Fractal geometry study on uniaxial compression fracture characteristics of sandstone subjected to freeze-thaw cycles
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摘要: 寒区岩石的力学特征往往受到冻融循环和荷载的共同影响，冻融岩石单轴压缩破坏断口蕴含着与冻融循环和荷载有关的损伤演化信息，冻融岩石单轴压缩破坏断口研究对冻融岩石断裂破坏机理分析有重要价值。为研究冻融岩石单轴压缩破坏断口形貌特征及其与宏观力学参数之间的关联性，通过摄影观测经历不同次数冻融循环的砂岩单轴压缩破坏断口形貌，采用像素点覆盖法计算断口分维值，探究了断口分维值与宏观力学参数之间的关系。结果表明：随着冻融次数的增加，冻融砂岩的力学性能劣化，单轴抗压强度、弹性模量、断口分维值、耗散能密度逐渐减小，峰值应变增大；单轴抗压强度、弹性模量、耗散能密度均与断口分维值之间存在指数关系，断口分维值越大，对应的单轴抗压强度、弹性模量、耗散能密度越大。冻融岩石单轴压缩破坏断口分维值可作为寒区岩体断裂破坏机理分析的有效参数。Abstract: The mechanical properties of rocks in cold regions are often affected by freeze-thaw cycles and loads. The uniaxial compression fractures of rocks subjected to freeze-thaw cycles contain damage evolution information related to freeze-thaw cycles and loads. It is of great value to study the uniaxial compression fracture of freeze-thaw rocks for the rock fracture failure mechanism after freeze-thaw degradation. To study the uniaxial compression fracture morphology of freeze-thaw rock and its correlation with the macro mechanical parameters, in this paper, fractures of sandstone under the uniaxial compression and different freeze-thaw cycles are observed by photography. The fracture fractal dimension is calculated by the pixel covering method, and the relationship between the fractal dimension and the macro-mechanical parameters is discussed. The results indicate that as the number of freeze-thaw cycles increases, the uniaxial compressive strength, elastic modulus, fracture fractal dimension, and energy dissipation density decrease gradually, and the peak strain increases. There are exponential relationships between the three parameters (uniaxial compressive strength, elastic modulus and dissipated energy density) and the fracture fractal dimension. The larger the fracture fractal dimension is, the greater the three parameters are. The fractal dimension of the freeze-thaw rock fracture under the uniaxial compression can be used as an effective parameter for the mechanism analysis of rock failure in cold regions.
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Key words:
- freeze-thaw cycle /
- uniaxial compression /
- fracture /
- fractal geometry
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图 5 不同次数冻融循环后砂岩的压缩破坏主断裂面图像
a1, a2, a3.0次；b1, b2, b3.5次；c1, c2, c3.10次；d1, d2, d3.15次；e1, e2, e3.20次；f1, f2, f3.25次；g1, g2, g3.30次
Figure 5. Main fracture images of sandstone under different freeze-thaw cycles
图 6 不同次数冻融循环下断口分维值
Figure 6. Fractal dimension of fracture under different freeze-thaw cycles
图 7 断口分维值随冻融循环次数变化情况
Figure 7. Relationship between the fracture fractal dimension and the number of freeze-thaw cycles
图 8 单轴抗压强度与断口分维值的关系
Figure 8. Relationship between uniaxial compressive strength and fracture fractal dimension
图 9 弹性模量与断口分维值的关系
Figure 9. Relationship between elastic modulus and fracture fractal dimension
图 10 耗散能密度与断口分维值的关系
Figure 10. Relationship between dissipated energy density and fracture fractal dimension
表 1 冻融循环后砂岩单轴压缩试验结果
Table 1. Uniaxial compression test results of sandstone after freezing and thawing
冻融次数n 0 5 10 15 20 25 30 单轴抗压强度σc/MPa 58.425 49.582 47.419 43.534 41.484 40.505 39.904 弹性模量E/GPa 16.582 11.558 10.258 9.727 8.785 8.602 8.392 峰值应变εc/‰ 5.454 5.713 6.064 5.806 6.348 6.333 6.326 
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表 2 不同次数冻融循环下砂岩破坏断口分维均值
Table 2. Fracture fractal dimension of sandstone under different freeze-thaw cycles
冻融次数 0 5 10 15 20 25 30 分维均值 2.219 20 2.219 01 2.218 72 2.217 74 2.218 56 2.218 07 2.215 63
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表 3 单轴压缩下岩石能量耗散特征值
Table 3. Energy dissipation characteristic value of rock failure under uniaxial compression
冻融次数n 0 5 10 15 20 25 30 耗散能密度Ud/(MJ·m-3) 39.498 37.594 35.442 28.390 32.314 31.731 28.177 能量耗散值/J 7.570 7.275 6.740 5.478 6.268 6.156 5.462
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