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OCR for page 87
Defonnation arid
Fracture of Rock
JOSEPH B. WALSH
Rock is not elastic In the usual sense of the word. Cracks, which are found
in nearly all rocks, close under compressive stresses and make the sample
stiffer. One side of a crack slips over the opposite side under differential stress,
and energy is lost to friction. As a consequence, stress-stra~n curves are non-
linear, and hysteresis occurs in complete loadin~unloading cycles. The tensile
strength of rock is much less than the compressive strength. Strength is not
affected appreciably by moderate changes In temperature or by the rate at
which the load is applied. The cracks and pores in rock form a continuous,
interconnected network, and rock under natural conditions is usually saturated
with fluid. Him pressure or chemical activity of these pore fluids decreases
strength. The strength of rock increases dramatically as confining pressure
increases.
The deformation of most materials used in construction is described
for each by a stress-strain curve showing how strain (deformation per
unit length) varies with stress tIoad per unit area). The stres~strain
curve is approximately linear with most solid materials for small changes
in stress, and the well-known Hooke's law applies. Materials for which
Joseph B. Walsh is Senior Research Scientist, Department of Earth and Planetary Sci-
ences, Massachusetts Institute of Technology, Cam budge.
This work was supported by the U.S. Geological Survey under Contract- No. 14-08-
0001-18212 and by the Army Research Office, Durham, under Contract No. D^AG29-
79-C-0032.
87
OCR for page 88
88
CONSERVATION OF HISTORIC STONE BUILDINGS
stress is proportional to strain until fracture occurs are called linearly
elastic; the stres~strain curve for glass, which is such a matenal, is
shown in Figure 1. Elastic matenals have the characteristic that strain
is a single-valued function of stress; Figure 1 shows that the strain at
any specific stress when the Toad is being increased is the same as the
strain when the load is being decreased. Some matenals Rubber, for
example) are descnbed as nonlinearly elastic; in such cases, strain is
a single-valued function of stress, but the stres~strain curve is not a
straight line.
Elastic
/
cry
in
oh
111
en
. _,
/ ~ Elastic
L UP
Plastic ~
f
STRAIN
FIGURE 1 Deformation can be divided into elastic and plastic. The
stress-strain curve for an elastic material like glass is the same
during the loading and unloading portions of a complete cycle. Duc-
tile materials like many metals may be elastic until a yield stress,
oryx is reached. Plastic flow occurs at higher stresses, and the com-
plete curve describes a hysteresis loop with permanent strain sp.
OCR for page 89
Deformation and Fracture of Rock
89
The deformation of a large class of materials Most metals, for ex-
ample) is elastic for stresses less than the yield stress, and further
increases in load result in plastic deformation. In plastic deformation
the movement of dislocations allows whole planes of atoms to translate
relative to the adjacent plane, with the consequence that relatively
large strains occur for small changes in stress. The atomic planes do
not translate in the opposite sense when the Toad is lowered, and so
the stress-strain curve in the loading cycle is not the same as that
during the unloading cycle. A stress-strain curve for a material de-
fo~'ed into the plastic region is shown in Figure 1; note that the
specimen has undergone a permanent change in length.
The type of deformation that a sample undergoes depends on the
type of stresses applied, as well as on their magnitudes. The stresses
acting on a body can be considered to be the sum of two stress sys-
tems the hydrostatic component and the shear or deviatoric com-
ponent. Most materials, even ductile materials, are found to behave
elastically when only hydrostatic stresses are applied. Elastic materials
are those that behave elastically under both hydrostatic and deviatoric
stresses, whereas ductile materials undergo plastic deformation at de-
viatoric stresses greater than the yield stress.
When the load is increased to a sufficiently high level, a specimen
eventually fractures. Fracture also can be divided into subcategories
that include most engineering materials. "Brittle" failure is said to
have occurred when the fractured pieces can be fitted back together
that is, when the sample has undergone a negligible arno~,nt of per-
manent deformation before and during the fracture process. Glass, of
course, is a common example of a brittle material. A fracture is called
"ductile" when the sample undergoes an appreciable amount of plastic
flow before fracture. A relatively large amount of energy is absorbed
by materials that fail in this way, and so such materials are used where
toughness is important.
