Brittle Evaluation Based on Energy Evolution at Pre-Peak and Post-Peak Stage
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摘要: 为了准确评价油气储藏水力压裂及岩爆等工程中岩石的脆性，总结了目前国内外已有的基于能量理论计算岩石脆性的方法，并指出了它们的局限性.综合考虑岩石峰前和峰后的能量演化特征，建立了一种基于全应力应变曲线的反映岩石变形破坏全过程的脆性指数评价方法，更加全面地描述岩石的脆性特征.为了验证新方法的合理性，收集了4组岩石力学试验对新指数进行检验.试验结果表明：由峰前指数与峰后指数合成的脆性指数都随着围压的增加而减小，低围压下煤岩和页岩2组均具有较强的脆性，而高围压下红砂岩和页岩1组的脆性明显减弱，表现了随围压增大岩石发生脆延转换的特性.在实际边坡工程中通过对板岩进行脆性评价，验证了本文所提出的脆性指数在工程应用中的合理性，该成果有望对岩石脆性评价提供参考.Abstract: Rock brittleness is one of the important mechanical properties of rock mass, which is so crucial for accurately evaluating hydraulic fracturing of oil and gas reservoir and rock bursting engineering. Existing methods of rock brittleness based on energy theory were summarized, and limitations of these indexes were analyzed in detail. In this study, energy evolution characteristics at pre-peak and post-peak stage are comprehensively considered. A new method to determine brittleness index of rocks based on complete stress-strain curves is established, which more reasonably describes the rock brittleness. To verify the rationality of the method, four sets of rock mechanics tests are collected to test the new index. Test results show that the new brittleness index gradually increases with the increase of confining pressure. Under low confining pressure, both coal and group 1 of shale exhibit strong brittleness, while under high confining pressure, the brittleness of red sandstone and group 2 of shale is obviously weakened, showing that the characteristics of brittle-ductile transition of rocks with increasing of the confining pressure. Then in actual slope engineering, the rationality of the new brittleness index is further validated by the tests of slate, which may be expected to offer some references for evaluating rock brittleness.
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Key words:
- rock /
- brittleness index /
- stress-strain curve /
- energy evolution /
- engineering geology
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图 2 基于本文方法确定的不同岩石的脆性指数：(a)红砂岩；(b)煤岩；(c)页岩1组；(d)页岩2组
Fig. 2. The brittleness index of different rocks determined by the proposed method: (a) red sandstone; (b) coal; (c) group 1 of shale; (d) group 2 of shale
图 3 归一化后脆性指数随围压的变化趋势
Fig. 3. Change trends of brittleness index with confining pressure after normalization
图 4 不同方法确定的脆性指数的比较：(a)红砂岩；(b)煤岩；(c)页岩1组；(d)页岩2组
Fig. 4. Comparison of brittleness indexes determined by different methods: (a) red sandstone; (b) coal; (c) group 1 of shale; (d) group 2 of shale
图 5 归一化后不同脆性指数的对比：(a)红砂岩；(b)煤岩；(c)页岩1组；(d)页岩2组
Fig. 5. Comparisons for different brittleness indexes after normalization: (a) red sandstone; (b) coal; (c) group 1 of shale; (d) group 2 of shale
图 7 对比脆性指数不能考虑的情况
Fig. 7. Cases that cannot be considered by these brittleness indexes for comparison
表 1 汇总基于能量理论定义的脆性指数
Table 1. Summary of the existing methods based on energy theory
