PE-07-Effective-Stress

# PE-07-Effective-Stress - 165 Solved Problems in Effective...

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Unformatted text preview: 165 Solved Problems in: Effective Stresses *01: The concept of effective stress. *02: The concept of effective stress with multiple strata. *03: Effective and porewater pressure profiles with depth. *04: The effects of hydrostatic uplift upon a thin stratum. *05: Effective stress at any point. *06: What depth will produce a “quick” condition? *07: Uplift forces during dewatering excavations. *08: Find an expression for the critical gradient. *09: Combined problem with “quick” and other conditions. *10: Depth of embedment D for a sheet-pile cofferdam. 166 Symbols Effective Stresses D x & Diameter of the grains distributed (represent % finer by weight). e & The voids ratio. G S & Specific gravity of the solids of a soil. H & Maximum depth of excavation or thickness of a soil layer. h soil & depth of the soil. i critical & Critical hydraulic gradient. k H & Horizontal permeability. k V & Vertical permeability. u & pore water pressure. ¡ ’ & Effective stress. ¡ V ’ & Vertical Effective stress. & ’ & Bouyant unit weight of a soil. ¡ SAT & Saturated unit weight of a soil ¡ W & Unit weight of water. V W & Volume of water. w & water content. 167 *Effective Stress–01: The concept of effective stress. (Revision: Aug-08) A sample was obtained from point A in the submerged clay layer shown below. It was determined that it had a w = 54%, and a G s = 2.78. What is the effective vertical stress at A? Solution: The effective stress & ’ at the point A consists solely of the depth of the soil (not the water) multiplied by the soil buoyant unit weight. ( ) ' ' ' ' ' In order to find there are a number of derivations, such as this one, where the voids ratio can be found through 1 and noticing that 1 becaus soil b SAT W S W W S h where G e e Se wG e S σ γ γ γ γ γ γ γ γ γ = = =- + & ¡ =- = ¢ £ + ¤ ¥ = ( ) ( ) ( ) ( ) ( ) ' The concept of bouyancy is also easily illustr ' e the soil is 100% saturated, 0.54 (2.78) 2.78 0.54 10 (2.78) (9.81) ' 9.81 15 1 1 0.54 (2.78) 5 S S W soil W soil kPa e wG G e h h m e σ γ σ γ γ = = & ¡ + ¦ § & ¡ + & ¡ ¨ ¨ ¤ ¥ = =- =- ¢ £ © ª ¢ £ + + ¨ ¨ ¢ £ « ¥ = ¤ ¥ ¬ ¤ ated by this question: What force is required to hold just below the water surface an empty box that has a 3 volume of 1 ? ft water A saturated clay h 2 = 25 m h s = 15 m 168 *Effective Stress–02: Effective stress with multiple strata. (Revision: Aug-08) The City of Houston, Texas has been experiencing a rapid lowering of its phreatic surface (draw-downs) during the past 48 years due to large volumes of water pumped out of the ground by industrial users. a) What was the effective vertical stress at a depth of 15 m in 1960?...
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## This note was uploaded on 09/11/2011 for the course CEG 4011 taught by Professor Staff during the Summer '10 term at FIU.

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PE-07-Effective-Stress - 165 Solved Problems in Effective...

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