Consolidation. Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University

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1 Consolidation Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University

2 Some Definitions Settlement: change in elevation Compression: change in thickness

3 settlement S i = compresseion of layer i Total settlement = n i= 1 S i S = ε H = εl

4 σ ε logσ ε reload rebound Virgin consolidation curve

5 logσ ε L/L s e e Virgin consolidation curve Usually use e for clay, n for sand

6 σ 0 σ i σ f 0 logσ Virgin consolidation curve ε S = εl = el s e = 1+ e L s height of solids L 0 original height of sample (layer) e 0 original void ratio 0 L 0

7 Consolidation Tests An effort to measure stress-strain-time relationship for soils under partial or complete drainage

8 Dial gauge 1 Loading Porous Stone Soil Specimen Porous Stone

9 Restrictions of Consolidation Tests Suitable for cohesive soils Sand compresses instantly, difficult to measure strain-time relationship Sudden shock makes the measured deformation inaccurate Simplified stress surface (profile of u vs. H) Coupled with theory

10 History of Consolidation Test 1809 Thomas Telform was the first to use the term consolidation 1901 Consolidation test was invented 1910 D. E. Morgan invented the floating ring 1923 Karl Terzaghi worked on consolidation theory

11 We usually do not run consolidation test on sand Volume change takes place instantly We can still get the relationship between volume change and stress

12 If we got more than one consolidation curves from lab tests put all the data on the plot, then Use analytical method to define the consolidation curve (average consolidation curve)

13 logσ σ reload ε rebound ε Semilog plot: Improves linearity Easier to use in low stress range

14 Nowadays, we don t have to use semilog plot anymore Input all experimental data, compute compression through linear interpolation logσ ε

15 There is no point to use a log-plot the time is waste in taking log

16 Some thoughts on Terzaghi s words ε σ is linear for small strain which is based on linear elasticity and is not true in most cases

17 If we use strain ε R r = recompression ratio R c = compression ratio σ S = m H σ RH log 2 v = σ S = av cr σ i c H σ = H log + 1+ e 1+ e σ c e H σ f log σ i

18 Scale of strain σ Recompression Virgin compression ε dε = dσ m v = 1 E R r = dε d logσ R c = dε d logσ e de = d σ a v de c r = d logσ de c c = d logσ Recompression index Compression index

19 m v = coefficient of volume compressibility a v = coefficient of comprssibility m 1 = 1 + e v a v

20 Some Corrections of the Measured Change in Height Machine deflection deformation of the apparatus itself, i.e., porous disks, loading cap, piston

21 Settlement-Time Relationship Square root time method Taylor (MIT) Log time method Casagrande (Harvard) Primary consolidation the period of consolidation where the volume change of soil is due to the drainage of water driven by excess pore water pressure

22 Square Root Time Method t S = U S u s T = c t H v 2 t = T H c v 2 Fox s equation, for U 60% t = FS 2 T = π 4 U At least for U 60%, t 1/2 ~ S is a straight line if T s theory is valid 2

23 Initial portion may be higher or lower than S 0 t s Straight line portion d 50 Peat s 90 9/5 d 50 Extension from the straight line portion

24 t s For some soils, such as peat, k changes very much when subjects to change in effective stress; thus, Terzaghi s theory does not work at all. In addition, Terzaghi s theory does not account for secondary effect.

25 How Do We Get the Factor 1.15? d = F d 50 = F d 90 F = = d F It makes no difference if we use d 40 and T 40 to construct d 90 and T 90, we get the same results S 100 = 10 S 9 90

26 The square root time method works well based on the assumption of NO secondary consolidation Used strictly for vertical drainage

27 Log Time Method Log t s t 1 s 1 t 2 s 1 Pick t 1, t 2, so that t 2 =4t 1 to get s 0 s 100 Most of the time, it is difficult to get this straight line, since the secondary effect does not necessarily produce a straight line

28 Square Root t vs. Log t There was a war going on between MIT and Harvard To decide which one is correct compare with k value Generally, square root t method is better s 100 from log t method is ambiguous Square root t method only gives one c v, log t method gives different c v by different people Square root t method usually gives higher c v

29 k c computed from c v almost always smaller than k m actually measured Secondary effects lead to a delay in settlement in addition to that caused by the real k If all causes of delayed compression are lumped into k c k c < k m Smaller k slower compression

30 Special Aspects of Consolidation Testing Rapid loading Increase loading as soon as s 100 is reached Continuous loading Boundary impedence Ring friction Effect of temperature Rates of dissipation of pore water pressures Effects of non-linear stress-strain curve

31 Rapid Loading Standard c v Rapid log σ Smaller c v means smaller k Rapid loading reduces the delay effect of secondary consolidation

32 Boundary Impedence t s I = kh d k H Impedence factor I increases d New porous stone, NO filter paper Old porous stone, NO filter paper (likely to be clogged by fine particles) Old porous stone PLUS filter paper

33 H d is the thickness of the porous disc The smaller the better k d is the hydraulic conductivity of the porous disc The larger the better Free drainage I = 0 I should be kept less than 0.01 I affects the time rate of consolidation, but it does not affect the total settlement

34 How to Reduce I Keep the porous stone clean Use filter paper to keep the fine particles from entering porous stone Boil the porous stone before use to get the trapped air out

