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Experimental investigation on dilatancy behavior of water-saturated sandstone
International Journal of Mining Science and Technology xxx (2017) xxx–xxx
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International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Experimental investigation on dilatancy behavior of water-saturated sandstone Jiangyu Wu a,b, Meimei Feng a,b,⇑, Bangyong Yu a,c, Wenli Zhang b, Xiaoyan Ni a, Guansheng Han a a
State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221116, China School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China c Institute of Construction Engineering Technology, Changzhou Vocational Institute of Engineering, Changzhou 213164, China b
a r t i c l e
i n f o
Article history: Received 18 January 2017 Received in revised form 1 June 2017 Accepted 13 August 2017 Available online xxxx Keywords: Rock mechanics Dilatancy behavior Confining pressure Pore pressure Water-saturated
a b s t r a c t It is important to study the dilatancy property of water-saturated rock for understanding the engineering behavior of loaded rock mass. This study carried out the uniaxial and triaxial compressive experiments on the water-saturated red sandstone, analyzed the influences of confining pressure and pore pressure on dilatancy property of water-saturated rock, and discussed the reasonable basis of the stress of dilatancy onset as a strength design parameter of rock engineering, finally established the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure. The results show that the strength parameters (the stress of dilatancy onset and peak strength) and deformation parameters (axial strain and circumferential strain) of water-saturated sandstone increase with the confining pressure, and the relations can be fitted with a positive linear function. The cohesion and internal friction angle obtained from the stress of dilatancy onset decrease by 11.57% and 7.33%, respectively, when compared with those obtained from the peak strength. The strength parameters and deformation parameters of water-saturated sandstone decrease basically with the increase of pore pressure, in which the relations between strength parameters or axial strain and pore pressure can be fitted with a negative linear function. However, the relation between the peak circumferential strain and the pore pressure should be characterized by a negative exponential function, and the circumferential strain at dilatancy onset isn’t affected by the pore pressure. Ó 2017 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction The transition from compression to dilatancy of rock mass in the deformation process under loading causes the full development of structural defects such as original fissures, pores and new cracks, which results in the irreversible damage in rock. Consequently, the failure of rock mass and the safety problem in engineering easily occur [1–4]. For example, during the construction of tunnel in the mountainous areas with the red sandstone including Hunan, Hubei, and Jiangxi provinces, the dilatancy of rock frequently caused the failure of fissure structure in rock mass under the effects of excavation, geological structure and erosion of long-term rainwater, which resulted in the geological hazards such as collapse and water inrush [5,6]. In coal mining, the dilatancy displacement increased sharply under the impacts of mining and ⇑ Corresponding author at: State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China. E-mail address: [email protected] (M. Feng).
groundwater, and then the fissures in rock mass fully developed to form the underground watercourses, which causes the water bursting disaster [7,8]. Therefore, it is important to study the dilatancy property of water-saturated rock for understanding the engineering behavior of loaded rock mass. Abundant studies including experiment and numerical simulation have been performed to investigate the dilatancy behavior of rock under loading. For example, some scholars discussed the variations of porosity and permeability of rock in the stage of dilatancy, and the full development of microcracks among rock grain was confirmed by the microstructure observation. Even if the deformation is extremely small, the permeability increases with magnitude because of the expansion and propagation of cracks in rock [9,10]. Because the engineering rock mass in some areas is under the condition of high pore pressure, Alkan et al. studied the effect of pore pressure on the stress of dilatancy onset through the conventional triaxial experiment of rock [11]. In order to obtain the influence of rock dilatancy on the stability of tunnel, Tan and Alejano et al. calculated the dilatancy region of tunnel by constructing the constitutive equation of dilatancy [12–14]. The deep rock mass is usually
https://doi.org/10.1016/j.ijmst.2017.09.003 2095-2686/Ó 2017 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: Wu J et al. Experimental investigation on dilatancy behavior of water-saturated sandstone. Int J Min Sci Technol (2017), https://doi.org/10.1016/j.ijmst.2017.09.003
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under three-directional compression, so lots of researches about the relations between confining pressure and dilatancy parameters were carried out [15–18]. And some scholars investigated the dilatancy property of different rocks under creep deformation for understanding the dilatancy behavior of rock mass under longterm loading [19–21]. Due to the cracks, microcracks, joints and other defects are widely distributed in the engineering rock mass, Yang and Trivedi et al. analyzed the impact of pre-existing fissures on dilatancy parameters of rock [22,23]. In addition, the effect of dilatancy property on mechanisms of crustal fault, floor heave deformation of roadway, rock burst and precursor information of earthquake was discussed [24,25]. There are many factors that affect the dilatancy property of rock. However, due to the different external loads, the dilatancy parameters of rock are difficult to quantify, and it is difficult to give the optimal parameter selection in engineering design. For this purpose, Martin and Chandler suggested that the 50% uniaxial compressive strength (UCS) can be used as the strength design parameter of rock material to reduce the occurrence of safety accident in engineering [26]. However, this is only an empirical criterion, and its mechanism isn’t revealed clearly. Consequently, the uniaxial and triaxial compressive experiments of water-saturated red sandstone under different confining pressures and pore pressures were carried out, the influences of confining pressure and pore pressure on dilatancy property of water-saturated rock were analyzed, the rationality of the stress of dilatancy onset as a strength design parameter of rock engineering was discussed, and the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure was established.
2. Experimental materials and method In this test, the red sandstone specimens were obtained from Hongyang Mine in Shandong, China. The average density is about 2.43 g/cm3, and the X-ray diffraction (XRD) spectrum is shown in Fig. 1. According to the test method proposed by the International Society for Rock Mechanics (ISRM), the rock specimens were processed into cylinders of /50 mm 100 mm, which two ends were polished, and the non-parallelism and non-perpendicularity were controlled within ±0.02 mm [27]. Then the processed rock specimens were soaked with distilled water for more than 96 h until the qualities of specimens weren’t increased to ensure that it reached saturation. The average moisture content is about 2.51% under the condition of saturation [28,29]. This study uses MTS815 rock mechanics test system for experiment, as shown in Fig. 2. The Vaseline was applied between the both ends of specimen and the indenter to eliminate the effect of the indenter loading on acoustic emission (AE) signals. The MTS815 system was controlled to load rock specimen at axial loading rate of 0.002 mm/s, and the initial prestress is 0.5 kN [30,31]. The confining pressure levels were set respectively at 0, 5, 10, 15
Fig. 1. XRD spectrum of red sandstone.
Fig. 2. MTS 815 system.
and 20 MPa in triaxial compressive experiment at a rate of 0.04 MPa/s, after the confining pressure loaded to the specified value, the axial displacement of 0.002 mm/s was conducted with the constant confining pressure. And the pore pressure levels were set respectively at 0, 3, 5 and 8 MPa at a rate of 0.02 MPa/s in compressive experiment. After the pore pressure loaded to the specified value, the axial displacement of 0.002 mm/s was conducted with the constant pore pressure. In this paper, the symbol of r3 is the confining pressure and the symbol of ru is the pore pressure. 3. Experimental results In order to test the difference among the sandstone specimens, a group of specimens were randomly selected for the uniaxial compressive experiment as shown in Fig. 3. The results show that the UCS of the four rock specimens are 113.74, 107.38, 104.36 and 101.28 MPa, the average value is 106.67 MPa, and the coefficient of variation only is 6.63%. It can be seen that the discrepancy among the different specimens processed by the same rock mass is small and can be used for the comparative test. According to the literatures, the initial point of e1 < |e2 + e3| (or the end point of e1 |e2 + e3|) during the load process can be defined as the cd point of dilatancy onset [32,33]. Fig. 4 presents the mechanical behavior of water-saturated red sandstone to denote the dilatancy characteristic, which shows that the load process of red sandstone specimens can be divided five stages, including o-cc stage of pore compaction, cc-ci stage of elastic deformation, ci-cd stage of initiation and stability expansion of crack, cd-c stage of damage and unstable propagation of crack and failure stage. The characteristics of each stage are described in detail below: (1) o-cc stage of pore compaction: The existences of the original cracks and pores in rock specimen compact with the increase of axial stress, which causes the stress-strain to present nonlinearity. The AE signals are weak in this stage. However, the circumferential strain remains the same on
Fig. 3. Axial stress-axial strain curves of water-saturated sandstone under uniaxial compression.
