Determination of Class I and Class II rocks from Conventional method based on the Mechanism of rock Deformation Process - Juniper publishers
Journal of Insights in Mining Science & Technology
Abstract
This
research work is intended to study the post-failure characteristic behaviour of
rocks and the techniques of controlling the post-failure regime based on the
mechanism of rocks deformation process. It is impossible to determine the
post-failure regime of rocks using conventional laboratory testing equipment.
As rock specimens are often in an unstable state at the point of failure as
most testing machines tend to be soft. Rock specimens break explosively at
their ultimate strength and no further information could be obtained. The only
practical means is the use of closed-loop servo-controlled system, which is
difficult to achieve. Stress-strain deformation tests were conducted using both
conventional and unconventional method (i.e. the closed loop servo-controlled
testing machine) in accordance to ISRM [1]. Normalised pre-failure curves were
constructed to show the stages in the deformation process. The author’s use of
normalised pre-failure curves enables identification of additional type of
deformation process with very brittle response under axial loading. The
difficulty in obtaining the post-failure curves increases as the total
volumetric strain approaches a positive value. In other words, difficulty in
obtaining the post-failure curves increases from the first type to the second
type and finally the additional third type deformation process. For the first
and second types, the four stages of deformation process are identifiable while
only three stages of deformation process could be identified with the third
type. It was practically impossible to determine the post-failure regime for
the third type as result of high accumulated strain energy. The first type
contains the Class I and progress to Class II with low strength soft brittle
rocks. The second type shows entirely Class II characteristic behaviour. The
third type is extremely brittle under axial loading, resulted in explosive
failure, so its class could not be determined. Testing the third type without
confinement could cause equipment damage. Identification of the deformation
process with the rock classes using conventional test could guide the personnel
conducting tests using closed-loop servo-controlled system, if dangerous
situation or equipment damage could occur (especially with the third type
deformation process) so that testing is performed safely. It could also be
useful in understanding the total process of specimen deformation, routine
determination of rock classes, and estimation of the rock’s brittleness (e.g.
brittle for Class II and less brittle or ductile for Class I).
Keywords: Post-failure; Pre-failure normalised curves; Conventional testing
equipment; Closed-loop servo-controlled system; Deformation
Introduction
There is difficulty with the laboratory determination of the
post-failure curve of rocks using conventional equipment. Rock specimens are
often in an unstable state at the point of failure as most testing machines
tend to be soft. Rock specimens break explosively at their ultimate strength
and no further information could be obtained. Simon et al. [2] observed that
the laboratory determination of the post-failure properties during uniaxial
compression test on brittle rocks is often difficult to realize. Shimizu et al.
[3] concurred that there are still complications in achieving post-failure
stress-strain curves of brittle rocks in the laboratory experiments. Javier
& Alejano [4] opined that significant success has not been achieved in
terms of methodologies for estimating reasonably good post-failure behaviour,
mainly due to the difficulties associated with defining a model that adequately
reflects observed complete stress–strain curves. However, Alejano et al. [5]
obtained quite reproducible post-failure results for unconfined compressive
tests in moderately weathered granite. Similarly, Brijes [6] presented
post-failure tests on coal and coal measure rock specimens obtained from various
coal mines in West Virginia and Hiawatha. Nonetheless, it is almost impossible
to obtain a good post failure curves on homogeneous hard brittle rocks without
explosive breakage in unconfined condition.
A closed loop
servo-controlled testing machine is the only practical way to avoid explosive
breakage of rock specimen when the ultimate strength is reached. Figure 1 shows
the principle of a closed loop, servo-controlled testing machine. A transducer
is attached to the rock specimen. It generates a signal that is compared with
the program instruction where constant strain rate or deformation is considered
as the control variable. If the transducer signal is not equal to the program
instruction value, the hydraulic system automatically adjust the servo-valve
until the transducer signal agrees with the program value. The efficiency of
the testing machine therefore depends on the capability of the servo-valve to
respond quickly enough to correct the error and prevent release of strain
energy after the peak strength of the rock is reached.
Figure 2 shows the pre-failure and post-failure stress-strain
curves that were obtained from a closed-loop servo-controlled testing machine.
Wawersik & Fairhurst [7] classified rocks into Class I and Class II
according to their failure behaviour in a uniaxial compression test. Beyond the
post-peak region, either the curve increases continuously in strain or it does
not. If it increases in strain, it is Class I, if it does not, then it is a
Class II rock. He et al. [8] demonstrated that the striking difference between
Class I and Class II types was the increase in non-elastic strain. Both Class I
and Class II rocks tend to decrease in elastic strain in the post-failure
region with a decrease in the load-bearing capacity. They showed that the
difference between Class I and Class II was the magnitude of the non-elastic
strain. In other words, if the decrease in elastic strain is accompanied by a
faster increase in non-elastic strain, the rock demonstrates Class I, otherwise
it shows Class II behaviour.
