IIT Bombay Principle of 10/09/2009 Lecture: 19 Effective stress Sub-topics � Effective and total stress � Phreatic and capillary water Ground failure due to soil liquefaction in 1964 Niigata earthquake, Japan CE 303 19 Instructor: AJ
IIT Bombay Physical interaction between soil particles and pore fluid soil γ sat z σ = γ Total vertical stress at depth z in soil mass z sat = γ u z Pore water pressure w Inter-granular or effective stress σ ’ σ = σ − ' u CE 303 19 Instructor: AJ
IIT Bombay Pore water pressure Is called neutral stress WHY? � Liquid has only normal stress which acts equally in all directions; it has no shear component σ and σ ’ have normal and shear components � σ and u can be measured � can also be estimated from � density and thickness of soil layers and location of GWT Effective stress cannot be measured can only be calculated by subtracting pore water pressure from total stress CE 303 19 Instructor: AJ
IIT Bombay Total stress and pore pressure measuring instruments CE 303 19 Instructor: AJ
IIT Bombay Effective stress Mechanical behaviour of soil mass is linked with σ ’ and not σ or u σ ’ ↑ ? σ & u ↑ but d σ ’ = 0 ? σ ’ is not the same as grain-to-grain contact stress ! Two soil particles in contact over area A c Total/ gross area in plan = A PWP acts over area = A - A c ( ) u = + − ' P P A A c ( ) u − ⎛ − ⎞ ' A P P A A σ = σ + = + ' ⎜ ⎟ c Or c 1 u ⎝ ⎠ A A A A In granular materials � contact area approach point area in other ' + words A c � zero σ = σ u CE 303 19 Instructor: AJ
IIT Bombay Effective stress We have assumed that the plane passing through the two soil particles is horizontal (is this true? Or are we making an implicit assumption?) True horizontal surface through soil at any depth would cut through many particles wavy plane through points of inter-particle contact Horizontal plane is taken : 1. For the sake of simplicity 2. Wavy plane is really indistinguishable from true horizontal plane because of small size of particles on mass scale CE 303 19 Instructor: AJ
IIT Bombay Effective stress principle can be applied to fine-grained soils Mineral crystals are not in physical contact tightly bound film of water Interparticle force-fields which contribute to effective stress are difficult to interpret Experimental evidence (Skempton 1960) has shown that principle of effective stress holds for ALL saturated soils NOTE: This principle does not hold for partially saturated soils or saturated rocks and concrete CE 303 19 Instructor: AJ
IIT Bombay Phreatic & capillarity water Ground water exists in 2 forms (i) Phreatic (pronounced free-attic) or gravitational water (ii) Capillary water Gravitational water � Completely saturates voids � Can be removed from soils by drainage � Upper surface is called ground water table or phreatic surface � Pore water pressure balances atmospheric pressure at GWT CE 303 19 Instructor: AJ
IIT Bombay PWP at phreatic surface = zero ( “gauge” pressure? Absolute pressure? ) CE 303 19 Instructor: AJ
IIT Bombay Capillary water Soils can be saturated up to some height above the phreatic surface and partially saturated up to some more height Recall: Surface tension – tendency of fluid to reduce its exposed surface to the smallest possible area Capillarity � arises from adhesion and cohesion � occurs at interface of water, mineral-grains, and air CE 303 19 Instructor: AJ
IIT Bombay Capillarity illustrated by small diameter glass tubes Molecular bonding Adhesion forces = tend to reduce cause water to rise surface area of water Tube represent voids between soil grains Meniscus formed is concave upward in water CE 303 19 Instructor: AJ
IIT Bombay T = surface tension (force/ unit length) P atm α T acts along the perimeter at angle α to wall of T tube h c P atm W Force ↓ = height of water column Force ↑ = vertical component of T around the d circumference π 2 d γ = π α h dT cos Clean glass tube / pure water, α = 0 c w 4 4 T = h γ c T is physical property of water and is d w about 73 mN/m; γ w = 9.81kN/m 3 0 . 03 h c = meters if d is in mm d CE 303 19 Instructor: AJ
IIT Bombay Stress distribution in water: above & below phreatic surface Below the surface: pressure is hydrostatic Above the surface: pressure is negative or less than zero gauge pressure Tension -z = − γ u h c c w 4 T = − h c γ w - d h c h c W Pressure, u d hydrostatic z γ w + +z Compression CE 303 19 Instructor: AJ
IIT Bombay Capillary tube analogy helps explain capillary phenomenon observed in real soils CE 303 19 Instructor: AJ
IIT Bombay Capillarity in soils Regime of subsurface water divided into 4 zones Above the phreatic surface • lower part is fully saturated • water fills only narrowest voids in upper part 4 T = h γ c d w h c = maximum capillary rise Soil is completely saturated only up to h cs The zone between h cs and h c remains partially saturated CE 303 19 Instructor: AJ
IIT Bombay Soil Capillary rise (m) Coarse sand 0.03 to 0.15 Medium sand 0.12 to 1.1 Fine sand 0.3 to 3.5 Silt 1.5 to 12 Clay > 10 Capillary rise in different soils CE 303 19 Instructor: AJ
IIT Bombay Empirical method Terzaghi and Peck (1967) ( ) C = h in cm c eD 10 where D 10 = effective grain size in cm C = empirical constant (between 0.1 and 0.5 cm 2 ) Alternate theoretical height of capillary rise : replace d by 20% of effective grain size D 10 0 . 03 hc = meters if d is in mm d CE 303 19 Instructor: AJ
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