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3.1. Effect of confining pressure on the dilatancy property of watersaturated red sandstone
Fig. 4. Stress-strain-AE curves of water-saturated sandstone denoted dilatancy.
(2)
(3)
(4)
(5)
the whole, which resulted in a linear relationship between volumetric strain and axial strain. cc-ci stage of elastic deformation: The AE signals gradually increase with the axial deformation, which are caused by the occlusion and friction of rough surface in rock samples after the compaction of the original cracks and pores. The axial and circumferential strains in this stage are in linear variations, resulting in the volumetric strain also showed linear characteristics. The end point of ci in this stage is the initial point of volumetric strain that deviates from the linear variation, and the criterion of e1 > |e2 + e3| is permanent establishment before this point. ci-cd stage of initiation and stability expansion of cracks: The closed original cracks, pores and new cracks in rock start to expand and propagate with the increase of axial stress, which caused the AE signals fluctuate and the stress-strain behavior deviate from the linear variation. The circumferential strain of rock specimen gradually increases because of the expansion and propagation of cracks, so that the increase rate of volumetric strain gradually decreases and deviates from the linear variation, thus, the criterion of e1 > |e2 + e3| transforms to e1 = |e2 + e3|. cd-c stage of damage and unstable propagation of cracks: When the axial stress reaches the value of dilatancy onset, the volumetric strain of rock specimen is the maximum value in the whole loading process, and the variable rate of volumetric strain is 0. The criterion of e1 > |e2 + e3| is permanent establishment after this point, thus, the volumetric strain of rock specimen began to decrease, that is, the rock specimen transforms from compression to dilatancy. This turning point is due to the irreversible damage in rock, which results in a rapid increase in the volume deformation of rock specimens. The fluctuant AE signals are more significant because of the damage and unstable propagation of cracks in this process. The large expansion and propagation of cracks will result in the sudden increase in AE signals. Failure stage: The axial stress of rock specimen is characterized by strain softening in this process. When the stress drops, the macroscopic fracture surface is formed by the expansion and propagation of cracks in rock specimen, and the AE signals are suddenly increased and the volumetric strain of rock specimen is further decreased. When the stress decreases to the residual strength, the rock specimen can still bear the axial load by the friction and slip between the fracture surface and the grain.
Fig. 5 shows the stress-strain curves of water-saturated sandstone under different confining pressures. Table 1 presents the mechanical parameters of specimens at dilatancy onset and peak point. The relations between mechanical parameters and confining pressures are shown in Figs. 6–8, and the corresponding relation expressions are list in Table 2. It can be seen from Figs. 6–8 that the mechanical parameters of water-saturated sandstone at dilatancy onset and peak point increase with the confining pressure, and the relationships which can use the positive linear functions to characterize by r1 = Ar3 + B and ei = Ar3 + B. The influence of confining pressure on mechanical parameters at peak point is larger than that at dilatancy onset, and the corresponding parameter representation is reflected in the difference of coefficient A. This is mainly due to the frictions and slippages among the particles inside rock materials causing the full development of cracks after dilatancy onset. The cohesive force among particles has been instability under the condition of high confining pressure, and the rock specimen can rely on the friction among the particles to bear the axial load. Obviously, the high confining pressure greatly effects on the internal friction characteristic of rock specimen. It causes the sensitivity of mechanical parameters to confining pressure at peak point to be higher than that at dilatancy onset. It is worth noting that the correlation coefficients between mechanical parameters and confining pressure at dilatancy onset are always higher than that at peak point. The correlation coefficient between circumferential strain at peak point and confining pressure is only 0.4523, and the circumferential strain at peak point presents a larger discretization. It can be interpreted as the propagation of cracks in cd-c stage of rock specimen under loading is developed, and the evolution of cracks causes the rock specimen to produce irreversible damage. Even for the optimal uniformity of rock material, it also affects the strength and deformation of rock specimen under loading in the cd-c stage due to the existence of defects in rock such as original fissures, microcracks, pores and grain boundaries. Considering these characteristics, in order to avoid the large deformation and the full development of cracks in the engineering rock mass, it is feasible to use the stress of dilatancy onset as the strength parameter in the engineering design. According to Table 2, the strength parameters at the dilatancy onset and peak point of the rock specimens can be obtained by using the M-C strength criterion, as shown in Table 3.
Fig. 5. Stress-strain curves of water-saturated sandstone under different confining pressures.
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Table 1 Mechanical parameters of water-saturated sandstone under different confining pressures.
r3 (MPa)
r1cd (MPa)
e1cd (103)
e3cd (104)
evcd (103)
r1c (MPa)
e1c (103)
e3c (103)
evc (103)
0 0 5 5 10 10 15 15 20 20
87.37 96.14 108.63 107.26 124.09 129.58 144.59 143.48 160.62 163.97
7.62 8.54 8.14 8.69 9.12 9.26 9.77 9.84 10.44 10.39
0.95 0.84 0.96 1.13 1.30 1.26 1.44 1.36 1.54 1.60
5.71 6.87 6.22 6.43 6.52 6.73 6.88 7.12 7.36 7.19
101.28 107.38 134.28 131.79 147.10 158.26 170.27 167.52 183.70 187.93
8.82 9.42 10.28 10.39 11.42 11.65 12.23 12.33 12.52 12.57
2.49 1.62 3.37 3.03 4.38 3.91 4.32 4.51 3.65 3.77
3.85 6.19 3.53 4.33 2.66 3.82 3.62 3.31 5.22 5.03
Note: r1cd is the axial stress of dilatancy onset; e1cd the axial strain of dilatancy onset; e3cd the circumferential strain of dilatancy onset; evcd the volumetric strain of dilatancy onset; r1c the peak strength; e1c the axial peak strain match with the peak strength; e3c the circumferential peak strain match with the peak strength; and evc the volumetric peak strain match with the peak strength.
Table 2 Fitting relationship between mechanical parameters and confining pressures. Mechanical parameter
Fitting relationship
Correlation coefficient
r1cd r1c e1cd e1c e3cd e3c
r1cd = 3.5434r3 + 91.1390 r1c = 3.9766r3 + 109.1850 e1cd = 0.1212r3 + 7.9690 e1c = 0.1759r3 + 9.4040 e3cd = 0.0341r3 + 0.8970 e3c = 0.0905r3 + 2.6000
0.9994 0.9795 0.9861 0.9313 0.9890 0.4523
Table 3 Strength parameters of dilatancy onset and peak point.
Fig. 6. Relation between axial stress and confining pressure.
Content
M (MPa)
N
c (MPa)
u (°)
Dilatancy onset Peak point
91.1390 109.1850
3.5434 3.9766
24.2083 27.3764
34.0420 36.7353
where M and N are the strength parameters; c the cohesion, MPa; and u the internal friction angle, °. It is easy to see that the strength parameters obtained from dilatancy onset are lower than those from peak point in Table 3. The cohesion and internal friction angle are 24.2083 MPa and 34.042° obtained from dilatancy onset, which decrease by 11.57% and 7.33%, respectively, compared with those obtained from peak point.
Fig. 7. Relation between axial strain and confining pressure.
