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HKIE-GD Workshop on Foundation Engineering
7 May 2011
Shallow Foundations
Dr Limin ZhangHong Kong University of Science and Technology
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OutlineSummary of design requirementsLoad eccentricityBearing capacitySettlement analysis
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Shallow foundations: spread footings(a) Square(b) Rectangular(c) Circular(d) Continuous(e) Combined(f) Ring
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Shallow foundations: Mats (rafts)Very large spread footings that
usually encompass the entire footprint of structure
Good forLarge load or poor soil conditionsErratic soils prone to differential settlementErratic loads prone to differential settlementUnderground spaceNonuniform lateral loadWater-proofing
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Shallow foundations: EconomyShallow foundations, where applicable, are often the cheapest foundation type.
The foundation below is for a 16-story building (1 Beacon Hill). It sits on CDG and has a depth of 3.0 m, which is just slightly larger than the pile cap thickness for deep foundations at the same site.
HKUST 10-story student hostel
HKUST Enterprise Center
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Eiffel TowerEach of the legs of Eiffel Tower is supported by a footing. Once the tallest structure in the world (1889), its foundation has not experienced any excessive settlement.
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Eiffel Tower (not on scale)
Firm alluvial soils
Soft alluvial
Soft silt
River Seine
mbgl 0
mbgl 12 m
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Design summary (I): Depth
Bearing capacityShear capacity Depth of surface weak soilDepth of frost penetrationDepth of greatest moisture fluctuation(expansive or collapsible soils)Depth of potential scourPossible landslides (see footings on slopes)
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Design summary (II): PlanLoad eccentricity requirement - no tension
Allowable vertical bearing capacity requirementfor concentric loads
for eccentric loadsB’ =B-2eB, L’ =L-2eL
Allowable horizontal shear capacity requirementV ≤ Va
Allowable total settlement and differential settlementS ≤ [S], ΔS ≤ [ΔS]
166≤+
Le
Be LB
aDf qu
BLWP
q <−+
=
aDf qu
LBWP
q <−+
=''
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Shallow Foundations
Summary of design requirementsLoad eccentricityBearing capacitySettlement analysis
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Bearing pressure (I): One-way eccentric loading
To maintain compressive stress along the entire base area,
qmin ≥ 0 or e ≤ B/6
⎟⎠⎞
⎜⎝⎛ +⎟⎟
⎠
⎞⎜⎜⎝
⎛−
+=
⎟⎠⎞
⎜⎝⎛ −⎟⎟
⎠
⎞⎜⎜⎝
⎛−
+=
Beu
AWP
q
Beu
AWP
q
Df
Df
61
61
max
min
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Bearing pressure (II): Two-way eccentric loading
To maintain compressive stress along the entire base area, the resultant force must be located within the parallelogram kern,
⎟⎠⎞
⎜⎝⎛ ±±⎟⎟
⎠
⎞⎜⎜⎝
⎛−
+=
Le
Beu
AWP
q LBD
f 661
166≤+
Le
Be LB
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Problem: a mat foundation for four silosWsilo=29 MN, Wgrain=110 MN, Wmat=60 MN(1) One-way loading: two full
P=4x29 + 2x110=336 kNM=2x110x12 = 2640 MNme=M/(P+Wf)=2640/(336+60)=6.7 me <B/6=50/6=8.3 m
(2) Two-way loading: one fullP=4x29+110=226 MNM=110x12=1320 MNmeB=eL=1320/(226+60)=4.62 m6eB/B + 6eL/L=2x6x4.62/50=1.11>1
(3) To let the resultant within the kern,
B=55.4 m
Bearing pressure (III): Silo example
162.46266=
×=+
BLe
Be LB
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Shallow Foundations
Summary of design requirementsLoad eccentricityBearing capacitySettlement analysis
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Bearing capacity (I): Failure modes(a) General shear
failure (strongly dilative)
(b) Local shear failure
(c) Punching shear failure (contractive)
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Terzaghi’s bearing capacity theory (II)
Assumptions
Rigid strip foundation Concentric loadThe bottom of the foundation is sufficiently rough that no sliding occurs between foundation and soilSlip surface at a max depth of B below the baseShear strength of soil τ = c+ σ tan φGeneral shear failure mode governsNo consolidation of soil occursThe soil within a depth D has no shear strength.
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Terzaghi’s bearing capacity theory (III)Basic equation for a strip footing:qult= c’Nc + σzD’ Nq + 0.5γ’BNγ
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Vesic’s bearing capacity theory (1973, 1975) (IV)
Vesic retained Terzaghi’s basic format and added additional factors
sc, sq, sγ = shape factorsdc, dq, dγ = depth factorsic, iq, iγ = load inclination factorsbc, bq, bγ = base inclination factorsgc, gq, gγ = ground inclination factorsγ’: need correction when Dw<B+D
γγγγγγγ+σ+= gbidsBNgbidsNgbidsNcq qqqqqqzDccccccult '5.0' ,
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Vesic’s bearing capacity theory (V)
Notation for load inclination, base inclination and ground inclination.
