J. Mt. Sci. (2 2015) 12(1): 2118-231 DOI: 10.100 07/s11629-013-2946-4
e-m mail: jms@imd de.ac.cn
http://jm ms.imde.ac.cn
Effectt of Free eze-Tha aw Cycles on Mechani M ical Pro operties s and Permeability y of Red d Sandsttone un nder Triiaxial C Compression YU Jin n1
e-mail: bugyu0717@1 b 63.com;
0 0000-0003-0 088-7652
CHEN Xu1 e-mail: goodmancx@ @sina.com; LI Hon ng2 e-mail:
[email protected] du.cn;
0000-0001--8522-8941 00 000-0002-76114-3484
ZHOU Jia-wen3 e--mail:
[email protected]; an-yan1 e-ma ail: yycai@hqu u.edu.cn; CAI Ya
0000-00 002-6817-10711 0000-0001-5 5884-5952
1 Institu ute of Geotechn nical Engineerin ng, Huaqiao Un niversity, Xiameen, Fujian 36102 21, China 2 Schoo ol of Civil and Hydraulic H Engin neering, Dalian University of Technology, T Dallian 116024, Ch hina 3 State Key Laboratorry of Hydraulicss and Mountain n River Engineeering, Sichuan University, U Chen ngdu 610065, China C on: Yu J, Chen X, Li H, et al. (2015) ( Effect off freeze-thaw cyccles on mechan nical properties and permeabiliity of red Citatio sandsto one under triaxiial compression n. Journal of Mo ountain Science 12(1). DOI: 10.11007/s11629-0113-2946-4
© Scieence Press and Institute I of Mou untain Hazards and Environmeent, CAS and Sp pringer-Verlag B Berlin Heidelberrg 2015
d willl happen in cold Abstract: Geological disasters regions because of the efffects of freezze-thaw cyclees on rocks or soils, so studyiing the effectts of these cyycles aracteristics and a permeab bility on the mecchanical cha properties of o rocks is very v importan nt. In this study, red sandsto one samples were w frozen an nd thawed wiith 0, 4, 8 and 12 1 cycles, ea ach cycle including 12 h of freezing and d 12 h of thaw wing. The P-w wave velocitiees of these samp ples were meeasured, and d the mechan nical properties and evolu ution of the steady-sstate axial permeabilitties were inveestigated in a series of unia and triaxiall compression tests. Expeerimental ressults show that, with the inccreasing of cyyclic freeze-tthaw times, the P-wave velocity of thee red sandsttone haw cycles has a decreases. The numberr of freeze-th xial compresssive significant influence on the uniax e modullus, cohesion n, and anglee of strength, elastic internal fricction. The evolution of peermeability off the rock samplees after cycless of freeze-th haw in a comp plete stress-strain n process un nder triaxiall compression is closely related to the va ariation of th he microstruccture ock. There is a highlyy correspond ding in the ro relationship p between volumetricc strain and permeabilitty with axiall strain in all a stages of the stress-strain n behaviour. Received: 3 December 2013 3 Accepted: 9 July 2014
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ywords: Freeeze-thaw cyccles; Red sand dstone; Key Tria axial compresssion; Permeaability; Mechanical properties
Inttroduction n At present,, with the co ontinuous development d of the econom my in cold rregions thro oughout the worrld, many rock projeccts have been b under con nstruction, in ncluding und derground engineering, e min ning, and ga as and oil exxploration (N Nicholson et al. 2000). Ma any geologiccal disasterss and rock eng gineering eveents involvin ng freezing, thawing and perrmeating pro ocesses are beeing or to bee carried out all over o the worrld (Cheng ett al. 2003), such s as rock slop pe, sliding, landslides l (M Matsuoka 20 001; Azania et al. a 2010), tun nnels (Zhang g et al. 2004)) and so on. Forr these engin neering even nts, the pheenomena of miccro-damage, frost shaattering, frrost heave defo formations, denudation d and instabillity of rock masss caused byy cyclic tran nsition from pore water and d fissure watter to ice arre considered d to be the trig ggering facto ors of rock w weathering and a erosion, nott only in veryy cold region ns, but also in n temperate
