| THEORY & FORMULAE |
Consolidation is the slow settlement of soil due to expulsion of pore water. When soil is loaded undrained, the pore pressure increases particularly in fine soils (silts and clays) with low permeabilities. Seepage occurs and the excess pore pressures dissipate gradually. For the vast majority of practical settlement problems in geotechnical engineering, it is sufficient to consider that both seepage and strains take place in one vertical direction only. One-dimensional consolidation specifically occurs when there is no lateral strain, e.g. it can be assumed to be occurring under wide foundations.
Terzaghi's basic equation for the 1-D consolidation case is given by the differential equation (1) below. Eq. (2) is the dimensionless form of this equation and Eq. (4) is the solution of the equation assuming the excess pore pressure is uniform with depth.
where
u = is excess pressure at depth z and after time t since load applied
Cv = coefficient of consolidation
Uz = degree of consolidation at depth t
Ut = average degree of consolidation at time t
Tv = dimensionless time factor
Z = drainage path ratio = z/d
d = drainage path length; [d = H for one-way drainage, d = H/2 for two-way]
H = thickness of clay layer
In the implementation here, the infinite series is approximated by summation from m=0 => 250, with insignificant loss of accuracy.
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