Soil Mechanics In Situ Stresses Chih-Ping Lin National Chiao Tung Univ. cplin@mail.nctu.edu.tw Outline Without seepage Upward seepage Downward seepage Seepage Force
The total stress at the elevation of point A σ = H w + (H A H) sat Effective Stress σ = σ + u =(HA-H) Stress Components in Soils Loading Reference particle σ = σ ig + u (1 as' ) A'+ R' For soil with low plasticity: σ ig = σ ' σ u
Calculation of Effective Stress Surcharge q Layer 1 bulk = 1 d 1 Layer 2 bulk = 2 z d 2 Layer 3 bulk = 3 d 3 σ v Calculation of Total Vertical Stress Elevation q Force on base = Force on top + Weight of soil d 1 A σ v = A q + A 1 d 1 + A 2 d 2 + A 3 ( z - d 1 -d 2 ) z d 2 σ v = q + 1 d 1 + 2 d 2 + 3 ( z - d 1 -d 2 ) σ v Plan A
Calculation of pore water pressure Water table H P u ( P)= H w w The water table is the level of the water surface in a borehole. It is the level at which the pore water pressure u w = 0 Example: determining the effective stress Step 1: Draw ground profile showing soil stratigraphy and water table Dry bulk = dry 2 m Saturated bulk = sat 3m
Step 2: Calculation of relevant bulk unit weights Voids V v =e V s = 0.7m 3 W w =0 W = V kn w v w = 07. 98. kn = 686. kn Solid V s = 1m 3 W = V G s s s w = 1 27. 98. kn = 2646. kn W = V G s s s w = 1 27. 98. kn = 26. 46 kn Distribution by Volume dry Distribution by weight for the dry soil 26. 46 kn 3 = = 1556. kn / m = 3 170. m Distribution by weight for the saturated soil G s w 1 + e sat = ( 26. 46 + 6. 86) kn 170. m 3 3 = 19. 60 kn / m = w ( G + e) s 1 + e Step 3 Calculate total stress 2 σ v = 1556. 2 + 19. 60 3 = 89. 92 kpa ( kn / m ) 2 m Step 4 Calculate pore water pressure 3m u w = 3 98. = 29. 40 kpa Step 5 Calculate effective stress σ = σ u = 89. 92 29. 40 = 60. 52 v v w kpa
Vertical stress and pore pressure variation 0m 0 50 100 150 kpa 2m Depth 4m 6m pore water pressure Total Stress Effective stress (5m) 8m No seepage 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.
Upward seepage Boiling/quick condition 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Downward seepage 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.
Seepage Force Seepage Force No seepage Upward seepage Downward seepage 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Heaving due to seepage Seepage Force 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.
Seepage Force Example 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Seepage Force Use of filters to increase FS against heave
Surface Tension Two forms of soil moisture Absorbed Free moisture Polar nature of water Molecular attraction Water to water contract to least possible area Waxed surface Air water interface Water to glass Balancing forces Surface tension T o = -0.075 gm/cm T o F Demo: http://www.wtamu.edu/~crobinson/soilwater/capact.html Capillary Tension α F α T o d F u c u c T o π F A d 4T o cos( α) π d T o cos α d π d 2 4 ( ) cos( α) 0.3 u c d gm/cm Negative sign denoted Tension in the pore water
Capillary Tension (cont.) F W h c F v F W y F T o π W d π 4 d2 h c w At equilibrium h c is at a maximum, therefore Solving for h cmax yields h cmax 4T o d w 0.3 d w Capillary Tension (cont.) h c1 h c2 Height of capillary rise is a function of diameter h c3 h c4 of capillary tube For soils d D 10 5
Height of the capillary rise and radius effects Capillary effect in sandy soil 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.
Capillary Rise in Soil Soil Type Course Gravel Fine Gravel Silty Gravel Medium Sand Silt Clay D 10 Size 0.82 0.3 0.06 0.02 0.006 < 2 mm Capillary Head (cm) 6 20 68 120 180 Meters Implication of capillarity σ ' = σ ( z c w ) = σ + zcw The pore water pressure due to capillarity is negative (suction), so it will increase the effective stress.
Capillary Rise in Soil (Stress Profile) It is reasonable to assume that pore spaces between soil particles of various diameters, behaves in much the same manner as that of a capillary tubes -h c w h c u c h c w Capillary Rise in Soil Surface Tension air/water surface Interface u S r Discontinuous Water -h c w Capillary Fringe h c Capillary Saturation
Effective Stresses Due to Capillarity G.S. σ T u σ dry -h c w dry sat w wsat - w