### One-Dimensional Consolidation Testing.

In the following discussion, a soil sample to be tested is assumed to be a saturated clay contained in a thin-walled steel tube used for sampling. The sampling tube is typically 3 in. (75 mm) in diameter. The consolidation cell to be used is shown in Figure 3.6. The usual steps in preparing a consolidation test are as follows:

- The cell is dismantled and cleaned prior to testing.
- The inside surface of the conﬁning ring is given a thin coating of silicone grease to minimize friction between the ring and soil and to seal the interface from seepage in order to force the ﬂuid ﬂow to be in the vertical
- direction.
- The ring is weighed and has a weight of 77.81 g.
- The soil is trimmed into the ring so that it ﬁlls the ring as exactly as possible (volume 60.3 cc), and the ring and soil are weighed together (176.50 g).
- The soil is covered, at the top and bottom, with a single layer of ﬁlterpaper to keep the soil from migrating into the porous stones, and the consolidation cell is assembled.
- The cell is placed in a loading frame, and a small seating pressure (60 psf or 3 kPa) is applied. A dial indicator or displacement transducer, capable of reading to 0.0001 in., is mounted to record the settlement of
- the loading cap.
- The tank around the ring is ﬁlled with water and the test begins.

- If the soil swells under the seating load, then the seating load is increased until equilibrium is established.
- The applied pressure is then increased in increments, usually with the stress doubled each time.
- Settlement observations are recorded at various times after the application of each load level. A set of settlement readings obtained for a pressure of 16,000 psf (766 kPa) are shown in Figure 3.13 as an example. When testing most clay soils are tested, each load is left in place for 24 hours.
- After the maximum pressure has been applied, the load acting on the soil specimen is unloaded in four decrements (e.g., down from 64,000 psf to 16,000 psf to 4000 psf).
- When a suitably low pressure is reached, the rest of the remaining load is removed in a single step and the apparatus is dismantled rapidly to minimize any additional moisture taken in by the soil.

Because the settlements under each pressure were measured, the change in void ratio from the beginning of the test to that pressure is calculated using Eq. 3.60:

Figure 3.13 Example data form for recording the time-settlement data during a onedimensional consolidation test.

Figure 3.14 Sample data form for a one-dimensional consolidation test.

The apparatus settlement is caused by compression of the porous stones above and below the specimen (Figure 3.6) and the ﬁlter paper, and to a trivial extent by compression of other parts of the apparatus. Numerical values for Sa are usually obtained by literally performing a full consolidation test with no soil in the ring. Either a metal block is used in place of the sample or theFigure 3.15 Sample data form for calculation of the void ratios at various consolidation pressures.

The engineer reads the time needed to achieve 50% consolidation, t50,n, from the laboratory S-t curve. At U 50%, T 0.197 (from Table 3.3), so from Eq. 3.52

Once cv has been calculated, the entire theoretical S-t curve can be calculated by successively entering the appropriate values of T into Eq. 3.63 and plotting the theoretical curve on the same graph for comparison with the measured curve. If the theory is correct, then the theoretical and experimental curves should be identical. The theoretical curve is calculated as follows using the symbols deﬁned previously. A table is prepared with values of U and T (from Table 3.3) in the ﬁrst two columns. For each value of U, the settlement S is calculated at time t using

The dimensionless time factors needed to calculate a theoretical curve of settlement versus time are presented in Table 3.3 The theoretical curve is shown in Figure 3.16, and it clearly does not ﬁt the measured curve very well. The only points in common are at time zero, where both curves must start at S = 2301 divisions; at U =50% where the calculations force the two curves to be identical; and at times indeﬁnitely.

To examine the discrepancies in more detail, the data are redrawn to a semi-log scale in Figure 3.17. The most obvious discrepancy is found over long time period where the experimental curve continues sloping downward, whereas the theoretical curve should level off. Apparently, the Terzaghi model is not quite correct over long times. Apparently, the soil compresses, perhaps like a spring, but then it creeps, causing continued settlement at large times.

Figure 3.16 Measured and theoretical time settlement curves.

Figure 3.17 Measured and theoretical settlement versus logarithm of time.

Terzaghi recognized this effect. He termed the part of consolidation (settle-ment) that obeys his theory the primary consolidation and the postprimary creep the secondary compression. Casagrande and Fadum (1940) proposed a simple construction to separate primary from secondary settlements. They drew one tangent line to the secondary settlement curve and another to the primary curve at the point of inﬂection (where the direction of curvature reverses), as shown in Figure 3.17, and found that the intersection of these two lines deﬁnes approximately the settlement at the end of primary consolidation. This settlement is deﬁned as S100,n where 100 indicated the point of 100% primary consolidation.

Further studies indicate some non-Terzaghian consolidation right at the beginning too. The correction is based on Eq. 3.56. The correction, also originated by Casagrande and Fadum (1940), is performed as follows: a point is selected on the laboratory S-log(t) curve near U = 50% (Figure 3.17), and the time is recorded as 4t and the settlement as S4t The point on the curve is now located corresponding to t and settlement St (this symbol was used previously for a different variable) is recorded. The corrected settlement at the beginning of primary settlement S0 is

Further studies indicate some non-Terzaghian consolidation right at the beginning too. The correction is based on Eq. 3.56. The correction, also originated by Casagrande and Fadum (1940), is performed as follows: a point is selected on the laboratory S-log(t) curve near U = 50% (Figure 3.17), and the time is recorded as 4t and the settlement as S4t The point on the curve is now located corresponding to t and settlement St (this symbol was used previously for a different variable) is recorded. The corrected settlement at the beginning of primary settlement S0 is

where the subscript n’s have been left off for simplicity.

The coefﬁcient of consolidation cv is now calculated as before, but the U= 50% point is deﬁned at S50 where

and S0 and S100 are the settlements at the beginning and end of primary consolidation. The theoretical curve calculated using this value of cv is compared with the measured curve in Figure 3.17, and the curves compare very well for the range 20 <U <90%. More complicated theories exist that ﬁt the experimental curves better, but the mathematics associated with their use is formidable and the theories have not been used successfully in engineering practice.The coefﬁcient of consolidation cv is now calculated as before, but the U= 50% point is deﬁned at S50 where

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