Review of soil mechanics

Review of Soil Mechanics
Prof. Jie Han, Ph.D., PE
The University of Kansas
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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

Introduction

Soil Mass
Solids (or particles
or grains)Liquid
Air

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

Soil Particle Size Distribution

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

Soil Particle (Grain) Size
Analysis
• Sieve analysis
Suitable for particle size > 0.075mm
• Hydrometer analysis
A sedimentation method and used for particle
size < 0.075mm

Cover
No. 4
No. 8
No. 16
No. 30
No. 50
No. 100
No. 200
Pan
m1
m2
m3
m4
m5
m6
m7
m8
∑= imM
Dry weight
of soil
Retained
% of
Soil
Retained
r1=(m1/M)x100%
r2=(m2/M)x100%
r3=(m3/M)x100%
r4=(m4/M)x100%
r5=(m5/M)x100%
r6=(m6/M)x100%
r7=(m7/M)x100%
r8=(m8/M)x100%
∑ = %100ir
p1=100%-R1
p2=100%-R2
p3=100%-R3
p4=100%-R4
p5=100%-R5
p6=100%-R6
p7=100%-R7
p8=100%-R8=0%
Cumulative
% of Soil
Passing
∑ = %pi 100
Cumulative
% of Soil
Retained
R1=r1
R2=R1+r2
R3=R2+r3
R4=R3+r4
R5=R4+r5
R6=R5+r6
R7=R6+r7
R8=R7+r8=100%
Sieve Analysis

L
0
60
R reading
Hydrometer Test

Definition of D10, D30, D50, and D60
(Cumulative)PercentofPassing(Finer)
100
80
60
40
20
(Cumulative)PercentofRetained
0
20
40
60
80
100
10 1 0.1 0.01 0.001
Particle Size (mm)– log Scale
D10D30D50D60

Coefficients of Uniformity and
Curvature
Coefficient of uniformity
10
60
u
D
D
C =
Coefficient of curvature
( )
1060
2
30
c
DD
D
C =

Type of Gradation Curves
Cu > 4 (gravel) or 6 (sand)
Others
1 < Cc < 3
Well-graded
Poorly-graded
Well-graded: particle sizes over a wide range
Poorly-graded: particle sizes within a
narrow range

(Cumulative)PercentofPassing(Finer)
100
80
60
40
20
(Cumulative)PercentofRetained
0
20
40
60
80
100
10 1 0.1 0.01 0.001
Particle Size (mm) – log Scale
Well-graded
Poorly-graded
Gap graded
Example of Gradation Curves

Index Properties

Vs = 1
Vw
Va
Vv
V
Ws
Ww
W
Air
Liquid (water)
Solid
Volume - Weight Diagram

Index Properties
Porosity
V
V
n v
=
Void ratio
s
v
V
V
e =
Degree of saturation
v
w
V
V
S =

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

Index Properties
Water content
s
w
W
W
w =
Unit weight of soil
V
W
=γ
Dry unit weight of soil
V
Ws
d =γ

Typical Values of Void Ratio
and Unit Weight
Soil
description
Uniform sand
Dry unit
weight(pcf)
Void ratio Saturated unit
weight(pcf)
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 (50%<2µµµµ)
1.0 - 0.4
0.9 - 0.3
0.95 - 0.2
0.85 - 0.14
1.8 - 0.25
0.7 - 0.13
2.4 - 0.5
12 - 0.6
83 - 118
87 - 127
85 - 138
89 - 146
60 - 135
100 - 148
50 - 112
13 - 106
84 - 136
88 - 142
86 - 148
90 - 155
100 - 147
125 - 156
94 - 133
71 - 128
(NAVFAC DM 7.1, 1982)

Index Properties
Unit weight of water
w
w
w
V
W
=γ
Unit weight of solids
s
s
s
V
W
=γ
Specific gravity of solids
w
s
sG
γ
γ
=

