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- 1. CE-632 Foundation Analysis and DesignDesign LateralEarth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure 1
- 2. Foundation Analysis andDesign: Dr. Amit Prashant Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure Lateral earth pressures are a function of type and amount of wall movement shear strength properties weight of soil andwall movement, shear strength properties, weight of soil and drainage 2
- 3. Foundation Analysis andDesign: Dr. Amit Prashant Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure Lateral Earth pressure is a function of wall movement (or relative lateral movement in the backfill soil) 3
- 4. Foundation Analysis andDesign: Dr. Amit Prashant Lateral Earth Pressure at RestLateral Earth Pressure at Rest Coefficient of earth pressure at rest, o h vK σ σ′ ′= (No Lateral Movement) p , The vertical al stress at any depth, z, is: o h v v q zσ γ′ ′= + K′ ′ + u = pore water pressureh o vK uσ σ= + u = pore water pressure Elastic Solution: 1 oK ν ν = − Poisson’s ratio 4
- 5. Foundation Analysis andDesign: Dr. Amit Prashant Coefficient of Earth Pressure at RestCoefficient of Earth Pressure at RestCoefficient of Earth Pressure at RestCoefficient of Earth Pressure at Rest For coarse-grained soils (Jaky 1944)For coarse grained soils (Jaky, 1944) K0 = 1 – sin φ’ For fine-grained normally consolidated soils (Massarch 1979)For fine grained, normally consolidated soils (Massarch, 1979) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ += 100 (%) 42.044.0 PI Ko Brooker and Ireland, 1965 K0 = 0.95 – sin φ’ ⎦⎣ 100 0 φ For overconsolidates clays OCRKK COC )()( = cP OCR = Mayne and Kulway, 1982 K0 = (1 – sin φ’).OCRsin φ’ OCRKK NCoOCo )()( = o OCR 'σ 5 K0 (1 sin φ ).OCR
- 6. Foundation Analysis andDesign: Dr. Amit Prashant Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy 6
- 7. Foundation Analysis andDesign: Dr. Amit Prashant Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy ( ) 21 sin tan 45K φ φ′− ′⎛ ⎞ ⎜ ⎟ ( ) ( ) tan 45 1 sin 2 aK φ = = −⎜ ⎟′+ ⎝ ⎠ D th f 2c′ Depth of Tension Crack c a z Kγ = 7
- 8. Foundation Analysis andDesign: Dr. Amit Prashant Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy 8
- 9. Foundation Analysis andDesign: Dr. Amit Prashant Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy ( ) ( ) 21 sin tan 45K φ φ′+ ′⎛ ⎞ = = +⎜ ⎟ ⎝ ⎠( ) tan 45 1 sin 2 pK φ +⎜ ⎟′− ⎝ ⎠ 9
- 10. Foundation Analysis andDesign: Dr. Amit Prashant Rankine’sRankine’s Theory: Special CasesTheory: Special Casesy py p Submergence: h a vK uσ σ′= + Pore Pressure v v u u σ σ′ = −⎡ ⎢ =⎣⎣ Inclined Backfill: β ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 cos cos cos cos cos cos aK β β φ β β φ ′− − = ′+ − 1 p a K K = Thrust β( ) ( ) ( )cos cos cosβ β φ+ a β Inclined but Smooth Back face of wall: w β w PA1 is w PA1 PA 1A AP W P= + w PA1 PA β H1 A1 calculated for H1 height 10 β