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areas where temperatures sometimes reach freezing (Coutard et al. 1989; Matsuoka 1990; Prick 1995; Nicholson et al. 2001; Yang et al. 2004; Dixon et al. 2005; Hall 2007; Seto 2010; MartínezMartínez et al. 2013). In China, the Qing-Tibet Railway Engineering was carried out between 2001 and 2005. Water inrushing occurred in parts of the tunnels, such as Guanjiao tunnel, which was likely associated with both the freezing and thawing actions and the change of the pressure of surrounding rock (Zhang et al. 2002; Wang et al. 2007). Many geological disasters of rock mass engineering related to seepage in cold areas are also caused by the coupling of freeze-thaw action and seepage effect (Lai et al. 1999). Freeze-thaw damages, peeling, leaking, watering and ice covering of the surrounding rocks have greatly weakened the service capacity and life of highway and railway tunnels (Lai et al. 2000; Zhang et al. 2004). In recent years, underground storage tanks have been constructed and are usually used for the storage of liquefied natural gas (LNG) at a very low temperature with the surrounding rocks frozen (Neaupane et al. 1999). If the rock masses undergo cycles of freezing and thawing, thermal stress and displacement are induced, along with volume change. The response of rock masses to this engineering problem is a phenomenon involving fluid-solid coupling issues (Neaupane et al. 2001). For these reasons, in the past few decades many scholars have attempted to investigate issues involving mechanical behaviours and permeability properties varying with the freezing and thawing actions of rocks (Ondrasina et al. 2002). Researchers focused their attention on the mechanical behaviours and structural features of porous rock samples subjected to freeze-thaw cycles through a variety of laboratory testing methods. For example, the evolution of the void structure subjected to freeze-thaw cycles was studied by using the computed x-ray tomography technique (Ruiz de Argandoña et al. 1999; Kodama et al. 2013). Several freeze-thaw experiments were performed to characterize the changes of strength, deformation characteristics, Young's modulus, cohesive strength and internal frictional angle in a series of uniaxial and triaxial compression tests (Yavuz et al. 2006; Tan et al. 2011; Chen et al. 2014). A porosity database was built and a non-
linear regression method was used to derive correlations to quantify the changes in the porosity due to freezing, by means of rock porosity experiments (Chamberlain et al. 1979; He et al. 2013). In terms of permeability and hydraulic conductivity, most of the previous work suggested that the impact on the cycles of freeze-thaw action was mainly concentrated on clay and soil without rocks (Othman et al. 1993; Kraus et al. 1997; Viklander 1998). But above all, there is a lack of experimental studies linking permeability to freeze-thaw action for rocks. In an attempt to remedy this deficit, the main objective of this study is to emphasize the following: (i) The influence of freeze-thaw cycles on Pwave velocity and damage parameter for red sandstone. (ii) The impact on mechanical properties subjected to freeze-thaw action for rock samples under uniaxial and triaxial compression. (iii) The evolution of permeability and the relationship between permeability tendency and change of volume strain in the triaxial tests. In a word, from theoretical significance, this research highlights the effect of freeze-thaw cycles on mechanical properties and permeability of rock, as well as improves the mechanical and seepage theory of rock under bitter cycle of freezing and thawing. From practical purposes, this paper contributes to the design, construction and safety evaluation of cold region rock engineering.
1
Materials and Methods
1.1 Sample preparation The red sandstone cores studied in the present work were drilled out of a large single block without macroscopic cracks. This red sandstone block was carefully extracted from a natural stone quarry near Ganzhou, Jiangxi Province, China. The reason for choosing the red sandstone from Jiangxi is that this area has been affected less by the freezing-thawing action. The rock cores were prepared in a cylindrical shape with a diameter of 25 mm and a height of 50 mm. In order to enhance the accuracy of the tests, the error of unevenness of both the bedding planes of the rock samples should be polished to within 0.05 mm, and the error of
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Table 1 Initial physical parameters of samples Sample no.
