7) Flow Nets for Anisotropic Materials

7) Flow Nets for Anisotropic Materials

1. Anisotropic materials - layered soil deposits

   • Different permeability

2. Horizontal flow in layered soil deposits

   • v=(Q1+Q2)/(d1+d2)=khΔh/L
     • kh=(k1d1+k2d2)/(d1+d2)
   • v1=k1Δh/L
   • Q1=k1Δhd1/L
   • v2=k2Δh/L
   • Q2=k2Δhd2/L

3. Vertical flow in layered soil deposits

   • v=kvΔh/L
     • kv=(d1+d2)/(d1/k1+d2/k2)
   • v=k1Δh1/d1
   • v=k2Δh2/d2
   • Hydrolic gradient
     • Δh/d=(vd1/k1+vd2/k2)/(d1+d2)

4. Laplace`s equation of continuity

   • Flow in = Flow out
   • 0 = δ^2h/δx^2 + δ^2h/δz^2

5. Purpose for drawing flow nets

   • Determining pore pressure and effective stresses
   • Determining the quantity of flow
     • ΔQ=kΔh
       • k=keq=√khkv
   • Equivalent permeability for anisotropic floa
     • Transformed scale
       • ΔQ=keq*t*Δh/x`
     • Natural scale
       • ΔQ=kh*t*Δh/x

6. Piping

   • Critical hydrolic gradient
     • icrit=(γsat-γw)/γw
   • Factor of saftey = icrit/i
   • Occurs when
     • (h1-h2)/(z1-z2)>(γsat-γw)/γw
       • i>icrit

7. Fliters

   • Prevent erosion and piping
     • Prevent movement of soil particles but allows seepage water to escape

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