35 Ring Friction Effects of ring friction During loading reduce stress acted on the specimen specimen compresses less During rebound reduce the swelling tendency specimen swell less Flatten the swelling curve at low stress level

36 Taylor (1942) q = pλ λ D H [1 exp( 4K µ o 4Koµ )] D H = Make λ 1 to reduce friction P Q = P τ z π D τ τ = σ v K o µ Q z The stress in the ring is not uniform

37 Use consolidation rings made of cadmium, nickel, hard chrome will be fine Don t use Teflon, although it has the lowest friction coefficient Teflon is too soft and will be scrapped by soils with hard materials and get stuck λ of greased steel > ungreased plastic>cadmium coated steel λ increases as consolidation pressure goes up less error

38 Use larger D/H ratio, the larger D/H the smaller the effect of friction Wide and thin specimen For D/H about 3, greased steel, total error is about 10%

39 Effect of Temperature Stress-strain curve The higher the temperature, the lower the e-log p curve This may due to the change of volume of the consolidation ring at higher temperature The ring expands such that the friction decreases

40 logσ e Reduction in e As temperature goes up

41 Effect on c v and k As temperature goes up, c v increases since k decreases as the viscosity of water gets smaller The water flows faster

42 Effects of Non-Linear Stress- Strain Curve Effect on settlement-time relationship Effect on u b u i Effect on c v and a v

43 Effect on Settlement-Time Relationship σ e (2)NC clay, concave upwards Resultant c v decreases (1) (3)OC clay, concave downwards Resultant c v increases

44 t U (2) NC clay (3) OC clay U = 90%

45 Influence of Secondary Compression on Subsequent Behavior Stress-strain behavior Subtract the secondary compression to get the stress-strain curve (e logp)?

46 Settlement-time relationship Loading rate in the lab is very high Slow loading in the field Drainage distance in the field is far greater than in the lab May be difficult to see secondary effect

47 log t s H = 5.5 H = 0.37 Almost totally secondary compression

48 Secondary compression may not affect the primary consolidation of next load incremental Materials such as peat also has primary stage, but its properties changes a lot during this period Difficult to obtain meaningful parameters

49 Secondary compression Secondary effect exists through out the whole consolidation, including in the primary stage ε α = d dε log t S s α H 0 log t t = ε 0 c α = d de logt c t S s = α H 0 log 1+ e t 0

50 Peat Very high water content Loose or no contact between solids Lab test demonstrate limited primary consolidation but very large secondary compression Squeezing out of water Reorientation of particles Properties changed a lot The significance of secondary effect is often overlooked

51 In many cases involving peat, secondary compression controls Must not follow the standard consolidation test procedure and get useless data lead to wrong analysis

52 Quick Loading Test Monitor the s ~ t relationship Apply next incremental load once the primary consolidation completes Eliminate the secondary effect?

53 Continuous Loading Tests Constant rate of strain (CRS) test Controlled deformation rate Constant gradient test Constant rate of loading test

54 Constant Gradient Test Constant isochrone Maintain the same stress surface Use stepping motor ~ 200 to 2000 step/revolution to control the stepping rate u i u b Transducer

55 Constant Rate of Strain Test In CRS test, the strain rate is uniformly high throughout the test In conventional incremental loading test, the strain rate is very small at the end of any load standard CRS c v cv,crs ~ cv,inc σ v

56 Advantages of CRS Test Reduced testing time Automated data collection and reduction Continuous definition of properties Not at specific loads Reduced extrusion of solids Reduced space requirements

57 Disadvantages of CRS Test Increased capital cost Increased maintenance cost Require better-trained technicians Periodic down-time when something went wrong Require backpressuring No data on secondary effects Secondary effects are hidden in primary stages Higher strain rates than in the field

58 Consolidation Test with k Measurement Performed after primary consolidation No free drainage in the bottom of the consolidation cell Water flow through the specimen from bottom to top

59 Can perform constant head test or falling head test Constant head test is better, at least the state of stress of the specimen remains the same throughout the test Can also use additional air pressure to raise the hydraulic gradient Do not use high gradient because Darcy s law is valid only for constant volume condition

60 logσ e Average stress during k test Elevate pore pressure at the bottom

61 Radial Flow Consolidation Test Drainage column in the center of the specimen A hole is drilled in the center of the specimen and filled with sand or other drainage material Use radial flow theory for data reduction

62 Effect of Partial Saturation Soils with inter-connected air voids k increases with the degree of saturation Soils with occluded air voids Major reason for instantaneous initial compression As the soil becomes saturated almost no instantaneous initial compression Backpressure saturation Can be done with some types of consolidation cells

63 Gas = 5% t U k w 6% 9% 12%

64 Effect of Sampling Disturbance Stress-strain curve Round off Smaller e for given σ The difference between the slope of e log p curve of undisturbed and remolded soil is not very large c v decreased σ max Reduced secondary effects, c α decreased Obtained soil properties

65 logσ remolded 3 tube Sampling disturbance Stress relief e c v 2 tube

66 There are fissures in the field, but we tend to use uniform and good sample in the lab reduced k and c v

Compressibility & Consolidation

CHAPTER Compressibility & Consolidation Settlement If a structure is placed on soil surface, then the soil will undergo an elastic and plastic deformation. In engineering practice, the deformation or reduction