Height (mm)
Diameter (mm)
Density (g·cm–3)
Porosity (%)
0-1 0-2 0-3 4-1 4-2 4-3 8-1 8-2 8-3 12-1 12-2 12-3
49.88 49.76 49.64 49.74 49.86 48.80 48.64 48.82 49.96 48.84 48.78 49.82
24.98 24.86 24.90 24.84 24.92 24.88 24.98 24.94 24.92 25.00 24.82 24.88
2.51 2.52 2.51 2.51 2.53 2.52 2.53 2.52 2.51 2.52 2.51 2.52
5.50 5.44 5.18 4.88 5.51 5.39 4.86 5.52 4.90 6.41 4.99 4.57
length along with the two pairs of the height edge should be polished to within 0.3 mm. Moreover, to ensure that both bedding planes of the rock samples were parallel, all the samples were drilled in the direction perpendicular to the bedding planes. This was necessary to avoid cracks when the samples were processed. The initial physical parameters of the samples are shown in Table 1. The data of the velocity of Pwaves and S-waves were collected using a Tektronix digital phosphor oscilloscope 3012. Based on the data in Table 1 the measured values of density (average of 2.519 g·cm–3), porosity (average: 5.226%), S-wave velocity (average: 1983.367 m·s–1) and P-wave velocity (average: 3452.274 m·s–1) are comparatively close to their average values, which ensures the rock samples' uniformity. Freezing-thawing cycle characteristics were defined to be close to the in situ conditions. Freezing temperature and melting temperature were set as -20°C and +20°C respectively in the freeze-thaw cycle treatment process. The rock samples were placed in a deep-freeze cabinet during the frost phase, where the temperature was -20°C, then immersed in near-constant +20°C distilled water during the thaw phase. The test was conducted for each cycle of the freeze-thaw process,
Figure 1 Generalized temperature curve for the 40°C freeze-thaw cycle.
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S-wave velocity P-wave velocity (m·s–1) (m·s–1)
2001.91 1998.26 1987.15 1990.76 1954.39 1981.90 1998.94 1984.65 1999.39 1986.24 1982.79 1971.24
3506.61 3489.06 3472.80 3439.53 3338.20 3478.28 3395.45 3481.42 3501.29 3511.00 3469.81 3455.49
including 12 h of freezing and 12 h of thawing. Since Newton’s Law of cooling and heating was applied in this freezing and thawing cycle, the temperature change followed the same route at each cycle (as shown in Figure 1). In this study, the freeze-thaw cycles were set to be 0, 4, 8 and 12 times. 1.2 Experimental device and procedure The experiments were conducted on the selfdesigned TAW-1000 electro-hydraulic servo controlled testing system. The maximum loading capacity of the system was 1000 kN, and the maximum confining pressure and pore pressure were 70 and 40 MPa, respectively. In addition, the system had the capability to perform permeability tests of rocks and concrete. A diagram of the experimental device is presented in Figure 2a. Before the permeability tests, each rock sample was circumferentially jacketed with a plastic membrane and tightened with heat-shrink pipe to isolate the osmotic pressure from the confining pressure. Next, the axial and radial strain gauges were installed and the assembled sample was placed into the chamber on the lower plate of the load frame (Figure 2b). Then the triaxial cell was lowered and filled with oil and the confining pressure was applied. In the tests, the confining pressures of 5, 10 and 20 MPa were selected. Osmotic pressure was designed as a difference of 2.0 MPa between two ends. With the aid of three independent closed loops, the axial loading, confining pressure and osmotic pressure can be independently and precisely controlled. Thermal effects were not studied here and all tests were carried out under isothermal conditions at a room
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temperaturre 20±2°C. ( (a) (b) Permeeability desccribes the ease with w which a fluid circulates through t a porous and dep network, pends mainly on n the pore size, tortuosity and connecctivity of the porous p nettwork (Guéguen et al. 1992)). For the measu urement of rock permeabilitty, two diffferent experimenttal techn niques Figur re 2 (a) Diagra am of the deviice and (b) sam mple assemblyy. were used:: the steadyy-state typical results from tthe P-wave velocity flow (or peermanent reg gime) method d, and pulse test mea asurements of sample 12-2 are pllotted as a (or transien nt regime) technique. t Th he choice off the fun nction of thee number of the freeze-tthaw cycles. one or thee other meth hod mainly depends on the As shown in Fiigures 3, thee P-wave velocity of the range of peermeability to be determiined. In geneeral, red d sandstone reduces r with h the increasing number for materials with rellatively high her permeab bility -16 6 2 of freeze-thaw f c cycles. For sample 12-2, the P-wave (e.g. >10 m ), it is ea asy to reach h the perman nent velo ocity falls to 2679.31 m/ss