The type of fracture that occurs does not depend completely on the
material involved. The configuration of the specimen is important:
The presence of cracks and sharp notches tends to inhibit ductility
and, in extreme cases, ductile material can fail by brittle fracture. The
loading rate Once the temperature can also affect the type of fracture
that occurs, with high loading rates and low temperatures enhancing
the likelihood of brittle failure.
This brief discussion of deformation and fracture is intended to pro-
vide only a framework for describing the behavior of rock. Deformation
and fracture are well-developed scientific fields, and the paragraphs
OCR for page 90
90
CONSERVATION OF HISTORIC STONE BUILDINGS
here do not provide even an elementary introduction to these complex
processes. A comprehensive introduction to the subject can be found
in Mechanica] Behavior of Materialist
PROPERTIES OF ROCK
The pressures and temperatures of interest in building construction
are at the low end of the broad range of conditions that has been studied
in geology. Even in this restricted range, rock is found to have unusual
properties. The deformation cannot be characterized as either elastic
or plastic, and fracture involves elements of both brittle and ductile
behavior. Most of the minerals that make up rock are elastic, hard,
and brittle. Rock-forming minerals are hard and brittle because of the
low symmetry of their crystallographic structures. Dislocations cannot
move easily in these complicated structures, so plastic flow is almost
completely inhibited. One common mineral, calcite, of which marble
and limestone are composed, is exceptional in that it can be deformed
plastically along one crystallographic plane. However, calcite crystals
of most orientations cleave when stressed, and the overall behavior
must be classified as brittle.
The question, then, is how can rocks that are composed of elastic,
brittle crystals exhibit anything but elastic, brittle behavior?
DEFORMATION OF ROCK
The measurement of -the compressibility of a sample of rock is a stan-
dard test that-provides basic information about the rock's internal
structure. Typically, a specimen is sheathed with an impermeable
jacket and put in a pressure vessel. Strain gauges on the jacket, or
various other devices, are used to measure the decrease, TV, in the
volume, V, of the sample as the pressure, p, in the vessel is increased.
A curve of volumetric strain t^V/V) as a function of pressure is de-
veloped from these data, and compressibility, A, is calculated from the
inverse slope (^V/Vp) of the curve.
An example of a volumetric strain-pressure curve for a granite from
Westerly, R.I., is shown in Figure 2. Note that the curve is nonlinear.
At low pressure, the slope is relatively low; the slope increases with
increasing pressure until at a pressure of approximately 2 kbar (about
30,000 psi) the curve becomes linear. Note also that the curve relating
strain and pressure when pressure is decreased is virtually the same
as the curve when pressure is increased. Hysteresis is negligible, and
behavior is nonlinearly elastic.
OCR for page 91
Deformation and Fracture of Rock
6
5
4
Q
CC
an
~ 3
UJ
cr
cot
/
2
1 _
/
O ,/ 1 1 1 1 1
O -1 -2 -3 ~ -5
LINEAR STRAIN, 10-3
FIGURE 2 Volumetnc strain of a sample of Westerly granite as a
function of pressure. Note that this rock is nonlinearly elastic under
hydrostatic pressured
91
The generally accepted explanation for this behavior, which is ob-
served for virtually all types of rock, is that rock contains cracks. At
low pressure the cracks are open, and the rock is compliant. Cracks
close as the pressure is~increased, and the sample becomes stiffer. At
sufficiently high pressures, typically 2 kbar, all cracks are closed, and
the sample behaves like its constituent minerals, which are linearly
elastic.
The cracks found in rock arise from several natural causes. The
cooling of a rock after it has solidified creates thermal stresses that
are sufficient to fracture the crystalline framework. Likewise, micro-
cracking can result from the decrease in stress that a sample experi-
ences when it moves from its origin at depth to the surface or from
the increases in stress that occur during tectonic deformation.
OCR for page 92
92 CONSERVATION OF HISTORIC STONE BUILDINGS
The exsolution of gases dunng solidification or the imperfect sin-
tenng of grains, for example, also increases porosity. Pores are cavities
that are not cracklike (i.e., one dimension is not much smaller than
the others) and their effect on deformation is entirely different. Figure
3a shows a rock sample, containing both cracks and pores, under low
pressure. When sufficiently high pressure is applied, as in Figure 3b,
the cracks close, but the pores do not. Therefore, the nonlinearity in
the pressure-strain curve is caused by the cracks, not by the pores.
