Arch. Min. Sci., Vol. 60 (2015), No 2, p. 517534 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.1515/amsc-2015-0034 MIROSLAWA BUKOWSKA* MECHANICZNE WLACIWOCI POKRYTYCZNE SKAL OSADOWYCH W GÓRNOLSKIM ZAGLBIU WGLOWYM (POLSKA) In this paper, we present the results of a study of the Upper Carboniferous sedimentary rocks of the Upper Silesian Coal Basin (USCB) in Poland. We examined the hard coals, which belong to various stratigraphic units of Upper Carboniferous coal-bearing strata, and waste rocks, i.e., sandstones, mudstones, s. We present the results of tests of their post-critical mechanical properties. These results are from tests of the post-critical modulus, residual stress and residual deformation from experiments using a servo-controlled testing machine (MTS) with uniaxial compression and conventional triaxial compression. We applied confining pressures of up to 50 MPa at a strain rate of 105 101 s1 (0.003-6.0 mm/ sec). The confining pressure applied in the triaxial compression tests reflected the conditions of current and future mining activities in the USCB at depths exceeding 1.300 metres. The strain rate applied in the tests reflected the values observed in the rockmass surrounding the mine workings and the rate of certain geodynamic phenomena occurring in the Carboniferous rockmass in the USCB, e.g., rock bursts. We present the values of the sub-critical modulus of coals and waste rocks, the functional relationships between the post-critical modulus and uniaxial compression strength, which are described using an exponential function of high correlation coefficients of the given rocks, and an exponential relationship between the post-critical modulus and the longitudinal elasticity modulus (Young's modulus). Based on the results of tests of the post-critical properties of the Carboniferous rocks under triaxial compression and at various strain rates, we devised the functional relationships between the properties of the rocks and the confining pressure. The dependence of the post-critical modulus of the sandstones and s on the confining pressure is described using a polynomial function of degree 2, and that of the coals is described using an exponential function. The relationship between the residual stress and residual deformation in the rocks and the confining pressure was described using a linear function. The obtained results of tests have a practical application in forecasting behaviour of rocks located deep, and designing safe exploitation of mineral deposits. Confining pressures of up to 50 MPa used in the conventional triaxial compression tests allowed us to predict the behaviour of the rock mass at large depths. These data provide general knowledge of the tendencies in behaviour of rocks at substantial depths and the ability to design safe methods of mining deposits of various raw materials, including energy sources. These deposits are mined from increasingly great depths as the reserves are gradually exhausted and collieries of the largest European coal basins are continuously reconfigured. Keywords: post-critical properties of rocks, post-critical modulus, residual deformation, residual stress, Upper Silesian Coal Basin * CENTRAL MINING INSTITUTE, PLAC GWARKÓW 1, 40-166 KATOWICE, POLAND. E-MAIL: firstname.lastname@example.org Wlaciwoci skal uzyskane z pokrytycznej krzywej napreniowo-odksztalceniowej opisuj pokrytyczne parametry mechaniczne: modul pokrytyczny, wytrzymalo resztkowa i odksztalcenie resztkowe. We wspólczesnej geomechanice górniczej, znajomo wartoci pokrytycznych parametrów mechanicznych skal jest nie do przecenienia. Wartoci tych parametrów s, bowiem wykorzystywane do rozwizywania zada zwizanych z projektowaniem i prowadzeniem podziemnej eksploatacji górniczej. Przykladem ich zastosowania jest ocena dynamiki destrukcji skal i górotworu i ocena wystpienia zagroe naturalnych w górotworze spowodowanych prowadzeniem podziemnej eksploatacji górniczej. Dotyczy to glównie zagroe geomechanicznych i wodnych, zwlaszcza w kopalniach prowadzcych eksploatacj w pobliu zbiorników wodnych utworzonych w zrobach zlikwidowanych kopal. Ponadto, wartoci tych parametrów slu do interpretacji warunków w obrbie ródel zagroenia wodnego oraz stanowi podstaw do wyznaczania filarów bezpieczestwa i stref bezpieczestwa i maj szerokie zastosowanie w wyznaczaniu zasigu stref zniszczenia wokól wyrobisk podziemnych i wymiarowania filarów technologicznych w filarowo-komorowym systemie eksploatacji. W artykule przestawiono wyniki bada wlaciwoci pokrytycznych wgli kamiennych nalecych do rónych ogniw stratygraficznych serii wglononej górnego karbonu w Górnolskim Zaglbiu Wglowym i skal plonnych piaskowców i mulowców oraz ilowców. Wyniki bada modulu pokrytycznego, naprenia resztkowego i odksztalcenia resztkowego uzyskano z eksperymentów przeprowadzonych w serwosterowanej maszynie wytrzymalociowej MTS-810. Badania przeprowadzano w jednoosiowym ciskaniu na próbkach w ksztalcie szecianu i boku podstawy 50 mm i w osiowosymetrycznym stanie naprenia, gdy spelniony jest warunek napreniowy 1 > 0, 2 = 3 = p na próbkach w ksztalcie walca o rednicy 30 mm i o smukloci 2. Stosowano cinienia okólne do wartoci 50 MPa. Stosowane w badaniach trójosiowego ciskania