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

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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 /
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Geostatic Stresses These self-weight stresses (a y, 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, =a y 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
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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:[email protected] .. ~ .•..•.•.. O - _ ~-.O _ .. - 20'- ~:"'o. "'2. "0' 30' ;\~~~:>~c-. 22.8 ~: . 82. 0r- c ~ ~ 10' - - "0- .--. - ···0 20' •.. ..... •. .,~"'.'.:-_1tz. . ~8Z. . 30' .. ~;~~:;;~..: 22.8 ~::,- 1248 ConeIY.Jon: E"'~ ttrna df!CfNI ...... GWT n W M~Oln. ~ ttM 0"" .. above ttl. 8018Ul'f&ee. CNoIIlhst errKll'te ttrftt In~ the OWl r.1o-.wfeCJ1)
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S1 Stresses Changes Due to Surface Loads (Aerv) o Stresses within a soil mass will change as a result of surface loads. The change in total stress spreads and diminishes with distance from the load. Equations and charts are available to calculate both the vertical and horizontal stress change (6.0' ... and 6.O'h). a If for some reason the complete total stress at a point is required, then add the geostatic stress, cr v or Oh, to the load-induced stress change, .6.0' ... or 6.011_ a We are normally most interested in vertical stress increases due to surface compression loads. (As a rule, we assume that soil cannot withstand tension stresses.) o Often we need to know !1cr v to determine how much a structure will settle.
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