In our development of the various ideas on consolidation settlement, we will assume:
- A homogeneous, saturated soil
- The soil particles and the water to be incompressible
- Vertical fl ow of water
- The validity of Darcy’s law
- Small strains
We will conduct a simple experiment to establish the basic concepts of the one-dimensional consolidation settlement of fi ne-grained soils. Let us take a thin, soft, saturated sample of clay and place it between porous stones in a rigid, cylindrical container with a frictionless inside wall (Figure ). The porous stones are used to facilitate drainage of the porewater from the top and bottom faces of the soil. The top half of the soil will drain through the top porous stone and the bottom half of the soil will drain through the bottom porous stone. A platen on the top porous stone transmits applied loads to the soil. Expelled water is transported by plastic tubes to a burette. A valve is used to control the fl ow of the expelled water into the burette. Three porewater pressure transducers are mounted in the side wall of the cylinder to measure the excess porewater pressure near the porous stone at the top (A), at a distance of one-quarter the height (B), and at mid-height of the soil (C). Excess porewater pressure is the additional porewater pressure induced in a soil mass by loads. A displacement gage with its stem on the platen keeps track of the vertical settlement of the soil.
Experimental setup for illustrating basic
concepts of consolidation.
We will assume that the porewater and the soil particles are incompressible, and the initial porewater pressure is zero. The volume of excess porewater that drains from the soil is then a measure of the volume change of the soil resulting from the applied loads. Since the side wall of the container is rigid, no radial displacement can occur. The lateral and circumferential strains are then equal to zero (εr 5 εu 5 0), and the volumetric strain (εp 5 εz 1 εu 1 εr) is equal to the vertical strain, εz 5 Dz/Ho, where Dz is the change in height or thickness and Ho is the initial height or thickness of the soil.
Let us now apply a load P to the soil through the load platen and keep the valve closed. Since no excess porewater can drain from the soil, the change in volume of the soil is zero (DV 5 0) and no load or stress is transferred to the soil particles (Ds9z 5 0). The porewater carries the total load. The initial excess porewater pressure in the soil (Duo) is then equal to the change in applied vertical stress, Dsz 5 P/A, where A is the cross-sectional area of the soil, or more appropriately, the change in mean total stress, Dp 5 (Dsz 1 2Dsr)/3, where Dsr is the change in radial stress. For our thin soil layer, we will assume that the initial excess porewater pressure will be distributed uniformly with depth so that at every point in the soil layer, the initial excess porewater pressure is equal to the applied vertical stress. For example, if Dsz 5 100 kPa, then Duo 5 100 kPa, as shown in Figure .
Instantaneous or initial excess porewater pressure when a vertical
load is applied.
Excess porewater pressure distribution and settlement during