cinienia okólne byly odpowiednie dla warunków prowadzonej i przyszlej eksploatacji w GZW na glbokociach przekraczajcych 1300 m. Próbki byly ciskane w kierunku prostopadlym do uwarstwienia. Sterowanie maszyn wytrzymalociow odbywalo si za pomoc prdkoci odksztalcenia podlunego mierzonego w systemie pomiarowym prasy przemieszczeniem tloka. Eksperymenty przeprowadzano z prdkoci odksztalcenia rzdu 105 101 s1, co po uwzgldnieniu wysokoci próbek odpowiada prdkociom przemieszczenia tloka (0,003-6,0 mm/s). Prdkoci odksztalcenia stosowane w badaniach odpowiadaly prdkoci odksztalcania si skal w otoczeniu wyrobisk eksploatacyjnych i prdkoci niektórych zjawisk geodynamicznych, które zachodz w górotworze karboskim w GZW, na przyklad tpni. Na podstawie bada skal w warunkach jednoosiowego ciskania podano wartoci modulu pokrytycznego wgli i skal plonnych w poszczególnych grupach stratygraficznych górnego karbonu w Górnolskim Zaglbiu Wglowym. Wartoci modulu pokrytycznego zmieniaj si w szerokim zakresie (Tab. 1, 2). Sformulowano równania matematyczne zalenoci geomechanicznych parametrów pokrytycznych od wytrzymaloci na jednoosiowe ciskanie i od cinienia okólnego. Kluczowymi skladnikami opracowanych równa byl modul pokrytyczny, naprenie resztkowe i odksztalcenie resztkowe. Wyniki bada s zrónicowane w zalenoci od typu skaly, cinienia okólnego i prdkoci odksztalcenia. Zalenoci funkcyjne modulu pokrytycznego od wytrzymaloci na jednoosiowe ciskanie opisano funkcj potgow o wysokich wspólczynnikach korelacji dla poszczególnych skal (Tab. 3). Wykazano, e wgle kamienne w GZW w porównaniu ze skalami plonnymi osigaj wiksze wartoci modulu pokrytycznego przy mniejszych wartociach wytrzymaloci na jednoosiowe ciskanie. Po przekroczeniu wytrzymaloci na jednoosiowe ciskanie dynamika rozpadu wgli jest wiksza ni dynamika rozpadu skal plonnych. Na podstawie wyników bada skal karboskich podano zaleno potgow midzy modulem pokrytycznym a modulem Younga (Tab. 4). W warunkach osiowo-symetrycznego stanu naprenia, gdy spelniony jest warunek 1 > 2 = 3, wzrost wartoci cinienia okólnego powoduje przejcie skaly ze stanu kruchego w stan cigliwy przy wysokich cinieniach okólnych. W czci pokrytycznej krzywej napreniowo-odksztalceniowej zmniejsza si warto spadku naprenia, co oznacza, e ze wzrostem cinienia okólnego wzrasta warto naprenia resztkowego a krzywa pokrytyczna jest lagodniej nachylona w stosunku do osi poziomej. Skutkuje to mniejszymi wartociami modulu pokrytycznego, który obrazuje dynamik niszczenia skaly w obszarze pozniszczeniowym. Badania wlaciwoci pokrytycznych skal karboskich w trójosiowym ciskaniu wykonano w warunkach wzrastajcych cinie okólnych do 50 MPa, przy rónych wartociach prdkoci odksztalcenia. Wykazano liczne zmiany wartoci parametrów pokrytycznych wynikajce ze stosowanych wartoci cinienia okólnego. Modul pokrytyczny maleje ze wzrostem cinienia okólnego dla piaskowca i wgla zgodnie z funkcj wielomianu drugiego stopnia lub wykladnicz (Tab. 5, Rys. 7, 8). Dla ilowca nie stwierdzono zalenoci pomidzy modulem oslabienia a cinieniem okólnym 0-50 MPa w zakresie prdkoci odksztalcenia 104 101 s1. Wykazano równie, e modul pokrytyczny wgla w warunkach wzrastajcych cinie okólnych jest mniejszy ni dla skal plonnych. Badania wplywu prdkoci odksztalcenia na wartoci modulu pokrytycznego skal karboskich nie wykazaly regularnych jego zmian wraz z prdkoci odksztalcenia. Zaleno naprenia resztkowego i odksztalcenia resztkowego od cinie okólnych (0-50 MPa) w zakresie prdkoci odksztalcenia 105÷101 s1 dla badanych skal osadowych karbonu GZW opisano funkcj liniow (Tab. 6, Rys. 9; Tab. 7. Rys. 10). Dla wyszych cinie okólnych rónice midzy wartociami naprenia resztkowego i odksztalcenia resztkowego dla poszczególnych skal s coraz wiksze. Piaskowce wykazuj najwiksze wartoci naprenia resztkowego w miar wzrostu cinienia okólnego a wgle wartoci najmniejsze. Z przebiegu krzywych wida równie, e skaly plonne charakteryzuj si mniejszymi wartociami odksztalcenia resztkowego w porównaniu z wglem kamiennym. Sporód parametrów geomechanicznych najwiksze zmiany wartoci ze wzrostem cinienia okólnego wykazuje naprenie resztkowe, które odzwierciedla nono pokrytyczn górotworu w rejonach eksploatacji (np. none strefy spkanych filarów wglowych). Dla piaskowca, ilowca i wgla zaleno naprenie resztkowe cinienie okólne 0-50 MPa, odpowiadajce warunkom eksploatacji w GZW, ma przebieg prostoliniowy. Analiza wplywu prdkoci odksztalcenia i cinienia okólnego na wartoci parametrów pozniszczeniowych skal karboskich GZW wykazala, e cinienie okólne w zakresie 0-50 MPa ma wikszy wplyw na warto parametrów pozniszczeniowych ni prdko odksztalcenia w zakresie 105 101 s1 (0,003-6,0 mm/sec). Stosowane w eksperymentach trójosiowego konwencjonalnego ciskania cinienia okólne do 50 MPa daj podstaw prognozowania zachowania si górotworu na duych glbokociach. Daje to ogóln wiedz o tendencjach zachowania si skal na duych glbokociach i moliwociach wnioskowania dla celów projektowania bezpiecznej eksploatacji zló rónych surowców, w tym równie surowców energetycznych, których eksploatacja schodzi na coraz to wiksze glbokoci w zwizku ze stopniowym wyczerpywaniem si zló bilansowych i postpujc restrukturyzacj kopal w najwikszych zaglbiach europejskich. Slowa kluczowe: wlaciwoci pokrytyczne skal, modul pokrytyczny, odksztalcenie resztkowe, naprenie resztkowe, Górnolskie Zaglbie Wglowe 1. Introduction It was possible to examine the post-critical behaviour of rocks using servo-controlled testing machines in the tests of mechanical properties of rocks. During the process of compressing rock samples (uniaxial load, conventional triaxial compression, true triaxial compression), we may obtain a destruction curve for the entire range of its loading when the stiffness of the testing machine is greater than the stiffness of the tested rock sample, and when the machine is servocontrolled, the system provides an appropriately high reaction rate for the removal of the load during the process of destroying a sample. This arrangement lowers the requirements concerning stiffness of the frame loading the testing machine (Cain, 1996). The works of Cook (1965), Bieniawski (1970) and Wawersik and Fairhurst (1970) are pioneering studies in this area. The rock properties obtained from post-critical stress-strain curves describe the post-critical mechanical parameters: post-critical modulus, residual strength, and residual deformation. The post-critical mechanical parameters are used to solve problems of mining geomechanics. These parameters may be used directly to assess natural hazards, such as the dynamics of rocks and rockmass deformation, which is indispensable for describing such methan hazards (Krause & Lukowicz, 2012; Dziurzyski & Krause, 2012; Kopto & Wierzchowski, 2014) and geomechanical hazards as sejsmic hazard (Butra et al., 2001; Mutke et al., 2009; Marcak & Mutke, 2013), and rockbursts (Kabiesz 2010), cave-ins, and gas and rock outbursts. They also play an important role in forecasting rockburst hazards in the mined areas by using them to evaluate the susceptibility of the rockmass to rockbursts (Bukowska 2006, 2012). The post-critical mechanical parameters of rocks are also used in forecasting other natural hazards associated with mining activities, e.g., water hazards (Bukowski, 2009, 2015; Bukowski & Augustyniak 2013), especially in collieries in the vicinity of water reservoirs formed in goafs of abandoned collieries (Bukowski, 2010). The parameters are used for interpreting conditions near the source of the water hazard and are the basis for designing support pillars and protective zones. They are widely used in determining the range of a failure zone around workings of various cross-sectional shapes and the sizes of pillars in the room-and-pillar mining method. Moreover, disadvantageous geotechnical conditions in the rock mass require the development and application of innovative techniques of coal mining (Kabiesz et al., 2008; Drzewiecki & Kabiesz, 2008). Considering the above-mentioned data we conducted tests of geomechanical properties of Carboniferous rocks of different various load conditions, in the full range of their deformation. The fact that, as a result of mining activity, the rock mass is destroyed was also taken into consideration. Around underground workings there is a destruction zone of the rock mass and that is why it is necessary to forecast deformation of the rock mass and stability of underground workings (Prusek, 2010; Prusek & Jdrzejec, 2008; Majcherczyk et al., 2006) and determine the complete stress tensor (Makówka, 2014; Makówka & Drzewiecki, 2011). Nowadays, to do this in numerical calculations, also full stress-strain characteristics of rocks is considered. 2. Upper Carboniferous rocks in the Upper Silesian Coal Basin The Upper Silesian Coal Basin (USCB) is one of several Upper Carboniferous basins. These coal basins are found in western North America, Europe, North Africa, and western Asia. The formation of the Upper Silesian Coal Basin is associated with the Variscan orogeny. It initially was a premontane basin that later transformed into an intramontane basin. The coal-bearing unit of the Upper Carboniferous Upper Silesian Coal Basin is composed of clastic and clayey sedimentary rocks, organogenic rocks and subordinate chemical rocks. Sedimentation of coal-bearing deposits of the Upper Carboniferous of the USCB is characterised by its distinctive sequence of rock types and bedding types. Sedimentary cyclothems in various parts of the basin generally have thicknesses ranging between a few and a few dozen meters. The cyclothems contain primarily sandstones of various grain sizes, mudstones, s and coals. Molasse formations are found together with rocks of chemical and organic origin (siderites, clay siderites, coal shales and refractory shales). This paper presents the results of investigation of these sandstones, mudstones, s and coals. The characteristics of the rocks are presented below. Sandstones of the Upper Carboniferous of the USCB are medium-grained clastic rocks, typically arenite. Based on their grain sizes, they are divided into coarse-grained (grain diameter of 2-1 mm), medium-grained (grain diameter of 1-0.5 mm) and fine-grained (grain diameter of 0.5-0.1 mm) sandstones. The most common components of the sandstones are quartz and other mineral forms of silica (opal, chalcedony), feldspars, i.e., primarily sodium/potassium (orthoclase) and subordinate plagioclase (often