Geoscience Reference
In-Depth Information
(a)
(b)
1
2
140
130
80
300
70
60
200
40
3
4
20
100
Limestone
0 0 2 4 6 8 10 12 14 16
Strain, e (%)
Fig. 3.102 (a) Strain-stress diagram showing several curves corresponding to limestone samples of the same composition at different confining
pressures (in MPa); (b) Differences in confining pressure give way to different fracturing or deformation modes. Confining pressure from samples
(from 0.1 to 35 MPa in the fractured samples and 100 MPa for the ductile flow).
t
Effective stress
Applied stress
s n
s 3
s 1
s 1
0
s 2
s 2
s 3
E
E
E
Pore fluid pressure
( P f )
s xx t xy t xz
t yx
s pf 0 0
0
s xx - s pf t xy t xz
t yx
s yy
t yx
0
0 0 σ pf
s pf
τ yx
t zx t zy s zz - s pf
s yy -
s pf
Es =
t zx t zy s zz
Es =
Applied stress
(rock)
Hydrostatic stress
(fluid)
Fig. 3.103 When there is some pressurized fluid in the rock pores, part of the stress is absorbed. The state of stress is lowered and an effective stress
tensor can be defined subtracting the values of the normal stresses from those of the fluid. The Mohr circle moves toward lower values by an
amount equal to the pore pressure ( P f ) sustained by the fluid.
pressure in the rocks, so that ductility decreases and frac-
tures are produced more easily. Being hydrostatic in nature,
the effectiveness of the normal stresses is lowered but the
shear stresses remain unaltered. The control of pore pres-
sure in the rocks is of key importance in fracture formation
and will be discussed in some more detail in Section 4.14.
Other important factors are the time of application of the
stresses: the instantaneous or long-term application of a
certain level of stress may cause different rheological behav-
iors, like the case of the silicon putty discussed earlier. Rock
strength decreases when the stresses are applied for long
times under small differential stresses (creep experiments).
Also in relation to time, the rates of loading (velocity of
increased loading in the experiments) also have important
implications for the production of strain. In a single exper-
iment, the rate of strain is generally maintained constant
but the rates of strain can be changed from one experiment
to another. When changes in strain are produced rapidly
(high loading rates) the rock samples become ductile and
break at higher stress levels.
 
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