Coefficient of consolidation from the linear
Trang 1Coefficient of consolidation from the linear
Tao-Wei Feng and Yi-Jiuan Lee
The discussion is appreciated and replied to as follows
The discussed paper has included a review of the
discussers’ early log t method for determining the coefficient
of consolidation Apparatus deformation, sometimes called
machine deflection, is only responsible for part of the
mea-sured instantaneous deformation Therefore, the correction
of apparatus deformation does not improve the shape of the
measured consolidation curve, but it does improve the
com-pression curve (i.e., void ratio – effective stress relationship)
The most widely used apparatus for conventional oedometer
tests does not provide a mean to saturate the specimen In
other words, the oedometer test is usually run without
back-pressure In this case, it has been commonly observed that
the initial segment of the measured compression versus
loga-rithmic of time curve is not parabolic However, like what is
done by Casagrande and Fadum (1940), the discussers still
assume that the initial segment of the measured compression
time curve is parabolic The discussers are therefore still
us-ing the directly measured consolidation curve to determine
0% consolidation Different 0% consolidation may be
ob-tained using different pairs of time of t1and t2with t2= 4t1
Therefore, the initial compression would still affect the use
of the early log t method proposed by the discussers It is
suggested in the discussed paper that the effect of initial
compression may become insignificant when U > 20% The
question is whether or not t1 corresponds to U > 20%?
The comments from the discussers on the proposed t1/2
method are based on the partial differentiation of the
theoret-ical U–T1/2relationship It may be noted that the variable in
the denominator of the discussers’ eq [2] should be T1/2 A
partial differentiation of the theoretical U–T1/2relationship at
U = 60% gives the slope of the tangent at that point But, it
should be noted that eq [5] of the discussed paper is based
on eq [4] of the same paper That means eq [5] actually
cal-culates the total differentiation of eq [4] Thus it would have
been better if eq [5] were written as (dU/dT1/2)60 = 1.128
On the other hand, the t1/2curve fitting method (Taylor 1948)
is actually doing the total differentiation graphically Figure
D1 shows the variation of the total differentiation with the
average degree of consolidation U It can be seen from Fig D1 that the value of the total differentiation for U < 45% is equal to 1.128 and for U = 60% it is equal to 1.122 The
ra-tio between 1.122 and 1.128 is equal to 0.995, which is only slightly less than 1 This slight difference is necessary in ap-plying the curve fitting method by hand to discern a point at which the measured consolidation curve deviates from the straight segment Figure D1 also shows that the value of
dU/dT1/2increases rapidly with increasing values of U for U >
60% Thus, it is believed that the characteristic point
deter-mined by using the proposed t1/2 curve fitting method is in
fact near or at U = 60% Identification of this characteristic
Can Geotech J 39: 1002–1003 (2002) DOI: 10.1139/T02-044 © 2002 NRC Canada
1002
Received 10 January 2002 Accepted 11 January 2002 Published on the NRC Research Press Web site at http://cgj.nrc.ca on
27 July 2002
T.-W Feng 2 and Y.-J Lee Department of Civil Engineering, Chung Yuan Christian University, Chung-li, Taiwan, Republic of
China
1Discussion by R.G Robinson and M.M Allam This issue Canadian Geotechnical Journal, 39: 1000–1001.
2Corresponding author (e-mail: twfeng@cycu.edu.tw)
Average Degree of Consolidation, U (%)
0.7 0.8 0.9 1.0 1.1 1.2
U = 60%
dU/dT 1/2 = 1.128
dU/dT 1/2 = 1.122
Fig D1 Variation of the total differentiation of the theoretical
U–T1/2relationship dU/dT1/2 with the average degree of
consoli-dation U.
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Trang 2point from the U–T1/2plot in Fig 1 of the discussed paper is
not as difficult as that implied by the discussers
References
Casagrande, A., and Fadum, R.E 1940 Notes on soil testing for
engineering purposes Harvard University Graduate School
En-gineering Publication, No 8, Cambridge, MA
Taylor, D.W 1948 Fundamentals of soil mechanics John Wiley & Sons, New York 700 pp
Feng and Lee
© 2002 NRC Canada
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