HKIE-GD Workshop on Foundation Engineering 7 May 2011 Shallow Foundations Dr Limin Zhang Hong Kong University of Science and Technology 1
Outline Summary of design requirements Load eccentricity Bearing capacity Settlement analysis 2
Shallow foundations: spread footings (a) (b) (c) (d) (e) (f) Square Rectangular Circular Continuous Combined Ring 3
Shallow foundations: Mats (rafts) Very large spread footings that usually encompass the entire footprint of structure Good for Large load or poor soil conditions Erratic soils prone to differential settlement Erratic loads prone to differential settlement Underground space Nonuniform lateral load Water-proofing 4
Shallow foundations: Economy Shallow foundations, where applicable, are often the cheapest foundation type. HKUST Enterprise Center 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 5
Eiffel Tower Each 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. 6
Eiffel Tower (not on scale) River Seine Soft silt mbgl 12 m Soft alluvial Firm alluvial soils mbgl 0 7
Design summary (I): Depth Bearing capacity Shear capacity Depth of surface weak soil Depth of frost penetration Depth of greatest moisture fluctuation (expansive or collapsible soils) Depth of potential scour Possible landslides (see footings on slopes) 8
Design summary (II): Plan Load eccentricity requirement - no tension 6eB 6eL + 1 B L Allowable vertical bearing capacity requirement P + W for concentric loads q = ud < BL P + W f q = ud < B' L' f q q a a for eccentric loads B =B-2e B, L =L-2e L Allowable horizontal shear capacity requirement V V a Allowable total settlement and differential settlement S [S], ΔS [ΔS] 9
Shallow Foundations Summary of design requirements Load eccentricity Bearing capacity Settlement analysis 10
11 Bearing pressure (I): One-way eccentric loading To maintain compressive stress along the entire base area, q min 0 or e B/6 + + = + = B e u A W P q B e u A W P q D f D f 6 1 6 1 max min
12 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, ± ± + = L e B e u A W P q L B D f 6 6 1 1 6 6 + L e B e L B
Bearing pressure (III): Silo example Problem: a mat foundation for four silos W silo =29 MN, W grain =110 MN, W mat =60 MN (1) One-way loading: two full P=4x29 + 2x110=336 kn M=2x110x12 = 2640 MNm e=m/(p+w f )=2640/(336+60)=6.7 m e <B/6=50/6=8.3 m (2) Two-way loading: one full P=4x29+110=226 MN M=110x12=1320 MNm e B =e L =1320/(226+60)=4.62 m 6e B /B + 6e L /L=2x6x4.62/50=1.11>1 (3) To let the resultant within the kern, 6eB 6eL 6 4.62 + = 2 = 1 B L B B=55.4 m 13
Shallow Foundations Summary of design requirements Load eccentricity Bearing capacity Settlement analysis 14
Bearing capacity (I): Failure modes (a) General shear failure (strongly dilative) (b) Local shear failure (c) Punching shear failure (contractive) 15
Terzaghi s bearing capacity theory (II) Assumptions Rigid strip foundation Concentric load The bottom of the foundation is sufficiently rough that no sliding occurs between foundation and soil Slip surface at a max depth of B below the base Shear strength of soil τ = c+ σ tan φ General shear failure mode governs No consolidation of soil occurs The soil within a depth D has no shear strength. 16
Terzaghi s bearing capacity theory (III) Basic equation for a strip footing: q ult = c N c + σ zd N q + 0.5γ BN γ 17
Vesic s bearing capacity theory (1973, 1975) (IV) Vesic retained Terzaghi s basic format and added additional factors q ult, = c' N s d i b g + σ N s d i b g + 0.5γ' BN s d i b g c c c c s c, s q, s γ = shape factors d c, d q, d γ = depth factors i c, i q, i γ = load inclination factors b c, b q, b γ = base inclination factors g c, g q, g γ = ground inclination factors γ : need correction when D w <B+D c c zd q q q q q q γ γ γ γ γ γ 18
