Environmental Engineering Reference
In-Depth Information
H is the one half the stratum thickness if there is drainage at both interfaces, or the stra-
tum thickness if there is a drainable layer at only one interface, and c v the coefficient of
consolidation.
The theoretical time factor T v is a pure number that has been determined for all condi-
tions of importance, given in terms of percent consolidation U . The values given in Figure
3.83 apply to the common cases of (1) a consolidating stratum free to drain through both
its upper and lower boundaries, regardless of the distribution of the consolidation pres-
sure, or (2) a uniform distribution of the consolidation pressure throughout a layer free to
drain through only one surface. The cases of consolidation pressure increasing or decreas-
ing through a consolidating stratum with an impervious boundary can be found in
Terzaghi and Peck (1967, p. 181).
The coefficient of consolidation c v is found from the compression-log time curve. Tangents
are drawn to the primary section of the curve at its point of inflection and to the second-
ary sections of the curve to locate e 100 of primary consolidation. The initial void ratio e o is
found by taking the amount of compression between 0.25 and 1.0 min and adding this
value to the void ratio for 0.25 min. The void ratio corresponding to U
50% is midway
between e o and e 100 and the corresponding time t 50 represents the time for 50% consolida-
tion. The theoretical time factor for U
50% is 0.197 (Figure 3.83), and c v is found from
c v
T v h 2 / t
0.197 h 2 / t 50 (cm 2 /sec, in 2 /min, ft 2 /day)
(3.68)
where h is one half the thickness of the sample, since it has double drainage. The square
root of time method is an alternative procedure (Lambe and Whitman, 1969).
Analysis of time rates: Consolidation is essentially complete at t 90 (time factor
0.848)
since T , for U 100 is infinity. Field time rates of consolidation can be quickly determined
from c v with the nomograph given as in Figure 3.84 or computed from Equation 3.67. The
values are usually only approximations because field time rates are normally much higher
than laboratory rates because stratification permits lateral drainage. Studies where time
rates are critical employ piezometers to measure in situ pore pressures (see Section 4.4.2).
Computing coefficient of permeability k: The relationship between k and c v may be
expressed as
0
10
20
30
40
50
60
70
80
90
100 0
0.1 0.2
0.3 0.4 0.5 0.6
Time fractor T v
0.7 0.8
0.9
1.0 1.1 1.2
U
T v
U
T v
10
20
30
40
50
0.0077
0.0314
0.0707
0.126
0.197
60
70
80
90
100
0.286
0.403
0.567
0.848
Infinity
FIGURE 3.83
Theoretical time factor T v vs. percent
consolidation U .
 
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