The
research question, therefore, is it possible to identify rock classes from
conventional testing results? This research therefore intended to study the
possibility of identifying the rock classes (Class I or Class II) based on the
rocks’ deformation process studied from normalised axial stress-volumetric
strain curves using tests result from conventional machine. A closed loop
servo-controlled testing machine which is the only practical way to determine
rock classes is a difficult test to perform (requiring enough personnel
training and vigorous specimen preparation). The use of conventional test to
classify rocks (into Class I or Class II) will be useful in understanding the
total process of specimen deformation and in the routine determination of rock
classes. In addition, it would be helpful in the estimation of the rock’s
brittleness (e.g. brittle for Class II and less brittle or ductile for Class I)
since the post-failure part is the part that characterizes the brittle
behaviour of a rock.
Similarly, the knowledge of the
post-peak behaviour of rocks will assist in the evaluation of the potential
failure of an excavation and the rock burst potential near underground openings
(e.g. Class I failure gradual, Class II failure explosive). Identification of these
deformation processes with their rock classes could
guide the personnel
conducting tests with closed-loop servo-controlled system, if
dangerous situation or equipment damage could occur so that testing is
performed safely.
Literature review
Deformation
and fracture characteristics of brittle rock have been studied by many
researchers [7,9,10]. The common agreement among them is that the failure
process occurs in stages. The stages are determined from stress-strain
characteristic curves obtained from axial and lateral deformation measurements
during laboratory uniaxial compression test.
Brace
et al. [11] & Bieniawski [12] evaluated stress-strain behaviour of a
deformed material and classified the deformation steps in the brittle fracture
process (Figure 3) as follows:
a) Closing of cracks
(or crack closure) (stage I),
b) Linear elastic
deformation (or fracture initiation) (stage II),
c) Stable fracture
propagation (or Critical energy release) (stage III),
d) Unstable fracture
propagation (or material failure) (stage 1V) and
e) Failure and
post-failure behaviour (or structure failure) (stage V).
In order to evaluate
the stages of deformation in rocks, Martin [13] conducted uniaxial compression
tests on cylindrical samples of continuous, homogenous, isotropic, linear and
elastic (CHILE) massive Lac du Bonnet Granite obtained from the Underground
Research Laboratory (URL) at 420m below ground surface. The test was carried
out to identity a suitable site for the disposal of radioactive wastes. The
stages in the failure process are identified in the stress-strain curves
(Figure 3).
Similarly, a study of compression
tests on two South African hard rocks, namely a Norite (igneous rock) and
Quartzite (metamorphosed sedimentary rock) was done in “order to eliminate, for
the purpose of” the “investigation, the influence of non-homogeneity and
anisotropy on the mechanism of rock” failure [9] (Figure 4). It shows similar
steps in the failure process (Figure 3). The steps in the failure process in
Figures 3 & 4 are discussed next.
Crack closure occurs during the early stage of loading (crack
closure corresponds to Stage 1 in Figures 3 & 4). At this stage, the stress-strain
curve is slightly inclined towards the axial strain. As a result, the
pre-existing cracks inclined to the applied load are closed [14]. At the crack
closure stage, the stress-strain curve is nonlinear and expresses an increase
in axial stiffness (i.e. deformation modulus). The size of this nonlinearity
depends “on the initial crack density and geometrical characteristics of the
crack population” [14]. After the bulk of pre-existing cracks are closed,
linear elastic deformation takes place. During the elastic deformation stage,
the relationship between stress-strain curves is linear (Stage II in Figures 3
& 4). The elastic constants (Young’s modulus, Poisson’s ratio) of the rocks
are estimated from this linear portion of the stress-strain curve. Crack
initiation stress (Figure 4) represents the stress level when micro-fracturing
begins. Zhang et al. [15] defined crack initiation as the stress level that
marks the start of dilation and crack propagation.
Besides, crack propagation is considered as either stable or
unstable [13]. Stable crack (fracture) propagation begins at the end of Stage
II while unstable propagation starts at Stage IV. At Stage III, cracks increase
by a small quantity as a result of an increase in stress, but these do not
continue to extend in this stage to form macroscopic failure. At this stage
(Stage III) fracture propagation is a function of the applied stress. At the
beginning of crack propagation, it obeys Griffith’s criteria in Equation 1.
