6.5 Strain-stress diagrams and interpretation of strain-stress curves
6.5.2 Interpretating strain and stress curves
Oberti, in a paper read in 1960 to the Salzburg meeting of the Austrian Society of Rock Mechanics, submitted several typical strain and stress curves characteristic of good, indifferent and poor rock (fig. 6.24). In the case of good rock (type 1), the k value is small, and elastic deformation is reached rapidly. It is obvious that the rock shown in the type 2 diagram is less reliable and that type 3 has very poor characteristics.
Experts try to analyse the curves a = a(e) in detail. If the deformation curve is a straight line, it indicates an elastic behaviour of the rock (fig. 6.25a).
A point of discontinuity (point A on fig. 6.256) may indicate some internal rupture in the rock mass, possibly a local shear failure. A departure from a straight line of deformation may suggest internal plastic deformation (fig. 6.25c).
(a) (b) (c)
Fig. 6.25 Types of deformation curves.
(d)
More information about the behaviour of rock masses can be obtained from systematic analysis of the successive loops of the strain-stress curves.
Mazenot has carried out such an analysis using a large number of strain and stress measurements supplied by Electricite de France. His interpretation of the curve is based on a theory developed by Talobre (see section 6.5.3).
Some curves clearly show not one, but two points of discontinuity. Shuk (1963) produced a curve (Fig. 6.25rf) on metamorphic rock described as a phyllite-quartzite. There are two points where the elastic limit had been reached: A, for the phyllitic phase (small crystals), and B, a higher limit for the quartzite phase with larger crystals. The general curvature and direction of the line should also be observed.
The shape of the curve obtained when unloading the rock also has to be analysed for possible discontinuities or indications of internal failures.
When the load decreases sharply, without a corresponding reversal of defor- mations, the curve may confirm that some internal areas of rupture are no longer behaving elastically (Talobre). It is normal practice to load the rock in at least two directions, in order to detect possible directions of weakness.
These exist in any stratified rock, and may even exist in most crystalline or metamorphic rocks. In stratified rock masses, the modulus of elasticity
parallel to the strata is often two or three times greater than the modulus measured in a direction normal to the strata. Assuming the values E± > E2
to be known in the direction parallel and perpendicular to the main rock stratification, the value Ea at any angle a to Ex can be calculated assuming the deformation by analogy to the sketch in fig. 6.25a. The E values are given by an ellipse with Ex and E2 as the main axis (Jaecklin, 19656); fig- 6.26a.
In this respect the circular jacking of a gallery allows a far closer examination p
50 000-•
100 000
(a) 150 000-1
50 000 100 000
*-; • E2 (kg/cm2)
/+— variable E value
• (ellipse)
El (kg/cm2)
Fig. 6.26a Modulus of elasticity in stratified rocks. Ex and E2 have been measured parallel and perpendicular to the rock main stratification. E varies from E2 to Ex
depending on angle a (after Jaecklin, 19656).
mm 2.0
direction of strata 1,6 2.0 mm
Fig. 6.26b Typical radial deformation diagram obtained in the Kaunertal pressure tunnel. Broken line, elastic deformations; solid line, total deformations (parallel layers of marl, 0.30 m thick, 2.00 m distant) (after Seeber, 1964).
of rock-masses. It is possible to record the deformations, €, in any direction for any load, a, in a circular diagram (fig. 6.26b). The contour lines corresponding to elastic deformations can be traced. And, in addition, the characteristic directions of maximum deformations (normal to stratification) and minimum deformations (parallel to stratification) a = o(e) can be found and analysed.
These are needed for planning the lining of a tunnel or gallery.
Strain-stress diagrams 133 The strain-stress diagram can also be used to detect possible creep of the rock masses. In fig. 6.27 rock deformation increases by Ae as rock stress decreases, which obviously corresponds to rock creep as a function of time.
Constant load tests were carried out at Electricite de France over a period of 240 hours, with loads varying between 19 kg/cm2 for decomposed granite, 30 kg/cm2 for a weak schist (curve E) and 80 to 160 kg/cm2 for very hard limestone and gneiss. Curve E in fig. 6.21 is interesting because it shows the accelerated creep of a weak schist after about 200 hours.
Fig. 6.27 Strain-stress diagram.
These French tests show that creep deformations can be reversible or non-reversible, instantaneous or delayed, but that it is difficult on a strain- stress diagram to separate instantaneous and delayed non-reversible de- formations. It is believed that delayed deformations may represent about 5 % to 20 % of apparently instantaneous deformations. Furthermore it is difficult to expect test results obtained on a few cubic metres of rock over a period of ten days to represent exactly the deformation of a dam rock abutment after several years under varying hydrostatic loads. In some cases the creep
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50
100 200 300
Fig. 6.28 Concave strain-stress curve (after French National Committee on Large Dams).
Fig. 6.29 The strain-stress curve is first convex (a), then straight (b).
deformation is practically reversible. In one case, it was found that the deformation e had returned to e = 0 three months after suppression of the load (p = 0).
The general trend of the strain-stress curve may give some further infor- mation on the rock structure. Figure 6.28 shows that after several loading and unloading cycles the envelope to the strain curve is concave, which indi- cates progressive compression of voids and fissures and consolidation of the rock. In fig. 6.29 the general trend of total deformations is a straight line, which probably means there was some initial residual stress on the rock.
Diagrams (a) and (b) of fig. 6.30 published by a research team of Electricite
(a) (b)
Fig. 6.30 Strain-stress curves: (a) dry rock; (b) impregnated rock (after French National Committee on Large Dams).
de France refers to dry and to impregnated gneiss showing the effect of im- pregnation of rock masses.