Arch. Min. Sci., Vol. 52 (2007), No 3, p

Transkrypt

1 Arch. Min. Sci., Vol. (7), No 3, p MANABU TAKAHASHI* PERMEABILITY AND DEFORMATION CHARACTERISTICS OF SHIRAHAMA SANDSTONE UNDER A GENERAL STRESS STATE PRZEPUSZCZALNOŚĆ I WŁAŚCIWOŚCI ODKSZTAŁCENIOWE PIASKOWCA SHIRAHAMA W WARUNKACH ZŁOŻONEGO STANU NAPRĘŻENIA In this paper, results of experimental studies on the dependence between the permeability and the deformation mode of Shirahama sandstone subjected to an axi-symmetric triaxial compressive stress state and a true triaxial compressive stress state are presented. Under conventional triaxial compression conditions, in the brittle faulting regime, permeability decreases with increasing axial strain until the onset of dilatancy when it increases significantly with ongoing axial strain. For specimens subjected to effective confining pressures of less than 1 MPa, the final permeability is greater than the initial value; by contrast, in both the brittle ductile transition and ductile regimes the permeability following the onset of dilatancy increases only slightly. Deformed and failed specimens show a final value of permeability that is lower than the initial pre-deformation value. Whether shear displacement exerts a significant control on the permeability of faults in rock masses is a major topic of concern in the fields of engineering and earth sciences. To clarify the relation between permeability and the internal structure of a rock sample, the three principal strains and permeability along the intermediate principal stress direction were measured during deformation as a function of the three principal stresses. The specimen was deformed under a true triaxial compression stress state in which the intermediate principal stress was different to the minimum and maximum principal stress. Keywords: deformational properties, dilatancy, faulting, intermediate principal stress, permeability, triaxial compression W artykule przedstawione są wyniki badań nad zależnością pomiędzy przepuszczalnością a charakterem deformowania się próbek piaskowca Shirahama w warunkach osiowo-symetrycznego i asymetrycznego (prawdziwie trójosiowego) stanu naprężeń ściskających. Mioceński piaskowiec Shirahama pochodzi z półwyspu Kii na wyspie Honsiu w środkowej Japonii. Jest to skała zbudowana głównie z ziaren kwarcu (44,3%) i okruchów skał (46,41%). Wielkość ziaren kwarcu wynosi średnio ok.,1 mm. W piaskowcu dominują pustki o wielkości 1 µm; całkowita porowatość skały wynosi ok. 13% (rys. 1). RESEARCH CORE FOR DEEP GEOLOGICAL ENVIRONMENTS, AIST TSUKUBA CENTRAL 7, TSUKUBA, IBARAKI 3-867, JAPAN