During the stable condition, crack development can be arrested by the removal
of the applied stress. On the other hand, unstable crack growth occurs at the
point of reversal of the volumetric strain curve (Figures 3 & 4). This
stage is known as the point of critical energy release or crack-damaged stress
threshold [13]. Bieniawski [16] defined unstable crack propagation as the
condition which occurs when the relationship between the applied stress and the
crack length ceases to exist. Therefore, this is when the crack growth
velocity, takes over in the propagation process. Unstable fracture propagation
starts when the strain energy release rate in Equation 1 attains a critical
value [17]. The cracks continue to extend because of the strain energy stored
within the specimen.
In addition, the velocity
of the crack propagation increases from Stage III and reaches its maximum
(terminal velocity) at Stage IV (Figure 4). In the opinion of Craggs [18], as
crack velocity increases, the force needed to uphold crack propagation
decreases. Using Craggs analysis Bieniawski [9] claimed that at the onset of
unstable fracture propagation, the fracture process is self-sustaining until
failure. According to Robert and Wells [19]; Dulaney and Brace [20]; and
Bieniawski [9], the terminal velocity is given by:
Where VT is the
terminal velocity; E is the modulus of elasticity and ρ is the density of the
rock. Also, the increase in velocity causes a general increase in volume
(dilation). Figure 5 shows dilatancy in Quartzite under uniaxial compression
test. Using dilatancy, failure process was grouped into regions [21] (Figure
5). Yathavan & Stacey [22] summarized the procedure for obtaining the stages
of the deformation process from laboratory tests, as shown in Table 1. This
summary is adopted in this work to plot the stress-strain curves and to
identify the stages of the deformation process.
Method for
Determining Axial Stress-Volumetric Strain Curves
Stress-strain
curves were determined for different 18 rocks types (ranging from soft Quartz
Arenite of 35 MPa to Quartzite2 of about 514 MPa; and with different rock
types, igneous, sedimentary and metamorphic) in unconfined uniaxial compression
test using conventional Amsler rock testing machine in accordance to ISRM [1].
Stress-axial, radial and total volumetric strain curves were constructed
according to Martin & Chandler [10] and Bieniawski [21] to show the stages
in the deformation process (Table 1) and group them into the different
deformation process.
Method
for the determination of post-failure regime of rocks in uniaxial compression
During
the uniaxial compression testing to determine the post-failure stress-strain
curves using the servo-controlled testing machine, the following control steps
were employed: The axial extensometer was installed at 1200 apart and contacts
the specimen at 25% and 75% of its full length while the circumferential
extensometer was located at mid-height of the specimen. The specimen was then
installed on the lower platen of the load unit assembly. A small preload was
applied with the force cell drive to contact the specimen in force control mode
using the output of the axial force as the feedback signal. This made the
specimen ‘seat’ to the lower loading platen and the upper loading platen
becomes spherically seated. The readings of both axial, radial extensometer and
axial force were reset to zero. Ductile (i.e. less brittle) specimens were
continuously loaded at an axial strain rate of 0.001mm/mm/sec. This was
continued up to 70% of the predetermined peak load of the specimen determined
using the conventional method. After this point the loading rate was reduced by
switching to a lower strain rate of 0.000001 mm/mm/sec. The loading continued
at an axial strain rate of 0.000001 mm/mm/sec until the applied load drops
close to 50% of its peak load. At this point, a post-failure load-deformation
curve was obtained.
In the case of
specimens with a brittle behaviour (i.e. Class II), the control switch over
method is as follows. The control mode was switched from axial force to axial
strain control mode. The specimens were continuously loaded at an axial strain
rate of 0.001 mm/mm/sec. This was continued up to 70% of the predetermined peak
load of the specimen. At 70% of peak load, instead of a slower or reduced axial
strain rate, the control mode was switched to circumferential control mode at a
rate of 0.0001mm/mm/sec. This continued until the applied load reduces to about
50% of peak load. At this point a post-failure load-deformation curve was
obtained. Five tests were performed per each rock type and the average result
reported.
Results and
Discussion
The author use of
normalised pre-failure curves enables identification of another type of
deformation process with very brittle response under axial loading in
additional to Martin & Chandler [10] and Bieniawski [12]. Together there
are three types of deformation process. The first type has a negative total volumetric
strain and with a point of reversal at crack damage stress. The second type has
positive total volumetric strain with reversal point at crack-damaged stress
and the third type has a positive total volumetric strain without a reversal
point. Relationships exist among the different volumetric strain curves [23].
