Determination of the Coeffi cient of Consolidation
There are two popular methods that can be used to calculate Cv. Taylor (1942) proposed one method, called the root time method. Casagrande and Fadum (1940) proposed the other method, called the log time method. The root time method utilizes the early time response, which theoretically should appear as a straight line in a plot of square root of time versus displacement gage reading.
Root Time Method (Square Root Time Method) Let us arbitrarily choose a point:
C, on the displacement versus square root of time factor gage reading, as shown in Figure. We will assume that this point corresponds to 90% consolidation (U 5 90%) for which Tv 5 0.848 (Figure 9.9). If point C were to lie on a straight line, the theoretical relationship between U and Tv would be U 5 0.98!Tv; that is, if you substitute Tv 5 0.848, you get U 5 90%.
At early times, the theoretical relationship between U and Tv is given by Equation ; that is,
The laboratory early time response is represented by the straight line OA in Figure 9.13. You should note that O is below the initial displacement gage reading because there is an initial compression of the
Root time method to determine Cn.
soil before consolidation begins. This compression can be due to the breaking of particle bonds in lightly cemented soils. The ratio of the gradient of OA and the gradient of the theoretical early time response, line OCB, is
We can use this ratio to establish the time when 90% consolidation is achieved in the one-dimensional consolidation test.
The procedure, with reference to Figure 9.14, is as follows:
1. Plot the displacement gage readings versus square root of times.
2. Draw the best straight line through the initial part of the curve intersecting the ordinate (displacement reading) at O and the abscissa 1!time2 at A.
3. Note the time at point A; let us say it is !tA.
4. Locate a point B, 1.15!tA, on the abscissa.
5. Join OB.
6. The intersection of the line OB with the curve, point C, gives the displacement gage reading and the time for 90% consolidation (t90). You should note that the value read off the abscissa is !t90. Now when U 5 90%, Tv 5 0.848 (Figure) and from Equation we obtain.