Review of Soil Mechanics

1
Review of Soil Mechanics

• Prof. Jie Han, Ph.D., PE
• The University of Kansas

2
Outline of Presentation

• Introduction
• Soil Particle Size Distribution
• Index Properties
• Soil Classification
• Water Flow in Soil
• Soil Compaction
• Stresses in soil
• Soil compressibility
• Soil strength
• Slope stability

3
Introduction
4
Soil Mass
Air
Solids (or particles or grains)
Liquid
5
Formation of Soil

• Weathering
• Break down rock into small pieces by mechanical
• and chemical processes
• Transportation of weathering products
• - Residual soil stay in the same place
• - Glacial soil formed by transportation and
• deposition of glaciers
• - Alluvial soil transported by running water
  and
• deposited along streams
• - Marine soil formed by deposition in the sea

6
Soil Particle Size Distribution
7
Textural Soil Classification
Soil Name
Particle Size (mm)
U.S. Sieve No.
Boulders
gt 300
Cobbles
300 - 75
Gravel
Coarse
3 - 3/4 in.
75 - 19
Fine
3/4 in. to No. 4
19 - 4.75
Sand
No. 4 to No. 10
Coarse
4.75 - 2.00
No. 10 to No. 40
Medium
2.00 - 0.425
No. 40 to No. 200
Fine
0.425 - 0.075
Clays and silts
lt 0.075
8
Soil Particle (Grain) Size Analysis

• Sieve analysis
• Suitable for particle size gt 0.075mm
• Hydrometer analysis
• A sedimentation method and used for particle
• size lt 0.075mm

9
Sieve Analysis
Dry weight of soil Retained
of Soil Retained
Cumulative of Soil Passing
Cumulative of Soil Retained
Pan
10
Hydrometer Test
0
R reading
L
60
11
Definition of D10, D30, D50, and D60
100
0
20
80
60
40
(Cumulative) Percent of Retained
(Cumulative) Percent of Passing (Finer)
40
60
20
80
D30
D10
D50
D60
100
10
1
0.1
0.01
0.001
Particle Size (mm) log Scale
12

Coefficients of Uniformity and Curvature
Coefficient of uniformity
Coefficient of curvature
13

Type of Gradation Curves
Well-graded particle sizes over a wide range
Poorly-graded particle sizes within a narrow
range
14
Example of Gradation Curves
0
100
Poorly-graded
20
80
Well-graded
60
40
(Cumulative) Percent of Passing (Finer)
(Cumulative) Percent of Retained
40
60
Gap graded
20
80
100
10
1
0.1
0.01
0.001
Particle Size (mm) log Scale
15
Index Properties
16
Volume - Weight Diagram
Va
Air
Vv
Liquid (water)
Vw
Ww
V
W
Ws
Solid
Vs 1
17

Index Properties
Porosity
Void ratio
Degree of saturation
18

Degree of Saturation of Sand
Condition of sand
Degree of Saturation()
Dry
0
Humid
1 - 25
Damp
26 - 50
Moist
51 - 75
Wet
76 - 99
Saturated
100
19

Index Properties
Water content
Unit weight of soil
Dry unit weight of soil
20

Typical Values of Void Ratio and Unit Weight
Soil description
Dry unit weight(pcf)
Void ratio
Saturated unit weight(pcf)
Uniform sand
Silty sand
Clean, well-graded sand
Silty sand and gravel
Sandy or silty clay
Well-graded gravel, sand, silt, and clay mixture
Inorganic clay
Colloidal clay (50lt2?)
(NAVFAC DM 7.1, 1982)
21

Index Properties
Unit weight of water
Unit weight of solids
Specific gravity of solids
22

Weight-Volume Relationship
23

Relative Density
emax maximum void ratio emin minimum void
ratio e0 void ratio of the soil in place
24

Qualitative Description of Degree of Density
Dr ()
Description
0 - 15
Very loose
15 - 50
Loose
50 - 70
Medium
70 - 85
Dense
85 - 100
Very dense
25
Consistency of Soil - Atterberg Limits
Stress
Strain
Shrinkage limit, SL
Plastic limit, PL
Liquid limit, LL
Liquid
Solid
Semisolid
Plastic
Moisture content
Plastic index, PI
Strength and modulus decrease
Compressibility increases
26

