Experimental study of different typical shape falling-rocks impacting on the sand cushion and dimensionless analysis
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摘要: 开展了球形、锥形和平头3种典型形状落石撞击垫层的冲击力及侵入深度的试验研究。结果表明,落石形状对冲击试验结果有显著影响:相同条件下,平头落石的冲击力最大,侵入深度和冲击力峰值时间最短,锥形落石反之,而球形落石介于两者之间。采用无量纲化分析方法,将落石的质量、速度、形状、特征尺寸,垫层的强度、密度转换为无量纲强度冲击因子I、密度冲击因子λ和形状冲击因子ψ,并对冲击因子与侵入深度的试验数据进行了相关性分析,结果表明:(1)冲击因子I和λ在决定最终侵深zm/d 中所起到的作用比较相近;(2)冲击因子I和λ对侵入深度的影响分析表明,I和λ的相对独立性较强,相互影响较小,在不同的λ值下,I对侵入深度的影响规律基本一致。Abstract: An experimental study on the impact force and penetration of falling rocks with three typical shapes, including spherical, conical and flat shapes, against the cushion was carried out. The experimental results show that the shape of the falling rock has a significant influence on the impact results. Under the same conditions, the flat blocks have the highest impact force, the lowest penetration depth and the shortest peak impact time, and the opposite for the conical falling rocks, with spherical blocks are between the two. The dimensionless analysis method was adopted to convert the mass, velocity, shape, size of the falling rock, the strength and density of the cushion layer into the dimensionless strength impact factor I, density impact factor λ and shape impact factor ψ. The correlation analysis between the impact factors and penetration test data shows that: (1) The effects of the impact factors I and λ on the final depth of penetration zm/d are similar. (2) The analysis of the impact factors I and λ effects on penetration depth shows that I and λ are relatively independent. The pattern of the I effects on the depth of penetration is generally consistent for different λ values.
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Key words:
- falling rock’s shape /
- impact force /
- penetration depth /
- dimensionless /
- cushion
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表 1 球形落石冲击砂垫层试验工况
Table 1. Conditions of impact test by spherical falling rocks
编号 m/kg v0/(m·s−1) H/m d/m I λ zm/d S-01 10 4.43 1.00 0.12 1.73 5.22 1.45 S-02 10 6.26 2.00 0.12 3.47 5.22 1.88 S-03 10 8.85 4.00 0.12 6.93 5.22 2.67 S-04 10 13.28 9.00 0.12 15.60 5.22 3.46 S-05 50 4.43 1.00 0.25 0.96 2.89 1.00 S-06 50 6.26 2.00 0.25 1.92 2.89 1.15 S-07 50 8.85 4.00 0.25 3.83 2.89 1.47 S-08 50 13.28 9.00 0.25 8.63 2.89 1.84 S-09 100 4.43 1.00 0.36 0.64 1.93 0.71 S-10 100 6.26 2.00 0.36 1.28 1.93 0.76 S-11 100 8.85 4.00 0.36 2.57 1.93 1.06 S-12 100 13.28 9.00 0.36 5.78 1.93 1.17 表 2 锥形落石冲击砂垫层试验工况
Table 2. Conditions of impact test by conical falling rocks
编号 m/kg v0/(m·s−1) H/m d/m I λ zm/d C-01 10 4.40 1.00 0.12 1.73 5.22 1.89 C-02 10 6.30 2.00 0.12 3.47 5.22 2.00 C-03 10 8.90 4.00 0.12 6.93 5.22 2.75 C-04 50 2.40 0.30 0.25 0.29 2.89 0.76 C-05 50 6.30 2.00 0.25 1.92 2.89 1.06 C-06 50 8.90 4.00 0.25 3.83 2.89 1.27 C-07 50 13.30 9.00 0.25 8.63 2.89 1.59 C-08 50 17.10 15.00 0.25 14.38 2.89 2.16 表 3 平头落石冲击砂垫层试验工况
Table 3. Conditions of impact test by flat falling rocks
编号 m/kg v0/(m·s−1) H/m d/m I λ zm/d F-01 50 4.40 1.00 0.25 0.96 2.89 0.52 F-02 50 6.30 2.00 0.25 1.92 2.89 0.68 F-03 50 8.90 4.00 0.25 3.83 2.89 0.86 F-04 50 13.30 9.00 0.25 8.63 2.89 1.06 F-05 50 6.30 2.00 0.30 1.11 1.67 0.37 F-06 50 13.30 9.00 0.30 4.99 1.67 0.68 表 4 无量纲冲击因子之间及与侵入深度的相关性
Table 4. Correlation between dimensionless impact factors and penetration depths
冲击因子 I λ zm/d I 1.00 0.24 0.71 λ 0.24 1.00 0.77 zm/d 0.71 0.77 1.00 表 5 不同形状落石3种拟合公式的拟合参数比较
Table 5. Comparison of parameters of three fitting formulas for falling rocks with different shapes
落石形状 zm/d=Aλ ln(1+CI/λ)拟合参数 A C 球形 0.18 11.67 锥形 0.12 47.64 平头 0.10 15.09 -
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