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# sma13 - Settlement of Structures Solutions using theory of...

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Settlement of Structures Solutions using theory of elasticity

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Soil Layer Rigid bedrock H P Settlement of a footing on a finite soil layer

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s dz zz H = ∆ε 0 Surface Settlement Calculation of settlement using theory of elasticity
s dz zz H = ∆ε 0 Surface Settlement For an elastic soil ∆ε zz zz xx yy zz E = + - + + ( ) ( ) 1 ν σ ν σ σ σ Calculation of settlement using theory of elasticity

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s dz zz H = ∆ε 0 Surface Settlement For an elastic soil ∆ε zz zz xx yy zz E = + - + + ( ) ( ) 1 ν σ ν σ σ σ For undrained conditions ∆ε ∆σ ∆σ ∆σ ∆σ zz u zz u xx yy zz u E = + - + + ( ) ( ) 1 ν ν Calculation of settlement using theory of elasticity
Q r s r Surface deflection of an infinitely deep elastic layer s Q Er r = - ( ) 1 2 ν π Boussinesq’s solution

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dr r d θ Plan of a circular footing of radius a, uniformly loaded with stress q Settlement of centre of a flexible circular footing
dr r d θ Plan of a circular footing of radius a, uniformly loaded with stress q s Er qrd dr centre a = - ( ) 1 2 0 2 0 ν π θ q a E = - ( ) 2 1 2 ν π Settlement of centre of a flexible circular footing

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Soil Layer Rigid bedrock h P a p av = π 2 rigid Rigid circular footing on an elastic layer on a rigid base 2a
Soil Layer Rigid bedrock h P a p av = π 2 rigid Rigid circular footing on an elastic layer on a rigid base 2a s p a E I av = ρ

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0.0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 0.0 h/a a/h 1.6 1.2 0.8 0.4 0.0 Settlement Factor for rigid circular footing on a layer 2a P a p av = π 2 h s p a E I av = ρ ν = 0.0 0.2 0.4 0.5 I ρ
3m 9m 500 kN Young’s Modulus = 5 MPa Poisson’s ratio = 0.3 Example: Rigid circular footing

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3m 9m 500 kN Young’s Modulus = 5 MPa Poisson’s ratio = 0.3 Example: Rigid circular footing Long term settlement required. Effective stress parameters E' , v' must be used
3m 9m 500 kN Young’s Modulus = 5 MPa Poisson’s ratio = 0.3 Example: Rigid circular footing Long term settlement required. Effective stress parameters E' , v' must be used To use chart calculate a/h = 1.5/9 = 0.167

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0.0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 0.0 h/a a/h 1.6 1.2 0.8 0.4 0.0 Settlement Factor for rigid circular footing on a layer ν = 0.0 0.2 0.4 0.5 I ρ
3m 9m 500 kN Young’s Modulus = 5 MPa Poisson’s ratio = 0.3 Example: Rigid circular footing I = 122 . ρ for a/h = 0.167 , ν = 0.3 by interpolation

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3m 9m 500 kN Young’s Modulus = 5 MPa Poisson’s ratio = 0.3 Example: Rigid circular footing I p kPa av = = x = 122 500 15 70 7 2 . ( . ) . ρ π for a/h = 0.167 , ν = 0.3 by interpolation
3m 9m 500 kN Young’s Modulus = 5 MPa Poisson’s ratio = 0.3 Example: Rigid circular footing I p kPa s m av = = x = = x x = 122 500 15 70 7 707 1 5 122 5000 0 026 2 .

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