SEEPAGE FORCES

1. Consider a random element of a flow net: Each side has the same length, b SEEPAGE FORCES A b B b θ D C the direction of flow is inclined at an angle of θ to the horizontal lines AB and DC define the elemental flow channel lines AD and BC are equipotentials, with a drop in head of ∆h when water seeps from AD to BC

2. Geometrically: SEEPAGE FORCES A B θ θ θ D θ θ C Four congruent right angle triangles are formed from vertical and horizontal lines projected inwards from the four corners of the flow net element The difference in elevation between A and D is the same as between B and C and is equal to bcosθ. The difference in elevation between A and B is the same as between D and C and is equal to bsinθ. Each has an angle θ as shown

3. The pore pressure distributions acting on each side of the element are shown below: If the pore water pressure at point A is uA, and u = w(h-z), and The change in pore water pressure from point A to point B is due to a loss in total head -∆h and the elevation drop, bsinθ The change in pore water pressure between point B and point C is due only to the elevation drop, bcosθ, SEEPAGE FORCES bsinθ -∆h bcosθ the change in pore water pressure between point A and point D is due only to the elevation drop, bcosθ, bcosθ uD = uA + w bcosθ uB = uA + w(bsinθ-∆h) uC = uB + wbcosθ or uC = uA + w(bsinθ-∆h) +wbcosθ or uC = uA + w(bsinθ+bcosθ-∆h)

4. The pore pressure distribution acting on AD will be cancelled by that acting on BC, leaving: The pore pressure distribution acting on AB will be cancelled by that acting on DC leaving: The equivalent point load (net boundary water force) acting on DC is: b x wbcosθor wb2cosθ The net boundary water force acting on BC is: b x w(bsinθ-∆h)or wb2sinθ - ∆hwb uD-uA = uC-uB = w bcosθ w(bsinθ-∆h) SEEPAGE FORCES uB-uA = uC-uD = w(bsinθ-∆h) b b wb2sinθ - ∆hwb w bcosθ uD = uA + w bcosθ uB = uA + w(bsinθ-∆h) w b2cosθ uC = uA + w(bsinθ+bcosθ-∆h)

5. What would the boundary water forces be if seepage stopped? (i.e., the static case) ∆h would be 0, and the forces on DC and BC would be wb2cosθand wb2sinθrespectively, orthogonal vectors with a resultant of wb2 , (acting vertically) The only difference between the static and seepage cases is the force ∆hwb called the seepage force, J SEEPAGE FORCES If the average hydraulic gradient, i across the element is: wb2sinθ - ∆hwb Then: If b2 x 1 m is the volume of the element, V then the seepage pressure, j is defined as the seepage force per unit volume: j = iw w b2cosθ

6. the total weight of the element = satb2 = vector ab How will seepage affect the effective stress at any point in the soil mass? If the effective stress is reduced too much by upward seepage, then the soil will lose its ability to support loads. In the extremes: if the seepage direction is downward, the effective stress will be increased or if upward the effective stress will be decreased Therefore, let’s consider all the gravitational and seepage forces acting on the soil element à la a vector diagram. First, the SEEPAGE case: The concern is with the support conditions of the soil. Boundary water force on CD = wb2cosθ = vector bd Boundary water force on BC = wb2sinθ-∆hwb = vector de Resultant boundary water force = vector be SEEPAGE FORCES Resultant body force = vector ae = Effective Stress, σ’ wb2sinθ - ∆hwb w b2cosθ SEEPAGE CASE

7. Now consider the STATIC case: the total weight of the element = satb2 = vector ab Boundary water force on CD = wb2cosθ = vector bd Boundary water force on BC = wb2sinθ= vector dc Resultant boundary water force = wb2 = vector bc SEEPAGE FORCES Resultant body force =  ’b2vector ac = Effective Stress, σ’ wb2sinθ - ∆hwb w b2cosθ STATIC CASE

8. This brings up an alternative solution to the seepage case: Effective weight of the element =  ’b2 = vector ac Seepage force = ∆hwb = vector ce SEEPAGE FORCES Resultant body force vector ac = Effective Stress, σ’ To summarize, the resultant body force (effective stress) can be obtained by considering: B) the equilibrium of the soil skeleton, add the effective weight of the soil mass (ac) to the seepage force (be) to find effective stress (ae) • the equilibrium of the whole soil mass, • add the total saturated weight of the soil mass (ab) • to the resultant boundary water force (ce) • to find effective stress (ae) OR SEEPAGE CASE (reprise)