from 3421.8 81 m/s after flow regime, and the stteady-state flow f is preferrred 12 cycles c of freeeze-thaw. In o other words,, the P-wave (Brace et all. 1968). In the t case of th he red sandsttone velo ocity of samp ple 12-2 redu uces by moree than 20%. studied heere, its initia al permeabillity is relatiively -16 2 Thee reason for the decrease is that thee damage of high, estim mated at abou ut 10 m , th hus we chosee the the rock leads to changes off the microstructure and steady-statte flow meth hod. The peermeability was mecchanical performance iin an envirronment of calculated by the classiic Darcy’s la aw (Darcy 18 856), freeezing and thawing ccycles. Thee dropping which show wed that theere was a lin near relationsship 3 tendency of P-w wave velocityy with the in ncreasing of between the flow Q (m /s) and d the presssure 2 2 freeeze-thaw cyccle has comee to a similarr conclusion gradient ( P1 − P2 ) / p0 (Pa), and d defined the with h the previou us research on granite and andesite permeabilitty k (m2) of a connected porous med dium (Liu u et al. 2012)). by the follo owing equatio on:
k=
2Qp0 μ L ( P12 − P2 2 ) A
(1)
where coeffficient μ stands for thee dynamic fluid f viscosity coefficient off nitrogen, and a is equa al to 1.758×10-5 Pa ⋅ s under a room temp perature of 20°C; 2 L and A aree the height and a cross-seection area off the rock samplle, respectiveely.
2
Resultts
2.1 P-wav ve velocity The P--wave velocitty (Vp) in a rock r dependss on the rock lithology, porosity p and d clay con ntent (Domenico o 1984; Han n et al. 198 86). During the freeze-thaw w cycles, th he P-wave velocities were w measured several s timees and the reesults from both b rock samplles were show wn to be sim milar. In Figurre 3,
Fiigure 3 Varia ation of P-wavve velocity for sample 12-2 du uring freeze-th haw cycles.
to According the macroscopic m pheenomenologiical damage mechanics, the damage with the folllow formula variable Dn can n be defined w (Od da et al. 1984 4):
⎛ Vp ⎞ Dn ≈ 1 − ⎜ pn ⎜ V ⎟⎟ ⎝ p0 ⎠
2
(2)
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where Vpn is the P-wave velocity of rock sample after n (1, 2…) freeze-thaw cycles, and Vp0 is the initial P-wave velocity of rock sample before freezethaw cycles. Figure 4 illustrates the relation curve between damage variables Dn and freeze-thaw cycles. It can be seen from the figure that the damage variables Dn increase with number of freeze-thaw cycles. And the dispersed coordinate points are fitted by quadratic function as follow:
Dn = −0.025 + 0.045n − 8.871× 10−5 n 2
about 41.50%, from 12.51 GPa to 7.32 GPa. These act as further evidence that freeze-thaw damage was accumulated with an increase in freeze-thaw cycles, which weakened the material properties of the rock skeleton, increased the void ratio, and lowered the strength.
(3)
Compared with previous researches on the relationship between damage variable Dn and freeze-thaw cycles for red sandstone (Liu et al. 2008; Chen 2012), the variation tendency is pretty close. Though different damage variables Dn were defined in different researches, the results shown in this paper are quite reasonable. It is clear that Dn<1, which indicates that the microfractures are formed in the process of the freezing and thawing cycles. Based on the value of Dn, the damage degree of the rock under the conditions of the freeze-thaw cycles can be approximately estimated.
Figure 4 Relation curves between damage variable Dn and freeze-thaw cycles and comparison with previous researches.
2.2 Mechanical properties under uniaxial and triaxial compression Four groups of uniaxial compression tests were conducted to compare the mechanical behaviours under the freeze-thaw cycles. Figure 5 shows the uniaxial compression test stress-strain curves subjected to 0, 4, 8 and 12 freeze-thaw cycles. Figure 6 illustrates the relation between the elastic modulus and number of freeze-thaw cycles for the red sandstone samples. The elastic modules are calculated, in the process of triaxial compression, by following the equation from the theory of elasticity (Timoshenko et al. 1951):
E=
σ 1 − 2 μσ 3 ε1
(4)
where σ 3 is the confining pressure; μ is the Poisson's ratio; σ 1 is the axial stress of 50% peak stress, and ε 1 is the corresponding axial strain of σ 1 . It can be observed from Figures 5 and 6 that the number of freeze-thaw cycles has a significant influence on the uniaxial compressive strength and elastic modulus. The uniaxial compressive strength of the red sandstone decreases from 58.71 to 40.85 MPa after 12 repetitions of freeze-thaw action. For the elastic modulus, the decrease in the average is
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Figure 5 Several stress-strain curves under freezethaw cycles.
