TY - JOUR
AU - Fu,, Huanran
AB - Abstract Inner stress exists in rocks, affecting rock engineering, yet has received very little attention and quantitative investigation because of uncertainty about its characteristics. Previous studies have suggested that the inner stresses of rock materials are closely related to their physical state variation. In this work, a novel mold was designed to simulate the storage process of inner stress in specimens composed of quartz sands and epoxy. Then, thermal tests were carried out to change the physical state of the specimens, and expansion of the specimens was monitored. The results indicated that inner stress could be partly locked by the mold and it could also be released by heating. It can be inferred from the analysis that one necessary condition of storage and release of inner stress is physical state variation. Additionally, by using an XRD method, the variations in the interplanar spacing of the quartz sands were detected, and the results reflect that inner stress could be locked-in aggregates (quartz sands) by a cement constraint (solid epoxy). The inner stress stored in quartz sands was calculated using height and interplanar spacing variations. inner stress, storage and release, simulated rock material, physical state 1. Introduction Inner stress, representing the stress present in a body under an unloaded state reference configuration (Hoger 1985), refers to recoverable elastic strain according to the definition of residual strain. It can also be referred to as the recoverable elastic distortions of constituent crystals or grains that satisfy internal equilibrium conditions and that exist in a given volume of a block with no external loads across its boundaries (McClintock and Argon 1966, Voight 1967). Therefore, when the body force and surface traction are both zero, the inner stress field is in equilibrium, and it is characterized by the storage of elastic strain energy (Hoger 1985, 1986). The inner stress was initially discovered in the material field and is divided into volume stress and structure stress (Shigeru 1983). Volume stress is produced by uniform loads, thermal stress, and chemical reactions. Volume stress exists in homogeneous materials such as steel and glass. On the other hand, structure stress is normally induced by the uneven structure of materials or the internal constraints, under the premise that different yielding behaviors are due to differences in concentration and uniformity of load. Inner stress in metals and glasses have been extensively studied during the past 30 years (Shigeru 1983, Kudryavtsev et al2000, Kudryavtsev and Kleiman 2004, Wang et al2013, Jiang and Yang 2013). However, the study of inner stress in rocks, according to the literature (Friedman 1967, 1972, Friedman and Logan 1970, Handin 1970, 1972), is at an elementary stage of development; in particular in terms of the storage process and geological cause (Yue 2013, 2014, 2015). Inner stress affects rocks’ mechanical behavior (Tan 1979, Tan and Kang 1980, Lu and Jiao 2004, He 2011, Qian and Zhou 2013). The deformation mechanism of a rock medium is complicated and it may be affected by various factors, thus making the evolution of inner stress in rocks a complex process. Previous studies have shown that inner stress relaxation may occur by several mechanisms, such as elevated temperature creep, crack growth in a tensile stress field (Stefanescu 2004), and plastic flow (James 1982, McClung 2007). The inner stress of a rock medium also satisfies the internal equilibrium and zero boundary force conditions according to its definition. No inner stress will be generated under coordinated deformation because the elastic stress will be released if there is no plastic deformation constraint. Therefore, uneven elastic–plastic deformation is possibly the root cause of inner stress in rocks. Thus, the inner stress in rock possibly consists of two parts: (1) locked-in stress, reflecting previous external loads, which are locked-in aggregates, and (2) stress constraining them (e.g. cement) called locking stress. Therefore, the structure of rock with inner stress could consist of compressive aggregates and cementing materials constraining them. However, it is difficult to simulate the real inner stress of rock due to the complicated geological stress history and high magnitude of real inner stress, which has been proven to be more than 20 MPa using XRD methods (table 1). In addition, the inner stress of natural rock samples is uncertain and detection tests are usually destructive. Thus materials such as photo-elastic (Xu and Chen 1998, Xu et al2006) and