3.2. Effect of pore pressure on the dilatancy property of watersaturated red sandstone
Fig. 8. Relation between circumferential strain and confining pressure.
r1 ¼ M þ Nr3
ð1Þ
M¼
2c cos u 1 sin u
ð2Þ
N¼
1 þ sin u 1 sin u
ð3Þ
Fig. 9 shows the stress-strain curves of water-saturated sandstone under different pore pressures. It isn’t difficult to see that the stress-strain behavior of rock specimens presents the obvious plasticization with the increase of pore water pressure. Table 4 lists the mechanical parameters of specimens at dilatancy onset and peak point. The relations between mechanical parameters and pore pressures are shown in Figs. 10–12, and the corresponding relation expressions are list in Table 5. It should be pointed out that the confining pressure of rock specimens under different pore pressures is the same value of 10 MPa, which simulates the influence of pore pressure on mechanical behavior of water-saturated sandstone under the deep ground stress of 10 MPa. It can be seen from Figs. 10–12 that the mechanical parameters of water-saturated sandstone at dilatancy onset and peak point decrease with the increase of pore pressure, and the relationships which can use the negative linear functions to characterize by r1 = Cru + D and ei = Cru + D. This is mainly due to the existence of defects such as original fissures and pores in the rock specimens,
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Fig. 10. Relation between axial stress and pore pressure.
Fig. 9. Stress-strain curves of water-saturated sandstone under different pore pressures.
and the new cracks constantly evolve under the action of axial load. These weak planes can be expanded and extended under the action of water pressure. The higher pore pressure is, the greater damage on the rock, which results in the deterioration in the strength and deformation properties of rock material. And the influence of pore pressure on mechanical parameters at peak point is larger than that at dilatancy onset, and the corresponding parameter representation is reflected in the difference of coefficient C. This can be explained by the fact that the increase of pore pressure can effectively weaken the friction effect among the particles in rock materials, it can weak the increase behavior of axial stress of rock specimens in cd-c stage under the condition of compression shear, which also can be proved from the relationship between residual strength of rock specimen and pore pressure. The rock specimen can rely on the friction among the particles to bear load after compression shear failure under the confining pressure, thus, the residual strength isn’t 0 MPa. However, in Fig. 9, the residual strength of rock specimen is about 55 MPa when the pore pressure is 0 MPa, the final strength of rock specimen is only 17 MPa when the pore pressure is 8 MPa, and there is still a decreasing trend. So it is shown that it isn’t reasonable to use the peak strength of rock as the design parameter of engineering rock under high pore pressure. And in Fig. 12, the circumferential strains of rock specimens at dilatancy onset with different pore pressures tend to a certain value of 1.242 103. However, the circumferential strains at peak point are approximately negative exponentially with the pore pressure, which indicates that the damage of pore pressure on the cd-c stage is significantly stronger than o-cd stage in the compression process. So it can be seen that the deformation of rock before dilatancy onset is still controllable under high pore pressure. After the dilatancy onset, the damage
Fig. 11. Relation between axial strain and pore pressure.
Fig. 12. Relation between circumferential strain and pore pressure.
Table 5 Fitting relationship between mechanical parameters and pore pressures. Mechanical parameter
Fitting relationship
Correlation coefficient
r1cd r1c e1cd e1c e3cd e3c
r1cd = 4.0588ru + 127.7253 r1c = 5.4224ru + 149.7525 e1cd = 0.1866ru + 9.2309 e1c = 0.2833ru + 11.3992 e3cd = 1.2420 e3c ¼ 1:3873eru=1:1382 þ 2:6991
0.8770 0.9216 0.9486 0.9297 0.9999 0.8821
Table 4 Mechanical parameters of water-saturated sandstone under different pore pressures.
ru (MPa)
r1cd (MPa)
e1cd (103)
e3cd (104)
evcd (103)
r1c (MPa)
e1c (103)
e3c (103)
evc (103)
0 0 3 3 3 5 5 8 8
124.09 129.58 120.68 113.64 109.39 109.30 117.44 93.00 90.82
9.12 9.26 9.53 8.56 8.08 8.10 8.78 7.71 7.55
1.30 1.26 1.33 1.18 1.24 1.17 1.25 1.16 1.34
6.52 6.73 6.87 6.19 5.61 5.76 6.28 5.39 4.88
147.10 158.26 131.07 124.53 126.08 120.42 130.11 106.52 107.64
11.42 11.65 10.79 9.90 10.04 9.78 10.48 9.05 9.26
4.38 3.91 2.34 2.38 2.98 3.00 2.93 2.38 2.96
2.66 3.82 6.12 5.15 4.07 3.78 4.61 4.28 3.34
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evolution of cracks is more likely to cause the deformation and failure of rock to form the underground watercourse, which results in the water inrush disaster. From this point, in order to prevent the failure of engineering rock mass and the water inrush disasters caused by the development of watercourse in rock, it is recommended to choose the stress of dilatancy onset as the strength design parameter in engineering. 4. Discussion The dilatancy onset of rock has exceeded the elastic stage under loading in the stress-strain behavior. However, it is easy to find that the stress of dilatancy onset linearly varies with its strength and deformation characteristics, and the rock damage is still small before the dilatancy onset. Therefore, the relation between the stress of dilatancy onset and the physical parameters can be established to predict the strength parameters in rock engineering. It is significant for the preventions of engineering rock mass deformation and underground water hazard. Fig. 13 shows the relationship between the stress of dilatancy onset and the elastic modulus of water-saturated sandstone. It can be found that the relationship presents positive linearity, and the correlation coefficient is 0.86. In fact, the stress of dilatancy onset of rock is also related to its external load, assuming that the stress of dilatancy onset is affected by confining pressure and pore pressure, the relationship is easy to build
r1cd ¼ f ðr3 ; ru ; EÞ
ð4Þ
The elastic modulus of rock is also affected by the external load
E ¼ f ð r3 ; ru Þ
ð5Þ
Therefore, the prediction model of the stress of dilatancy onset can be rewritten as
r1cd ¼ f ðr3 ; ru Þ
ð6Þ
According to the experiment, Fig. 14 shows the prediction model of the stress of dilatancy onset
Fig. 13. Relation between stress of dilatancy onset and elastic modulus.
Fig. 14. Prediction model.
r1cd ¼ ar3 þ bru þ cr3 ru þ d
ð7Þ
where a is the influence coefficient of confining pressure on stress of dilatancy onset, and a 0; b the influence coefficient of pore pressure on stress of dilatancy onset, b 0; c the coupled influence coefficient of confining pressure and pore pressure on stress of dilatancy onset; and d the UCS when the pore pressure is 0 MPa. Obviously, the parameters of the above model are related to the physical and mechanical properties of rock material. Under this experimental condition, a is 0.5434, b is 4.0588, c is 0.01215 and d is 91.4958. The correlation coefficient between the obtained model and the experimental data is 0.9670, which can be well used to predict the stress of dilatancy onset. Meanwhile, the model can reflect the common influence of confining pressure and pore pressure on stress of dilatancy onset, and the corresponding influence degree is reflected in parameter c. When the sensitivity of rock to the confining pressure is higher than the pore pressure, c should be positive; otherwise, c should be negative. 5. Conclusions The uniaxial and triaxial compressive experiments on the watersaturated red sandstone were carried out to study the mechanical properties of rock material. The influences of confining pressure and pore pressure on dilatancy property of water-saturated rock were analyzed. The rationality of the dilatancy onset stress as a strength design parameter in engineering was discussed. And the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure was established. (1) The strength parameters (the stress of dilatancy onset and peak strength) and deformation parameters (axial strain and circumferential strain) of water-saturated sandstone increase with the confining pressure, and the relations can be fitted with a positive linear function. The confining pressure enhances the frictional behavior of rock in the cd-c stage of damage and unstable propagation of cracks. It causes the sensitivity of the mechanical parameters to the confining pressure at peak point always to be higher than that at dilatancy onset. The cohesion and internal friction angle obtained from the stress of dilatancy onset are 24.2083 MPa and 34.042°, respectively, decrease by 11.57% and 7.33% compared with those obtained from the peak point. (2) The strength parameters and deformation parameters of water-saturated sandstone decrease basically with the increase of pore pressure, of which the relations between strength parameters or axial strain and pore pressure can be fitted with a negative linear function. However, the relation between the peak circumferential strain and the pore pressure should be characterized by a negative exponential function, which isn’t affected by the pore pressure at dilatancy onset. The pore pressure deteriorates the frictional behavior of rock specimen during the cracks damage and the unstable propagation cd-c stage. It causes the sensitivity of the mechanical parameters to the pore pressure at peak point always to be higher than that at dilatancy onset. (3) The prediction model of the stress of dilatancy onset is related to the physical and mechanical properties (elastic modulus) of rock material and the external load (confining pressure and pore water pressure). Due to the elastic modulus is also affected by the external load, finally, the explicit expression of this model is r1cd ¼ ar3 þ bru þ cr3 ru þ d. The parameters of a, b, c and d have a clear physical meaning, and the reliability of this model is relatively high under the condition of this article.
