1. Ch. 11
Compressibility of soil

2. 11.4 ONE-DIMENSIONAL LABORATORY CONSOLIDATION TEST

3. 11.4 ONE-DIMENSIONAL LABORATORY CONSOLIDATION TEST
※The one-dimensional consolidation testing procedure was first suggested by Terzaghi.
consolidometer (sometimes referred to as an oedometer)
The specimens are usually 2½ in. (63.5 mm)
in diameter and 1 in. (25.4 mm) thick.
Each load is usually kept for 24 hours.
After that, the load is usually doubled.
At the end of the test, the dry weight of the test specimen is determined.

4. 11.4 ONE-DIMENSIONAL LABORATORY CONSOLIDATION TEST
The general shape of the plot of deformation of the specimen against time : Figure11.8
Three distinct stages
Stage Ⅰ: Initial compression,
which is mostly caused by preloading.
Stage Ⅱ: Primary consolidation,
during which excess pore water pressure gradually is transferred into effective stress because of the expulsion of pore water.
Stage Ⅲ: Secondary consolidation,
which occurs after complete dissipation of the excess pore water pressure, when some deformation of the specimen takes place because of the plastic readjustment of soil fabric.

5. 11.4 ONE-DIMENSIONAL LABORATORY CONSOLIDATION TEST

6. 11.5 VOID RATIO-PRESSURE PLOTS
void ratio of the specimen – pressure relation
Calculate the height of solids, Hs, in the soil specimen (Figure 11.9)
𝐻 𝑠 = 𝑊 𝑠 𝐴 𝐺 𝑠 𝛾 𝑤 = 𝑀 𝑠 𝐴 𝐺 𝑠 𝜌 𝑤
where Ws = dry weight of the specimen
Ms = dry mass of the specimen
A = area of the specimen
Gs = specific gravity of soil solids
𝛾 𝑤 = unit weight of water
𝜌 𝑤 = density of water
(11.14)

7. 11.5 VOID RATIO-PRESSURE PLOTS
2. Calculate the initial height of voids as
𝐻 𝑣 =𝐻 − 𝐻 𝑠
3. Calculate the initial void ratio, eO, of the specimen,
𝑒 𝑂 = 𝑉 𝑣 𝑉 𝑠 = 𝐻 𝑣 𝐻 𝑠 𝐴 𝐴 = 𝐻 𝑣 𝐻 𝑠
4. For the first incremental loading, 𝜎 1 (total load/unit area of sample), which causes a deformation ∆ 𝐻 1 , calculate the change in the void ratio as
∆𝑒 1 = ∆ 𝐻 1 𝐻 𝑠
∆ 𝐻 1 is obtained from the initial and the final dial readings for the loading.
(11.15)
(11.16)
(11.17)

8. 11.5 VOID RATIO-PRESSURE PLOTS
5. Calculate the new void ratio, 𝑒 1 , after consolidation caused by the pressure increment.
𝑒 1 = 𝑒 𝑂 − ∆ 𝑒 1
For the next loading, 𝜎 2 , which causes additional deformation ∆ 𝐻 2 ,
The void ratio 𝑒 2 at the end of consolidation can be calculated as
𝑒 2 = 𝑒 1 − ∆ 𝐻 2 𝐻 𝑠
※ The effective stress 𝜎′ and the corresponding void ratios (e) at the end of consolidation are plotted on semilogarithmic graph paper. – Figure 11.10
(11.18)
(11.19)

9. 11.5 VOID RATIO-PRESSURE PLOTS

10. 11.5 VOID RATIO-PRESSURE PLOTS

11. 11.6 NORMALLY CONSOLIDATED AND OVERCONSOLIDATED CLAYS
※Figure showed that the upper part of the e-log σ’ plot is somewhat curved with a flat slope, followed by a linear relationship for the void ratio, with log σ’ having a steeper slope.
※maximum effective past pressure in its geologic history.
This maximum effective past pressure may be equal to or greater than the existing overburden pressure at the time of sampling.
※When this specimen is subjected to a consolidation test, a small amount of compression (that is, a small change in void ratio) will occur when the total pressure applied is less than the maximum effective overburden pressure in the field to which the soil has been subjected in the past.

12. 11.6 NORMALLY CONSOLIDATED AND OVERCONSOLIDATED CLAYS
When the total applied pressure on the specimen is greater than the maximum effective past pressure, the change in the void ratio is much larger, and the e – log σ’ relationship is practically linear with a steeper slope.
Figure leads us to the two basic definitions of clay based on stress history :
1.Normally consolidated(정규압밀), whose present effective overburden pressure is the maximum pressure that the soil has been subjected to in the past.
2.Overconsolidated(과압밀), whose present effective overburden pressure is less than that which the soil has experienced in the past. The maximum effective past pressure is called the preconsolidation pressure(선행압밀하중).

13. 11.6 NORMALLY CONSOLIDATED AND OVERCONSOLIDATED CLAYS

14. 11.6 NORMALLY CONSOLIDATED AND OVERCONSOLIDATED CLAYS
Casagrande (1936) method to determine the preconsolidation pressure,
By visual observation, establish point a at which the e – log σ’ plot has a minimum radius of curvature.
Draw a horizontal line ab.
Draw the line ac tangent at a.
Draw the line ad, which is the bisector of the angle back.
Project the straight-line portion gh of the e – log σ’ plot back to intersect ad at f. The abscissa of point f is the preconsolidation pressure, σ’c.

