Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

Transcription

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2 Module 3: Lecture - 8 on Compressibility and Consolidation

3 Contents Stresses in soil from surface loads; Terzaghi s 1-D consolidation theory; Application in different boundary conditions; Ramp loading; Determination of Coefficient of consolidation; Normally and Over-consolidated soils; Compression curves; Secondary consolidation; Radial consolidation; Settlement of compressible soil layers and Methods for accelerating consolidation settlements.

4 Effect of sample disturbance on e-logσ curves Curve I: e log σ variation for an undisturbed normally consolidated clay in the field. Curve II: e log σ variation obtained from consolidation test on a carefully recovered specimen. Curve III: e log σ variation obtained from consolidation test on a remoulded specimen. NC Clay e log σ curves intersect at 0.4e 0 (Terzaghi and Peck, 1967)

5 Effect of sample disturbance on e-logσ curves Curve I: e log σ variation for an undisturbed over consolidated clay in the field. Curve II: e log σ laboratory specimen. curve on Schmertmann (1953) concluded that the field recompression branch (ab) has approximately the same slope as the laboratory unloading branch, cf. OC Clay e log σ curves intersect at 0.4e 0 (Terzaghi and Peck, 1967) C r C c /5 - C c /10

6 Effect of load increments Standard 1D Consolidation tests are conducted with a soil specimen having a thickness of 25.4 mm in which the load on the specimen is doubled every 24 hours. This means that σ =1 σ What will be the effect of any deviation from the standard procedure? Striking changes in the shape of the compression-time curves for 1D consolidation tests are noticed if the σ magnitude of < 0.25 σ

7 Effect of load increments Leonards and Altschaeffl (1964) conducted several tests on Mexico city clay with different load increment ratios and with the variation of excess PWP measurement with time. σ < 0.25 For σ, the position of end of primary consolidation is somewhat difficult to resolve and also C α /C c increases with the decrease of loadincrement ratio. After Leonards and Altschaeffl (1964)

8 Effect of load increments σ <1 When σ, the ability of individual particles to readjust to their positions is small, which results in a smaller compression compared σ to 1 σ Void ratio, e σ >1 σ σ =1 σ σ <1 σ Log σ

9 Effect of load duration In conventional consolidation test, in which a soil specimen left under given load for about a day, a certain amount of secondary consolidation takes place before the next load increment is added. For soils that display secondary compression vol. changes occur after the end of primary consolidation (if each load increment is in place for a longer period). Most common for NC and lightly OC soils. Heavily OC soils are less prone for secondary compression. Shape of curves become less distinct with longer period/duration and it is more difficult to determine σ c Volume change due to secondary compression Load duration just sufficient for primary consolidation Increasing load duration

10 Effect of sample thickness For similar load increment ratios proportion of secondary to primary compression increases with a decrease in sample thickness. Also, the ratio of secondary to primary compression increases with decrease of load settlement ratio.

11 Effect of secondary consolidation The continued secondary consolidation of a natural clay deposit has some influence on the preconsolidation pressure σ c. A clay that has recently been deposited and comes to equilibrium by its own weight can be called a young, normally consolidated clay. Curve a is for young NC clay σ c = σ 0 at e 0. If the same clay is allowed to remain undisturbed for 10,000 yrs, for example, under the same effective overburden pressure σ 0, there will be creep or secondary consolidation. This will reduce the void ratio to e 1. The clay may now be called an aged NC clay.

12 Effect of secondary consolidation If the clay at e 1 and effective overburden pressure σ 0, then curve looks like b. The preconsolidation pressure, when determined by standard procedure, will be σ 1. Now, σ c = σ 1 > σ 0. This is sometimes referred to as a quasi preconsolidation effect (More pronounced in plastic clays) Bjerrum (1972) gave an estimate of the relation between the plasticity index and the ratio of quasipreconsolidation pressure to effective overburden pressure σ c /σ 0 for late glacial and postglacial clays.

13 If a series of load-increments is applied to specimen which is initially very wet, the resulting equilibrium states will appear, as shown below. Terzaghi s equilibrium states

14 The outermost curve connecting the points when the specimen is in the looses possible states is referred as the virgin compression line, because it is strictly the line connecting equilibrium states whereas consolidation is a term used only for the time dependent process between any pair of equilibrium states. Equation of virgin compression line:

15 Equation of virgin compression line will also be denoted by the equation: And equation for swelling and recompression loop will be represented by a single straight line of the form; Where λ and κ are characteristic constants for the soil. Virgin compression λ - line represents an irreversible process, whereas the swelling and recompression κ-lines represent reversible processes.

16 1D compression and swelling Equation for normal compression line OACD is given by: e = e 0 C c logσ z Equation for swelling and recompression line ABC is given by: e = e κ C s logσ z e B O A C D e e 0 e κ O B Slope -C s Slope -C c A, C NCL D σ o σ y σ z σ = 1 kpa σ 0 σ y logσ z

17 1D compression and swelling Since δv = δe and log 10 x = 0.43lnx, we get C c = 2.3λ and C s = 2.3κ For OC soil at a point such as B the yield stress ratio Y 0 is given by: Y 0 = σ y /σ 0 ; where is the current stress and is the yield point which lies at the intersection of the swelling line through B with normal compression line.

18 1D consolidation and swelling of soil in the ground due to deposition and erosion Deposition w w a w c A C B Erosion σ z σ h z a z b z c σ z A B Erosion σ z = σ h K 0 = 1 σ a σ c σ b logσ σ h

19 1D consolidation and swelling of soil in the ground due to deposition and erosion

20 Variation of water content in the ground in NC and OC soils Consider variation of water content with depth for a deposit which is lightly eroded (i.e. depth of erosion Z c is small) or heavily eroded (i.e. depth of erosion is large) z c z c A σ a z a z b C σ c B σ b D σ d

21 Variation of water content in the ground in NC and OC soils For the lightly eroded soil the difference between the water contents at A and B is relatively large, while for heavily eroded soil the difference between the water contents at C and D is much smaller. w Low water contents σ at C and D attributed a w A to the very large past C A B stress. σ b C D B D σ a σ b σ z z

22 Example An oedometer test was performed on a clay sample 30 mm thick, drained on both sides, and taken from midstratum shown below. Seventy percent consolidation was attained in 6.67 minutes. Find: a) The time required to attain 70% consolidate of the clay stratum b) The magnitude of that settlement in that time

23 Example

24 Solution

25 Example An oedometer test is performed on a 100 mm thick specimen, drained on top and bottom. It was observed that 45% consolidation (T v = 0.15) was attained in 78 hours. Determine the time required to attain 70% consolidation (T v = 0.40) in a job site where the clay stratum is shown in the figure.

26 Solution In such situations, if the significant amount consolidation settlements can occur in the designed life of a structure, there is a need for accelerating consolidation of soils