Basics of groundwater hydrology in geotechnical engineering: Permeability - Part A

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Basics of permeability and groundwater flow

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Basics of groundwater hydrology in geotechnical engineering: Permeability - Part A

  1. 1. Basics of groundwater hydrology in geotechnical engineering Part A Prepared by Dr O. Hamza o_hamza at hotmail dot com Lecture reference: OH GA03 A OH_GA03_A Permeability – Part A Dr O.Hamza
  2. 2. Content • Soil as porous media • Hydraulic head and gradient • Darcy's law and permeability • Laboratory d t L b t determination of coefficient of permeability i ti f ffi i t f bilit • Summary • Quizzes and example problems Permeability – Part A Dr O.Hamza
  3. 3. Soil as porous media • Nature of soil • Seepage velocity Permeability – Part A Dr O.Hamza
  4. 4. Soil as a porous media Nature of soil So soil can be considered as a porous media media. (1) Solid (mineral particles) (2) Gas (air, co2), (3) Liquid (usually water, but also possibly oil, chemical solutions) Soil is a natural particulate earth material which has three intermixed phases: Permeability – Part A Dr O.Hamza
  5. 5. Soil as a porous media Nature of soil A material is said to be permeable if it contains continues voids. Can any porous material be permeable? Permeability – Part A Dr O.Hamza
  6. 6. Soil as a porous media Nature of soil Void ratio, e = Vv / Vs Degree of saturation, Sr =Vw / Vv Water content, w = Mw/Ms Porosity, n = Vv/V Permeability – Part A Dr O.Hamza
  7. 7. Soil as a porous media Seepage velocity q A The volume flow rate q is calculated as the product of flow velocity v and total cross sectional area A : q = v. A B Assume a column of soil and water flowing through. q Permeability – Part A Dr O.Hamza
  8. 8. Soil as a porous media Seepage velocity A Flow line The ratio of volume flow rate q to the average area of voids Av on a cross section normal to the macroscopic direction of flow is called the seepage velocity vs q vs = Av B At the particulate level the water follows a tortuous path through the pores pores. Permeability – Part A Dr O.Hamza
  9. 9. Soil as a porous media Seepage velocity A Flow line In general, the velocity of water through soil has been found to be relatively small (e.g. less than 0.61 m/min). B Permeability – Part A Dr O.Hamza
  10. 10. Hydraulic head d hydraulic H d li h d and h d li gradient di t • Pressure elevation and total head Pressure, • Hydraulic gradient Permeability – Part A Dr O.Hamza
  11. 11. Hydraulic head and hydraulic gradient Pressure, Pressure Elevation and total head Pressure head The height of the water column is the pressure head (hw) u hw = γw Pore pressure at a given point (e.g. point A in the diagram) can be measured by the height of water in a standpipe located at that point. y g Pore pressures are often indicated in this way on diagrams. Permeability – Part A Dr O.Hamza
  12. 12. Hydraulic head and hydraulic gradient Pressure, Pressure Elevation and total head Elevation head The elevation head (hz) of a point is its height above the datum line. hw Total head The height above the datum of the water level in the standpipe is the total head (h). h = hz + hw To identify significant differences in pore pressure at different points, we need to eliminate the effect of the points' position A height datum is required from which points position. locations are measured. Permeability – Part A Dr O.Hamza
  13. 13. Hydraulic head and hydraulic gradient Pressure, Pressure Elevation and total head Total head, h = Elevation head, hz + Pressure head, hw + Velocity head, hv hw The total head h includes also velocity head hv; this head in soils is usually neglected. However, neglected However the velocity head must be considered when dealing with flow through pipe and open channels. Permeability – Part A Dr O.Hamza
