CEG 4012 Notes Fall 2011

CEG 4012 Notes Fall 2011 - Lecture 1 Review of Geostatic...

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Unformatted text preview: Lecture 1 Review of Geostatic Stresses Unit Weights Yw = unit weight of water Ym = moist unit weight of unsaturated soil Ysat = unit weight of saturated soil y' = "effective" unit weight of soil = (Ysat -Yw) if soil saturated = Y m if soil not saturated = Yb' "buoyant" unit weight of soil Geostatic Stresses (due to the soil's own weight) Review concept of stress at a point (P): Total Vertical Str~s: U y = LYi~ Y m orYslll as appropriate (= cr.) > ~ster Pressur~: u = Yv7-w hydrostatic (no flow) (u o initial condition) or u = yvJlp general, h p = pressure head (flow net) VertJcatE~ve Stres~ u' y = u y-U granUlar contact stress . ~-!-~ve Stress: u'h = Kcr'y K = coefficient of lateral stress / Geostatic Stresses These self-weight stresses (ay, a'y, ah' a'h) are called geostatic stresses For a level surface there are no shear forces induced by the geostatic stresses, and therefore they are also principal stresses: a, =ay and a3 = ah Karl Terzaghi's principle of effective stress (a' or 0) governs most soil behavior (probably the most important point in this class). Examples: Pressure on a retaining wall depends on stress due to soil weight Shear strength, t. of soli depends on cohesion and O'n due to soil weight T = C + an tan 0:. failure surface Geostatic Stress Example 1 Determine the total horizontal stress at point P: (,';~ ll:'~ '" Sand v." 100 Del. K .. 0.4 6' ~* ~~ Sand y... " 118 pet. K .. 0.4 4' Clay Yw" 126 pet. K .. 0.6 6' Clay 1..... 120 pet, K = 0.5 t 4' 8'-i--:-p U = 0" = v I = O'h O'h = = LYjZj = 6' (100 pet) + 4' (118 pet) + 6' (126 pet) + 4' (120 pet) = 600 pst + 472 pst + 756 pst + 480 pst = 2308 pst 14' (62.4 pet) = 874 pst (a y-U) = 2308 pst 874 pst = 1434 pst K a'y = 0.5 (1434 pst) = 717 pst (a' h + u) = 717 pst + 874 psf = 1591 psf 1591 pst x (0.04788 kN/m z 11 pst) = 76.18 kN/m z using the effective weight concept: = 6'(100 pet} + 4'(118-62.4 pet} + 6'(126-62.4 pet}+4'(120-62.4 pet} = 600 pst + 222 pst + 382 pst + 230 pst: 1434 pst 0" h = K (J'y : 0.5 (1434 pst) : 717 pst U-14' (62.4 pet): 874 pst (a' h + u): 717 pst + 874 pst: 1591 pst Geostatic Stress Example 2 .. j'O ~'500' ~. 'ODD ;..~-:. .-~ What happens when the GWT (ground water table) rises? Look at a sample profile: o~ . ~ ._. ... ~ . . ~ ..... ~ .. _ ":'jJ~l .. .:=~ . . . ~.o .. poI .... . 10' ". 0 0,, .0 20' ~;2~-.-~~fr~ . 1124----0-' . ~-,-1124 3Q""" ~~= __ .2248,-D', ~~fij::.22.8 I:~@ .. ~ .. .. O- _ ~-.O _ .. -20'-~:"'o. "'2. "0' 30' ;\~~~:>~c-. 22.8 ~: . 82. 0r-c ~ ~ 10'--"0- .--. -0 20' .. ..... . .,~"'.'.:-_1tz. . ~8Z. ....
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This note was uploaded on 02/10/2012 for the course CEG 4012 taught by Professor Staff during the Fall '08 term at University of Florida.

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CEG 4012 Notes Fall 2011 - Lecture 1 Review of Geostatic...

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