SOILS AND FOUNDATIONSSOILS AND FOUNDATIONS

Testing

Experience

Theory

Lesson 02Lesson 02Chapter 2 Chapter 2 –– Stress and Strain in SoilsStress and Strain in Soils

Lesson PlanLesson Plan

ggTopic 1 (Section 2.0, 2.1)Topic 1 (Section 2.0, 2.1)-- Phase relations, size/shape of particlesPhase relations, size/shape of particles-- Effect of water on soilEffect of water on soil

ggTopic 2 (Section 2.2, 2.3, 2.4)Topic 2 (Section 2.2, 2.3, 2.4)-- Overburden pressureOverburden pressure-- Principle of effective stressPrinciple of effective stress

ggTopic 3 (Section 2.5, 2.6)Topic 3 (Section 2.5, 2.6)-- Vertical stress due to external loadingsVertical stress due to external loadings-- Load deformation processLoad deformation process-- Consolidation in fineConsolidation in fine--grained soilsgrained soils

Lesson PlanLesson Plan

ggTopic 4 (Section 2.7, 2.8)Topic 4 (Section 2.7, 2.8)-- Lateral stresses in foundation soilsLateral stresses in foundation soils-- Shear strength of soilsShear strength of soils

ggTopic 5 (Section 2.9)Topic 5 (Section 2.9)-- Lateral earth and water pressuresLateral earth and water pressures

Stress and Strain in Soils Stress and Strain in Soils

Lesson 02 Lesson 02 -- Topic 1Topic 1Phase relations, Size/Shape of particles,Phase relations, Size/Shape of particles,

Effect of water on soilEffect of water on soil(Section 2.0, 2.1)(Section 2.0, 2.1)

Aerial View of Interstate BridgesAerial View of Interstate Bridges

Stresses Imposed by StructuresStresses Imposed by Structures

ggThe approach embankments also induce The approach embankments also induce stresses in the foundation soilstresses in the foundation soil

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Differentiate the basic phase relations in Differentiate the basic phase relations in

geotechnical materialsgeotechnical materials-- Express the importance of soil particle size and Express the importance of soil particle size and

shapeshape-- Describe the role of water on soil behaviorDescribe the role of water on soil behavior

Phase RelationsPhase Relations

ggSoil is a Three Phase SystemSoil is a Three Phase System

Voids(air + water)

Soil Particles AirVa

Vw

Vs

Wa≈ 0

Ww

Ws

Vv

V W

Volume

1

Weight

Water

Solid

Volume RatiosVolume Ratios

ggPorosity (Porosity (EqEq. 2. 2--1)1)

AirVa

Vw

Vs

Wa≈ 0

Ww

Ws

Vv

V W

Volume

1

Weight

Water

Solid

x100VvVn =

Volume RatiosVolume Ratiosgg Void Ratio (Void Ratio (EqEq. 2. 2--2)2)gg Relative Density (Relative Density (EqEq 22--2a)2a)

AirVa

Vw

Vs

Wa≈ 0

Ww

Ws

Vv

V W

Volume

1

Weight

Water

Solid

S

V

VV

e =

100x)ee(

)ee(Dminmax

maxr −

−=

Volume RatiosVolume Ratios

ggDegree of Saturation (Degree of Saturation (EqEq. 2. 2--3)3)

AirVa

Vw

Vs

Wa≈ 0

Ww

Ws

Vv

V W

Volume

1

Weight

Water

Solid

100xvVwVS =

Weight RatiosWeight Ratios

ggWater Content (Water Content (EqEq. 2. 2--4, 24, 2--4a)4a)

AirVa

Vw

Vs

Wa≈ 0

Ww

Ws

Vv

V W

Volume

1

Weight

Water

Solid

100xsWwWw =

100xsWwW

sWsWWw =

−=

WeightWeight--Volume Ratios (Unit Weights)Volume Ratios (Unit Weights)

ggUnit Weights Unit Weights -- Total Unit WeightTotal Unit Weight

-- Saturated Unit Weight Saturated Unit Weight (when S=100%)(when S=100%)