organic materials (Gallagher 1971) were introduced to simulate inner stress in order to present inner stress in rocks. However, the mechanism of inner stress in rock materials is still ambiguous because of the paucity of data on the storage and release process, and it is difficult to repeat these experiments because of a lack of experimental details. Table 1. Rock inner stress determined by XRD. Lithology Positions σ1 MPa-1 σ2 MPa-1 σ3 MPa-1 References Sandstone Pennsylvania (US) 11.0 -5.0 -14.0 Friedman 1967 Pennsylvania (US) 12.0 2.0 -12.0 Friedman 1967 Pennsylvania (US) 14.0 -6.0 -27.0 Friedman 1967 Pennsylvania (US) 13.0 -7.0 -17.0 Friedman 1972 Pennsylvania (US) 8.0 -1.0 -4.0 Friedman 1972 Pennsylvania (US) 11.0 -2.0 -9.0 Friedman 1972 Tennessee (US) 0.0 -4.0 -8.0 Friedman and Logan 1970 Pennsylvania Webb (US) 7.0 2.0 -6.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -10.0 Handin 1970 Pennsylvania Webb (US) 11.0 -2.0 -7.0 Handin 1970 Pennsylvania Webb (US) 10.5 -2.0 -10.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -6.0 Handin 1970 Pennsylvania Webb (US) 7.0 2.0 10.0 Handin 1967–1972 Coconino (US) 11.0 -1.0 -12.0 Handin 1971 Mesa Verde (US) 20.0 -3.0 -15.0 Handin 1970 Quartzite Elliot Lake (US) 11.0 0.0 -23.0 Handin 1970 Elliot Lake (US) 10.0 -0.1 -23.0 Handin 1970 Chllhowee (US) 20.0 15.0 3.0 Handin 1967–1972 Unita Mountain (US) 22.0 3.0 -9.0 Friedman and Logan 1970 Qianxi (China) 11.4 3.7 — An 2011 Granite Chelmsford (US) 24.0 -1.0 -14.0 Handin 1967–1972 Chelmsford (US) 24.0 -1.5 -13.0 Handin 1967–1972 Barre (US) 19.0 -1.0 -6.0 Handin 1967–1972 Barre (US) 22.0 6.0 -12.0 Bur et al1969 Barre (US) 4.0 -4.0 -20.0 Nichols 1975 Limestone i River (Japan) -10.0 12.3 0.0 Hoshino et al1978 Dan Dan mountain (Japan) -22.0 -1.2 -20.0 Hoshino et al1978 Qianxi (China) 11.6 3.9 — An 2011 Gneiss Qianxi (China) 11.8 4.0 — An 2011 Mudstone Bonita Fault Zone (Mexico) 12.0 -4.0 -22.0 Handin 1967–1972 Lithology Positions σ1 MPa-1 σ2 MPa-1 σ3 MPa-1 References Sandstone Pennsylvania (US) 11.0 -5.0 -14.0 Friedman 1967 Pennsylvania (US) 12.0 2.0 -12.0 Friedman 1967 Pennsylvania (US) 14.0 -6.0 -27.0 Friedman 1967 Pennsylvania (US) 13.0 -7.0 -17.0 Friedman 1972 Pennsylvania (US) 8.0 -1.0 -4.0 Friedman 1972 Pennsylvania (US) 11.0 -2.0 -9.0 Friedman 1972 Tennessee (US) 0.0 -4.0 -8.0 Friedman and Logan 1970 Pennsylvania Webb (US) 7.0 2.0 -6.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -10.0 Handin 1970 Pennsylvania Webb (US) 11.0 -2.0 -7.0 Handin 1970 Pennsylvania Webb (US) 10.5 -2.0 -10.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -6.0 Handin 1970 Pennsylvania Webb (US) 7.0 2.0 10.0 Handin 1967–1972 Coconino (US) 11.0 -1.0 -12.0 Handin 1971 Mesa Verde (US) 20.0 -3.0 -15.0 Handin 1970 Quartzite Elliot Lake (US) 11.0 0.0 -23.0 Handin 1970 Elliot Lake (US) 10.0 -0.1 -23.0 Handin 1970 Chllhowee (US) 20.0 15.0 3.0 Handin 1967–1972 Unita Mountain (US) 22.0 3.0 -9.0 Friedman and Logan 1970 Qianxi (China) 11.4 3.7 — An 2011 Granite Chelmsford (US) 24.0 -1.0 -14.0 Handin 1967–1972 Chelmsford (US) 24.0 -1.5 -13.0 Handin 1967–1972 Barre (US) 19.0 -1.0 -6.0 Handin 1967–1972 Barre (US) 22.0 6.0 -12.0 Bur et al1969 Barre (US) 4.0 -4.0 -20.0 Nichols 1975 Limestone i River (Japan) -10.0 12.3 0.0 Hoshino et al1978 Dan Dan mountain (Japan) -22.0 -1.2 -20.0 Hoshino et al1978 Qianxi (China) 11.6 3.9 — An 2011 Gneiss Qianxi (China) 11.8 4.0 — An 2011 Mudstone Bonita Fault Zone (Mexico) 12.0 -4.0 -22.0 Handin 1967–1972 View Large Table 1. Rock inner stress determined by XRD. Lithology Positions σ1 MPa-1 σ2 MPa-1 σ3 MPa-1 References Sandstone Pennsylvania (US) 11.0 -5.0 -14.0 Friedman 1967 Pennsylvania (US) 12.0 2.0 -12.0 Friedman 1967 Pennsylvania (US) 14.0 -6.0 -27.0 Friedman 1967 Pennsylvania (US) 13.0 -7.0 -17.0 Friedman 1972 Pennsylvania (US) 8.0 -1.0 -4.0 Friedman 1972 Pennsylvania (US) 11.0 -2.0 -9.0 Friedman 1972 Tennessee (US) 0.0 -4.0 -8.0 Friedman and Logan 1970 Pennsylvania Webb (US) 7.0 2.0 -6.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -10.0 Handin 1970 Pennsylvania Webb (US) 11.0 -2.0 -7.0 Handin 1970 Pennsylvania Webb (US) 10.5 -2.0 -10.