Soil Mechanics I 3 Water in Soils. 1. Capillarity, swelling 2. Seepage 3. Measurement of hydraulic conductivity 4. Effective stress in the ground

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1 Soil Mechanics I 3 Water in Soils 1. Capillarity, swelling 2. Seepage 3. Measurement of hydraulic conductivity 4. Effective stress in the ground 1

2 Influence of Water - Basics WATER IN SOIL - affects soil behaviour (e.g., consistency, consistency limits) Adsorbed water Mechanisms of water adsorption to clay surfaces: hydrogen bonds, ion hydration, osmosis, dipole attraction... The effects neglected in the basic SM 'Free' water Effect of gravity - effective stress, capillarity, seepage 2

3 Influence of Water - Basics WATER IN SOILS [2] 3

4 Influence of Water - Basics Shrinking w > ws saturated soil (?) Suppose the Terzaghi principle of effective stresses valid and u < 0: for hc 50 m u kpa σ' 500 kpa (+ σ) Swelling Due to mineralogy (smectites) partial saturation unloading Disintegration of cohesive soil on submerging in water elimination of capillary forces elimination of cementation Capillarity 4

5 Influence of Water - Basics GT Practice the role of water Hydrostatic pressure basis for computing effective stresses (only with no seepage, i.e. no hydraulic gradients) Steady state seepage the pore pressure is generally different from the hydrostatic pressure the pressure heads does not have to correspond to phreatic water table Laplace equation a flow net Consolidation dissipation of excess pore pressures 5

6 Steady Flow Darcy's Law Steady flow H. DARCY (1856) q Ak i q flow quantity (volume per time unit) i hydraulic gradient i - Δh/Δx vki k hydraulic conductivity (coefficient of permeability; coefficient of filtration) v seepage velocity Real velocity vreal q / (n A) v / n 6

7 Steady Flow Darcy's Law Permeability Κ: a property of the porous medium, independent of the permeating fluid Κkμ/γ [m2] Κ permeability k hydraulic conductivity, i.e. coefficient of Darcy's law μ dynamic viscosity [N s m-2] (μ kinematic viscosity ρ) γ unit weight of permeating fluid 7

8 Steady Flow Darcy's Law Re v def ρw / μ Initial gradient v seepage velocity μ dynamic viscosity [N s m-2] Change from laminar to turbulent flow at critical velocity vcr Re cr μ /(ρw def) 8

Measurement of Hydraulic Conductivity Hydraulic conductivity ( filtration coefficient coefficient of permeability) Constant Head Permeameter Q A v t; Q volume of water; v discharge velocity; t time

9 Measurement of Hydraulic Conductivity Hydraulic conductivity ( filtration coefficient coefficient of permeability) Constant Head Permeameter Q A v t; Q volume of water; v discharge velocity; t time vkikh/l k Q L / (h A t) At low permeability (h. conductivity: k < 10-6 ms-1), the device cannot be used insufficient readability / accuracy the set-up needs to be refined: closed system for discharge water, or triaxial apparatus / flexible wall permeameter (+avoiding preferential flow at the rigid wall) Another alternative Falling Head Permeameter (accuracy not good though) 9

10 Measurement of Hydraulic Conductivity Hydraulic conductivity ( filtration coefficient coefficient of permeability) Falling Head Permeameter q in - a dh/dt q out Ak i q in q out - a dh/dt Ak h/l - a dh / h k A / L dt - a (ln h2 ln h1) k A (t2-t1) / L a (ln h1 ln h2) k A (t2-t1) / L k a L ln(h1/h2) / (A Δt) 10

11 Measurement of Hydraulic Conductivity Lab Class 11

12 Measurement of Hydraulic Conductivity Hydraulic conductivity ( filtration coefficient permeability coefficient) In situ For example [ k q / (2π D H) ln(r / r) ] Indirect determination For example FOR SANDS: Hazen k [ms-1] 0,01D102 [mm] 12

13 Measurement of Hydraulic Conductivity Typical values Gravel 10-1 to 10-3 ms-1 Sand 10-2 to 10-4 ms-1 Fine Sand 10-5 ms-1 Silt 10-6 ms-1 Sandy Loam 10-6 to 10-8 ms-1 Clay <10-8 ms-1 13

14 Seepage Equation for Seepage isotropy: kxkykz Δh 0 δ2h / δx2 + δ2h / δy2 + δ2h / δz2 0 Hydraulic head does not have to correspond with the phreatic surface seepage...the actual height in the piezometer definition of equipotential lines 14

15 Seepage A flow net in 2D saturated soil, GWT at the surface, steady percolation 15

16 Seepage A flow net in 2D (long dam / embankment) Hydraulic head does not have to correspond with the phreatic surface seepage...the actual height in the piezometer definition of equipotential lines 16

17 Seepage Influence of seeping water on soil grains: Seepage Forces - DRAG vki Loss of hydraulic head due to drag effect of water Δp γw Δh Δ S Δp area γw Δh Δy Δz γw Δh Δy Δz Δx/Δx γw i (Δx Δy Δz) γw i ΔV Force acting on the soil skeleton: S γw i V Force acting on the soil skeleton in the unit volume: p γw i 17

18 Seepage Influence of seeping water on soil grains: Seepage Forces - DRAG Bernoulli equation: γw (z + u/γw + v2/(2g) + hs) const v2/(2g) can be neglected (v small) Loss of energy between two cross section (distance s): ΔE γw Δhs (z2 +u2/γw - (z1 +u1/γw)) ΔE / Δs γw Δhs / Δs γw i The loss of energy: p γw i 18

