Frequency and duration dependence analysis of structural blasting vibration response
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摘要: 明确结构爆破振动响应对频率与持续时间的依赖性有助于进行爆破参数设计和爆破振动安全评价。本文从频域上推导单段爆破振动、多段爆破振动、单自由度系统振动响应三者之间的关系，以延迟时间和爆破段数作为纽带分析爆破振动频率和持续时间对结构爆破振动响应的影响，最后以一组实测试验数据进行验证。结果表明，在延迟时间∆τ下，多段爆破振动出现间隔1/∆τ的频带现象，频率成分向优势频率fi=n/∆τ集中（n
$\in$ Z +），且随段数增加，优势频率幅值增大。爆破振动中接近结构自振频率fn的优势频率成分使结构产生较大振动响应，为此延迟时间的选择应保证在n/∆τ优势频率处不会引起结构的共振。多段爆破振动在其多个优势频率n/∆τ附近的结构振动响应放大系数均比单段大，其余处与单段相差不大，特别的，当优势频率fi、单段爆破振动主频fm和结构物自振频率fn三者相近时，结构可能产生最大的响应。爆破段数的增加，使爆破振动持续时间增加，但仅在一定范围内使结构爆破振动响应增加，增加到一定值后，结构响应与持续时间关系不大。Abstract: It is helpful to blasting parameter design and blasting vibration safety evaluation to make clear the dependence of blasting vibration response on frequency and duration. The relationship between single-delay blasting vibration, multi-delay blasting vibration and single-degree-of-freedom system response is derived from the frequency domain. The influence of blasting vibration frequency and duration on the vibration response of structure is analyzed by taking the delay time and the number of blasting stages as the link. Finally, a set of measured test data is used to verify. The results show that under the delay time ∆τ, the multi-delay blasting vibration has a frequency band phenomenon of 1/∆τ. The frequency component is concentrated to the dominant frequency${f_{\rm{i}}} = n/\Delta \tau \left( {n \in {Z^ + }} \right)$ , and as the number of segments increases, the dominant frequency amplitude increases. The structure produces a large vibration response when the dominant frequency component in blasting vibration is close to the natural frequency fn of the structure. Therefore, the delay time should be selected to ensure that the resonance of the structure is not caused at the dominant frequency of n/∆τ. In the response spectrum, the structural amplification factor of multi-delay blasting vibration is larger than that of a single-delay when frequency near its multiple dominant frequencies fi, which is basically consistent with the single-delay at the rest. In particular, when the dominant frequency fi, the single delay blasting vibration frequency fm, and the structure natural vibration frequency fn are similar, the structure may produce the maximum response. The increase of the number of blasting sections increases the duration of blasting vibration when the sections within a certain range. After increasing to a certain value, the structural response has little relationship with the duration.-
Key words:
- multi-delay /
- single-degree-of freedom systems /
- delay time /
- response spectrum
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图 1 单自由度系统的振动响应示意图
Figure 1. Schematic diagram of response of single degree of freedom system under blasting vibration excitation
图 2 典型多段爆破振动速度时程曲线
Figure 2. Typical multi-delay blast vibration velocity time-histories
图 3 单段和多段爆破振动的频谱对比
Figure 3. The spectral comparison of single delay and multi-delay blasting vibration
图 4 单自由度系统的单段和多段爆破振动速度响应谱对比
Figure 4. Velocity response spectrum of single degree of freedom system under single delay and multi-delay blasting vibration
图 5 段数对爆破振动频谱的影响
Figure 5. Effect of the number of delays on the blasting vibration spectrum
图 6 段数对爆破振动反应谱的影响
Figure 6. Effect of the number of delays on the response spectrum of blasting vibration
图 7 延迟时间对反应谱比值（10段比单段）的影响
Figure 7. Effect of delay time on the ratio of response spectrum (10 delays to single delay)
图 8 段数对反应谱峰值比值（多段比单段）的影响
Figure 8. Effect of the number of delays on the ratio of peaks of response spectrum (multi-delay to single delay)
图 9 光面爆破设计及测点布置示意图
Figure 9. Schematic diagram of smooth blasting design and measuring point layout
图 11 各单段归一化的爆破振动速度时程
Figure 11. Normalized blasting vibration velocity time history for each delay
图 12 单段与多段爆破振动的频谱、反应谱对比
Figure 12. Comparison of spectrum, response spectrum between single delay and multi-delay
图 13 段数对反应谱峰值比值（多段比单段）的影响
Figure 13. Effect of the number of delays on the ratios of peaks of response spectra (multi-delay to single delay)
表 1 单自由度系统的爆破振动速度响应特征值
Table 1. Characteristic values of blasting vibration velocity response of single degree of freedom system
自振频率/Hz 振动响应优势频率/Hz 振动响应峰值/(cm∙s−1) 单段 多段 单段 多段 15.0 30.0 16.6/24.9/33.0 2.72 2.94 25.0 28.8 24.9/33.0 4.11 5.72 
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表 2 光面爆破参数
Table 2. Parameters of smooth blasting
钻孔类型 孔径/mm 孔深/mm 药卷直径/mm 孔距/m 单孔药量/kg 最大单响药量/kg 堵塞长度/m 光爆孔 76 10 32/70 0.6 2.2 13.2 1.0
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