Question

9 The data shown in the table below were obtained from a laboratory consolidation test on a normally consolidated undisturbed MH soil with a liquid limit of 65. The sample was 62 mm in diameter, 25 mm tall and was tested under a double drainage condition Compute c, using the square root of time fitting method Time Since Loading (HH:MM:SS) 00:01:01 Dial Reading (mm) 7.21 7.74 00:03:06 00:08:35 00:16:39 8.40 9.01 9.60 00:30:15 00:59:17 10.11 01:54:29 10.35

Answer 1

Given information: Sample diameter (D) = 62 mm Sample height (H) = 25 mm Since the consolidation test was conducted under double drainage condition 22 Taylor's method: If you plot change in height (or dial gauge reading) as a function of the square root of time, it should plot as a straight line as long as U <60%. If you extrapolate the linear portion of the laboratory consolidation curve back toward the origin, after the immediate settlement has occurred). Taylor noted that if you extrapolate the linear portion of the laboratory consolidation curve forward (beyond 60% consolidation) it gives you a T90 that's about 15% too low. That's because the parabolic approximation gives 190 = (0.9)* = 0.636 where the actual value is closer to T90 =1.78 -0.933 log (10) = 0.848 Thus, on a plot of U as a function of the square root of T. the ratio of the correct value to the extrapolated value is V0.848 = 1.1545 V0.636

Thus, if you draw a line starting from (0, Ro) with a slope 15% shallower than the linear portion of the laboratory consolidation curve, its intersection with the nonlinear portion of the laboratory curve defines 90% consolidation 02 Therefore, coefficient of consolidation (c) can be determined as c, = 0.848 | 90 U=0% Initial compression cotipression 1 U= 0% 6.65=RON Dial reading (mm) Primary consolidation 0.15 x U = 100% Secondary consolidation too = 10.12 Time (min)

If degree of consolidation is 50% U= 50% =0.5 Time factor, T=FU2 = X(0.5)2 = 0.197 From the above graph, T90 =10.12 min >c, = 0.848 190 C, =coefficient of consolidation. d =length of drainage path.

Plugging in values, =0.848 (12.5)) * 10.12 =0.848 (15.439)