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STUDY ON EVALUATION INDEX OF BRITTLENESS CHARACTERISTICS OF GRANITE UNDER DIFFERENT WATER CONTENT CONDITIONS
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摘要: 准确评价花岗岩在不同含水率条件下的脆性特征对此类工程岩体稳定性评价具有重要的意义。总结国内外现有岩石脆性评价指标，着重对基于应力-应变曲线特征的指标适用性和准确性进行详细分析和讨论，结合单轴压缩条件下花岗岩脆性特征随含水率增加而逐渐降低的试验规律，指出目前常用的基于应力-应变曲线特征的指标难以全面准确反映不同含水率花岗岩脆性特征。基于此，综合考虑全过程应力-应变曲线及峰后破坏时间，应用峰值应变表征峰前脆性特征、峰后应力跌落速率及应变增长速率表征峰后脆性特征，由此提出一种能全面反映花岗岩变形破坏全过程的脆性评价新指标Bd。经试验证实，新指标Bd能够准确地反映出花岗岩在不同含水率条件下的脆性变化趋势，相比其他脆性评价指标具有一定优越性。研究成果对丰富和改进现有的岩石脆性评价指标具有一定的参考意义和价值。Abstract: Accurately evaluation of brittleness characteristics of granite under different water content is of great significance to rock mass stability evaluation. The existing rock brittleness evaluation indices are summarized. The indices based on stress-strain curve are analyzed in detail. The brittleness of granite decreases with the increase of water content under uniaxial compression,but experiment results show that the indices which based on the stress-strain curve are difficult to accurately reflect the brittleness characteristics of granite under different water contents. So a new brittleness index Bd is proposed and can fully reflect the whole process of granite deformation and failure. Considering the whole process stress-strain curve and the post peak failure time,the new index Bd uses the peak strain to characterize the pre-peak brittleness characteristics and uses the post peak stress drop rate and the post peak strain growth rate to characterize the post-peak brittleness characteristics. It is proved by experiments that the index Bd can accurately reflect the trend that the granite brittleness decreases with the increase of water content. The new index Bd has superiority over the other brittleness indices. The research results can provide some references and help to enrich and improve the rock brittle characteristics evaluation methods.
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Key words:
- Rock mechanics /
- Brittleness index /
- Hydrous granite /
- Stress-strain curve /
- Failure time
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图 2 不同含水率花岗岩应力-应变曲线图
Figure 2. Stress-strain curves of granite under different water contents
图 3 花岗岩试样单轴压缩结果示意图
a. 1-2；b. 3-3；c. 5-2；d. 6-4；e. 7-1；f. 8-1
Figure 3. Diagram of text results of granite with different water content under uniaxial compression
