review of soil mechanics
TRANSCRIPT
Review of Soil Mechanics
Prof. Jie Han, Ph.D., PE
The University of Kansas
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 mechanicaland 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 anddeposited 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
CoarseFine
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
(Cu
mu
lati
ve)
Perc
en
t o
f P
assin
g (
Fin
er)
100
80
60
40
20
(Cu
mu
lati
ve)
Perc
en
t o
f R
eta
ined
0
20
40
60
80
10010 1 0.1 0.01 0.001
Particle Size (mm)– log Scale
D10D30D50D60
Coefficients of Uniformity and Curvature
Coefficient of uniformity
10
60u
D
DC =
Coefficient of curvature
( )
1060
2
30c
DD
DC =
Type of Gradation Curves
Cu > 4 (gravel) or 6 (sand)
Others
1 < Cc < 3Well-graded
Poorly-graded
Well-graded: particle sizes over a wide range
Poorly-graded: particle sizes within a narrow range
(Cu
mu
lati
ve)
Perc
en
t o
f P
assin
g (
Fin
er)
100
80
60
40
20
(Cu
mu
lati
ve)
Perc
en
t o
f R
eta
ined
0
20
40
60
80
10010 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
Vn v=
Void ratio
s
v
V
Ve =
Degree of saturation
v
w
V
VS =
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
Ww =
Unit weight of soilV
W=γ
Dry unit weight of soilV
Wsd =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
ww
V
W=γ
Unit weight of solids
s
ss
V
W=γ
Specific gravity of solidsw
ssG
γ
γ=
Weight-Volume Relationship
SewGs =
Relative Density
%100xee
eeD
minmax
0maxr
−
−=
emax = maximum void ratioemin = minimum void ratioe0 = 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
Str
ess
Strength and modulus decrease
Compressibility increases
Consistency of Soil - Atterberg Limits
Liquid Limit Test
35mm300
Penetration (mm)
Mo
istu
re c
on
ten
t (%
)
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 soils50% or more passes No. 200 sieve
� Coarse-grained soils50% or more is retained on No. 200 sieve
� Highly organic soilshas fibrous to amorphous texture
Symbols in the USCS System
Prefix
Suffix
G →→→→ Gravel S →→→→ Sand M →→→→ Silt C →→→→ ClayO →→→→ Organic Pt →→→→ Peat
W →→→→ Well-graded P →→→→ Poorly-graded M →→→→ SiltyC →→→→ 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 gravelSW-SM →→→→ Well-graded sand with siltCL-ML →→→→ Low plasticity silty clayOH →→→→ 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
hkkiv ==
Rate (quantity) of flow
AL
hkkiAq ==
Actual velocity of flow
n
vva =
h
Q
A
SoilL
Constant Head Test
Falling Head Test
Soil
AValve
h1
h2
At t=t1
At t=t2
dh
a
L
∆=
2
1
h
h
tA
aLk ln
Field Pumping Test
h2h1
r2
r1
r
drdh
h
Phreatic levelbefore pumping
Phreatic levelafter pumping
Test well
Observation wells
Impermeable layer
q
Permeability from Field Pumping Test
Permeability
( )22
21
2
1
hh
rr
q
k−π
=
ln
Typical Permeability of Soils
Soil or rock formation Range of k (cm/s) Gravel 1 - 5Clean sand 10-3 - 10-2
Clean sand and gravel mixtures
Medium to coarse sandVery 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
BiLi
Bi = Li
Flow Net
d
f
id
if
N
Nkh
LN
1xBNkhA
L
hkkiAq ====
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)
LayersBlows
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
wsd
/+
γ=γ
Dry unit weight
w1d
+
γ=γ
wG1
G
s
wsdzav
+
γ=γ
Moisture Content (%)
Dry
Un
it W
eig
ht
Zero air voids (S=100%)
Optimum moisture content, wopt
Maximum unit weight
Wet of optimumDry of optimum
Compaction Curve
Moisture Content (%)
Dry
Un
it W
eig
ht
Zero air voids (S=100%)
Line of optimumLow energy
High energy
Effect of Compaction Energy
Moisture Content
Perm
eab
ilit
y
Moisture Content (%)
Dry
Un
it W
eig
ht
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@0 standard
.2in.pressure@0 measured
.1in.pressure@0 standard
.1in.pressure@0 measuredCBR
=
CBR Values of Compacted Soil
Moisture Content
Dry
Un
it W
eig
ht
CBR
CBR as compacted
CBR after soaking
Moisture Content
Moisture Content
Axia
l S
hri
nkag
eo
r S
well (
%) Kneading
Vibratory
Static
Moisture Content
Dry
Un
it W
eig
ht
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
zSoil layer, γγγγ
Vertical Overburden Stress
A
zA
Az
A
Pz γ=
γ==σ
P
z Soil layer, γγγγ
z
σσσσz
σσσσz=γγγγz
Vertical Stress Profile
