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ISSN 2411-3336: e-ISSN 2541-9404
Research article UDC 620.17
Evaluation of deformation characteristics of brittle rocks beyond the limit of strength in the mode of uniaxial servohydraulic loading
Alexander P. GOSPODARIKOV1, Andrey V. TROFIMOV2, Alexander P. KIRKIN1 H
1 Saint Petersburg Mining University, Saint Petersburg, Russia
2 OOO Gipronikel Institute, Saint Petersburg, Russia
How to cite this article: Gospodarikov A.P., Trofimov A.V., Kirkin A.P. Evaluation of deformation characteristics of brittle rocks beyond the limit of strength in the mode of uniaxial servohydraulic loading. Journal of Mining Institute. 2022. Vol. 256, p. 539-548. DOI: 10.31897/PMI.2022.87
Abstract. One of the most reliable methods for assessing the physical and mechanical properties of rocks as a result of their destruction are laboratory tests using hard or servo-driven test presses. They allow to obtain reliable information about changes in these properties beyond the limit of compressive strength. The results of laboratory tests of rich sulfide ore samples are presented, which made it possible to obtain graphs of their extreme deformation. Both monolithic samples and samples with stress concentrators in the form of circular holes with a diameter of 3, 5 and 10 mm were tested. It was revealed that during the destruction of the samples, the modules of elasticity and deformation decrease by 1.5-2 times, and in the zone of residual strength - by 5-7 times.
Keywords: physical and mechanical properties; laboratory tests; extreme deformation; servohydraulic test presses; lateral deformations; modulus of elasticity; modulus of deformation
Received: 20.06.2022 Accepted: 07.10.2022 Online: 03.11.2022 Published: 03.11.2022
Introduction. With an increase in the productivity of underground mining deposits development, in order to maintain the pace of production, it is necessary to open up new horizons, which are often deeper than existing ones. With an increase in the depth of development, the risks of complication of the geotechnical situation increase [1-3], which can manifest themselves in the form of increased rock pressure, including in a dynamic form [4-6]. For example, the depth of development of the Talnakh mines in some areas reaches more than 1000 m with a critical depth of rock-burst hazard of 700 m [7-9]. Accordingly, at such great depths and high stress values, the destruction of the marginal part is characteristic for the rock mass. It manifests itself potentially in a brittle form with the release of elastic energy in the form of a rock burst. Pillars become especially dangerous, since they take on an increased load from the overlying rock strata. In this case, shock-proof measures are used, the purpose of which is to form a local zone of compliance by inducing fracturing by a blasting method [10-12] or by gradual destruction of rocks caused by drilling a line of discharge wells [13, 14]. However, it is quite difficult to assess the change in the physical and mechanical properties of rocks in the resulting zones of compliance. Standard laboratory tests within the framework of GOST standards are aimed at studying the properties of only monolithic rocks, and the assessment of the rock mass disturbance by rating systems focuses more on natural fracturing [15-17]. One of the ways to estimate the change in the modulus of elasticity is to determine the velocity of propagation of longitudinal waves before/after the destruction of the rock mass [18, 19]. But the solution of such a problem may be complicated by the impossibility of elastic wave propagation through the destroyed areas of the rock mass.
With the widespread development of computer technologies, the use of mathematical modeling based on effective numerical methods of finite or discrete elements is prevalent [20-22]. The elastic-plastic models implemented in them make it possible to obtain information (with some assumptions) about the state of the rock mass (pillars) and the redistribution of stresses in it as a result of the destruction of the latter. However, reliable data on the properties of the material is needed to build adequate geome-chanical models. So, for ideal elastic-plastic models, it is necessary to know the following parameters: adhesion and the angle of internal friction (or the limits of tensile and compressive strength), modulus of elasticity, Poisson's ratio. For geomechanical models with residual strength, it is necessary to have an idea of the residual strength of rocks. For example, when using the RS2 (Rocscience) program, when developing an elastic-plastic model taking into account the Coulomb - Mohr criterion with residual strength, data from the passport of the residual strength of rocks are required [23, 24]. The frequently used Hook - Brown strength criterion additionally requires workings mapping data to assess the disturbance of the rock mass [25-27]. Therefore, the necessary initial data can be obtained only as a result of laboratory tests and field studies.