Figure 6 Relation between elastic modulus En and number of freeze-thaw cycles for red sandstone.
With these elastic modules data, the damage variables Dn could be calculated by the following formula from the damage mechanics (Lemaitre et al. 2005):
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Dn = 1 −
E n E0
(5)
is the elastic modulus of red sandstone where E n that goes through n cyclic freezing and thawing; E0 is the elastic modulus of red sandstone that has not been frozen and thawed. The scatter diagram is plotted in Figure 7. Comparing them with the curve from Equation (3) which is also plotted in Figure 7, it proves again that the fitting Equation (3) is mostly in line with the damage mechanics. In addition, it also can be seen from Figure 7 that the higher the confining pressure is, the higher the elastic modulus will be. The results are in agreement with previous research (Gatelier et al. 2002; Wang et al. 2012).
(a)
(b)
Figure 7 the Comparison between the damage variables Dn calculated by Equation (5) with curve from Equation (3).
Figures 8, 9, 10 and 11 illustrate the stressstrain relationship and permeability evolution in the triaxial compression tests under the confining pressures of 5, 10 and 20 MPa for 0, 4, 8 and 12 cycles of freeze-thaw action, respectively. From these stress-strain curves, it is known that the confining pressure has a very significant influence on the peak stress. The relation between confining pressure σ3 and peak stress σ1 can usually be expressed with the following empirical equation:
σ1 =
2c ⋅ cos ϕ 1 + sin ϕ + σ3 1 − sin ϕ 1 − sin ϕ
(6)
where c is the cohesion, and φ represents the angle of internal friction. This equation is known as the Mohr-Coulomb criterion. For the uniaxial compression strength of rock ( σ 3 = 0 ) the corresponding equation is σ c = 2c ⋅ cos ϕ / (1 − sin ϕ ) . From the Mohr-Coulomb criterion, it can be seen that the peak stress increases with an increase of the confining pressure when the value of angle of the internal friction is determined. On the basis of the Mohr stress circles, the calculated parameters
(c) Figure 8 Stress-strain curves and permeability evolution in triaxial compression test under confining pressure of (a) 5 MPa, (b) 10 MPa and (c) 20 MPa for 0 cycle of freeze-thaw. Table 2 Shear strength parameters of rock samples No. of F-T cycles
0 4 8 12
Cohesion (MPa)
10.68 10.42 10.07 9.37
Angle of IF
51.01 48.42 44.67 39.80
Notes: No. of F-T cycles = Number of freeze-thaw cycles; Angle of IF = Angle of internal friction (°)
for shear strength for 0, 4, 8 and 12 cycles of freeze-thaw are shown in Table 2. It can be seen that both the value of cohesion c and the angle of internal friction φ decrease with an increase in the number of freeze-thaw cycles. Rock consists of mineral particles, adhesives and a small amount of pore. The major determinants of the cohesion are distance of mineral particles, degree of cementation and so on. The reason for the
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decreasing of cohesion is that the freezing-thawing action enhances the range and damages the cementation among particles in the rock. On the other hand, the internal friction angle is determined by sliding friction and occlusal friction. The secondary microcracks, after several cycles of freezing and thawing, increase the crack space and width and reduce the degree of occlusion, which leads to a decrease in internal friction angle.
(a)
(b)
(c)
Figure 9 Stress-strain curves and permeability evolution in triaxial compression test under confining pressure of (a) 5 MPa, (b) 10 MPa and (c) 20 MPa for 4 cycles of freeze-thaw.
