Presentation Transcript

1. CE 496 Senior Design

   Flow Nets II Lecture 9 Date: 2/7/2012 Professor Knur
2. Assumptions Soil is homogenous. Voids are completely filled with water No consolidation or expansion occurs in the soils Soils and water are incompressible Flow is laminar and Darcy’s law is valid q=k*i*A or Q=k*i*A*t
3. More Assumptions Like energy, water cannot be gained or destroyed Conservation of mass holds So water entering an element equals the water leaving the element
4. Flow Net Three dimensional Laplace equation Two dimensional Laplace equation
5. Flow Net Represented by two types of curves Stream Lines also known as flow lines Equipotential lines
6. Stream Line/Flow Line Flow line is the path water flows through the pore spaces in a soil The actual path dependent on where a water drop begins Number of paths nearly infinite, but do not cross Number of flow lines must remain the same throughout the net Natural boundaries dictate flow path
7. Stream Line/Flow Line
8. Stream Line/Flow Line Other Boundary conditions include: Drains Sheet pile walls Impermeable boundaries such as clay layer or rock surface
9. Equipotential Line As water flows through a soil energy is consumed by friction Open, interconnected spaces in gravels and boulders, consume less energy than tight spaces of silt or clay. Potential lines equate to lies of equal head
10. Equipotential Line
11. Dissimilar Materials Equipotential lines obey Snell’s Law.
12. Flow Net Basics Flow lines and equipotential lines must intersect at right angles to for areas that are basically squares Certain entrance and exit requirements must be met Basic deflection rules must be followed passing from one k to another k (Snell’s Law) Adjacent equipotential lines have equal head losses Same Q flows between adjacent flow lines
13. Confined Flow Systems Flow is confined within known saturation boundaries and Phreatic line is known. Ex. Flow beneath concrete weir and above impermeable boundary
14. Unconfined Flow Systems1-Zone (soil type) dam Phreatic line is the line of saturation Not always known in advance Phreatic line must be located simultaneously with drawing of flow net
15. Unconfined Flow Systems AB Maximum equipotential Line AC (Base of Dam) is flow line Position of Phreatic line, unknown But Expected to be in shaded zone BDE
16. Unconfined Flow Systems Divide Total head into in equal parts dh (headlines) Draw light line for first estimate of phreatic line Draw Equipotential Lines Draw Flow Lines at right angles to E. P. lines
17. Unconfined Flow Systems Note flow channel areas are not equal (cd and ef) Use scale to measure box proportions Note wide range of dimensions (0.4 to 1.5) Redraw flow net moving in direction of arrows
18. Unconfined Flow Systems Flow channels are now proportional throughout
19. Unconfined Flow on Less Permeable Foundation ke= 10kf Flow through embankment dominates Begin by drawing net through high k material
20. Unconfined Flow on Less Permeable Foundation Equipotential lines connect Extended into the less permeable area Balance and size by T. and E.
21. Unconfined Flow on Less Permeable Foundation Lines are dashed since not full Note flow line in embankment connects Shape factor embankment 1.32/7 = 0.19 Shape factor foundation 0.9/7 = 0.13 Foundation add 50% to Q
22. Unconfined Flow on MORE Permeable Foundation kf = 10 ke Flow through foundation dominates Begin by drawing flow net through foundation, Flow net drawn as if confined system Assume bottom of embankment is phreatic line
23. Unconfined Flow on MORE Permeable Foundation Divide embankment into equipotential drops Extend Equipotential lines into embankment Equipotential lines intersect correct head line Adjust lines in embankment and foundation until compatible with known coeff. of perm.
24. Unconfined Flow on MORE Permeable Foundation Phreatic line must be adjusted simultaneously with refinement of flow net. These class of flow net is most difficult to construct
25. Phreatic Line Entrance Studies have shown that Phreatic line enters 0.3*S Draw flow line accordingly (shown dashed)
26. Phreatic Line Exit (wetted surface) For slope Beta < 30 degrees (our case) The wetted surface, a
27. Phreatic Line Exit (wetted surface) For slope Beta < 30 degrees (our case) The wetted surface, a
28. Phreatic Line Exit (wetted surface) Calculate a, using: From Bowles, Ch 9-5, pg 286-289:
29. Seepage Quantities Isotropic Soils Anisotropic Soils nf/nd= shape factor (khkv)1/2 = effective permeability Example in CedergrenCh 3, pg 95
30. Seepage Force Seeping water imparts energy to soil grains V= Volume of soil
31. Seepage Force Calculate using the Gradient Method Determine the average hydraulic gradient in a soil element Calculate the magnitude of the seepage force acting on t the element Determine the direction of the seepage force Determine the line of action of the seepage force Example in Cedergren Ch. 3, pg 95.