sma12 - Settlement of Structures Elasticity for saturated...

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Settlement of Structures Elasticity for saturated soils
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Maximum Settlement Soil Layer Settlement of a loaded footing
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Settlement-time response of a loaded footing S t Immediate settlement Final or long term settlement
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Skeletal Material (incompressible) Pore water (incompressible) Voids Solid Voids Solid Initial State Deformed State Soil deformation - volume change Water + ∆ σ
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Undrained Deformation (no volume change) Soil Element Soil Element Soil deformation - constant volume
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The soil deformation process Deformation of saturated soil can occur due to: reduction of pore space & the squeezing out of pore water changes in shape at constant volume combinations of changes in volume and changes in shape Pore water can only be squeezed out at a finite rate and so immediately after a load is applied there is no volume change Initially deformation can only take place due to changes in shape at constant volume
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The soil deformation process Previously we have been looking at the deformation under one-dimensional conditions with no lateral strain (confined conditions). For such conditions there can be no change in shape and hence no immediate deformation. In the 1-D analysis of settlement under a footing this implies that there can be no immediate settlement. For more general 3-D conditions there can be lateral strains and vertical strains and changes in shape can occur at constant volume. Thus 3-D analyses of settlement will predict immediate settlement.
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The soil deformation process Beneath a loaded footing different points in the soil will experience different increases in stress Immediately after the load is applied deformation will be at constant volume, and excess pore pressures will develop in the soil Excess pore pressures will be greatest at points where the increase in stress is greatest
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Soil Layer Excess pore pressures under a loaded footing p 0.5 p 0.3 p 0.1 p Contours of excess pore pressure, u
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Region of high excess water pressure Region of low excess water pressure Flow Flow of water in a porous soil As time progresses water will flow until the excess pore pressures reduce to zero, and additional deformation will take place in the soil
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Total Stress Time Time Excess Pore Pressure Effective Stress Time Variation of stress and pore pressure with time
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Settlement Time Consolidation settlement Initial settlement Final settlement Typical settlement - time response
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Analysis of 3-D settlement Based on assumption of linear elastic soil response This is used because easily evaluated solutions can be obtained complex loadings can be split into simple loadings for which solutions can be superimposed only 2 material constants need to be specified solutions agree with intuition and experience despite non-linear real soil behaviour
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∆ε ∆σ ∆σ ∆σ ∆ε ∆σ ∆σ ∆σ ∆ε ∆σ ∆σ ∆σ xx xx yy zz yy yy zz xx zz zz xx yy E E E = - + = - + = - + ν ν ν ( ) ( ) ( ) Hooke’s Law for an Elastic Solid (1a)
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This note was uploaded on 08/30/2011 for the course CIVL 2410 taught by Professor Dairey during the Three '11 term at University of Sydney.

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sma12 - Settlement of Structures Elasticity for saturated...

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