Civil and Building Engineering.

When a soil is subjected to an increase in effective stress, the porewater is squeezed out in a manner similar to water being squeezed from a sponge, and the basic concepts presented above govern the time rate of settlement of the surface of a clay layer. The following sections describe the theory of onedimensional consolidation for the case of instantaneous loading. In cases where the loading of the surface of the consolidating layer of soil varies over time, more advanced analytical techniques have been developed. These advanced theories of consolidation also may include more nonlinear soil properties than the simple theory that follows.
The theory to be presented herein is Terzaghi’s theory of one-dimensional consolidation, first presented in 1923. It remains the most commonly used theory for computing the time rate of settlement, even though it contains simplifying assumptions that are not satisfied in reality. The theory yields results of satisfactory accuracy when applied to predicting time rates of settlement of embankments on soft, saturated, homogeneous clays.
Primary Consolidation Water is forced out of a porous body like a sponge by the water pressure developed inside the sponge. However, in the case of thick layers of soil, the water pressure increases with depth, as in a quiet body of water, even though no flow is present in the water. Instead, water is forced to flow by applying an external pressure to the soil, but it is not the total water pressure that governs. In a soil where no water flow is occurring, the porewater pressure is termed the static porewater pressure us and is equal to the product of the unit weight of water and the depth below the water table:
As discussed previously, the application of the load from an embankment increases the total porewater pressure and flow begins. The flow of water is caused by the part of the total pore pressure that is in excess of the static value. For convenience, the excess porewater pressure u is defined as
where u is the total porewater pressure and Us is the static water pressure. The rate of outflow of water is also controlled by how far the water must flow to exit and by the size of the openings in the soil. The average velocity of water flow in the soil v varies directly with u and inversely with flow distance L:
The total rate of water flow (flow volume per unit of time), q,is
where v is the average flow velocity and A is the cross-sectional area. Actual experiments with soils show that the flow rate varies with the permeability of the soil and that the total rate of water flow is
where k is a constant of proportionality termed the coefficient of permeability or the coefficient of hydraulic conductivity, and s is now used to indicate distance in the direction of flow. Equation 3.47 is one form of Darcy’s law, which states that water flows in response to an energy gradient in the soil.
Those familiar with fluid mechanics may also know this, as flow will occur in response to a differential in hydraulic head.
Darcy’s law is applied to the one-dimensional consolidation problem first in a qualitative sense. A clay layer is underlain by a freely draining sand (Figure 3.10). The water table is at the surface. An embankment is put into place in a very short period of time, and the total pore pressure increases by an amount yH, where
 is the unit weight of the embankment material and H is the thickness of the embankment. Excess pore pressures are developed in the sand layers too, but the sand consolidates so fast that the excess pore- water pressure in the sand is dissipated by the time the construction of the embankment is complete, even though very little consolidation has occurred in the clay at this stage. Thus, the sand is freely draining compared with the clay, and u is set equal to zero in the sand. The initial excess porewater pressure in the clay, u0 equals yH and is independent of depth. Because only u , 0 the excess porewater pressure causes water flow, the value of u is plotted