Liquid Limit Test
35mm
300
LL
Moisture content ()
20
Penetration (mm)
27
Plastic Limit Test
Defined as the moisture content at the soil
crumbles when rolled into threads of 1/8 in
(3.2mm) in diameter
28

Plasticity and Dry Strength of Soil
Plasticity
PI()
Dry strength
Field test on air-dried sample
Non-plastic
0 to 3
Very low
Falls apart easily
Slightly plastic
3 to 15
Slight
Easily crushed with fingers
Medium plastic
Difficult to crush
15 to 30
Medium
Highly plastic
gt 30
High
Impossible to crush with fingers
(Sowers, 1979)
29
Soil Classification
30
Soil Classification Systems

• AASHTO (the American Association of State
  Highway and Transportation Officials)
• USDA (the United States Department of
  Agriculture)
• USCS (the Unified Soil Classification Systems

31

USCS Soil Classification

• Fine-grained soils
• 50 or more passes No. 200 sieve
• Coarse-grained soils
• 50 or more is retained on No. 200 sieve
• Highly organic soils
• has fibrous to amorphous texture

32
Symbols in the USCS System
Prefix
G ? Gravel S ? Sand M ? Silt C ? Clay O ?
Organic Pt ? Peat
Suffix
W ? Well-graded P ? Poorly-graded M ? Silty C ?
Clayey L ? Low plasticity H ? High plasticity
Examples (the first letter to define general soil
type others are modifiers)
GP ? Poorly-graded gravel GC ? Clayey
gravel SW-SM ? Well-graded sand with silt CL-ML ?
Low plasticity silty clay OH ? High plasticity
organic clay or silt
33
Water Flow in Soil
34
Darcys Experimental Study
h
A
Flow
Sand Filter
1
2
L
35
Definition of Permeability (Hydraulic
Conductivity)
Velocity
Turbulent flow zone
Transition zone
Laminar flow zone
k
1
Hydraulic Gradient, i h/L
36

Darcys Law
Average velocity of flow
Actual velocity of flow
Rate (quantity) of flow
37
Constant Head Test
h
L
Soil
Q
A
38
Falling Head Test
a
At tt1
dh
At tt2
h1
h2
Soil
L
Valve
A
39
Field Pumping Test
r1
r
r2
Observation wells
q
dh
dr
Phreatic level before pumping
Phreatic level after pumping
h
h1
h2
Test well
Impermeable layer
40

Permeability from Field Pumping Test
Permeability
41
Typical Permeability of Soils
Soil or rock formation
Range of k (cm/s)
Gravel
1 - 5
Clean sand
10-3 - 10-2
10-3 - 10-1
Clean sand and gravel mixtures
Medium to coarse sand
10-2 - 10-1
Very fine to fine sand
10-4 - 10-3
10-5 - 10-2
Silty sand
10-9 - 10-7
Homogeneous clays
Shale
10-11 - 10-7
10-8 - 10-4
Sandstone
Limestone
10-7 - 10-4
Fractured rocks
10-6 - 10-2
42
Flow Net
h
Li
Nd
Bi
Bi Li
Nf
43
Example of Flow Net
4 m
1m
Permeable stratum
10 m
k3x10-5m/s
Impervious Stratum
Rate of flow
q k?hNf/Nd 3x10-5x3x5/95x10-5m3/s/m
44
Soil Compaction
45

Laboratory Compaction Tests
Type of test
Weight of Hammer (lb)
Drop distance (in)
Blows Per layer
Layers
Standard Proctor
5.5
12
3
25
Modified Proctor
10
18
5
25
46

Dry Unit Weight as Compacted
Moist unit weight
Dry unit weight
Zero air voids
47
Compaction Curve
Zero air voids (S100)
Maximum unit weight
Dry Unit Weight
Wet of optimum
Dry of optimum
Optimum moisture content, wopt
Moisture Content ()
48
Effect of Compaction Energy
High energy
Zero air voids (S100)
Dry Unit Weight
Low energy
Line of optimum
Moisture Content ()
49
Permeability of Compacted Soil
Permeability
Moisture Content
Dry Unit Weight
Moisture Content ()
50
California Bearing Ratio (CBR) Test
Weight
Piston
Standard values for a high- quality crushed stone
Penetration (in.)
Pressure (psi)
Soil
0.1
1000
0.2
1500
51
CBR Values of Compacted Soil
CBR as compacted
CBR
CBR after soaking
Moisture Content
Dry Unit Weight
Moisture Content
52
Shrinkage and Swell of Compacted Soil
Shrinkage
Kneading
Swell
Axial Shrinkage or Swell ()
Vibratory
Static
Moisture Content
Dry Unit Weight
Moisture Content
53
Spread Fill
54
Add Moisture to Fill
55
Compaction using A Vibratory Steel-Wheeled Roller
56
Compaction using A Pneumatic Rubber-Tired Roller
57
Compaction using A Vibratory Padded Drum Roller
58

