review of soil mechanics

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