Deformation Behavior of Soils

Consolidation

Hsin-yu ShanDept. of Civil Engineering

National Chiao Tung University

Some Definitions

Settlement: change in elevationCompression: change in thickness

settlement

∑=

∆n

iiS

1

∆Si = compresseion of layer i

Total settlement =

LHS εε ==∆

σ

εσlog

Virgin consolidation curve

reload

rebound

ε

σlog

Virgin consolidation curve

ε

∆L/Ls∆ee

Usually use e for clay, n for sand

fσ0σ iσ

σlog

Virgin consolidation curve

0

ε

001

LeeeLLS s +

∆−=∆−==∆ ε

Ls height of solidsL0 original height of sample (layer)e0 original void ratio

Consolidation Tests

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

Loading

Porous Stone

Dial gauge 1

3456

789

0

Soil Specimen

Porous Stone

2

Restrictions of Consolidation Tests

Suitable for cohesive soilsSand compresses instantly, difficult to measure strain-time relationshipSudden shock makes the measured deformation inaccurate

Simplified stress surface (profile of u vs. H)Coupled with theory

History of Consolidation Test

1809 Thomas Telform was the first to use the term “consolidation”1901 Consolidation test was invented1910 D. E. Morgan invented the floating ring1923 Karl Terzaghi worked on consolidation theory

We usually do not run consolidation test on sand

Volume change takes place instantlyWe can still get the relationship between volume change and stress

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

σlog

rebound

reloadσ

ε

εSemilog plot:Improves linearityEasier to use in low stress range

Nowadays, we don’t have to use semilog plot anymoreInput all experimental data, compute compression through linear interpolation

ε

σlog

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

Some thoughts on Terzaghi’swords

is linear for small strain which is based on linear elasticity and is not true in most cases

σε −

If we use strain εRr = recompression ratioRc = compression ratio

1

2logσσσ RHHmS v =∆=∆

i

fcirv He

cHe

cHe

aSσσ

σσσ log

1log

11 0 ++

+=∆

+=∆

e

ε

Virgin compression

RecompressionScale of strain

σε

logddRr =

σ

Em

dd

v1

==σε

σε

logddRc =

σlogddecr

−=

σlogddecc

−=

vadde

=−σ

Recompression indexCompression index

mv = coefficient of volume compressibilityav = coefficient of comprssibility

vv ae

m+

=1

1

Some Corrections of the Measured Change in Height

Machine deflection – deformation of the apparatus itself, i.e., porous disks, loading cap, piston

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

Square Root Time Methodt

S = U Su

2HtcT v=s

vcHTt

2

=

2

4UT π

=Fox’s equation, for U ≤ 60%

t = FS2 At least for U ≤ 60%, t1/2 ~ S is a straight line if T’s theory is valid

t

s

Initial portion may be higher or lower than S0

Straight line portion

d50

9/5 d50

s90

Peat

Extension from the straight line portion

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.

How Do We Get the Factor 1.15?

197.059

59

848.0

50

90

Fd

Fd

⋅=

=

15.11526.1197.05

9848.0

59

50

90 ≈=⋅

=F

Fd

d

It makes no difference if we use d40 and T40 to construct d90 and T90, we get the same results

90100 910 SS ∆=∆

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

Log Time MethodLog t

t1

t2

∆s1Pick t1, t2, so that t2=4t1 to get s0

∆s1

s

s100

Most of the time, it is difficult to get this straight line, since the secondary effect does not necessarily produce a straight line

Square Root t vs. Log t

There was a war going on between MIT and HarvardTo decide which one is correct compare with k valueGenerally, square root t method is betters100 from log t method is ambiguous

Square root t method only gives one cv, log tmethod gives different cv by different people

Square root t method usually gives higher cv

kc computed from cv almost always smaller than km actually measuredSecondary effects lead to a delay in settlement in addition to that caused by the real kIf all causes of delayed compression are lumped into kc kc < km

Smaller k slower compression

Special Aspects of Consolidation Testing

Rapid loadingIncrease loading as soon as s100 is reachedContinuous loading

Boundary impedenceRing frictionEffect of temperatureRates of dissipation of pore water pressuresEffects of non-linear stress-strain curve

Rapid LoadingStandard

cv

Rapid

σlogSmaller cv means smaller kRapid loading reduces the “delay” effect of secondary consolidation

Boundary Impedencet

Old porous stone PLUS filter paper

Old porous stone, NO filter paper(likely to be clogged by fine particles)

Impedence factor I increasesHk

kHId

d=s

New porous stone, NO filter paper

Hd is the thickness of the porous discThe smaller the better

kd is the hydraulic conductivity of the porous disc

The larger the betterFree drainage I = 0I should be kept less than 0.01I affects the time rate of consolidation, but it does not affect the total settlement