It is possible to evaluate the process of rock destruction only when modeling loading close to real conditions. For this purpose, it is possible to conduct sample preparation of cubic or cylindrical shape samples, to test under uniaxial compression conditions in accordance with GOST 21153.2 "Rocks. Methods for determining the ultimate strength in uniaxial compression". But in this case, the elastic energy accumulated by the press is released, which leads to the destruction of the sample with the fragments distribution. To avoid this, it is necessary to carry out tests on hard or servo-driven presses. In this case, it is possible to get a complete picture of the destruction of samples with the determination of the values of deformations beyond the strength limit of the rock. The methodological bases of such tests are presented in [28-30]. The presented methods have found their application for assessing the rock-burst hazard [31-33]. Such types of tests are very difficult to implement and require modern technological equipment.
A feature of testing on servo-driven presses is also the control of the growth rate of transverse deformations values, and, consequently, obtaining "loops" of decline and loading when leveling the deformation rate of the sample. However, this type of testing is laborious and time-consuming. Thus, in [30] it is indicated that when 70 % of the limit of strength is reached, it is necessary to control the loading by the values of transverse deformations, and the speed of loading by the press should ensure their growth rate of no more than 0.0001 mm/mm/s. A relatively easy-to-implement approach to assessing residual strength is presented in [34], which is more suitable for evaluating the rock mass of sides of open-pits than for underground mining conditions. This paper presents the results of tests for extreme deformation of rich sulfide ores of the Norilsk Industrial district to determine changes in deformation characteristics in the process of destruction. The absence of significant fracturing in the ore rock mass (Fig. 1), combined with high hardness and a high brittleness coefficient (the ratio of the compressive
0 10 20 30 40 50 60 70 80 90 100
Fig. 1. Core of rich sulfide ore in contact with gabbro-dolerites 1 - mechanical damage to the core; 2 - natural cracks
strength to the tensile strength), ranging from 9-12 with low values of the compressive strength in the image, make this type of ore rock-burst hazardous.
Methodology. Samples from a core of rich sulfide ore were prepared for testing, the diameter of which was 45±1 mm, the ratio of the sample height to diameter was 2:1. The samples were weighed, and non-destructive tests were carried out on them (determination of the propagation velocities of longitudinal and transverse waves and deformation characteristics). Deformation characteristics were determined using GOST 28985 "Rocks. Method for determining deformation characteristics under uniaxial compression" on the H100KU press, using LVDT sensors with an accuracy of 0.5 microns to assess changes in the measurement base during loading/unloading of the sample. In some samples, stress concentrators were created in the form of holes in the center of the longitudinal section of the sample. Samples were considered: standard cylindrical (without holes); with a hole 03; 5; 10 mm; with two holes 05 mm. Additionally, samples were made with two holes of 05 mm and a transverse crack simulating the unloading zone passing through these holes. The distance between the holes was assumed to be three of their diameters. After drilling, the samples with holes were repeatedly tested to determine the deformation characteristics (Young's modules and deformations).
For samples with a single hole of 03 and 5 mm, the results of repeated tests did not have significant discrepancies with the initial tests, which is explained by the different measurement base and the installation of sensors at different points. The initial data were accepted. The results of nondestructive testing of samples are presented in Table 1.
