Civil and Building Engineering.

The total vertical stress at a depth of 10 ft in a saturated clay that has an average water content of 22% will be calculated below as an example calculation of total and effective stresses:
Previously, it was noted that compression of clay is controlled by changes in effective stress, not total stress. The effective stress is calculated using Eq. 3.30. When the water table is static (i.e., no flow of groundwater in the vertical direction), the water pressure increases linearly with depth, just as if no soil were present. The depth in the soil where the top of the equivalent free water surface exists is the water table. At the water table, the water pressure is zero gage pressure (1 atmosphere absolute). Below the water table the water pressure u is equal to
where zw is the vertical distance below the water table. In a soil in the field, the water table is at a given depth and there is no sudden change in water content or any other property at the water table. In highly pervious soils, like sands and gravels, the water table is located by drilling an open hole in the soil and letting water flow into it from the soil until equilibrium occurs. The water level in the hole is then easily measured. For clays, the time needed to obtain equilibrium may be many days. To speed up equalization in clays, a
piezometer may be used. A simple piezometer is formed in the field by drilling a hole, packing the bottom of the hole with sand, embedding a small-diameter tube with its bottom end in the sand and its top end at the surface, and then backfilling the rest of the hole with clay. The water level will equilibrate inthe small-diameter tube much faster than in a large borehole because less water is needed to fill the tube. Once the water table is located, the pore water pressures below the water table are calculated using Eq. 3.40.
In many practical problems the water table moves up and down with the seasons, so the level of the water table at the time of the soil exploration may indicate only one point within its range of fluctuation.
To simplify the initial calculation of water pressure, the water table in the sample problem was assumed to be at the surface. Then at a depth of 10 ft the water pressure would be
The effective stress is then computed using Eq. 3.30:

More generally, Eqs. 3.30 and 3.40 may be combined as follows:
The term Y (z - zw) is clearly equal to the total stress and to the effective stress at the position of the water table (where uw = 0). The terms (Yzw -Y wZw) may be combined to yield Yzw, where Y is the effective unit weight, as found according to Archimedes’ principle.
The effective stress below the water table is then the sum of the effective stresses above and below the water table:
The expression for submerged unit weight is obtained by subtracting Yw from Ysat using Eq. 3.8 (or Eq. 3.12 if Sr is less than 100%) to derive an expression that does not use w or Sr:
The effective stresses in the soil prior to construction of the embankment are now known. Next, to determine the strains caused by the placement of the embankment fill, the effective stresses must be determined after settlement has been completed. This calculation is the same as the one used previously, except that now there is another layer of soil on the surface, so the depths are measured from the new surface.
The only question relates to the change in density that occurs during settlement. Since no solids are lost, the submerged weight of all the original soil above any depth remains the same (the loss of porewater during consolidation causes a decrease in void ratio and thus an increase in submerged unit weight, but this effect is exactly counterbalanced by the decreased thickness of the submerged soil above the depth in question).
However, if the elevation of the water table remains constant as the embankment settles, then some of the soil (including embankment soil) that was above the water table when the embankment was first placed will submerge below the water table after settlement has been completed. The amount of soil that is converted from total unit weight to submerged unit weight (Eq.3.41) depends on the settlement that occurs but calculation of settlement is needed. Thus, a trial solution is sometimes needed where the effect of submergence is ignored in the first calculation of settlement. The first computed settlement is used to estimate a submergence correction, and another (better) settlement is calculated. The process may be repeated until a settlement of satisfactory precision has been calculated from a plot of computed settlement versus assumed settlement (usually only two trials).