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -6.0 Handin 1970 Pennsylvania Webb (US) 7.0 2.0 10.0 Handin 1967–1972 Coconino (US) 11.0 -1.0 -12.0 Handin 1971 Mesa Verde (US) 20.0 -3.0 -15.0 Handin 1970 Quartzite Elliot Lake (US) 11.0 0.0 -23.0 Handin 1970 Elliot Lake (US) 10.0 -0.1 -23.0 Handin 1970 Chllhowee (US) 20.0 15.0 3.0 Handin 1967–1972 Unita Mountain (US) 22.0 3.0 -9.0 Friedman and Logan 1970 Qianxi (China) 11.4 3.7 — An 2011 Granite Chelmsford (US) 24.0 -1.0 -14.0 Handin 1967–1972 Chelmsford (US) 24.0 -1.5 -13.0 Handin 1967–1972 Barre (US) 19.0 -1.0 -6.0 Handin 1967–1972 Barre (US) 22.0 6.0 -12.0 Bur et al1969 Barre (US) 4.0 -4.0 -20.0 Nichols 1975 Limestone i River (Japan) -10.0 12.3 0.0 Hoshino et al1978 Dan Dan mountain (Japan) -22.0 -1.2 -20.0 Hoshino et al1978 Qianxi (China) 11.6 3.9 — An 2011 Gneiss Qianxi (China) 11.8 4.0 — An 2011 Mudstone Bonita Fault Zone (Mexico) 12.0 -4.0 -22.0 Handin 1967–1972 Lithology Positions σ1 MPa-1 σ2 MPa-1 σ3 MPa-1 References Sandstone Pennsylvania (US) 11.0 -5.0 -14.0 Friedman 1967 Pennsylvania (US) 12.0 2.0 -12.0 Friedman 1967 Pennsylvania (US) 14.0 -6.0 -27.0 Friedman 1967 Pennsylvania (US) 13.0 -7.0 -17.0 Friedman 1972 Pennsylvania (US) 8.0 -1.0 -4.0 Friedman 1972 Pennsylvania (US) 11.0 -2.0 -9.0 Friedman 1972 Tennessee (US) 0.0 -4.0 -8.0 Friedman and Logan 1970 Pennsylvania Webb (US) 7.0 2.0 -6.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -10.0 Handin 1970 Pennsylvania Webb (US) 11.0 -2.0 -7.0 Handin 1970 Pennsylvania Webb (US) 10.5 -2.0 -10.0 Handin 1970 Pennsylvania Webb (US) 6.0 -7.0 -6.0 Handin 1970 Pennsylvania Webb (US) 7.0 2.0 10.0 Handin 1967–1972 Coconino (US) 11.0 -1.0 -12.0 Handin 1971 Mesa Verde (US) 20.0 -3.0 -15.0 Handin 1970 Quartzite Elliot Lake (US) 11.0 0.0 -23.0 Handin 1970 Elliot Lake (US) 10.0 -0.1 -23.0 Handin 1970 Chllhowee (US) 20.0 15.0 3.0 Handin 1967–1972 Unita Mountain (US) 22.0 3.0 -9.0 Friedman and Logan 1970 Qianxi (China) 11.4 3.7 — An 2011 Granite Chelmsford (US) 24.0 -1.0 -14.0 Handin 1967–1972 Chelmsford (US) 24.0 -1.5 -13.0 Handin 1967–1972 Barre (US) 19.0 -1.0 -6.0 Handin 1967–1972 Barre (US) 22.0 6.0 -12.0 Bur et al1969 Barre (US) 4.0 -4.0 -20.0 Nichols 1975 Limestone i River (Japan) -10.0 12.3 0.0 Hoshino et al1978 Dan Dan mountain (Japan) -22.0 -1.2 -20.0 Hoshino et al1978 Qianxi (China) 11.6 3.9 — An 2011 Gneiss Qianxi (China) 11.8 4.0 — An 2011 Mudstone Bonita Fault Zone (Mexico) 12.0 -4.0 -22.0 Handin 1967–1972 View Large According to the inner stress of the aforementioned materials and previous studies on rock inner stress, it appears that only the physical state transformation can lead to the storage or release of inner stress. In order to verify the hypothesis that inner stress can be stored or released by physical state variation, we designed a new mold to consolidate inner stress with quartz sands and epoxy. Then, thermal tests and XRD analysis were carried out to detect inner stress in the specimens. Further analysis of storage and release process of inner stress in rocks are discussed. 2. Experiments and methods 2.1. Mold design and specimen preparation According to the inner stress composition, the locked-in stress and locking stress are possibly embodied in deformed aggregates and the cement constraining them. We, therefore, selected quartz sands as compressive aggregates and epoxy as cements to constrain them. Quartz sands are very hard, have good temperature resistance, and possess stable physical and chemical properties, while epoxy has a high cementation force. The materials’ properties are shown in table 2. Table 2. Basic properties of waterborne epoxy resin and quartz sands. Waterborne epoxy resin Density Compressive strength Tensile strength Linear shrinkage Thermal stability Operating time 1.25 g cm-3 45.0 MPa 12.5 MPa 0.8% 80 °C∼85 °C 180 min Quartz sands (2 mm) True density Compressive strength Tensile strength Linear expansion coefficient Elastic modulus Crystal type 2.65 g cm-3 80.0 MPa 10.0 MPa 5.5 × 10-7 °C 55 GPa trigonal system Waterborne epoxy resin Density Compressive strength Tensile strength Linear shrinkage Thermal stability Operating time 1.25 g cm-3 45.0 MPa 12.5 MPa 0.8% 80 °C∼85 °C 180 min Quartz sands (2 mm) True density Compressive strength Tensile strength Linear expansion coefficient Elastic modulus Crystal type 2.65 g cm-3 80.0 MPa 10.0 MPa 5.5 × 10-7 °C 55 GPa trigonal system View Large Table 2. Basic properties of waterborne epoxy resin and quartz sands. Waterborne epoxy resin Density Compressive strength Tensile strength Linear shrinkage Thermal stability Operating time 1.25 g cm-3 45.0 MPa 12.5 MPa 0.8% 80 °C∼85 °C 180 min Quartz sands (2 mm) True density Compressive strength Tensile strength Linear expansion coefficient Elastic modulus Crystal type 2.65 g cm-3 80.0 MPa 10.0 MPa 5.5 × 10-7 °C 55 GPa trigonal system Waterborne epoxy resin Density Compressive strength Tensile strength Linear shrinkage Thermal stability Operating time 1.25 g cm-3 45.0 MPa 12.5 MPa 0.8% 80 °C∼85 °C 180 min Quartz sands (2 mm) True density Compressive strength Tensile strength Linear expansion coefficient Elastic modulus Crystal type 2.65 g cm-3 80.0 MPa 10.0 MPa 5.5 × 10-7 °C 55 GPa trigonal system View Large The mold (figure 1) was made of steel (440 C) with 1% carbon content and a hardness between 56–58 HRC. The elastic modulus is about 205 GPa, and the Poisson’s ratio is between 0.27 ∼ 0.30. The tensile strength is 560 MPa. The linear expansion coefficient of steel is about 14 ∼ 17 ×10-6/°C. The mold mainly consists of the container device (figure 1(A) 4), loading handle (figure 1(A), 1), epoxy grouting port (figure 1(A), 3 and 6), and stress monitor sensor (figure 1(A), 7). Figure 1. View largeDownload slide Schematic diagram of mold. 1. Rotary handle. 