The above methods define stiffness as a function of stress alone. Full incorporation of the effects of moisture (as a pressure or suction) should necessitate use of an effective stress framework (see Section 9.5). However a more simple approach, at least in principle, is to adjust the stiffness value calculated by one of the above relationships using a factor that is dependent on the moisture (and, perhaps, other) condition. The AASHTO ‘Mechanistic-Empirical Pavement Design Guide’ (MEPDG) takes this approach, though it’s attention to many details makes the implementation rather complex (ARA, 2004). In this approach, the reference stiffness value, Mropt (the value of Mr at optimum conditions), is adjusted by a factor, Fenv, to allow for different environmental effects, with the value of each factor being computed for each of a range of depths, lateral positions and time increments. For moisture the adjustment factor is based on the equation
Mr
Mr oP^ min
Where km is a material parameter and Sr and Sropt = the actual saturation and the saturation ratio at optimum conditions, respectively. The actual saturation value is obtained from the use of the Soil Water Characteristic Curve (SWCC) see Chapter 2, Section 2.7.1. Other adjustments are included in the Fenv factor to allow for freezing, thawing and temperature. The full approach is too detailed to include here. Interested readers are directed to the relevant report (ARA, 2004).
Long et al. (2006) take another approach, relating modulus to suction and water content rather than to saturation ratio, but still including some stress influence:
(p — 0 ■ 5) + ^t34^ (1 + V)(1 — 2v)
Yh(0.435) (1 — v)
where p is the mean normal stress on the element of soil, 0 and w are the volumetric and gravimetric water contents, respectively, 5 is the matric suction pressure, S0 is the slope of the soil desorptive curve (the rate of change of the logarithm of 5 with the logarithm of 0), Yh is the suction volumetric change index (an indicator of the sensitivity of volume change to change in matric suction) and v is Poisson’s ratio.
