• 353 review
– Consolidation
– Settlement (differential)
– Weight volume relationships
– Excess Pore pressure
– Effective/total stress
• Soil Strength
– Peak ultimate and residual
– t vs s and Mohr Coulomb
– Undrained vs drained
– Skempton’s A & B
– Loading and unloading
• Slopes
– Wedges and circular failures
– Mitchell charts (Ru)
– Simple derivations
• Bearing Capacity
– Terzaghi BC equation
– Rafts and footings
– Undrained and drained
– Settlement: elastic - consol
– Rocks, and N values
– Eccentricity
• Retaining Walls
– Earth pressures
– Rankine and Coulomb
– Factors of safety

• Assumptions
1. Vertical wall
2. No vertical wall friction
3. Failure planes @…
Active 
45


2
Passive

45


2
• Deviate from Ko
• **
  h
K o
 v
K a
 tan
2
45


2
• Active state soils push wall back
• Wedge is steeper than passive case

• Inclined deviates by:
K a
 cos
 cos
  cos
  cos
2
  cos
2
 cos
2
  cos
2
 therefore
P a




H 2 K a
2

2 c K a

2 c
2



However must still project by cos
 horizontal sin
 vertical

• First term is soil pressure
• Second term removes cohesion
• Third term decreases cohesion to account for tension cracks
P a




H 2 K a
2

2 c K a

2 c
2




Pa acts at H/3 unless…

 c
=25 d
=16
Solve for sliding and Pa

• What do you do when it is given
– Can you trust it
– Should it be there
• Water is bad, can appear even in freedraining materials. Freezing? Uplift pressure?

• According to C.F.M.:
– Two times the strain required for K a for full development of K p
• @ K a use 0.5 K p is needed

• Slopes was a big section, but we didn’t have time to quiz you on a lot of it because of time constraints, but on an exam there is lots of time….
• Sliding blocks
• Wedges
• Bishops long hand
• Mitchell charts
• Free body diagrams

Force balance
F s
 c ' L
W

N sin tan

 driving resisting
Weight
Water?
Friction
Cohesion
Water?
You need to be able to understand the force systems from a first principles standpoint

• Produces a factor of safety on a given slip circle
• No inter-slice forces
• No inter-slice shear
• Factor of safety for all slices is the same
• Assumes soil is a rigid plastic
• Simplified analysis but generally good for Fs>1.2
• The circle with the the lowest Fs is the critical circle
• When the slope angle exceeds 53 degrees the critical circle will pass through the toe
• Must analyze on a slice by slice basis

F s

 cdx

 dW ( 1

R u
) tan


 dW m  sin

R u

 w
H w
 slice
H slice m 
 cos
 

 tan
 sin

Fs assumed


Can you use this method on a wedge?
What is angle
?
Why does factor of safety appear twice?
Is a drawn slip circle necessarily the lowest factor of safety circle?
Where is ground surface?

• Design charts solved for lowest factor of safety circle
• Three charts Ru=0.0, 0.3, and 0.6
• Calc and use average Ru for slope and linear interpolate factor of safety between charts
• Remember using it backwards?
Use
 h c ' tan(

) cot(

)
F s
R u
0
To get tan(

)
F c '
 hFs
0.3

• What about water at the toe
• Excavated slopes?
• To dewater or not to dewater that is the question
• Rapid drawdown
• Tension cracks and slopes
– Not out of the question
– There are even allowances on Mitchell charts for this
• Excavated slopes and stress path

q a q f q f
 c ' N c
S c i c
 
' o
N q
S q i q


' BN  S  i 
2
F s
 q f q a
 max q a
 q f
F
 
' o
Take note of the omission of

D. Oversight, I think not.
Assumptions?
What is the physical meaning of each term?

• Don’t forget about inclined loading
• Settlement
– Immediate drained
– Immediate undrained
– Consolidation settlement
– Layer model with m
1 m
0
• Stress distributions and settlement
• Fadum is Dr. Knight’s
Favourite
• Could also use table from text if provided
• Don’t forget RQD but don’t obsess either
• N values re: q f

Critical depth = 2B
What about Fadum with a point of interest outside of the footing
I see another stress distribution approximation for point loadds

e

M
P
q max



P

W
A f  m

 
1
6 e
B
B '

B

L '

L

2 e
2 e q mim



P

W
A f  m

 
1
6 e
B
• Use q f from bearing capacity and it terns out that using B’ and L’ in the shape factors is more work than it is worth
• If e>B/6 then must use B’ and L’ in q max
& q min
• What about strip footings and retaining walls?

M-C Failure Envelope
Test 1 Failure Circle t ’ t failure (2) t failure (1) c’

3(1)

1(1)

1(2)

1(3)

1
(Failure)

3(2)
 ’ n

1(1)

1(2)

1(3)

1
(Failure)
Sample will fail at intersection with envelope
Test 2 Failure Circle
NOTE: all stresses are effective
Each test is performed at a set void ratio

• Develpoed “B” for a measure of satuation
B

 m
 
3
• Developed “A” parameter for indication of the denseness
A of a sample

(

1
 m
  i
3
) i where :
What about negative values of A f
 m i m o


( m i initail
 m o
) pore pressure m i
 pore pressure at point
(

1
 
3
) i
 deviatoric of interest stress at point of interest

(

1
-

3
)/2 = t
Radius of Circle t d d = c' cos

' tan y
= sin

'
1
S
sin
 ’ = tan  ’
 ’
3
Stress Path of Sample
2 t = d' + S tan

' s s = (

1
' +

3
')/2
Centre of Circle

• Things to note
– Ko line, how do you get it
– Loading 1:1 to the right
– Unloading 1:1 to the left
– Time rate of dissipation of pwp
– Stress path line
– Better or worse than M-C?

• Pore pressure is the difference
– Effective the what the soil “feels”
• Can effective exceed total?
• What does Drained mean.
• What are the implications of undrained?
• Bearing capacity and slopes

• Spring analogy
• Time rate of consolidation
• Differential settlement
• Excess pwp
• OCR

• Redo the buoyancy question from your first assignment.
– Dry density
– Saturation
– Void ratio
– Water content

• Bearing capacity
– Raft or footing
– Fs against load, against settlement
– Inclined load, eccentric load
– Two layer settlement
• Retaining walls
– Rankine
– Two layer
– Inclined
– Passive resistance
– Water

• Stress
– Calc and plot stress paths
– Convert M-C data to t&s
– Peak vs ultimate  and c
– Dilatency
–
• Slopes
– Be prepared for a slice analysis
– Draw force diagrams
– Water effects
– Excavations

• Redo the buoyancy question from your first assignment.
– Dry density
– Saturation
– Void ratio
– Water content
• Theory
– Assumptions
– Coulomb
– A f
– Total vs Effective
– Consolidation
– Mitchell vs Bishop

• In central America several ancient structures that rivaled the pyramids existed.
• Some were destroyed some remain
• How could you use geotech to determine if you were on the site of a large temple that had been destroyed
• The panama government has a site that may be of significance to archeologists, but a mining company wants access to subsurface ore deposits. If mining begins al archeological evidence will be destroyed.
• Can you help determine if the site is important?

• Assumptions
• What would you look for?
• Calculations?