2. Bolt. 3. Grout outlet. 4. Cylinder mold. 5. Quartz sand aggregate. 6. Grouting port. 7. Mechanical sensor. 8.Loading axle. 9. Bearing plate. 10. Mold handle. Figure 1. View largeDownload slide Schematic diagram of mold. 1. Rotary handle. 2. Bolt. 3. Grout outlet. 4. Cylinder mold. 5. Quartz sand aggregate. 6. Grouting port. 7. Mechanical sensor. 8.Loading axle. 9. Bearing plate. 10. Mold handle. We first added uniform quartz sands (particle size 2 mm) into the mold (figure 1(A), 4), and then put a bearing plate (figure 1(A), 9) on the top of quartz sands. This was followed by placing a mechanical sensor (figure 1(A), 7) on the bearing plate. The quartz sands were loaded by the rotary handle (figure 1(A), 1) and we stopped the loading by fixing the rotary handle when the predetermined pressure was attained. With these steps completed, configured epoxy was injected from grouting port (figure 1(A), 6). The grouting pressure was not more than 0.30 MPa. We stopped injecting the epoxy when the slurry from the grouting outlet (figure 1(A), 3) was stable. In addition, during grouting, we simultaneously monitored the axial load variation. At the end of grouting, the amount of configured epoxy and quartz sands, grouting pressure, and time of epoxy were calculated (table 3). According to the tensile strength of the solidified epoxy (table 2), we selected 0 MPa, 2 MPa, 4 MPa, 6, MPa, and 8 MPa as our predetermined pressures, because the inner stress should be smaller than the tensile strength of solidified epoxy. Accordingly, the specimens were marked as S0, S2, S4, S6, and S8. Samples were removed from the mold after curing for 72 h. It should be noted that the quartz sands were compressed during the whole grouting process, while the configured epoxy permeated through the pores of the quartz sands from the bottom to the top under no preloading. In other words, the quartz sands were compressed but the epoxy was unstressed. Table 3. Specimen composition and parameters. Specimens number Solidification pressure (MPa) Quartz sands consumption (g) Epoxy consumption (ml) Grouting pressure (MPa) Grouting time (min) S0 0 ± 0.1 354.3 92.5 0.11 14 S2 2 ± 0.1 364.1 78.5 0.19 47 S4 4 ± 0.1 381.8 52.8 0.21 53 S6 6 ± 0.1 397.5 30.3 0.27 67 S8 8 ± 0.1 405.3 13.8 0.30 78 Specimens number Solidification pressure (MPa) Quartz sands consumption (g) Epoxy consumption (ml) Grouting pressure (MPa) Grouting time (min) S0 0 ± 0.1 354.3 92.5 0.11 14 S2 2 ± 0.1 364.1 78.5 0.19 47 S4 4 ± 0.1 381.8 52.8 0.21 53 S6 6 ± 0.1 397.5 30.3 0.27 67 S8 8 ± 0.1 405.3 13.8 0.30 78 View Large Table 3. Specimen composition and parameters. Specimens number Solidification pressure (MPa) Quartz sands consumption (g) Epoxy consumption (ml) Grouting pressure (MPa) Grouting time (min) S0 0 ± 0.1 354.3 92.5 0.11 14 S2 2 ± 0.1 364.1 78.5 0.19 47 S4 4 ± 0.1 381.8 52.8 0.21 53 S6 6 ± 0.1 397.5 30.3 0.27 67 S8 8 ± 0.1 405.3 13.8 0.30 78 Specimens number Solidification pressure (MPa) Quartz sands consumption (g) Epoxy consumption (ml) Grouting pressure (MPa) Grouting time (min) S0 0 ± 0.1 354.3 92.5 0.11 14 S2 2 ± 0.1 364.1 78.5 0.19 47 S4 4 ± 0.1 381.8 52.8 0.21 53 S6 6 ± 0.1 397.5 30.3 0.27 67 S8 8 ± 0.1 405.3 13.8 0.30 78 View Large Figure 2. View largeDownload slide Elastic velocity and porosity of specimens under different solidification pressures. Figure 2. View largeDownload slide Elastic velocity and porosity of specimens under different solidification pressures. 