图 4 脆性指标B6、B7、B10、B11计算结果曲线
a.脆性指标B6；b.脆性指标B7；c.脆性指标B10；d.脆性指标B11
Figure 4. Curves of brittleness indices B6, B7, B10, B11
表 1 现有岩石脆性评价指标汇总表
Table 1. Summary of existing brittleness indices
分类依据 公式含义及说明 基于拉压强度特征的脆性指标 $ {B_1} = {\sigma _c}/{\sigma _t}, {B_2} = \left({{\sigma _c} - {\sigma _t}} \right)/\left({{\sigma _c} + {\sigma _t}} \right), {B_3} = {\sigma _c}{\sigma _t}/2, {B_4} = \sqrt {{B_3}} $
σc、σt分别为岩石的单轴抗压强度和劈裂抗拉强度(Hucka et al., 1974)基于拉压强度和起裂应力水平的脆性指标 $ B_{5}=\left(\sigma_{c}-\sigma_{t}\right) /\left(\sigma_{c}+\sigma_{t}\right)=(8-K) /(8+K), K=\sigma_{c i} / \sigma_{c}$，闪长岩(王宇等，2014)
σc、σt分别为岩石的单轴抗压强度和劈裂抗拉强度，σci为起裂应力基于应力-应变曲线的脆性指标 B6=(τp-τr)/τp，τp为峰值强度，τr为残余强度(Altindag，2010)
B7=(εr-εp)/εp，εp为峰值应变，εr为残余应变(Altindag，2010)
B8=εr/ε，εr为加载后可恢复应变，ε为加载过程总应变(Hucka et al., 1974)
$B_{9}=R_{9}^{\prime}+B_{9}^{\prime \prime}, B_{9}^{\prime}=\left(\varepsilon_{\mathrm{BRTT}}-\varepsilon_{n}\right) /\left(\varepsilon_{m}-\varepsilon_{n}\right), B_{9}^{\prime \prime}=\alpha C S+\beta C S+\eta, C S_{\mathrm{BRTT}}=\left[\varepsilon_{p}\left(\sigma_{p}-\sigma_{r}\right)\right] /\left[\sigma_{p}\left(\varepsilon_{r}-\varepsilon_{p}\right)\right] $
其中，εBRIT为岩样峰值应变；εm为最大峰值应变；εn为最小峰值应变；α、β、η均为标准化系数；σp为峰值应力；σr为残余应力；εp为峰值应变；εr为残余应变，页岩(李庆辉等，2012)
$ B_{10}=\left[\left(\tau_{p}-\tau_{r}\right) / \tau_{p}\right] \times\left[\lg \left|k_{a c}\right| / 10\right], \tau_{p}$为峰值强度，τr为残余强度，kac为峰后曲线斜率，花岗岩(周辉等，2014)
$B_{11}=B_{11}^{\prime}+B_{11}^{\prime \prime}, B_{11}^{\prime}=\left[\left(\sigma_{p}-\sigma_{r}\right)\left(\varepsilon_{r}-\varepsilon_{p}\right)\right] /\left(\sigma_{p} \varepsilon_{p}\right), B_{11}^{\prime \prime}=\left(\sigma_{p}-\sigma_{r}\right) /\left(\varepsilon_{r}-\varepsilon_{p}\right) $，其中，σp为峰值应力；σr为残余应力；εp为峰值应变；εr为残余应变，胜利油田某储层(夏英杰等，2016)
$ B_{12}=B_{12}^{\prime}+B_{12}^{\prime \prime}, B_{12}^{\prime}=\left[\left(\sigma_{p}-\sigma_{i}\right) / \sigma_{p}\right] /\left[\left(\varepsilon_{p}-\varepsilon_{i}\right) / \sigma_{p}\right], B_{12}^{\prime \prime}=\left[\left(\sigma_{p}-\sigma_{r}\right) / \sigma_{p}\right] /\left[\left(\varepsilon_{r}-\varepsilon_{p}\right) / \varepsilon_{p}\right]$，其中，σp为峰值应力；σi为起裂应力；σr为残余应力；εp为峰值应变；εr为残余应变，εi为起裂应变(陈国庆等，2018)基于内摩擦角的脆性指标 $ B_{13}=\sin \varphi, B_{14}=45^{\circ}+\varphi / 2, \varphi$为内摩擦角(Hucka et al., 1974) 基于硬度的脆性指标 $ B_{15}=\left(H_{U}-H\right) / K, H_{U}$为微观硬度，H为岩石宏观硬度，K为常数(Lawn et al., 1979)
