IIT Bombay Soil with water 25/09/2009 Lecture: 23 Sub-topics � Seepage forces & � Quick sand conditions Ground failure due to soil liquefaction in 1964 Niigata earthquake, Japan CE 303 23 Instructor: AJ
IIT Bombay Seepage forces Water flow exerts drag force called “seepage force” on soil grains Force act in direction of flow � cause change in PWP and σ ’ Flow conditions : inflow overflow overflow (3) outflow inflow valve (1) closed (2) No flow condition Downward flow Upward flow [hydrostatic case] Constant water level maintained in the tank CE 303 23 Instructor: AJ
IIT Bombay No flow condition Water level at top, bottom and at any intermediate position of soil layer is the same (why?) � no VERTICAL flow takes place when water level in the standpipe is the same at all depths Variation of σ , u, and σ ’ for “no flow” condition σ σ ’ u H 1 H 1 γ w z (H 1 +z) γ w z( γ sat - γ w ) H H 1 γ w + z γ sat (H 1 +H) γ w H( γ sat - γ w ) H 1 γ w + H γ sat valve closed CE 303 23 Instructor: AJ
IIT Bombay Downward flow head loss h = = Flow occurs under hydraulic gradient � i length of flow H inflow Total head difference between A and B = h H 1 A h H ∴ h = (Total head at A – Total head at B) or h = (H + H 1 ) – Total head at B B or Total head at B = (H + H 1 ) – h outflow Elevation head at B = 0 (B is taken as datum); � ∴ pressure head at B = (H + H 1 ) – h CE 303 23 Instructor: AJ
IIT Bombay Stress distribution for downward flow condition inflow σ σ ’ u H 1 A h z ? [ ] w = + − γ u H 1 z iz H z B outflow At A: At B: σ = H γ σ = γ + γ H H Total stress A 1 w B 1 w sat [ ] w = γ ( ) = + − γ Pore water pressure u H u H H h A 1 w B 1 Recall PWP = Pressure head x unit weight of water [ ] w ( ) ( ) ( ) σ = σ − = σ = γ + γ − + − γ ' ' Effective stress u A 0 H H H H h A B 1 w sat 1 ⇒ σ = γ + γ ' ' H h B w CE 303 23 Instructor: AJ
IIT Bombay Compare σ ’ B for no flow and downward flow conditions inflow H 1 A A h H seepage B pressure act in B direction of flow outflow valve closed No flow Downward flow σ = H γ σ = γ + γ ' ' ' ' H h B B w Increase in σ ’ at any point iz γ (= seepage pressure in general) at depth z below surface is w CE 303 23 Instructor: AJ
IIT Bombay Effective stress is increased by h γ γ = γ h or H iH w w w H γ γ h or iH is referred to as seepage pressure w w CE 303 23 Instructor: AJ
IIT Bombay Upward flow head loss h = = Flow occurs under hydraulic gradient � i length of flow H h overflow overflow Total head difference between A and B = h H 1 A H ∴ h = (Total head at B – Total head at A) or h = Total head at B - (H + H 1 ) B or Total head at B = (H + H 1 ) + h inflow Elevation head at B = 0 (B is taken as datum); � ∴ pressure head at B = (H + H 1 ) + h CE 303 23 Instructor: AJ
IIT Bombay Stress distribution for upward flow condition h σ σ ’ overflow overflow u H 1 A ? [ ] w z = + γ + u H 1 z iz z H B inflow At A: At B: σ = H γ σ = γ + γ Total stress H H A 1 w B 1 w sat [ ] w ( ) = γ = + + γ Pore water pressure u H u H H h A 1 w B 1 ( ) [ ] w ( ) ( ) σ A = σ − = σ = γ + γ − + + γ ' ' Effective stress u A 0 H H H H h A B 1 w sat 1 ⇒ σ = γ − γ ⇒ σ = γ − γ ' ' ' ' H h H iH B w B w CE 303 23 Instructor: AJ
IIT Bombay Stress distribution for upward flow condition Effective stress is decreased by iH γ w CE 303 23 Instructor: AJ
IIT Bombay Quick sand condition http://picasaweb.google.com/melaniejbonk During upward flow, seepage pressure can sometimes be very high h overflow overflow � can result in effective stress = 0 H 1 σ = γ − γ A ' ' H iH B w H γ = γ ' H iH σ ’ B = 0 if w γ ' = or when i B γ w inflow This hydraulic gradient is called critical hydraulic gradient i cr CE 303 23 Instructor: AJ
IIT Bombay Quick sand condition Soil (mainly sand) loses all shear strength and cannot support load Soil becomes “quick” or “alive” and boiling occurs Popular name for this phenomenon is quicksand Quicksand is not a type of sand but only a hydraulic condition As long as i < i cr , only part of head loss is used in friction Contrary to popular belief, it is not possible to drown in quicksand !! CE 303 23 Instructor: AJ
IIT Bombay More on critical hydraulic gradient….. ( ) − γ G 1 γ = ' Recall : buoyant unit weight s w + 1 e ( ) − G 1 = ∴ Critical hydraulic gradient � s i + cr 1 e Typical values of i cr (e.g. assume G s = 2.65) Approximate relative Void ratio i cr density 0.5 Dense 1.12 0.75 Medium 0.96 1.0 Loose 0.84 i cr ~ 1 is a relatively easy number to remember CE 303 23 Instructor: AJ
IIT Bombay Quick conditions for clays? YES – In very sensitive clays quick conditions can occur Other e.g: 1. Excavations below water table � excavate first and then pump out water (NOT GOOD) or first pump out water and then excavation (BETTER) clay γ sat z y sand 1. Confined aquifer in an artesian pressure condition CE 303 23 Instructor: AJ
IIT Bombay Soil liquefaction CE 303 23 Instructor: AJ
IIT Bombay Soil liquefaction Loose saturated sand subjected to large loads within short duration (e.g. earthquakes, pile driving, and blasting) Loose sand densifies; this tends to squeeze water out of the pores Under static loading, sand has sufficient permeability so water can escape and induced PWP dissipates For loads induced in short duration, water does not have time to escape and PWP increase σ ’ � tend to zero and the soil loses all strength CE 303 23 Instructor: AJ
IIT Bombay Soil liquefaction CE 303 23 Instructor: AJ
IIT Bombay Image courtesy NASA/GSFC/LaRC/JPL CE 303 23 Instructor: AJ
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