Dynamic characteristics and damage constitutive model of high-temperature bedding sandstone under cyclic impact
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摘要: 为研究循环冲击下高温层理砂岩的动力学特性及动态损伤本构模型，首先对高温（300~
1100 ℃）作用后层理砂岩的物理特性进行测试；其次利用霍普金森压杆（split Hopkinson pressure bar，SHPB）装置开展了循环冲击下高温层理砂岩动力学特性研究；最后，基于层理岩石黏弹性损伤元件模型，构建了考虑高温-冲击荷载耦合损伤的层理岩石动态本构模型，并通过实验数据对模型进行了验证。结果表明：砂岩主要矿物晶体石英的变晶温度处于500~700 ℃之间。温度越高，砂岩表观颜色越深，质量越小，波速和峰值应力先减小后增大。温度对0°、45°层理砂岩造成的损伤更大，900 ℃时损伤最为显著。在1300 V冲击电压下，层理砂岩的峰值应力随冲击次数的增加呈现先升后降的趋势。冲击荷载使高温后的0°层理砂岩更容易破坏，而45°和60°层理砂岩表现出较强的抗冲击能力。模型预测曲线与试验曲线相差较小，表明该模型在描述高温层理砂岩循环冲击力学特性方面具有良好的适用性。Abstract: To investigate the dynamic characteristics and dynamic damage constitutive model of high-temperature bedding sandstone under cyclic impact, the physical properties of bedding sandstone after exposure to 300−1100 ℃ were first examined, and the influence of temperature on the color, mineral composition, mass and wave velocity of the specimens was recorded. Second, the dynamic characteristics of high-temperature bedding sandstone under cyclic impact were studied with a split Hopkinson pressure bar (SHPB) apparatus, and the dynamic responses of bedding sandstone at different strain rates and impact numbers were analyzed. Finally, on the basis of the visco-elastic damage element model for bedding rock, a dynamic constitutive model that accounts for high-temperature-impact-load coupling damage was established and verified against experimental data. The results show that the crystallization temperature of the dominant mineral quartz lies between 500 ℃ and 700 ℃; the higher the temperature, the darker the apparent color of the rock and the lower its mass. With increasing temperature, the wave velocity and peak stress first decrease and then increase. Temperature inflicts greater damage on 0° and 45° bedding sandstone, and the damage is most pronounced at 900 ℃. Under an impact voltage of1300 V, the peak stress of bedding sandstone increases and then decreases with increasing impact number. Impact loading renders 0° bedding sandstone more susceptible to failure after high-temperature exposure, whereas 45° and 60° bedding sandstone exhibit strong impact resistance. The difference between the predicted and experimental curves is small, indicating that the model satisfactorily describes the cyclic-impact mechanical behavior of high-temperature bedding sandstone. The findings provide a valuable theoretical reference for the prevention and control of rock dynamic disasters in complex deep geothermal engineering environments.-
Key words:
- rock dynamics /
- high temperature /
- bedding sandstone /
- cyclic impact /
- constitutive model
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图 1 试件的单轴抗压强度和纵波波速
Figure 1. Uniaxial compressive strength and longitudinal wave velocity of specimens
图 2 高温层理砂岩SHPB试验系统
Figure 2. SHPB system for bedding sandstone under high temperatures
图 3 试件单次冲击动态应力平衡曲线
Figure 3. Dynamic stress balance curves of specimen under single impact
图 7 试件质量损失率随温度的变化
Figure 7. Variation of specimen average mass loss ratio with temperature
图 8 试件波速衰减率随温度的变化
Figure 8. Variation of specimen wave velocity decay ratio with temperature
图 11 不同温度下试件的动态应力-应变曲线
Figure 11. Dynamic stress-strain curves of specimens at different temperatures
图 12 不同角度层理砂岩在各个温度区间的损伤变化规律
Figure 12. Damage evolution of bedded sandstone with different bedding angle at various temperatures
图 13 不同角度层理砂岩在各个温度区间的损伤增长量（相对增量）
Figure 13. Damage growth (relative increase) of sandstone with different angle bedding in various temperature ranges
图 14 试件循环冲击动态应力-应变曲线（
1300 V冲击电压下）Figure 14. Dynamic stress-strain curves of specimen with cyclic impacts (under a impulse voltage of
1300 V)
图 15 循环冲击下砂岩试件的破坏模式
Figure 15. Failure modes of sandstone specimens under cyclic impact
表 1 高温后砂岩基质部分的主要矿物成分
Table 1. Major mineral compositions of sandstone matrix fractions after high temperatures
温度/℃ 物质 质量分数/% 25 石英 47.2 钠长石 31.2 钙长石 10.5 钾长石 4.4 高岭石 6.7 500 石英 66.5 钠长石 33.5 700 石英 62.6 钠长石 37.4 900 石英 55.7 钠长石 44.3 1100 石英 62.1 钠长石 37.9 
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表 2 高温处理后砂岩层理部分的主要矿物成分
Table 2. Major mineral compositions of sandstone bedding fractions after high temperatures
温度/℃ 物质 质量分数/% 25 石英 26.9 钠长石 20.1 钙长石 11.4 钾长石 6.1 高岭石 35.5 500 石英 42.1 钠长石 36.5 高岭石 21.4 700 石英 62.7 钠长石 37.3 900 石英 65.2 钠长石 34.8 1100 石英 73.5 钠长石 26.5
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表 3 主要矿物的熔融温度范围
Table 3. Melting temperature ranges of major minerals
物质 温度/℃ 状态 钠长石 950～ 1100 熔融 石英 ≥ 1350 熔融
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表 4 循环冲击后试件的损伤
Table 4. The damage of specimens after cyclic impact
层理角度/(°) 一次冲击峰值应力/MPa 临界破坏强度/MPa 损伤 0 21.97 17.56 0.20 15 20.78 16.25 0.21 45 26.04 12.42 0.52 60 23.41 10.66 0.54 90 38.87 26.57 0.31
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表 5 $ \mathrm{\mathit{A}}(T) $和$ \mathrm{\mathit{B}}(T) $与温度的关系
Table 5. Relationship of $ \mathit{\mathrm{\mathit{A}}}(T) $ and $ \mathit{\mathit{\mathrm{\mathit{B}}}}(T) $ with temperature
温度/℃ A(T) B(T) 温度/℃ A(T) B(T) 25 1.000 1.000 700 1.888 0.791 300 1.155 1.598 900 2.012 0.799 500 1.644 1.069 1100 1.333 1.023
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