Article(id=1241421932374053749, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241421928813089644, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2025.02.021, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1730304000000, receivedDateStr=2024-10-31, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773907653182, onlineDateStr=2026-03-19, pubDate=1748707200000, pubDateStr=2025-06-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773907653182, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773907653182, creator=13701087609, updateTime=1773907653182, updator=13701087609, issue=Issue{id=1241421928813089644, tenantId=1146029695717560320, journalId=1240670690148397066, year='2025', volume='42', issue='2', pageStart='1', pageEnd='210', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773907652332, creator=13701087609, updateTime=1773908080242, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241423723643859829, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241421928813089644, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241423723643859830, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241421928813089644, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=178, endPage=181, ext={EN=ArticleExt(id=1241421932910924668, articleId=1241421932374053749, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Study on Prediction Formula of Peak Particle Velocity Induced by Open-pit Mine Blasting, columnId=1240702076553065119, journalTitle=Blasting, columnName=BLASTING SAFETY, runingTitle=null, highlight=null, articleAbstract=
To enhance the accuracy of blasting vibration predictions in an open-pit mine stripping project, a new peak particle velocity (PPV) prediction formula is proposed, incorporating geological elevation differences and slope effects. Based on the principles of dimensional analysis, the traditional Sadovsky formula was modified by introducing the elevation difference (H) and slope coefficient (γ), resulting in a new prediction model (Formula 11). Notably, when H=0, the new formula reverts to the traditional Sadovsky formula, ensuring its reliability. A field vibration monitoring test was conducted in the mine, with 5 monitoring points at elevation differences of 0.222 m, 0.176 m, 0.865 m, 1.617 m, and 2.465 m. Using the TC-4850 blasting vibration meter, vibration data were recorded, and multiple predictions, including the Sadovsky and the newly proposed formula, were fitted using multivariate nonlinear regression. Results show that the proposed formula achieves the highest correlation coefficient (R2=0.905), surpassing other models. Furthermore, the new formula exhibits improved prediction accuracy, with a maximum relative error of 20.85% and an average error of 8.11%, compared to 24.89% and 10.31% for the original Sadovsky formula. By considering the factors of elevation and slope, the proposed prediction formula significantly improves the precision of PPV predictions under complex terrain conditions, providing a scientific basis for blasting vibration control and safety management. Applying the specific scheme and data proves the effectiveness and practicality of the formula.
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GUO Lian-jun (1963-), male, born in Beipiao city, Liaoning province, professor, doctoral supervisor, Ph. D, mainly engaged in research on mining engineering and blasting theory technology, (E-mail)
guolj@sut.edu.cn.
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为提高某露天矿山剥岩工程爆破振动预测的准确性，本文提出了一种考虑地质高程与坡度影响因素的质点峰值振动速度预测公式。基于量纲分析原理，对传统的萨道夫公式进行修正，引入高程差H和坡度系数γ，形成新的预测公式（11）。当高差H=0时，此预测公式可转化为萨道夫公式，表明此预测公式可靠性。在矿山现场进行了振动监测试验，布置了5个监测点，高程差为0.222 m、0.176 m、0.865 m、1.617 m、2.465 m，使用TC-4850爆破测振仪记录振动数据。通过多元非线性拟合方法，对包括原始萨道夫公式和新提出的公式（11）在内的多个预测公式进行了拟合计算。拟合结果显示：新提出的公式（11）具有最高的相关性系数R2=0.905，优于其他公式。预测精度对比表明，公式（11）的相对误差最大值为20.85%，平均误差为8.11%，相较于原始萨道夫公式的24.89%和10.31%，预测精度有显著提升。通过考虑高程与坡度影响因素，新提出的预测公式在复杂地形条件下显著提高了露天矿山爆破振动速度预测的准确性，为爆破振动控制和安全管理提供了科学依据。具体方案和数据的应用证明了该公式的有效性和实用性。
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郭连军（1963-），男，辽宁北票人，博士、教授、博士生导师，主要从事采矿工程及爆破理论技术相关方面的研究工作，（E-mail）
guolj@sut.edu.cn。
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邵磊（2002-），男，河南商丘人，硕士研究生，主要从事爆破理论相关方面的研究工作，（E-mail）1753563708@qq.com。
SHAO Lei (2002-), male, born in Shangqiu city, Henan province, postgraduate student, mainly engaged in blasting theory, (E-mail)1753563708@qq.com.
