Rock

1
Rock Soil Mechanics

• Course Coordinator
• Donald A. Cameron
• 2006

2
Course outline - Rocks

• Module 1 core drilling and logging
  groundwater rock testing hemispherical
  projection methods rock mass classification
  stress theories and strength criteria bearing
  capacity slope stability

3
Module 1 Soil Mechanics

• Estimate the influence of surface loads on soil
  stresses
• Understand the principles of consolidation
• Have a knowledge of direct shear and triaxial
  tests and their applicability to common soil
  engineering problems
• Prepare the design of non-embedded retaining
  walls
• Analyse slope stability with pore water pressures

4
Module 2 Soil Mechanics

• Estimate immediate long term settlements
• Design shallow footings for bearing capacity
• Design deep footings for vertical loading
• Design a site investigation program with an
  understanding of the available methods of
  investigation and sampling

5
1. Soil Stresses

• Revision of dead weight stresses and effective
  stress
• Horizontal earth pressures at rest
• Simple analyses - for uniformly loaded areas,
  over a deep layer of homogeneous and isotropic
  material material
• Stress bulb concept

6

• HORIZONTAL STRESSES ?
• ??H in a soil mass,
• are not the same as the
• vertical stresses, ???z

Z
7
An Earth Pressure State

• AT REST PRESSURE
• K Ko
• The soil is unable to move laterally
• - it cannot expand OR contract
• e.g soil confined in a large body of soil
• no buildings, no cuttings

8
NOTE

• The earth pressure coefficient is a ratio of
  EFFECTIVE soil stresses
• SO,
• must take into account the pore water pressures
• ? ?? total stress pwp
• ? - u

9
Soil Response to an External Load

• THEORY OF ELASTICITY
• Hookes Law
• Youngs Modulus, Es
• Poissons ratio, ?s
• Soil is a non-Hookean material
• Non-linear elasticity up to peak strength

10
Elastic theory Boussinesq (1885)

• Extra soil stresses, ??v (or ??z) , due to a
  surface loading for
• Homogeneous soil
• Isotropic soil
• Linear elastic
• Semi-infinite layers

11
Stress influence factor,
Note only about 10 of q felt at z 4r
12
Stress Bulb Concept

• ??v 10 q in soil plots almost as a circle
  (strip footings) or a sphere (square or circular
  pad footings)

Zone of influence
13
Most useful Elastic Stress solutions

• corner of a flexible rectangle, uniformly
  loaded, finite soil

q
h
14
Corners of rectangles

• GEOMETRIC SUPERPOSITION to get stresses below any
  point
• e.g. point A 3 rectangles

A
Rectangles must meet at a common corner
15
In conclusion

• Soil carries stresses due to self weight, water
  and past external forces.
• New external loads due to buildings, embankments
  or dams increases these pressures.
• Elastic theory is commonly used to estimate the
  stress increase for analysis of settlements.

16
GEOMETRIC SUPERPOSITION Centre of a rectangle
L (gtB)
A
B
4 rectangles meeting at at a common corner
17
1D CONSOLIDATION - SCOPE

• 1D consolidation testing
• Consolidation parameters
• Settlement
• Rate of settlement
• Pre-consolidation pressure
• Excess pwp
• 1D consolidation
• Isochrones of excess pwp
• Geotechnical Practice!

18
Introduction

• Non-recoverable or plastic settlement when loaded
• Saturated soils and time dependent consolidation

19
WET SOIL RESPONSE

• No air voids in the sample
• External loading cant produce any immediate
  change in volume of the soil!
• undrained loading of a saturated soil, or
  short term loading response
• HOWEVER with time, the water can escape
• soil drainage

20
UNDRAINED LOADING

• Drainage is very slow
• permeability, k ? m/sec
• Settlement can only occur in the short term under
  external vertical pressure, if the soil can
  expand laterally
• (since ?V 0)
• In 1-D loading, the soil is completely restrained
  laterally

21
The Long Term Response (constant load)

• Despite the low permeability, the soil will
  drain, over months, or maybe years
• reduction in void ratio, e
• Settlement!
• ?Vsoil ?Vwater
• sc ?Vw 1D consolidation

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Consolidation - definition

• Long-term settlement under constant external
  pressure
• through drainage of some pore water
• Equilibrium is reached, when the increase of
  effective stress in the soil the increase of
  total stress arising from the applied surface
  pressure, i.e.
• ??v ??'v

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Equilibrium?
When the pwp returns to what it was before
external pressure was applied The spring then
takes all the extra stress, ??v
EXCESS pwp, ue, is lost through drainage
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In Summary

• Consolidation in saturated, low permeability
  soils, under external loading, is about building
  up the effective vertical stress by dissipating
  the initial excess water pressure in the soil
  through drainage
• - or shedding of load back to the soil skeleton,
  so that ?v? ?v

25
End Note

• A consolidated soil is a physically improved
  soil!
• Less void space
• Greater contact between soil particles
• Stronger and stiffer!