  14. 14. Hydraulic head and hydraulic gradient Hydraulic gradient The hydraulic gradient is the rate of change Δh i= of total head along the direction of flow Δs Datum It is the difference in total head that are important. The direction of flow depends on these differences Flow of pore water in soils is driven from differences. positions of higher total head towards positions of lower total head. Permeability – Part A Dr O.Hamza
  15. 15. Hydraulic head and hydraulic gradient Hydraulic gradient Datum Example. In each diagram there are two points, a small distance Δs apart, hz1 and hz2 above datum. Permeability – Part A Dr O.Hamza
  16. 16. Hydraulic head and hydraulic gradient Hydraulic gradient Δh The hydraulic gradient i = Δs Datum Δh=0 thus i =0 No flow In the first diagram, the total heads are equal. The difference in pore pressure i entirely d t th difference i altitude of th t is ti l due to the diff in ltit d f the two points and th i t d the pore water has no tendency to flow Permeability – Part A Dr O.Hamza
  17. 17. Hydraulic head and hydraulic gradient Hydraulic gradient Δh The hydraulic gradient i = Δs Datum Δh 0 Δh=0 thus i =0 0 No flow Δh ≠ 0 thus i = (h2 - h1) / Δs ( flow In the second diagram, the total heads are different. The hydraulic gradient is i ≠ 0 and the pore water tends to flow. Permeability – Part A Dr O.Hamza
  18. 18. Darcy’s law and permeability • Darcy's law • Soil permeability • Temperature and p p permeability y • Stratified soil and permeability Permeability – Part A Dr O.Hamza
  19. 19. Darcy’s law and permeability Darcy’s law v ~ i or q ~ i In a saturated porous media, the flow velocity v or the rate of flow of water q (volume/time) through cross-sectional area A is found to be proportional to hydraulic gradient i ti l t h d li di t in 1856, a French hydraulic engineer named Henry Darcy published an equation for flow through a porous medium. Permeability – Part A Dr O.Hamza
  20. 20. Darcy’s law and permeability Darcy’s law q v = = k.i A where v is flow velocity k is coefficient of permeability with dimensions of velocity (length/time) Q Quantity of water q is flow rate = = ----------------------- t Time Higher hydraulic gradient i faster flow ? agree disagree Higher coefficient of permeability k faster flow ? agree disagree Permeability – Part A Dr O.Hamza
  21. 21. Darcy’s law and permeability Darcy’s law Higher hydraulic gradient i faster flow ? agree disagree Higher coefficient of permeability k faster flow ? agree disagree The coefficient of permeability of a soil is a measure of the water flow conductivity. Permeability – Part A Dr O.Hamza
  22. 22. Darcy’s law and permeability Soil permeability Gravel G l Coefficient of permeability k clay Coefficient of permeability may vary from as large as 1 m/s for clean gravels to a small value of the order of 10-10m/s for very fine soil such as clay-silt (BS 8004, 1986). Permeability – Part A Dr O.Hamza
  23. 23. Darcy’s law and permeability Temperature and permeability The values of k at 0°C and 10°C are 56% and 77% respectively of the value measured at 20°C. An alternative permeability K (dimensions: length²) is sometimes used as a more absolute coefficient depending only on the characteristics of the soil skeleton. (Ref. Geotechnical on the Web) The flow of water through confined spaces is controlled by its viscosity η and the viscosity is controlled by temperature. Permeability – Part A Dr O.Hamza
  24. 24. Darcy’s law and permeability Stratified soil and permeability Representative graphic lithology log and core photos of an insitu In nature, soil is stratified
