Soil with water 22/09/2009 Lecture: 20 Sub-topics Capillary rise - PowerPoint PPT Presentation

IIT Bombay Soil with water 22/09/2009 Lecture: 20 Sub-topics � Capillary rise (contd.) � Soil permeability Ground failure due to soil liquefaction in 1964 Niigata earthquake, Japan CE 303 20 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 20 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 20 Instructor: AJ

IIT Bombay Capillary menisci “hangs” onto particles � holds particles together This attractive force � Soil Suction intergranular contact stress σ ’ are introduced = − γ u h c c w ( ) σ = σ − − ' u c σ = σ + ' u c effective stress is increased by u c CE 303 20 Instructor: AJ

IIT Bombay σ ’ ↑ ⇒ shear strength ↑ Apparent or true cohesion?? – a point to note! Examples of soil capillarity: increase in effective stress and apparent cohesion sand beach CE 303 20 Instructor: AJ

IIT Bombay unsupported excavations in fine sands and silts Capillary moisture allow unsupported excavations CE 303 20 Instructor: AJ

IIT Bombay Bulking � capillary menisci surrounding soil grains produces “apparent cohesion” which holds sand particles together in cluster Large voids (honey-combs Moist sand Bonding due to apparent cohesion Capillary siphoning � water flow over crest of an impermeable core in dam even if the water table is lower than the crest Capillary menisci are easily destroyed by saturation due to rainfall or by evaporation CE 303 20 Instructor: AJ

IIT Bombay Soil permeability Flow through soils is mostly laminar Permeability describes quantitatively the ease with which water flows through the soil CE 303 20 Instructor: AJ

IIT Bombay Soil permeability Darcy’s Law flow is same at 1-Dimensional and 2-Dimensional flow cross-section perpendicular to flow direction standpipes Δ h water h 2 reservoirs X-sectional (constant 2 h 1 area A water levels) h 0 d n a S 1 L Datum CE 303 20 Instructor: AJ

IIT Bombay standpipes Total head (or total potential) Δ h = pressure head + elevation h 2 head + velocity head 2 h 1 h 0 d n a S 1 L Datum Potential difference that cause flow = Total head 1 – Total head 2 ( ) = − + Potential difference h h h 1 2 0 Note: Potential difference is also = Δ h (difference between the two water levels) ∴ to determine total head difference between 2 points, one needs to insert standpipes at the points and note difference in water levels in standpipes CE 303 20 Instructor: AJ

IIT Bombay Darcy (1856) varied the variables Δ h, L and A, and established Δ Δ h h α = q A or q k A L L q = flow (units of volume/time) k = constant; defined as coefficient of permeability Δ q = If is the hydraulic gradient, i , then h kiA L q = = The above can also be written as ki or v ki A v = superficial velocity of flow (because actual flow is through pores and not through the entire X-sectional area) We redefine permeability? …… as “superficial velocity” of flow under unit hydraulic gradient CE 303 20 Instructor: AJ

IIT Bombay True velocity of flow through voids is called seepage velocity v s = = q vA v s A A v = area of voids v A = total cross-sectional area v A V = ≈ = v v n v A V s = or v nv s n = porosity Since n < 1 ⇒ v < v s In engineering practice, v is used instead of v s Darcy’s law originally developed for clean filter sands Although some investigations indicate that k could be nonlinear at low gradients in some clays, Darcy’s law is still universally accepted to be valid for most geotechnical problems CE 303 20 Instructor: AJ

IIT Bombay Measurement of permeability k determined in 3 ways – laboratory tests field tests empirical approach In laboratory, a device called permeameter is used and either constant head test or falling head test conducted In field, pumping tests are usually conducted, although it would be possible in principle to utilise either constant- or falling-head test CE 303 20 Instructor: AJ

IIT Bombay Constant head test Falling head test at t = t 1 dh h h 1 L soil at t = t 2 h 2 Q Q A soil L a Volume of water Q flowing out of soil A collected in time t = • Water flows through sample from q kiA graduated standpipe q QL = = or k iA hAt • Time taken for water to drop from fixed height is recorded Q = total discharge volume in time t CE 303 20 Instructor: AJ