Drained loading, undrained loading and consolidation

The relative rates at which total stresses are applied and at which the seepage takes place are of critical importance in determining soil behaviour. The limiting conditions are illustrated in Figs. 6.10 and 6.11.

Figure 6.10(a) illustrates an increment of total stressσ applied slowly, over a long period of time. This could represent loading in a laboratory test or in the ground. If the loading is applied very slowly water will be able to seep from the soil as the total stresses increase. There will be no change of pore pressure, as shown in Fig. 6.10(c), and the volume changes will follow the change of loading, as shown in Fig. 6.10(b).

Figure 6.10 Characteristics of drained loading. Figure 6.11 Characteristics of undrained load-

Because the pore pressures remain constant at u0, the changes of effective stress follow the change of total stress, as shown in Fig. 6.10(d). When the stresses remain constant at σ

0+σ
, the volume remains constant at V0−V. This kind of relatively slow loading is called drained because all the drainage of water takes place during the loading. The most important feature of drained loading is that the pore pressures remain constant at u0, which is known as the steady state pore pressure.

Figure 6.11(a) illustrates the same increment of total stressσ as in Fig. 6.10 but now applied so quickly that there was no time for any drainage at all and so the volume remains constant, as shown in Fig. 6.11(b). If the loading was isotropic with no shear distortion and undrained with no volume change then nothing has happened to the soil. From the principle of effective stress this means that the effective stress must remain constant, as shown in Fig. 6.11(d), and, from Eq. (6.16), the change in pore pressure is given by

σ
= σ − u = 0 (6.17)

u = σ (6.18)

This increase in pore pressure gives rises to an initial excess pore pressure ui, as shown in Fig. 6.11(c). Notice that the pore pressure u consists of the sum of the steady state pore pressure u0and the excess pore pressure u; if the pore pressures are in equilib- rium u= u0 and u = 0. Relatively quick loading is known as ‘undrained loading’ because there is no drainage of water during the loading. The most important feature of undrained loading is that there is no change of volume.

At the end of the undrained loading the pore pressure is u= u0+ ui, where u0is the initial steady state, or equilibrium, pore pressure and ui is an initial excess pore pressure. This excess pore pressure will cause seepage to occur and, as time passes, there will be volume changes as shown in Fig. 6.11(b). The volume changes must be associated with changes of effective stress, as shown in Fig. 6.11(d), and these occur as a result of decreasing pore pressures, as shown in Fig. 6.11(c). The pore pressures decay towards the long term steady state pore pressure u_∞. Fig. 6.11(c) shows u_∞= u0 but there are cases in which construction, especially of excavations changes the steady state groundwater and u_∞can be greater or smaller than u0.

At some time t the excess pore pressure is utand this is what drives the drainage and so, as the excess pore pressure decreases, the rate of volume change, given by the gradient dV/dt, also decreases, as shown in Fig. 6.11(b). Notice that while there are excess pore pressures in the soil, water pressures outside the surface of the soil will not be the same as the pore pressures; this means that the pore pressure in soil behind a new quay wall need not be the same as the pressure in the water in the dock.

This dissipation of excess pore pressure accompanied by drainage and volume changes is known as consolidation. The essential feature of consolidation is that there are excess pore pressures u that change with time. Usually, but not always, the total stresses remain constant. Consolidation is simply compression (i.e. change of volume due to change of effective stress) coupled with seepage. At the end of consolidation, when u_∞= 0, the total and effective stresses and the volume are all the same as those at the end of the drained loading shown in Fig. 6.10. Thus, the changes of effective stress for undrained loading plus consolidation are the same as those for drained loading.

The processes of undrained loading followed by consolidation can be represented by an experiment with a packet of crisps. Put the packet on the table and put a mass of a few kilos on it. The packet will inflate as the pressure in it increases. This represents undrained loading. Puncture the packet with a pin. The air will escape and as the pressure in the packet reduces the mass settles and you can hear crisps breaking as load is transferred from the air pressure to the crisps. This represents consolidation. The analogy is not exact but the experiment nicely illustrates the processes. If the crisp packet is punctured before the mass is applied the air escapes immediately and the load is taken by the crisps. This represents drained loading.

In the simple examples of drained and undrained loading illustrated in Figs. 6.10 and 6.11, the increment of loading was positive so that the soil compressed as water was squeezed out. Exactly the same principles apply to unloading where the increment is negative and the soil swells as water is sucked in by the negative excess pore pressure. You should sketch diagrams like Figs. 6.10 and 6.11 for an increment of unloading.

Remember the final steady state pore pressure at the end of consolidation u∞need not be same as the initial steady state pore pressure u0before the undrained loading. The excess pore pressure which causes consolidation is the difference between the current pore pressure and the final steady state pore pressure so after a long time u_∞ is always zero. Sometimes only the external water levels are changed as, for example, when a dam is filled or emptied. In this case there will be consolidation in the soil as the pore pressures adjust to the new external water levels.

Consolidation is any process in which effective stresses change as excess pore pres- sures dissipate towards their long term steady state values. If excess pore pressures are positive, effective stresses increase with consolidation and the soil compresses. On the other hand, if excess pore pressures are negative, effective stresses decrease with consolidation and the soil swells.