1. Chapter 2 Seepage in Soil “In engineering practice, difficulties with soils are almost exclusively due not to the soils themselves, but to the water contained in their voids. On a planet without any water there would be no need for soil mechanics”. Karl Terzaghi

3. Definitions Groundwater table (GWT) or Phreatic surface) – top of groundwater flow Phreatic zone – subsurface below GWT Vadose zone – subsurface above GWT Aquifer - a geologic formation that is under GWT and is capable of yielding water as a water supply. – Confined Aquifer - soil or rock below the land surface that is saturated with water. – Unconfined Aquifer - an aquifer whose upper water surface (water table) is at atmospheric pressure. Aquaclude - geologic formation that can not transmit water rapidly. Artesian water - groundwater that is under pressure.

5. Total head: ht = hv + he + hpht = hv + he + hp 1 1. h v ~ 0 in groundwater flow because seepage flow is slow 2. h e depends on the location of datum z 3. h p depends on water pressure in soil pores 4. Seepage flow in soil is always from a higher total head to a lower total head.

6. Relation between the Pressure head (h p, in meter) ) & Pore water pressure (u, in kPa) : u  h p  w (unit :kPa) (unit :m) hp hp  u wu w

7. o Total Head at Point “P” h  h p  z Ground surface GWT P h p is measured vertically down from GWT or piezometer hphp hphp z z z is measured vertically up from the datum o Datum

8. Example (Coduto p. 265) Compute the pore water pressure at points A and B el.(m) 90 89 87 83 80

9. Groundwater Flow in Soil The total head difference (  h) is the driving force of groundwater flow in soil. 1m X X P 1m P Impermeable stratum No GW flow Impermeable stratum GW flow from X to P

10. Important Reminder The absolute value of the total head is not important because it depends on the selection of datum; To solve groundwater flow problems, we select a datum and use it as the reference for the total heads at all points of interests; Groundwater always flows from a higher total head to a lower total head, regardless the location of datum.

11. Darcy’s Law  h Soil Sample A LL Darcy (1856) found that the flow rate in a porous medium (e.g. soil) is 1. proportional to the total head difference  h 2. proportional to the cross-sectional area A perpendicular to the flow direction 3. inversely proportional to the length of the soil sample  L

12. Darcy’s s Law Q = k h i A Q (m 3 /s) = flow rate k h (m/s) = coefficient of permeability or hydraulic conductivity. i = hydraulic gradient [ - ] A = cross-sectional area perpendicular to direction of flow (m 2 )

13. Alternatively, Darcy’s Law may be expressed in terms of Flow Velocity q=ki(unit: m/s) whereihydraulic gradient [-] q = Q/ADarcy velocity (m/s)

14. Hydraulic Gradient, i dh dx i  i    The negative sign of hydraulic gradient – to ensure the flow direction is towards the positive hydraulic gradient  We often use i =  h/  L in 1D calculation – but remember to indicate the direction of flow

15. Darcy’s Law is valid when  The flow is laminar (no turbulence) – this is valid for flow in all soils;  Soil is nearly saturated – S ~ 100%;  The flow is steady (time independent) – known as the steady state seepage flow

16. Hydraulic Conductivity k h The most reliable way of determining k h is from experiments (lab or in-situ) Empirical equations have been developed under specific conditions Everything else being equal, k h is the highest when a soil is saturated

18. Typical k h Values 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 -8 10 -9 10 -10 10 -11 10 -12 GravelsSandsSiltsHomogeneous Clays Fissured & Weathered Clays Unit: meter/second, m/s X 100, cm/s

19. Constant head device – for k h measurement of granular soils

20. Falling head device for k h measurement of fine grained soils

21. Empirical Estimate of k h Kozeny-Carman Equation (Read pp. 280 - 282) For sandy soils only kh kh   e 3  1  e k h is a function of – Grain size – Shape factor – Void ratio – Unit weight of fluid – Viscosity of fluid

22. Seepage Velocity  In Darcy’s law, q = i k, where q is the “apparent” flow velocity. The “true” flow velocity is the velocity of water molecules flowing through a tortuous path in soil – seepage velocity v.  The relationship between the seepage velocity (v) and Darcy velocity (q) is qnqn v   Therefore the seepage velocity is always higher then Darcy’s velocity

23. Computing 1 1--D Groundwater Flow Flow Rate Q = k i A(unit: m 3 /s) q=ki(unit: m/s, or cm/s) Flow Velocity Steps: 1. 2 2. 3. Calculate the hydraulic gradient, i =  h/  L ; Measure the hydraulic conductivity, k h ; Determine the area perpendicular to the groundwater flow, A.

