.  For example, the stress in a particular element of pavement cannot be solved with one simple equation because the functions that describe its stresses are particular to its specific location.  However, the finite element method can be used to divide a continuum (e.g., the pavement volume) into a number of small discrete volumes in order to obtain an approximate numerical solution for each individual volume rather than an exact closed-form solution for the whole pavement volume.  Fifty years ago the computations involved in doing this were incredibly tedious, but today computers can perform them quite readily.

In the FEM analysis of a flexible pavement, the region of interest (the pavement and subgrade) is discretized into a number of elements with the wheel loads are at the top of the region of interest (see Figure 6.6).  The finite elements extend horizontally and vertically from the wheel to include all areas of interest within the influence of the wheel. 

4.1.2.1  Assumptions

The FEM approach works with a more complex mathematical model than the layered elastic approach so it makes fewer assumptions.  Generally, FEM must assume some constraining values at the boundaries of the region of interest.  For instance, the computer program developed by Hongyu Wu and George Turkiyyah at the University of Washington (Wu, 2001), called EverFlex, uses a 6-noded foundation element to model the Winkler Foundation.  This program also uses free boundaries on the four sides of the flexible pavement model.  Additionally, the choice of element geometry (size and shape) as well as interpolation functions will influence overall model performance.

4.1.2.2  Inputs

The typical finite elements method approach involves the following seven steps (Huebner et al., 2001):

1. Discretize the Continuum.  The region of interest is divided into small discrete shapes.
2. Select Interpolation Functions.  Nodes are assigned to each element and then a function is chosen to interpolate the variation of the variable over the discrete element.
3. Find the Element Properties.  Using the established finite element model (the elements and their interpolation functions) to determine matrix equations that express the properties of the individual elements.
4. Assemble the Element Properties to Obtain the System Equations.  Combine the matrix equations expressing the behavior of the elements and form the matrix equations expressing the behavior of the entire system.
5. Impose the Boundary Conditions.  Impose values for certain variables at key boundary positions (e.g., the bottom and sides of the chosen region of analysis).
6. Solve the System Equations.  The above process results in a set of simultaneous equations that can then be solved.
7. Make Additional Computations If Desired.  The unknowns are displacement components.  From these displacements element strains and stresses can be calculated.

4.1.2.3  Outputs

The outputs of a FEM analysis are the same as for a layered elastic model:

In addition, the finite elements method allows for extremely powerful graphical displays of these values (see Figures 6.7 through 6.10).

Figure 6.7: 3-D Strain Diagram	Figure 6.8: Surface Strain Diagram	Figure 6.9: Section View Strain Diagram	Figure 6.10: Sample Load Profiles
Screen Shot Thumbnails from EverFlex (Wu, 2001).  Click on each thumbnail to see a larger version of the picture.

4.2 Failure Criteria (or Transfer Functions)

The main empirical portions of the mechanistic-empirical design process are the equations used to compute the number of loading cycles to failure.  These equations are derived by observing the performance of pavements and relating the type and extent of observed failure to an initial strain under various loads.  Currently, two types of failure criteria are widely recognized, one relating to fatigue cracking and the other to rutting initiating in the subgrade.  A third deflection-based criterion may be of use in special applications.  Note that since these failure criteria are empirically established, they must be calibrated to specific local conditions and are generally not applicable on a national scale.

4.2.1 Fatigue Failure Criterion

Many equations have been developed to estimate the number of repetitions to failure in the fatigue mode for asphalt concrete.  Most of these rely on the horizontal tensile strain at the bottom of the HMA layer (e_t) and the elastic modulus of the HMA.  One commonly accepted criterion developed by Finn et al. (1977) is:

The above equation defines failure as fatigue cracking over 10 percent of the wheelpath area.  Figure 6.11 shows the relationship between tensile strain in the asphalt concrete and the number of cycles to failure for two levels of asphalt concrete elastic modulus.  This relationship assumes bottom-up cracking rather than top-down cracking.

4.2.2 Rutting Failure Criterion

Rutting can initiate in any layer of the structure, making it more difficult to predict than fatigue cracking.  Current failure criteria are intended for rutting that can be attributed mostly to a weak pavement structure.  This is typically expressed in terms of the vertical compressive strain (e_v) at the top of the subgrade layer:

The above equation defines failure as 12.5 mm (0.5-inch) depressions in the wheelpaths of the pavement.  Figure 6.12 illustrates how the vertical compressive strain relates to the number of cycles to failure.

4.2.3 Deflection Failure Criterion

A number of deflection based criteria have been developed by various agencies over the last 40 years or so.  The AASHO Road Test and Roads and Transportation Association of Canada (RTAC) criteria are shown here.  Both these criteria were developed based on spring seasonal deflections.

4.2.3.1  AASHO Road Test Criterion

The AASHO Road Test results were used to develop the following relations (Highway Research Board, 1962b):

This criterion was based on data from Loops 2 through 6 and single axle loads of 6, 12, 18, 22.4, and 30 kips (1 kip = 1,000 lbs.). The following equation is obtained if L₁ = 18,000 lbs. (a standard ESAL):

4.2.3.2 Roads and Transportation Association of Canada (RTAC) Criterion

The RTAC criterion can be calculated as follows (after RTAC (1977) and Haas et al. (1994)):

Table 6.2 shows the limiting deflections for both criteria:

Table 6.2: Limiting Deflections

4.3  A Mechanistic Computer Program

The Washington State DOT has developed a layered elastic-based software package called the Everseries Pavement Analysis Programs (Sivaneswaran, Pierce and Mahoney, 2001).  Everseries (for short) contains three independent programs:

1. Layered elastic analysis (Everstress)
2. FWD pavement modulus backcalculation (Evercalc)
3. Flexible pavement overlay design (Everpave)

To install the Everseries programs on your computer, click the install icon below:

The Everseries Pavement Analysis Programs can also be downloaded from the Washington State DOT Materials Lab at: http://www.wsdot.wa.gov/biz/mats.   Volume 3 of the WSDOT Pavement Guide (WSDOT, 1998) is available at the same site for download and contains detailed instructions on how to run the Everseries programs.