Effective Stress

1
Settlement

• Immediate settlement Caused by elastic
  deformation of dry and moist soil without any
  change in moisture content
• Primary Consolidation Settlement Volume change
  caused by expulsion of water from voids in
  saturated cohesive soils
• Secondary Consolidation Settlement Volume
  change after primary consolidation as a result of
  plastic adjustment of soil matrix

2
Consolidation Settlement

• We will focus on consolidation settlement

?h
h
3
Consolidation Settlement

• Lets look at how a saturated clay reacts to an
  applied load, starting at time 0 (immediately
  after load was applied). Assuming some clay
  layer of thickness H with drainage both above and
  below (sand layers)

?sv
?uv
?sv


H
H
H


4
Consolidation Settlement

• Now at some time gt 0
• The water slowly is squeezed out of soil and
  takes the path of least resistance
• Pore pressure is decreasing while the effective
  stress increases

?sv
?uv
?sv


H
H
H


5
Consolidation Settlement

• Finally at time 8
• Pore water is in equilibrium and the soil
  skeleton is carrying the entire load
• This process will take time weeks, months, even
  years
• Why and what might this depend on?

?sv
?uv
?sv


H
H
H


6
Laboratory Consolidation Test

• In the lab a soil consolidation test is used to
  determine settlement characteristics of a soil

• All settlement will occur in voids
• HsA Vs
• HsA Ws/Gsdw
• Hs Ws/AGsdw
• Hv H Hs
• eo Vv/Vs HvA / HsA Hv/Hs
• eo void ratio at time 0
• ?e ?H1/Hs
• e1 eo ?e
• e1 void ratio at time gt 0

Hv
Hs
A
7
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8
Consolidation Curve

• Plotting e vs. Log p (void ratio on a linear
  scale vs the load on a log scale)

Cr Recompression Index Slope of line
Cc Compression Index Slope of line
e
Cr also (called Cs in book)
Log p
9
Consolidation Curve
10
Consolidation Curve
11
Overconsolidated Normally Consolidated

• Overconsolidated Some past stress was greater
  than current stress
• Normally Consolidated Current stress is max

At the break in the curve, this value of s is
called sc The PreConsolidation Pressure This
is the max pressure this soil has ever felt
e
sc
Log p
12
Overconsolidated Normally Consolidated

• Overconsolidated Some past stress was greater
  than current stress
• Normally Consolidated Current stress is max

• Once sc is found from the curve
• It is compared to the actual s in the field
  (?z)
• If sc sv Normally Consolidated
• If sc gt sv Overconsolidated
• ie Sample depth 10, no water table, ? 120
  pcf, the actual
• s 1200 psf
• Compare that to sc from consol curve

e
sc
Log p
13
Overconsolidation Ratio
sv OC

• The OCR is the ratio of past effective stress to
  present effective stress
• OCR sc / sv
• OCR 1 means what?

e
sc
Log p
14
Finding Pc Casagrandes Method
4
2
3
1
5
15
Calculation of Settlement

• Consider a layer of clay under an external load

?e eo-e1
?H
?V
Voids
Vve
Voids
Vve
Soil
V0
H

V1
Solids
Solids
Vs1
Vs1
?V V0-V1 HA (H-?H)A ?HA
We know eVv/Vs Also ?e ?Vv/Vs as Vs does
not change
?sv
16
Calculation of Settlement
?V V0-V1 HA (H-?H)A ?HA
We know e Vv/Vs Also ?e ?Vv/Vs as Vs
does not change Solve for ?Vv ?e Vs
Therefore ?V ?Vv ?HA now
?HA ?e Vs
Equation 1
Vs V0 / (1e0) AH / (1e0)
Equation 2
Solve Both Equations for Vs
17
Calculation of Settlement
?HA / ?e HA / (1 e0)
We get ?H H ?e / (1e0) The General
Settlement Equation We will show how this is
the slope of the consol curve rise / run
18
Calculation of Settlement
Normally Consolidated Soil sv sc ?H Cc H /
(1 e0) log (sv ?sv) / sv
Soil stress due to its own weight is here prior
to application of load (OCR 1)
e
Stress is here after application of load
sc
Log p
19
Calculation of Settlement
Normally Consolidated Soil ?H Cc H / (1 e0)
log (sv ?sv) / sv
Review this equation It is simply rise / run
H / (1 e0) is from the general settlement eq.
derived earlier
Cc log (sv ?sv) / sv is the slope ?e Why?
20
Calculation of Settlement
Over Consolidated Soil If (sv ?sv) gt sc ?H
Cr H / (1 e0) log sc / sv CcH / (1e0)
log (sv ?sv) / sc
Soil stress due to its own weight is here prior
to application of load (OCR 1)
e
Stress is here after application of load
sc
Log p
21
Calculation of Settlement
Over Consolidated Soil If (sv ?sv) lt sc ?H
Cr H / (1 e0) log (sv ?sv) / sv
Soil stress due to its own weight is here prior
to application of load (OCR 1)
e
Stress is here after application of load
sc
Log p
22
Calculation of Settlement
The text covers several methods for determining
the values of Cr and Cc. Take a look at those
?sv

• Recall the plot at left
• Now consider a layer of clay to be analyzed for
  settlement
• Now look at the settlement equations
• Given an H How do you determine the values of
  the stresses in that layer?

z
23
Settlement
Lets plot all the stresses
?sv
sv ?sv
gt sc
z
sv
lt sc
sc
24
Settlement
To solve any settlement problem with an
overconsolidated soil you MUST do this plot (or
at least calc the data points) to solve
?sv
sv ?sv
gt sc
z
sv
lt sc
sc
25
Suggested Problems
10.3 10.5 10.8 10.13