The 'Terzaghi consolidation equation' is written as ∂u/∂t = cv × ∂²u/∂z². The boundary conditions for a clay layer drained top and bottom are:
Choose the correct answer
u = u0 everywhere at all times (no drainage)
u = 0 at top and bottom drainage boundaries (free drainage); u = u0 initially throughout the layer
du/dz = 0 at both boundaries (impermeable)
Only one boundary condition needed
Correct Answer
B. u = 0 at top and bottom drainage boundaries (free drainage); u = u0 initially throughout the layer
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Terzaghi 1D consolidation PDE: ∂u/∂t = cv·∂²u/∂z². For double drainage (top and bottom): boundary conditions: u(0,t) = 0 and u(2Hdr,t) = 0 (excess pore pressure = 0 at both drainage boundaries); initial condition: u(z,0) = u0 (initial excess pore pressure = applied stress). Solution: Fourier series. Hdr = half-thickness (half the layer for double drainage).
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