How to Reduce I

Keep the porous stone cleanUse filter paper to keep the fine particles from entering porous stoneBoil the porous stone before use to get the trapped air out

Ring Friction

Effects of ring frictionDuring loading reduce stress acted on the specimen specimen compresses lessDuring rebound reduce the swelling tendency

specimen swell lessFlatten the swelling curve at low stress level

Taylor (1942)

λpq =

)]4exp(1[4 H

DK

KH

Do

o

µµ

λ −−= Make λ 1 to reduce friction

Q

Q = P – τ z π DP

The stress in the ring is not uniform

zτ

τ = σv Ko µ

Use consolidation rings made of cadmium, nickel, hard chrome will be fineDon’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 steelλ increases as consolidation pressure goes up less error

Use larger D/H ratio, the larger D/H the smaller the effect of friction

Wide and thin specimenFor D/H about 3, greased steel, total error is about 10%

Effect of Temperature

Stress-strain curveThe higher the temperature, the lower the e-log pcurve

This may due to the change of volume of the consolidation ring at higher temperature

The ring expands such that the friction decreases

σlog

Reduction in eAs temperature goes up

e

Effect on cv and kAs temperature goes up, cv increases since kdecreases as the viscosity of water gets smallerThe water flows faster

Effects of Non-Linear Stress-Strain Curve

Effect on settlement-time relationshipEffect on

Effect on cv and av

i

b

uu

Effect on Settlement-Time Relationship

σ

(2)NC clay, concave upwardsResultant cv decreases

(1)

e

(3)OC clay, concave downwardsResultant cv increases

t

(2) NC clay

(3) OC clayU = 90%

U

Influence of Secondary Compression on Subsequent Behavior

Stress-strain behaviorSubtract the secondary compression to get the stress-strain curve (e – log p)?

Settlement-time relationshipLoading rate in the lab is very highSlow loading in the fieldDrainage distance in the field is far greater than in the lab

May be difficult to see secondary effect

log t

H = 5.5”

H = 0.37”

s

Almost totally secondary compression

Secondary compression may not affect the primary consolidation of next load incrementalMaterials such as peat also has primary stage, but its properties changes a lot during this period

Difficult to obtain meaningful parameters

Secondary compression

Secondary effect exists through out the whole consolidation, including in the primary stage

tddlogεεα =

00 log

ttHSs αε=

tddeclog

=α

00 log

1 ttH

ecSs +

= α

PeatVery high water contentLoose or no contact between solidsLab test demonstrate limited primary consolidation but very large secondary compression

Squeezing out of waterReorientation of particlesProperties changed a lot

The significance of secondary effect is often overlooked

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

Quick Loading Test

Monitor the s ~ t relationshipApply next incremental load once the primary consolidation completesEliminate the secondary effect?

Continuous Loading Tests

Constant rate of strain (CRS) testControlled deformation rate

Constant gradient testConstant rate of loading test

Constant Gradient Test

Constant isochroneMaintain the same stress surface

Use stepping motor ~ 200 to 2000 step/revolution to control the stepping rate

bu

iu

Transducer

Constant Rate of Strain Test

In CRS test, the strain rate is uniformly high throughout the testIn conventional incremental loading test, the strain rate is very small at the end of any load

standard CRS

vσ

cv

cv,CRS ~ cv,inc

Advantages of CRS Test

Reduced testing timeAutomated data collection and reductionContinuous definition of properties

Not at specific loadsReduced extrusion of solidsReduced space requirements

Disadvantages of CRS TestIncreased capital costIncreased maintenance costRequire better-trained techniciansPeriodic “down-time” when something went wrongRequire backpressuringNo data on secondary effects

Secondary effects are hidden in primary stagesHigher strain rates than in the field

Consolidation Test with kMeasurement

Performed after primary consolidationNo free drainage in the bottom of the consolidation cellWater flow through the specimen from bottom to top

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

σlog

Elevate pore pressure at the bottom

e

Average stress during k test

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

Effect of Partial SaturationSoils with inter-connected air voids

k increases with the degree of saturationSoils with occluded air voids

Major reason for instantaneous initial compressionAs the soil becomes saturated almost no instantaneous initial compression

Backpressure saturationCan be done with some types of consolidation cells

tGas = 5%

6%

9%

kwU

12%

Effect of Sampling DisturbanceStress-strain curve

Round offSmaller e for givenThe difference between the slope of e –log p curve of undisturbed and remolded soil is not very large

cv decreasedReduced secondary effects, cα decreasedObtained soil properties

σmaxσ

σlog3” tube

2” tube

remolded Sampling disturbanceStress relief

e

cv

There are fissures in the field, but we tend to use “uniform” and “good” sample in the lab reduced k and cv