LRFD Design ofLRFD Design ofShallow FoundationsShallow Foundations

Nominal Geotechnical Nominal Geotechnical ResistancesResistances

ASD Failure ModesASD Failure Modes Overall StabilityOverall Stability Bearing CapacityBearing Capacity SettlementSettlement SlidingSliding OverturningOverturning

Nominal Geotechnical Nominal Geotechnical ResistancesResistances

LRFD Service Limit StateLRFD Service Limit State Overall StabilityOverall Stability Vertical (Settlement) and Horizontal Vertical (Settlement) and Horizontal

MovementsMovements

LRFD Strength Limit StateLRFD Strength Limit State Bearing ResistanceBearing Resistance SlidingSliding Eccentricity Limits (Overturning)Eccentricity Limits (Overturning)

StabilizeStabilize DestabilizDestabilizee

Service Limit StateService Limit State

Global StabilityGlobal Stability

Global Stability Factor of Safety Global Stability Factor of Safety – Method of Slices– Method of Slices

+

WT

WT

WTWT

NN

TT

TT

l lcl

cl

N tan N tan

ASD Factors of SafetyASD Factors of Safety

Soil/Rock Parameters and Soil/Rock Parameters and Ground Water Conditions Ground Water Conditions

Based On:Based On:

Slope Supports Slope Supports Abutment or Abutment or

Other Other Structure?Structure?

YesYes NoNo

In-situ or Laboratory Tests and In-situ or Laboratory Tests and MeasurementsMeasurements 1.51.5 1.31.3

No Site-specific TestsNo Site-specific Tests 1.81.8 1.51.5

Resistance FactorsResistance Factors

LRFDLRFD

Stability Wrap-UpStability Wrap-Up

Unfactored loadsUnfactored loads Service Limit StateService Limit State

Applied stress must be limitedApplied stress must be limited Footings supported in a slopeFootings supported in a slope ≤≤ 0.65 (FS ≥ 1.5)0.65 (FS ≥ 1.5)

Stress criteria for stability can control Stress criteria for stability can control footing designfooting design

Service Limit State Design – Service Limit State Design – SettlementSettlement Cohesive SoilsCohesive Soils

Evaluate Using Consolidation TheoryEvaluate Using Consolidation Theory

Cohesionless SoilsCohesionless Soils Evaluate Using Empirical or Other Conventional Evaluate Using Empirical or Other Conventional

MethodsMethods Hough MethodHough Method

Impact on StructuresImpact on Structures

Settlement of Granular vs. Settlement of Granular vs. Cohesive SoilsCohesive Soils Relative importance of settlement Relative importance of settlement

components for different soil typescomponents for different soil types ElasticElastic Primary ConsolidationPrimary Consolidation Secondary Settlement (Creep)Secondary Settlement (Creep)

Settlement of Granular vs. Settlement of Granular vs. Cohesive SoilsCohesive Soils Structural effects of settlement Structural effects of settlement

componentscomponents Include Transient Loads if Drained Include Transient Loads if Drained

Loading is Expected and for Computing Loading is Expected and for Computing Initial Elastic SettlementInitial Elastic Settlement

Transient Loads May Be Omitted When Transient Loads May Be Omitted When Computing Consolidation Settlement of Computing Consolidation Settlement of Cohesive SoilsCohesive Soils

Hough MethodHough MethodSettlement of Cohesionless SoilsSettlement of Cohesionless Soils

Stress Stress Below Below FootingFooting

Boussinesq Boussinesq Pressure Pressure IsobarsIsobars

1B 2B2B 1B

1B

2B

3B

4B

5B

1B

2B

3B

4B

5B

0.2q

0.1q

0.08q

0.06q

0.04q

0.4q

0.3q

0.2q

0.1q

0.6q

0.8q

0.4q

0.6q

qo

B/2B/2STRIP SQUARE

Nominal Bearing Resistance at Nominal Bearing Resistance at Service Limit StateService Limit State

Rn

Bf

For a constant valueof settlement

ML MB

PPP

Eccentricity of Footings on SoilEccentricity of Footings on Soil

eeBB = M = MBB / P / PeeLL = M = MLL / P / P

ML MB

P

Effective Dimensions for Effective Dimensions for Footings on SoilFootings on Soil

BB′′ = B – 2e = B – 2eBB

LL′′ = L – 2e = L – 2eLL

ML MB

P

q

Applied Stress Beneath Effective Applied Stress Beneath Effective Footing AreaFooting Area

Stress Applied to SoilStress Applied to SoilStrip FootingStrip Footing

P

M

q = P/B'f

B'f

qmin

qmax

Bf

RESULTANT

eBf

Footings on RockFootings on RockTrapezoidal DistributionTrapezoidal Distribution

qmax

Bf

RESULTANTeBf

B1

B1/3

Footings on RockFootings on RockTriangular DistributionTriangular Distribution

Use of Eccentricity and Effective Use of Eccentricity and Effective Footing DimensionsFooting Dimensions

Service Limit StateService Limit State Nominal Bearing Resistance Limited by Nominal Bearing Resistance Limited by

SettlementSettlement

Strength Limit StateStrength Limit State Nominal Bearing Resistance Limited by Bearing Nominal Bearing Resistance Limited by Bearing

ResistanceResistance

Prevent OverturningPrevent Overturning All Applicable Limit StatesAll Applicable Limit States

Strength Limit StateStrength Limit StateBearing ResistanceBearing Resistance

Strength Limit State Design – Strength Limit State Design – Bearing ResistanceBearing Resistance Footings on SoilFootings on Soil