Table 1
Physical and mechanical properties of rocks before testing
Diameter, mm Height, mm Modulus of deformation, MPa Modulus of elasticity, MPa Modulus of deformation (holes), MPa Modulus of elasticity (holes), MPa Coefficient of transverse deformation Poisson's ratio Hole
44.62 90.65 48400 56700 48400 56700 0.148 0.143
44.54 87.67 65300 68600 65300 68600 0.218 0.187
44.63 87.99 60500 64000 60500 64000 0.249 0.246
44.58 91.92 40300 45300 40300 45300 0.198 0.158 Without holes
44.80 89.26 38500 44400 38500 44400 0.127 0.117
44.96 89.53 34100 37700 34100 37700 0.186 0.140
44.94 89.80 52200 52300 52200 52300 0.201 0.201
44.47 89.12 59200 61300 59200 61300 0.202 0.202
44.63 86.48 31900 36700 31900 36700 0.151 0.151
44.62 89.12 66100 72100 66100 72100 0.203 0.194 One hole 03 mm
44.34 90.68 64100 64800 64100 64800 0.229 0.221
44.25 88.79 30300 36000 30300 36000 0.154 0.166
44.74 89.55 66700 71200 66700 71200 0.224 0.219
44.61 87.53 58400 62700 58400 62700 0.205 0.201 One hole 05 mm
44.67 89.72 79000 80800 79000 80800 0.155 0.140
44.58 87.45 65000 66600 61000 62500 0.206 0.192
44.74 88.58 81900 82200 78000 78300 0.201 0.198
44.66 88.88 50800 54100 42700 45500 0.122 0.119 One hole
44.95 90.5 43600 49300 36600 41400 0.149 0.172 010 mm
44.75 89.17 50100 58000 42200 47500 0.173 0.170
44.64 88.27 63400 74800 59400 69500 0.185 0.177
44.61 87.71 48600 52200 44200 47500 0.172 0.172
44.69 87.99 76300 76900 63100 63600 0.203 0.194
44.65 88.71 40900 44100 24900 32800 0.141 0.148 Two holes
44.94 91.24 53900 59200 49700 54300 0.200 0.206 05 mm
44.54 89.70 72900 76000 61100 67400 0.151 0.138
44.62 88.76 57300 65000 45900 52700 0.171 0.136
44.65 89.35 56200 64300 32200 43600 0.118 0.102
45.00 89.18 38100 45000 32100 38300 0.14 0.136
44.92 89.81 37300 40800 31800 31400 0.172 0.172 Two holes 05 mm
44.93 90.2 39400 46600 32900 40100 0.176 0.178 + transverse crack
44.77 89.55 44600 56900 35800 43100 0.171 0.181
44.71 86.65 31000* 37400* 10200 - - -
* The initial deformation characteristics of the sample were determined taking into account the transverse crack obtained as a result of sample preparation.
Fig.2. Testing: a - stress - strain graph with "loops" of unloading and loading; b - Epsilon longitudinal and transverse strain extensometers; c - test installation; d - loading graph with "loops" formed by software "Horizont" 1 - "loops"; 2 - movements of the radial extensometer; 3 - movements of the longitudinal extensometer
The methodological basis for determining the modulus of elasticity of a weakened sample was section VI "Assessment of the rock-burst hazard on the brittleness of rocks by means of extreme deformation" of the Methodological Recommendations for assessing the propensity of ore and non-ore deposits to rock bursts. For the tests, a test servo-controlled press TO Super L60 with a maximum load of 300 kN was used. The servo drive allows the testing machine to equalize the load in accordance with a constant deformation rate, which is analogous to the loading mode on hard test presses. A feature of loading with the help of a servo drive is the construction of characteristic "loops" of sharp decline and loading to equalize the rate of deformation with smooth destruction of the sample (Fig.2, a).
In order to obtain a clear decline curve (extreme deformation), the control of maintaining a given deformation rate was carried out by transverse deformations, which made it possible at an early stage to fix the growth of cracks and an increase in cross-section due to dilatancy and prevent the destruction of the sample by elastic energy. Deformations were measured by strain gauges extensometers specialized for testing rocks: transverse - Epsilon 3544-100M-060M-HT2, longitudinal - Epsilon 3542RA2- 100M-600M-HT2 (Fig.2, b).
The measurement base of the longitudinal sensors is constant and was equal to 100 mm. Longitudinal deformation was controlled by steel punches, between which a sample was installed (Fig.2, c). When the sample is destroyed, the individual parts formed during the formation of new surfaces experience movements in unpredictable directions and can move relative to each other without reflecting the
0.00005 0.0001 0.00015 0.0002 0.00025 Deformation, mm/mm
b 120
100
80
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s
60
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00 40
20
0
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3 •
y = 7477430.57x2 + 24960.17x-0.89 .