19 Seepage Flow net [1]) Boundary conditions: (constant) water levels equipotentials (GA; CF) impermeable boundaries flow lines (AB; BC; DE; detto axis of symmetry EF) Upward seepage possibility of hydraulic failure - boiling sand ; piping 19

20 Seepage hcr... critical height, i.e. height at liquefaction neglecting friction on sides; cross section area A thrust water pressure on A: u A hcr γw A equilibrium: hcr γw A A z γsat ( γsat γ) hcr z γ / γw icr (hcr z) / z (z γ / γw z) / z γ / γw 1 (γ - γw)/γw icr (γ γw) / γw 20

21 Seepage What is the necessary embedment depth t of the sheet pile wall? icr (γ γw) / γw icr 1 i (H + h) / (h + t + t) < 1 icr H<2t t >½H 21

22 Capillarity Capillary height hc Downward Force: W ρwg V ρwg hc π d2 / 4 Upward Force: π d T cosα surface tension of water T kNm-1 Equilibrium: ρw g hc π d2 / 4 π d T cosα hc 4 T cosα / (ρw g d) clean water vs glass α 0 hc 4 T / (ρw g d) 4 T / ( γw d) hc [m] / (d [m]) [m] For example: d 1μm hc 30m 22

23 Capillarity Capillary height hc depends on PORE SIZE Theoretical values for soils (α 0 a capillary tube of constant diameter d) silt d 1mm hc 30 mm fine silt d 1μm hc 30 m clay d 10nm hc 3 km Realistic values for soils sand hc 0,03 0,1 m loamy sand hc 0,5 2 m loam (silt) hc 2 5 ( 10) m clay hc tens of metres 23

24 Capillarity In Capillary Fringe soil is saturated Principle of effective stress is valid, u < 0 hc 50 m u kpa σ' σ kpa Unsaturated Zone Three Phase Medium Terzaghi's principle QUESTIONABLE (the expression for pore pressure not clear to date?) ua- uw T (1/rm-1/r) capillary suction r is the radius of meniscus Bishop: u χ uw+ (1 - χ) ua σ' σ (χ uw+ (1 - χ) ua) σ' σ ua + χ (ua - uw) χ function of S, way of loading... Very approximate assumption: χ Sr 24

1 should be) then pore pressure u S uw capillary suction s - uw Procedure: M.C.

25 Capillarity Lab Class Capillary water in sand unconfined compression of wet sand Assumed: Bishop's Effective Stress σ' σ (χ uw+(1-χ) ua) Pore Pressure u χ uw+ (1 - χ) ua for χ S u S uw+ (1 - S) ua If the air phase continuous (at w 0.1 should be) then pore pressure u S uw capillary suction s - uw Procedure: M.C. for total stress; Failure envelope; Determination of capillary cohesion; M.C. for effective stress. From its shift the pore pressure and suction in the sand castle (assuming the Bishop's stress and χ S) 25

26 Capillarity Lab Class Sand without capillary water (dry or saturated) Angle of repose: continuous slope failure ideal plasticity critical state τmax σ' tg φcr' Equilibrium: T W sin α τmax 1 W cos α tg φcr tg α tg φcr α φcr 26

27 Effective vertical stress in the ground σv (hi γi) u hwγw (z - zw) γw σv' σv u (hi γi) hwγw detto for increments 27

28 Effective vertical stress in the ground Δσv' Δσv Δu Δσv >0 Δu 0 (drained event) Δσv' Δσv >0 increase in effective stress deformation settlement under loaded area 28

29 Effective vertical stress in the ground Δσv' Δσv Δu Lowering of GWT increase of effective stress: before: 1u hw γw 1 σv h γsat after: 1 σv h γsat 2 u(hw-δhw) γw (soil remains saturated - capillarity) Δu 2u 1u - Δhw γw Δσv 0 Δσv' - Δu > 0 increase of effective stress deformation settlement on lowering GWT 29

30 Effective vertical stress in the ground increase in effective stress 30

31 Effective vertical stress in the ground σ u σ' kpa kpa kpa σ u σ' , kpa kpa kpa σ u σ' kpa kpa kpa 31

32 Literature for SM1 Atkinson, J.H. (2007) The mechanics of soils and foundations. 2nd ed. Taylor & Francis. Further reading: Wood, D.M. (1990) Soil behaviour and critical state soil mechanics. Cambridge Univ.Press. Mitchell, J.K. and Soga, K (2005) Fundamentals of soil behaviour. J Wiley. Atkinson, J.H: and Bransby, P.L. (1978) The mechanics of soils. McGraw-Hill, ISBN Bolton, M. (1979) A guide to soil mechanics. Macmillan Press, ISBN Craig, R.F. (2004) Soil mechanics. Spon Press. Holtz, R.D. and Kovacs, E.D. (1981) An introduction to geotechnical engineering, Prentice-Hall, ISBN Feda, J. (1982) Mechanics of particulate materials, Academia-Elsevier.) 32

33 References used figures etc. [1] Atkinson, J.H. (2007) The mechanics of soils and foundations. 2nd ed. Taylor & Francis. [2] Santamarina, J (2003) in Mitchel, J.K. and Soga, K (2005) Fundamentals of soil behaviour 33

Instructor : Dr. Jehad Hamad. Chapter (7)

Instructor : Dr. Jehad Hamad. Chapter (7) Instructor : Dr. Jehad Hamad Chapter (7) 2017-2016 Soil Properties Physical Properties Mechanical Properties Gradation and Structure Compressibility Soil-Water Relationships Shear Strength Bearing Capacity