A study of the similar material characteristics of fragmenting rock mass physical model
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摘要:
高速远程滑坡物理模型试验中，岩石相似材料的选择是模型试验成功的关键，然而目前滑坡相似材料强度高、难以在缩尺试验中模拟滑坡破碎过程。以重晶石、石英砂为骨料，石膏为胶结剂，羧甲基纤维素钠、甘油、水作为辅助材料，进行可破碎岩石相似材料的配比试验。采用控制变量法研究重晶石与石英砂比例（重石比）、骨料与胶结物比例（骨胶比）、羧甲基纤维素钠含量、拌合水量、甘油含量对相似材料物理力学性质的影响。试验结果表明：所有配比情况下各相似材料物理力学参数的范围分别为单轴抗压强度为0.12～1.47 MPa，弹性模量为25.51～148.12 MPa，黏聚力为1.63～87.39 kPa，内摩擦角为22.70°～35.89°，脆性指标主要分布在0.033～0.145之间；重石比主要控制岩石相似材料的内摩擦角；骨胶比减小，对应的黏聚力和内摩擦角先增大后减小；羧甲基纤维素钠对材料的单轴抗压强度、弹性模量、黏聚力等材料的力学特性以及材料的脆性指标影响均比较大，其中对单轴抗压强度的影响最大。因此，控制羧甲基纤维素钠和拌合水量的含量，并合理调节重石比与骨胶比，在相似比约为1∶600的试验尺度下，最终确定了适用于高速远程滑坡碎屑化过程模拟的低强度高脆性岩石相似材料的配比区间。
Abstract:Similar materials in the physical model test of avalanche are the key to the success of the model test. However, the strength of similar materials is high at present, it is difficult to be fractured within the scope of the experiment. The materials can reproduce the clastic process of landslide in the scale model experiment. Thus, we choose five raw materials to formulate similar materials. The five raw materials are barite, quartz sand, gypsum, sodium carboxymethyl cellulose, glycerin and water content. Five influencing factors are analyzed, including the ratio of barite to quartz sand, the ratio of aggregate to gypsum, contents of sodium carboxymethyl cellulose and glycerin, and water content. The aggregate consists of barite and quartz sand. The results show that (1) in all the experiments, the uniaxial compressive strength ranges from 0.12 to 1.47 MPa, the elastic modulus, from 25.51 to 148.12 MPa, the cohesion, from 1.63 kPa to 87.39 kPa, the angle of internal friction, from 22.70° to 35.89°, and the brittleness index, from 0.033 to 0.145. (2) The ratio of barite to quartz sand has the great effect on the angle of internal friction. (3) With the decrease in the ratio of aggregate and cement, the cohesion first increases and then decreases. Sodium carboxymethyl cellulose has the greatest influence on the parameters of the similar materials, especially the uniaxial compressive strength. Therefore, it is important to control the sodium carboxymethyl cellulose, glycerin and water content and adjust the mass ratio of barite to quartz sand and the mass ratio of aggregate and cement. The obtained similar materials can be used to simulate the clastic process of avalanche when the similarity ratio is approximately 1∶600.
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Key words:
- rockslide /
- rock similar material /
- fragmentation /
- low strength and high brittleness /
- model test
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表 1 相似材料配制中主要物理量之间相似比
Table 1. Ratios of the key parameters in the similar materials production
物理量 量纲 相似比 物理量 量纲 相似比 应力 ML−1T−2 1∶600 内摩擦角 M0L0T0 1∶1 弹性模量 ML−1T−2 1∶600 长度 L 1∶600 应变 M0L0T0 1∶1 密度 ML−3 1∶1 泊松比 M0L0T0 1∶1 重力加速度 LT−2 1∶1 黏聚力 ML−1T−2 1∶600 
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表 2 模型相似材料力学参数
Table 2. The mechanical parameters of the similar materials
强度参数 抗压强度/MPa 黏聚力/MPa 内摩擦角/（°） 弹性模量/GPa 泊松比 原岩 100～250 30～50 45～60 40～69 0.1～0.3 相似材料 0.17～0.42 0.050～0.083 45～60 0.067～0.120 0.1～0.3
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表 3 模型相似材料配比方案
Table 3. Matching schemes of the model materials
编号 重石比 骨胶比 羧甲基纤维素钠含量/‰ 拌合水量/% 甘油含量/‰ S1 10∶0 30∶1 1.0 22.50 0.5 S2 8∶2 30∶1 1.0 22.50 0.5 S3 6∶4 30∶1 1.0 22.50 0.5 S4 5∶5 30∶1 1.0 22.50 0.5 S5 4∶6 30∶1 1.0 22.50 0.5 S6 7∶3 15∶1 1.0 22.50 0.5 S7 7∶3 20∶1 1.0 22.50 0.5 S8 7∶3 30∶1 1.0 22.50 0.5 S9 7∶3 35∶1 1.0 22.50 0.5 S10 7∶3 40∶1 1.0 22.50 0.5 S11 7∶3 30∶1 0.0 22.50 0.5 S12 7∶3 30∶1 0.5 22.50 0.5 S13 7∶3 30∶1 1.0 22.50 0.5 S14 7∶3 30∶1 1.5 22.50 0.5 S15 7∶3 30∶1 2.0 22.50 0.5 S16 7∶3 30∶1 1.0 17.50 0.5 S17 7∶3 30∶1 1.0 20.00 0.5 S18 7∶3 30∶1 1.0 22.50 0.5 S19 7∶3 30∶1 1.0 25.00 0.5 S20 7∶3 30∶1 1.0 27.50 0.5 S21 7∶3 30∶1 1.0 22.50 0.0 S22 7∶3 30∶1 1.0 22.50 4.0 S23 7∶3 30∶1 1.0 22.50 8.0 S24 7∶3 30∶1 1.0 22.50 16.0 S25 7∶3 30∶1 1.0 22.50 20.0
