clays
Long term stability
The interaction of soil structure and pore water
As pointed out in Chapter 2, the uniquely time dependent engineering behaviour of ®ne-grained saturated soils is derived from the interaction of the compressible structural soil skeleton and the relatively incompressible pore water. Rapid changes in external loading do not immediately bring about a volume change due to the viscous resistance to pore water displa- cement. Therefore, the soil structural con®guration does not immediately change and thus, by Hooke's Law, the structural loading does not change. However, while the compressible soil structure requires a volume change to change its loading, the relatively incompressible pore water may change its pressure without much volume change. The external load- ing change is therefore re¯ected by a change in pore pressure. With time, this `excess' pore pressure will dissipate, volume change occurring by pore-water ¯ow until the consequent change in structural con®guration brings the structural loading into equilibrium with the changed external loading. This process may be examined using the spring±dashpot analogy demonstrated in Fig. 3.1.
The soil structure is modelled by a spring, the soil voids modelled by the chamber under the piston and the soil permeability modelled by the lack of ®t of the piston in the cylinder ± thus a soil of high permeability is modelled by a piston which allows much leakage whereas a soil of low permeability is modelled by a piston which allows very little leakage. It is assumed the piston is frictionless. Pore pressure is indicated by the water level in a standpipe whose bore is very much smaller than that of the piston. Initially the piston is uniformly loaded by a loading intensity pp, including the weight of the piston.
The instant immediately after rapidly decreasing the loading byp, as shown in Fig. 3.1, the spring is again unaffected because insuf®cient time has elapsed for viscous ¯ow past the piston to increase the volume of the chamber under the piston and thus allow the spring to expand and shed some load.
The loading reduction p is thus initially re¯ected by a numerically equal decrease in pore pressure. As before, as time elapses, ¯ow takes place, the piston displacing upwards, the loading reduction p being shared between the spring and the pore pressure. Ultimately, the negative pore pressure increases to the equilibrium value and the loading in the spring reduces to p.
The generation of pore pressure in the loading of real soils
The stability considerations of foundations and earthworks in saturated ®ne grained soils are highly time dependent. This is because the average size of the interconnecting pores are so small that the displacement of pore water is retarded by viscous forces. The resistance that a soil offers to water ¯ow is its `permeability' which is the velocity of ¯ow under a unit hydraulic gradient. It can be seen from Table 3.1 that permeability is the largest quantitative difference between soils of different time depen- dent stability (as pointed out by Bishop and Bjerrum (1960)).
Note in Table 3.1 that the sand and normally-consolidated clay marked with an asterisk have similar shear strength parameters but the perme- ability of the clay is several orders of magnitude lower, thereby accounting for its unique time dependency whereas the more permeable sand reacts to loading changes almost immediately.
The unloading condition
If a saturated clay is unloaded, such as may occur in an excavation or cutting, an overall reduction in mean total stress occurs. In a ®ne-grained soil like clay, the viscous resistance to pore water ¯ow prevents the soil structure, partially relieved of its external loading, from rapidly expanding and sucking in pore water from the surrounding soil. With time, this suction is dissipated by drainage into the area of lowered pore pressure Fig. 3.1 Spring±dashpot analogy for soil swelling
from the surrounding area of higher pore pressure unaffected by the excavation. This migration of pore water causes an increase in soil volume in the zone of in¯uence, the soil swelling and the soil structure softening, giving rise to a reduction in strength. The minimum factor of safety occurs at the equilibrium long-term condition.
The time dependent behaviour of ®ne-grained soils whose in situ total stresses are subject to change may be usefully considered under condi- tions of unloading and loading. For example, consider the time-dependent stability of a cutting as represented in Fig. 3.2.
The reduction in the in situ total stresses (Fig. 3.3(a)) causes a reduction in pore water pressure dependent on the actual change in principal stress difference and the appropriate value of A (Fig. 3.3(b)). The consequent migration of pore water causes the soil structure to swell reducing the strength and hence stability (Fig. 3.3(d)).
Table 3.1 Effective stress strength parameters and permeabilities for soils of widely varying particle size, after Bishop and Bjerrum (1960)
Soil Permeability: m/s c0: kPa 0: degrees Rock®ll 5 0 45 Gravel 5 10ÿ4 0 43 Medium sand ± 0 33 Fine sand 1 10ÿ6 0 20±35* Silt 3 10ÿ7 0 32
Normally-consolidated clay of low plasticity
1:5 10ÿ10 0 32*
Normally-consolidated clay of high plasticity
1 10ÿ10 0 23
Over-consolidated clay of low plasticity 1 10ÿ10 8 32
Over-consolidated clay of high plasticity 5 10ÿ11 12 20
Original ground water level for static water table
Final ground water level for steady seepage Equipotential line p hf ho End of excavation pore water pressure