Quality Control of Soil Compaction
Field determination of soil unit weight
Jar
- Sand cone method
Valve
Steel plate
- Rubber balloon method
Sand
Compacted soil
- Nuclear gauge method
59
Stresses in Soil
60
Vertical Stress at A Point in Soil
p
?z Vertical overburden stress or insitu stress
induced by weight of soil ??z
Additional stress induced by external loads
61
Vertical Overburden Stress
P
Soil layer, ?
z
A
62
Vertical Stress Profile
?z
z
Soil layer, ?
szgz
z
63
Vertical Stress Profile in Multi-Layer System
sz
Soil layer 1, ?1
z1
A
g1z1
z2
Soil layer 2, ?2
B
g1z1 g2z2
z3
Soil layer 3, ?3
C
g1z1 g2z2 g3z3
z
64
Effective Stress and Pore Water Pressure
Soil layer, ?sat
z
Water, ?w
P
Pui
Pi
? total stress ? effective stress u pore
water pressure
A
65
Vertical Stress Profile with A Ground Water Table
sz
zw
Soil, ?
szgzw
sz gzw gsat(z-zw)
Soil, ?sat
z
Water, ?w
A
ugw(z-zw)
sz?zw(gsat- gw)(z-zw)
z
66
Boussinesq Solution - A Point Load
P
x
r
y
x
??z
z
L
y
??x
??y
z
67
Vertical Stress Induced by A Rectangularly Loaded
Area
p
x
dx
dy
B
L
y
??z
z
68
Example 1
1
2
A
3
4
69
Example 2
A

-
1
2
3
4
A
A
70
Stress Distribution Method
p
L
?
B
z
??z
L
B
If tan? 1/2
71
Soil Compressibility
72
Definitions of Settlements
L
Structure
S2
S1
Total settlement, S1 or S2
Differential settlement, ?S
Distortion
73
Total Settlement
Total settlement
Se immediate settlement (elastic deformation)
Sc primary consolidation settlement (due
to dissipation of excess pore water pressure)
Ss secondary consolidation settlement (due
to adjustment of soil fabric)
74
Consolidation Process
Valve closed
P
Valve closed
A
S0 ??0 ?u0
S0 ??0 ?uP/A
(a) Initial condition
(b) At the moment of load
75
Consolidation Process (Continued)
P
Valve opened
P
Valve opened
?(t)
?p
S?(t) ??k?(t) ?uP/A-k?(t)
S?p ??k?pP/A ?u0
(c) At a time, t
(d) At completion of consolidation
76
Consolidation Test
Dial gauge
Load
Oedometer
77
Consolidation Curve
Time (log scale)
Stage I Initial compression
Stage II Primary consolidation
Deformation
tp
Stage III Secondary consolidation
78
Over-Consolidation Ratio
Highest ground surface in the past
h
Current ground surface
?
z
A
Preconsolidation stress (pressure) - the maximum
effective stress the soil has experienced in the
past
pc (or ?p) ?(hz)
OCR pc/?z
OCR gt 1 Overconsolidated soil OCR
1 Normally-consolidated soil OCR lt
1 Under-consolidated soil
79
Determination of Preconsolidation Stress from Lab
Results
g
e
a
b
?
Void Ratio, e
d
?
c
f
pc
Pressure, p (log scale)
80
Effect of Soil Disturbance
Lab consolidation curve
e0
Field consolidation curve
Void Ratio, e
Remolded specimen Consolidation curve
Disturbance increases
0.42e0
Pressure, p (log scale)
81
e - logp Curve for Normally Consolidated Soil
Lab consolidation curve
e0
Virgin consolidation curve
Cc
Void Ratio, e
Cc Compression index
0.42e0
pc?z
Pressure, p (log scale)
82
e - logp Curve for Overconsolidated Soil
e0
Lab consolidation curve
Virgin consolidation curve
Cc
Void Ratio, e
Lab rebound curve
Cr
Cr Recompression index
0.42e0
?z
pc
Pressure, p (log scale)
83
e - logt Curve for Secondary Consolidation
Void Ratio, e
C??e/log(t2/t1)
ep
?e
t2
t1
Time, t (log scale)
84
Typical Compression Indices
For soils
Cc 0.1 to 0.8 and Cc 0.009(LL-10)
Cr Cc/5 to Cc/10
C?/Cc 0.01 to 0.07
85
Primary Consolidation Settlement of Normally
Consolidated Soil
pc ??z
??
Void Ratio, e
Stress, ? (log scale)
H Thickness of soil layer
86
Primary Consolidation Settlement of
Overconsolidated Soil
?z
?
?z
pc
??
pc
??
Cr
Cr
Void Ratio, e
1
1
Void Ratio, e
Cc
1
Stress, ? (log scale)
Stress, ? (log scale)
87
Rate of Consolidation
Hdr
H
Clay
Sand
For Ult60
For Ugt60
88
Soil Strength
89
Direct Shear Test
P
Porous stone
T
Soil
Shear box
Normal stress
Shear stress
90
Direct Shear Test Data
Peak shear strength, tf
Shear Stress, t (kPa)
Residual shear strength, tr
Shear Displacement, d (mm)
91
Mohr-Coulomb Failure Envelope
Shear stress, tf (kPa)
f
c
Normal stress, sn (kPa)
92
Triaxial Shear Test
??
Deviator stress
?1?3??
?3
?1
?3
?3
Rubber membrane
Cell (confining) pressure
Drainage or pore pressure measurement or back
pressure
93
Triaxial Shear Test vs. Direct Shear Test
Triaxial shear test