Weight-Volume Relationship
SewGs =

Relative Density
%100x
ee
ee
D
minmax
0max
r
−
−
=
emax = maximum void ratio
emin = minimum void ratio
e0 = void ratio of the soil in place

Qualitative Description of
Degree of Density
Dr (%)
0 - 15
Description
Very loose
15 - 50
50 - 70
70 - 85
85 - 100
Loose
Medium
Dense
Very dense

Moisture content
Solid Semisolid Plastic Liquid
Shrinkage limit, SL Plastic limit, PL Liquid limit, LL
Plastic index, PI
Strain
Stress
Strength and modulus decrease
Compressibility increases
Consistency of Soil - Atterberg Limits

Liquid Limit Test
35mm300
Penetration (mm)
Moisturecontent(%)
LL
20

Plastic Limit Test
Defined as the moisture content at the soil
crumbles when rolled into threads of 1/8 in
(3.2mm) in diameter

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

Soil Classification

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

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

Symbols in the USCS System
Prefix
Suffix
G →→→→ Gravel S →→→→ Sand M →→→→ Silt C →→→→ Clay
O →→→→ Organic Pt →→→→ Peat
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

Water Flow in Soil

h
L
A
1 2
Flow Sand Filter
Darcy’s Experimental Study

Hydraulic Gradient, i = h/L
Velocity
Laminar flow zone
Transition zone
Turbulent flow zone
1
k
Definition of Permeability
(Hydraulic Conductivity)

Darcy’s Law
Average velocity of flow
L
h
kkiv ==
Rate (quantity) of flow
A
L
h
kkiAq ==
Actual velocity of flow
n
v
va =

h
Q
A
SoilL
Constant Head Test

Falling Head Test
Soil
A
Valve
h1
h2
At t=t1
At t=t2
dh
a
L 





∆
=
2
1
h
h
tA
aL
k ln

Field Pumping Test
h2
h1
r2
r1
r
dr
dh
h
Phreatic level
before pumping
Phreatic level
after pumping
Test well
Observation wells
Impermeable layer
q

Permeability from Field
Pumping Test
Permeability
( )2
2
2
1
2
1
hh
r
rq
k
−π






=
ln

Typical Permeability of Soils
Soil or rock formation Range of k (cm/s)
Gravel 1 - 5
Clean sand 10-3 - 10-2
Clean sand and gravel mixtures
Medium to coarse sand
Very fine to fine sand
Silty sand
Homogeneous clays
Shale
Sandstone
Limestone
10-3 - 10-1
Fractured rocks
10-2 - 10-1
10-4 - 10-3
10-5 - 10-2
10-9 - 10-7
10-11 - 10-7
10-8 - 10-4
10-7 - 10-4
10-6 - 10-2

h
Nd
Nf
Bi
Li
Bi = Li
Flow Net
d
f
id
if
N
N
kh
LN
1xBN
khA
L
h
kkiAq ====

Example of Flow Net
Impervious Stratum
4 m 1m
Permeable
stratum
k=3x10-5m/s
10 m
Rate of flow
q = k∆∆∆∆hNf/Nd =3x10-5x3x5/9=5x10-5m3/s/m

Soil Compaction

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

Dry Unit Weight as Compacted
Moist unit weight
V
W
=γ
Zero air voids
SwG1
G
s
ws
d
/+
γ
=γ
Dry unit weight
w1
d
+
γ
=γ
wG1
G
s
ws
dzav
+
γ
=γ

Moisture Content (%)
DryUnitWeight
Zero air voids (S=100%)
Optimum moisture
content, wopt
Maximum unit
weight
Wet of optimumDry of optimum
Compaction Curve

DryUnitWeight
Zero air voids (S=100%)
Line of optimumLow energy
High energy
Effect of Compaction Energy

Moisture Content
Permeability
DryUnitWeight
Permeability of Compacted Soil

California Bearing Ratio (CBR) Test
Soil
WeightPiston
Standard values for a high-
quality crushed stone
Penetration (in.)
0.1
0.2
Pressure (psi)
1000
1500
%,max 100x
.2in.pressure@0standard
.2in.pressure@0measured
.1in.pressure@0standard
.1in.pressure@0measured
CBR 