2.2. Basic properties of the specimens There was no resilience of the specimens when they were removed from the mold. After curing for seven days, we determined the basic properties of the specimens such as bulk density, porosity, water absorption, longitudinal wave velocity, and contraction (table 4). The elastic modulus, uniaxial compressive strength, and tensile strength of the specimens were determined according to the ISRM suggested methods (Bieniawski and Hawkes 1978, 1979). Table 4. Basic properties of epoxy mortar consolidation. Specimens number Solidification pressure (MPa) Bulk density (g cm-3) Porosity (%) Water absorption (%) Contraction (%) σc (MPa) σt (MPa) E (GPa) S0-1 0 2.06 23.57 0.88 0.06 61.9 5.8 1.640 S2-1 2 2.11 20.42 0.64 0.02 70.1 6.1 1.983 S4-1 4 2.20 13.46 0.48 0.01 73.0 6.7 2.218 S6-1 6 2.28 7.73 0.33 0.00 76.3 7.7 2.469 S8-1 8 2.32 3.05 0.21 0.00 77.3 8.3 2.557 Specimens number Solidification pressure (MPa) Bulk density (g cm-3) Porosity (%) Water absorption (%) Contraction (%) σc (MPa) σt (MPa) E (GPa) S0-1 0 2.06 23.57 0.88 0.06 61.9 5.8 1.640 S2-1 2 2.11 20.42 0.64 0.02 70.1 6.1 1.983 S4-1 4 2.20 13.46 0.48 0.01 73.0 6.7 2.218 S6-1 6 2.28 7.73 0.33 0.00 76.3 7.7 2.469 S8-1 8 2.32 3.05 0.21 0.00 77.3 8.3 2.557 Note: σc uniaxial compressive strength; σt tensile strength; E elastic modulus. View Large Table 4. Basic properties of epoxy mortar consolidation. Specimens number Solidification pressure (MPa) Bulk density (g cm-3) Porosity (%) Water absorption (%) Contraction (%) σc (MPa) σt (MPa) E (GPa) S0-1 0 2.06 23.57 0.88 0.06 61.9 5.8 1.640 S2-1 2 2.11 20.42 0.64 0.02 70.1 6.1 1.983 S4-1 4 2.20 13.46 0.48 0.01 73.0 6.7 2.218 S6-1 6 2.28 7.73 0.33 0.00 76.3 7.7 2.469 S8-1 8 2.32 3.05 0.21 0.00 77.3 8.3 2.557 Specimens number Solidification pressure (MPa) Bulk density (g cm-3) Porosity (%) Water absorption (%) Contraction (%) σc (MPa) σt (MPa) E (GPa) S0-1 0 2.06 23.57 0.88 0.06 61.9 5.8 1.640 S2-1 2 2.11 20.42 0.64 0.02 70.1 6.1 1.983 S4-1 4 2.20 13.46 0.48 0.01 73.0 6.7 2.218 S6-1 6 2.28 7.73 0.33 0.00 76.3 7.7 2.469 S8-1 8 2.32 3.05 0.21 0.00 77.3 8.3 2.557 Note: σc uniaxial compressive strength; σt tensile strength; E elastic modulus. View Large Specimens under different applied pressures showed different characteristics in both their basic physical properties and mechanical behavior. The density and longitudinal wave velocity increased with increasing applied pressure and porosity (figure 2). The compressive and tensile strength also increased with an increase in applied pressure. The uniaxial compressive strength increased from 61.9 MPa to 77.3 MPa when applied pressure increased from 0 MPa to 8 MPa. Also, the elastic modulus increased from 1.64 GPa to 2.557 GPa with an increase in applied pressure (table 4). Figure 3 shows that specimens under different solid pressures performed differently in terms of strength and elastic modulus. In the compaction phase (figure 3, OP1′ ⁠) the stress–strain curves of the specimens were similar. In the elastic deformation phase (figure 3, P1′P2′ ⁠), however, specimens S2-3 to S8-3 showed a higher stress–strain slope and elastic limitation stress than specimen S0-3 (σe′>σe). With an increase in external loads, plastic deformation possibly occurred, and the peak strengths of S2-3, S4-3, S6-3, and S8-3 were higher than S0-3. However, the peak strain of S0-3 was higher than the peak strain of S2-3, S4-3, S6-3, and S8-3 (εp′<εp). Figure 3. View largeDownload slide Stress–strain curves of specimens under different solidification pressures. Figure 3. View largeDownload slide Stress–strain curves of specimens under different solidification pressures. These results suggest that the specimens’ strength and elastic modulus were improved by colloidal processing technique at preloading, but the deformation ability was weakened. Two possible explanations could be presented as follows. (1) inner stress was probably released or partly released during the plastic deformation phase and the release of elastic inner stress (strain) possibly contributed to the resistance of the applied external loads. The release of tensile elastic strain, which opposes compressive deformation, would reduce the overall compressive strain, and (2) the increase in the portion of quartz sands raises the strength and Young’s modulus. 2.3. Thermal tests Thermal stress often produces plastic deformation. The consolidation of epoxy is sensitive to temperature. Epoxy will soften when the temperature reaches the glass transition temperature (Tg) (Anita and Martin 1999, Plazek and Ngai 2007). Therefore, if the elastic strain of quartz sands was locked in the specimens, they are likely released when the solidified epoxy which constrains the quartz sands becomes soft. Figure 4. View largeDownload slide Specimens for thermal tests. Figure 4. View largeDownload slide Specimens for thermal tests. In order to figure out whether the inner stress was stored or not, and to check if the inner stress was released or not under thermal stress, we selected 25 °C, 35 °C, 40 °C, 45 °C, 50 °C, 55 °C, and 60 °C as the heating temperatures during the thermal tests. The heating temperatures were selected according to the properties of the epoxy (table 2). The specimens (figure 