- 11. Foundation Analysis andDesign: Dr. Amit Prashant Rankine’s Theory: Special CasesRankine’s Theory: Special CasesRankine’s Theory: Special CasesRankine’s Theory: Special Cases β Inclined Backfill with c‘ φ‘ soil: Thrust β Inclined Backfill with c -φ soil: ⎧ ⎫′⎛ ⎞ β 2 2 2 2cos 2 cos sin 1 1 cos a c z K β φ φ γ φ ⎧ ⎫′⎛ ⎞ ′ ′+⎪ ⎪⎜ ⎟ ⎝ ⎠⎪ ⎪ = −⎨ ⎬ ′ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪ ( )2 2 2 2 2 cos 4cos cos cos 4 cos 8 cos cos sin c c z z φ β β φ φ β φ φ γ γ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪ ′ ′ ′ ′− − + +⎜ ⎟ ⎜ ⎟⎪ ⎪ ⎝ ⎠ ⎝ ⎠⎩ ⎭ 2 2 2cos 2 cos sin 1 1 c z K β φ φ γ ⎧ ⎫′⎛ ⎞ ′ ′+⎪ ⎪⎜ ⎟ ⎝ ⎠⎪ ⎪ = −⎨ ⎬ ( ) 2 2 2 2 2 2 2 1 cos 4cos cos cos 4 cos 8 cos cos sin pK c c z z φ β β φ φ β φ φ γ γ ⎨ ⎬ ′ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪ ′ ′ ′ ′+ − + +⎜ ⎟ ⎜ ⎟⎪ ⎪ ⎝ ⎠ ⎝ ⎠⎩ ⎭ 11
- 12. Foundation Analysis andDesign: Dr. Amit Prashant Coulomb’s Theory: Active Earth PressureCoulomb’s Theory: Active Earth Pressure Wall Friction: Coulomb’s theory underestimates Active EPActive EP 12
- 13. Foundation Analysis andDesign: Dr. Amit Prashant Coulomb’s Theory: Passive Earth PressureCoulomb’s Theory: Passive Earth Pressure Wall Friction: Coulomb’s theory overestimates Passive EPPassive EP 13
- 14. Foundation Analysis andDesign: Dr. Amit Prashant Coulomb’s Theory: SolutionsCoulomb’s Theory: Solutionsyy 14
- 15. Foundation Analysis andDesign: Dr. Amit Prashant Culmann’sCulmann’s Graphical Method: Active EPGraphical Method: Active EPpp δ = Wall friction C1 C2 C3 C4 C B 1 E4 E θ E2 E3 E4 E1 D3 D4 D φ'A D1 D2 φ ψ =90-θ-δ A 15
- 16. Foundation Analysis andDesign: Dr. Amit Prashant Culmann’sCulmann’s Graphical Method: Passive EPGraphical Method: Passive EPpp δ = Wall friction C1 C2 C3 C4 C E1 f B C1 2 E2 E3 E4 E θ 4 A φ' ψ =90 θ+δ Ea Pres Lin A D1 D2 φ' 16 =90-θ+δ rth sure ne D3 D4 D
- 17. Foundation Analysis andDesign: Dr. Amit Prashant Seismic EarthSeismic Earth Pressure:byPressure:by MononobeMononobe--Okabe MethodOkabe Method Active Earth PressureActive Earth Pressure Wall movement : angle of internal friction of soil θ b tt l f ll vk W β θ: batter angle of wall δ: angle of friction between the wall and the backfill hk W W φ Failure surface H wall and the backfill β: slope of the backfill top surfaceW φ α θ AEP δ F ( ) 1 tan 1 h v k k ψ − = − and ( )ψ φ β≤ − AEα ( )2 cos K φ θ ψ− − = ( ) ( ) ( ) ( ) ( ) ( ) 2 2 sin sin cos cos cos 1 cos cos AEK δ φ φ β ψ ψ θ δ θ ψ δ θ ψ β θ = ⎡ ⎤+ − − + + +⎢ ⎥ + + −⎢ ⎥⎣ ⎦ 17 ⎣ ⎦ ( )21 1 2 AE v AEP H k Kγ= − Assumed to be acting at H/2.
- 18. Foundation Analysis andDesign: Dr. Amit Prashant Seismic EarthSeismic Earth Pressure:byPressure:by MononobeMononobe--Okabe MethodOkabe Method Passive Earth PressurePassive Earth Pressure Wall movement vk W β hk W v W φPEP F Failure surface H W PEα θ δ ( ) 1 tan 1 h v k k ψ − = − ( )ψ φ β≤ +and PEα ( )2 cos K φ θ ψ+ − = ( )v ( ) ( ) ( ) ( ) ( ) 2 2 sin sin cos cos cos 1 cos cos PEK δ φ φ β ψ ψ θ δ θ ψ δ θ ψ β θ = ⎡ ⎤+ + − − + −⎢ ⎥ − + −⎢ ⎥⎣ ⎦ 18 ⎣ ⎦ ( )21 1 2 PE v PEP H k Kγ= −