-- Total, Total, γγtt = Saturated, = Saturated, γγsatsat

-- Dry Unit Weight (S=0%)Dry Unit Weight (S=0%)

AirVa

Vw

Vs

Wa≈ 0

Ww

Ws

Vv

V W

Volume

1

Weight

Water

Solid

VWW

VW SW

t+

==γ

VWS

d =γ

Specific Gravity of SolidsSpecific Gravity of Solids

Basic WeightBasic Weight--Volume Volume InterrelationshipsInterrelationshipsggTable 2Table 2--22

w)+ n)(1 - (1G =S

wG + 1

G w)+ (1 =

e + 1Se) + G( =

e + 1G w)+ (1

=

wst

sws

t

wst

wst

γγ

γγ

γγ

γγ

γ⎟⎠⎞

⎜⎝⎛γγ

γγγ

γγ

γγ

γγ

γγ

γγ

wsatd

wsatd

wd

sws

d

wsd

wsd

td

e + 1e - =

n - = we) + (1

eS =

SwG + 1

G =

n) - (1G = e + 1

G =

w+ 1 =

γ⎟⎠⎞

⎜⎝⎛γγ

γγγ

γ⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛γ

γ⎟⎟⎠

⎞⎜⎜⎝

⎛γ

γγ

γγ

wdsat

wdsat

wsat

wss

sat

wssat

wssat

e + 1e + =

n + = e + 1

w+ 1we =

GG w+ 1

w+ 1 =

n] + Gn) - [(1 = e + 1e) + G( =

CoarseCoarse--Grained and FineGrained and Fine--GrainedGrainedSoilsSoilsggHow do we differentiate soil sizes and How do we differentiate soil sizes and

shapes?shapes?

Size of Grains in Solid PhaseSize of Grains in Solid Phase

ggTable 2Table 2--3 3 –– Sieve SizesSieve Sizes

Grain Grain Size Size Distribution Distribution CurvesCurves

Gap Graded

Shape of Shape of Grains in Grains in Solid PhaseSolid Phase

gg1: Angular1: Angulargg2: 2: SubangularSubangulargg3:Subrounded3:Subroundedgg4: Rounded4: Roundedgg5: Well rounded5: Well rounded

1

2

3

4

5

Grain Grain Size Size Distribution Distribution CurvesCurves

Gap Graded

Platy ShapePlaty Shape

ggBentoniteBentoniteggElectron Electron

PhotomicrographPhotomicrograph-- Clay Spur, WyomingClay Spur, Wyoming-- Picture width, 7.5 Picture width, 7.5 μμmm

gg1 gram of 1 gram of bentonitebentonitehas surface area of has surface area of 950 yd950 yd22

Reference Tovey (1971)

Effect of Water on SoilsEffect of Water on SoilsVolume, V

Water Content, w

Shrinkage Limit (SL)

Plastic Limit (PL)

Liquid Limit (LL)

SolidPhase

Semi-solidPhase

PlasticPhase

LiquidPhase

A

BC

D

Plasticity Index, PI=LL-PL Liquidity Index,PI

PLwLI −=

Liquidity Index, LI (Liquidity Index, LI (Table 2Table 2--4)4)

Liquidity Index, LI

Soil Phase Soil Strength (Soil Deformation)

LI ≥ 1 Liquid Low strength (Soil deforms like a viscous fluid)

0 < LI < 1 Plastic

Intermediate strength • at w ≈ LL, the soil is considered soft and very compressible • at w ≈ PL, the soil is considered stiff (Soil deforms like a plastic material)

LI ≤ 0 Semi-solid to

Solid

High strength (Soil deforms as a brittle material, i.e., sudden, fracture of material)

Liquidity Index,PI

PLwLI −=

Plasticity ChartPlasticity Chart

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Differentiate the basic phase relations in Differentiate the basic phase relations in

geotechnical materialsgeotechnical materials-- Express the importance of soil particle size and Express the importance of soil particle size and

shapeshape-- Describe the role of water on soil behaviorDescribe the role of water on soil behavior

Any Questions?Any Questions?

