## Effective stress analysis

The methods for analysing a slip circle that have been discussed so far can be used to give an indication of the factor of safety immediately after construction has been completed, but they are not applicable in the case of an existing embankment if water pressures are present. However, if an analysis is carried out in terms of effective stress then it can be used to determine F after drainage has occurred or for any intermediate value of ru between undrained and drained, such an analysis affording a better estimate for stability immediately after construction than the total stress methods.

Before this system can be examined, the determination of the pore pressure ratio, ru, must be considered.

5.5.1 Pore pressure ratio, ru

The prediction of pore pressures in an earth dam or an embankment has been discussed by Bishop (1954). There are two main types of problem: those in which the value of the pore water pressure depends upon the magnitude of the applied stresses (e.g. during the rapid construction of an embankment), and those where the value of the pore water pressure depends upon either the ground water level within the embankment or the seepage pattern of water impounded by it.

Rapid construction of an embankment

The pore pressure at any point in a soil mass is given by the expression:

u = uo + Au where uq = initial value of pore pressure before any stress change Au = change in pore pressure due to change in stress.

From Chapter 3:

Skempton (1954) showed that the ratio of the pore pressure change to the change in the total major principal stress gives another pore pressure coefficient Ë:

The coefficient B can be used to determine the magnitude of pore pressures set up at any point in an embankment if it is assumed that no drainage occurs during construction (a fairly reasonable thesis if the construction rate is rapid). Now u i.e.

uo BAff|

A reasonable assumption to make for the value of the major principal stress is that it equals the weight of the material above the point considered. Hence

For soils placed at or below optimum moisture content, u0 is small and can even be negative, its effect is of little consequence and may be ignored so that the analysis for stability at the end of construction is often determined from the relationship ru = B.

The pore pressure coefficient B is determined from a special stress path test known as a dissipation test and has been described by Bishop and Henkel (1962). Briefly, a sample of the soil is inserted in a triaxial cell and subjected to increases in the principal stresses Ao\ and Aaj, of magnitudes approximating to those expected in the field. The resulting pore pressure is measured and B obtained.

### Steady seepage

It is easy to determine ru from a study of the flow net (Fig. 5.19). The procedure is to trace the equipotential through the point considered up to the top of the flow net, so that the height to which water would rise in a standpipe inserted at the point is hw. Since u = 7whw:

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