Long-term hydraulic limit states

Hydraulic limit states: The application allows performing long-term heave (uplift) and piping (internal erosion) verifications of a sheet pile wall.

Uplift involves the loss of equilibrium of the structure or the soil due to the water uplift pressure (buoyancy phenomena of underground structures, such as underground parking lots, subway stations, etc., or heave of the excavation bottom).

Soil erosion and piping are generated by seepage flows (hydrodynamic conditions) from the bottom upwards, with a hydraulic gradient such as to produce the cancellation of effective stresses.

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Uplift verification

Destabilizing force (seepage forces due to the hydrodynamic component of the pore pressure)

S_w = γ_w · H_c · D/2

Stabilizing force (submerged weight of the soil wedge)

W’ = γ’ · D · D/2

Verification condition

FS = W’/S_w

Piping verification

FS = (i_C / J_R) / i_E

Assuming a linear head loss with depth and neglecting the thickness of the diaphragm wall, the exit gradient i_E is given by:

i_E = H / (H + 2D) = H / 2D

While

i_C = γ’ / γ_w