highly altered to sericite or kaolinite), clay minerals (kaolinite, mica) and carbonates. The micas are minor components: the biotite is often highly altered and the muscovite is mechanically weathered. The rudzkie and orzeskie beds contain heavy and subsidiary minerals: zirconium, tourmaline, and apatite. In marginal beds and saddle beds, biotite dominates the subsidiary minerals. A group of clay minerals (hydromica, kaolinite, chlorite, minerals of mixed structure, i.e., illite/montmorillonite) dominates the minerals form- ing the binder, whereas carbonate minerals (dolomite, siderite, calcite) and silica are rarer. The dominant sandstones in the USCB are fine-grained (Fig. 1) and grey, medium-grained sandstones. These are characterised by chaotic or oriented textures. Quartz sandstones dominate in the saddle beds and rudzkie beds. Polymict sandstones dominate the upper part of the Upper Silesian sandstone series, mudstone series and Cracow sandstone series. The sandstones of marginal beds (porbskie, jaklowieckie, gruszowskie and pietrzkowickie beds) are primarily greywacke or polymict sandstones interbedded with rare local thin quartz sandstones. Rigid framework of grains (transmitted light) Lamina with organic matter (transmitted light) Fig. 1. Photomicrographs (transmitted light) of a sample of fine-grained quartz sandstone, medium sorted, of porous and contact clay cementation The proportion of sandstones in the USCB varies (Fig. 2) both vertically and horizontally along the bedding. Among the molasse formations, which form the main core of the coal-bearing deposits in the USCB, the proportion of sandstones in the Upper Silesian sandstone series exceeds 50%, and they dominate the Cracow sandstone series, where their proportion in the laziskie beds exceeds 95%. Thick layers of sandstones that are coarse-grained, medium-grained and fine-grained and coal deposits, s and mudstones are the basic components of the saddle beds and lower part of the rudzkie beds. In the rudzkie beds in the northern part of the basin, the proportion of fine clastic sediments is greater, especially in the upper part, where the thick layers of sandstones are interbedded with clay/mud containing coal deposits. The sandstones form layers of various thicknesses. Mudstones are fine-grained clastic rocks intermediate between sandstones and s, in which the proportion of grains smaller than 30 mm exceeds 75%. Their primary components are grains of quartz, feldspars, fine-grained rock clasts, micas and carbonates. The clay mineral component is subordinate. Bedding of the mudstones is primarily parallel, in the form of layers of dusty and sandy material highlighted by the presence of mica on the diagonal or wavy cleavage planes. The mudstones play the primary role in the mudstone series, where their proportion reaches 40% (Fig. 2). The proportion of mudstones is also significant in the paralic series and marginal beds, where they accounts for 38%. Compared to the sandstones, the mudstones are present in thin layers, although their compressional strength is often higher than that of the Carboniferous sandstones and exceeds 100 MPa. Fig. 2. Proportion of rocks in stratigraphic series of Upper Carboniferous USCB: CSS Cracow Sandstone Series; MS Mudstone Series; USSS Upper Silesian Sandstone Series; PS Paralic Series The s (Fig. 3) contain over 50% grains smaller than 0.002 mm. Clay minerals dominate their mineral composition. The s display indistinct lamination, which is primarily parallel. They contain abundant plant detritus. The s that feature easily separated flat beds, usually parallel to the bedding, are typically clay shales (clayey admixtures) or sandy shales (sandy admixtures). The largest proportion of s is observed in the samples from boreholes in the mudstone series, where they account for approximately 26% of the rock. In the area of the USCB, the s are of various types: those with plant detritus, of various sand admixtures, with local concentrations of clay siderites or bedded with s or sandstones. Generally, the s display the lowest values of geomechanical parameters, whereas locally stronger rock (e.g., with sand, with clay siderite) may result in a considerable increase in the parameters. Hard coal is a caustobiolith created via accumulating plant matter under appropriate environmental and climate conditions. Thus, hard coal belongs to the group of rocks of organic origin. Fig. 3. Photomicrographs of ; transmitted light, polarised, with one nicol prism The organic matter underwent a lengthy series of processes, initially of biogenic transformation (open peat bog) and then of geochemical transformation. The primary components of coals are carbon, hydrogen, oxygen, sulphur and nitrogen. Coal contains additional mineral substances (e.g., silicates, sulphides, Figs. 4, 5) and rare elements (e.g., arsenic, gallium). The colour of coal reflects its petrographic composition and rank. Depending on the petrographic composition, the colour changes from pitch black through black and grey-black to grey. With the increase in the rank of coal, the colour changes from dark brown, through black, and grey-black to steel-grey. Coal deposits in the USCB are primarily found together with