Dimensionless analysis on peak particle vibration velocity induced by slope casting blast
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摘要: 为研究边坡抛掷爆破振动波传播过程所诱发的地表质点振动情况，运用量纲分析理论构建考虑高程影响的振动峰值速度公式，在此基础上依据边坡抛掷爆破模型将炮孔药包划分为无数微元体进行积分运算，最终得到边坡抛掷爆破振动峰值速度公式。结果显示，同一地理环境和爆破工艺条件下，峰值速度主要由炸药性能、装药深度、测点与爆源间距以及爆破作用指数所决定。同时对某边坡爆破现场进行试验测振，将实测峰值速度数据分别代入萨氏公式、3个常用萨氏修正公式以及通过无量纲理论推导出的速度公式进行非线性回归运算，得到坡表面实测值与各峰值速度公式预测值之间平均误差分别为32%、34.25%、29.58%、39%和7%，坡体内实测值与各峰值速度公式预测值之间平均误差分别为27.63%、23.5%、16.88%、33.889%和13.25%。Abstract: To study the surface particle vibration of vibration wave propagation on slope casting blast, we utilize dimensional analysis to construct the vibration peak velocity formula including the factor of elevation. On the basis of the above theory and slope casting blast model, we divide a blasthole charge into sumless micro-units for integral operation, and eventually obtain the formula of particle vibration peak velocity on slope casting blast. The results show that under the same condition of geographical environment and blasting technology, peak velocity primarily depends on explosive performance, charge depth, monitoring point, explosion source space and blasting acting index. We obtain a series of peak velocity on explosion site, and put the measured data at the slope surface and in the slope body into the Saudorsky formula, the average errors between the predicted peak velocity values by the formulas and the measured values at the slope surface are 32%, 34.25%, 29.58%, 39% and 7%, respectively. The average errors between the predicted peak velocity values by the formulas and the measured values in the slope body are 27.63%, 23.5%, 16.88%, 33.889% and 13.25%, respectively.
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Key words:
- dimensional analysis /
- casting blast /
- peak velocity /
- elevation amplification effect
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图 3 监测点C4水平方向地表振动速度
Figure 3. Surface vibration velocity in horizontal direction at the measured point C4
图 4 监测点C4垂直方向地表振动速度
Figure 4. Surface vibration velocity in vertical direction at the measured point C4
图 5 监测点C4 z轴方向地表振动速度
Figure 5. Surface vibration velocity in z direction at the measured point C4
图 6 地表x、y向峰值振速随测点距炮孔水平距离的变化
Figure 6. Peak vibration velocities in x and y directions of the surface varying with horizontal distances of measuring points away from blasting holes
图 7 地表z、y向峰值振速随测点距炮孔水平距离的变化
Figure 7. Peak vibration velocities in z and y directions of the surface varying with horizontal distances of measuring points away from blasting holes
图 8 地表x、y方向峰值振速随测点高程差的变化
Figure 8. Peak vibration velocities in x and y directions of the surface varying with elevation differences of measuring points
图 9 地表z、y方向峰值振速随测点高程差的变化
Figure 9. Peak vibration velocities in z and y directions of the surface varying with elevation differences of measuring points
表 1 试验参数
Table 1. Test parameters
测点编号 Q/kg L/m H/m vx, max/(cm·s−1) vy, max/(cm·s−1) vz, max/(cm·s−1) H2/m H1/m A1 575 291.8 71 0.179 2 0.233 4 0.153 6 5 2 A2 575 301.4 88 0.158 0 0.201 2 0.147 4 5 2 A3 575 311.2 105 0.136 7 0.177 1 0.135 1 5 2 A4 575 320.9 122 0.110 3 0.152 4 0.128 7 5 2 B1 575 279.4 71 1.973 6 2.177 6 1.740 2 5 2 B2 575 288.6 88 1.692 2 1.746 2 1.583 7 5 2 B3 575 298.1 105 1.313 5 1.452 1 1.395 2 5 2 B4 575 307.7 122 1.009 7 1.282 2 1.316 7 5 2 C1 975 176.19 22 2.583 8 2.207 7 1.913 2 9 4 C2 975 178.28 37 2.671 5 2.508 3 2.084 6 9 4 C3 975 176.26 52 2.781 4 2.835 1 2.194 6 9 4 C4 975 177.42 67 2.943 3 3.221 7 2.284 6 9 4 
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表 2 实测与预测峰值速度对比表
Table 2. The peak velocity contrast table of measured values and predictive values
测点编号 vy, max/
(cm·s−1)公式（1） 公式（2） 公式（3） 公式（4） 公式（13） $ v_{{y},\max }^{(1)}/$
(cm·s−1)$ {\varepsilon ^{(1)}}/ $
%$ v_{{{y}},\max }^{(2)}/ $
(cm·s−1)$ {\varepsilon ^{(2)}}/ $
%$v_{{{y}},\max }^{(3)}/ $
(cm·s−1)$ {\varepsilon ^{(3)}}/ $
%$ v_{{{y}},\max }^{(4)}/$
(cm·s−1)$ {\varepsilon ^{(4)}}/ $
%$ v_{{{y}},\max }^{(13)}/$
(cm·s−1)$ {\varepsilon ^{(13)}}/ $
%A1 0.233 4 0.299 1 28 0.259 9 10 0.322 1 11 0.292 7 46 0.255 2 10 A2 0.191 2 0.248 7 30 0.237 8 24 0.229 2 20 0.240 0 26 0.175 6 8 A3 0.157 1 0.214 1 36 0.221 5 41 0.173 4 15 0.208 9 33 0.129 5 18 A4 0.132 4 0.172 8 31 0.291 5 49 0.130 1 2 0.190 7 44 0.092 2 30 B1 2.177 6 1.458 9 33 1.418 5 35 2.655 9 22 1.546 1 29 1.869 8 14 B2 1.846 2 1.253 4 32 1.229 9 33 1.510 5 40 0.992 6 46 1.769 4 4 B3 1.552 1 1.077 9 31 2.216 4 37 1.184 1 24 1.034 9 32 1.470 3 5 B4 1.382 2 0.944 5 32 0.943 1 32 0.946 8 32 0.706 3 49 1.451 3 5 C1 2.207 7 3.047 3 62 2.896 0 31 2.902 4 31 3.404 8 54 2.633 6 2 C2 2.508 3 2.958 7 18 3.013 9 20 2.672 9 21 3.366 7 34 2.574 7 3 C3 2.835 1 2.924 6 3 3.129 3 10 2.571 3 9 3.383 2 19 2.516 1 11 C4 3.221 7 2.811 2 13 3.315 9 3 2.374 5 26 3.269 1 15 2.438 6 24
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