When a saturated cohesive or organic soil is loaded, there is an increase in the pore water pressure,
known as the initial excess pore water pressure uo. As water flows out of the soil, this excess pore
water pressure slowly dissipates. In order to determine how fast this consolidation process will take,
Terzaghi (1925) developed the one-dimensional consolidation equation to describe the time-dependent
settlement behavior of clays. The purpose of the Terzaghi theory of consolidation is to estimate the
settlement versus time relationship after loading of the saturated cohesive or organic soil.
The Terzaghi equation is a form of the diffusion equation from mathematical physics. There are
other phenomena that can be described by the diffusion equation, such as the heat flow through solids.
In order to derive Terzaghi’s diffusion equation, the following assumptions are made