Environmental Engineering Reference
In-Depth Information
suction zone, the intermediate zone, and the high-suction
zone of the SWCC are, respectively,
to a lower value). The percent shift of the SWCC boundary
curves, ξ , can be mathematically written as follows:
100 log ψ ad
log ψ a w
ψ = ( 10 ) ( w u w)/S 1
1
ψ<ψ aev
ξ =
(4.48)
ψ = ψ aev ( 10 ) ( w aev w )/S 2
ψ aev ψ<ψ r
(4.47)
where:
ψ = ( 10 ) ( 6 w /S 3 )
ψ< 10 6 kPa
ψ r
ψ ad
=
suction at the point of inflection, kPa,
The three equations proposed by Fredlund and Pham
(2006) cover the entire range of suctions from a small
value to a value of 10 6 kPa.
ad
=
subscript for the a fitting parameter on the drying
curve,
aw
=
subscript for the a fitting parameter on the wetting
curve, and
4.6.2.3 Percent Error in Soil Suction Depending on the
Hysteresis Shift in the SWCC
The desorption (or drying) SWCC is generally the first curve
determined for a soil (Fredlund et al., 2001b, 2007). Then the
adsorption (or wetting) curve is usually estimated by assum-
ing an appropriate lateral shift for the bounding SWCC. The
drying and wetting curves are assumed to be congruent or
parallel to one another.
The adsorption and median SWCC is always shifted to
the left on a plot of the type shown in Fig. 4.99. The a
fitting parameter in the SWCC equations generally controls
the lateral shift of the boundary SWCCs. The Fredlund and
Xing (1994) SWCC equation can be used to illustrate the
lateral translation of the SWCCs. Figure 4.101 shows the
effect of changing the a fitting parameter. The n and m
fitting parameters were kept constant.
The “percent shift” of the SWCC boundary curves, ξ , can
be defined on a logarithmic scale. Therefore, a 100% shift of
the inflection point corresponds to one log scale of change.
This means that the a fitting parameter will change by one
order of magnitude. Similarly, a 50% shift means that the
a fitting parameter is shifted
ψ a w =
suction at the point of inflection, a w , on the wet-
ting curve, kPa.
The same equation can be used when moving from the
drying SWCC to the median SWCC:
100 log ψ ad
log ψ am
ξ m =
(4.49)
where:
ψ ad
=
suction at the point of inflection on the drying
curve, kPa,
ψ am =
suction at the point of inflection, a m , on the
“median” curve, kPa, and
ξ m =
percent shift between the point of inflection on
the drying curve and the point of inflection on the
median SWCC.
Since the drying SWCC and the wetting SWCC (and the
median SWCC) are assumed to be congruent, the lateral
shift defined by Eq. 4.48 (and Eq. 4.49), ξ , applies not only
1 / 2 log cycle to the left (i.e.,
100
90
80
70
60
a = 1
a = 100
50
a = 10
a = 1000
40
30
20
10
0
10 6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 4.101 Effect of changing inflection point fitting parameter a on SWCC.
 
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