R2 = 1.00
V'
0.0005 0.001 0.0015 0.002 0.0025 Deformation, mm/mm
0.0008
0.0007
s e 0.0006
e e 0.0005
e 0.0004
0.0003
<2 0.0002
Q 0.0001
0.0000
y = 0.0001285977x°-3926718162 .. ■
R2 = 0.98
» •
7
20
40 60 Stress, MPa
80
100
100 90 80 70 60 50 40 30 20 10 0
• — —•—
• • • —•—
} •
} Q
a*
T • 10
M • • • 11
m —
0.0005 0.001 0.0015 0.002 0.0025 Deformation, mm/mm
a
d
c
4
0
Fig.3. Determination of the calibration function: a - initial test (LVDT) on the loading curve; b - test for extreme deformation (elastic section); c - finding the approximation dependence; d - comparison of the experimental data and the obtained approximation
1 - loading curve (Epsilon); 2 - loading curve (approximation); 3 - polynomial loading curve (Epsilon); 4 - experimental curve (30-90 MPa); 5 - approximation; 6 - experimental curve (0-90 MPa); 7 - power experimental curve (30-90 MPa); 8 - deformations (LVDT); 9 - deformations (Epsilon); 10 - deformation difference (experimental curve); 11 - deformation
difference (approximation)
general direction of deformation. The resulting type of destruction is compressive deformation. For its reliable registration, it is necessary to install a longitudinal extensometer on load plates (punches). This approach reduces the distortion of the measurement results when the sample is destroyed, since it eliminates the loss of contact of the extensometer with the surface. In this case, additional deformations occurring at the contact of the end surface of the sample and the punch are recorded. When interpreting the measurement results, this effect must be taken into account, especially in the area of elastic deformations, where the movements are relatively small.
The creation of the test methodology and process control took place through the shell of the specialized software "Horizon" (Fig.2, d), supplied together with the presses TO Super L60. The first stage of testing: compression of the sample at a constant rate of transverse deformations change (changes in the circumference of the sample) 0.02-0.04 mm/min. The calculation of the rate of change in the values of transverse deformations was carried out by recalculation from the loading rate of the sample in 0.1 mm/min. This loading rate is typical for testing rock-burst hazard rocks [35, 36].
After significant destruction of the sample and failure to achieve residual strength, the second (third, if necessary) stage of testing was carried out with an increased loading speed by 2-3 times, since in this case brittle destruction is no longer possible, and an increase in the loading speed only reduces the time of testing.
The values of longitudinal movements were used to analyze the results obtained. The elastic and deformation modulus were determined at the deformation sites beyond the tensile strength at the moments when the servo drive of the press equalized the deformation rate of the sample and formed "loops" of sharp decline and loading on the graph.
140000 120000 100000 80000 60000 40000 20000 0
•it
.V if
0.00 0.10 0.20 0.30 Movement, mm
0.40
0.50
90 80 70 60
Ph
S 50 t/i 2 40
30 20 10
0
0.000
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If"' !7f'£!ftf
U Mr/J
•• • fi • r / / tf • • • • •
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0.001 0.002 0.003 0.004 Deformation, mm/mm
0.005
Fig.4. Test graphs: a - initial (load - movement); b - stress - deformation before/after calibration
1 - initial graph; 2 - calibration
b
a
Calibration of test graphs. Since movements between loading punches were measured using longitudinal extensometers, the results could be distorted due to the fixation of additional deformations at the ends of the samples, which led to an underestimation of the values of elastic and deformation modulus. Moreover, the difference in values logically increased with increasing hardness of the sample.
To cut off unnecessary deformations, the graphs were calibrated according to the elasticity zone (Fig.3). The calibration assumes that the deviation As is a function off(P), where P is the load on the sample, MPa.
To identify this dependence, the approximating functions of the load branches were determined during the initial determination of deformation characteristics (in the case of samples with holes, the determination of deformation characteristics after drilling) using LVDT sensors (deformations (LVDT) and in the elastic zone during the test for extreme deformation (deformation (Epsilon). The values of deformations on the approximated curves are revealed at the same stress values, the values of As are calculated, which is the difference between Epsilon and LVDT deformations, "stress -deformation" graphs are constructed. The greatest convergence was achieved when approximated by a power function.