=

CBR Values of Compacted Soil
Moisture Content
DryUnitWeight
CBR
CBR as compacted
CBR after soaking
Moisture Content

Moisture Content
AxialShrinkage
orSwell(%)
Kneading
Vibratory
Static
Moisture Content
DryUnitWeight
Swell
Shrinkage
Shrinkage and Swell of
Compacted Soil

Spread Fill

Add Moisture to Fill

Compaction using A Vibratory Steel-
Wheeled Roller

Compaction using A Pneumatic
Rubber-Tired Roller

Compaction using A Vibratory
Padded Drum Roller

Quality Control of Soil Compaction
Field determination of soil unit weight
- Rubber balloon method
- Sand cone method
- Nuclear gauge method Compacted soil
Sand
Jar
ValveSteel plate

Stresses in Soil

Vertical Stress at A Point in Soil
p
z
σσσσz
∆σ∆σ∆σ∆σz
σσσσz = Vertical overburden stress or insitu stress induced
by weight of soil
∆σ∆σ∆σ∆σz = Additional stress induced by external loads

z
Soil layer, γγγγ
Vertical Overburden Stress
A
z
A
Az
A
P
z γ=
γ
==σ
P

z Soil layer, γγγγ
z
σσσσz
σσσσz=γγγγz
Vertical Stress Profile

Soil layer 1, γγγγ1
z1
z2
z3
z
σσσσz
γγγγ1z1
γγγγ1z1 + γγγγ2z2
γγγγ1z1 + γγγγ2z2 + γγγγ3z3
Vertical Stress Profile in
Multi-Layer System
A
B
C

z
Soil layer, γγγγsat
Water, γγγγw
Effective Stress and
Pore Water Pressure
P’i
Pui
P
A
u
A
PuP
A
P 'i
'
i
+σ=
+
==σ
∑ ∑
σσσσ = total stress; σσσσ’ = effective stress
u = pore water pressure

z Soil, γγγγsat
Water, γγγγw
z
σσσσz
σσσσz= γγγγzw +γγγγsat(z-zw)
u=γγγγw(z-zw)
σσσσz
’=γγγγzw+(γ(γ(γ(γsat- γγγγw)(z-zw)
zw
σσσσz=γγγγzw
A
Soil, γγγγ
Vertical Stress Profile with A
Ground Water Table

x
y
z
z
x
y
L
P
∆σ∆σ∆σ∆σy
∆σ∆σ∆σ∆σx
Boussinesq Solution - A Point Load
r
( ) 122522
3
2
3
I
z
P
zr
zP
/z =
+π
=σ∆

x
y
z
dx
dy
B
L
p
Vertical Stress Induced by A
Rectangularly Loaded Area
















+−+
++
+







++
++
+++
++
π
= −
1
12
1
2
1
12
4
1
2222
22
1
22
22
2222
22
nmnm
nmmn
tan
nm
nm
nmnm
nmmn
I
pIz =σ∆
z/Bm = z/Ln =

A
1 2
3 4
Example 1
[ ]4321 IIIIpz +++=σ∆

Example 2
A
=
A
1 2
-
A
3 4
[ ]4321 IIIIpz −−+=σ∆

Stress Distribution Method
( )( )α+α+
==σ∆
tanzBtanzL
LB
p
BL
LB
p ''z
22
B
L
p
B’
L’
z
αααα
If tanαααα = 1/2
( )( )zBzL
LB
pz
++
=σ∆

Soil Compressibility

Definitions of Settlements
Total settlement, S1 or S2
Differential settlement, ∆∆∆∆S
Distortion
21 SSS −=∆
Structure
S1
S2
L
LS /∆

Total Settlement
Total settlement
scet SSSS ++=
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)