15. 11.6 NORMALLY CONSOLIDATED AND OVERCONSOLIDATED CLAYS
overconsolidation ratio (OCR) (과압밀비)
𝑂𝐶𝑅= 𝜎′ 𝑐 𝜎′
(11.20)

16. 11.7 EFFECT OF DISTURBUNCE ON VOID RATIO-PRESSURE RELATIONSHIP
※A soil specimen will be remolded when it is subjected to some degree of disturbance.
Normally Consolidated Clay of Low to Medium Plasticity (Figure 11.14)
In Figure 11.14, curve 2 is the laboratory e-log σ’ plot. From this plot, determine the preconsolidation pressure ( 𝜎′ 𝑐 ) = ( 𝜎′ 𝑂 ) (that is, the present effective overburden pressure). Knowing where 𝜎′ 𝑐 = 𝜎′ 𝑂 , draw vertical line ab.
Calculate the void ratio in the field, 𝑒 𝑂 . Draw horizontal line cd.
Calculate 0.4 𝑒 𝑂 and draw line ef.
Join points f and g. g is the point of intersection of lines ab and cd. This is the virgin compression curve.
If a soil is remolded completely, the general position of the e-log 𝜎′ plot will be as represented by curve 3.

17. 11.7 EFFECT OF DISTURBUNCE ON
VOID RATIO-PRESSURE RELATIONSHIP

18. 11.7 EFFECT OF DISTURBUNCE ON VOID RATIO-PRESSURE RELATIONSHIP
OverConsolidated Clay of Low to Medium Plasticity (Figure 11.15)
In Figure 11.15, curve 2 is the laboratory e-log σ’ plot(loading), and curve 3 is the laboratory unloading, or rebound, curve. From curve 2, determine the preconsolidation pressure 𝜎′ 𝑐 . Draw the vertical line ab.
Determine the field effective overburden pressure 𝜎′ 𝑂 . Draw vertical line cd.
Determine the void ratio in the field, 𝑒 𝑂 . Draw the horizontal line fg. The point of intersection of lines fg and cd is h.
Draw a line hi, which is parallel to curve 3. The point of intersection of line hi and ab is j.
Join points j and k. Point k is on curve 2, and its ordinate is 0.4 𝑒 𝑂 .
The field consolidation plot will take a path hjk. The recompression path in the field is hj and is parallel to the laboratory rebound curve(Schmertmann, 1953)

19. 11.7 EFFECT OF DISTURBUNCE ON
VOID RATIO-PRESSURE RELATIONSHIP

20. 11.8 CACLULATION OF SETTLEMENT FROM
ONE-DIMENTIONAL PRIMARY CONSOLIDATION
※ settlement caused by primary consolidation in the field, assuming one-dimensional consolidation.

21. 11.8 CACLULATION OF SETTLEMENT FROM
ONE-DIMENTIONAL PRIMARY CONSOLIDATION
※A soil specimen will be remolded when it is subjected to some
(11.25)
(11.26)
(11.27)
(11.28)

22. 11.8 CACLULATION OF SETTLEMENT FROM
ONE-DIMENTIONAL PRIMARY CONSOLIDATION
(11.29)
For normally consolidated clays
(11.30)
𝐶 𝐶 = Compression index(압축지수) – 단위 : 없음

23. 11.8 CACLULATION OF SETTLEMENT FROM
ONE-DIMENTIONAL PRIMARY CONSOLIDATION
(11.31)
For a thicker clay layer

24. 11.8 CACLULATION OF SETTLEMENT FROM
ONE-DIMENTIONAL PRIMARY CONSOLIDATION
In overconsolidated clays, for
(11.32)
(11.33)
If , then
(11.34)
※However, if the e-log p curve is given, it is possible to simply to pick Δe off the plot for the appropriate range of pressures.

25. 11.9 COMPRESSION INDEX (Cc) (압축지수)
Terzaghi and Peck (1967)
For undisturbed clays :
For remolded clays :
Rendon-Herrero (1983)
(11.35)
(11.36)

26. 11.9 COMPRESSION INDEX (Cc) (압축지수)
Nagaraj and Murty (1985)
(11.37)

27. 11.10 SWELL INDEX (Cs)
Nagaraj and Murty(1985)
(11.41)

28. 11.11 SECONDARY CONSOLIDATION SETTLEMENT
secondary consolidation : Plastic adjustment of soil fabrics

29. 11.11 SECONDARY CONSOLIDATION SETTLEMENT
secondary compression index
(11.43)
magnitude of the secondary consolidation
(11.44)
(11.45)
ep = void ratio at the end of primary consolidation (Figure 11.20)
H = thickness of clay layer

30. 11.11 SECONDARY CONSOLIDATION SETTLEMENT

31. 11.11 SECONDARY CONSOLIDATION SETTLEMENT
The general magnitude of C’α as observed in various natural deposits are given in Figure
Secondary consolidation settlement is more important than primary consolidation in organic and highly compressible inorganic soils. In overconsolidated inorganic clays, the secondary compression index is very small and of less practical significance.
The ratio of secondary to primary compression for a given thickness of soil layer is dependent on the ratio of the stress increment(Δp) to the initial effective stress(p).
For small Δp/p ratios, the secondary-to-primary compression ratio is larger.