Effects of Cracks and Pores
Some progress has been made in evaluating quantitatively the relative
effects of cracks and pores on the elastic properties of rock (for a recent
review, see Walsh).3 Using techniques in the theory of elasticity, we
find that cracks have a very much greater effect on compliance than
do pores of equivalent volume. For example, spherical pores that con-
stitute a few percent of the volume of a sample cause an increase in
compressibility of a few percent. A crack is found theoretically to have
(a)
O.'
D .. a.....
1~'../ ~
.. . . .
.-
olN~ o
O ~ V
-_ Cracks
AT ZERO PRESSURE
Grain Boundaries
Pores
(b)
. .
a.. to
·-../ ::/
. . . .
-
\
/ \
\ \
UNDER CONFINING PRESSURE
FIGURE 3 A schematic description of the effect of confining pressure on cracks and
pores. Note that cracks close under pressure, whereas pores do not.
OCR for page 93
Deformation and Fracture of Rock
4.2
Q
u, 0.8
u'
us
A:
-
tn
in
UJ
~ 0.4
o
cow
o
+1.0
~ 1 1
//
//11
/
o
Ll NEAR STRAI N. 10-3
-1 .0 -2.0
FIGURE 4 Longitudinal and lateral strain of Westerly granite under
uniaxial compressions Note that the stres~strain curves are non-
linear and nonelastic.
93
nearly the same effect on compressibility as a pore of the same di-
ameter. The porosity associated with such a crack is negligibly small
compared with the pore, of course. A rule of thumb is that the effect
of cracks on elastic properties depends on the total surface area of the
crack phase bind is independent of its volume), whereas the effect of
pores is in direct proportion to the volume of the pore phase. The
compressibility of the Westerly granite sample in Figure 2, for example,
is 8.3 mbar- ~ at atmospheric pressure and 1.87 mbar- ~ at high pressure.
Cracks in this rock, which account for a porosity of only 0.5 percent,
have increased compressibility by a factor of nearly 6. The effect of
the pores in the sample, which account for a porosity of approximately
1 percent, is negligible.
Cracks also have a pronounced effect on the deformation of rock
when stresses other than hydrostatic pressure are applied. Figure 4
shows the longitudinal and lateral strain caused by increasing the
uniaxial compressive load on a cylindrical sample of Westerly granite.
Compare the longitudinal strain-stress curve in Figure 4 with the
volumetric strain-pressure curve in Figure 2. The slope of both curves
OCR for page 94
94
CONSERVATION OF HISTORIC STONE BUILDINGS
1
_. ~
J ,
— ~
FIGURE 5 A schematic description of the effect of sliding of crack faces against friction.
Note that slip does not occur immediately as the stress is lowered. A hysteresis loop
is formed, and the system undergoes permanent displacement.
increases with increasing stress. The reason for this is the same in
both cases: Increasing compressive stress or pressure causes cracks to
close, and the specimen becomes stiffer. Eventually all, or nearly all,
cracks close, and strain is a linear function of stress.
However, note in Figure 4 that the curve when the applied stress is
being decreased is not the same as when the stress is being increased,
in contrast to the response to hydrostatic-pressure changes in Figure
2. This behavior is typical of most rocks—that is, rocks are nonlinearly
elastic under hydrostatic-pressure changes and are nonelastic under
changes in deviatoric stress.
Cracks are responsible for the nonelasticity as well as for the non-
linearity of rocks. Cracks under changes in hydrostatic pressure merely
open and close. However, one side of a suitably oriented crack can
slide relative to the other side when the applied stresses contain a
OCR for page 95
Deformation and Fracture of Rock
95
deviatoric. component. This relative motion means that the longitu-
dinal strain of the sample is somewhat greater than the strain from
compression of the solid matrix; as a consequence, yo~,ng's modulus
(the slope clcr/~) of the ascending portion of the curve in Figure 4 is
less then Young's modulus for the mineral components.