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Acknowledgments The authors would like to express their sincere thanks and appreciation to Prof. Mao Xianbiao and Chen Zhanqing for guiding and to Prof. Li Yushou for the equipment support. This work was supported by the National Natural Science Foundation of China (Nos. 51404266 and 11502229) and the National Program on Key Basic Research Project of China (No. 2013CB227900). References [1] Bridgman PW. Volume changes in the plastic stages of simple compression. J Appl Phys 1950;20(12):1241–51. [2] Brace WF, Paulding BW, Scholz C. Dilatancy in the fracture of crystalline rocks. J Geophys Res 1966;71(16):3939–53. [3] Liang ZZ, Xing H, Wang SY, Williams DJ, Tang CA. A three-dimensional numerical investigation of the fracture of rock specimens containing a preexisting surface flaw. Comput Geotech 2012;45(45):19–33. [4] Lu XL, Liu QS, Su PF. Constitutive model of rocks considering dilatancy-bulking behaviour and its calibration. Chin J Rock Mech Eng 2013;32(9). 2886-1893. [5] Zhang KN, Zhou B, Peng HY, Hu HH. Engineering properties and stability analysis of red sandstone in Xiangxi expressway. J Univ South China (Sci Technol) 2009;23(3):5–9. [6] Feng MM, Wu JY, Ma D, Ni XY, Yu BY, Chen ZQ. Experimental investigation on seepage property of saturated broken red sandstone of continuous gradation. B Eng Geol Environ 2017. https://doi.org/10.1007/s10064-017-1046-z. [7] Yang TH, Liu J, Zhu WC, Elsworth D, Tham LG, Tang CAA. Coupled flow-stressdamage model for groundwater outbursts from an underlying aquifer into mining excavations. Int J Rock Mech Min 2007;44(1):87–97. [8] Yang TH, Jia P, Shi WH, Wang PT, Liu HL, Yu QX. Seepage-stress coupled analysis on anisotropic characteristics of the fractured rock mass around roadway. Tunn Undergr Sp Tech 2014;43(7):11–9. [9] Zhu W, Wong TF. Network modeling of the evolution of permeability and dilatancy in compact rock. J Geophys Res 1999;104(B2):2963–71. [10] Peach CJ, Spiers CJ. Influence of crystal plastic deformation on dilatancy and permeability development in synthetic salt rock. Tectonophysics 1996;256(1– 4):101–28. [11] Alkan H, Cinar Y, Pusch G. Rock salt dilatancy boundary from combined acoustic emission and triaxial compression tests. Int J Rock Mech Min 2007;44 (1):108–19. [12] Tan T, Wen XM. Swelling rock and stability of tunnels. Chin J Rock Mech Eng 1983;2(1):1–10. [13] Tan T, Shi ZQ, Yu ZH, Wu XY. Dilatancy creep and relaxation of brittle rocks measured with the 8000 KN multipurpose triaxial apparatus. Phys Earth Planet In 1989;55(3):335–52.
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[14] Alejano LR, Alonso E. Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min 2005;42(4):481–507. [15] Ismail IAH, Murrell SAF. Dilatancy and the strength of rocks containing pore water under undrained conditions. Geophys J Int 2007;44(1):107–34. [16] Wong TF, David C, Zhu W. The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation. J Geophys Res 1997;102 (B2):3009–26. [17] Kranz RL. The effects of confining pressure and stress difference on static fatigue of granite. J Geophys Res 1980;85(B4):1854–66. [18] Yuan SC, Harrison JP. An empirical dilatancy index for the dilatant deformation of rock. Int J Rock Mech Min 2004;41(4):679–86. [19] Kranz RL, Scholz CH. Critical dilatant volume of rocks at the onset of tertiary creep. J Geophy Res 1977;82(30):4893–8. [20] Heap MJ, Baud P, Meredith PG, Bell AF, Main IG. Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res 2009;114(B7):1–22. [21] Brantut N, Heap MJ, Meredith PG, Baud P. Time-dependent cracking and brittle creep in crustal rocks: A review. J Struct Geol 2013;52(5):17–43. [22] Yang SQ, Liu XR. Experimental investigation on dilatancy behavior of marble with pre-existing fissures under different confining pressures. Chin J Geotech Eng 2012;34(12):2188–97. [23] Trivedi A. Strength and dilatancy of jointed rocks with granular fill. Acta Geotech 2010;5(1):15–31. [24] Kang HP, Lu SL. An analysis on the mechanism of roadway floor heave. Chin J Rock Mech Eng 1991;10(4):362–73. [25] Tan T. Rockbursts, case records, theory and control. Chin J Rock Mech Eng 1987;6(1):1–18. [26] Martin D, Chandler NA. The progressive fracture of Lac du Bonnet Granite. Int J Rock Mech Min Sci Geomech Abstr 1994;31(6):643–59. [27] Kovari K, Tisa A, Einstein HH, Franklin JA. Suggested methods for determining the strength of rock materials in triaxial compression: revised version. Int J Rock Mech Min Sci Geomech Abstr 1983;20(6):285–90. [28] Zhou H, Li Zhen, Song YZ, Feng XT, Cheng CB. Chemo-thermodynamical method for precisely preparing rock sample with different water contents. Rock Soil Mech 2013;34(2):311–5. [29] Feng MM, Wu JY, Chen ZQ, Mao XB, Yu BY. Experimental study on the compaction of saturated broken rock of continuous gradation. J China Coal Soc 2016;41(9):2195–202. [30] Zhou H, Meng FZ, Liu HT, Zhang CQ, Lu JJ, Xu RC. Experimental study on characteristics and mechanism of brittle failure of granite. Chin J Rock Mech Eng 2014;33(9):1822–7. [31] Zhang ZN, Wang DY, Zheng H, Ge XR. Interactions of 3D embedded parallel vertically inclined cracks subjected to uniaxial compression. Theor Appl Fract Mech 2012;61(1):1–11. [32] Cai MF, He MC, Liu DY. Rock mechanics and engineering. Beijing: Science Press; 2002. [33] Zhou WY, Yang Q. Numerical computational methods for rock mechanics. Beijing: China Electric Power Press; 2005.
