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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 3D 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.
 Fall '08
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