The process is Illustrated schematically in Figure 5. Slip between
the faces of a microcrack in rock is physically similar to sliding a block
against friction on a plane. The spring in Figure 5 represents the elastic
element in the deformation owing to the mineral grains. Note that
the block does not irnrnediately begin to move in the opposite sense
when the load is decreased, much as a door forced against a wedge
must be yanked in the opposite direction to dislodge it. Consider the
situation at the highest stresses in Figure 5, where all cracks are closed
and those cracks that can slide are sliding. Using the analogy of a block
sliding on a plane, we see that all these cracks will be jarnrned when
the Toad initially is Towered;. The inference is that the initial slope of
the unloading curve in Figure 4 represents the response of only the
mineral components. The response of the minerals in the rock under
conditions in which cracks do not affect behavior can be measured in
other ways. We find that, indeed, the initial slope of the unloading
curve in Figure 4 represents an adequate approximation of the behavior
of intact rock: Young's modulus for intact rock is 730 kbar, and the
value from Figure 4 is 710 kbar.
Effects of Water and Temperature
The deformation of rock is influenced by factors in addition to stress.
The porosity in most rocks forms a phase that is largely interconnected.
As a result, rock in a wet environment becomes permeated with water.
The response to uniaxial stress of two sandstone samples, one of them
saturated with water and the other one dry, is shown in Figure 6. The
wet sample is more compliant than the dry one. The analogy of a block
sliding on a plain offers a plausible explanation for this behavior: Water
lubricates the microcracks, slip on cracks is facilitated, and conse-
quently compliance is increased.
Relatively small changes in temperature do not affect the defor-
mational characteristics of rock appreciably as long as the temperature
variations do not change the degree of fluid saturation. The elastic
properties of the constituent minerals do not vary with temperature
to an appreciable extent until the temperature reaches a level of ap-
proximately half the melting temperature (in keIvins); these temper-
atures are well above those that most building stone is subjected to
OCR for page 96
96
FIGURE 6 Stres~strain curves
for dry and wet sandstone sam-
ples. The wet sandstone is more
compliant than the dry.4
CONSERVATION OF HISTORIC STONE BUILDINGS
500
400
N
~ 300
-
cn
LL
cr
In
200
100
o
0 1 2
f
1
f f
Dry
Wet
5
3 4
-
STRAIN (x10-~)
under normal circumstances. Temperature changes of 20° C to 30° C,
however, are sufficient to cause measurable thermal cracking in com-
petent granites,4 thereby changing their compliance. Presumably, how-
ever, most building materials aIrea`dy will have been subjected to sea-
sonal changes of that magnitude during their history. Although
excursions in temperature beyond the range that the sample has ex-
OCR for page 97
Deformation and Fracture of Rock
97
perienced may cause cracking, repeated cycling to some given level
does not appear to have any cumulative effect.
FRACTURE OF RO CK
A specimen eventually fractures when the stress acting on it is raised
to sufficiently high levels. The stress at which fracture occurs depends
not only on the type of rock and its previous history but also on factors
such as the types of stresses that are applied, the degree of saturation
and pressure of the pore fluid, and the rate at which the load is applied.
Temperature change over the range experienced in building construc-
tion is not a factor of major importance in the discussion here.
Fracture research has benefited greatly in recent years from the de-
velopment of the scanning electron microscope. Photographs of the
interior of two samples of Westerly granite that were taken on a scan-
ning electron microscope are shown in Figure 7. Figure 7a shows cracks
that were produced by the applied stress at a level before the specimen
was completely fractured. The photomicrograph in Figure 7b illustrates
the damage produced by the applied stress approximately at the instant
of fracture. Note that fracture at the microscopic scale is a brittle
process. The crack surface in Figure 7a could be rejoined with virtually
no gaps remaining; the microshards in Figure 7b are angular, with none
of the rounded or stretched features typical of ductile fracture, ant]
presumably the tiny blocks could be rejoined, with sufficient patience,
to re-create the original state.
The cracks in these photographs have fractured individual mineral
crystals to produce the fracture pattern that we see. The fracture strength
of the rock, one might suppose, must be directly related to the strengths
of the minerals involved. The strengths of single crystals have been
investigated theoretically using several different approaches. In aD cases
the fracture strength, (a, is given approximately by the relationship:
~ _ cat, O
cry ~ E/10,
(1)
where E is Young's modulus. Young's modulus for quartz, for example,
to an order of magnitude, is 106 tears, 7 so the theoretical strength is
105 bars. The fracture strength of a quartz crystal is less than 104 bars
in compression and less than 103 bars in tension, and the values for
quartzite {polycrystalline quartz rock) are lower by a factor of 10.8 Why
is the measured strength so low?
