## Residual strength of soil

In an investigation concerning the stability of a clay slope, the normal procedure is to take representative samples, conduct shear tests, establish the strength parameters c' and <\$>' from the peak values of the tests, and conduct an effective stress analysis. For this analysis the shear strength of the soil can be expressed by the equation:

There have been many cases of slips in clay slopes which have afforded a means of checking this procedure. Obviously when a slope slipped its factor of safety was 1.0 and, knowing the mass of material involved and the location of the slip plane, it is possible to deduce the value of the average shear stress on the slip plane, s, at the time failure occurred. It has often been found that s is considerably less than Sf, especially with slopes that have been in existence for some years, and Professor Skempton, in his Rankine lecture of 1964, presented a comprehensive study of the subject supported by case records.

Figure 3.39a shows a typical stress-to-strain relationship obtained in a drained shear test on a clay. Normal practice is to stop the test as soon as the peak strength has been reached, but if the test is continued it is found that as the strain increases the shear strength decreases and finally levels

Strain a' Effective normal stress

Fig. 3.39 The residual strength of clays (after Skempton, 1964).

Strain a' Effective normal stress

Fig. 3.39 The residual strength of clays (after Skempton, 1964).

out. This constant stress value is termed the residual strength, sr, of the clay. The strength envelopes from the two sets of strength values are shown in Fig. 3.39b, it will be seen that the cohesive intercept, based on residual strength, is so negligible that it may be taken as zero.

For clays, residual strength tests can be carried out in a shear box with a large travel of about 150 mm so that the sample can be continually strained in the one direction. The normal shear box can be used provided that it is capable of reversing its direction at the end of the travel. The reduction down to zero and back to its original value of applied stress at the point of reversal can be assumed as occurring over zero strain. The total displacement of the sample is taken to be the length of travel of the box times the number of reversals.

The reversable shear box has become a standard piece of laboratory equipment but it is now believed that, due to the absence of a large one-directional displacement, the values obtained for sr tend to be on the high side.

A more acceptable test can be carried out in the ring shear apparatus which was developed originally by Hvorslev (and others independently) in about 1934. A thin annular soil specimen is sheared by clamping it between two metal discs which are then rotated in opposite directions. The apparatus did not become popular, mainly because of the concentration at the time on the study of peak values, so readily obtained from the triaxial test, but probably also because the ring shear apparatus was complicated and it took a long time to carry out a test.

As a result of Skempton's work interest in the determination of soil strength after large displacement was re-established and, in 1971, Bishop et al. redeveloped the ring shear apparatus (Fig. 3.40) which is now considered as the most reliable means for determining residual strengths of cohesive soils.

### Residual strength of clays

The reduction from peak to residual strength in clays is considered to result primarily from the formation of extremely thin layers of fine particles orientated in the direction of shear; these particles would originally have been in a

Axis

Axis

Plane of relative rotary motion

Fig. 3.40 Ring shear test sample (after Bishop et al., 1971).

Plane of relative rotary motion

Fig. 3.40 Ring shear test sample (after Bishop et al., 1971).

random state of orientation and must therefore have had a greater resistance to shear than when they became parallel to each other in the shear direction.

The development of residual strength in a soil is a continuous process. If at a particular point the soil is stressed beyond its peak strength, its strength will decrease and additional stress will be transmitted to other points in the soil; these likewise becoming overstressed and decreasing in strength, the failure process continues once it has started (unless the slope slips) until the strength at every point along the potential slip surface has been reduced to residual strength.

Clays, especially overconsolidated deposits, contain fissures, such as those in London Clay which occur some 150-200 mm apart; these fissures are already established points of weakness, the strength between their contact surfaces probably being about residual. An important feature of fissures is that they can tend to act as stress concentrators at their edges, leading to overstressing beyond the peak strength and hence to a progressive strength decrease.

Tests carried out by Skempton indicate that the residual strength of clay under a particular effective stress is the same, whether the clay was normally or overconsolidated. Hence in any clay layer, provided the particles are the same, the value of if>'r will be constant.

### Residual strength of silts and silty clays

From a study of case records Skempton showed that the value of tp'r decreases with increasing clay percentage. Sand-sized particles, being roughly spherical in shape, cannot orientate themselves in the same way as flakey clay particles and when they are present in silts or clays the residual strength becomes greater as the percentage of sand increases.

### Residual strength of sands

Shear tests on sand indicate that the stress-displacement curve for the loose and dense states are as shown in Fig. 3.41. The residual strength is seen to correspond to the peak strength of the loose density and is usually reached fairly quickly in one travel of the shear box, succeeding reversals having little effect.

Displacement

Fig. 3.41 Stress-displacement characteristics of sands.

Residual factor, R

In the slips investigated by Skempton, some were found to have an s value corresponding to sr and some an s value lying between and Sf and sr. The use of the term residual factor, R, was therefore suggested, where R is the proportion of the total slip surface in the clay along which strength has fallen to the residual value:

sf-sr

If there is no reduction in strength, s = Sf and R = 0.0, but if there is a complete reduction in strength then s = sr and R = 1.0. The work so far carried out on residual strength has involved existing slopes and cuttings, for which Skempton's findings may be summarised as follows:

Unfissured clays: R = 0.0 Pre-existing slip: R = 1.0 Fissured clays: R varies from 0.0 to 1.0

Indications are that R increases with time, but there is at present no way of predicting its value from soil tests and it is not known if residual strengths can become evident in compact material; standard practice is to base stability analyses on peak soil strengths. If an earth embankment settles unevenly fissures can develop within it, but bearing pressures are generally kept within reasonable limits. With coal spoil heaps higher bearing capacities are often used which could lead to larger settlements. Such tips may also be subjected to mining subsidence (sometimes of several metres) and it does not seem impossible for Assuring to occur under these conditions. If there is Assuring then a potential slip surface will tend to travel through this weakened zone (which may have a strength closer to the loose than the compacted density), leading to a reduction in stability.

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### Responses

• Simon
What is residual strength in soil?
1 year ago
• mewael
Is a soil at residual shear strength?
9 months ago
• linda
When should the residual strength of a soil be used to evaluate the factor of safety?
7 months ago
• teresa
Does sand have residual strength?
1 month ago
• sisko
How to calcul;ate residual shear strength of soil?
1 month ago