THE ROAD TOUNDERSTANDING

SOILSAND

FOUNDATIONS

Stress and Strain in Soils Stress and Strain in Soils

Lesson 02 Lesson 02 -- Topic 2Topic 2Overburden Pressure, Principle of Effective Overburden Pressure, Principle of Effective

StressStress(Section 2.2, 2.3, 2.4)(Section 2.2, 2.3, 2.4)

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Distinguish between total and effective stressDistinguish between total and effective stress-- Calculate and construct Calculate and construct ppoo--diagramdiagram

Overburden PressureOverburden Pressure

ggSection 2.4Section 2.4ggTotal overburden pressure, pTotal overburden pressure, ptt

-- ppt t = = γγtt (depth)(depth)ggPore water pressure, uPore water pressure, u

-- uu = = γγww (depth of water)(depth of water)ggEffective overburden pressure, Effective overburden pressure, ppoo

ppoo = pptt –– uu

Principle of Effective StressPrinciple of Effective Stress

ggOnly Only intergranularintergranular contact stress is contact stress is EFFECTIVEEFFECTIVE in resisting shear/compressionin resisting shear/compression

ggThe effective stress on any plane within a The effective stress on any plane within a soil mass is the difference between the total soil mass is the difference between the total stress and pore water pressure.stress and pore water pressure.

20′

γT = 110 pcf10′

0′

Find Find ppoo at 20 feet below ground in a sand deposit with a total unit at 20 feet below ground in a sand deposit with a total unit weight of 110 weight of 110 pcfpcf and the water table 10 feet below ground. Plot and the water table 10 feet below ground. Plot pptt and and ppoo verses depth from 0’ verses depth from 0’ –– 20’. 20’.

Solution: Solution: ppoo = p= ptt -- uu

pptt @ 10’ = p@ 10’ = p00 @ 10’ = 10’ @ 10’ = 10’ ××110 110 pcfpcf = 1100 = 1100 psfpsf

pptt @ 20’ = p@ 20’ = ptt @ 10’ + (10’ @ 10’ + (10’ ××110 110 pcfpcf) = 2200 ) = 2200 psfpsf

uu @ 20’ = 10’ @ 20’ = 10’ ××624 624 pcfpcf = 624 = 624 psfpsf

pp00 @ 20’ = p@ 20’ = ptt @ 20’ @ 20’ -- u @ 2u @ 20’ 0’ == 2200 2200 –– 624 = 1576 624 = 1576 psfpsf

ppoo DiagramDiagram

ggppoo = Effective Overburden Pressure= Effective Overburden Pressure

pt

po

po = pt

1576

1100

2200

Pressure (psf)300020001000

Depth (ft)

0

20

10

u

Student Exercise No. 1Student Exercise No. 1

Sand Sand γγtt = 110 = 110 pcfpcf

Clayey Silt Clayey Silt γγtt = 125 = 125 pcfpcf

Depth Depth (Ft.)(Ft.)

5050

3030

002020′′

Existing Ground Existing Ground

Rock Rock

Assume buoyant unit weights below static water level ( ). Assume buoyant unit weights below static water level ( ). Buoyant unit weight is total unit weight minus unit weight of Buoyant unit weight is total unit weight minus unit weight of water, water, γγtt -- γγww. This is also known as effective unit weight, . This is also known as effective unit weight, γγ′′, , or submerged unitor submerged unit weightweight, , γγsubsub..

Compute and plot both the total and effective overburden Compute and plot both the total and effective overburden stress diagrams for the soil profile below.stress diagrams for the soil profile below.