24. Flow through Anisotropic Soils

25. ( k( k  kvkv k H  kiHiHikiHiHi ) HHiHHi iiii i kiHHikiHHi

26.  Example: Calculate k h and k v for the layered soil k = k 1 = 10 -6 m/s k = k 2 = 10 -10 m/s d1= 1 md2= 1 md1= 1 md2= 1 m Layer 1 Aquifer Layer 2 Aquitar kHkH  k 1 d 1  k 2 d 2 d 1  d 2 k Vk V d 1 + d 2 d 1 d 2 k 1 k 2 

27. Lessons learnt When subsurface soil is stratified Horizontal seepage is controlled by aquifer; Vertical seepage controlled by aquitar

28. Seepage Pressure When water flows through a soil, the viscous drag tends to move soil grains and produces a force, known as a seepage pressure. Upward flow Liquefaction : If an upward flowing water passing through a sand, and the seepage pressure equals to the submerged weight of the sand, the inter- granular pressure becomes zero. The sand then is in a "quick" condition and is incapable to support a load on its surface. Erosion: the upward flowing water tends to remove some of the fines, often known as "piping”. Bottom heave (blow out): If the upward flowing water passing through a clay, and the seepage pressure equals to the submerged weight of the clay, the clay will heave and crack. Downward flow Downward flowing water will generate additional pressure on soil, which is equivalent to additional loading on soil, generating settlement.

29. Soil liquefaction/piping Soil suddenly suffer a transition from a solid state to a liquefied state Occur in loose to moderately saturated granular soils during cyclic loading

30. Blowout / Bottom Heave of Clays in Excavation Clay Sand Aquifer Piezometer

31. Conditions for Liquefaction, Piping and Blowout u 2 (z=z 2, h=h 2, u=u 2 ) Elevation (z=z 1, h=h 1,u=u 1 ) u 1 Area =A Plan A soil element experiencing upward flow of water

32. Uplift Force  A(u 1  u 2 ) Force due to Soil weight  A  sat (z 2  z 1 ) u2u2 Pore water pressure u2 w(h2 z2)u1 w(h 1z1)u1u2 w(h2 z2)u1 w(h 1z1)u1

33. Uplift Force Force due to weight  A(u 1  u 2 ) A  sat (z 2  z 1 ) For piping to occur,uplift force > soil weight A(u 2  u 1 )  A  sat (z 2  z 1 )  w (h 1  h 2 )  w (z 1  z 2 )  sat (z 2  z 1 )  w (h 1  h 2 )   sat (z 2  z 1 )  w (z 2  z 1 )  ( h 1  h 2 ) (z 2  z 1 )  sat  w  w

34. u 2 (z=z 2, h=h 2 ) ( h 1  h 2 ) (z 2  z 1 )   sat  w  w (z=z 1, h=h 1 ) u1u1 But= i= Hydraulic gradient ( h 1  h 2 ) (z 2  z 1 ) so the condition for piping may be written as i > i c

35. Critical Hydraulic Gradient for Piping/Blowout  ic ic  G s 1 1  e  sat  w  w 1. When the upward hydraulic gradient in soil i > i c, liquefaction/piping/blowout will occur in soil. 2. Critical hydraulic gradient is a soil property and is not related to the hydro-geologic condition of the site. 3. FS against liquefaction/piping/blowout: 4. FS = 2 is required in design i cii ci F.S. 

36. Example: Basal stability of landfill Waste bulk unit weight = 7 kN/m 3 50 m x 50 m z ?m 10 m B 11m CL, bulk unit weight = 20 kN/m 3 A Piezometer SP 1. 2. Calculate the maximum excavation can be made for this landfill; If the excavation has to be 6.5 m deep to meet the design capacity, what would you do?

37. Erosion problems in earth works Seepage pressure below or within dams has led to several catastrophic failures. It may be prevented if we cover the surface, where the seepage emerges, with coarser materials that help the escape of the water but prevent the erosion of the fines. If the seepage pressure has a rather great upward component, it may be necessary to add weight to the top of the filter to counterbalance the upward forces.

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39. Impact Discharge of a mixture of 600-700 thousand cubic metres of red mud and water. Nine people were killed, and approx. 120 people were injured. The spilling red mud flooded 800 hectares of surrounding areas. The main component contained in the red mud is Fe2O3 (iron oxide - which gives it its characteristic red colour) at 40-45%. Other components are Al2O3, SiO2, CaO, TiO2, and Na2O, according to MAL. The red mud contains: – 110 mg/kg for arsenic, – 1.3 mg/kg for mercury, – 660 mg/kg for chromium (of which 0.46 mg/kg for the highly toxic hexavalent chromium Cr-VI), – 40 mg/kg for antimony, – 270 mg/kg for nickel, – 7 mg/kg for cadmium. 39

40. Ajka Tailings Dam Failure (2010- -10-4) W E West North 40

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44. Summary y 1. The total head governs the seepage flow in soil, which includes – elevation head – pressure head – velocity head, which is negligible in soils 2. The seepage flow is always from a higher total head to a lower total head; 3. Darcy’s law states that the seepage flow depends on – Hydraulic conductivity of soil and – Hydraulic gradient of the site 4. The true seepage velocity in soil is higher than Darcy’s s velocity along a torturous path; 5. The Seepage will generate pore water pressure in soil – Upward pressure – piping and blow out – Downward pressure – settlement 6. The seepage flow in earth works can be controlled by –––– Selection of soil Compaction