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?