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Distinguish between total and effective stressDistinguish between total and effective stress-- Calculate and construct Calculate and construct ppoo--diagramdiagram

Any Questions?Any Questions?

THE ROAD TOUNDERSTANDING

SOILSAND

FOUNDATIONS

Stress and Strain in Soils Stress and Strain in Soils

Lesson 02 Lesson 02 -- Topic 3Topic 3Vertical Stress Distribution Due to External Vertical Stress Distribution Due to External

Loadings, Load Deformation Processes, Loadings, Load Deformation Processes, ConsolidationConsolidation

(Section 2.5, 2.6)(Section 2.5, 2.6)

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Discuss depth of significant influence (DOSI)Discuss depth of significant influence (DOSI)-- Explain soil consolidation in fineExplain soil consolidation in fine--grained soilsgrained soils

Vertical Vertical Stress Due Stress Due to External to External LoadingsLoadings

p = γthh

0.6p

0.4p

0.8p

0.2p

ggDepth of Depth of Significant Significant Influence Influence (DOSI), D(DOSI), Dss

ChartsChartsFigure 2Figure 2--1111ggDDss = 4B to 6B = 4B to 6B

for continuous for continuous footingsfootings

ggDDss = 1.5B to 2B = 1.5B to 2B for square for square footingsfootings

gg Lateral EffectsLateral Effects

2:1 Stress Distribution (Figure 22:1 Stress Distribution (Figure 2--12)12)

Combined Plot of StressesCombined Plot of StressesggWhat does this mean?What does this mean?

zw

po pt

Δp

Pressure

Depth, z

Legend:zw = depth to groundwaterpo = effective overburden pressurept = total overburden pressureΔp = pressure due to external loadspf = p0 + Δp

pf

DOSI

Example 2Example 2--2:2:

ggFigure 2Figure 2--14, Page 214, Page 2--3434

LoadLoad--Deformation Process in SoilsDeformation Process in Soils

ggCompressionCompression-- Expulsion of air from voidsExpulsion of air from voids

ggConsolidationConsolidation-- Expulsion of water from voidsExpulsion of water from voids

ggCollapseCollapse-- Breakdown of bonds between particlesBreakdown of bonds between particles

ggCompactionCompaction-- Reduction of voids due to impactReduction of voids due to impact--type loadingtype loading

ggDilationDilation-- Increase in volume during shearIncrease in volume during shear

Icon

Consolidation ProcessConsolidation Process

ggMost complex and problematicMost complex and problematic

ConsolidationConsolidation

W

W

Before application of load

At time t = 0Water Pressure = uLoad in Spring = 0

After application of load

At time t = xWater Pressure, u → 0Load in Spring → W

Water Spring

Valve open Valve shut Valve openPiston

ConsolidationConsolidation

Applied Force,WW

Force

Time, t

Spring force

Water pressure, u

Drainage RatesDrainage Rates(Rapid and Long(Rapid and Long--term Drainage)term Drainage)

Maximum Excess Pore Water Pressure, u

Excess Pore Water Pressure, u

Time, t

Coarse-grained soil

Fine-grained soil

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Discuss depth of significant influence (DOSI)Discuss depth of significant influence (DOSI)-- Explain soil consolidation in fineExplain soil consolidation in fine--grained soilsgrained soils

Any Questions?Any Questions?

THE ROAD TOUNDERSTANDING

SOILSAND

FOUNDATIONS

Stress and Strain in Soils Stress and Strain in Soils

Lesson 02 Lesson 02 -- Topic 4Topic 4Lateral Stresses in Foundation SoilsLateral Stresses in Foundation Soils

Strength of Soils to Resist Imposed StressesStrength of Soils to Resist Imposed Stresses(Section 2.7, 2.8)(Section 2.7, 2.8)

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Discuss importance of lateral stress in Discuss importance of lateral stress in

foundation soilsfoundation soils-- Summarize the MohrSummarize the Mohr--Coulomb failure criterionCoulomb failure criterion