• Complex but versatile
• Better representation of stress conditions
• Better way to determine soil strength

94
Total Strength Envelope
?1
?
?n
?
?f
?f
?3
?3
?
2?
c
?
?3
?1
?n
?1
95
Effective Strength Envelope
?
Effective strength
?
?
Total strength
?
u
96
Undrained Shear Strength
?
?1
?3
?3
?1
cu or Su
?u0
?
Unconsolidated Undrained Test (UU)
97
Unconfined Compression Strength
?
?1
cu qu/2
?1
cu or Su
qu unconfined compression strength
?u0
?
?30
?1qu
Unconfined Compression Test
98
Slope Stability
99
Natural slope
Reinforced slope
100
Steepen Slope to Wall
Increase Space
101
Components of Slopes
Crest
Facing
1
Toe
m
Slope angle
Foundation
Reinforcement
Reinforced fill
Retained fill
Foundation
102
Possible Failure Modes of Slopes
Slope failure
Global failure
Local failure
Surficial failure
103
Typical Surfical Failure
Original Ground Surface
Slide Mass
Slip Surface
104
Surficial Failure

• Shallow failure surface up to 1.2m (4ft)
• Failure mechanisms
• Poor compaction
• Low overburden stress
• Loss of cohesion
• Saturation
• Seepage force

105
Earthquake-Induced Landslide
106
Definitions of Factor of Safety
Shear strength vs. shear stress
Resisting force vs. driving force
Resisting moment vs. driving moment
107
Required Factor of Safety
Limit equilibrium
Required FS under static loads
Required FS under seismic loads
108
Surficial Slope Stability - No Seepage
L
d
a
F
W
N
Td
c
F
Tr
H
b
?
if c0
109
Surficial Slope Stability - With Seepage
L
Equipotential line
d
f
Seepage
a
F
W
N
Td
hHcos2?
c
F
e
H
Tr
b
?
if c0
110
Stability of Slope with Circular Surface -
Bishop Method
Rsin?i
?li
O
R
Ti
bi
Pi
Ti1
R
B
C
Pi1
Wi
Wi
A
?i
Tr
?i
Nr
?i
R
111
Search for Minimum Factor of Safety
Search centers
R
Minimum FS
R
B
C
A
Tangential limits
112
Slope Stability with Seepage
O
R
bi
R
B
C
h
Equipotential line
A
ui?wh