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
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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,
Shear Strength of Soils
Normal Stress,
C
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Shear Strength of Soils
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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