Lateral StressesLateral Stresses

ggVertical Stresses Cause Lateral StressesVertical Stresses Cause Lateral StressesggKK is Coefficient of Lateral Pressureis Coefficient of Lateral Pressure

-- In elastic media, use In elastic media, use νν (Poisson’s Ratio)(Poisson’s Ratio)

ph = K poν−

ν=

1K

Effect of Lateral StressesEffect of Lateral Stresses

Lateral Lateral Stress Due Stress Due to External to External LoadingsLoadingsggNote Lateral Note Lateral

Stresses Stresses Beyond Beyond Loaded Loaded AreaArea

Zone of Tensile Stresses

0.2p

0.4p0.6p

p = γthh

SoftLayer

Effect of Shear Strength on Lateral Effect of Shear Strength on Lateral PressuresPressures

Angle of reposeAngle of repose

Introduction to Shear Strength Introduction to Shear Strength

Tangential Force, Fa

X Y

Block B

Shearing Resistance, Fr

Normal Force, Pn

Representation of Shear StrengthRepresentation of Shear Strength

Shear Strength, τ

Normal Stress, σn

Friction angle, φ

(a)

Shear Strength = τ = σn tanφ

Representation of Shear StrengthRepresentation of Shear StrengthShear Strength, τ

Normal Stress, σn

Friction angle, φ

Cohesion, c

τ = c + σn tanφ

Mohr-Coulomb Failure Envelope

Meaning of MMeaning of M--C Failure EnvelopeC Failure EnvelopeShear Strength, τ

Normal Stress, σn

Not Possible

Safe State of Stress

Failure

MM--C Criteria in Effective StressesC Criteria in Effective StressesShear Strength, τ

Normal Stress, σn

τ = c + σn tanφ τ = c′ + (σn - u) tan φ′ τ = c′ + σ′ tan φ′

Mohr-Coulomb Failure Envelope

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Discuss importance of lateral stress in Discuss importance of lateral stress in

foundation soilsfoundation soils-- Summarize the MohrSummarize the Mohr--Coulomb failure criterionCoulomb failure criterion

Any Questions?Any Questions?

THE ROAD TOUNDERSTANDING

SOILSAND

FOUNDATIONS

Stress and Strain in Soils Stress and Strain in Soils

Lesson 02 Lesson 02 -- Topic 5Topic 5Strength of soils related to lateral earth Strength of soils related to lateral earth

pressurespressures(Section 2.9)(Section 2.9)

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Explain active and passive lateral earth Explain active and passive lateral earth

pressurespressures-- Recognize the role of water in lateral earth Recognize the role of water in lateral earth

pressure calculationspressure calculations

Strength of Soils Related to Lateral Strength of Soils Related to Lateral Earth PressuresEarth Pressures

AtAt--RestRest AtAt--RestRest ActiveActive PassivePassive

po

ph=Ko po pz po

ph=Ko po W

all

po

ph=Ka po

δa

po

ph=Kp po

δp

φ′+φ′−

=sin1sin1Ka φ′−

φ′+=

sin1sin1Kp

Active and Passive Failure ZonesActive and Passive Failure Zones

Lateral Earth Pressure DistributionsLateral Earth Pressure Distributions

(a)

(b) Active pressure at depth z: pa = Ka γ z Active force within depth z: Pa = Ka γ z2/2

Passive pressure at depth z: pp = Kp γ z Passive force within depth z: Pp = Kp γ z2/2

Combined Combined Earth Earth and Water and Water Lateral Lateral PressuresPressures

Learning OutcomesLearning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:be able to:-- Explain active and passive lateral earth Explain active and passive lateral earth

pressurespressures-- Recognize the role of water in lateral earth Recognize the role of water in lateral earth

pressure calculationspressure calculations

Any Questions?Any Questions?

THE ROAD TOUNDERSTANDING

SOILSAND

FOUNDATIONS