The modulus of stiffness of asphalt, by analogy with the modulus (E) of elastic solids, is the relationship between stress (σ) and strain (ε). However, the modulus of rigidity of a viscoelastic material depends on the loading time (t) and the temperature (T) (3). Therefore, the modulus of stiffness of asphalt can be determined by Equation 1:
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( 1 ) |
Where:
is the asphalt's modulus of stiffness at a given temperature and with a given load application time (frequency), in Pascals (Pa).
σ is the applied stress or load, in Pa.
is the deformation relative to the original dimensions due to the application of the load, for a given temperature and time (frequency). It is usually measured in percentage (%).
It is difficult to experimentally demarcate a viscoelastic solid from a viscoelastic fluid at a defined temperature, since the precise nature of the response depends on the loading rate (8). For very short load application times, the modulus of rigidity is practically constant and asymptotic towards 3 × 109 Pa, regardless of temperature. In these cases the asphalt behaves as an elastic solid. On the contrary, when the load application time is high or the temperature increases, the stiffness modulus decreases considerably, reflecting the viscous behavior of the asphalt. At the usual pavement service temperatures and under the usual traffic loads, the behavior can be generalized as viscoelastic (2).
The fact that a material exhibits viscoelastic fluid behavior at a given temperature and frequency, and simultaneously that same sample can exhibit viscoelastic solid behavior at the same temperature and at a much higher frequency is known as the principle of time-temperature superposition. and it is a fundamental property of viscoelastic materials. This rule is very useful because it allows us to study the nature of asphalt at frequencies that cannot be experimentally achievable and will be explored in greater depth later.
The fact that a material exhibits viscoelastic fluid behavior at a given temperature and frequency, and simultaneously that same sample can exhibit viscoelastic solid behavior at the same temperature and at a much higher frequency is known as the principle of time-temperature superposition. and it is a fundamental property of viscoelastic materials. This rule is very useful because it allows us to study the nature of asphalt at frequencies that cannot be experimentally achievable and will be explored in greater depth later.
Viscosity is a fundamental characteristic property of asphalt as it determines how it will behave at a specific temperature or range of temperatures. Viscosity is defined as a measure of the resistance to flow (shear or tensile stresses) due to internal friction between molecules (10). In asphalt, viscosity is affected inversely to temperature; the higher the temperature, the lower the viscosity.
In the fundamental way of measuring viscosity, the space between two planes movable relative to each other (straight as in parallel plates or curved as in concentric cylinders) is filled with asphalt. The force that opposes the movement of one of the planes due to the applied shear stress is developed solely due to the presence of the material. This force is proportional to the area and the relative speed of movement from one plane to another and inversely proportional to the distance between the plates. The constant that relates the variables is the viscosity, as shown in equation 2.
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( 2 ) |
Where:
FIn the fundamental way of measuring viscosity, the space between two planes movable relative to each other (straight as in parallel plates or curved as in concentric cylinders) is filled with asphalt. The force that opposes the movement of one of the planes due to the applied shear stress is developed solely due to the presence of the material. This force is proportional to the area and the relative speed of movement from one plane to another and inversely proportional to the distance between the plates. The constant that relates the variables is the viscosity, as shown in equation 2. In the fundamental way of measuring viscosity, the space between two planes movable relative to each other (straight as in parallel plates or curved as in concentric cylinders) is filled with asphalt. The force that opposes the movement of one of the planes due to the applied shear stress is developed solely due to the presence of the material. This force is proportional to the area and the relative speed of movement from one plane to another and inversely proportional to the distance between the plates. The constant that relates the variables is the viscosity, as shown in equation 2.
A is the surface between both planes that contains the fluid, in square meters (m2).
A is the surface between both planes that contains the fluid, in square meters (mA is the surface between both planes that contains the fluid, in square meters (mA is the surface between both planes that contains the fluid, in square meters (m
A is the surface between both planes that contains the fluid, in square meters (mA is the surface between both planes that contains the fluid, in square meters (m
A is the surface between both planes that contains the fluid, in square meters (m
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( 3 ) |
Where:
A is the surface between both planes that contains the fluid, in square meters (m
A is the surface between both planes that contains the fluid, in square meters (m
 |
For viscoelastic materials such as asphalt, the shear modulus is composed of a loss modulus (viscous component, G'') and a storage modulus (elastic component, G'), the relative magnitude of which determines how the material responds to loads. applied. The two components are linked to the complex modulus by the phase angle in a vector sum as shown in Figure 1. Therefore, the different components can be related using equation 4: |