Griffith was the first to explain the discrepancy.9 i0 He reasoned that
no material was perfect and that flaws in the form of tiny cracks could
OCR for page 98
98
CONSERVATION OF HISTORIC STONE BUILDINGS
FIGURE 7a A photornicrograph of Westerly granite at a stress well below
the fracture. strengths Note that cracks have begun to extend and that the.
fracture is- brittle.
OCR for page 99
Deformation and Fracture of Rock
50~
FIGURE 7b A photomicrograph of Westerly granite on the verge of fractured
Note that fracture on the microscale is brittle, although the stres~strain curve
has the characteristics of a ductile material.
99
OCR for page 100
100
CONSERVATION OF HISTORIC STONE BUILDINGS
be found in solid samples of any size. Using a theoretical analysis of
the stresses around cracks, he showed that the maximum stress, which
is found at the tip of a crack, is very much greater than the applied
stress. The stress, cry, required to break a specimen is therefore very
much less than the theoretical strength, cry, given by equation 1, needed
to extend the crack. Griffith's analysis showed that, in fact, the actual
strength should be Tower for materials having longer cracks. In an
elegant experiment using samples of smaller and smaller size, he ex-
trapolated to a sample of zero size (and zero crack length) and found
the theoretical strength to be in agreement with the value given by
equation 1.
Griffith's first analysis was restricted to fracture under tensile load-
ing, but he generalized the results in his second analysis to loading
under compressive states of stress. Griffith's theory showed that the
strength of brittle materials like rock in compression should be about
10 times the tensile strength. Further, his theory showed that the
compressive strength should rise dramatically when confining pressure
is superposed. These theoretical predictions have been verified, at least
in a general way, for rock and masonry materials by subsequent ex-
perimentation.
- Griffith's theory, although it describes in broad outline how the
strength of rock depends on the types of stresses applied, does not
accurately describe the fracture process itself.6 ~2 Griffith visualized
that fracture in compression occurs as it does in tension: Cracks are
inactive until- the fracture stress is reached, when the largest crack
grows across the specimen, separating it into two pieces. The stress-
strain curve for a rock sample in Figure 8 shows that this mode! cannot
be correct.
Figure 8 shows that the slope of the stress-strain curve first increases
as cracks close and then begins to decrease. The decrease in slope is
due to the growth of cracks in the sample. A careful examination of
stress-strain curves like that in Figure 8 shows that cracks begin to
extend when the applied stress is about one-~ird of the fracture strength.
The number and length of cracks increase as the applied load is in-
creased, and gradually the specimen is weakened until finally a fault
is formed, fracturing the sample. Fracture in compression, then, is a
complex process involving the growth and coalescence of many cracks.
The total nonelastic deformation that can be attributed to the growth
of cracks (and also the fracture strength) is found to increase with
increasing confining pressure. At sufficiently high confining pressures,
the stress-strain curves and the shape of the specimen cannot be dis-
tinguished from those for truly ductile materials, although the mech-
OCR for page 101
Deformation and Fracture of Rock
2.5
2.0
Q 1.5 _
In
In
UJ
1.0 _
0.5
o
'a?
/
/
/ 1 1 1
—.ooo
, 1—
STRAI N
FIGURE 8 A complete stres~stra~n curve for Westerly grarute under un~-
ax~al compression.
101
anism on the microscale in one is brittle failure and, in the other,
plastic flow.
Effects of Fluids
The pressure of fluid in the pores in the rock has a direct effect on
fracture strength. Theoretical analysis and laboratory experiments show
that pore pressure can be handed effectively by using the "law of
effective stress." The effective stress for fracture is given by the applied
stress less the pore pressure. The law of effective stress requires that
all combinations of applied stress and pore pressure that produce the
same effective stress must have the same effect on fracture. As a
consequence, the fracture strength for any value of pore pressure and
confining pressure can be found once the fracture strength has been
established for one set of conditions. An example of how strength and
effective stress are related can be found in Figure 9.
