This document discusses two methods for determining the coefficient of consolidation (Cv) of soil through consolidation testing: the square root of time fitting method and the logarithm of time fitting method. The square root of time fitting method involves plotting dial readings versus the square root of time to obtain Cv. The logarithm of time fitting method involves plotting dial readings versus the log of time and using the 50% consolidation point to calculate Cv based on drainage path and time.

2. Determination of Co-efficient
 The similarity between the laboratory
curve and theoretical curve is used for
the determination of the co-efficient of
consolidation (Cv) of soil.

3. Methods
 Generally used methods are:
 Square root of time fitting method
 Logarithm of time fitting method

4. Square root of time fitting method
 This method, developed by Taylor, utilizes theoretical
relationship between U and √Tv.
 The relationship is linear up to value of u equal to
about 60%.
 It was observed that at U=90%, value of √Tv is 1.15
times value obtained by extension of the initial
straight line portion.
 A curve is plotted from consolidation test results
between dial gauge reading (R) as ordinate and √T.

5. Time Consolidation Curve

6. Co-efficient of Consolidation (Cv)
 From curve, cv (cm2/sec)
T90 = time factor
when U is 90%
d = drainage path
t50 = time when U is
50%
U = percent of
primary consolidation

7. Logarithm of time fitting method
 This method, developed by A.
Casagrande, determines 100% U on semi log
plot of laboratory time consolidation curve
by theoretical curve between U and log Tv.

8. Logarithm of time fitting method
 Construct a plot of dial reading vs. log of time
 To determine
 Ho = Initial height of specimen
 Rstart = 0 (if you zeroed the dial at the beginning of the
test)
 R50 you determine from the plot

9. Coefficient of Consolidation (cv)
Casagrande log time method: R50
 determine Ro, when U = 0%
 this is NOT your first reading
 determine R100, when U = 100%
 then average to find R50,
 which then graphically corresponds to t50

11. Ro
R100

12. Ro
R50 = (R100-Ro) / 2
R100

13. Coefficient of Consolidation (cv)
 cv (cm2/sec)
 T50 = time factor at U =
50%
 d = drainage path
 t50 = time at U = 50%
 U = percent of primary
consolidation
 If Uavg = 50%, T50 = 0.197