Page 232 - MODELING OF ASPHALT CONCRETE

210 Cha pte r Ei g h t

Often the RM is used simply as a parameter (modulus) to evaluate, for example, the
vertical deflection in a pavement. The RM can be used to characterize the stress-strain
behavior of a material in the resilient state by using mathematical functions such as
hyperbola, parabola, and (combination of) exponential functions (Witczak and Uzan
1988; Huang 1993; Lytton et al. 1993; Desai 2001). Then, it can be implemented as a
nonlinear or piecewise linear elastic model in a solution (finite element) procedure,
which can yield stresses and strains. Such quantities can be used in empirical formulas
for various distresses; for example, in the M-E approach, Fig. 8-1(b). A finite element
procedure with the piecewise nonlinear RM approach with interface and infinite
elements is developed by Desai (2000a) for incorporation in the NCHRP 1-37A
Mechanistic-Empirical Pavement Design Guide (NCHRP 2004). Details of RM are given in
various publications and other chapters. Some comments are given below.

Comments

1. Poisson’s Ratio. When M is used in the context of nonlinear elasticity, it can
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take the place of the traditional tangent elastic modulus E . Then for isotropic
t
materials, Poisson’s ratio n can be assumed constant or can also be expressed as
a function of stress (Lytton et al. 1993). In the nonlinear elastic formulation, the
behavior of the material is still treated as elastic during each increment of
loading. Hence, in the context of the theory of elasticity, the value of Poisson’s
ratio needs to be less than 0.5; otherwise, the formulation will collapse due
to the singularity in the stress-strain matrix (Desai et al. 1984; Desai and
Kundu 2001).
2. Efforts have been made to express strain ratio (lateral strain e to the axial
3
strain e ), the value of which may be greater than 0.5. Indeed, such a ratio can
1
be termed as Poisson’s ratio only up to the behavior when n < 0.5, that is, only
t
during the contractive (volume) state and before dilation. Such formulations in
the context of linear elastic theory may not be realistic. Theories such as
plasticity can be used to accommodate the (dilative) behavior. More details
regarding the Poisson’s ratio of asphalt concrete are presented in Chap. 3.
3. Since M is defined usually based on uniaxial (triaxial) tests, it is valid mainly
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for the calculation of uniaxial (vertical) strains and displacements.
4. When M is employed in the incremental nonlinear analysis, it represents a
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piecewise linear elastic model. Hence, it is not capable of accounting for the
plastic or irreversible deformations.
5. When M is used as an elastic modulus, it is tacitly assumed that the material is
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isotropic. In other words, M may not allow for anisotropic behavior.
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6. The resilient modulus is evaluated from the tests that involve only one stress
path; for example, conventional triaxial compressions (CTC) in triaxial testing
(Fig. 8-3). However, a real pavement can experience different stress paths under
the wheel load. Hence, the RM approach is valid only for one stress path, and
it will need different sets of material parameters for different stress paths.
Hence, it may not provide accurate predictions for the real situations.
7. The bound (asphalt, concrete) and unbound (subbase, base, and subgrade) geologic
materials experience volume change response under shear stresses caused by