OCR for page 102
102
_~0
5 ~
20
15
1 10
~0
o
CONSERVATION OF HISTORIC STONE BUILDINGS
O Pp= 100b
O Pp = 300b
O Pp= 7.00b
o
2
4
As—Pp. kb
6
FIGURE 9 Compressive strengths for samples with different pore
pressures all fall on the same curve when plotted in terms of effective
stress.l1
to
OCR for page 103
Deformation and Fracture of Rock
103
Pore fluids con also affect strength indirectly. Some fluids, including
water, have a corrosive effect on rock-forming minerals. These fluids
weaken rock in two ways. The corrosive action in situations where
fluid can circulate through the pore and crack network gradually erodes
the passages and weakens the matrix. This mechanism is not partic-
ularly important when fluids of natural origin are involved, except
where the fluids are unusually corrosive to the rock minerals or the
fluid is unusually hot. Fluids are also found to affect strength through
a mechanism involving surface tension. The fracture strength of sam-
ples of a quartzitic shale is shown in Figure 10. Saturating rock with
a fluid having low surface tension increases its Toad-ca~rying capacity.
Another indirect way in which fluids affect strength involves the
permeability of the rock, the size of the sample, and the rate at which
the load is applied. Consider a large sample of a relatively impermeable
rock that is saturated with water, and assume that the load in the
sample is increased very quickly. Fluid in the rock, though it has access
to the outside, is trapped in the pores and cracks because of the low
permeability and the long path. The pore pressure rises, and the strength
decreases because of the law of effective pressure. Appreciable de-
creases in strength have been observed in the laboratory on samples
of granite as small as a few centimeters.~°
Size of Samples
Griffith's theory shows that specimens with long cracks have low
strength. This suggests that large samples may be weaker than small
samples because the probability that a sample contains a long crack
is greater for larger samples. The effect of size, which is a matter of
concern in manufacturing engineering practice where the range of sizes
is relatively small, could be a major factor where the strength of rock
is important because the range of interest can be enormous. A number
of studies on specimens having a range of sizes (of the order of 1 to 10
cm) suitable for experiments in the laboratory have demonstrated that
bigger samples of rock are indeed weaker than smaller ones. These
studies show that, in general, the weaker the rock, the larger the effect
of size on strength. The relationship between size and strength deter-
mined in these studies is usually expressed in the form
cry ~(size) -a'
/,2)
where a for strong rocks like competent marbles and granites is near
O.l-and, for a weaker rock like coal, is 0.5.
OCR for page 104
04
CONSERVATION OF HISTORIC STONE BUILDINGS
1 0,000 _
. _
.
a,
-
1 8,000
C)
cry 6,000
in
>
en
in
at: 4,000
o
Cal
X 2.000
he
,
o .
·. o
.
C) A
w
x
I
c
._
.O
A)
o
-
O ~
0 0.04 0.08 0.12 0.16
POUN DALS PE R FOOT
1 1 1 1
I I I ~ I I 1 1
0 10 20 30 40 50 60 70
DYNES PER CENTIMETER
SURFACE TENSION ~ OF IMMERSION LIQUIDS
AT 20 C (68° F ~
FIGURE 10 Compressive strengths of samples saturated with var-
ious fluids. Note that strength is high for fluids with low surface
tensions
The range of sizes used in these laboratory studies is barely in the
range of interest in building construction. Studies in the field on very
large specimens are rare because they are expensive and very difficult
to do. The very limited number of observations that have been made
on the strength of large samples suggests that equation 2 is valid only
for samples less than a critical size, and the strength of larger samples
is nearly the same. An example is shown in Figure 11.
Increasing the confining pressure tends to mitigate the effect of size.
Griffith's theory shows that weak rocks have large cracks, and the
above discussion of rock deformation demonstrates that cracks close
OCR for page 105
Deformation and Fracture of Rock
]50
100
70
50
30
20
15
~ 10
at:
z
7
5
4
Iron Ore
b°
~ Diorite
-\ ~
~ O\
— \ O\
~ ~ Jahns (1966}
o
Pratt et al. (1972)
,& Bieniawski (1968)
0 0.5 1.0 1.5 2.0
SPECIMEN SIDE LENGTH, m
105
2.5 3.0
FIGURE 11 The compressive strength of rock is found to be smaller for larger sam-
ples 15,16,17
under compressive stress. A large crack in a large sample that is closed
under confining pressure acts like a collection of small cracks. There-
fore, the strength of large samples and small samples under confining
pressure is closer than one would predict from an examination of their
microstructures at atmospheric pressure.