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Source: GEO (2006). Foundation design and construction. GEO publication No.1/2006.
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Design example with program Bearing
• ProblemDesign of a square spread footing in a sand. Embedment depth D=1.8 m, γ=17.5 kN/m3, c’=0, φ’=31°. Ground water table is at a great depth. Dead load=2500 kN, live load=785 kN
• SolutionTotal load=2500+785=3285 kNUsing Terzaghi’s bearing capacity theory and FS=3.0B=2.8 mPa=3296 kN using Excel spreadsheet BEARING
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Accuracy of bearing capacity analysisFootings in sand:
Very difficult to induce failure in large footings. Usually controlled by settlement.
Footings on sands
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Factor of safetyAllowable bearing capacity qa is given by
Fqq ult
a =
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Shallow Foundations
Summary of design requirementsLoad eccentricityBearing capacitySettlement analysis
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Settlement is caused by induced stresses in soil! (I)
q
D
Bearing pressure: q
Net bearing pressure: q – σZD’
Induced stress at z:
Δσz = Iσ (q – σZD’)
Iσ=stress influence factorwhich may be calculated based on Boussinesq’smethod
σzo+Δσz
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Settlement analysis: Components (II)Total settlement ρ = ρi + ρc+ ρs
Distortion (immediate?) settlement ρi
The change in shape or distortion of the soil beneath the foundation (at no volume change).Primary consolidation settlement ρc
Occurs during dissipation of pore water pressure and expulsion of water from voids in the soil. Often takes substantial time in cohesive soils, but is insignificant in cohesionless soils.Secondary compression settlement ρs
A form of creep that is largely controlled by the rate at which the skeleton of compressible soils can yield and compress, particularly for foundations on clay, silts and peats.
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Immediate settlement analysis based on elastic theory (III)
Calculate induced stress beneath foundationΔσv and ΔσhFind strain at depth z and integrate
Settlement at the center of loaded area
Iρ = influence coefficient
∫ ε=ρσΔμ−σΔ=εZ
vhvv dzE 0
)2(1
footingSquare1
footingCircular
2 )(IEBq
IERq
s
s
μΔρ
Δρ
ρ
ρ
−=
=
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Plate load test• The test is mainly used to derive the
deformation modulus of soil for predicting the settlement of a shallow foundation.
• Guidelines and procedures for conducting plate loading tests are given in BS EN 1997-1:2004 (BSI, 2004) and DD ENV 1997-3:2000 (BSI, 2000b). ASTM D1194-94 Standard Test Method for Bearing Capacity of Soil for Static Load and Spread Footings was withdrwan.
• The elastic soil modulus Es can be determined as:
qnet = net ground bearing pressureδp = settlement of the test plateIs = shape factorb = diameter of test plate, 350, 450, or 600 mmνs = Poisson’s ratio of the soil
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Secondary consolidation (V)Causes: Slippage and re-
orientation of soil particles under constant effective stresses. Compression of secondary pore series
Cα =secondary compression indexOC clays (OCR> 2 or 3): >0.001Organic soils: >0.025NC clays: 0.004 ~0.025
⎟⎟⎠
⎞⎜⎜⎝
⎛+
=
⎟⎟⎠
⎞⎜⎜⎝
⎛Δ
=
α
α
1
2
1
2
log1
log
tt
eHCS
tteC
p
cs
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Methods of settlement calculation
Schmertmann’s method (1970, 1978) for sands
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Evaluation of immediate settlement based on in-situ tests (Schmertmann’s method)Most of the methods for sands are purely empirical. Schmertmann’smethod is based on elastic theory and calibrated using empiricaldata. The total settlement is the sum of settlements of layers:
H: layer thicknessIε: influence factor at layerEs: equivalent modulus of elasticity of layer (not Young’s modulus E)C1, C2 and C3: correction factors for depth, secondary creep and shape, respectivelyC1=1-0.5σ’zD/(q-σ’zD); C2 =1+0.2log(time in year/0.1); C3=1.03-0.03L/B > 0.73
εΔ
=σΔμ−σΔμ−σΔ=ε IE
pE s
lhvv )(1
∑ εσ−=ρs
zD EHIqCCC )'(321
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Schmertmann’s method (II)
Strip footing
Square orcircular
,
,
1.05.0zp
zDp
qIσ
σ−+=ε
Peak value of strain influence factor
TrueBilinear simplification
q=bearing pressure
σ’zD=vertical effective stress at depth D
σ’zp=vertical effective stress at peak Iεp
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Schmertmann’s method (III)Es value from CPT
Es value from SPT 6010 NOCREs β+β=(Kulhawy and Mayne 1990):
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Schmertmann’s method: example (V)
Rectangular footing 2.5 m x 30 mDW=2.0 mD=2.0 mLoad=375 kN/m x 30 m
=11250 kNEs to be evaluated by CPTEs=2.5 qc
Find d at t=0.1 and t=50 years
Spreadsheet SchmertmannDepth of influence =D+4B=12 mAnswer: d =39.5 mm at t=0.1a
=60.8 mm at t=50 aIf da=50 mm, then B=2.92 m