  25. 25. Darcy’s law and permeability Stratified soil and permeability Consider a stratified soil having horizontal layers of thickness t1, t2, t3, etc. with coefficients of permeability k1, k2 k3, etc y For a single layer, Darcy's law To help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content. indicates: Δh i q i = Aki = Ak i ti How can we apply the concept of hydraulic gradient and coefficient of permeability? Permeability – Part A Dr O.Hamza
  26. 26. Darcy’s law and permeability Stratified soil and permeability Vertical flow V ti l fl Which condition of these two is valid for vertical flow? (1) total flow rate q = q1= q2= q3.. head drop Δh= Δh1 + Δh2+ Δh3 (2) total flow rate q = q1+ q2+ q3.. head drop Δh= Δh1 = Δh2 = Δh3 For vertical flow, the flow rate q through area A of each layer is the same. Hence the head drop across a series of layers can be given. Permeability – Part A Dr O.Hamza
  27. 27. Darcy’s law and permeability Stratified soil and permeability Vertical flow V ti l fl Head drop across a series of layers is The average coefficient of permeability is q = q1= q2= q3.. Δh= Δh1 + Δh2+ Δh3 For vertical flow, the flow rate q through area A of each layer is the same. Hence the head drop across a series of layers can be given. Permeability – Part A Dr O.Hamza
  28. 28. Darcy’s law and permeability Stratified soil and permeability The flow rate through a layered block of soil Horizontal flow of breadth B The average coefficient of permeability q = q1+ q2+ q3.. Δh= Δh Δh1 = Δh2 = Δh3 For horizontal flow, the head drop Δh over the same flow path length Δs will , p p g be the same for each layer. So i1 = i2 = i3 etc. Permeability – Part A Dr O.Hamza
  29. 29. Determination of coefficient of permeability • Laboratory measurement of the coefficient of permeability L b t t f th ffi i t f bilit • Field measurement of the permeability • Empirical relations for the coefficient of permeability Permeability – Part A Dr O.Hamza
  30. 30. Determination of coefficient of permeability Laboratory measurements of permeability Permeameter 1. Constant head Permeability test Δh Recommended for coarse-grained soils coarse grained soils. The soil sample is subjected to steady total head d op Δh causing a water flows ( t ead drop caus g ate o s (with flow rate q) In this test, an element of the soil with length L is placed into a cylindrical container with a sectional area of A. Permeability – Part A Dr O.Hamza
  31. 31. Determination of coefficient of permeability Laboratory measurements of permeability Permeameter 1. Constant h d Permeability test 1 C t t head P bilit t t Δh q Darcy’s law v = = k.i A Δh Hydraulic gradient i= Δs Thus, Thus A Δh Permeability – Part A Dr O.Hamza
  32. 32. Determination of coefficient of permeability Laboratory measurements of permeability Permeameter 2. Falling h d P 2 F lli head Permeability test bilit t t Recommended for fine-grained soils Hydraulic gradient Δh/L varies with time. Total head h in standpipe of area ‘a’ is allowed to fall; heads h1 and h2 are pp ; measured at times t1 and t2. Permeability – Part A Dr O.Hamza
  33. 33. Determination of coefficient of permeability Laboratory measurements of permeability 2. Falling head Permeability test Permeameter The quantity of flow through the sample in time dt: a dQ = -adh h A k dt = − a dh L dQ= Ak i dt A 1 h2 aL dh or dt = − Ak h By integrating between two test limits and re-arranging the equation: Permeability – Part A Dr O.Hamza
  34. 34. Determination of coefficient of permeability Laboratory measurements of permeability Oedometer Coefficient of permeability k can be indirectly estimated from Oedometer test k = cv.mv.γw cv coefficient of consolidation mv one-dimensional compliance Permeability – Part A Dr O.Hamza
  35. 35. Quizzes and example problems Work on: • Quizzes: only quiz 1, 2 and 3 • Example problems: only problem 1 and problem 2 Permeability – Part A Dr O.Hamza