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Testing for Consolidation Parameters
Void ratio and 1D Strain
- 1D only
27
Time, t, after load application but before
equilibrium

• Intermediate level of pore water pressure
• u 0 at drainage surfaces, any time!
• soil drains though top or bottom face of sample
• Maximum path length?
• h H/2

28
Intermediate pwp distribution, i.e. before
equilibrium is reached

x 0 kPa
x ut lt ueo
x 0 kPa
Drainage faces, u 0
29
Information from testing

• Each stage
• Time rate of consolidation
• All loading stages
• Compressibility of the soil
• Pre-consolidation history of the soil
• Unloading stages
• rebound or swelling index

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coefficient of consolidation

• Is estimated from plots of settlement against
  EITHER
• SQRT(time)
• LOG10 (time)
• AND using Terzaghis 1D Consolidation theory

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Terzaghis coefficient of volume compressibility,
mv
32
Compressibility Index, Cc
Void ratio, e
log10??v at end of test (kPa)
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Compressibility Index, Cc
Definition
34
Preconsolidation pressure
Void ratio, e
OC
NC
NCL or virgin consolidation line
log10??v at end of test
35
Over Consolidation Ratio (OCR)

• The ratio of the maximum past effective stress
• to the current effective stress
• Casagrande construction demonstrated in
  practical

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Summary

• CONSOLIDATION TESTING
• provides
• Pre-consolidation ratio and hence OCR
• Compressibility
• from which estimates of settlements may be made
• The time rate of settlement

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TERZAGHIS CONSOLIDATION EQUATION
rate of change of excess pwp fn(distribution of
pwp with depth)
38
Normalized Parameters
Time factor
Depth factor
h maxm. length of flow path z depth from top
of soil layer
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USEFUL SOLUTIONS

• The initial ue is constant with depth
• Possible, if the consolidating layer of soil is
  thin and the loaded area is extensive

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Soft saturated clay layer
???z
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SOLUTION Isochrones for ueo uniform throughout
soil
Z, against consolidation ratio, Uz
42
Consolidation ratio a pwp term

•  
•  
• ue,z excess pwp at depth, z, at time, t
• ue,z,o excess pwp at depth, z, at time, t 0

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Interpretation

• Double draining layer
• Single draining layer
• use only half the plot, top or bottom

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IN SUMMARY

• Isochrones represent the distribution of the
  excess pwp at any given time throughout the soil
  layer
• MUST KNOW
• The initial distribution of ue with depth, z
• The faces which drain
• cv

45
CONSOLIDATION SETTLEMENT

• SINCE the amount of 1D consolidation settlement
  is ? volume of water lost
• THEN
• the change in the distribution of ue with time
  represents the of settlement that has occurred
  

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Settlement with time
A1 lost excess pwp A2 remaining excess
pwp A1/ (A1A2) settlement, U
47
U consolidation with time
U
0
100
1
TIME FACTOR, T
0
48
Further Considerations

• 1. Lowering of water tables also causes
  consolidation
• as the effective stress in the soil is increased
  
• (since pwp is decreased)

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DEALING with CONSOLIDATION

• Get it over and done with
• Pre-loading
• Vertical sand drains
• Wick drains
• Avoid the problem
• Deep piling (only if soft soil is shallow)
• Stone columns
• Drainage and stiffening of soil

50
In Summary

• Consolidation in saturated, low permeability
  soils, under external loading, is about building
  up the effective vertical stress by dissipating
  the initial excess water pressure in the soil
  through drainage
• - shedding of load back to the soil skeleton
• So that ?v? ?v

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Summary, contd

• Consolidation settlements are slow and large
• Settlements predicted from consolidometer testing
• needs good samples
• Must take account of p? (OCR)
• Overestimates if lateral movements can occur
• The time for settlement can be estimated
• But is often inaccurate (thin permeable soil
  layers promote side drainage)