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International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Experimental investigation on dilatancy behavior of water-saturated sandstone Jiangyu Wu a,b, Meimei Feng a,b,⇑, Bangyong Yu a,c, Wenli Zhang b, Xiaoyan Ni a, Guansheng Han a a
State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221116, China School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China c Institute of Construction Engineering Technology, Changzhou Vocational Institute of Engineering, Changzhou 213164, China b
a r t i c l e
i n f o
Article history: Received 18 January 2017 Received in revised form 1 June 2017 Accepted 13 August 2017 Available online xxxx Keywords: Rock mechanics Dilatancy behavior Confining pressure Pore pressure Water-saturated
a b s t r a c t It is important to study the dilatancy property of water-saturated rock for understanding the engineering behavior of loaded rock mass. This study carried out the uniaxial and triaxial compressive experiments on the water-saturated red sandstone, analyzed the influences of confining pressure and pore pressure on dilatancy property of water-saturated rock, and discussed the reasonable basis of the stress of dilatancy onset as a strength design parameter of rock engineering, finally established the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure. The results show that the strength parameters (the stress of dilatancy onset and peak strength) and deformation parameters (axial strain and circumferential strain) of water-saturated sandstone increase with the confining pressure, and the relations can be fitted with a positive linear function. The cohesion and internal friction angle obtained from the stress of dilatancy onset decrease by 11.57% and 7.33%, respectively, when compared with those obtained from the peak strength. The strength parameters and deformation parameters of water-saturated sandstone decrease basically with the increase of pore pressure, in which the relations between strength parameters or axial strain and pore pressure can be fitted with a negative linear function. However, the relation between the peak circumferential strain and the pore pressure should be characterized by a negative exponential function, and the circumferential strain at dilatancy onset isn’t affected by the pore pressure. Ó 2017 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction The transition from compression to dilatancy of rock mass in the deformation process under loading causes the full development of structural defects such as original fissures, pores and new cracks, which results in the irreversible damage in rock. Consequently, the failure of rock mass and the safety problem in engineering easily occur [1–4]. For example, during the construction of tunnel in the mountainous areas with the red sandstone including Hunan, Hubei, and Jiangxi provinces, the dilatancy of rock frequently caused the failure of fissure structure in rock mass under the effects of excavation, geological structure and erosion of long-term rainwater, which resulted in the geological hazards such as collapse and water inrush [5,6]. In coal mining, the dilatancy displacement increased sharply under the impacts of mining and ⇑ Corresponding author at: State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China. E-mail address: [email protected] (M. Feng).
groundwater, and then the fissures in rock mass fully developed to form the underground watercourses, which causes the water bursting disaster [7,8]. Therefore, it is important to study the dilatancy property of water-saturated rock for understanding the engineering behavior of loaded rock mass. Abundant studies including experiment and numerical simulation have been performed to investigate the dilatancy behavior of rock under loading. For example, some scholars discussed the variations of porosity and permeability of rock in the stage of dilatancy, and the full development of microcracks among rock grain was confirmed by the microstructure observation. Even if the deformation is extremely small, the permeability increases with magnitude because of the expansion and propagation of cracks in rock [9,10]. Because the engineering rock mass in some areas is under the condition of high pore pressure, Alkan et al. studied the effect of pore pressure on the stress of dilatancy onset through the conventional triaxial experiment of rock [11]. In order to obtain the influence of rock dilatancy on the stability of tunnel, Tan and Alejano et al. calculated the dilatancy region of tunnel by constructing the constitutive equation of dilatancy [12–14]. The deep rock mass is usually
https://doi.org/10.1016/j.ijmst.2017.09.003 2095-2686/Ó 2017 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: Wu J et al. Experimental investigation on dilatancy behavior of water-saturated sandstone. Int J Min Sci Technol (2017), https://doi.org/10.1016/j.ijmst.2017.09.003
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under three-directional compression, so lots of researches about the relations between confining pressure and dilatancy parameters were carried out [15–18]. And some scholars investigated the dilatancy property of different rocks under creep deformation for understanding the dilatancy behavior of rock mass under longterm loading [19–21]. Due to the cracks, microcracks, joints and other defects are widely distributed in the engineering rock mass, Yang and Trivedi et al. analyzed the impact of pre-existing fissures on dilatancy parameters of rock [22,23]. In addition, the effect of dilatancy property on mechanisms of crustal fault, floor heave deformation of roadway, rock burst and precursor information of earthquake was discussed [24,25]. There are many factors that affect the dilatancy property of rock. However, due to the different external loads, the dilatancy parameters of rock are difficult to quantify, and it is difficult to give the optimal parameter selection in engineering design. For this purpose, Martin and Chandler suggested that the 50% uniaxial compressive strength (UCS) can be used as the strength design parameter of rock material to reduce the occurrence of safety accident in engineering [26]. However, this is only an empirical criterion, and its mechanism isn’t revealed clearly. Consequently, the uniaxial and triaxial compressive experiments of water-saturated red sandstone under different confining pressures and pore pressures were carried out, the influences of confining pressure and pore pressure on dilatancy property of water-saturated rock were analyzed, the rationality of the stress of dilatancy onset as a strength design parameter of rock engineering was discussed, and the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure was established.
2. Experimental materials and method In this test, the red sandstone specimens were obtained from Hongyang Mine in Shandong, China. The average density is about 2.43 g/cm3, and the X-ray diffraction (XRD) spectrum is shown in Fig. 1. According to the test method proposed by the International Society for Rock Mechanics (ISRM), the rock specimens were processed into cylinders of /50 mm 100 mm, which two ends were polished, and the non-parallelism and non-perpendicularity were controlled within ±0.02 mm [27]. Then the processed rock specimens were soaked with distilled water for more than 96 h until the qualities of specimens weren’t increased to ensure that it reached saturation. The average moisture content is about 2.51% under the condition of saturation [28,29]. This study uses MTS815 rock mechanics test system for experiment, as shown in Fig. 2. The Vaseline was applied between the both ends of specimen and the indenter to eliminate the effect of the indenter loading on acoustic emission (AE) signals. The MTS815 system was controlled to load rock specimen at axial loading rate of 0.002 mm/s, and the initial prestress is 0.5 kN [30,31]. The confining pressure levels were set respectively at 0, 5, 10, 15
Fig. 1. XRD spectrum of red sandstone.
Fig. 2. MTS 815 system.
and 20 MPa in triaxial compressive experiment at a rate of 0.04 MPa/s, after the confining pressure loaded to the specified value, the axial displacement of 0.002 mm/s was conducted with the constant confining pressure. And the pore pressure levels were set respectively at 0, 3, 5 and 8 MPa at a rate of 0.02 MPa/s in compressive experiment. After the pore pressure loaded to the specified value, the axial displacement of 0.002 mm/s was conducted with the constant pore pressure. In this paper, the symbol of r3 is the confining pressure and the symbol of ru is the pore pressure. 3. Experimental results In order to test the difference among the sandstone specimens, a group of specimens were randomly selected for the uniaxial compressive experiment as shown in Fig. 3. The results show that the UCS of the four rock specimens are 113.74, 107.38, 104.36 and 101.28 MPa, the average value is 106.67 MPa, and the coefficient of variation only is 6.63%. It can be seen that the discrepancy among the different specimens processed by the same rock mass is small and can be used for the comparative test. According to the literatures, the initial point of e1 < |e2 + e3| (or the end point of e1 |e2 + e3|) during the load process can be defined as the cd point of dilatancy onset [32,33]. Fig. 4 presents the mechanical behavior of water-saturated red sandstone to denote the dilatancy characteristic, which shows that the load process of red sandstone specimens can be divided five stages, including o-cc stage of pore compaction, cc-ci stage of elastic deformation, ci-cd stage of initiation and stability expansion of crack, cd-c stage of damage and unstable propagation of crack and failure stage. The characteristics of each stage are described in detail below: (1) o-cc stage of pore compaction: The existences of the original cracks and pores in rock specimen compact with the increase of axial stress, which causes the stress-strain to present nonlinearity. The AE signals are weak in this stage. However, the circumferential strain remains the same on
Fig. 3. Axial stress-axial strain curves of water-saturated sandstone under uniaxial compression.