  36. 36. Working on Quizzes and Example problems Quiz 1 (3 minutes) A well's ti i l ll' tip is located at an elevation 180 m above sea l t d t l ti b level. l The length of the water column in the well is 27 m. What is the total head at the well, if we use the plane at 20 m above sea level as the datum level? Choose an answer and explain why a)180 m b)187 m Solution The total head is defined as h = hz (elevation) + hw (pressure head). Here, Here hz = 180 - 20 = 160 m hw = 27 m h = 187 m m, m, Permeability – Part A Dr O.Hamza
  37. 37. Working on Quizzes and Example problems Quiz 2 (2 minutes) In the well of Problem 1, what is the water pressure, in Pascal (Pa, or kPa = 1000 Pa)? Recall that γw = 9.81 kPa. Choose an answer and explain why a) 264.87 kPa b) 27 kPa u Pressure head hw = γw pore water pressure u = 27 x 9.81 = 264.87 kPa. Permeability – Part A Dr O.Hamza
  38. 38. Working on Quizzes and Example problems Quiz 3 (10 minutes) A horizontal cylinder of homogonous sand is tested as shown in the figure. Imaginary points A B C D and E are l I i i t A, B, C, d located at th centreline of th t d t the t li f the cylinder. What is the hydraulic gradient expected along the soil. Determine the pressure, elevation and total head at different points to be able t plot th bl to l t them versus h i horizontal di t t l distance. 5 cm Datum 5 cm A B C D E 4 cm 5 5 3 Permeability – Part A Dr O.Hamza
  39. 39. Working on Quizzes and Example problems Quiz 3 5 cm Δh= -5 cm Datum L 10 L=10 cm 5 Solution S l ti cm A C D E B The hydraulic gradient along the soil is 4 cm 5 5 3 iBC = Δh / L = -5/10= -0.5 Since thi gradient i Si this di t is constant along the soil: iBC= iCD= iBD= - 0.5 iBC = ΔhBC/LBC=(hC-hB)/ LBC - 0.5 = (hC – 5)/ 5 hC = 2 5 2.5
  40. 40. Working on Quizzes and Example problems Problem 1 Hydraulic head and hydraulic gradient 1. For the soil shown in the figure calculate the total head and pore water pressure at point P and Q. Then determine the direction of the flow. What is the hydraulic gradient between these two points? 5m Pressure head ead Pressure head Recall: h (total head) = hz (elevation head) + hw (pressure head) pressure head hw = height of water above the point Permeability – Part A Dr O.Hamza
  41. 41. Working on Quizzes and Example problems Problem 1 Hydraulic head and hydraulic gradient 1. Solution Total head h = hz (elevation head) + hw (pressure head) hP= -0.5 + 1.7 = 1.2 m hQ= -2.2 + 2.2 = 0 m Pore water pressure: Pressure head u hw = γw thus, pore water pressure at P: uP = 1.7 x 9.81 ≈ 17 kPa; p pore water p pressure at Q uQ = 2.2 x 9.81 ≈ 22 kPa Q: Hydraulic gradient iPQ = Δh / ΔS = (0 -1.2)/ 5 = - 0.24 ( ) Direction of flow: Water moves from P to Q i.e. from high head to low head Permeability – Part A Dr O.Hamza
  42. 42. Working on Quizzes and Example problems Problem 2. Laboratory measurement of the coefficient of y permeability The results of a constant head permeability test for a cylindrical fine sand sample having a diameter of 150mm and a length of 300mm are as follows: Constant head difference = 500 mm Time of collection of water = 5 min Volume of water collected = 350 cc Δh Find the coefficient of permeability for the soil in m/s. Note. cc is cubic centimetre, cm3 Permeability – Part A Dr O.Hamza
  43. 43. Working on Quizzes and Example problems Problem 2. Laboratory measurement of the coefficient of y permeability Solution: Using the equation of constant head permeability test A Δh where: - Δh is the constant head difference = 500 mm - The cross-section area of the sample, A=πD2/4 = 17662 mm2 - The flow rate i.e. the quantity of water that flows in a unit of time rate, i e time, q = volume of water collected (mm) / time of this collection (sec) = 350x10-6 / (5x60) = - Thus k = …………. Permeability – Part A Dr O.Hamza

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