sandstones, mudstones, s and in lesser amounts with conglomerates, sedimentary clastic and phytogenic rocks, which are classified as the lower paralic series and have characteristic regular structure; and in the upper land series of the Variscan Upper Carboniferous molasse. The research presented in this paper refers to the sandstones, mudstone, s and coals. Coal is an organic rock, and its petrographic composition varies greatly, which significantly Fig. 4. Duroclarite composed of z inertinite (lightest colour), liptinite (darkest colour) and basic vitrinite mass with veinlets of pyrite Fig. 5. Inertinite (light fragment at the top of the photo) and clarodurite (bottom of the photo) with single crystals of pyrite and cracks influences its properties, including its geomechanical properties. 3. Methods of research into post-critical properties of rocks The Carboniferous rockmass in the USCB is not homogenous. It is anisotropic, discontinuous and of nonlinear deformation. These qualities result in significant variations in rock properties along the bedding (horizontally) and with the depth (vertically). Significant variations in the values of the parameters make it necessary to use an average value of a given parameter, which consists of several values obtained during tests. The results of research into the mechanical properties of the sandstones, mudstone, s and coals presented in this paper were obtained from tests conducted using a stiff testing machine, the MTS-810. The tests included uniaxial compression test of 50×50×50 mm cubic samples (in an axially symmetric stress-strain state (1 > 0, 2 = 3 = 0), meeting the conditions 1 > 0 and 2 = 3 = p on toroid samples of 30 mm diameter and a slenderness ratio of 2. The samples were compressed perpendicular to bedding. Control of the stiff testing machine was performed via the longitudinal strain rate measured in the system of the press with the stroke of the piston. The tests were conducted at strain rates of 105 101 s1 (0,003-6,0 mm/s). In tests of conventional triaxial compression, we used a pressure chamber with a maximum confining pressure of 70 MPa. An integral element of the equipment for testing rocks in a pressure chamber is a pump that the side pressure to be maintained at a given, steady level. The confining pressure in the chamber for triaxial tests was produced using oil. Using a liquid medium requires the rock samples to be sealed against potential permeation of liquid into pores and micro-cracks. To do so, before the test, the samples were sealed with latex covers and covered with heat shrink wrap tightly covering the entire surface of the rock sample. The tests were conducted in accordance with the procedures of conventional single-stage triaxial testing by Kovari et al. (1983). The laboratory testing of the rocks was conducted in accordance with ISRM recommendations (Ulusay & Hudson (ed.), 2007) and our own procedures based on experience, collected over many years, in interpreting the strength data obtained using a serco-controled testing machine. 4. Results of research into post-critical mechanical properties of Carboniferous rocks in USCB Based on the post-failure stress-strain characteristics obtained during the uniaxial compression tests and triaxial compression tests in the stiff testing machine, we determined the postcritical modulus, residual strength and residual deformation (Fig. 6). The method of determining these parameters has not yet been firmly established. In research centres around the world and in Poland, these parameters are determined at various loads and using various methods of control of the stiff testing machine. One way to determine the post-critical modulus is to determine the tangent of the angle of the linear approximation of a stress-strain curve in its falling portion (Fig. 6) or to calculate its value using the equation M (1) where -- is the decrease in strain in the falling portion of the stress-strain curve, and -- is the increase in deformation in the falling portion of the stress-strain curve. The residual deformation corresponds to the residual stress (Figure 6) and is determined using the dependence where h 1000 h (2) h -- is the height of the sample, in mm, before the test, h -- is the change in the height of the sample determined on the border of residual strength in the post-critical portion of the stress-strain curve of the compressed sample, mm. Fig. 6. Determining post-critical modulus M, residual stress (r), and residual strain (r) based on the shape of the stress-strain curve In the post-critical portion of the stress-strain curve, the stress decreases until it reaches the residual value. The decrease in stress in the post-critical area corresponds to an increase in the residual deformation. The value of the residual stress reflects the value of residual deformation (Fig. 6). 