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3.1. Effect of confining pressure on the dilatancy property of watersaturated red sandstone
Fig. 4. Stress-strain-AE curves of water-saturated sandstone denoted dilatancy.
(2)
(3)
(4)
(5)
the whole, which resulted in a linear relationship between volumetric strain and axial strain. cc-ci stage of elastic deformation: The AE signals gradually increase with the axial deformation, which are caused by the occlusion and friction of rough surface in rock samples after the compaction of the original cracks and pores. The axial and circumferential strains in this stage are in linear variations, resulting in the volumetric strain also showed linear characteristics. The end point of ci in this stage is the initial point of volumetric strain that deviates from the linear variation, and the criterion of e1 > |e2 + e3| is permanent establishment before this point. ci-cd stage of initiation and stability expansion of cracks: The closed original cracks, pores and new cracks in rock start to expand and propagate with the increase of axial stress, which caused the AE signals fluctuate and the stress-strain behavior deviate from the linear variation. The circumferential strain of rock specimen gradually increases because of the expansion and propagation of cracks, so that the increase rate of volumetric strain gradually decreases and deviates from the linear variation, thus, the criterion of e1 > |e2 + e3| transforms to e1 = |e2 + e3|. cd-c stage of damage and unstable propagation of cracks: When the axial stress reaches the value of dilatancy onset, the volumetric strain of rock specimen is the maximum value in the whole loading process, and the variable rate of volumetric strain is 0. The criterion of e1 > |e2 + e3| is permanent establishment after this point, thus, the volumetric strain of rock specimen began to decrease, that is, the rock specimen transforms from compression to dilatancy. This turning point is due to the irreversible damage in rock, which results in a rapid increase in the volume deformation of rock specimens. The fluctuant AE signals are more significant because of the damage and unstable propagation of cracks in this process. The large expansion and propagation of cracks will result in the sudden increase in AE signals. Failure stage: The axial stress of rock specimen is characterized by strain softening in this process. When the stress drops, the macroscopic fracture surface is formed by the expansion and propagation of cracks in rock specimen, and the AE signals are suddenly increased and the volumetric strain of rock specimen is further decreased. When the stress decreases to the residual strength, the rock specimen can still bear the axial load by the friction and slip between the fracture surface and the grain.
Fig. 5 shows the stress-strain curves of water-saturated sandstone under different confining pressures. Table 1 presents the mechanical parameters of specimens at dilatancy onset and peak point. The relations between mechanical parameters and confining pressures are shown in Figs. 6–8, and the corresponding relation expressions are list in Table 2. It can be seen from Figs. 6–8 that the mechanical parameters of water-saturated sandstone at dilatancy onset and peak point increase with the confining pressure, and the relationships which can use the positive linear functions to characterize by r1 = Ar3 + B and ei = Ar3 + B. The influence of confining pressure on mechanical parameters at peak point is larger than that at dilatancy onset, and the corresponding parameter representation is reflected in the difference of coefficient A. This is mainly due to the frictions and slippages among the particles inside rock materials causing the full development of cracks after dilatancy onset. The cohesive force among particles has been instability under the condition of high confining pressure, and the rock specimen can rely on the friction among the particles to bear the axial load. Obviously, the high confining pressure greatly effects on the internal friction characteristic of rock specimen. It causes the sensitivity of mechanical parameters to confining pressure at peak point to be higher than that at dilatancy onset. It is worth noting that the correlation coefficients between mechanical parameters and confining pressure at dilatancy onset are always higher than that at peak point. The correlation coefficient between circumferential strain at peak point and confining pressure is only 0.4523, and the circumferential strain at peak point presents a larger discretization. It can be interpreted as the propagation of cracks in cd-c stage of rock specimen under loading is developed, and the evolution of cracks causes the rock specimen to produce irreversible damage. Even for the optimal uniformity of rock material, it also affects the strength and deformation of rock specimen under loading in the cd-c stage due to the existence of defects in rock such as original fissures, microcracks, pores and grain boundaries. Considering these characteristics, in order to avoid the large deformation and the full development of cracks in the engineering rock mass, it is feasible to use the stress of dilatancy onset as the strength parameter in the engineering design. According to Table 2, the strength parameters at the dilatancy onset and peak point of the rock specimens can be obtained by using the M-C strength criterion, as shown in Table 3.
Fig. 5. Stress-strain curves of water-saturated sandstone under different confining pressures.
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Table 1 Mechanical parameters of water-saturated sandstone under different confining pressures.
r3 (MPa)
r1cd (MPa)
e1cd (103)
e3cd (104)
evcd (103)
r1c (MPa)
e1c (103)
e3c (103)
evc (103)
0 0 5 5 10 10 15 15 20 20
87.37 96.14 108.63 107.26 124.09 129.58 144.59 143.48 160.62 163.97
7.62 8.54 8.14 8.69 9.12 9.26 9.77 9.84 10.44 10.39
0.95 0.84 0.96 1.13 1.30 1.26 1.44 1.36 1.54 1.60
5.71 6.87 6.22 6.43 6.52 6.73 6.88 7.12 7.36 7.19
101.28 107.38 134.28 131.79 147.10 158.26 170.27 167.52 183.70 187.93
8.82 9.42 10.28 10.39 11.42 11.65 12.23 12.33 12.52 12.57
2.49 1.62 3.37 3.03 4.38 3.91 4.32 4.51 3.65 3.77
3.85 6.19 3.53 4.33 2.66 3.82 3.62 3.31 5.22 5.03
Note: r1cd is the axial stress of dilatancy onset; e1cd the axial strain of dilatancy onset; e3cd the circumferential strain of dilatancy onset; evcd the volumetric strain of dilatancy onset; r1c the peak strength; e1c the axial peak strain match with the peak strength; e3c the circumferential peak strain match with the peak strength; and evc the volumetric peak strain match with the peak strength.
Table 2 Fitting relationship between mechanical parameters and confining pressures. Mechanical parameter
Fitting relationship
Correlation coefficient
r1cd r1c e1cd e1c e3cd e3c
r1cd = 3.5434r3 + 91.1390 r1c = 3.9766r3 + 109.1850 e1cd = 0.1212r3 + 7.9690 e1c = 0.1759r3 + 9.4040 e3cd = 0.0341r3 + 0.8970 e3c = 0.0905r3 + 2.6000
0.9994 0.9795 0.9861 0.9313 0.9890 0.4523
Table 3 Strength parameters of dilatancy onset and peak point.
Fig. 6. Relation between axial stress and confining pressure.
Content
M (MPa)
N
c (MPa)
u (°)
Dilatancy onset Peak point
91.1390 109.1850
3.5434 3.9766
24.2083 27.3764
34.0420 36.7353
where M and N are the strength parameters; c the cohesion, MPa; and u the internal friction angle, °. It is easy to see that the strength parameters obtained from dilatancy onset are lower than those from peak point in Table 3. The cohesion and internal friction angle are 24.2083 MPa and 34.042° obtained from dilatancy onset, which decrease by 11.57% and 7.33%, respectively, compared with those obtained from peak point.
Fig. 7. Relation between axial strain and confining pressure.
