Effects of temperature on Brazilian splitting characteristics of sandstone with different sizes
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摘要: 為研究高溫與尺寸效應耦合作用下的砂巖巴西劈裂特性，分別對經過25、200、400、600、800和1000 ℃高溫處理后的標準砂巖試件進行巴西劈裂室內試驗，并基于顆粒流軟件開展不同尺寸高溫砂巖巴西劈裂數值模擬，研究砂巖巴西劈裂強度及其劣化規律、孔隙率增加相對于裂紋擴展貫通的滯后性規律。研究結果表明：（1）在25～1000 ℃的溫度范圍和50～100 mm的直徑范圍內，溫度與尺寸效應對砂巖巴西劈裂強度均有顯著影響，且尺寸效應影響程度更大。在加熱過程中，由于巖石內部首先發生熱膨脹，然后在熱應力作用下產生損傷，因此砂巖劈裂強度先有所增大，在400 ℃之后持續降低，劈裂強度下降約34.66%～35.10%；隨著尺寸增大，巖石內部積聚的能量釋放產生大量微裂隙，導致砂巖試樣劈裂強度降低，下降約55.61%～56.99%。（2）砂巖巴西劈裂強度劣化幅值與其直徑之間滿足負指數函數關系，可用于預測不同尺寸高溫砂巖的巴西劈裂強度。（3）砂巖在巴西劈裂過程中的孔隙率增加相對于裂隙擴展貫通滯后的荷載差值隨溫度升高以及尺寸增大而增大；考慮兩因素的耦合作用，尺寸效應對荷載差值的影響程度隨溫度的升高而降低，溫度對荷載差值的影響程度隨砂巖尺寸的增大而降低。研究成果對火災后頂板維護，初步預測頂板強度具有一定參考意義，也可為核廢料處理、地熱資源開發和深井工程等涉及高溫和尺寸變化的巖體工程設計提供有益參考。Abstract: To study the Brazilian splitting characteristics of sandstone under the coupling effect of high temperature and sandstone’s size, Brazilian splitting laboratory tests were carried out on standard sandstone specimens treated at 25, 200, 400, 600, 800, and 1000 ℃, respectively. A Brazilian splitting numerical simulation of sandstone with different sizes under high temperature was carried out based on particle flow software to study the Brazilian splitting strength and deterioration law of sandstone. In addition, the hysteresis law of porosity rise relative to the crack propagation and penetration was also investigated. Results are as follows: (1) In the temperature range of 25?1000 ℃ and in the diameter range of 50–100 mm, the temperature and size significantly affect the Brazilian splitting strength of sandstone, with size having a greater influence. During the heating process, due to the initial thermal expansion in the rock and subsequent damage under the action of thermal stress, the splitting strength of sandstone first increases and then decreases by approximately 34.66%–35.10% after 400 ℃. With the increase in the size, the energy accumulated in the rock is released, and a large number of microfractures are produced, resulting in decreasing the splitting strength of sandstone samples by approximately 55.61%–56.99%. (2) The relationship between the degradation amplitude of the Brazilian splitting strength of sandstone and its diameter satisfies a negative exponential function, which can predict the Brazilian splitting strength of sandstone with different sizes at high temperatures. (3) The porosity of sandstone increases during Brazilian fracturing, and the load difference relative to fracture propagation and penetration increases with increasing temperature and size. Considering the coupling effect of the two factors, the influence of size and temperature on the load difference decreases with increasing temperature and sandstone’s size. This study is of high significance for roof maintenance and preliminary prediction of the roof strength after a fire. In addition, it can also provide a useful reference for rock engineering design involving high temperatures and size changes, such as nuclear waste treatment, geothermal resource development, and deep well engineering.