Soil layer 1, γγγγ1
Soil layer 2, γγγγ2
Soil layer 3, γγγγ3
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’iPui
P
A
uA
PuP
A
P 'i
'
i+σ=
+==σ∑ ∑
σσσσ = total stress; σσσσ’ = effective stressu = 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
zx
y
L
P
∆σ∆σ∆σ∆σy
∆σ∆σ∆σ∆σx
∆σ∆σ∆σ∆σz
Boussinesq Solution - A Point Load
r
( ) 122522
3
2
3I
z
P
zr
zP/z =
+π=σ∆
x
y
z
dxdy
B
L
∆σ∆σ∆σ∆σz
p
Vertical Stress Induced by A Rectangularly Loaded Area
+−+
+++
++
++
+++
++
π= −
1
12
1
2
1
12
4
12222
221
22
22
2222
22
nmnm
nmmntan
nm
nm
nmnm
nmmnI
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
LBp
BL
LBp
''z22
BL
p
B’
L’
z
∆σ∆σ∆σ∆σz
αααα
If tanαααα = 1/2( )( )zBzL
LBpz
++=σ∆
Soil Compressibility
Definitions of Settlements
Total settlement, S1 or S2
Differential settlement, ∆∆∆∆S
Distortion
21 SSS −=∆
Structure
S1S2
L
LS /∆
Total Settlement
Total settlement
scet SSSS ++=
Se = immediate settlement (elastic deformation)
Sc = primary consolidation settlement (due todissipation of excess pore water pressure)
Ss = secondary consolidation settlement (due toadjustment 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
LoadDial gauge
Oedometer
Consolidation Test
Consolidation Curve
Time (log scale)
Def
orm
ati
on
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 effectivestress 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)
Vo
id R
ati
o, e
pc
a b
c
d
e
f
g
αααα
αααα
Determination of PreconsolidationStress from Lab Results
Pressure, p (log scale)
Vo
id R
ati
o, e
e0
Field consolidation curve
Lab consolidation curve
Remolded specimenConsolidation curveDisturbance
increases
0.42e0
Effect of Soil Disturbance
Pressure, p (log scale)
Vo
id R
ati
o, e e0
Virgin consolidation curve
Lab consolidation curve
0.42e0
Cc
pc=σσσσz’
e - logp Curve for Normally Consolidated Soil
Cc = Compression index
Pressure, p (log scale)
Vo
id R
ati
o, e
e0
Virgin consolidation curve
Lab consolidation curve
0.42e0
Cc
pcσσσσz’
Cr
Lab rebound curve
e - logp Curve for Overconsolidated Soil
Cr = Recompression index
Vo
id R
ati
o, e
ep
∆∆∆∆e
Time, t (log scale)
t1t2
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)
Vo
id R
ati
o, e
pc = σ σ σ σz’
∆σ∆σ∆σ∆σ
Primary Consolidation Settlement of Normally Consolidated Soil
σ
σ∆+σ
+=
'z
'z
o
cc log
e
HCS
1H = Thickness of soil layer
Primary Consolidation Settlement of Overconsolidated Soil
Stress, σσσσ’ (log scale)
Vo
id R
ati
o, e
σσσσz’∆σ∆σ∆σ∆σ pc
σσσσ
Cr1
Stress, σσσσ’ (log scale)
Vo
id R
ati
o, e
σσσσz’
∆σ∆σ∆σ∆σ
pc
Cr1
Cc
1
σ
σ∆+σ
+=
'z
'z
o
rc log
e
HCS
1
σ∆+σ
++
+=
c
'zc
o
rc
plog
e
HC)OCRlog(
e
HCS
011
Rate of Consolidation
For U<60%
2
v100
U
4T
π=
( )U10093307811Tv −−= log.. For U>60%
2dr
vv
H
tCT =
Clay
Sand
H
Hdr
Soil Strength
Direct Shear Test
P
T
Shear box
Porous stone
Soil
Normal stressA
Pn =σ Shear stress
A
T=τ
Shear Displacement, δδδδ (mm)
Sh
ear
Str
ess,
ττ ττ(k
Pa)
Peak shear strength, ττττf
Direct Shear Test Data
Residual shear strength, ττττr
Normal stress, σσσσn (kPa)
Sh
ear
str
ess,
t f(k
Pa)
c
φφφφ
Mohr-Coulomb Failure Envelope
φσ+=τ tannf c
Cell (confining) pressure
Rubber membrane
Drainage or pore pressure measurement or back pressure
σσσσ3
∆σ∆σ∆σ∆σ
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
cσσσσ
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
σσσσ1cu 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
m1
Facing
Foundation
Reinforcement
Reinforced fill Retained
fill
Components of Slopes
Possible Failure Modes of Slopes
Local failure
Surficial failure
Slope failureGlobal 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
fFSτ
τ=
Resisting force vs. driving force
d
r
T
TFS =
Resisting moment vs. driving moment
d
r
T
TFS =
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
WNTd
Tr
β
φ+
βγ=
tan
tan
sin 2H
c2FS
β
φ=
tan
tanFS if c=0
Surficial Slope Stability - With Seepage
Equipotential line
ββββ
H
L
a
b
d
c
F
F
WN Td
Tr
h=Hcos2ββββ
f
e
Seepage
β
φ′
γ
γ′+
βγ
′=
tan
tan
sin satsat 2H
c2FS
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
RNr
Tr ααααi
∆∆∆∆li
( )
( )∑
∑
=
=
α
φα+∆
=n
1iii
n
1iiii
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
1iii
n
1iiiiii
W
luWlc
FS
sin
tancos