CalME is a pavement design program, for new pavement design as well as for rehabilitation design. CalME has three levels of design:
- Caltrans current empirical methods, the “R-value” method for flexible structures and the “Deflection Reduction” method for rehabilitation design,
- a “Classical” Mechanistic-Empirical design, largely based on the Asphalt Institute method, using ESALs and a weighted mean annual environmental condition, and
- an IRME model in which the materials properties are updated in terms of damage for each time increment, using the “time hardening” approach, and used (recursively) as input to the next time increment. This approach predicts the pavement conditions at any point in time during the pavement life.
The IRME mode may also be used to simulate HVS tests or sections from test tracks. For this mode the climatic conditions and the loading during the test is imported into the CalME database. Temperatures measured at different depths and the number of applications of different loads and their load levels, are imported for each hour of the test. This data is used by CalME to determine the layer parameters and for calculating the response, for each one hour increment of the simulation. For the simulations described here the response model LEAP was used (Symplectic Engineering
Corporation, 2004). LEAP allows partial slip between the layers, which was observed at a number of the test sections.
The measured pavement response (resilient deflections at different depths in this case) and the permanent deformations are also imported, so that the results of the simulation can be quickly compared to actual test data. If backcalculated layer moduli from FWD testing are available, this may also be imported into the database for comparison to simulated values.
Some of the sub-models used in CalME are briefly described in the following.
Master curve for Asphalt Materials
The master curve was determined from frequency sweep tests supplemented by FWD testing. The format used for the master curve is the same as used in the MEPDG (NCHRP, 2004). For intact asphalt the format is:
Equation 1: Asphalt modulus versus reduced time
| Where |
Ei is the modulus in MPa,
tr is reduced time in seconds and
α, β, γ, and δ are constants determined from frequency sweep tests.
Log is the logarithm to base 10. |
Reduced time is found from:
Equation 2: Reduced time as a function of loading time and viscosity
| Where |
lt is the loading time (in sec),
viscref is the binder viscosity at the reference temperature,
visc is the binder viscosity at the present temperature, and
aTg is a constant. |
Damage to asphalt materials
During HVS testing the resilient deflections normally show a considerable increase. An example is shown in Figure 1. The initial deflection, under a 40 kN load, is a little more than 0.2 mm, whereas the deflection (under the same wheel load) is at about 0.9 mm towards the end of the test. This means that the pavement response is changing dramatically during the test. It is essential that the damage causing this change in response is captured in the simulation, otherwise there would be no purpose in trying to calibrate the empirical sub-models for predicting pavement performance.
For damaged asphalt concrete the modulus was determined from:
Equation 3: Modulus of damaged asphalt concrete (variables same as in Equation 1)
where the damage, ω, was calculated from:
Equation 4: Damage as a function of loads, strain, modulus and temperature
| Where |
MN is the number of load applications in millions,
με is the tensile strain at the bottom of the asphalt layer,
E is the modulus,
t is the temperature in ºC,
μεref is a reference constant with 200 μstrain value,
Eref is a reference constant with 3000 MPa value, and
A, α, β, γ, and δ are constants (not related to the constants of Equation 1) |
Figure 1: Example of increase in resilient deflection during HVS test.
The constant γ in Equation 4 was assumed equal to β/2, making damage a function of the strain energy. The parameters of Equation 4 were determined from four point beam, controlled strain, fatigue testing, by minimizing the Root Mean Square (RMS) of the difference between the measured modulus and the modulus calculated from Equation 3. The minimization was done in Excel using Solver.
Permanent deformation of asphalt materials
Permanent deformation of the asphalt may be caused by post compaction of the material or by shearing. The post compaction is normally small and is assumed to be proportional to the reduction in air voids. In CalME it may be imposed during the initial loading phase. The shear deformation is more important and is determined using a shear-based approach, developed by Deacon et al. (2002). The phenomenon is roughly illustrated by Figure 2, where the triangular area slides downwards pushing material outwards and upwards.
The permanent, or inelastic, shear strain, γi, will depend on the shear stress,τ, the elastic shear strain, γe, and the number of load repetitions. The relationship is determined from Repeated Simple Shear Tests at Constant Height (RSST-CH) in the laboratory. The best fitting relationship for the materials used was found to be a gamma function:
Equation 5: Gamma function for permanent shear strain.
| Where |
γe is the elastic shear strain,
τ is the shear stress,
N is the number of load repetitions,
τref is a reference shear stress (0.1 MPa), and
A, α, β, and γ are constants determined from the RSST-CH. |
Figure 2: Illustration of shear deformation.
The permanent deformation of the asphalt is calculated from:
Equation 6: Calculation of permanent deformation.
| Where |
K is a calibration factor determined from HVS testing,
hi is the thickness of layer i, and
γii is the permanent (inelastic) shear strain in layer i.
The summation is done for the top 100 mm of the asphalt. |
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