As I understand your problem, you plan to install a sheet pile wall in a river. It sounds like a cofferdam; the mudline will be the same on both sides of the sheet pile wall, but the water level will be drawn down on one side.
The effective stress soil parameters are calculated based on the piezometric level at a given point. The differential water pressure is also calculated using the piezometric levels. If the sheets are driven a "sufficient" penetration into a low permeability clay, you can probably ignore the pressure changes due to seepage around the bottom of the sheet piling. In this case, the piezometric level is dependent on the depth below the phreatic surface. The key to this approach is the determination of what constitutes sufficient penetration...
When you assume no underseepage, the net pressure diagram due to water is zero at the top of the upper water level and linearly increases until you reach the lower water table. The water pressure is uniform below this depth,
but it isn't zero. The water loads constitute the loads on the bulkhead; the soils exert active and passive pressures on the embedded portion of the sheet piling and offer resistance to the water loads. But they don't contribute to the loads on the sheet piling.
If the sheets are driven into sands, gravels, silts, etc. - or a depth into clay that would permit seepage beneath the bottom of the sheeting, then you will need to do a seepage analysis. The results of the seepage analysis will provide you with the piezometric pressures along both sides of the sheet pile.
I generally recommend that engineers "new" to these kinds of analyses perform a seepage analysis regardless of the problem geometry. And don't forget to check the stability of the "dry" side of the sheet pile wall due to the uplift forces from seepage pressures...
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