Lecture 4 - ρ 1 SETTLEMENT IN CLAY SUMMARY • Strains due...

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Unformatted text preview: ρ 1 SETTLEMENT IN CLAY SUMMARY • Strains due Surface Load: Surface loads cause a change in the stresses within the soil mass and induce two types of soil strain. Linear Elastic, Homogeneous, Isotropic: E = Young's modulus Poisson's ratio, x y al longitudin lateral ε ε = ε ε = μ Normal Strain, ( ) ) ( E 1 z y x x σ + σ μ- σ = ε Volumetric Strain, ( ) z y x v ε + ε + ε = ε Shear Strain, G xy xy τ = γ Bulk Stress, σ + σ + σ = σ 3 z y x Shear Modulus, ) 1 ( 2 E G μ + = Bulk Modulus, ) 2 1 ( 3 E K v μ- = ε σ = Note that for Saturated Clay μ = 0.5 and K = ∞ (water is incompressible) • Settlement: A clay layer under a surface load may "settle" (strain) significantly. This settlement under load has three basic components. "Immediate settlement" occurs rapidly and is distortional - due to rotational strains. The settlement component with the largest magnitude, the "consolidation settlement" , is due to volume change and may continue for many years because the pore water must be squeezed from the soil. After the primary phase of consolidation is complete, a long term creep or "secondary consolidation" may continue for hundreds of years. In general, the total settlement is given by; ρ = ρ i + ρ c + ρ s where ρ = total settlement ρ i = immediate settlement ρ c = primary consolidation settlement ρ s = secondary consolidation (creep) (immediate settlement, ρ i , is sometimes referred to as distortional settlement, ρ d .) γ yz x y z γ xy γ zx σ x σ y σ z x y z τ zx τ xz τ xy τ yx τ yz τ zy ε x ε y ε z 3-D soil element with & normal ( σ ) & shear ( τ ) stress Normal strain ( ε ) due to normal stress Rotational strain ( γ ) due to shear stress ρ ρ s ρ C Time ρ i ρ 2 Immediate Settlement ( ρ i ): This settlement is due to rotational strain (distortion) within the soil – not a change in volume. (Note that if no shear strain, say a blanket load, then no immediate settlement.) Immediate settlement is typically much smaller in magnitude than ρ c and occurs rapidly, i.e. during construction. It is affected by: 1. footing rigidity 2. footing shape 3. location beneath footing 4. soil stiffness parameters E and μ 5. soil layering 6. presence of rigid layer (rock) o Compute ρ I Using Theory Of Elasticity Superposition is valid: For relatively uniform clay strata E and μ can be assumed constant and, for sufficiently low stress levels, elastic theory gives satisfactory estimates of ρ i . o Uniformly Loaded Flexible Footing A flexible loaded area deforms into a dish shape, producing a uniform reaction (e.g. a tank). The settlement, ρ i , under the corner of a flexible rectangular loading is one half of the settlement at the center....
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This note was uploaded on 09/12/2011 for the course CEG 4012 taught by Professor Staff during the Fall '08 term at University of Florida.

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Lecture 4 - ρ 1 SETTLEMENT IN CLAY SUMMARY • Strains due...

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