4) were heated in an oven for 24 h (figure 5) and cooled to 25 °C after the specimen was removed from the oven. The axial displacement, radial deformation, and height of the specimens were monitored during the process. Figure 5. View largeDownload slide Specimens heating in oven. Figure 5. View largeDownload slide Specimens heating in oven. Heating is an energy input process and would possibly expand specimens. The final variation in specimen dimensions was measured after cooling to 25 °C so that most of the thermal expansion of specimens would recover evenly. If the inner stress was stored, the minimum calculated strain caused by consolidation of epoxy is 1.45 × 10-4 (according to the minimum solidification pressure and elastic modulus of quartz sands), and the maximum calculated strain by heating is only 1.93 × 10-5 (according to the maximum heating temperature and linear expansion coefficients of quartz sands). Therefore, it could be considered that the heating process slightly influenced the expansion of quartz sands. 2.4. XRD analysis XRD serves as a proper method to measure inner stress because of its strict optical principles and mature technology (Firedman 1967, An 2011, 2014). The method has been widely used in the determination of inner stress in metals and glasses (Withers et al2001, Epp 2016). The basic theory of the XRD method is based on Bragg’s law, which states that an x-ray with the wavelength of λ will refract when it penetrates crystals. The interplanar spacing (d) of the crystal affects the refraction of the x-ray, reflecting the changes in diffraction angle (θ). The interplanar spacing (d) could be calculated by the Bragg equation (1). d=nλ/2sinθ 1 The interplanar spacing is usually an invariant constant for certain crystals, but changes with external loads (figure 6). The interplanar spacing reflects the elastic strain of crystals since the interplanar spacing is stable during plastic deformation (Bemporad et al2014). Therefore, the displacement measured by the XRD method reflects the elastic strain of crystals. If the elastic strain of quartz sands were locked in, the interplanar space of quartz sands would decrease accordingly. Thus, it is possible to detect inner stress according to the XRD method since micro-interplanar space variation is consistent with the macroscopic strain of the specimen based on elastic theory calculation (Sebastiani et al2011). Figure 6. View largeDownload slide The relationship between crystal interplanar spacing and inner stress. 1. Source ray. 2. Diffracted ray. Figure 6. View largeDownload slide The relationship between crystal interplanar spacing and inner stress. 1. Source ray. 2. Diffracted ray. The crystal included in the specimens is simply quartz. We carried out XRD tests to obtain diffraction curves of specimens under different applied pressures. Then, according to Bragg’s law, interplanar spacing was calculated and analyzed. The instrument used was Rigaku D/Max 2500 V, produced by Rigaku Company, Japan. The instrument parameters were set as 40 KV and 100 mA, and a continuous θ/2θ scanning method was applied. The incident x-ray wave was Cuka with a wavelength of 0.154 06 nm. 3. Release of inner stress 3.1. Inner stress evolution under thermal tests Based on deformation monitored during thermal tests, corresponding axial strain, radial strain, and volume strain were calculated (figures 7–9). Height changes of specimens are shown in figure 10. Figure 7. View largeDownload slide Axial strain variation after heating. Figure 7. View largeDownload slide Axial strain variation after heating. Figure 8. View largeDownload slide Radial strain variation after heating. Figure 8. View largeDownload slide Radial strain variation after heating. Figure 9. View largeDownload slide Volume strain variation after heating. Figure 9. View largeDownload slide Volume strain variation after heating. Figure 10. View largeDownload slide Height variation before and after heating. Figure 10. View largeDownload slide Height variation before and after heating. Figures 7–9 show that the strain increased with an increase in applied pressure. Compared with specimen S0-4, which solidified under no pressure, other specimens produced more axial strains after heating at 60 °C for 24 h. The axial strain increased by 550% (S2-4), 775% (S4-4), 1150% (S6-4), and 1850% (S8-4). A possible explanation is that the elastic strain of the specimens under higher applied pressure was released because the epoxy became soft after heating. The strain increased linearly with temperature when the heating temperature was below 45 °C, but the strain slowly increased with an increase in temperature above 45 °C, however, it remained stable after 55 °C. Thus, it could be inferred that the elastic deformation stored was partly released with the increase in temperature and would be released completely when the heating temperature was high enough. Figure 10 showed the height variation of the specimens before and after heating at 60 °C. The final displacement of specimens became larger as the applied pressure increased. The height of the specimen that solidified under no pressure (S0-4) was increased by 0.50%, while the height of the specimen that solidified under 8 MPa (S8-4) was increased by 0.56%. 