Photographs of the fracture patterns of rock specimens taken from the plastic seal cartridge after the test are shown in Figure 12. With the confining pressure increases from 5 to 20 MPa, the failure modes have changed in the angles of the macrocracks. Under low confining pressure, the macrocracks form at close to a 0 degree angle from the axial direction and the failure pattern of the
224
(a)
(b)
(c) Figure 10 Stress-strain curves and permeability evolution in triaxial compression test under confining pressure of (a) 5 MPa, (b) 10 MPa and (c) 20 MPa for 8 cycles of freeze-thaw.
rock specimen show splitting failures. This is because the axial load leads to the expansion in the radial direction under low confining pressure because of Poisson effect. This type of crack occurs when the transverse tensile stress generated internally exceeds the tensile strength. The rock samples form a lean-to shear failure mode under confining pressure of 10-20 MPa. This is due to the maximum shear stress on the failure surface, which exceeds the limit value. From the cyclic freezingthawing perspective, it seems that the shattering degree increases with more freezing and thawing cycles after the triaxial compression experiments. 2.3 Permeability of red sandstone in a complete stress-strain process It is also can be seen from Figures 8 to 11 that
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(a)
(b)
(c) Figure 11 Stress-strain curves and permeability evolution in triaxial compression test under confining pressure of (a) 5 MPa, (b) 10 MPa and (c) 20 MPa for 12 cycles of freeze-thaw.
the permeability evolution of the rock samples after the cycles of freeze-thaw in a complete stress-strain process under triaxial compression is closely related to the variation of the microstructure in the rock. According to the test results, gas permeability can be characterized into different stages, as follows. (1) In the stage of primary micro-cracks and pore compaction inside the rock, the stress-strain curves are nonlinear and concave, and the strain increment decreases as the stress increases. A slight drop in permeability from the initial value is displayed in the curves. This is because the initial pores and micro-cracks in the rock specimen are compressed and close in a direction perpendicular to the principal stresses. (2) In the stage of linear elastic deformation, the stress-strain curves develop in a basically linear
fashion. The increase in the axial stress makes it possible for the initial pores to grow in size in their preferred directions. Several new micro-cracks form in the rock samples under the coupling of gas osmotic pressure and compression stress. The pores and micro-cracks, however, do not fully connect in this stage to produce a significant increase in permeability. (3) In the stage of nonlinear elastic-plasticity, the stress-strain curves deviate from the straight line and dive downwards. The slope of the curves decreases gradually. The rock specimens approach the peak stress and tend to fail. The evolution, connection, concentration and coalescence of the micro-cracks form macro-fractures in the rock samples, enabling the permeability to be enhanced sharply by about one or two orders of magnitude. (4) On the peak stress point, induced macrocracks may occur and brittle fractures may even be penetrated. The permeabilities continue to grow at a lower ratio. (5) In the stage of strain softening, the bearing capacities of the rock samples decrease gradually with the increase of axial strain. Sliding and rotation of the fractured rocks along the irregular rough surface produces a larger or smaller gap on the interface, which gives rise to changing permeability curves trending towards two different shapes: rising or falling. At this stage, macro-cracks or macro-fractures have been already forced and connected, so permeability is related to several parameters including the fracture width, the roughness of the fracture surface, and distribution and connection of fracture networks. The reason for the rise in permeability is that the gaps of fracture interface are filled with particle aggregates and debris as further deformation develops. But the reason for decreasing permeability is quite different. The roughness staggers both interfaces of fractures, which forces a good channel to permeate. The results of permeability characteristics in a complete stress-strain process agree with the findings of Yinzhuang sandstone (Li et al. 1997). For red sandstone, which is a porous medium, permeability is related to several factors on both the microscopic and macroscopic scales. On the microscopic scale, the critical factors include the shape, size, density and orientation of the initial and induced pores. On the macroscopic scale, the factors are the apertures, roughness, distribution
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(a) 0 cycle
(b) 4 cycles
(c) 8 cycles
(d) 12 cycles
Figure 12 Fracture patterns of rock specimens after the tests: (a) 0 cycle; (b) 4 cycles; (c) 8cycles and (d) 12 cycles.