方法 公式 参数描述 来源 基于能量理论定义脆性指数 $B{I_1} = \frac{{{W_{{\rm{et}}}}}}{{{W_{{\rm{et}}}} + {W_{\rm{p}}}}}$ Wet=总弹性能；Wp=塑性能 Hucka and Das, 1974 $B{I_2} = \frac{{{W_{\rm{a}}}}}{{{W_{\rm{e}}}}}$ Wa=峰后附加能量；We=耗散的弹性能 Munoz et al., 2016 $B{I_3} = \frac{{{W_{{\rm{et}}}}}}{{{W_{\rm{p}}} + {W_{\rm{r}}}}}$ Wr=断裂能 Munoz et al., 2016 $B{I_4} = \frac{{{W_{{\rm{et}}}} + {W_{\rm{p}}}}}{{{W_{\rm{p}}} + {W_{\rm{r}}}}}$ Munoz et al., 2016 $B{I_5} = \frac{{{W_{{\rm{et}}}}}}{{{W_{\rm{r}}}}}$ Munoz et al., 2016 $B{I_6} = \frac{{{W_{\rm{p}}} + {W_{\rm{r}}}}}{{{W_{\rm{e}}} + {W_{\rm{p}}}}}$ Ai et al., 2016 $B{I_7} = \frac{{{W_{\rm{a}}}}}{{{W_{\rm{e}}} + {W_{\rm{p}}}}}$ Ai et al., 2016 $B{I_8} = \frac{{{W_{{\rm{eAB}}}}}}{{{W_{{\rm{eAB}}}} + {W_{{\rm{AB}}}}}}$ WeAB=峰后可释放弹性能；WAB=峰后吸收能 侯振坤，2018 $B{I_9} = \frac{{{W_{\rm{e}}}}}{{2{W_{\rm{r}}}}} + \frac{{{W_{\rm{e}}}}}{{2\left({{W_{{\rm{et}}}} + {W_{\rm{p}}}} \right)}}$ Rahimzadeh Kivi et al., 2018 $B{I_{10}} = \frac{{{W_{{\rm{AB}}}}}}{{{W_{{\rm{eAB}}}}}} + \frac{{{W_{\rm{A}}}}}{{U_{\rm{A}}^{\rm{e}}}}$ WA=峰值处总吸收能；UAe=峰值处弹性应变能 宋洪强等，2019 $B{I_{11}} = \frac{{\Delta {U_{\rm{e}}}}}{{U_{\rm{e}}^{\rm{p}}}} + \frac{{\Delta U_{\rm{e}}^{\rm{r}}}}{{U_{\rm{e}}^{\rm{p}}}}$ ΔUed表征残余强度处耗散能量的能力；Uep=峰值处弹性应变能；ΔUer表征峰后释放能量的能力 Zhang et al., 2018 $B{I_{12}} = 1 - \frac{{{E_{\rm{d}}}}}{{{E_{\rm{d}}} + {E_{\rm{G}}}}}$ Ed=抗震变形能；EG=产生新的破裂面所需能量 Feng et al., 2020 $B{I_{13}} = \frac{{U_{\rm{e}}^{\rm{p}}}}{{U_{\rm{e}}^{\rm{p}} + d{W_{\rm{d}}}}} \times \frac{{d{W_{\rm{e}}}}}{{d{W_{\rm{r}}}}}$ dWd=峰前耗散能 Li et al., 2019 $B{I_{14}} = \frac{{U_{\rm{e}}^{\rm{p}}}}{{U_{\rm{e}}^{\rm{p}} + d{W_{\rm{d}}}}} \times \left({1 - D_{\rm{e}}^{\rm{p}}} \right) \times \frac{{{\sigma _{\rm{p}}} - {\sigma _{\rm{r}}}}}{{{\sigma _{\rm{p}}}}}$ Dep=峰值处损伤系数；σp=峰值强度; σr=残余强度 Li et al., 2019 
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表 2 不同岩石的压缩试验力学参数
Table 2. Mechanical parameters of compression tests for different rocks
岩样 围压（MPa） 峰值强度（MPa） 损伤应力（MPa） 峰值应变（%） 残余应变（%） 红砂岩 0 69.79 14.44 0.593 0.791 10 132.35 65.78 0.914 1.230 20 173.26 133.16 1.156 1.472 30 211.76 158.82 1.423 1.976 40 251.87 202.14 1.680 2.342 煤岩 6 34.30 10.53 1.260 1.766 12 43.81 20.72 1.518 2.041 18 65.55 34.64 2.050 2.920 24 68.94 46.53 2.290 3.249 30 83.21 66.91 2.778 4.003 页岩1组 0 121.91 0 0.910 0.915 10 162.38 67.52 0.963 1.134 20 173.33 105.14 1.043 1.366 30 223.14 154.95 1.182 1.527 页岩2组 0 112.17 0 0.788 0.792 10 167.33 73.24 0.810 1.045 20 194.48 113.33 1.025 1.392 30 222.76 155.71 1.127 1.447
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表 3 不同岩石的脆性指数
Table 3. Brittleness indexes for different rocks
岩样 红砂岩 煤岩 页岩1组 页岩2组 围压 0 10 20 30 40 6 12 18 24 30 0 10 20 30 0 10 20 30 BIpre 1.96 2.44 2.42 2.58 2.95 2.61 2.64 2.88 3.31 3.68 1.52 1.98 2.41 1.98 1.22 2.06 2.06 2.16 BIpost 0.69 0.50 0.37 0.30 0.24 0.53 0.49 0.42 0.32 0.20 0.99 0.71 0.48 0.44 0.99 0.59 0.47 0.44 BInew 1.36 1.22 0.89 0.78 0.71 1.38 1.30 1.20 1.05 0.72 1.51 1.41 1.45 0.88 1.21 1.12 0.98 0.96
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表 4 料场边坡区岩石脆性指数
Table 4. Brittleness indexes in Liaochang slope areas
围压(MPa) 5 10 15 20 脆性指数BInew 2.409 1.926 1.799 1.081
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