3.2. Effect of pore pressure on the dilatancy property of watersaturated red sandstone
Fig. 8. Relation between circumferential strain and confining pressure.
r1 ¼ M þ Nr3
ð1Þ
M¼
2c cos u 1 sin u
ð2Þ
N¼
1 þ sin u 1 sin u
ð3Þ
Fig. 9 shows the stress-strain curves of water-saturated sandstone under different pore pressures. It isn’t difficult to see that the stress-strain behavior of rock specimens presents the obvious plasticization with the increase of pore water pressure. Table 4 lists the mechanical parameters of specimens at dilatancy onset and peak point. The relations between mechanical parameters and pore pressures are shown in Figs. 10–12, and the corresponding relation expressions are list in Table 5. It should be pointed out that the confining pressure of rock specimens under different pore pressures is the same value of 10 MPa, which simulates the influence of pore pressure on mechanical behavior of water-saturated sandstone under the deep ground stress of 10 MPa. It can be seen from Figs. 10–12 that the mechanical parameters of water-saturated sandstone at dilatancy onset and peak point decrease with the increase of pore pressure, and the relationships which can use the negative linear functions to characterize by r1 = Cru + D and ei = Cru + D. This is mainly due to the existence of defects such as original fissures and pores in the rock specimens,
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Fig. 10. Relation between axial stress and pore pressure.
Fig. 9. Stress-strain curves of water-saturated sandstone under different pore pressures.
and the new cracks constantly evolve under the action of axial load. These weak planes can be expanded and extended under the action of water pressure. The higher pore pressure is, the greater damage on the rock, which results in the deterioration in the strength and deformation properties of rock material. And the influence of pore pressure on mechanical parameters at peak point is larger than that at dilatancy onset, and the corresponding parameter representation is reflected in the difference of coefficient C. This can be explained by the fact that the increase of pore pressure can effectively weaken the friction effect among the particles in rock materials, it can weak the increase behavior of axial stress of rock specimens in cd-c stage under the condition of compression shear, which also can be proved from the relationship between residual strength of rock specimen and pore pressure. The rock specimen can rely on the friction among the particles to bear load after compression shear failure under the confining pressure, thus, the residual strength isn’t 0 MPa. However, in Fig. 9, the residual strength of rock specimen is about 55 MPa when the pore pressure is 0 MPa, the final strength of rock specimen is only 17 MPa when the pore pressure is 8 MPa, and there is still a decreasing trend. So it is shown that it isn’t reasonable to use the peak strength of rock as the design parameter of engineering rock under high pore pressure. And in Fig. 12, the circumferential strains of rock specimens at dilatancy onset with different pore pressures tend to a certain value of 1.242 103. However, the circumferential strains at peak point are approximately negative exponentially with the pore pressure, which indicates that the damage of pore pressure on the cd-c stage is significantly stronger than o-cd stage in the compression process. So it can be seen that the deformation of rock before dilatancy onset is still controllable under high pore pressure. After the dilatancy onset, the damage
Fig. 11. Relation between axial strain and pore pressure.
Fig. 12. Relation between circumferential strain and pore pressure.
Table 5 Fitting relationship between mechanical parameters and pore pressures. Mechanical parameter
Fitting relationship
Correlation coefficient
r1cd r1c e1cd e1c e3cd e3c
r1cd = 4.0588ru + 127.7253 r1c = 5.4224ru + 149.7525 e1cd = 0.1866ru + 9.2309 e1c = 0.2833ru + 11.3992 e3cd = 1.2420 e3c ¼ 1:3873eru=1:1382 þ 2:6991
0.8770 0.9216 0.9486 0.9297 0.9999 0.8821
Table 4 Mechanical parameters of water-saturated sandstone under different pore pressures.
ru (MPa)
r1cd (MPa)
e1cd (103)
e3cd (104)
evcd (103)
r1c (MPa)
e1c (103)
e3c (103)
evc (103)
0 0 3 3 3 5 5 8 8
124.09 129.58 120.68 113.64 109.39 109.30 117.44 93.00 90.82
9.12 9.26 9.53 8.56 8.08 8.10 8.78 7.71 7.55
1.30 1.26 1.33 1.18 1.24 1.17 1.25 1.16 1.34
6.52 6.73 6.87 6.19 5.61 5.76 6.28 5.39 4.88
147.10 158.26 131.07 124.53 126.08 120.42 130.11 106.52 107.64
11.42 11.65 10.79 9.90 10.04 9.78 10.48 9.05 9.26
4.38 3.91 2.34 2.38 2.98 3.00 2.93 2.38 2.96
2.66 3.82 6.12 5.15 4.07 3.78 4.61 4.28 3.34
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evolution of cracks is more likely to cause the deformation and failure of rock to form the underground watercourse, which results in the water inrush disaster. From this point, in order to prevent the failure of engineering rock mass and the water inrush disasters caused by the development of watercourse in rock, it is recommended to choose the stress of dilatancy onset as the strength design parameter in engineering. 4. Discussion The dilatancy onset of rock has exceeded the elastic stage under loading in the stress-strain behavior. However, it is easy to find that the stress of dilatancy onset linearly varies with its strength and deformation characteristics, and the rock damage is still small before the dilatancy onset. Therefore, the relation between the stress of dilatancy onset and the physical parameters can be established to predict the strength parameters in rock engineering. It is significant for the preventions of engineering rock mass deformation and underground water hazard. Fig. 13 shows the relationship between the stress of dilatancy onset and the elastic modulus of water-saturated sandstone. It can be found that the relationship presents positive linearity, and the correlation coefficient is 0.86. In fact, the stress of dilatancy onset of rock is also related to its external load, assuming that the stress of dilatancy onset is affected by confining pressure and pore pressure, the relationship is easy to build
r1cd ¼ f ðr3 ; ru ; EÞ
ð4Þ
The elastic modulus of rock is also affected by the external load
E ¼ f ð r3 ; ru Þ
ð5Þ
Therefore, the prediction model of the stress of dilatancy onset can be rewritten as
r1cd ¼ f ðr3 ; ru Þ
ð6Þ
According to the experiment, Fig. 14 shows the prediction model of the stress of dilatancy onset
Fig. 13. Relation between stress of dilatancy onset and elastic modulus.
Fig. 14. Prediction model.
r1cd ¼ ar3 þ bru þ cr3 ru þ d
ð7Þ
where a is the influence coefficient of confining pressure on stress of dilatancy onset, and a 0; b the influence coefficient of pore pressure on stress of dilatancy onset, b 0; c the coupled influence coefficient of confining pressure and pore pressure on stress of dilatancy onset; and d the UCS when the pore pressure is 0 MPa. Obviously, the parameters of the above model are related to the physical and mechanical properties of rock material. Under this experimental condition, a is 0.5434, b is 4.0588, c is 0.01215 and d is 91.4958. The correlation coefficient between the obtained model and the experimental data is 0.9670, which can be well used to predict the stress of dilatancy onset. Meanwhile, the model can reflect the common influence of confining pressure and pore pressure on stress of dilatancy onset, and the corresponding influence degree is reflected in parameter c. When the sensitivity of rock to the confining pressure is higher than the pore pressure, c should be positive; otherwise, c should be negative. 5. Conclusions The uniaxial and triaxial compressive experiments on the watersaturated red sandstone were carried out to study the mechanical properties of rock material. The influences of confining pressure and pore pressure on dilatancy property of water-saturated rock were analyzed. The rationality of the dilatancy onset stress as a strength design parameter in engineering was discussed. And the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure was established. (1) The strength parameters (the stress of dilatancy onset and peak strength) and deformation parameters (axial strain and circumferential strain) of water-saturated sandstone increase with the confining pressure, and the relations can be fitted with a positive linear function. The confining pressure enhances the frictional behavior of rock in the cd-c stage of damage and unstable propagation of cracks. It causes the sensitivity of the mechanical parameters to the confining pressure at peak point always to be higher than that at dilatancy onset. The cohesion and internal friction angle obtained from the stress of dilatancy onset are 24.2083 MPa and 34.042°, respectively, decrease by 11.57% and 7.33% compared with those obtained from the peak point. (2) The strength parameters and deformation parameters of water-saturated sandstone decrease basically with the increase of pore pressure, of which the relations between strength parameters or axial strain and pore pressure can be fitted with a negative linear function. However, the relation between the peak circumferential strain and the pore pressure should be characterized by a negative exponential function, which isn’t affected by the pore pressure at dilatancy onset. The pore pressure deteriorates the frictional behavior of rock specimen during the cracks damage and the unstable propagation cd-c stage. It causes the sensitivity of the mechanical parameters to the pore pressure at peak point always to be higher than that at dilatancy onset. (3) The prediction model of the stress of dilatancy onset is related to the physical and mechanical properties (elastic modulus) of rock material and the external load (confining pressure and pore water pressure). Due to the elastic modulus is also affected by the external load, finally, the explicit expression of this model is r1cd ¼ ar3 þ bru þ cr3 ru þ d. The parameters of a, b, c and d have a clear physical meaning, and the reliability of this model is relatively high under the condition of this article.