2 36 Badania nad przepuszczalnością piaskowca Shirahama w warunkach konwencjonalnego trójosiowego ściskania przy różnych ciśnieniach okólnych zostały przeprowadzone za pomocą aparatury przedstawionej na rysunku. Badane były próbki walcowe o średnicy 3 mm i wysokości 6 mm. Przy niskich ciśnieniach okólnych próbki skały doznawały dylatancji i pękały ścięciowo w stadium pokrytycznym. W warunkach wysokich ciśnień skała zachowywała się ciągliwie, a odkształcenie objętościowe i zmiany objętości porów wskazywały na stałą, trwałą kompakcję materiału skalnego podczas próby na ściskanie (rys. 4). Należy jednak dodać, że wyniki pomiarów porowatości całkowitej wykonanych za pomocą porozymetru rtęciowego pokazały, że porowatość rośnie ze wzrostem ciśnienia okólnego (rys. ). Odkrycie to potwierdzone zostało pomiarami powierzchni właściwej przestrzeni porowej skały wykonanymi za pomocą metody BET (rys. 6). Wynika stąd, że im większa głębokość w górotworze, tym większa porowatość towarzyszy odkształceniom niesprężystym. A więc w warunkach dużych ciśnień na dużych głębokościach i wysokiego naprężenia dewiatorowego skały mają wysoką zdolność do magazynowania płynów (zdolność zbiornikową). Próby na tzw. prawdziwe trójosiowe ściskanie próbek piaskowca Shirahama przeprowadzono w celu zbadania przepuszczalności materiału skalnego w kierunku równoległym do pośredniego naprężenia głównego. W aparacie trójosiowym Koidego i Takahashiego, którego fragment pokazany jest na rysunku 7, badano próbki prostopadłościenne o wymiarach 34 mm 34 mm 7 mm. Przepuszczalność mierzona była w sposób ciągły podczas całego procesu deformowania się próbki skalnej: od stadium odkształceń sprężystych, poprzez stadium odkształceń plastycznych, aż do stadium poślizgu na ściankach ostatecznego makropęknięcia. W wyniku przeprowadzonych badań stwierdzono, że przemieszczeniom stycznym wzdłuż płaszczyzny makropęknięcia ścięciowego (uskoku) w próbce nie towarzyszą istotne zmiany przepuszczalności (rys. 8 i 9). Słowa kluczowe: dylatancja, pośrednie naprężenie główne, przepuszczalność, trójosiowe ściskanie, uskokowanie, własności odkształceniowe 1. Introduction The permeability of geologic materials is dependent on the porosity of the material and the degree of connectivity between pores. The specific storage of geologic materials is dependent on the porosity of the material and the compressibility of both the material and the included fluid; accordingly, both the permeability and specific storage of geologic materials vary over wide ranges. For example, the permeability of geologic materials may vary from cm/s for gravel to less than 1 11 m/s for clay and intact rock, representing variation by a factor of 1 1. Whether shear displacement exerts a significant control on the permeability of faults in rock masses is a major topic of concern in the fields of engineering and earth sciences. To clarify the relation between permeability and the internal structure of a rock sample, the three principal strains and permeability along the intermediate principal stress direction were measured during deformation as a function of the three principal stresses. The specimen was deformed under a true triaxial compression stress state in which the intermediate principal stress was different to the minimum and maximum principal stress. The general equation that describes the transient pulse test method has been used to quantitatively evaluate transient variations in the hydraulic head and the transient distributions of hydraulic gradient within a test specimen.

3 37. Theoretical evaluation of the transient pulse technique for permeability measurements The general equation that describes the transient pulse permeability test was given by Hsieh et al. (1981) as follows: h( x, t) 1 H 1 exp( m) [ cos m ( m/ ) sin m ] ( 1 m / ) cosm m( 1 / ) sinm m (1) where x Kt AL s,,, L L Ss Su S S S d u and φ m are roots of the following equation: ( 1) tan / in which: h(x,t) hydraulic head in the specimen (L), x distance along the specimen (L); x = and L are the downstream and upstream faces of the specimen, respectively, t time from the start of the experiment (T), H instantaneous increase in hydraulic head (L) at the upstream reservoir at t =, A cross-sectional area of the sample (L ), L length of the specimen (L), S u compressive storage of the upstream reservoir (L ), S d compressive storage of the downstream reservoir (L ), K permeability of the specimen (L/T), S s specific storage of the specimen(l 1 ). An explicit expression for the transient pulse test can then be obtained by re-writing Equation (1) as Equation (3). Equation (3) can be used to evaluate the time-dependent changes in the hydraulic head across the full length of the specimen, including the specimen ends. () h( x, t) H 1 1 m1 Kt x exp m cos m L Ss L m 1 cosm m m1 x sinm L sin m (3)

4 38 The distribution of the hydraulic gradient, i(x,t), within the specimen can be obtained by differentiating Equation (3) with respect to the variable x: i( x, t) H m1 m L Kt x m x exp m sin m cos m L Ss L L m 1 cosm m 1 sinm (4) The mathematical analysis developed by Brace et al. (1968) for the transient pulse test assumes no compressive storage in the rock specimen, in which case the pressure decay at the upstream reservoir is exponential: where Vd t P1 Pf H e () V V u d ( KA / L)( 1/ V 1/ V ) (6) w u d in which: V u volume of the upstream reservoir (L 3 ), V d volume of the downstream reservoir (L 3 ), P f final pressure (L), λ fluid compressibility (L /M), γ w specific weight of the fluid (M/L 3 ), P 1 pressure at the upstream reservoir (L). To reduce the testing time, practical evaluations of the permeability can be carried out using the same-sized pressure reservoirs and assuming that P 1 is approximately half the head difference across the entire specimen. In this case, Equation () can be reduced to Equation (7): in which: P pressure at the downstream reservoir (L). P P 1 t e (7) H

