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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 sheetpile 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: Aug08) 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: Aug08) The City of Houston, Texas has been experiencing a rapid lowering of its phreatic surface (drawdowns) 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.
 Summer '10
 STAFF

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