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Lecture 13 - BC7 • General Shear Failure Bearing Capacity...

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Unformatted text preview: BC7 • General Shear Failure Bearing Capacity: o Form of Terzaghi equation essentially correct: bearing factors and extensions improved o Desirable to analyze deeper footings (D f > B), inclined loads, eccentric loads, sloped ground, and tilted footing base o Several important solutions available: • Meyerhof (1963) – uses ψ = (45 + φ /2) and includes shear strength in soil above footing, inclined and eccentric loads • Hansen (1970) – similar to Meyerhof, adds slope and tilted base • Vesic (1973) – similar to Hansen with modified inclination, slope, and tilt factors • All three methods use same N c and N q , but have different N γ • Do not mix the methods , compare if time & project dictate extra effort • Meyerhof Bearing Capacity Equation: (for general shear failure) q u = (q c + q q + q γ ) = cN c λ cs λ cd λ ci + qN q λ qs λ qd λ qi + ½ γ BN γ λ γ s λ γ d λ γ i where: q u = ultimate bearing capacity c = cohesion (q c due to c) q = stress at depth of foundation = γ D f (q q due to q) γ = average unit weight of soil under footing (q γ due to γ ) (if completely submerged, use γ = γ ’ = γ b ) B = width of foundation (= diameter for circular foundation) λ cs , λ qs , λ γ s = shape factors λ cd , λ qd , λ γ d = depth factors λ ci , λ qi , λ γ i = load inclination factors N c , N q , N γ = bearing capacity factors Shape Factors ( λ s ): for ( φ = 0°) λ cs + = L B 20 . 1 λ qs = λ γ s = 1.00 for (0 ≤ φ <10°) interpolate between ( φ = 0°) and ( φ = 10°) for ( φ ≥ 10°) λ cs φ + + = 2 45 tan L B 20 . 1 2 λ qs = λ γ s φ + + = 2 45 tan L B 10 . 1 2 Depth Factors( λ d ): for ( φ = 0°) λ cd + = B D 20 . 1 f λ qd = λ γ d = 1.00 for (0 ≤ φ < 10°) interpolate between ( φ = 0°) and ( φ = 10°) for ( φ ≥ 10°) λ cd φ + + = 2 45 tan B D 20 . 1 f λ qd = λ γ d φ + + = 2 45 tan B D 10 . 1 f B Q q = γ D f D f Soil: γ , c, φ α BC8 Inclination Factors ( λ i ): for ( α = 0°) λ ci = λ qi = λ γ i = 1.00 for ( φ = 0°) λ ci = λ qi 2 90 1 ° ° α- = λ γ i = 0 for ( φ > 0°) λ ci = λ qi 2 90 1 ° ° α- = λ γ i 2 1 ° φ ° α- = (= 0 if α > φ ) Bearing Factors (N): ) 2 / 45 ( tan e N 2 tan q φ + = φ π b ( π in radians) φ- = tan 1 N N q c , N c = 5.14 for φ...
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Lecture 13 - BC7 • General Shear Failure Bearing Capacity...

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