4.1. Results of tests of post-critical modulus of Carboniferous rocks in a uniaxial compression test The post-critical modulus of the rocks in the USCB, determined under uniaxial compression, varies greatly depending on the stratigraphic unit of the Upper Carboniferous series. The ranges of these parameters together with their average values and the size (n) of the data sets are presented in Table 1, and those for waste rocks are presented in Table 2. TABLE 1 Post-critical modulus of coals in USCB Stratigraphic series of Upper Carboniferous Stratigraphic coal group; number of sets Average of postcritical modulus, GPa Minimum of post-critical modulus, GPa Maximum of post-critical modulus, GPa CSS CSS MS USSS USSS PS PS Libiz Beds (n = 12) Laziskie Beds(n = 912) Orzeskie Beds (n = 592) Ruda Beds (n = 1964) Siodlowe Beds (n = 1922) Porbskie Beds (n = 55) Jaklowieckie Beds (n = 228) TABLE 2 Post-critical modulus of waste rock in USCB Rocks; number of sets Average of postcritical modulus, GPa Minimum of postcritical modulus, GPa Maximum of postcritical modulus, GPa conglomerates (n = 20) coarse-grained sandstones (n = 76) medium grit sandstone (n = 381) fine-grained sandstones (n = 3817) mudstones (n = 1084) s (n = 2785) The multiple-year study of the properties of the rocks in the USCB indicated a dependence of the post-critical modulus on the uniaxial compressive strength of rocks. The results of statistical analysis of data from the primary types of rocks of the Upper Carboniferous USCB are presented in Table 3. These figures contain graphs of the dependence, regression equations, correlation coefficients (r) and the size (n) of the data sets. The connection between the compressive strength and post-critical modulus displays the characteristics of an exponential relationship with correlation coefficients of 0.86 for the coals, 0.78 for the s, 0.69 for the mudstones and 0.88 for the sandstones. The functional relationships between the uniaxial compressive strength (UCS) and uniaxial post-critical modulus have a significance level of 0.001. TABLE 3 Dependence of post-critical modulus and uniaxial compression stress of coals and waste rocks in USCB Rocks; number of sets Equation Correlation Coefficient r coals (n = 5685) s (n = 2713) mudstones (n = 1075) sandstones (n = 1425) M = 91.163 UCS1,4627 M = 43.543 UCS1,5274 M = 376.0 UCS0,990 M = 91.568 UCS1,3267 We conclude that the hard coals in the USCB have higher values of the post-critical modulus at lower values of compressive strength compared to the waste rocks. These uniaxial compression strengths indicate that the dynamics of failure of the coals are greater than that of the waste rocks. We demonstrated a dependence between the pre-critical and post-critical mechanical properties of the Upper Carboniferous rocks in the USCB. There is a distinct relationship between the post-critical modulus and longitudinal elasticity modulus (Young's modulus), and this relationship is an exponential one (Table 4). TABLE 4 Dependence of post-critical modulus and longitudinal elasticity modulus of coals and waste rocks in USCB Rocks; number of sets Equation Correlation Coefficient r coals (n = 4180) waste rocks (n = 4575) M = 0.0321 E1,51 M = 0.0322 E1,66 4.2. Results of tests of post-critical properties of Carboniferous rocks under triaxial compression at various strain rates In an axially symmetric stress-strain state, when the compression condition 1 > 2 = 3 is met, an increase in the confining pressure results in the transition of rocks from brittle fracture to ductile flow at high confining pressures. In the post-critical part of the stress-strain curve, the strain decreases. In other words, with the increase in the confining pressure, the residual stress increases and the post-critical curve makes a smaller angle with the horizontal axis. This nature of the post-critical curve results in lower values of the post-critical modulus, which reflects the dynamics of rock deformation in the post-failure area. At low values of confining pressure in highly brittle rocks, e.g., crystalline, certain researchers have observed, with increases in the confining pressure, only a slight decrease in the post-failure modulus (Arzua, Alejano 2013). In the postcritical part of the stress-strain curve, the stress decreases. In other words, with the increase in confining pressure, the residual stress increases and the post-critical curve has a lower gradient. This gradient results in lower values of the post-critical modulus, which reflects the dynamics of the rock deformation in the post-failure area and higher values of residual strain. In the case of fine-grained sandstones and s in the USCB, the dependence of the post-critical modulus on confining pressures between 0 and 50 MPa is best described using a polynomial function of degree 2 (Table 5). For s tested using a strain rate of 104 101 s1 (0,006 6,0 mm/s), there were no significant functional relationships. This finding most likely was caused by diversity among the tested s and the difficulties in preparing a sufficient number of samples for the tests. In the case of coals in the USCB, the dependence of the post-critical modulus on confining pressures between 0 and 50 MPa is best described using an exponential function of high correlation coefficients (Table 5). TABLE 5 Dependence of post-critical modulus on confining pressures of 0-50 MPa and various strain rates (Bukowska 2005) Rock Strain Rate (1) Equation Correlation Coefficient r sandstone coal (Fig. 7) 5·105 104 103 102 101 5·105 5·105 104 103 102 101 M = 0.01p2 0.92p + 162.15 M = 0.07p2 