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邵磊（2002-），男，河南商丘人，硕士研究生，主要从事爆破理论相关方面的研究工作，（E-mail）1753563708@qq.com。
SHAO Lei (2002-), male, born in Shangqiu city, Henan province, postgraduate student, mainly engaged in blasting theory, (E-mail)1753563708@qq.com.
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邵磊（2002-），男，河南商丘人，硕士研究生，主要从事爆破理论相关方面的研究工作，（E-mail）1753563708@qq.com。
SHAO Lei (2002-), male, born in Shangqiu city, Henan province, postgraduate student, mainly engaged in blasting theory, (E-mail)1753563708@qq.com.
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爆炸载荷下岩质边坡动力响应及控制[M]. 北京: 科学出版社,
2011., articleTitle=null, refAbstract=null)], funds=[Fund(id=1241439662238134832, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, awardId=51974187, language=EN, fundingSource=Supported by the National Natural Science Foundation of China(51974187), fundOrder=null, country=null), Fund(id=1241439662317826612, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, awardId=51974187, language=CN, fundingSource=国家自然科学基金资助项目(51974187), fundOrder=null, country=null), Fund(id=1241439662489793084, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, awardId=null, language=EN, fundingSource=Study on the Energy Dissipation Mechanism of Rock Breakage under Impact Based on Microscopic Features, fundOrder=null, country=null), Fund(id=1241439662607233604, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, awardId=null, language=CN, fundingSource=基于细观特征的岩石冲击破碎能量耗散机理研究, fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241439649915269343, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, xref=1., ext=[AuthorCompanyExt(id=1241439649923657953, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, companyId=1241439649915269343, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=
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1.沈阳工业大学 建筑与土木工程学院，沈阳 110870)]), AuthorCompany(id=1241439650036904173, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, xref=2., ext=[AuthorCompanyExt(id=1241439650045292783, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, companyId=1241439650036904173, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=
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Blasting hole arrangement, figureFileSmall=HcNmJfqYhnXJ3mh5geienw==, figureFileBig=XC+mFrHx7K1CvN3U+YLskQ==, tableContent=null), ArticleFig(id=1241439658672976370, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=CN, label=图1, caption=
采区布孔示意图, figureFileSmall=HcNmJfqYhnXJ3mh5geienw==, figureFileBig=XC+mFrHx7K1CvN3U+YLskQ==, tableContent=null), ArticleFig(id=1241439658802999795, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=EN, label=Table 1, caption=
Prediction formula for blasting vibration velocity