3.2. XRD analysis XRD was conducted on specimens that solidified under different applied pressures. Diffraction curves are shown in figure 11. According to the XRD results, diffraction angles were determined and interplanar spacing was calculated (figure 12). Figure 11 shows that the diffraction angles increased with an increase in applied pressure. This means that interplanar spacing becomes closer under high applied pressures according to Bragg’s law. The diffraction angle was 13.187° in specimen S0-5 and it sharply increased to 15.957° in specimen S8-5 (figure 11(a)). These differences may be attributed to the fact that the quartz crystals were compressed, making the interplanar spacing smaller. Figure 11. View largeDownload slide XRD results: (a) specimens before heating and (b) specimens after heating. Main diffraction peak 1: quartz. Figure 11. View largeDownload slide XRD results: (a) specimens before heating and (b) specimens after heating. Main diffraction peak 1: quartz. Figure 12. View largeDownload slide Interplanar spacing variety. Figure 12. View largeDownload slide Interplanar spacing variety. Comparing the same specimens before and after the thermal test, we found out that all the diffraction angles decreased. After the thermal test, the diffraction angle of specimen S0-5 was reduced to 13.161°. This may be due to self-expansion of the quartz mineral during the heating process, because the pressure was not applied to the specimen. But in specimen S8-5, the diffraction angle reduced from 15.957°–15.813° (figure 11(b)). The decrease was 0.911%, which could possibly be produced by inner stress. To further explain this phenomenon, we calculate the interplanar spacing according to Bragg’s equation (figure 12). The interplanar spacing becomes smaller as the pressure increases. The spacing reduced from 0.3377 nm–0.2802 nm. In addition, interplanar spacing expanded after heating. The interplanar spacing of specimens S0-5 to S8-5 expanded by 0.18%, 0.48%, 0.58%, 0.79%, and 0.88%, respectively. This means that the interplanar spacing expansion increased with applied pressure on the specimens, hence it could be inferred that specimens under high applied pressure stored high inner stress. 4. Discussion During specimen preparation, we found that the specimens consolidated under different applied pressures and developed no spring back when removed from the mold. In addition, all specimens expanded after thermal tests, and this may be as a result of thermal expansion. More importantly, the volume expansions of the specimens that consolidated under higher preloading were higher. The tensile strength of pure epoxy consolidation (12.5 MPa) is higher than the maximum applied pressure (8 MPa). Therefore, we concluded that (1) the inner stress was stored or partly stored when epoxy turned from soft to hard, and (2) inner stress was released or partly released when epoxy turned from hard to soft. The interplanar spacing variation was considered as elastic strain (Sebastiani et al2011, Bemporad et al2014) so that inner stress could be calculated by Hooke’s law. The inner stress is the product of quartz sands’ interplanar spacing expansion and elastic modulus. The deformation caused by thermal stress was ignored since the maximum deformation was no more than 1.92 × 10-5 mm (based on the highest temperature (60 °C)). Then, according to the strain of interplanar spacing variation and elastic modulus (table 2), we calculated inner stress based on Hooke’s law (figure 13). The inner stress increased along with applied pressure. The stresses calculated according to interplanar spacing were higher than the stresses calculated using the specimens’ height expansion. A possible explanation is that the expansion of quartz sands was squashed into the epoxy, since the epoxy went soft when heated. Therefore, the inner stress calculated by the interplanar spacing variety of quartz sands was probably the real inner stress. Figure 13. View largeDownload slide Inner stress calculation results. 