Environmental Engineering Reference
In-Depth Information
The experimental calibration curve evidence indicates that
separate equations should be used for the contact filter paper
and for the no-contact filter paper. Total and matric suction
calibration data can be best fit in the region above and below
the changes in slope on the calibration curves.
The matric suction calibration curves for Whatman No. 42
filter paper can be written as follows:
The van Genuchten (1980) equation for the Schleicher
and Schuell No. 589 filter paper for matric suction can be
written as
⎡
⎤
251
w
f
5
.
621
0
.
896
⎣
⎦
ψ
=
0
.
048
−
1
(4.25)
The van Genuchten (1980) equation for total suction can
be written as
log
ψ
=
2
.
909
−
0
.
0229
w
f
when
w
f
≥
47%
(4.15)
⎡
⎤
44
w
f
0
.
464
2
.
516
log
ψ
=
4
.
945
−
0
.
0673
w
f
when
w
f
<
47%
(4.16)
⎣
⎦
ψ
=
64
,
940
−
1
(4.26)
The total suction calibration equations can be written as
Applying the Fredlund and Xing (1994) equation to the
Whatman No. 42 filter paper calibration data yields the fol-
lowing equation for matric suction:
log
ψ
=
8
.
778
−
0
.
222
w
f
when
w
f
≥
26%
(4.17)
log
ψ
=
5
.
31
−
0
.
0879
w
f
when
w
f
<
26%
(4.18)
0
.
23
e
(
268
/
w
f
)
0
.
629
−
e
2
.
101
ψ
=
(4.27)
The matric suction calibration curves for Schleicher and
Schuell No. 589 filter paper can be written as follows:
The Fredlund and Xing (1994) equation for total suction
can be written as
log
ψ
=
2
.
659
−
0
.
018
w
f
when
w
f
≥
54%
(4.19)
18
,
500
e
(
37
/
w
f
)
0
.
242
−
e
2
.
248
log
ψ
=
5
.
438
−
0
.
069
w
f
when
w
f
<
54%
(4.20)
ψ
=
(4.28)
The total suction calibration equations can be written as
The Fredlund and Xing (1994) equation for the Schleicher
and Schuell No. 589 filter paper for matric suction can be
written as
log
ψ
=
8
.
778
−
0
.
191
w
f
when
w
f
≥
32%
(4.21)
0
.
844
e
(
282
/
w
f
)
1
.
071
−
e
0
.
779
log
ψ
=
5
.
26
−
0
.
0705
w
f
when
w
f
<
32%
(4.22)
ψ
=
(4.29)
Two sets of calibration equations are required for each
of the filter papers because of changes in sensitivity of the
filter paper in the different suction ranges and whether matric
suction or total suction is measured.
The filter paper calibration curves can also be viewed as a
water retention curve for filter paper. Consequently, it is pos-
sible to use either the van Genuchten (1980) or the Fredlund
and Xing (1994) equations proposed for a SWCC as a single
equation to fit either the total suction or matric suction cal-
ibration data. Applying the van Genuchten (1980) equation
to the Whatman No. 42 filter paper calibration data yields
the following equation for matric suction:
The Fredlund and Xing (1994) equation for total suction
can be written as
20
,
000
e
(
42
/
w
f
)
0
.
246
−
e
2
.
058
ψ
=
(4.30)
Equations 4.23-4.30 require only one equation for either
matric or total suction. The van Genuchten (1980) and the
Fredlund and Xing (1994) provide a reasonable fit of the cali-
bration data and are convenient to use. However, the equations
used for an independent fit for the low- and high-suction range
are slightly more accurate (i.e., Eqs. 4.15-4.22).
4.3.3.5 Use of the Filter Paper Method in Engineering
Practice
A question in the mind of the practicing geotechnical engi-
neers is, “What is the accuracy of suction measurement made
when using the filter paper method?” This question is still
being addressed, but comparisons between measurements
with psychrometers and filter paper provide an indication
of the accuracy that can be anticipated when using the filter
paper method (Fig. 4.84). The results from the no-contact fil-
ter paper agree fairly closely with the psychrometer results,
indicating that total suction was measured.
⎡
⎤
248
w
f
9
.
615
0
.
473
⎣
⎦
ψ
=
0
.
051
−
1
(4.23)
The van Genuchten (1980) equation for total suction can
be written as
⎡
⎤
37
w
f
0
.
44
2
.
361
⎣
⎦
ψ
=
56
,
180
−
1
(4.24)
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