1D CONSOLIDATION Terzaghi Part 3 D A Cameron Barnes Chapter 6

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1D CONSOLIDATION TerzaghiPart 3D A
CameronBarnes Chapter 6
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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

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DARCYS LAWrevision

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

B
h
Length l
A
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(No Transcript)
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Continuity- rate of change of volume V
is dependent on flow velocity v
By substitution for velocity v
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Coefficient of volume compressibility mv
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Combining..
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TERZAGHIS CONSOLIDATION EQUATION
rate of change of excess pwp fn(distribution of
pwp with depth)
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Normalized Parameters
Time factor
Depth factor
h maxm. length of flow path z depth from top
of soil layer
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Generalized Consolidation Equation
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USEFUL SOLUTIONS

• The initial ue is constant with depth
• Possible if the consolidating layer of soil is
  thin and the loaded area is extensive

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Soft saturated clay layer
z
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SOLUTION Isochrones for ueo uniform
throughout soil
Z against consolidation ratio Uz
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Consolidation ratio a pwp term

•  
•  
• uez excess pwp at depth z at time t
• uezo excess pwp at depth z at time t 0

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Interpretation
Z
0
T
1
2
0
1
Uz

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

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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
uez1m (1 Uz)90 kPa (0.52)90
kPa 47 kPa
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EXAMPLE 2 as before but single drainage (top
only)
Z
0
0.25
T 0.3
1
0.55
2
0
1
Uz
uez1m (1 Uz)90 kPa (0.45)90
kPa 40.5 kPa
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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
uez1m (1 Uz)90 kPa (0.6)90
kPa 54 kPa
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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

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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
  

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Settlement with time
Area A1
Area A2
A1 lost excess pwp A2 remaining excess
pwp A1/ (A1A2) settlement U
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U consolidation with time
U
0
100
1
TIME FACTOR T
0
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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

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De-watering
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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

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Pre-loading
embankment
structure
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Vertical Drains Barnes p152
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Vertical Drains
Solutions after Barron 1948
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Vertical Drains - typical effect
Log (Time)
1 mth 1 yr 10 yrs
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without drains
Settlement
with drains
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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

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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

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Exercises

Try Barnes 6.1 to 6.8
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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.
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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 eg. 2 m thick layers Step
2 existing average stress levels Step 3 final
effective stresses
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Stress data
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mv method
sc (mv.v.z)
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Cc method

• Requires void ratios eo at initial stress
  levels to convert e to H
• The equation to the NCL
• e 2.5 Cclogvo
• e.g. at vo 100 kPa
• eo 2.5 0.65(2)
• 2.5 1.3
• eo 1.2

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Cc method
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• Then
• And
• Where Ho 2 m

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Cc solution
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• 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
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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!)

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Depth Factor

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

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From Isochrone for T 1/3
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Website to quiz yourself with

• http//xnet.rrc.mb.ca/geotechnical/GEOWEB/geocal3/
  geoweb/geowebz.htm