The difficulty in obtaining the post-failure curves increases as the total
volumetric strain approaches a positive value. In other words, difficulty in
obtaining the post-failure curves increases from the first type to the second
type and finally the third type. For the first and second types, the four
stages of deformation process are identifiable while only three stages of
deformation process are identifiable with the third type. For rocks that exhibit
the first type of deformation process, the normalised stress-axial, radial and
total volumetric strain curves and post-failure curves are shown in Figures 6-9
as example for the type. The post-failure stress-strain curves for this type of
rock was relatively easy to perform.
Figures 10 & 11
show the second type and the stages of deformation process. For this type of
stress-axial, radial and total volumetric strain curves, the process of
unstable crack propagation (stage IV) has a small duration and for this reason
cracks propagate by their own accord. Thus, the rocks exhibit a higher velocity
of micro-crack propagation. This made it difficult to control the post-failure
curves than the type one stress-axial, radial and total volumetric strain
curves because of the short duration of the crack damage stress threshold to
rupture. The normalized stress-axial, radial and total volumetric strain curves
and the post-failure curves are shown in Figures 10-13. For the third type of
stress-axial, radial and total volumetric strain curves, the crack induced
stress and the structural failure of the rock specimen occurred together
(Figures 14-16). There was no reversal of the total volumetric strain so there
was continued decrease in rock volume. The control feedback, the circumferential
strain, does not continuously increase with the applied load after the peak
load. Instead, the deformation became a self-sustaining failure and, as a
result the micro-cracking of the material continued its own accord.
Furthermore, unstable crack growth occurs at the onset of the crack initiation
stress. The critical energy release rate or crack damage stress threshold
started much earlier for this type of curve than observed with others. Under
this condition, the relationship between the applied stress and the crack
length ceases to exist and other parameters, such as the crack growth velocity,
take control of the propagation process.
Conclusion
This work has demonstrated the possibility of using results from
conventional laboratory equipment to be classified rocks into Class I and Class
II with the use of deformation process of rocks constructed according to Martin
& Chandler [10] and Bieniawski [21]. It is therefore possible to have
knowledge of the post-failure regime of rocks using conventional testing
system. Three types of deformation curves were identified. The first type has a
negative total volumetric strain and with a point of reversal at crack damage
stress. The second type has positive total volumetric strain with reversal
point at crack-damaged stress and the additional third type has a positive
total volumetric strain without a reversal point. The difficulty in obtaining
the post-failure curves using close-loop system increases as the pre-failure
total volumetric strain approaches a positive value. In other words, difficulty
in obtaining the post-failure curves increases from the first type to the
second type and finally the third type. For the first and second types, the
four stages of deformation process are identifiable while only three stages of
deformation process could be identified with the third type. The first type
contains the Class I and progress to Class II with low strength brittle soft
rocks e.g. Quartz Arenite. The second type is entirely Class II rocks.
Identification of the deformation process could guide the personnel conducting
tests using closed-loop servo-controlled system, if dangerous situation or
equipment damage could occur especially with the third type deformation process
so that testing is performed safely. In addition, could be useful for
understanding the total process of specimen deformation and routine
determination of rock classes. It could indicate rocks brittleness (e.g.
brittle for Class II and less brittle or ductile for Class I) since the
post-failure part is the part that characterizes the brittle behaviour of a
rock. Moreover, the knowledge of the post-peak behaviour of rocks will assist
in the evaluation of the potential failure of an excavation and the rock burst
potential near underground openings (e.g. Class I failure gradual, Class II
failure explosive) [24].
Further
Research
Further research could be initiated to study the normalised pre-failure
curves to serve as a measure of rocks brittleness potential and for predicting
fragmentation. As it has been shown that there is a connection between
obtaining the post-failure curves and the total volumetric strain approaches a
positive value, therefore the total volumetric strain may be explore for
predicting/estimating post-failure moduli of rocks. In addition, such research
could study the first type of deformation process in order to demarcate
precisely the line between the rocks that contains the Class I and low strength
soft brittle Class II rocks. Additionally, research could be initiated to study
various sensor guidance technologies that could improve the control performance
of closed-loop servo-controlled testing system for post-failure determination
of very brittle rocks. Sensor based programmable systems such as laser
scanning, infrared (IR), ultrasonic and high speed micro-acoustic sensors etc.
could be explore for reliably and safely operating control of the third type of
deformation process with very brittle response under axial loading.
Acknowledgment
This article is a
part of a PhD thesis approved by The University of the Witwatersrand South
Africa. The School of Mining Engineering, University of the Witwatersrand South
Africa is acknowledged for providing support towards the success of this
research. Specifically, the Centennial Trust Fund for Rock Engineering is appreciated
for funding part of this research. Rock Engineering Department, Aalto
University Finland is equally acknowledged for allowing part of the work to be
done there.
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