5 39 3. Sample description The tested sample of Shirahama sandstone was obtained from the Kii Peninsula, Wakayama prefecture, central Japan. The sandstone is a Miocene sedimentary rock that consists mainly of quartz grains (44.3%) and rock fragments (46.41%) that are aggregations of various kinds of minerals. The quartz grains have an average size of about 1 µm. The rock fragments have irregular shapes and are relatively easy to deform or crush. Figure 1 shows the pore-size distributions for intact specimens measured using mercury intrusion porosimetry. The pre-existing pore sizes are predominantly approximately 1 µm in size, and the total porosity is about 13%. 3 Intact Porosity = 13.37% Volumetric Ratio (%) Log Radius ( m) Fig. 1. Pore-size distribution of intact Shirahama sandstone determined using mercury intrusion porosimetry Rys. 1. Rozkład wielkości porów w nienaruszonym piaskowcu Shirahama oznaczony za pomocą porozymetru rtęciowego 4. Permeability and deformation characteristics of Shirahama sandstone under an axi-symmetric triaxial state of compressive stresses 4.1. Experimental techniques The experimental system consisted of a conventional triaxial compression apparatus, a permeability apparatus, and a pore volume apparatus, as shown in Figure.

6 36 1) Conventional triaxial compression apparatus: The maximum axial loading capacity was 1 kn and the pressure vessel had a maximum capacity of 1 MPa and 1 feedthroughs for strain measurement. Solid cylindrical specimens 6 mm long and 3 mm in diameter were placed in the pressure vessel and connected to a pore pressure line. Figure 3 shows the specimen assemblage and displacement transducers for the axial and radial directions. The specimen was jacketed with a. mm thick heat-shrinkable tube. The specimen was positioned between two hardened steel end-plugs, each of which had a small concentric hole at the center to enable pore fluid to access the upstream or downstream pore pressure line. CTC apparatus Permeability apparatus Pore volume apparatus 1 Up stream PT DPT PT Valve MicroMetering valve Specimen Valve Pc Tank (1 ml) Tank (1 ml) Drainage Buffer tank for pore water volume measurement ( ml) Vacuum pump Pressure vessel 1 Pressure gauge Pump Fig.. Schematic diagram of the mechanical and hydraulic experimental system Rys.. Schemat aparatury do badania mechanicznych oraz hydraulicznych właściwości skał ) Permeability apparatus: The permeability was measured using the transient pulse method originally developed by Brace et al. (1968). After the pore pressure had equilibrated within the specimen, the pore pressure was raised instantaneously by kpa on the upstream side of the specimen. The pressure on the upstream side was then reduced as the pressure on the downstream side was gradually increased as the fluid flowed through the specimen. Permeability was calculated from the upstream pressure decay or the differential pressure decay. The design of this

7 361 Buck up ring O-ring O-ring Local Deformation Transducer End piece Specimen covered with Jacket of heat shrinkable tubing ( 3 mm H6 mm) O-ring Local Deformation Transducer End piece Sperical seat Fig. 3. View of the sample assemblage and displacement transducers in the axial and radial directions Rys. 3. Widok próbki z przetwornikami do pomiaru przemieszczeń osiowych i radialnych permeability apparatus is appropriate to enable the application of Brace's equation to the question of specimen permeability at various deformation stages. 3) Pore volume apparatus: When the pore pressure was constant during deformation of the specimen, the volume change of the pore water that flowed out or was extracted from the specimen was measured using a micro-metering valve in which the inner piston could be moved forward or backward to maintain constant pore pressure. The change in pore volume could then be calculated based on the diameter of the metering valve piston and the rotation degree of the valve handle. The sensitivity of this system was about cm 3, corresponding to a in volumetric strain. 4. Experimental results To investigate the relationship between the volumetric strain and permeability, four specimens were deformed under various confining pressures up to 1 MPa and a constant pore pressure of MPa (Fig. 4). A transition from strain softening to strain hardening and transition from distinct dilatant to persistent compactant behavior was observed with

