Modelling of layered system

The layered system of pavement structure consists of layers of asphalt at the surface supported by high quality granular materials. The granular layers transfer the tyre load to the subgrade materials.

In reality, asphalt materials illustrate complex viscoelastoplastic behaviour. In this research the focus of modelling is on the UGM. As AC layers always have far stiffer properties, it is not unrealistic to assume linear behaviour for this layer. In practice there may be several layers on the surface consisting of different asphalt materials, but in this modelling all of the asphalt layers are assumed to be a single structural layer whose behaviour is linear elastic. This simplification enables a clearer investigation of UGM behaviour.

150 The granular layer lies beneath the structural layer (AC) and transfers the tyre load to the existing layer (SG). It is usually made up of two layers of UGM called base and subbase. With respect to design and cost, the differences between these layers are meaningful, but for the purpose of analyzing their mechanical behaviour, the differences are negligible. Therefore, in this simulation all granular layers beneath the AC are assumed to have the same mechanical behaviour.

The final layer is the existing subgrade, which can vary from being strong bedrock to a very soft clay layer. Therefore, two extreme cases are considered for this layer.

4.3.1 Plane strain, Axisymmetric and Three Dimensional Analysis

Figure 4.1 demonstrates the difference between plane strain, axisymmetric and 3-D models.

As described in Chapter 2, the three major geometrical aspects of modelling are formulation, model dimension and mesh distribution.

As the results of analysis indicate (see Chapter 5) the simulation of pavement layers in plane strain leads to a considerably conservative design. Therefore, after a comparison of the three types of modelling, plane strain modelling was ignored for the rest of simulation.

The results of the axisymmetric and 3-D analysis were quite close, and with respect to the computational efficiency provided by axisymmetric formulation, this type of modelling is preferable. However, the main disadvantage of axisymmetric modelling is its restriction for modelling multiple axles and tyres.

151 For this reason, the axisymmetric model was used in verification modelling (simulating the results of a triaxial test) or the loading of a single circular tyre on the pavement. The main simulation undertaken in the current study was conducted using full 3-D modelling.

Figure 4.1 - Axisymmetric, Plane Strain and 3D Model

152 Regarding the model’s dimensions, a series of analyses were conducted to investigate the influence of the model’s limits and boundary conditions on the critical response of the pavement in the studied area. The results of the FEM were compared against the results calculated by the CIRCLY and KENLAYER programs which are based on analytical solutions. Proper model dimensions were then chosen for each case of axisymmetric and 3-D simulation.

For the dynamic analysis, a set of boundary elements (described in Chapter 3) was used to eliminate the wave reflection phenomenon in the simulated medium.

However, to achieve greater accuracy, the limit of the models was set to be further than what was calculated in the static analysis.

While there are unlimited possibilities for layer composition, the general mechanical behaviour of pavement structure can be categorized as either thin asphalt layer or thick asphalt layer. The thickness of the UGM layer is then determined according to the thickness of the AC layer. In this regard, two typical thickness compositions were selected to study the different mechanical responses of pavement structure.

The first composition was a thin layer of asphalt concrete lying on a thicker layer of UGM supported by SG. The second model simulated a relatively thick layer of asphalt on a thinner layer of aggregates. Since the subgrade layer is supposed to be the final layer included in the simulation, sufficient depth is selected to eliminate the effects of boundary conditions.

4.3.2 Interface Element

153 Layer interaction can play a role when a dynamic analysis is considered. In dynamic analysis the difference between the responses of layers with different materials can produce inconsistencies in load translation between structural and granular layers.

The interface of layers with different material behaviour can have a meaningful effect on the final mechanical response of those layers. This effect is of interest to researchers and is called the ‘soil-structure interaction’ effect. The phenomenon has a greater effect if the materials’ mechanical properties are significantly different.

Where two different layers are assumed to stick together roughly, their deformation is the same in the shared area. However, in reality, the deformation of asphalt layer in respect to the granular layer depends on the mechanical behaviour of their interface. This interface may demonstrate a cohesive behaviour, a frictional behaviour or a roughly joined behaviour.

The AC-UGM interaction is induced for two main reasons. First of all, the stiffness of the layers (elastic modulus and Poisson ratio) is different. This difference leads to stress concentration on the interface layers. The second reason is the difference between the constitutive models used for AC and UGM. While the AC layer is assumed to be linear elastic, a different nonlinear elastoplastic behaviour is employed for the UGM layer.

To consider the effects of layer interaction in dynamic loading, frictional interface behaviour was assumed between the AC and UGM layers. The interaction between the UGM and SG layers was not considered because the mechanical

154 behaviour of the two is very similar and there is little difference between the material properties.

Figure 4.2 illustrates the interface elements used in this study.

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Figure 4.2 - Interface Elements

Interface elements are elements with virtual thickness. This means that while their physical thickness is zero, they can have two different sets of nodes in one place.

Using this technique, variation between the deformation of two adjacent elements is possible. This variation induces interaction force which is transferred through the interface elements to both neighbour elements.