Title: Effective Stress
1Settlement
- 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
2Consolidation Settlement
- We will focus on consolidation settlement
?h
h
3Consolidation 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
4Consolidation 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
5Consolidation 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
6Laboratory 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(No Transcript)
8Consolidation 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
9Consolidation Curve
10Consolidation Curve
11Overconsolidated 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
12Overconsolidated 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
13Overconsolidation 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
14Finding Pc Casagrandes Method
4
2
3
1
5
15Calculation 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
16Calculation 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
17Calculation 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
18Calculation 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
19Calculation 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?
20Calculation 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
21Calculation 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
22Calculation 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
23Settlement
Lets plot all the stresses
?sv
sv ?sv
gt sc
z
sv
lt sc
sc
24Settlement
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
25Suggested Problems
10.3 10.5 10.8 10.13