and connection of the macrocrack networks. Undoubtedly, the changes of the internal structure of the rock samples cause the variation of the permeability in the process of triaxial compression. In addition, from Figures 8 to 11 it is clear that the change in the confining pressure and number of freeze-thaw cycles do not affect the trends of the permeability development, only the relative values during all stages do. In the process of triaxial compression, the confining pressure plays a restricted role on the inner microcrack initiation, growth, propagation, connection and linkage. It also inhibits the apertures of the rock samples to restrain the increase of permeability. Due to the fact that the values of the permeabilities change in the complete stress-strain process and only a portion of the values can be measured, it is difficult to compare and analyze each value in every stage. The value of the initial permeability is the first result of the permeability test and the structure of the red sandstone samples remains unchanged at this moment. The relation between the values of initial permeability and number of the freeze-thaw cycles and the relation between initial permeability and damage variable Dn for red sandstone samples under the confining
226
pressure of 5, 10 and 20 MPa are shown in Figures 13 and 14, respectively. In Figure 14, the damage variables Dn are calculated by equation (3) and the values of Dn, when n=0, are fixed. As seen from the figures, as the number of freeze-thaw cycles increases, the value of the initial permeability also increases under certain confining pressures. This can be interpreted as follows: during the cyclic freeze-thaw action, water infiltrates into the initial fissures, and then turns into ice. Frost heave force which is induced by the ice leads to new microcracks in the rock samples, and these induced microcracks work as new flow channels of fluid. Therefore, the initial permeability increases with each cycle of freeze-thaw action. From the damage mechanics perspective, the larger the damaged degree is, the higher the rocks’ permeability. On the other hand, when the number of freeze-thaw cycles is held constant, the value of initial permeability decreases with the growing confining pressure. This is because the microcracks and pores were compressed with the action of the confining pressure, and these flow channels of gas downsize and some are even completely blocked. In addition, stages (2) and (3) can be analyzed, which are the courses of the accumulative damage
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σ = E0 (1 − Dn )(1 − DC ) ε
(9)
Parameter D can be signed as
D = Dn + DC + Dn DC
(10)
Then equation (7) can be written as
σ = E0 (1 − D ) ε
(11)
Permeabilities are calculated using equation (1) in these stages. It is easy to see that the only parameter relevant to damage variable D in equation (1) is the flow Q. The equation is written as Figure 13 Relation between the values of initial permeability and number of freeze-thaw cycles for red sandstone under different confining pressures.
Q = Q( D)
(12)
Then the Darcy’s law (equation (1)) is finally re-expressed as
k=
2 p0 μ L Q ( D) ( P12 − P2 2 ) A
(13)
Consequently, the relationship between stressstrain (equation (9)) and permeability (equation (11)) is built up by the sharing damage variable D. 2.4 Relationship between permeability and volume strain
Figure 14 Relation between the values of initial permeability and damage variable Dn for red sandstone under different confining pressures.
before peak stress, from a damage mechanics perspective. Based on the principle of strain equivalence (Lemaitre et al. 2005), the constitutive model for rocks that go through both cyclic freezing-thawing action and triaxial compression can be established as the follow equation:
σ = En (1 − DC ) ε
(7)
where DC is the damage variable during triaxial compression, and En is the elastic modulus of rock under the freezing-thawing damage condition (Figure 7), which can be described by follow formula: En = E0 (1 − Dn )
(8)
where Dn is the damage variable of rock after cyclic freezing-thawing action; E0 is the initial elastic modulus before freezing-thawing damage. From equations (5) and (6) the constitutive model is evaluated as follow:
In geotechnical engineering, a positive sign is usually used to indicate compressive strain and a negative sign to indicate tensile strain. In this paper, volume strains are calculated by the method which is most widely used in the theory of elasticity (Timoshenko et al. 1951). The specific expression is as follow:
ε vol = ε ax + 2ε lat
(14)
where εvol is the volume strain; εax represents axial strain, and εlat stands for lateral strain. Several typical curves are shared to analyze the link between permeability and volume strain, as shown in Figure 15. It can be seen from the figures that the volume strain and permeability have a rather highly corresponding relationship with the axial strain. At the beginning of the experiment, the microcracks are compressed under the action of axial and lateral loads, and the volume strain is positive. In this stage, the values of permeability decline slightly at the same time. When a certain axial load value is reached, cracks form, grow, develop and penetrate in the rock samples as the axial load increases and volumetric expansion
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(a) 0 cycles of freeze-thaw
(b) 4 cycles of freeze-thaw
(d) 12 cycles of freeze-thaw (c) 8 cycles of freeze-thaw Figure 15 Relationship between permeability and volume strain versus axial strain for samples under confining pressure of 10 MPa and different cycles of freeze-thaw.
occurs, which manifests as an increase in negative volume strain. Accordingly, the values of permeability begin to increase slowly. With the further development of crack propagation, fracture coalescence leads to failure in the rock samples and the negative volume strain grow rapidly. At this moment, the values of permeability also rise sharply until the stress-strain curves arrive at the post-peak. Therefore, the volume strain very accurately reflects the variation of permeability in the process of deformation, yield and failure.