Calibration of the complete deformation graph was carried out individually for each sample in the required stress interval, therefore, the power approximation of the "stress - deformation" graph (Fig.3, c) is unique in each case. The recalculation of deformations was carried out according to the formula
Scalibr = SEps "As (P ) , (1)
where sEps - deformations (Epsilon), mm/mm; As (P) - a power function of the type As = AP8,
mm/mm; P - the stress in the sample caused by the press load, MPa; A and B - empirical coefficients. An example of processing the test graph of one of the samples is shown in Fig.4.
After calibration of the graphs, the elastic and deformation modulus were estimated. In cases where the sample was tested in several stages, in the presence of "loops" of unloading and loading on the shelf of residual strength, the elastic and deformation modulus were determined in these areas.
Results discussion. The results of determining the values of elastic and deformation modulus after calibration are presented in Table 2. However, for some samples, it was not possible to identify the "loops" of unloading and loading.
Table 2
Physical and mechanical properties of samples after testing
Holes Modulus of deformation (with holes) Edi, MPa Modulus of elasticity (with holes) Eei, MPa Modulus of deformation (with holes) Epsilon Ed2, MPa Modulus of deformation (with holes) calibrated ED3, MPa Modulus of deformation during weakening Ed4, MPa Modulus of elasticity during weakening Ee4, MPa q q w 3 w w Uniaxial compressive strength, MPa Residual strength, MPa
No 48400 56700 25200 46000 7109 11219 6.81 5.05 42.83 3.2
No 65300 68600 33800 65100 17264 27047 3.78 2.54 63.24 -
No 60500 64000 45800 65300 30397 46038 1.99 1.39 87.27 -
No 40300 45300 31700 37200 - - - - 70.88 -
No 38500 44400 33700 38600 33598 38393 1.15 1.16 71.96 3.4
No 34100 37700 32000 35900 25136 25760 1.36 1.46 66.08 1.96
No 52200 52300 47400 54800 8388 12402 6.22 4.22 95.54 5.4
One (3 mm) 59200 61300 33400 47200 10349 11569 5.72 5.3 49.81 2.5
One (3 mm) 31900 36700 22300 33100 9173 8220 3.48 4.46 53.96 3.2
One (3 mm) 66100 72100 26400 63900 36444 21045 1.81 3.43 49.88 3.89
One (3 mm) 64100 64800 37500 62900 48613 53710 1.32 1.21 47.83 2.3
One (3 mm) 30300 36000 28200 30200 7984 7965 3.8 4.52 53.21 3.7
One (3 mm) 66700 71200 42833 58800 - - - - 87.23 -
One (5 mm) 58400 62700 31800 52900 - - - - 63.26 1.0
One (5 mm) 79000 80800 46100 76500 - - - - 100.08 -
One (10 mm) 42200 47500 34600 37100 - - - - 64.32 1.5
One (10 mm) 59400 69500 30100 52000 - - - - 71.20 1.0
One (10 mm) 61000 62500 25100 58600 - - - - 39.07 1.65
One (10 mm) 78000 78300 39100 74200 29259 24976 2.67 3.14 74.05 2.0
One (10 mm) 42700 45500 18600 43800 - - - - 33.62 2.5
One (10 mm) 36600 41400 26400 34200 18617 32614 1.97 1.27 58.60 2.2
Two (5 mm) 44200 47500 24200 43700 15414 - 2.87 - 42.33 4.1
Two (5 mm) 63100 63600 43000 61800 25453 17735 2.48 3.59 65.17 5.4
Two (5 mm) 24900 32800 17800 21200 14547 12621 1.71 2.6 32.03 11.2
Two (5 mm) 49700 54300 36400 45200 42257 41618 1.18 1.3 98.95 2.2
Two (5 mm) 61100 67400 52500 61900 39301 39167 1.55 1.72 104.28 1.34
Two (5 mm) 45900 52700 34900 45500 25176 24965 1.82 2.11 77.03 -
Two (5 mm) + crack Two (5 mm) + crack Two (5 mm) + crack Two (5 mm) + crack Two (5 mm) + crack Two (5 mm) + crack 32200 32100 31800 32900 35800 10200 43600 38300 31400 40100 43100 27200 28400 31200 30700 30000 32200 32600 32000 33000 37400 20250 15908 2572 5875 15182 5324 1.59 2.02 12.8 6.09 2.52 7.53 52.65 56.86 54.27 47.01 38.72 25.10 4.4 3.1 5.0 6.9
From the Table 2 it follows that the modulus of elasticity and deformation of the samples, determined to the limit of residual strength, decrease by 1.2-2 times compared to the initial characteristics, and when evaluating the "loops" on the "shelves" of residual strength, a decrease in modulus by 5-7 times is observed. Samples with two holes and a transverse crack were often brought to the shelf of residual strength during testing. However, the number of "loops" is smaller due to the uniform development of plastic deformations due to the presence of a crack, which did not allow to fully assess their deformation characteristics during the destruction process.