Please cite this article in press as: Wu J et al. Experimental investigation on dilatancy behavior of water-saturated sandstone. Int J Min Sci Technol (2017), https://doi.org/10.1016/j.ijmst.2017.09.003
J. Wu et al. / International Journal of Mining Science and Technology xxx (2017) xxx–xxx
Acknowledgments The authors would like to express their sincere thanks and appreciation to Prof. Mao Xianbiao and Chen Zhanqing for guiding and to Prof. Li Yushou for the equipment support. This work was supported by the National Natural Science Foundation of China (Nos. 51404266 and 11502229) and the National Program on Key Basic Research Project of China (No. 2013CB227900). References [1] Bridgman PW. Volume changes in the plastic stages of simple compression. J Appl Phys 1950;20(12):1241–51. [2] Brace WF, Paulding BW, Scholz C. Dilatancy in the fracture of crystalline rocks. J Geophys Res 1966;71(16):3939–53. [3] Liang ZZ, Xing H, Wang SY, Williams DJ, Tang CA. A three-dimensional numerical investigation of the fracture of rock specimens containing a preexisting surface flaw. Comput Geotech 2012;45(45):19–33. [4] Lu XL, Liu QS, Su PF. Constitutive model of rocks considering dilatancy-bulking behaviour and its calibration. Chin J Rock Mech Eng 2013;32(9). 2886-1893. [5] Zhang KN, Zhou B, Peng HY, Hu HH. Engineering properties and stability analysis of red sandstone in Xiangxi expressway. J Univ South China (Sci Technol) 2009;23(3):5–9. [6] Feng MM, Wu JY, Ma D, Ni XY, Yu BY, Chen ZQ. Experimental investigation on seepage property of saturated broken red sandstone of continuous gradation. B Eng Geol Environ 2017. https://doi.org/10.1007/s10064-017-1046-z. [7] Yang TH, Liu J, Zhu WC, Elsworth D, Tham LG, Tang CAA. Coupled flow-stressdamage model for groundwater outbursts from an underlying aquifer into mining excavations. Int J Rock Mech Min 2007;44(1):87–97. [8] Yang TH, Jia P, Shi WH, Wang PT, Liu HL, Yu QX. Seepage-stress coupled analysis on anisotropic characteristics of the fractured rock mass around roadway. Tunn Undergr Sp Tech 2014;43(7):11–9. [9] Zhu W, Wong TF. Network modeling of the evolution of permeability and dilatancy in compact rock. J Geophys Res 1999;104(B2):2963–71. [10] Peach CJ, Spiers CJ. Influence of crystal plastic deformation on dilatancy and permeability development in synthetic salt rock. Tectonophysics 1996;256(1– 4):101–28. [11] Alkan H, Cinar Y, Pusch G. Rock salt dilatancy boundary from combined acoustic emission and triaxial compression tests. Int J Rock Mech Min 2007;44 (1):108–19. [12] Tan T, Wen XM. Swelling rock and stability of tunnels. Chin J Rock Mech Eng 1983;2(1):1–10. [13] Tan T, Shi ZQ, Yu ZH, Wu XY. Dilatancy creep and relaxation of brittle rocks measured with the 8000 KN multipurpose triaxial apparatus. Phys Earth Planet In 1989;55(3):335–52.
7
[14] Alejano LR, Alonso E. Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min 2005;42(4):481–507. [15] Ismail IAH, Murrell SAF. Dilatancy and the strength of rocks containing pore water under undrained conditions. Geophys J Int 2007;44(1):107–34. [16] Wong TF, David C, Zhu W. The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation. J Geophys Res 1997;102 (B2):3009–26. [17] Kranz RL. The effects of confining pressure and stress difference on static fatigue of granite. J Geophys Res 1980;85(B4):1854–66. [18] Yuan SC, Harrison JP. An empirical dilatancy index for the dilatant deformation of rock. Int J Rock Mech Min 2004;41(4):679–86. [19] Kranz RL, Scholz CH. Critical dilatant volume of rocks at the onset of tertiary creep. J Geophy Res 1977;82(30):4893–8. [20] Heap MJ, Baud P, Meredith PG, Bell AF, Main IG. Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res 2009;114(B7):1–22. [21] Brantut N, Heap MJ, Meredith PG, Baud P. Time-dependent cracking and brittle creep in crustal rocks: A review. J Struct Geol 2013;52(5):17–43. [22] Yang SQ, Liu XR. Experimental investigation on dilatancy behavior of marble with pre-existing fissures under different confining pressures. Chin J Geotech Eng 2012;34(12):2188–97. [23] Trivedi A. Strength and dilatancy of jointed rocks with granular fill. Acta Geotech 2010;5(1):15–31. [24] Kang HP, Lu SL. An analysis on the mechanism of roadway floor heave. Chin J Rock Mech Eng 1991;10(4):362–73. [25] Tan T. Rockbursts, case records, theory and control. Chin J Rock Mech Eng 1987;6(1):1–18. [26] Martin D, Chandler NA. The progressive fracture of Lac du Bonnet Granite. Int J Rock Mech Min Sci Geomech Abstr 1994;31(6):643–59. [27] Kovari K, Tisa A, Einstein HH, Franklin JA. Suggested methods for determining the strength of rock materials in triaxial compression: revised version. Int J Rock Mech Min Sci Geomech Abstr 1983;20(6):285–90. [28] Zhou H, Li Zhen, Song YZ, Feng XT, Cheng CB. Chemo-thermodynamical method for precisely preparing rock sample with different water contents. Rock Soil Mech 2013;34(2):311–5. [29] Feng MM, Wu JY, Chen ZQ, Mao XB, Yu BY. Experimental study on the compaction of saturated broken rock of continuous gradation. J China Coal Soc 2016;41(9):2195–202. [30] Zhou H, Meng FZ, Liu HT, Zhang CQ, Lu JJ, Xu RC. Experimental study on characteristics and mechanism of brittle failure of granite. Chin J Rock Mech Eng 2014;33(9):1822–7. [31] Zhang ZN, Wang DY, Zheng H, Ge XR. Interactions of 3D embedded parallel vertically inclined cracks subjected to uniaxial compression. Theor Appl Fract Mech 2012;61(1):1–11. [32] Cai MF, He MC, Liu DY. Rock mechanics and engineering. Beijing: Science Press; 2002. [33] Zhou WY, Yang Q. Numerical computational methods for rock mechanics. Beijing: China Electric Power Press; 2005.
Please cite this article in press as: Wu J et al. Experimental investigation on dilatancy behavior of water-saturated sandstone. Int J Min Sci Technol (2017), https://doi.org/10.1016/j.ijmst.2017.09.003