52
Website to quiz yourself with

• http//xnet.rrc.mb.ca/geotechnical/GEOWEB/geocal3/
  geoweb/geowebz.htm

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THE SHEAR STRENGTH OF SOIL

• D. A. Cameron
• Soil and Rock Mechanics 2006

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SHEAR STRENGTH Scope

• Shear strength parameters
• c and ?
• c? and ??
• Typical values
• TESTS
• Direct shear test
• Triaxial test with pwp measurement
• undrained drained tests (short v long term)
• Vane shear

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Introduction

• Tensile strength is negligible
• Soil is ductile rather than brittle
• Confining pressure influences strength
• Loading of soil produces either ?V, or pwp
  increase , OR both

56
Defining strength parameter

• Shear strength!
• Soil masses fail usually along weakened surfaces
• sliding surface or slip surface develops
• Stability analyses
• What resisting shear forces exist within the soil
  to prevent sliding?

57
(1) Lab. Direct Shear Test

• Soil cut into box with split sides
• Vertical load applied

58
Direct Shear Test information

• Shear force (T) from load cell
• Shear stress (?) from shear force and current
  area
• Current shear area from displacement
• Displacement from time and rate of movement of
  box
• Normal stress (?N) from applied force N ? initial
  sample area, Ao

59
Load-deflection constant normal stress
Shear Stress, ? T/A
Shear Strain, ? ?/L
60
From the previous diagram ? v ?n
Peak strength
residual?
61
Shear Strength Parameters

• Equation to the failure line
• ?peak c (?N)tan?
• Coulomb strength criterion
• tan ? coefficient of friction
• c apparent soil cohesion

62
Limitations of Direct Shear

• Planar shear failure
• may not be the plane of weakness
• Boundary interruption
• changing area
• NO control of pwp
• total stresses only
• Regarded as,
• a drained shear test for sands
• Drained for clays if rate of shearing slowed in
  line with cv
• then u ? 0 and ? ? ??

63
VARIATIONS of PARAMETERS

• angle based on total stress
• fn(soil type, soil density,
• particle size, mineralogy)
• ?? effective angle of friction, based on
  effective stress
• Therefore must know pwps!
• ?D drained angle of friction ??
• (found from a slow test, which ensures drainage
  so no excess pwp!)
• Cohesion varies similarly
• SO strength varies with drainage condition

64
THE TRIAXIAL TEST

• A cylindrical sample of soil is placed in the
  triaxial cell
• The triaxial cell is placed in a compression
  testing machine
• All-round stress is applied by water under
  pressure
• cell pressure confining pressure, ?2 ?3
• cell pressure is applied also to the top and
  bottom of the sample
• so, the sample is held under an isotropic stress
  state

65
F/A ? (?1 - ?3)
?3
cell pressure, ?3
66
Conventional triaxial testing

• ?3 applied (to 400 kPa)
• sample conditioning?
• back-saturation?
• Isotropic consolidation
• drains opened under ?3

67
Conventional Testing

• Ram pushed down ? (?1 - ?3)
• Soil loaded at constant rate of strain
• UNDRAINED test drain closed
• DRAINED test at very slow rate with drain open
• pwp not measured if only c ? required
• pwp measured to provide c?, ?? in an UNDRAINED
  test
• pwp measured to check loading rate in a DRAINED
  test

68
Conventional Testing

• Axial strain measured
• Force through ram measured
• Testing stopped when failure reached
• soil bulges?
• area correction must be applied to find (?1 -
  ?3)max

69
Strength parameters?

• from Mohrs circles
• Need at least 3 identical specimens, each tested
  at different constant cell pressures
• ALTERNATIVE TO CIRCLES plot the apex
• t v s
• corrections apply

70
Failure planes
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IN SUMMARY

• Shear strength parameters, c, ?
• Depend on drainage conditions
• Direct shear test easy, but very limited
• Triaxial offers much more
• pwp control and measurement
• Constant strain rate tests
• Stress path tests

72
Shear Strength Clays v Sands
Sands no fines ?wet ? ?dry i.e. ?? ? ?
73
Dense Sand

• Has higher ??p
• Is strain softening
• Shows dilatancy
• Has same ??cv value as the same sand but less
  dense

74
Typical values of the strength
parameter for sands

• ??p ? 35 to 50?
• Strength fn(density, psd and grain shape)
• ??cv ? 27 to 35?