3
Discussions
The deterioration proceeds as freezing and thawing repeat, and the red sandstone gradually loses its stiffness and strength. It is commonly accepted that the mechanism of this type of deterioration is as follows (Matsuoka 1990; Hori et al. 1998; Chen et al. 2004; Yavuz et al. 2006; Takarli et al. 2008). When the rock is frozen, the
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volume of the mineral grains in the rock shrinks, but water stored in the initial micropores and microcracks expands by 9% in volume. In order to restrict the impact of this expansion, the great local tensile and compressive stress, which are known collectively as the frost-heave force, are formed among the rock mineral grains. The frost-heave force acts on the rock, and micropores and microcracks increase. Water then flows through the fractured micropores and microcracks when the rock is thawed, which accelerates the damage. However, the deterioration process is not clarified completely, because it depends on a large number of other external factors such as lithological characters (Nicholson et al. 2000), the repletion of freezing and thawing (Nicholson et al. 2000), the freezing-thawing rate, water saturation (Chen et al. 2004), the range of freezing and thawing temperatures (Chen et al. 2004) and so on. So more factors should be explored and additional essential causes should be researched in further study.
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As it is known, the relationship between stress-strain (equation (9)) and permeability (equation (11)) are built up by the shared damage variable D. Many previous literatures have introduced the relationship between damage and permeability (Li et al. 1994; Zhu et al. 1997; Davy et al. 2007; Yang et al. 2007). These literatures set forth preliminary relationship between permeability and strain in the process of triaxial compression. But the damage mechanical perspective has not been discussed yet. A further study is needed to find the specific function (equation (10)). What’s more, from Figures 8 to 11, the rising of permeability of rock usually lags behind the growing of the stress-strain curves, which is a similar result to previous studies (Li et al. 1994, Wang et al. 2002). In the author’s opinion, the lagging effect can be corrected by parameters such as time, strain or other factors, which also need to be explained in detail.
4
Conclusion
This study investigated the evolution of compressional wave velocities, mechanical properties and permeability characteristics of red sandstone in triaxial compression tests performed at the confining pressures 5, 10 and 20 MPa. The experimental study of red sandstone samples were carried out; the samples were divided into four groups, which respectively underwent 0, 4, 8 and 12 cycles of freezing and thawing. With the increasing of cyclic freeze-thaw times, the P-wave velocity in the red sandstone decreased, which was interpreted by the damage of rock leading to the changes of microstructure and mechanical performance in an environment of freezing and thawing cycles. Using the damage variable Dn based on damage mechanics concepts,
the change of the microstructure of the red sandstone was described. The number of freezethaw cycles had influences on the uniaxial compressive strength, elastic modulus, cohesion, and angle of internal friction. They were all lower with higher numbers of freezing and thawing cycles. Gas permeability of red sandstone in a complete stress-strain process varied with the evolution of microstructures in the rocks. Generally speaking, permeability decreased in the initial loading stage, then gradually increased with the load. Prior to the peak stress, the permeabilities were enhanced sharply by about one or two orders of magnitude. In the stage of strain softening, the changing curves of permeability trended towards two different shapes, rising or dropping. The relationship between stress-strain and permeability could be described by the damage variable D. Moreover, with the increase of freeze-thaw cycle number, the value of the initial permeability increased under certain confining pressures. And when the number of freeze-thaw cycles was determined, the value of the initial permeability decreased with the growing confining pressure. Also, there was a strongly corresponding relationship between the volumetric strain and permeability with axial strain in all stages of the stress-strain curves.
Acknowledgements This work was supported by the National Basic Research Program of China (973 Program) (Grant No. 2011CB013503), the National Natural Science Foundation of China (Grant No. 51374112), and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-PY112).
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