, figureFileSmall=null, figureFileBig=null, tableContent=
| 学者 | 预测公式 | 公式编号 |
|---|
| 朱传统等[8] |  | (2) |
| 贺高威等[9] |  | (3) |
| 周同岭等[10] |  | (4) |
| 何理等[11] |  | (5) |
| 叶海旺等[12] |  | (6) |
| 包松等[13] |  | (7) |
), ArticleFig(id=1241439659050463737, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=CN, label=表1, caption=
爆破振动速度预测公式
, figureFileSmall=null, figureFileBig=null, tableContent=
| 学者 | 预测公式 | 公式编号 |
|---|
| 朱传统等[8] | | (2) |
| 贺高威等[9] | | (3) |
| 周同岭等[10] | | (4) |
| 何理等[11] | | (5) |
| 叶海旺等[12] | | (6) |
| 包松等[13] | | (7) |
), ArticleFig(id=1241439659167904251, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=EN, label=Table 2, caption=
Physical parameters related to blasting vibration
, figureFileSmall=null, figureFileBig=null, tableContent=
| 物理量 | 量纲 | 物理量 | 量纲 |
|---|
| 介质密度ρ | ML－3 | 测点与爆源直线距离R | L |
| 测点与爆源水平距离D | L | 介质弹性模量E | ML－1 T－2 |
| 测点与爆源间高差H | L | 介质泊松比μ | 1 |
| 振动波速c | LT－1 | 质点加速度a | LT－2 |
| 最大单段装药量Q | M | 爆炸持续时间t | T |
| 振动频率f | T－1 | 质点位移u | L |
), ArticleFig(id=1241439659369230851, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=CN, label=表2, caption=
爆破振动相关物理参数
, figureFileSmall=null, figureFileBig=null, tableContent=
| 物理量 | 量纲 | 物理量 | 量纲 |
|---|
| 介质密度ρ | ML－3 | 测点与爆源直线距离R | L |
| 测点与爆源水平距离D | L | 介质弹性模量E | ML－1 T－2 |
| 测点与爆源间高差H | L | 介质泊松比μ | 1 |
| 振动波速c | LT－1 | 质点加速度a | LT－2 |
| 最大单段装药量Q | M | 爆炸持续时间t | T |
| 振动频率f | T－1 | 质点位移u | L |
), ArticleFig(id=1241439659604111876, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=EN, label=Table 3, caption=
Monitored data of blasting vibration
, figureFileSmall=null, figureFileBig=null, tableContent=
| 监测点 | H/m | R/m | v/(cm·s－1) |
|---|
| X | Y | Z |
|---|
| 1# | 0.222 | 98.283 | 4.55 | 5.50 | 10.18 |
| 2# | 0.176 | 108.514 | 2.70 | 4.06 | 9.79 |
| 3# | 0.865 | 118.314 | 3.09 | 4.29 | 8.03 |
| 4# | 1.617 | 128.102 | 3.23 | 4.82 | 7.38 |
| 5# | 2.465 | 137.908 | 1.70 | 2.81 | 4.70 |
), ArticleFig(id=1241439659843187208, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=CN, label=表3, caption=
爆破振动监测数据
, figureFileSmall=null, figureFileBig=null, tableContent=
| 监测点 | H/m | R/m | v/(cm·s－1) |
|---|
| X | Y | Z |
|---|
| 1# | 0.222 | 98.283 | 4.55 | 5.50 | 10.18 |
| 2# | 0.176 | 108.514 | 2.70 | 4.06 | 9.79 |
| 3# | 0.865 | 118.314 | 3.09 | 4.29 | 8.03 |
| 4# | 1.617 | 128.102 | 3.23 | 4.82 | 7.38 |
| 5# | 2.465 | 137.908 | 1.70 | 2.81 | 4.70 |
), ArticleFig(id=1241439659964822029, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=EN, label=Table 4, caption=
Fitted results of blasting vibration
, figureFileSmall=null, figureFileBig=null, tableContent=
| 公式 | K | α | β | γ | R2 |
|---|
| (1) | 1073.428 | 1.807 | | | 0.851 |
| (2) | 99.114 | 1.024 | 0.102 | | 0.882 |
| (3) | 99.242 | 1.126 | －0.102 | | 0.882 |
| (4) | 121.745 | 1.023 | －0.102 | | 0.882 |