4.97p + 192.86 M = 0.04p2 2.78p + 143.03 M = 0.05p2 2.44p + 146.56 M = 0.002p2 0.68p + 108.58 M = 0.01p2 1.22p + 97.11 M = 28.64e 0.05p M = 20.96e 0.04p M = 37.48e 0.07p M = 28.04e 0.06p M = 24.43e 0.03p Figure 8 shows variations in the post-critical modulus of the Carboniferous rocks at strain rates of 105 s1. The curves of the values of the post-critical modulus with increasing confining pressure show that the post-critical modulus of the coal is much lower than that of the waste rocks, despite the fact that the trends in their changes are similar. Fig. 7. Dependence of post-critical modulus of coal in USCB on pressure and strain rate Fig. 8. Dependence of post-critical modulus of sedimentary rocks of USCB on confining pressure Changes in the residual stress with confining pressure in sandstones, s and USCB coals is best approximated using a linear relationship of high correlation coefficients (Table 6). Figure 9 shows curves of changes in the residual stress with at confining pressures of up to 50 MPa. The curves show that, in the case of uniaxial compression (2 = 3 = 0), the values of residual stresses in the three types of rocks are similar. With the increase in confining pressure, there are distinct differences in the values of residual stress for the tested rocks. Sandstones display the highest values of residual stress with the increase in confining pressure, and coals display the lowest values. Increases in the confining pressure result in changes in the residual deformation of the rocks. The dependence of the tested rocks is described using a linear function, for which we obtained high correlation coefficients (Table 7). We also confirmed a pattern: the increases in certain parameters resulting from the increase in confining pressure is larger for the rocks of lower uniaxial compression strength. Figure 10 presents the dependences of the residual deformation on the confining pressure for coal and the surrounding rocks (Carboniferous sandstone and ). The curves show clear differences in the values of residual deformation for coals and waste rocks at confining pressures above zero. The curves also show that waste rocks have lower values of residual deformation than does hard coal. This trend is characteristic of all of the strain rates within the range of 105 101 s1. TABLE 6 Dependence of residual stress on confining pressure in the range of 0-50 MPa at various strain rates Rock Strain Rate (s1) Equation Correlation Coefficient r sandstone (Bukowska 2005) coal 5·105 104 103 102 101 5·105 104 103 102 101 5·105 104 103 102 101 r = 4.56p + 13.81 r = 4.21p + 25.78 r = 4.69p + 21.48 r = 3.49p + 51.96 r = 4.10p + 24.81 r = 3.07p + 16.78 r = 2.56p + 26.55 r = 3.63p + 16.67 r = 3.25p + 20.86 r = 3.17p + 22,92 r = 3.21p + 4.63 r = 2.01p + 14.88 r = 2.28p + 10.99 r = 2.83p + 17.38 r = 2.89p + 24.95 Fig. 9. Dependence of residual stress in sedimentary rocks of the USCB on the confining pressure TABLE 7 Dependence of residual strain on confining pressures of 0-50 MPa for various strain rates Rock Strain Rate (s1) Equation Correlation Coefficient r sandstone coal 5·105 104 103 102 101 5·105 104 103 102 101 5·105 104 103 102 101 r = 0.424p+12.41 r = 0.567p + 14.75 r = 0.423p + 13.78 r = 0.346p + 14.50 r = 0.460p + 16.79 r = 0.196p + 14.15 r = 0.439p + 8.837 r = 0.624p + 8,149 r = 0.227p + 15.06 r = 0.482p + 12.79 r = 0.928p + 18.80 r = 0.716p + 17.01 r = 0.878p + 28.48 r = 1.191p + 20.31 r = 0.979p + 25.21 Fig. 10. Dependence of residual strain in sedimentary rocks of the USCB on confining pressure Tests of the influence of confining pressure on the post-critical mechanical parameters of Carboniferous rocks were conducted by applying various strain rates in the range of 105 101 s1 during the experiments. Knowledge of the influence of the strain rate on the behaviour of rocks is used in solving many problems in mining geomechanics and geoengineering. The strain rates used in the experiments correspond with those of certain natural phenomena occurring in the rockmass and processes caused by mining activities. The rate of 105 103 s1 is characteristic of deformation of rocks in the vicinity of underground workings. Many undesirable phenomena in the rockmass occur at various deformation rates. For example, rockbursts are dynamic, whereas the convergence of workings, i.e., slow closing of workings, is pseudostatic. Strain rates corresponding to the phenomena of rockbursts and rock outbursts fall within the range of 102 102 s1. The influence of the strain rate on certain mechanical properties of rocks was described in foreign literature in the 1930s. Newer research dates to the 1960s and subsequent years (Peng, 1973; Paterson, 1978; Blanton, 1981; Okubo & Nishimatsu, 1985; Kwaniewski, 1986; Lis & Kijewski, 1987; Bezat, 1987; Chong et al., 1989; Krzyszto, 1990; Olsson, 1991; Lajtai et al., 1991; Li et al., 1999; Bukowska, 2000). These studies refer primarily to tests of the pre-critical parameters of rocks under uniaxial compression. Research into these post-critical parameters includes work by Bieniawski (1970), Peng (1973) and Bukowska (2000). The research and analyses of Carboniferous rocks in the USCB indicate that the post-critical modulus of the sandstone at