8 36 increasing effective confining pressure. The volumetric strain shows distinct dilatancy and persistent compaction with increasing axial strain. In the brittle regime, permeability decreases within the range of elastic deformation; upon the initiation of dilatant behavior, the permeability shows a remarkable increase at a constant stress level. A distinctive feature of the results is that once a shear fracture develops within the specimen, the permeability is higher than the initial permeability at the onset of axial loading. At the brittle ductile transition and within the fully ductile regime, the permeability increases within the inelastic deformation range but the rate of increase is slowed by Differential Axial Stress (MPa) Axial Strain (%) 3 Volumetric Strain (%) Axial Strain (%) Permeability Change Axial Strain (%) 9 1 Fig. 4. Axial differential stress, volumetric strain, and changes in permeability as a function of axial strain during a conventional triaxial compression test under four different confining pressures and a constant pore pressure of MPa Rys. 4. Osiowe naprężenie różnicowe, odkształcenie objętościowe i zmiany przepuszczalności w funkcji odkształcenia osiowego w warunkach konwencjonalnego trójosiowego ściskania przy czterech różnych ciśnieniach okólnych i stałym, równym MPa, ciśnieniu porowym

9 363 increasing confining pressure. It should be noted that the permeability at the end of loading is never higher than the maximum value recorded during the experiment. With progressive unloading during the unloading process, the permeability at the four different confining pressures decreased beyond the minimum value recorded under the loading process Microscopic observation using the mercury intrusion method and the gas adsorption method To investigate precisely the internal structural changes that occur within the stressed sandstone with increasing axial strain and confining pressure, the stress-induced volume change was measured by means of mercury intrusion porosimetry and the gas adsorption method. Figure shows the obtained pore-size distributions for various confining Volumetric Ratio (%) Volumetric Ratio (%) Volumetric Ratio (%) Log Radius ( m) Log Radius ( m) Log Radius ( m) Log Radius ( m) P c = MPa Porosity = 14.47% P c = MPa Porosity = 16.14% P c = 9MPa Porosity = 16.39% Log Radius ( m) Log Radius ( m) Fig.. Pore-size distribution for intact and deformed specimens under various confining pressures Rys.. Rozkład wielkości porów w próbce nienaruszonej i w próbkach odkształconych w warunkach konwencjonalnego trójosiowego ściskania przy różnych ciśnieniach okólnych Volumetric Ratio (%) Volumetric Ratio (%) Volumetric Ratio (%) a) b) P c = 4MPa, P p = MPa Porosity = 1.9% P c = 8MPa, P p = MPa Porosity = 13.% P c = 1MPa, P p = MPa Porosity = 16.4%

10 364 pressures and a constant pore pressure of MPa. Figures (a) and (b) represent dry and wet conditions, respectively. For both conditions, the peak volumetric ratio in the radius shifts to a larger scale. This behavior means that the thick stress-induced microcracks are dominant with increasing effective confining pressure. Figure 6 summarizes the relationship between the porosity as defined by mercury intrusion porosimetry and the confining pressure. In addition, the surface area determined through the gas adsorption method firmly supports the phenomenon of porosity increase with increasing confining pressure Porosity (%) porosity in deformed porosity in intact surface area without fault plane surface area with fault plane surface area in intact Confining Pressure (MPa) BET surface area (m /g) Fig. 6. Porosity and BET surface areas as a function of confining pressure Rys. 6. Porowatość i powierzchnia właściwa w funkcji ciśnienia okólnego. Permeability and deformation characteristics of Shirahama sandstone under a true triaxial compressive stress state.1. Loading system and strain measurement Tests were conducted using a system constructed by combining a Mogi-type true triaxial compressive apparatus and a permeability measurement device. One of the characteristics of this loading apparatus is that it generates two principal stresses in rock specimens using rigid pistons and the third stress directly by oil pressure. Figure 7 schematically shows the experimental arrangement of a rectangular prismatic specimen of size 34 mm 34 mm 7 mm. The specimen was jacketed with silicone rubber copper foil composite. A. mm thick teflon sheet and copper foil were placed between

