27.5.2. Mechanistic model

Mechanistic models are used to mathematically model pavement physics.

Mechanistic models are important tools in understanding how pavements behave. They allow engineers to simulate the physical actions within a pavement under different conditions. These models focus on understanding the stresses, strains, and deformations that occur when loads are applied to the pavement. By using these models, engineers can predict how the pavement will respond over time.

Think of a mechanistic model like a video game simulation where each action has a reaction. Just like in a game where you see how a character responds to obstacles, mechanistic models help see how a pavement 'responds' to the weight of vehicles driving over it.

There are a number of different types of models available today (e.g., layered elastic, dynamic, viscoelastic) but this section will present the layered elastic model.

This section focuses on the layered elastic model, which is one of the simplest and most commonly used models in pavement design. A layered elastic model assumes that each layer of the pavement structure is uniform in material properties (homogeneous), behaves the same in all directions (isotropic), and can return to its original shape after a load is removed (linearly elastic).

Imagine a stack of pancakes. Each pancake represents a layer of the pavement. Just as each pancake has its own thickness and consistency, each layer of the pavement has different properties. The way the pancakes bend under weight can help us visualize how each layer of the pavement behaves under pressure.

A layered elastic model can compute stresses, strains and deformations at any point in a pavement structure resulting from the application of a surface load.

The layered elastic model works by calculating how a surface load affects each layer of the pavement. When a vehicle drives over the road, it exerts a load that causes stresses and deformations in the layers below. The model computes these changes to determine how much the pavement will bend or compress at different points, helping engineers design roads to withstand expected traffic loads.

Consider stepping onto a trampoline. Where you step (the surface load) causes the trampoline fabric (the pavement layers) to stretch and sag beneath you. The layered elastic model is like calculating how much the trampoline will sag based on where and how hard you jump.

The layered elastic approach works with relatively simple mathematical models and thus requires the following assumptions: Pavement layer extends infinitely in the horizontal direction; The bottom layer (usually the subgrade) extends infinitely downwards; Materials are not stressed beyond their elastic ranges.

For the layered elastic model to be effective, there are certain foundational assumptions. First, it's assumed that the pavement layers stretch out infinitely sideways, meaning they cover a large area with uniform conditions. Also, the subgrade (the soil beneath the pavement) is considered to extend infinitely downward, ensuring that the load distribution is well modeled. Lastly, it is crucial that the materials used in the pavement are not pushed beyond their elastic limits, which means they should revert to their original shape after the load is removed.

Think of a sponge. If you press down on it slightly, it will return to its original shape. However, if you squeeze it too hard, it might never fully return to how it was. In pavement design, we want to ensure that we are not squeezing our materials too hard, just like with the sponge.

A layered elastic model requires a minimum number of inputs to adequately characterize a pavement structure and its response to loading. These inputs are: Material properties of each layer, like modulus of elasticity (E), Poisson’s ratio (ν); Pavement layer thicknesses; Loading conditions which include the total wheel load (P) and load repetitions.

To run a layered elastic model properly, several key inputs are necessary. These include specific material properties of each layer making up the pavement, such as how flexible (modulus of elasticity) and how susceptible to deformation (Poisson’s ratio) the materials are. Additionally, the thickness of each layer and the conditions of the load (the total weight from the vehicles and how many times that weight is applied) are essential to effectively model the pavement's response.

It's like baking a cake. To get the perfect cake, you need the right ingredients (material properties), the correct layers (how thick each layer of batter is), and the right baking conditions (load repetitions). If one of these elements is off, the cake might not turn out well, similar to how a road won't perform properly without the right inputs.

The outputs of the layered elastic model are the stresses, strains, and deformations in the pavements. Stress refers to the intensity of internally distributed forces experienced within the pavement structure at various points. Strain is the unit displacement due to stress, usually expressed as a ratio of change in dimension to the original dimension. Deformation is the linear change in dimension.

After running a layered elastic model, the results will provide critical outputs: stress, strain, and deformation. Stress tells us the internal forces acting on the pavement layers; strain indicates how much the material changes shape in response to that stress; deformation quantifies the actual changes in dimensions of the pavement. Understanding these outputs helps engineers assess the potential for failure or wear in the pavement.

Imagine stretching a rubber band. Stress would be the force you apply to stretch it, strain would be how much it stretches relative to its original size, and deformation would be the actual length that the rubber band has changed to when observed. Each aspect is crucial to understanding how materials respond to applied loads.

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.

Failure criteria are important because they help predict when a pavement will fail under repeated traffic loads. The mechanistic-empirical design process uses observed data from pavements to create equations that determine how many load applications a pavement can handle before it reaches a failure state, whether that be due to cracking or deformation.

Think of it like testing how many times you can bounce a basketball before it stops bouncing effectively. By recording how many bounces it takes before the ball loses its ability to rebound, you can predict its longevity on the court. Similarly, failure criteria in pavement design help predict how many vehicles can drive over a road before it starts to show significant wear.

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