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圖 1 巴西劈裂室內試驗。（a）YAW?600電液壓伺服巖石壓力試驗機；（b）巴西圓盤試件
Figure 1. Laboratory test of Brazilian splitting: (a) YAW?600 electro hydraulic servo rock pressure testing machine; (b) Brazilian disk specimen
圖 2 不同溫度下砂巖平均縱波波速。（a）康科瑞NM?4B非金屬超聲檢測分析儀；（b）縱波波速曲線
Figure 2. P-wave velocity of sandstone at different temperatures: (a) concrete NM?4B metalloid ultrasonic testing analyzer; (b) P-wave velocity curve
圖 3 砂巖礦物成分衍射強度隨溫度變化曲線
Figure 3. Variation curves of the mineral composition diffraction intensity of sandstone with temperature
圖 4 砂巖電鏡掃描圖像。（a）800 ℃時掃描電鏡圖像；（b）1000 ℃時掃描電鏡圖像
Figure 4. SEM images of sandstone at: (a) 800 ℃; (b) 1000 ℃
圖 5 砂巖試樣X射線衍射結果。（a）D8 DISCOVER X射線衍射儀；（b）衍射強度圖譜；（c）礦物成分含量
Figure 5. X-ray diffraction results of sandstone samples: (a) photograph of D8 DISCOVER X-ray diffractometer; (b) diffraction intensity pattern; (c) mineral composition content
圖 6 PFC中熱力學計算時熱存儲器和熱管示意圖
Figure 6. Schematic of the heat storage and heat pipe for the thermodynamic calculation of PFC
圖 8 砂巖數值模擬結果與室內試驗結果對比。（a）砂巖試樣；（b）顆粒流模型
Figure 8. Comparison of numerical simulation and laboratory test results of sandstone with a diameter of 50 mm: (a) sandstone sample; (b) particle flow model
圖 9 高溫與尺寸效應耦合作用下的砂巖巴西劈裂強度。（a）砂巖劈裂強度與溫度及尺寸的關系；（b）垂直方向投影圖
Figure 9. Brazilian splitting strength of sandstone under the coupling effects of high temperature and size: (a) relationship between the splitting strength of sandstone and temperature and size; (b) vertical projection
圖 10 不同溫度下各尺寸砂巖巴西劈裂強度的劣化幅值。（a）200 ℃；（b）400 ℃；（c）1000 ℃
Figure 10. Degradation amplitude of the Brazilian splitting strength of sandstone of different sizes at (a) 200 ℃; (b) 400 ℃; (c) 1000 ℃
圖 11 砂巖孔隙率增加相對裂隙擴展貫通滯后的荷載差值與溫度和尺寸的關系。（a）荷載差值；（b）垂直方向投影圖
Figure 11. Relationship between the load difference of the sandstone porosity relative to the fracture propagation and penetration and temperature and size: (a) load difference; (b) vertical projection
圖 12 常溫下直徑50 mm和100 mm砂巖裂隙演化過程
Figure 12. Evolution of sandstone fractures with diameters of 50 mm and 100 mm at room temperature
圖 13 不同溫度下砂巖試樣孔隙率測試值。（a）25 ℃；（b）400 ℃；（c）800 ℃；（d）1000 ℃
Figure 13. Test results of the porosity of sandstone samples at (a) 25 ℃; (b) 400 ℃; (c) 800 ℃; (d) 1000 ℃
表 1 不同溫度下砂巖試樣的劈裂強度
Table 1. Splitting strengths of sandstone samples at different temperatures
Temperature/℃ Splitting strength/MPa Average value/MPa A B C 25 2.238 2.237 2.254 2.243 200 2.341 2.588 2.226 2.385 400 2.425 3.832 2.439 2.432 600 2.221 1.955 2.404 2.193 800 1.964 2.260 2.249 2.158 1000 1.445 1.682 3.798 1.564 Note：A, B, C is the test values of three groups of Brazilian splitting tests; Average value is the average of three test values. 
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表 2 砂巖數值模型細觀參數組合
Table 2. Combination of meso-parameters of the sandstone numerical model
Parameters Value Parameters Value Minimum radius of particles/mm 0.10 Elastic modulus/GPa 5 Particle size ratio 1.50 Parallel bond modulus/GPa 5 Particle density/(kg·m?3) 2300 Local damping coefficient 0.70 Splitting strength/MPa 2.24 Thermal conductivity[35]/(W·m?1·K?1) 5.91 Friction coefficient 0.50 Coefficient of linear thermal expansion/(10?4 K?1) Quartz 1.37 Porosity 0.18 Kaolinite 0.53 Stiffness ratio 1.30 Mica 2.80
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表 3 不同砂巖在巴西劈裂模擬下的劈裂強度
Table 3. Splitting strengths of different sandstone samples under Brazilian splitting simulations
Sample number Temperature/℃ Diameter/mm Splitting strength/MPa Sample number Temperature/℃ Diameter/mm Splitting strength/MPa 1 25 50 2.239 13 600 50 2.190 2 25 60 2.015 14 600 60 2.013 3 25 80 1.276 15 600 80 1.223 4 25 100 0.963 16 600 100 1.004 5 200 50 2.364 17 800 50 2.145 6 200 60 2.151 18 800 60 1.798 7 200 80 1.371 19 800 80 1.174 8 200 100 1.040 20 800 100 0.862 9 400 50 2.320 21 1000 50 1.516 10 400 60 2.123 22 1000 60 1.275 11 400 80 1.361 23 1000 80 0.807 12 400 100 1.037 24 1000 100 0.673
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