SUMMARY
I have tried here to describe in a concise way the major elements
affecting the deformation and fracture of rock. Rock is found to be an
unusual material in that it does not fall into one of the traditional
classifications of elastic and plastic, describing deformation, or brittle
and ductile, describing fracture. Behavior is governed to a large extent
by the porosity found in nearly all rock. The opening and closing of
cracks causes nonlinearity in stress-strain curves, and sliding between
the faces of cracks against friction is the source of the nonelastic
behavior observed under deviatoric stresses. Likewise, cracks weaken
OCR for page 106
106
CONSERVATION OF HISTORIC STONE BUILDINGS
rock and determine how strength vanes with applied stresses rock
is weak In tension once relatively strong In compression, and com-
pressive strength increases dramatically with confining pressure.
REFERENCES
1. F.A. McClintock and A.S. Argon, Mechanical Behavior of Matenals, Addison-
Wesley (Reading, Mass.), 1966.
2. J.B. Walsh, The effect of cracks on Poisson's ratio of rocks, I. Geophys. Res., 70~20),
5249-5258 (1965~.
3. J.B. Walsh, Static deformation of rock, [. Eng. Mech. Div., Proc. Amer. Soc. Civil
Eng., 106 (EMS), 1005-1019 ( 1980~.
(1957~.
4. M. Nishihara, Stres~strain relation of rocks, Dosh~sha Kogaka Kaiser, 8, 32-54
5. T.-F. Wong and W.F. Brace, Thermal expansion of rocks: Some measurements at
high pressure, Tectonophysics, (57) 95-1 17, 1979.
6. T.-F. Wong, Post-failure behavior of Westerly granite at elevated temperatures,
Ph.D. thesis, Massachusetts Institute of Technology, 1980, submitted to Int. I. Rock
Mech. Min. Sci., 1980.
7. F. Birch, Compressibility; elastic constants, Handbook of Physical Constants (S.P.
Clark, Jr., ed.), 97-173, 1966
8. J. Handin, Strength and ductility, Handbook of Physical Constants (S.P. Clark,
Jr., ed.J, 223-300, 1966.
9. A.A. Griffith, The phenomenon of flow and rupture in solids, Phil. Trans. R. Soc.
London, A221, 163-198, 1921.
10. A.A. Griffith, Theory of rupture, Proc. 1st Intl. Congr. Appl. Mech., Delft, 55-63,
1924.
11. W.F. Brace, personal communication, 1980.
12. F.A. McClintock and J.B. Walsh, Friction on Griffith cracks in rocks under pres-
sure, Proc. 4th U.S. Congr. Appl. Mech., 1015-1021, 1962.
13. P.S.B. Colback and B.L. Wild, The influence of moisture content in the com-
pressive strength of rock, Rock Mech. Sympos. 3rd), Univ. of Toronto, 65-83, 1965.
14. W.F. Brace and R.J. Martin m, A test of the law of effective stress for crystalline
rocks of low porosity, Int. J. Rock Mech. Min. Sci., 5, 415-426, 1968.
15. Z.T. Bieniawski, The effect of specimen size on the compressive strength of coal,
Int. I. Rock Mech. Min. Sci., 5, 325-335, 1968.
16. H. Jahns, Measunng the strength of rock in-situ at an increasing scale [in German],
Proc. 1st Congress, Int. Soc. Rock Mech., Lisbon, 1, 477-482, 1966.
17. H.R. Pratt, A.D. Black, W.S. Brown, and W.F. Brace, The effect of specimen size
on the mechanical properties of unjointed diorite, Int. I. Rock Mech. Min. Sci. 9, 51
529, 1972.
OCR for page 107
Deformation and Fracture of Rock
BIBLIO GRAPHY
lOJ
This short review does not do justice to these fields. Rock deformation and fracture
have received considerable attention in recent years, and the literature describing ex-
perimental and theoretical studies is too voluminous to be listed here. For those who
need to read further in the subject, however, the following texts will provide a good
starting point:
Jaeger, J.C., Elasticity' Fracture and Flow, Methuen (London and John Wiley {New
York), 1956.
Jaeger, J.C. and N.G.W. Cook, Fundamentals of Rock Mechanics, Methuen, London,
1969.
McClintock, F.A. and A.S. Argon, Mechanical Behavior of Materials, Addison-Wesley,
Reading, Mass., 1966.
Stagg, K.G. and C).C. Zienkiewicz, Rock Mechanics in Engineering Practice, John Wiley,
London, 1968.
Representative terms from entire chapter:
confining pressure