B16=H/KIC，Tang et al. (1998)，B17=HE/KIC2，Quinn et al., (1997)，E为弹性模量，H为岩石宏观硬度，KIC为断裂韧性，陶瓷材料基于碎屑含量的脆性指标 B18=S20，S20为小于11.2 mm的碎屑百分比(Protodyakonov，1963)
B19=qσc，q为为小于0.6 mm的碎屑所占百分比，σc为单轴抗压强度(Blindheim et al., 1998)基于贯入试验的脆性指标 B20=Fmax/P，F为载荷，P为贯入深度(Copur et al., 2003)
B21=Pdec/Pinc，Pdec为衰减载荷，Pinc为增量荷载(Yagiz，2006)基于能量演化的脆性指标 B22=Wr/W，Wr为可恢复应变能，W为总应变能(Altindag，2002)
B23Wr/We，Wr为断裂能增量，We为卸载弹性能增量(Tarasov et al., 2013)
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表 2 不同含水率花岗岩单轴压缩试验现象描述
Table 2. Description of experimental phenomena of granite with different water contents under uniaxial compression
组号 声响 试验现象描述 1 爆炸式声响 试样外侧出现裂纹的发展和延伸，伴随着颗粒弹射，达到峰值后极短时间内发生崩落式破坏，碎片弹射最远可达10 m左右，破裂面以压致劈裂破坏为主，试样破碎 3 巨响 试样达到峰值后在试样两端出现鼓起现象，极短时间内发生崩落式破坏，碎片弹射距离最远为8 m左右，破裂面以压致拉裂破坏为主，试样较破碎 5 较响 试样外侧同样出现裂纹的发展和延伸，伴随着颗粒弹射，达到峰值后在试样两端出现鼓起现象，鼓起向试样中部扩展直至破坏，破裂面主要为压致劈裂破坏 6 较响 破坏前没有出现颗粒弹射现象以及裂缝，岩样破坏时先是上下端面出现鼓起，鼓起迅速向试样中部扩展直至破坏，破裂面以剪切破坏为主 8 声响较小 随着加载进行在试样外侧出现一条裂纹，伴随颗粒弹射现象，临近破坏前在试样下端面附近出现鼓起，破裂面以剪切破坏为主，破坏后试样完整性较前几种好
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表 3 脆性评价指标B6、B7、B10、B11计算结果统计表
Table 3. Calculated results of difference brittleness indices of B6、B7、B10、B11
组号 含水率/% σp/MPa εp/% σr/MPa εr/% B6 B7 B10 B11 1(干燥) 0 143.85 1.227 76.270 2.340 0.470 0.907 0.178 0.487 2(浸水6 h) 0.116 120.14 1.138 67.300 2.030 0.440 0.784 0.166 0.404 3(浸水12 h) 0.129 120.6 1.254 83.599 2.353 0.307 0.876 0.108 0.303 4(浸水24 h) 0.167 97.99 1.183 58.886 1.832 0.399 0.549 0.151 0.279 5(浸水48 h) 0.178 106.00 1.123 64.685 1.620 0.390 0.443 0.153 0.256 6(浸水72 h) 0.185 93.00 1.098 53.246 1.494 0.427 0.361 0.171 0.255 7(浸水96 h) 0.197 83.17 1.002 51.722 1.390 0.378 0.387 0.148 0.227 8(饱和) 0.223 77.95 1.069 44.359 1.315 0.431 0.230 0.178 0.236
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表 4 脆性评价指标Bd计算成果表
Table 4. Calculated results of brittleness index Bd
组号 t/s Bd1 Bd2 Bd 1(干燥) 0.9 0.382 1.530 1.912 2(浸水6 h) 1 0.389 1.224 1.613 3(浸水12 h) 1.1 0.380 1.076 1.456 4(浸水24 h) 1 0.385 0.948 1.333 5(浸水48 h) 1 0.390 0.832 1.222 6(浸水72 h) 1 0.392 0.788 1.180 7(浸水96 h) 1.1 0.400 0.696 1.096 8(饱和) 1.2 0.394 0.551 0.945
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表 5 验证性试验的脆性评价指标Bd计算结果
Table 5. Calculated results of brittleness index Bd of the new proven experiments
组号 含水率/% σp/MPa εp/% σr/MPa εr/% t/s Bd1 Bd2 Bd 9(浸水36 h) 0.17 132.418 2.012 42.392 2.305 0.9 0.339 0.916 1.255 10(浸水60 h) 0.182 117.323 1.153 68.779 1.723 1.1 0.387 0.824 1.211
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