Evaluate Using Conventional Bearing TheoryEvaluate Using Conventional Bearing Theory

Footings on RockFootings on Rock Evaluate Using CSIR Rock Mass Rating ProcedureEvaluate Using CSIR Rock Mass Rating Procedure

1122 22

3333

ddaad’d’ = C + = C + ’ tan ’ tan

Soil Shear StrengthSoil Shear Strength

DfDf

B>DfB>Df

BB

Ground Ground SurfaceSurface vv = = D Dff

PpPpPpPp

cccc bbaaIIb’b’

bbbb’’

Bearing Resistance MechanismBearing Resistance Mechanism

Table 10.5.5.2.1-1 Resistance Factors for Geotechnical Resistance of Shallow Foundations at the Strength Limit State

METHOD/SOIL/CONDITION RESISTANCE FACTOR

Bearing Resistance

b

Theoretical method (Munfakh, et al. (2001), in clay 0.50

Theoretical method (Munfakh, et al. (2001), in sand, using CPT

0.50

Theoretical method (Munfakh, et al. (2001), in sand, using SPT

0.45

Semi-empirical methods (Meyerhof), all soils 0.45

Footings on rock 0.45

Plate Load Test 0.55

Sliding

Precast concrete placed on sand 0.90

Cast-in-Place Concrete on sand 0.80

Cast-in-Place or precast Concrete on Clay 0.85

Soil on soil 0.90

epPassive earth pressure component of sliding resistance

0.50

Footings on RockFootings on Rock

Service Limit State – use published Service Limit State – use published presumptive bearingpresumptive bearing

Published values are Published values are allowableallowable therefore settlement-limitedtherefore settlement-limited

Procedures for computing settlement Procedures for computing settlement are availableare available

Very little guidance available for Very little guidance available for bearing resistance of rockbearing resistance of rock

Proposed Specification revisions Proposed Specification revisions provide for evaluating the cohesion and provide for evaluating the cohesion and friction angle of rock using the CSIR friction angle of rock using the CSIR Rock Mass Rating SystemRock Mass Rating System

Footings on Rock – Footings on Rock – Strength Limit StateStrength Limit State

CSIR Rock Mass Rating SystemCSIR Rock Mass Rating System

CSIR Rock Mass Rating developed for CSIR Rock Mass Rating developed for tunnel designtunnel design

Includes life safety considerations and Includes life safety considerations and therefore, margin of safetytherefore, margin of safety

Use of cohesion and friction angle Use of cohesion and friction angle therefore may be conservativetherefore may be conservative

LRFD vs. ASDLRFD vs. ASD

All modes are expressly checked at a All modes are expressly checked at a limit state in LRFDlimit state in LRFD

Eccentricity limits replace the Eccentricity limits replace the overturning Factor of Safetyoverturning Factor of Safety

Width vs. Resistance - ASDWidth vs. Resistance - ASDSettlementSettlementcontrolscontrols

Shear FailureShear Failurecontrolscontrols

Footing width, B (m)Footing width, B (m)0.00.0 1.01.0 2.02.0 3.03.0 4.04.0 5.05.0

800800

Beari

ng

Pre

ssu

re (

kP

a)

Beari

ng

Pre

ssu

re (

kP

a)

Allowable Bearing Capacity, FS = 3.0Allowable Bearing Capacity, FS = 3.0Bearing Pressure for 25-mm (1in) settlementBearing Pressure for 25-mm (1in) settlement

600600

400400

00

Settlement vs. Bearing Settlement vs. Bearing ResistanceResistance

00

1212

N=30N=30

B, ftB, ft

qqaa,

ksf

, k

sf

N=25N=25

N=5N=5

N=20N=20

N=15N=15

N=10N=10

22 44 66 1414101088 1212

22

00

44

66

88

1010

00

1212

N=30N=30

B, ftB, ft

qqaa,

ksf

, k

sf

N=25N=25

N=5N=5

N=20N=20

N=15N=15

N=10N=10

22 44 66 1414101088 1212

22

00

44

66

88

1010

Width vs. Resistance - LRFDWidth vs. Resistance - LRFD

Effective Footing width, B’ (m)Effective Footing width, B’ (m)00 44 88 1212 1616 2020

Nom

inal B

eari

ng

N

om

inal B

eari

ng

R

esis

tan

ce (

ksf)

Resis

tan

ce (

ksf)

Strength Limit StateStrength Limit StateService Limit StateService Limit State

55

1515

2525

3535

Recommended PracticeRecommended Practice

For LRFD design of footings on soil For LRFD design of footings on soil and rock;and rock; Size footings at the Service Limit StateSize footings at the Service Limit State Check footing at all other applicable Limit StatesCheck footing at all other applicable Limit States

Settlement typically controls!Settlement typically controls!

Summary Comparison of ASD Summary Comparison of ASD and LRFD for Spread Footingsand LRFD for Spread Footings Same geotechnical theory used to Same geotechnical theory used to

compute resistances, compute resistances, howeverhowever As per Limit State concepts, As per Limit State concepts,

presentation of design presentation of design recommendations needs to be modifiedrecommendations needs to be modified

METHOD/SOIL/CONDITIONRESISTANCE

FACTOR

BearingResistance

All methods, soil and rock 0.45

Plate Load Test 0.55

Sliding Precast concrete placed on sand

0.90

Cast-in-Place Concrete on sand

0.80

Clay 0.85

Soil on soil 0.90

ep Passive earth pressure component of sliding resistance

0.50

Strength Limit State Resistance Factors