Vesic s bearing capacity theory (V) Notation for load inclination, base inclination and ground inclination. 19
Source: GEO (2006). Foundation design and construction. GEO publication No.1/2006. 20
Design example with program Bearing Problem Design of a square spread footing in a sand. Embedment depth D=1.8 m, γ=17.5 kn/m 3, c =0, φ =31. Ground water table is at a great depth. Dead load=2500 kn, live load=785 kn Solution Total load=2500+785=3285 kn Using Terzaghi s bearing capacity theory and FS=3.0 B=2.8 m P a =3296 kn using Excel spreadsheet BEARING 21
Accuracy of bearing capacity analysis Footings in sand: Very difficult to induce failure in large footings. Usually controlled by settlement. Footings on sands 22
Factor of safety Allowable bearing capacity q a is given by q a = q F ult 23
Shallow Foundations Summary of design requirements Load eccentricity Bearing capacity Settlement analysis 24
Settlement is caused by induced stresses in soil! (I) Bearing pressure: q Net bearing pressure: q σ ZD Induced stress at z: Δσ z = I σ (q σ ZD ) I σ =stress influence factor which may be calculated based on Boussinesq s method q σ zo +Δσ z D 25
Settlement analysis: Components (II) Total settlement ρ = ρ i + ρ c + ρ s Distortion (immediate?) settlement ρ i The change in shape or distortion of the soil beneath the foundation (at no volume change). Primary consolidation settlement ρ c 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 ρ s 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. 26
Immediate settlement analysis based on elastic theory (III) Calculate induced stress beneath foundation Δσ v and Δσ h Find strain at depth z and integrate ε = 1 Δσ μδσ ρ = Z ( 2 ) ε dz v v h E 0 Settlement at the center of loaded area R ρ = Δqs I ρ Circular footing E B ρ = Δq I ( 1 2 s ρ μ ) Square footing E I ρ = influence coefficient v 27
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 E s can be determined as: q net = net ground bearing pressure δ p = settlement of the test plate I s = shape factor b = diameter of test plate, 350, 450, or 600 mm ν s = Poisson s ratio of the soil 28
Secondary consolidation (V) Causes: Slippage and reorientation of soil particles under constant effective stresses. Compression of secondary pore series C S α s Δe = t 2 log t1 C αh c t = log 1+ ep t C α =secondary compression index OC clays (OCR> 2 or 3): >0.001 Organic soils: >0.025 NC clays: 0.004 ~0.025 2 1 29
Methods of settlement calculation Schmertmann s method (1970, 1978) for sands 30
Evaluation of immediate settlement based on in-situ tests (Schmertmann s method) Most of the methods for sands are purely empirical. Schmertmann s method is based on elastic theory and calibrated using empirical data. The total settlement is the sum of settlements of layers: 1 Δp ε = ( Δσ μδσ μδσ = I v v h l ) E E s HI ρ = C ε 1C 2C 3 ( q σ' zd ) E s H: layer thickness I ε : influence factor at layer E s : equivalent modulus of elasticity of layer (not Young s modulus E) C 1, C 2 and C 3 : correction factors for depth, secondary creep and shape, respectively C 1 =1-0.5σ zd /(q-σ zd ); C 2 =1+0.2log(time in year/0.1); C 3 =1.03-0.03L/B > 0.73 ε 31
Schmertmann s method (II) Peak value of strain influence factor I εp = 0.5 + 0.1 q σ σ, zd, zp Square or circular q=bearing pressure σ zd =vertical effective stress at depth D σ zp =vertical effective stress at peak I εp Strip footing True Bilinear simplification 32
Schmertmann s method (III) E s value from CPT E s value from SPT E s = β0 OCR + β1n 60 (Kulhawy and Mayne 1990): 33
Schmertmann s method: example (V) Rectangular footing 2.5 m x 30 m D W =2.0 m D=2.0 m Load=375 kn/m x 30 m =11250 kn E s to be evaluated by CPT E s =2.5 q c Find d at t=0.1 and t=50 years Spreadsheet Schmertmann Depth of influence =D+4B=12 m Answer: d =39.5 mm at t=0.1a =60.8 mm at t=50 a If d a =50 mm, then B=2.92 m 34