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表 4 试验结果
Table 4. Experimental results
物理力学参数 抗压强度/
MPa弹性模量/
MPa黏聚力/
kPa内摩擦角/
（°）密度/
（g·cm−3）S1 0.3238 79.49 25.16 33.02 1.729 S2 0.2795 113.90 40.56 31.49 1.812 S3 0.2832 115.26 58.45 22.70 1.861 S4 0.2920 108.15 29.20 28.45 1.881 S5 0.3383 84.06 26.08 35.89 1.855 S6 0.3357 50.02 20.93 24.92 1.809 S7 0.3578 64.86 46.42 31.82 1.800 S8 0.3699 117.39 58.00 33.10 1.818 S9 0.3818 104.79 79.10 30.19 1.800 S10 0.3190 92.67 46.95 27.98 1.804 S11 0.1154 52.28 1.63 32.50 1.859 S12 0.1937 78.95 31.29 32.41 1.812 S13 0.3699 117.39 58.00 33.10 1.804 S14 0.7483 126.22 50.20 29.86 1.832 S15 1.4727 148.12 61.99 32.13 2.220 S16 0.4408 53.10 87.39 30.51 1.844 S17 0.3446 87.45 61.21 30.29 1.803 S18 0.2952 117.39 58.00 33.10 1.818 S19 0.2704 51.32 48.12 28.77 1.779 S20 0.2779 41.82 41.04 32.71 1.815 S21 0.2436 116.41 50.70 28.76 1.804 S22 0.2019 59.35 65.63 29.86 1.843 S23 0.1316 58.18 47.91 30.95 1.805 S24 0.1167 35.02 41.63 33.65 1.837 S25 0.1648 25.51 54.82 28.88 1.885
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表 5 单轴抗压强度敏感性分析
Table 5. Sensitivity analysis of the compressive strength
水平 A B C D E 1 0.32376 0.3357 0.11542 0.44076 0.24355 2 0.27947 0.35778 0.19366 0.34457 0.20190 3 0.28315 0.36988 0.36988 0.29523 0.13162 4 0.29197 0.38184 0.74828 0.27044 0.11672 5 0.33831 0.31899 1.47266 0.27786 0.16476 极差 0.05884 0.06285 1.35724 0.17032 0.12683 标准差 0.02620 0.02547 0.55552 0.07047 0.05185
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表 6 弹性模量敏感性分析
Table 6. Sensitivity analysis of the elastic modulus
水平设置 A B C D E 1 79.49 50.02 52.28 53.10 116.41 2 113.90 64.86 78.95 87.45 59.35 3 115.26 117.39 117.39 117.39 58.18 4 108.15 104.79 126.22 51.32 35.02 5 84.06 92.67 148.12 41.82 25.51 极差 35.77 67.37 95.84 75.57 90.90 标准差 17.08 27.95 38.47 31.54 35.33
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表 7 黏聚力敏感性分析
Table 7. Sensitivity analysis of cohesion
水平设置 A B C D E 1 25.16 20.93 1.63 87.39 50.70 2 40.56 46.42 31.29 61.21 65.63 3 58.45 57.99 57.99 57.99 47.91 4 29.20 79.10 50.20 48.12 41.63 5 26.08 46.95 61.99 41.04 54.82 极差 33.28 58.17 60.37 46.35 24.00 标准差 14.03 21.08 24.79 17.70 8.94
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表 8 内摩擦角敏感性分析
Table 8. Sensitivity analysis of the internal friction angle
水平 A B C D E 1 33.02 24.92 32.50 30.51 28.76 2 31.49 31.82 32.41 30.29 29.86 3 22.70 33.10 33.10 33.10 30.95 4 28.45 30.19 29.86 28.77 33.65 5 35.89 27.98 32.13 32.71 28.88 极差 13.19 8.18 3.23 4.33 4.89 标准差 5.03 3.24 1.24 1.80 2.01
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表 9 脆性指标敏感性分析
Table 9. Sensitivity analysis of the brittleness degree
水平设置 A B C D E 1 0.101 0.076 0.058 0.054 0.045 2 0.088 0.093 0.074 0.145 0.060 3 0.090 0.118 0.118 0.118 0.053 4 0.097 0.080 0.132 0.094 0.071 5 0.085 0.097 0.033 0.084 0.065 标准差 0.007 0.017 0.042 0.034 0.010
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表 10 归一化后的标准差
Table 10. Standard deviation after normalization
归一化后的标准差 A B C D E 单轴抗压强度 0.036 0.035 0.761 0.097 0.071 弹性模量 0.114 0.186 0.256 0.210 0.235 黏聚力 0.162 0.244 0.286 0.205 0.103 内摩擦角 0.377 0.243 0.093 0.135 0.151 脆性指标 0.061 0.153 0.381 0.314 0.092
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表 11 相似材料理论值与试验值
Table 11. Theoretical and experimental values of similar materials
相似材料强度参数 抗压强度/
MPa黏聚力/
kPa内摩擦角/
（°）弹性模量/
MPa理论值 0.17～0.42 50.0～83.3 45.0～60.0 66.7～115.0 实测值 0.12～1.47 25.5～148.1 22.70～35.89 25.5～148.1
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图(7)
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