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CLAYS Undrained Strength

• A Unconsolidated, Undrained (UU)
• The sample is not conditioned back to field
  state
• stress relief
• greater void space
• de-saturation ?
• Saturated NC clays (? ? 0)
• ?peak cu

76
cu undrained cohesion
?, shear stress
What is the unconfined compression strength ?
? ? 0
?3 50
100
200
2cu
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B Consolidated, Undrained Tests
(CIU)Consolidated Isotropically, Undrained

• A better test for the conditioning of the sample

• pwp measured - effective strength parameters, c?
  and ??
• CLAYS ?? ? 20 to 35?
• c? 0 kPa for NC clays
• BUT c? ? 30 kPa for OC clays

78
SOIL CONSISTENCY - descriptors

• CLEAN SANDS
• Based on density index, ID ()
• e.g. loose 15 35 dense 65 85
• Peg test?

• CLAYS
• Based on undrained shear strength ?
  cu (kPa)
• e.g. firm 25 50 stiff 50 100
• Thumbnail test?

79
Shear Vane

• Is useful for residual strengths of soft to firm
  clays
• Can measure SENSITIVITY of clays, silts
• SENSITIVITY cu undisturbed / cu remoulded
• QUICK clays , sensitivity 16 to 100!

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KEY POINTS

• Shear model
• Coulomb shear strength
• cohesion, friction
• Total v effective stress strength parameters
• Clean Sand v Clay
• Clay
• UNDRAINED loading
• NC clay - no frictional response
• same soil tested slowly, has c? ??
• Dilatancy - when does it occur?

81
SUMMARY, continued

• Strength tests
• Direct shear
• Triaxial
• Vane shear
• Mohrs circles
• failure planes
• Pole
• Stress paths
• t v s

82
SLOPE STABILITY - Infinite slopes?
b
Vertical slice
Sliding surface
h
b
83
Force equilibrium the slice
WN Wsin?
W
84
CASE 1 c? 0, so C 0
The natural angle of repose ?
85
Case 2 c 0, seepage down the slope

• Phreatic surface at slope surface
• Pore force, U, on sliding base due to pore water
  pressure
• Effective normal force reduced less friction!
• almost only half the FoS!

86
CIRCULAR SLIPS More common in cohesive soils
centre of circle
crest of slope
slope
87
CIRCULAR SLIPS Stability? Limit equilibrium
Case 1 ?? 0 c cu
centre of circle
88
CIRCULAR SLIPS c', ?? soil
? varies with position ? c? ?n?tan ??
Near crest
W
?
Near toe
?
89
CIRCULAR SLIPS Method of Slices
centre of circle
90
Reasons for Slices

• Frictional shear resistance varies with both ?N
  and ??
• Varying cohesion with depth
• Non-uniform pwps from seepage analysis

91
General Method of Slices

• FoS by summation over all slices for trial
  failure surface
• 100s of trial surfaces evaluated
• thank you for the pc!
• XSLOPE and GALENA
• Lowest FoS ? the critical failure surface

92
centre of circle
Stability of a Vertical Slice
Slice i
Wi
93
PWP influence
Wi
Wicos?
Wisin?
94
Simplified Bishop Method - a superior method

• Resultant of side forces acts horizontally
• Apply FoS (F) to restoring shear force
• T l(c? ?N?tan??)/F
• Sum all vertical forces
• W ?N?cos? (c?l N?tan??)sin?/F
• Solve for N?
• Substitute in

95
The Bishop Equation
Where
96
Simplified Bishop Method

• Requires iteration
• Assume initial F, then solve for F
• When trial F and determined F are equal, its a
  solution
• Spreadsheet for simple slopes
• XSLOPE and GALENA otherwise

97
What strength should be applied?

• MUST be appropriate to the field stress levels
• stresses may be quite low
• Undrained or Drained
• short term (just constructed) or long term
  stability?

98
What strength?

• Peak strength
• First time slides? Or compacted soils
• Softened strength (critical state)
• Fissured, stiff clays?
• Residual strength
• Evaluation of stability of slips or pre-existing
  slides
• Bedding shear planes

99
SUMMARY KEY POINTS

• Angle of repose for dry granular soils
• Influence of seepage on granular soils
• Slope stability for homogeneous slopes in
  saturated clay (NC)
• simple analyses
• Frictional soils more difficult
• Method of slices
• Slope stability programs use limit equilibrium

100
POINTS, continued

• Slope stability programs search for the failure
  surface with lowest FoS
• Bishops simplified method for circular slips
• Importance of shear strength parameters
• drained and/or undrained?
• peak, ultimate or critical state?