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1D CONSOLIDATION TerzaghiPart 3D A

CameronBarnes Chapter 6

Terzaghis theory of 1D consolidation

- ASSUMPTIONS
- The soil is saturated
- The soil is homogeneous
- Soil solids and water are incompressible
- 1D flow and settlement
- Darcys Law applies (q kiA)
- k mv remain constant
- Strains are small
- e v ?? relationship independent of time

DARCYS LAWrevision

- Steady flow in a saturated soil
- Total head lost as flow proceeds

B

?h

Length, l

A

(No Transcript)

Continuity- rate of change of volume, V,

is dependent on flow velocity, v

By substitution for velocity, v

Coefficient of volume compressibility, mv

Combining..

TERZAGHIS CONSOLIDATION EQUATION

rate of change of excess pwp fn(distribution of

pwp with depth)

Normalized Parameters

Time factor

Depth factor

h maxm. length of flow path z depth from top

of soil layer

Generalized Consolidation Equation

USEFUL SOLUTIONS

- The initial ue is constant with depth
- Possible, if the consolidating layer of soil is

thin and the loaded area is extensive

Soft saturated clay layer

???z

SOLUTION Isochrones for ueo uniform

throughout soil

Z, against consolidation ratio, Uz

Consolidation ratio a pwp term

- ue,z excess pwp at depth, z, at time, t
- ue,z,o excess pwp at depth, z, at time, t 0

Interpretation

Z

0

T

1

2

0

1

Uz

- Double draining layer
- Single draining layer
- use only half the plot, top or bottom

EXAMPLE 1 ueo 90 kPa

Find ue at T 0.3 z 1 m and H 4 m

Z

0

0.5

T 0.3

1

0.48

2

0

1

Uz

ue,z1m (1 Uz)90 kPa (0.52)90

kPa 47 kPa

EXAMPLE 2 as before but single drainage (top

only)

Z

0

0.25

T 0.3

1

0.55

2

0

1

Uz

ue,z1m (1 Uz)90 kPa (0.45)90

kPa 40.5 kPa

EXAMPLE 3 as before but single drainage (bottom

only)

Z

Top of layer no drainage

0

T 0.3

0.25

0.4

1

0

1

Uz

ue,z1m (1 Uz)90 kPa (0.6)90

kPa 54 kPa

IN SUMMARY

- Isochrones represent the distribution of the

excess pwp at any given time throughout the soil

layer - MUST KNOW
- The initial distribution of ue with depth, z
- The faces which drain
- cv

SETTLEMENT

- SINCE the amount of 1D consolidation settlement

is ? volume of water lost - THEN
- the change in the distribution of ue with time

represents the of settlement that has occurred

Settlement with time

Area A1

Area A2

A1 lost excess pwp A2 remaining excess

pwp A1/ (A1A2) settlement, U

U consolidation with time

U

0

100

1

TIME FACTOR, T

0

Further Considerations

- 1. Lowering of water tables also causes

consolidation - as the effective stress in the soil is increased

- (since pwp is decreased)
- e.g. Bangkok, Old Stockholm and Venice

De-watering?

2. DEALING with CONSOLIDATION

- Get it over and done with
- Pre-loading
- Vertical sand drains
- Wick drains
- Avoid the problem
- Deep piling (only

if soft is shallow) - Stone columns
- Drainage and stiffening of soil
- See websites in notes take a look at the sites

Pre-loading

embankment

structure

Vertical Drains Barnes p152

Vertical Drains

Solutions after Barron 1948

Vertical Drains - typical effect

Log (Time)

1 mth 1 yr 10 yrs

30

without drains

? Settlement

with drains

In Summary

- Consolidation in saturated, low permeability

soils, under external loading, is about building

up the effective vertical stress by dissipating

the initial excess water pressure in the soil

through drainage - - shedding of load back to the soil skeleton
- So that ?v? ?v

Summary, contd

- Consolidation settlements are slow and large
- Settlements predicted from consolidometer testing
- needs good samples
- Must take account of p? (OCR)
- Overestimates if lateral movements can occur
- The time for settlement can be estimated
- But is often inaccurate thin permeable

soil layers promote side drainage

Exercises

Try Barnes 6.1 to 6.8

Calculate the consolidation settlement of a 6 m

thick layer of soft saturated clay under the

centre of a uniformly loaded strip, 30 m wide.

The pressure on the strip is 240 kPa.

Compressibilities

- mv 0.73 MPa-1 (50-100 kPa)
- mv 0.62 MPa-1 (100-200 kPa),
- mv 0.67 MPa-1 (200-400 kPa)
- and Cc 0.64

Step 1 sub-layering e,g. 2 m thick layers Step

2 existing average stress levels Step 3 final

effective stresses

Stress data

mv method

sc ?(mv.??'v.?z)

Cc method

- Requires void ratios, eo, at initial stress

levels to convert ?e to ?H - The equation to the NCL
- e 2.5 Cclog??vo
- e.g. at ??vo 100 kPa
- eo 2.5 0.65(2)
- 2.5 1.3
- eo 1.2

Cc method

- Then
- And
- Where Ho 2 m

Cc solution

- Calculate the excess pwp distribution after 5

years, for the problem above if the coefficient

of consolidation, cv is equal to 0.6 m2/year

ueo av 225 kPa

Time Factor

- For a top and bottom draining layer,
- T (cvt) /h2
- 0.65/(3)2
- T 1/3
- (Note if the layer could only drain from the

top, - then T 1/12!)

Depth Factor

- Z z/h
- h 3 m maxm. length of drainage path
- z depth below the TOP of the drainage layer

From Isochrone for T 1/3

Website to quiz yourself with

- http//xnet.rrc.mb.ca/geotechnical/GEOWEB/geocal3/

geoweb/geowebz.htm

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