(a) Initial condition (b) At the moment of load
Consolidation Process
Valve closed
S=0
∆σ∆σ∆σ∆σ’=0
∆∆∆∆u=0
Valve closed
S=0
∆σ∆σ∆σ∆σ’=0
∆∆∆∆u=P/A
PA

Valve opened
Consolidation Process (Continued)
(c) At a time, t
S=δδδδ(t)
∆σ∆σ∆σ∆σ’=kδδδδ(t)
∆∆∆∆u=P/A-kδδδδ(t)
P
δδδδ(t)
Valve opened
S=δδδδp
∆σ∆σ∆σ∆σ’=kδδδδp=P/A
∆∆∆∆u=0
P
δδδδp
(d) At completion of
consolidation

Load
Dial gauge
Oedometer
Consolidation Test

Consolidation Curve
Time (log scale)
Deformation
Stage I: Initial compression
Stage II: Primary
consolidation
Stage III: Secondary
consolidation
tp

Over-Consolidation Ratio
A
Current ground surface
Highest ground surface
in the past
γγγγ z
h
Preconsolidation stress (pressure) - the maximum effective
stress the soil has experienced in the past
pc (or σσσσp’) = γγγγ(h+z)
OCR = pc/σσσσz’
OCR > 1 Overconsolidated soil
OCR = 1 Normally-consolidated soil
OCR < 1 Under-consolidated soil

Pressure, p (log scale)
VoidRatio,e
pc
a b
c
d
e
f
g
αααα
αααα
Determination of Preconsolidation
Stress from Lab Results

VoidRatio,e
e0
Field consolidation curve
Lab consolidation curve
Remolded specimen
Consolidation curveDisturbance
increases
0.42e0
Effect of Soil Disturbance

VoidRatio,e
e0
Virgin consolidation curve
0.42e0
Cc
pc=σσσσz’
e - logp Curve for Normally
Consolidated Soil
Cc = Compression index

VoidRatio,e
e0
Virgin consolidation curve
0.42e0
Cc
pcσσσσz’
Cr
Lab rebound curve
e - logp Curve for
Overconsolidated Soil
Cr = Recompression index

VoidRatio,e
ep
∆∆∆∆e
Time, t (log scale)
t1 t2
Cαααα=∆∆∆∆e/log(t2/t1)
e - logt Curve for
Secondary Consolidation

Typical Compression Indices
Cc = 0.1 to 0.8 and Cc = 0.009(LL-10)
Cr = Cc/5 to Cc/10
Cαααα/Cc = 0.01 to 0.07
For soils

Stress, σσσσ’ (log scale)
VoidRatio,e
pc = σσσσz’
∆σ∆σ∆σ∆σ
Primary Consolidation Settlement
of Normally Consolidated Soil








σ
σ∆+σ
+
= '
z
'
z
o
c
c log
e
HC
S
1 H = Thickness of soil layer

Primary Consolidation Settlement
of Overconsolidated Soil
VoidRatio,e
σσσσz’
∆σ∆σ∆σ∆σ pc
σσσσ
Cr
1
VoidRatio,e
σσσσz’
pc
Cr
1
Cc
1








σ
σ∆+σ
+
= '
z
'
z
o
r
c log
e
HC
S
1 






 σ∆+σ
+
+
+
=
c
'
zc
o
r
c
p
log
e
HC
)OCRlog(
e
HC
S
011

Rate of Consolidation
For U<60%
2
v
100
U
4
T 




π
=
( )U10093307811Tv −−= log.. For U>60%
2
dr
v
v
H
tC
T =
Clay
Sand
H
Hdr

Soil Strength

Direct Shear Test
P
T
Shear box
Porous stone
Soil
Normal stress
A
P
n =σ Shear stress
A
T
=τ

Shear Displacement, δδδδ (mm)
ShearStress,ττττ(kPa)
Peak shear strength, ττττf
Direct Shear Test Data
Residual shear strength, ττττr

