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354 Final Exam Tutorial Topics
• 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
Retaining Walls - Rankine
• 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
Rankine
• 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
Rankine Pa
• 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…
Example
c =25 d =16 Solve for sliding and Pa
Cohesion
• What do you do when it is given – Can you trust it – Should it be there • Water is bad, can appear even in free draining materials. Freezing? Uplift pressure?
Active vs Passive
• 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
Passive Aggressive
Slopes and Sliding
• 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 Weight Water?
resisting Friction Cohesion Water?
Wedgies
You need to be able to understand the force systems from a first principles standpoint
Bishop
• 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
Bishop
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?
Crap, don’t I need a bad ass table for this question
Mitchell Charts
• 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
Slippery slopes
• 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
Footings, I got your footing right here buddy
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?
Have I ever told you I hate footings
• 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
Like I need to talk to you about
Critical depth = 2B
stress.
What about Fadum with a point of interest outside of the footing I see another stress distribution approximation for point loadds
Eccentricity! Doesn’t that have
B
'
L
'
e
B L P M
something to do with Liberace
q
max
P
W A f
m 1 6
e B
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?
Soil Strength
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
Skempton
• 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
Soil Strength
( 1 3 )/2 = t Radius of Circle t d d = c' cos ' tan y = sin '
1 S
Soil Strength
sin ’ = tan ’ ’
3
Stress Path of Sample
2
t = d' + S tan ' s s = ( 1 ' + 3 ')/2 Centre of Circle
t vs s space the final frontier
T & S is that anything like S&M?
• 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?
Effective vs Total and Drained vs Undrained
• 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
Consolidation
• Spring analogy • Time rate of consolidation • Differential settlement • Excess pwp • OCR
Weight and Volume
• Redo the buoyancy question from your first assignment.
– Dry density – Saturation – Void ratio – Water content
Jojo’s Network
• 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
Jojo’s Network
• 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
Psychic Friends Network
• 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
Thought game
• 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?