Fig.5. The nature of the destruction of samples after testing with stress concentrators of various configurations: a - standard (without holes): development of vertical fracturing on the sample
surface; b - hole 03 mm: the concentration of cracks around the circular hole, the development of vertical cracks up and down; c - hole 010 mm: the concentration of cracks around the circular hole, the growth of vertical cracks from the axis of the hole; d - two holes 05 mm: the concentration of cracks around the hole of circular cross-section, there is a splicing of cracks
formed along adjacent holes; e - two holes 05 mm + crack: the concentration of cracks around the hole of circular cross-section, the development of vertical crack formation in the "pillar" between the holes
Regardless of the effect of the hole on the nature of the load drop, the presence of holes made it possible to keep the destroyed sample in a more stable state than samples without holes. So, out of seven monolithic samples, only three samples kept the shape after destruction, while all samples with holes retained their shape. Perhaps this is due to the fact that in monolithic samples, the destruction was evenly distributed throughout the sample, whereas in samples with holes, it was the holes that concentrated most of the destruction on themselves (Fig.5).
Conclusion. Despite the wide range of possibilities, to assess the destruction of rock under load, the best way is to conduct laboratory tests followed by the construction of graphs of extreme deformations. Extreme tests on servohydraulic test presses with the control of the growth rate of transverse deformations values, due to the construction of "loops" of unloading and loading, allow to estimate the elastic and deformation modules beyond the strength limit of the sample. The tests carried out on the example of samples of rich sulfide ore showed that in the process of destruction, the elastic and deformation modules decrease by about 1.5-2 times, and in the zone of residual strength by 5-7 times.
Stress concentrators (holes 03 and 5 mm) slightly affected the change in strength properties and almost did not affect the change in the initial value of the modulus of elasticity and deformation. However, holes of this size were enough to change the nature of the destruction of the samples -cracks developed near the holes. In the case of testing samples without holes, cracking occurred on the surface almost uniformly. The presence of stress concentrators such as two holes of 05 mm together with a transverse crack simulating the unloading area allows, due to a noticeable decrease
in strength, to conduct tests with a greater probability of achieving the shelf of the residual strength of the sample. However, they significantly reduce the number of "loops" of unloading and loading, which make it possible to accurately estimate the modules of elasticity and deformation.
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Authors: Alexander P. Gospodarikov, Doctor of Engineering Sciences, Head of the Department, https://orcid.org/0000-0003-1018-6841 (Saint Petersburg Mining University, Saint Petersburg, Russia), Andrey V. Trofimov, Candidate of Engineering Sciences, Head of the Laboratory, https://orcid.org/0000-0001-7557-9801 (OOO Gipronikel Institute, Saint Petersburg, Russia), Alexander P. Kirkin, Postgraduate Student, s195056@stud.spmi.ru, https://orcid.org/0000-0002-4830-8042 (SaintPetersburg Mining University, Saint Petersburg, Russia).
The authors declare no conflict of interests.