11 36 Local displacement transducer Lubricants (Copper shim + Teflon sheet Pore water dispersion plate Piston for intermediate principal stress Confining pressure medium in vessel Pore water inlet Piston for maximum principal stress Fig. 7. Schematic assemblage for permeability test under true triaxial compression conditions Rys. 7. Schemat wnętrza komory trójosiowej z próbką do badań przepuszczalności w warunkach prawdziwie trójosiowego ściskania the specimen and end pieces to reduce friction and eliminate interfacial flow. The three principal strains can be easily and accurately measured using curved-type local displacement transducers... Experimental results Throughout the entire deformation, the hydraulic conductivity in the direction of the intermediate principal stress was measured to quantify the advection-ability parallel to the final fault plane. Seven experiments were conducted for different σ 3 and σ values. Figure 8 shows the differential axial stress (a), volumetric strain (b) and normalized hydraulic conductivity (c) in the σ direction as a function of strain in the σ direction for various values of σ and σ 3. The minimum principal stress varied from 8 to 83 MPa, and the intermediate principal stress varied from 3 to 13 MPa. Five specimens, subjected to σ 3 values of less than 43 MPa, showed behavior indicative of the brittle regime, whereas two specimens, subjected to σ 3 values in excess of 63 MPa, showed behavior typical of the brittle-ductile transition and ductile regime.

12 366 Although the intermediate principal stress was applied independently to the specimen, the effect of the minimum principal stress on the nature of the deformation was observed in the same manner as that in the conventional confining pressure experiment. At the minimum principal stress of 8.13 MPa, permeability consistently decreased with increasing axial strain until dilatancy occurred. After the onset of dilatancy, the lateral strain for the minimum principal stress direction was dominant and the volumetric strain tended to show expansion; permeability increased with increasing axial strain prior to failure. Thus, for low σ 3 values the deformation was characterized by brittle behavior and dilatancy; the normalized hydraulic conductivity showed a negative correlation with volumetric strain, and the final permeability exceeded the initial value. In contrast, at higher values, with a minimum principal stress of MPa, the specimen showed brittle ductile behavior, and volumetric strain revealed dilatant behavior until yield, with compaction until shear fracture. The permeability decreased with increasing axial strain, but after the yield stress the rate of decrease slowed progressively. Thus, for higher σ 3 values the deformation was characterized by brittle ductile behavior and continuous compaction and the volumetric strain and permeability showed a positive correlation. As a result, the final permeability in failed specimens is less than the initial value. It appears that the effect of σ on the permeability is less than that of σ 3. Axial differential stress (MPa) (8,3) (3,63) (13,43) (63,13) (83,13) Axial strain (%) 1 Volumetric strain (%) V 3 (83,13) (13,43) (63,13) 1 (3,63) (63,13) 1 (83,13) (3,63) (8,3) (13,43) Axial strain 1(%) Axial strain 1 (%) a) b) c) Fig. 8. Deformation behavior and permeability evolution during true triaxial compression tests under various minimum and intermediate principal stress for Shirahama sandstone Rys. 8. Charakterystyki zachowania się i przepuszczalności próbek piaskowca Shirahama podczas prawdziwie trójosiowego ściskania przy różnych naprężeniach najmniejszych i pośrednich Normalized permeability (8,3).3. Changes in permeability within the faulted specimen during stable sliding The main purpose of this study was to investigate temporal changes in permeability along the final fault plane. In the next stage of the experiment, permeability along the intermediate principal stress direction during stable sliding was measured to investigate the influence of shear displacement. Two specimens were deformed at the same lateral