Normal stress, σσσσn (kPa)
Shearstress,tf(kPa)
c
φφφφ
Mohr-Coulomb Failure Envelope
φσ+=τ tannf c

Cell (confining)
pressure
Rubber membrane
Drainage or pore pressure
measurement or back pressure
σσσσ3
σσσσ3
σσσσ1
Triaxial Shear Test
Deviator stress
σσσσ3
σσσσ1=σσσσ3+∆σ∆σ∆σ∆σ

Triaxial Shear Test vs.
Direct Shear Test
Direct shear test
- Simple and quick
- Has a defined failure plane
- Not good representation of stress conditions
- Not the best way to determine soil strength
Triaxial shear test
- Complex but versatile
- Better representation of stress conditions
- Better way to determine soil strength

σσσσ3
φφφφ
c
σσσσ
ττττ
σσσσ3 σσσσ1
2θθθθ
σσσσn
ττττf
Total Strength Envelope
σσσσ1
σσσσ1
σσσσ3
θθθθ
σσσσn
ττττf
φσ+=τ tannf c

Effective Strength Envelope
σσσσ
ττττ
φφφφ
φφφφ’
Effective strength
Total strength
'tan' '
φσ+=τ nf c
φσ+=τ tannf c
u

Undrained Shear Strength
σσσσ
ττττ
cu or Su
σσσσ1
σσσσ1
σσσσ3 σσσσ3
φφφφu=0
Unconsolidated Undrained Test (UU)

Unconfined Compression Strength
σσσσ
ττττ
σσσσ3=0 σσσσ1=qu
φφφφu=0
σσσσ1
σσσσ1
cu or Su
Unconfined Compression Test
qu = unconfined
compression strength
cu =qu/2

Slope Stability

Natural slope
Reinforced slope

Steepen Slope to Wall
Increase Space

Foundation
Toe
Crest
Slope angle
m
1
Facing
Foundation
Reinforcement
Reinforced
fill Retained
fill
Components of Slopes

Possible Failure Modes of Slopes
Local failure
Surficial failure
Slope failure
Global failure

Typical Surfical Failure
Original Ground Surface
Slide Mass
Slip Surface

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

Earthquake-Induced Landslide

Definitions of Factor of Safety
Shear strength vs. shear stress
d
f
FS
τ
τ
=
Resisting force vs. driving force
d
r
T
T
FS =
Resisting moment vs. driving moment
d
r
T
T
FS =

Required Factor of Safety
01FS .=Limit equilibrium
5131FS .. −≥
Required FS under static loads
Required FS under seismic loads
11FS .≥

Surficial Slope Stability
- No Seepage
ββββ
H
L
a
b
d
c
F
F
WN
Td
Tr
β
φ
+
βγ
=
tan
tan
sin 2H
c2
FS
β
φ
=
tan
tan
FS if c=0

Surficial Slope Stability
- With Seepage
Equipotential line
ββββ
H
L
a
b
d
c
F
F
W
N Td
Tr
h=Hcos2ββββ
f
e
Seepage
β
φ′
γ
γ′
+
βγ
′
=
tan
tan
sin satsat 2H
c2
FS
β
φ
γ
γ′
=
tan
tan
sat
FS if c=0

Stability of Slope with
Circular Surface - Bishop Method
R
Wi
R
A
BC
Rsinααααi
ααααi
bi
O
Wi
Pi
Ti
Pi+1
Ti+1
ααααi
R
Nr
Tr ααααi
∆∆∆∆li
( )
( )∑
∑
=
=
α
φα+∆
= n
1i
ii
n
1i
iii
W
Wlc
FS
sin
tancos

Minimum FS
Search for Minimum Factor of Safety
R
R
A
BC
Tangential limits
Search centers

Slope Stability with Seepage
R
R
A
BC
bi
O
Equipotential
line
h
ui=γγγγwh
( )[ ]
( )∑
∑
=
=
α
φα∆−+∆
= n
1i
ii
n
1i
iiiii
W
luWlc
FS
sin
tancos

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