Engineering Rock Mechanics

Specimen geometry, loading conditions and environmental ekcts 97

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Size increases,

strength decreases

Figure 6.11 The size effect in the uniaxial complete stress-strain curve.

6.4.2 The shape effect
In Section 6.4.1, we discussed the size effect, i.e. when the shape of
the specimen is preserved but its size changes. Here, we discuss the
complementary effect, the shape effect, when the size (Le. volume)
of the specimen is preserved but its shape changes. In Fig. 6.12, we illustrate
the effect of shape variation in uniaxial compression.
The trends in the curves show that the elastic modulus is basically
unaffected by specimen shape, and that both the strength and the ductility
increase as the aspect ratio, defined as the ratio of diameter to length,
increases. The reason for these trends is different to that in the pure size
effect case. When a specimen is loaded in uniaxial compression, end platens
made of steel, and preferably of the same diameter as the specimen, are
used. Because of an unavoidable mismatch in the elastic properties of the
rock and the steel, a complex zone of triaxial compression is set up at
the ends of the rock specimen as the steel restrains the expansion of the
rock.
This end effect has little significance for a slender specimen, but can
dominate the stress field in the case of a squat specimen (Fig. 6.12). The
same end effect does occur during size effect testing, but the influence is
the same for different specimen sizes, because the aspect ratio remains
constant.
The effect of a confining pressure during the triaxial test has a dramatic
effect on the complete stress-strain curve and it is essentially this
confining effect which is causing the shape effect illustrated in Fig. 6.12. The
problem is easily overcome in the laboratory by choosing an appropriate
aspect ratio, greater than or equal to 2.5, but underground support pillars
in situ are much more likely to be squat than slender. Thus, the shape effect
has the converse effect to the size effect when the results are extrapolated
to the field: an in situ squat pillar will be stronger than a slender laboratory
specimen of the same rock, although there will be different loading
conditions in the field which could mitigate the effect.