confining pressures of 0-50 MPa decreases by approximately 10 and 50%, whereas the modulus of the coal under confining pressures of 0-50 MPa decreases from 124% (for strain rate of 105 s1) to 78% (for strain rate of 101 s1) of the maximum value occurring at a confining pressure p = 0 MPa. What is characteristic of the coal under confining pressures of 10-20 MPa is a decrease in the post-critical modulus of approximately 80%. At the same time, we can observe variations in the post-critical modulus of the coal depending on the strain rate at lower confining pressures. The post-critical modulus at a given strain rate decreases with higher confining pressures (20-50 MPa). For , we observed no dependence between the post-critical modulus and confining pressures of 0-50 MPa at strain rates of 104 101 s1. With increases in the confining pressure from p = 0 MPa to p = 50 MPa, the influence of the strain rate on the residual strain of the sandstone decreases, whereas the influence of the strain rate on residual stress of the coal increases. 5. Conclusions The scope of the research was the post-failure parameters of Upper Carboniferous sedimentary rocks of the Upper Silesian Coal Basin in Poland. The tests were conducted in a stiff testing machine, or MTS. The testing machine was controlled by setting the total strain of a sample, which is expressed as the piston stroke. Based on the tests of rocks under uniaxial compression, we obtained values of the sub-critical modulus of coals and waste rocks in particular stratigraphic groups of the Upper Carboniferous. We also determined the dependence of the post-critical modulus on the uniaxial compressive strength in sandstones, mudstones, s and coals. The dependences of the post-critical modulus on the uniaxial compressive strength were described using an exponential function of high correlation coefficients for the given rocks. We demonstrated that the coals of the USCB compared to the waste rocks display high values of the post-critical modulus at lower values of uniaxial compressive strength. After exceeding the uniaxial compressive strength, the dynamics of deformation of the coals are higher than the dynamics of deformation of the waste rocks. Based on the test results, we derived an exponential relationship between the post-critical modulus and longitudinal elasticity modulus (Young's modulus). The tests of the post-critical properties of the Carboniferous rocks under triaxial compression were conducted under confining pressures up to 50 MPa at various strain rates. We observed variations in the post-critical parameters depending on the confining pressure. · The post-critical modulus decreases with an increase in the confining pressure in sandstone and coal. This relationship may be described using a polynomial function of degree 2 or an exponential function. For , there was no dependence between the softening modulus and confining pressures of 0-50 MPa at strain rates of 104 101 s1. We also found that the post-critical modulus of the coal under increasing confining pressure is lower than that of the waste rocks. Tests of the influence of the strain rate on the postcritical modulus of the Carboniferous rocks did not exhibit any pattern associated with variations in the strain rate. · The dependence of the residual stress and residual deformation on the confining pressure (0-50 MPa) at strain rates of 105 101 s1 (0,003-6,0 mm/sec) in Carboniferous rocks of the USCB was described using a linear function. At higher confining pressures, the differences between the residual stress and residual deformation increased in a given rock. The sandstones displayed the highest residual stress with increases in the confining pressure, and the coals displayed the lowest values. The curves show that the waste rocks are characterised by lower values of residual deformation compared to the hard coal. Among the geomechanical parameters, the residual stress exhibited the largest variation in values with increases in the confining pressure, which reflects the post-critical bearing capacity of the rockmass in the mined areas (e.g., support zones of cracked coal pillars). For sandstone, and coal, the dependence of the residual stress on confining pressures of 0-50 MPa, which simulates mining conditions in the USCB, is a straightlinear relationship. · Analysis of the influence of the strain rate and confining pressure on the post-failure parameters of Carboniferous rocks in the USCB indicated that confining pressures of 0-50 MPa have a larger influence on the post-failure parameters than do strain rates of 105 101 s1 (0.003 6.0 mm/sec). Confining pressures of up to 50 MPa used in the conventional triaxial compression tests allowed us to predict the behaviour of the rock mass at large depths. These data provide general knowledge of the tendencies in behaviour of rocks at substantial depths and the ability to design safe methods of mining deposits of various raw materials, including energy sources. These deposits are mined from increasingly great depths as the reserves are gradually exhausted and collieries of the largest European coal basins are continuously reconfigured.
Archives of Mining Sciences – de Gruyter
Published: Jun 1, 2015