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10. In-Situ Stress (Das, Chapter 9) Sections: All except 9.5, 9.6, 9.7, 9.8, 9.9

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Stress in a Soil Mass Topics Introduction Geostatic Stress Stresses due to external loads

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3 Introduction

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4 Introduction

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5 Introduction

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6 Hydrostatic and Total stress

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7 When a load is applied to soil, it is carried by the water in the pores as well as the solid grains. The increase in pressure within the porewater causes drainage (flow out of the soil), and the load is transferred to the solid grains. The rate of drainage depends on the permeability of the soil. The strength and compressibility of the soil depend on the stresses within the solid granular fabric. These are called effective stresses

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8 Pore Water Pressure

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9 Effective Stress – General Expression

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10 Methods of Computations Effective Stress

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11 Diagram

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12 Total stress in multi-layered soil

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13 EXAMPLE Plot the variation of total and effective vertical stresses, and pore water pressure with depth for the soil profile shown below in Fig.

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14 Solution: Within a soil layer, the unit weight is constant, and therefore the stresses vary linearly. Therefore, it is adequate if we compute the values at the layer interfaces and water table location, and join them by straight lines.

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15 Solution

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16 Example 1 tt ’’

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17 Example 2 tt ’’

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Other Examples Example 9.1 Das, Chapter 9 18

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Stresses in Saturated Soils without Seepage (No flow) At A, Total Stress: A = H 1 w Pore water pressure: u A = H 1 w Effective stress: ’ A = 0 At B, Total Stress: B = H 1 w + H 2 sat Pore water pressure: u B = (H 1 + H 2 ) w Effective stress: ’ B = H 2 ( sat – w ) = H 2 ’ At C, Total Stress: C = H 1 w + z sat Pore water pressure: u C = (H 1 + z) w Effective stress: ’ C = z( sat – w ) = z ’

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Stresses in Saturated Soils without Seepage (No flow) Variations of the total stress, pore water pressure, and effective stress, respectively, with depth for a soil layer without seepage

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Stresses in Saturated Soils with Upward Seepage If water is seeping, the effective stress at any point in a soil mass will differ from that in the static case. It will increase or decrease, depending on the direction of seepage.

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Stresses in Saturated Soils with Upward Seepage Variations of the total stress, pore water pressure, and effective stress, respectively, with depth for a soil layer with upward seepage

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Note that h/H 2 is the hydraulic gradient I caused by the flow, and therefore: If the rate of seepage and thereby the hydraulic gradient gradually are increased, a limiting condition will be reached, at which ’ is zero: Where i cr : critical hydraulic gradient (for zero effective stress). Under such a situation, soil stability is lost. This situation generally is referred to as boiling, or a quick condition. For most soils, the value of icr varies from 0.9 to 1.1, with an average of 1. Stresses in Saturated Soils with Upward Seepage

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Stresses in Saturated Soils with Downward Seepage At B, Total Stress: B = H 1 w + H 2 sat Pore water pressure: u B = (H 1 + H 2 - h) w Effective stress: ’ B = H 2 ( sat – w ) + h w At C, Total Stress: C = H 1 w + z sat Pore water pressure: u C = (H 1 + z – h/H 2 z) w = (H 1 + z – i z) w Effective stress: ’ C = z( sat – w ) + iz w = z ’ + iz w

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Stresses in Saturated Soils with Downward Seepage Variations of the total stress, pore water pressure, and effective stress, respectively, with depth for a soil layer with downward seepage

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Seepage Force

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Seepage Force per unit volume See Example 9.3 Das, chapter 9

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