chapter 3 soil mechanics [compatibility mode]

7/21/2019 Chapter 3 Soil Mechanics [Compatibility Mode]

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Chapter 3: Soil MechanicsLecture No.1

3.1 Soil Composition 3.2 Soil Classification

3.3 Groundwater

3.4 Stress

Lecture No.2

3.5 Compressibility and settlement

Lecture No.3

3.6 Strength


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The Nature of Soil

The soil mass includes both solidsand voids

The voids ma be filled with either

air or water Thus, soil is inherently multi-phase

solid solid

liquid water

gas air


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The Mineral Skeleton

Solid Particles

Volume

Voids


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Three Phase Diagram

Air

Water

Solid

Mineral

Skeleton

Idealization:

Three Phase

Diagram


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Three Phase System

Air

Water

Wa=0

Ww

VVw

Va

Vv

Solid

Volume Weight,

or Mass

WsVs


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Volumetric Relationships

Void ratio, e = Vv/ Vs

Porosity, n (%) = (Vv/ V) x 100%

n= e/(1+e)x100%

Degree of saturation,

S (%) = (Vw/ Vv) x 100%


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Weight Relationships

Water content (based on weight),w= (Ww/ Ws) x 100%

Water content (based on mass),

w= (Mw/ Ms) x 100%


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Unit weight (lb/ft3 or kN/m3)Also See Table 3.2

Unit weight= WT/ V

d = Ws/ V

Buoyant (submerged) unit weightb = -w


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Sieve Analysis

(Mechanical Analysis)

This procedure issuitable for coarsegrained soils

E.g. No.10 sieve .has 10 apertures perlinear inch


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Hydrometer

Analysis

Also calledSedimentationAnalysis

Stokes Law

18

)(2

Lsw

GGDv

=


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Grain Size Distribution Curves


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Soil Plasticity

Further classification within fine-grainedsoils (i.e. soil that passes #200 sieve) isdone based on soil plasticity.

Albert Atterberg, Swedish Soil Scientist(1846-1916)..series of tests forevaluating soil plasticity

Arthur Casagrande adopted these testsfor geotechnical engineering purposes


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Consistency of fine-grained soil variesin proportion to the water content

Atterberg Limits

li uid

solid

semi-solid

plastic

Shrinkage limit

Plastic limit

Liquid limitPlasticity

Index


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Liquid Limit (LL or wL)

Empirical Definition

The moisture content at which a 2 mm-wide roove in a soil at will close for a

distance of 0.5 in when dropped 25times in a standard brass cup falling 1cm each time at a rate of 2 drops/secin a standard liquid limit device


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Casagrande Apparatus


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Casagrande Apparatus


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Liquid Limit Determination


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The moisture content at which a thread of soil

just begins to crack and crumble when rolledto a diameter of 1/8 inches

Plastic Limit (PL, w

P)


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Plasticity Index ( PI, IP )

PI = LL PL

-

Note: These are water contents, but

the percentage sign is not typically

shown.


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USCS Plasticity Chart


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Geostatic Stresses


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Geostatic Stresses; Vertical StressH1

H2

1

2

u

HHH

zz

z

=

++=

332211

H3 3


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3.5 Compressibility & Settlement

Settlement requirements often controlthe design of foundations

overview of principles involved insettlement analysis

The subject will be dealt with in greaterdetail in Chapters 4 and 7.


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Case Studies

(a)Leaning Tower, Pisa

(b) Palacio de las BellasArtes, Mexico City


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Palace of Fine Arts in Mexico City

Settled 3m!

Lacustrine Clay deposited in former LakeTexcoco

Av. Water content 281%, Void Ratio 6.90

Groundwater withdrawal; increase ineffective stress

Resulting Consolidation

43-story Tower Latino Americana


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SettlementDistortion Settlement (Immediate)

Consolidation (Time Dependent)Secondary Compression

Settlement


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Increase in Vertical Effective Stress

Due to a Placement of a fill

fillfillzzf H += 0

Due to an external load

( )inducedzzzf += 0


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Consolidation Settlement


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Laboratory Consolidation Testv 1 Place sample in ring

2 Apply load

3 Measure height change

4 Repeat for new loadConfiningstress

v

Solids

Voids

Solids

Voids

Vs

VvVv

Vs

V

Before After


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Laboratory Consolidation Test


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Consolidation Test


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Test Results

B


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Compression Index and

Recompression Index

ceeC

zbz

bcc

)(log)(log =

czdz

dcr

eeC

)(log)(log

=


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Compression Ratio and

Recompression Ratio

czbz

czbzcc

e

CC

)(log)(log

)()(

1 0

=

+=

czdz

czdzr

r e

CC

)(log)(log

)()(

1 0

=

+

=


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Consolidation Plot


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Consolidation Plot


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Consolidation Plot

5.5ft=109.4(1+0.171)

= 128.1 pcf

2.0ft

tsfpsfftftpcfz 42.08360.2)4.621.128()5.5)(1.128( ==+=


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e0


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Normally and

Over-Consolidated Soils

czo = .. Normally consolidated

czo .. Under consolidated

O C lid i i &


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Over-Consolidation Margin &

Over-consolidation Ratio

zccm = .. Over-consolidationMargin

zo

cOCR

= .. Over consolidation ratio


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Typical Range of OC Margins

C ibili f S d d


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Compressibility of Sand and

Gravels (Table 3.7)


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Example 3.3

S ttl t P di ti


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Settlement Predictions

N.C. Clays

+=

00

log1 z

zfcc H

e

C

S ttl t P di ti


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Settlement Predictions

O.C. Clays Case I

+=

00

log1 z

zfrc H

e

C


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Ex. 3.4

E l 3 4


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Example 3.4


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Ex. 3.5


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Example 3.5


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3.8 Shear Strength of Soils Soil is a particulate material; hence its

shear strength depends on interactionbetween particles

n so s s ear s reng s ear s reng sderived from:

Friction

Cohesion Coulomb Failure Criterion


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Bearing Capacity Failure;


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g p y ;

Fargo Grain Elevator, N. Dakota


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Shear Strength of Soils


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ShearStrength,


Normal Stress,

C


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TTcs tan+=

frictioninternalofanglecohesionc

T

T

==

Effect of Pore Water on Shear


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Effect of Pore Water on Shear

Strength

Pore water pressure

Total Stress, versus Effective Stress,

Shear Strength in terms of effective stress

Choice of total stress versus effective stressanalysis in practice

+= tancs


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Typical Values


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Typical Values


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Measuring Shear strength

Direct shear test

Triaxial compression test


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Direct Shear Test


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Direct Shear Test Device


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Triaxial Compression Test


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Types of Triaxial Compression


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Tests

Unconsolidated Undrained (UU-Test);Also called Undrained Test

-

Test)

Consolidated Drained (CD-Test); Also

called Drained Test

Unconsolidated Undrained Test


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(UU-Test)


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Unconfined Compression Test

Special Caseof theTriaxial CompressionTest

p

Confining Stress = 0 Pc = 3 = 0

p = 1

Pc = 0


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