1. Result calculated using interplanar spacing variety. 2. Result calculated using the specimens’ height expansion. Figure 13. View largeDownload slide Inner stress calculation results. 1. Result calculated using interplanar spacing variety. 2. Result calculated using the specimens’ height expansion. During the preparation of specimens, the original quartz sands were loose grains (figure 14, 1) when the external load was applied, the quartz sands were compressed (figure 14, 2), and then the fluid epoxy was grouted and transferred to the solid body (figure 14, 3). Compressed quartz sands may recover partly when external loads are removed (figure 14, 4), and those quartz sands that maintained a compressive state were possibly a reflection of the inner stress. Therefore, we concluded that one necessary condition of inner stress storage is that the specimens changed from fluid or partly fluid to solid state. When the solid specimens were heated and later cooled down, the inner stress was released or partly released (figure 14, 5). Thus, the release of inner stress may be accompanied by physical state variation, soft to hard or elastic to plastic for instance. Figure 14. View largeDownload slide Diagram of storage and release of inner stress on simulated rock. 1. Original quartz sands, 2. External load applied, 3. Epoxy grouting, 4. External load remove, 5. After heating. Figure 14. View largeDownload slide Diagram of storage and release of inner stress on simulated rock. 1. Original quartz sands, 2. External load applied, 3. Epoxy grouting, 4. External load remove, 5. After heating. The specimens prepared in this work contain quartz sands, consolidated epoxy, and voids. The possible targets that stored consolidated pressure were quartz sands and voids, since the epoxy was added last into the constrained system. As indicated by Yue (2013, 2014, 2015), microvoids or microgas in deep rocks possibly contains high inner stress, thus inner stress may be stored partly in voids. This could also be inferred from the XRD result which revealed that the calculated inner stress was smaller than the applied pressure. However, rock structures and external stress are complicated, leading to differences in mechanical behavior (Tan 1979, Sun and Sun 2011). Inconsistent plastic deformation could be produced under pressure and temperature variations (Wang 1984). Thus, the real storage and release process of inner stress in rock is very complicated. However, based on reasonable simplifications and assumptions, this work is a beneficial attempt to explain the inner stress storage and release of rock materials, and the tests and results should be helpful for further research on rock inner stress. 5. Conclusions In this work, we designed a mold to simulate the storage process of inner stress based on reasonable simplifications and assumptions. The specimens prepared by the mold in this work showed that the inner stress could be stored according to thermal test results and XRD analysis. The results indicate that quartz aggregate compressed and constrained by consolidated epoxy is one kind mechanism that shows how inner stress is stored. Based on this, we concluded that the necessary condition of inner stress storage and release is possibly material physical state variation, hard to soft variation for instance. In rock materials, real storage and release of inner stress is complicated, but the plastic–elastic transformation may be a proper explanation. As it is a very special case, further research on how the inner stress release operates and its effect on rock materials’ mechanical behavior should be conducted. Acknowledgments This work was supported by State Key Laboratory Program for Geological Hazard Prevention and Geological Environment Protection (SKLGP2016K001) and Basic Research Projects of Ministry of Finance of China (2014-JBKY-06). References An O . , 2011 , Residual Stress Field of Crust Beijing Seismological Press (pg. 19 - 28 ) (in Chinese) An O . , 2014 , Tectonic Energy Field Beijing Seismological Press (pg. 40 - 51 ) (in Chinese) Anita J H , Martin R T . , 1999 The Physics of Glassy Polycarbonate: Superposability and Volume Recovery, Structure and Properties of Glassy Polymers ACS Symp. 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TI - A novel design for storage of inner stress by colloidal processing on rock-like materials
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2140/aaaa8a
DA - 2018-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/a-novel-design-for-storage-of-inner-stress-by-colloidal-processing-on-J3J9qjBRh2
SP - 1023
VL - 15
IS - 3
DP - DeepDyve
ER -