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test #1 - cive 462 sp 04 120 100 110 90 100 80 90 70 80 60 70 50 60 50 40 40 30 0 10 20 30 40 50 Soil Stresses (ch10) Stress Assumptions Continuous material Homogeneous (eng. props. = at all locations) Isotropic (Modulus and n are = in all directions) Linear-elastic stress-strain properties Stress Concept Stress Concept sz x s normal stresses zx z Ten (-), Comp (+) xz sx sx xz zx shear stresses sz Clock (+), CC (-) Strain Concept g normal strain P shear strain g dL L dL L g = shear strain [radians] Stress vs. Strain = Modulus s E G g p n pa Stresses in Soils 1. Geostatic Stresses Due to soil’s self weight 2. Induced Stresses Due to added loads (structures) 3. Dynamic Stresses 0.248811 0.4 0.2 e.g., earthquakes AS i 0 g 0.2 0.241673 0.4 0 0 10 20 30 40 50 t i 60 70 80 90 81.95 Geostatic Stresses TOTAL VERTICAL STRESS AT A POINT Ground surface z = depth = 5 m Soil , g = 18 kN/m3 A s A g zA “total vertical stress at A” Geostatic Stresses SHEAR STRESSES If ground surface is flat, all geostatic shear stresses = zero Geostatic Stresses PORE WATER PRESSURE AT A POINT Ground surface z=5m Soil , g = 18 kN/m3 hpA A u A g w hp A “pore water pressure at A” Geostatic Effective Stress board Example board Special Case Board – submerged soils Induced Stresses P g z A sA = g z A = 0 g z A sA = g z + ? A = ? Bousinnesq - point loads Point load zf A See page 324 of your book… Area loads P B L g z Area, A A Terminology: q = bearing pressure = P/A B < or = to L Area loads – sz below corner B L zf sz below corner of a loaded area: see page 327 (book) Area loads – sz below center Circular loaded area q zf A 1 s z q 1 B 1 2 z f 1.5 2 Area loads – sz below center Square loaded area Strip loads Rectangular area See page 332 (text) Lateral Stresses Ground surface z Soil , g = 18 kN/m3 A s' = Vertical effective stress = s 'h = Horiz. eff. stress = ? sv' Lateral Stresses “Coefficient of lateral earth pressure” s 'h K s 'v Superposition We can only add total stresses Stresses on other planes… So far we have sx and sz Now we want sz sx sx sz Stresses acting on other planes The Mohr Circle Describes 2-D stresses at a point in a material Plots s and on an = scale Each point on the MC represents the s and on one side of an element oriented at a certain angle The angle between two points in the MC is = 2 times the angle between the planes they represent The Mohr Circle A2 A1 sB2 sB1 B2 B1 If we change A s sA2 sA1 B we will get two more points on the same MC. The Mohr Circle 1 21 The Mohr Circle – Principal Stresses Planes A and B are called principal planes when there are no shear stresses (only normal stresses) acting on them. s1 = major principal stress s3 = minor principal stress The Mohr Circle Direction of max principal stresses is 17 degrees c.c. from the vertical Effective Stress Mohr Circle board Seepage Force board Seepage Force - Example board