SOILS AND FOUNDATIONS SOILS AND FOUNDATIONS Testing Experience Theory Lesson 02 Lesson 02 Chapter 2 Chapter 2 – – Stress and Strain in Soils Stress and Strain in Soils
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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
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