13 367 differential stress (σ σ 3 ) equal to 4 MPa, and the minimum stresses were set to 3 and 43 MPa (Fig. 9). At the low minimum stress condition of 3 MPa, axial differential stress increases with increasing axial strain before attaining a peak value and falling to a constant residual stress after about mm of axial strain. In contrast, the higher minimum stress condition of 43 MPa leads to a gradual increase in residual stress with increasing axial strain. Lateral strain in the minimum stress direction and volumetric strains are similar for the two values of minimum stress. Changes in permeability along the fault plane (parallel to the intermediate stress direction) cannot be observed during stable sliding along the final fault plane. Axial differential stress (MPa) Lateral strain 3 and volumetric strain (%) V (3,63) 1 (3,63) - (3,63) 1 9 (3,63) v Axial strain 1(%) Axial strain 1(%) Axial strain 1 (%) Normalized hydraulic conductivity Fig. 9. Permeability changes during deformation of rock samples in the pre- and post-failure range Rys. 9. Zmiany przepuszczalności podczas odkształcania próbek skalnych w stadium przed- i pokrytycznym To investigate the effect of normal stress to the fault plane, a different loading path was employed after the specimen underwent faulting. After faulting, the specimen was unloaded so that all three principal stresses were decreased to a hydrostatic pressure of MPa, and then the piston for the maximum principal stress direction was pushed at a constant rate. The intermediate and minimum principal stresses were kept constant at a level of MPa during the so-called reloading process. Figure 1 shows the changes in permeability for the specimens subjected to unloading. Figure 1(a) shows shear stress and normal stress versus shear deformation. The shear stress and normal stress on the fault plane are approximately constant after about. mm of shear displacement. The normal displacements in the two specimens increase slightly with increasing shear displacement. The normalized permeability at different intermediate stresses increased slightly with increasing shear displacement, attaining approximately twice the value at the onset of shear displacement. The difference between the former loading path (Fig. 9), which is monotonic loading without unloading, and the reloading path after unloading (Fig. 1) may result from the different magnitudes of normal stress acting on the final fault planes during shear displacement.

14 368 Normalized permeability Normal Displacement (mm) Shear stress and normal stress (MPa) Shear displacement (mm) a. Shear stress and normal stress vs shear displacement Shear displacement (mm) b. Normal displacement vs shear displacement Pp = 3MPa Pp = 3MPa Pp = 3MPa Shear displacement (mm) c. Normalized permeability vs shear displacement 3 ss: 43MPa, 83MPa ss4: 63MPa, 13MPa ss, shear stress ss, normal stress ss4, shear stress ss4, normal stress ss ss4 ss ss4 Fig. 1. Permeability changes accompanying shear displacement along the fault plane in specimens which after having undergone faulting were first unloaded and, then, reloaded Rys. 1. Zmiany przepuszczalności towarzyszące przemieszczeniu stycznemu na płaszczyźnie makropęknięcia ścięciowego w próbkach, które uległszy zniszczeniu zostały wpierw odciążone i, następnie, obciążone ponownie

15 Conclusions Under low confining pressure conditions the behavior of the tested sandstone specimens is characterized by predominantly dilatant deformation and formation of a main fault. Under higher confining pressure, the specimens behave in a fully ductile mode and the volumetric strain measured by displacement transducers and changes in pore volume reveal persistent compaction throughout the experiments; however, measurements of total porosity undertaken using mercury intrusion porosimetry reveal increasing porosity with increasing confining pressure. This finding is supported by measurements of the BET surface area of the pore space obtained using the gas adsorption method. These findings indicate that the greater the burial depth, the greater the porosity with inelastic deformation, although it is acknowledged that the actual subsurface field is restricted. Porosity corresponds to specific storage in hydrogeology, and it determines the ability of the fluid to flow out of or be extracted from a rock or sedimentary layer. Thus, it can be concluded that a rock mass subjected to high confining compressive stress and high deviatoric stress has a high capacity for storing the pore-fluid volume. True triaxial compression tests of Shirahama sandstone were carried out to investigate the changes in permeability parallel to the intermediate principal stress direction. This combined experimental system made it possible to carry out continuous permeability measurements during the entire deformation process from elastic to plastic deformation and up to shearing along the eventual fracture. Shear deformation along the final fault did not result in a significant change in permeability. It has been confirmed that the measurement of permeability along the intermediate principal stress direction under a general stress state is effective as a new testing technique of shear deformation and fluid flow under high pore pressures, high differential axial stress and large shear deformation. REFERENCES Brace W.F., Walsh J.B., F r a n g o s W.T., Permeability of granite under high pressure. Journal of Geophysical Research, Vol. 73, No. 6, -36. Hsieh P.A., T racy J.V., Neuzil C.E., Bredehoeft J.D., S illiman S.E., A transient laboratory method for determining the hydraulic properties of tight rocks I. Theory. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 18, No. 3, 4-. Received: 14 March 7