| (5) | 98.650 | 1.408 | －0.283 | －0.102 | 0.882 |
| (6) | 99.222 | 1.126 | －0.102 | 0.537 | 0.882 |
| (7) | 98.143 | 1.124 | 0.193 | －0.296 | 0.882 |
| (11) | 270.577 | 1.263 | 0.002 | 0.002 | 0.905 |
), ArticleFig(id=1241439661504131607, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=CN, label=表4, caption=
爆破振动拟合结果
, figureFileSmall=null, figureFileBig=null, tableContent=
| 公式 | K | α | β | γ | R2 |
|---|
| (1) | 1073.428 | 1.807 | | | 0.851 |
| (2) | 99.114 | 1.024 | 0.102 | | 0.882 |
| (3) | 99.242 | 1.126 | －0.102 | | 0.882 |
| (4) | 121.745 | 1.023 | －0.102 | | 0.882 |
| (5) | 98.650 | 1.408 | －0.283 | －0.102 | 0.882 |
| (6) | 99.222 | 1.126 | －0.102 | 0.537 | 0.882 |
| (7) | 98.143 | 1.124 | 0.193 | －0.296 | 0.882 |
| (11) | 270.577 | 1.263 | 0.002 | 0.002 | 0.905 |
), ArticleFig(id=1241439661722235421, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=EN, label=Table 5, caption=
Comparison of prediction accuracy
, figureFileSmall=null, figureFileBig=null, tableContent=
| 式(1) | 式(2) | 式(3) | 式(4) |
| 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% |
| 10.82 | 6.29 | 10.31 | 10.52 | 3.34 | 8.95 | 10.54 | 3.54 | 8.90 | 10.52 | 3.34 | 8.95 |
| 9.05 | 7.56 | 9.73 | 0.61 | 9.75 | 0.41 | 9.73 | 0.61 |
| 7.74 | 3.61 | 7.57 | 5.73 | 7.58 | 5.60 | 7.57 | 5.73 |
| 6.70 | 9.21 | 6.55 | 11.25 | 6.56 | 11.11 | 6.55 | 11.25 |
| 5.87 | 24.89 | 5.82 | 23.83 | 5.82 | 23.83 | 5.82 | 23.83 |
| 式(5) | 式(6) | 式(7) | 式(11) |
| 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% |
| 10.46 | 2.75 | 8.88 | 10.52 | 3.34 | 8.88 | 10.51 | 3.24 | 8.93 | 10.58 | 3.93 | 8.11 |
| 9.71 | 0.82 | 9.74 | 0.51 | 9.73 | 0.61 | 9.41 | 3.88 |
| 7.56 | 5.85 | 7.58 | 5.60 | 7.57 | 5.73 | 7.86 | 2.12 |
| 6.54 | 11.38 | 6.56 | 11.11 | 6.55 | 11.25 | 6.66 | 9.76 |
| 5.81 | 23.62 | 5.82 | 23.83 | 5.82 | 23.83 | 5.68 | 20.85 |
), ArticleFig(id=1241439661848064545, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241421932374053749, language=CN, label=表5, caption=
预测精度对比
, figureFileSmall=null, figureFileBig=null, tableContent=
| 式(1) | 式(2) | 式(3) | 式(4) |
| 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% |
| 10.82 | 6.29 | 10.31 | 10.52 | 3.34 | 8.95 | 10.54 | 3.54 | 8.90 | 10.52 | 3.34 | 8.95 |
| 9.05 | 7.56 | 9.73 | 0.61 | 9.75 | 0.41 | 9.73 | 0.61 |
| 7.74 | 3.61 | 7.57 | 5.73 | 7.58 | 5.60 | 7.57 | 5.73 |
| 6.70 | 9.21 | 6.55 | 11.25 | 6.56 | 11.11 | 6.55 | 11.25 |
| 5.87 | 24.89 | 5.82 | 23.83 | 5.82 | 23.83 | 5.82 | 23.83 |
| 式(5) | 式(6) | 式(7) | 式(11) |
| 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% | 预测v/ (cm·s－1) | 相对误差/% | 平均误差/% |
| 10.46 | 2.75 | 8.88 | 10.52 | 3.34 | 8.88 | 10.51 | 3.24 | 8.93 | 10.58 | 3.93 | 8.11 |
| 9.71 | 0.82 | 9.74 | 0.51 | 9.73 | 0.61 | 9.41 | 3.88 |
| 7.56 | 5.85 | 7.58 | 5.60 | 7.57 | 5.73 | 7.86 | 2.12 |
| 6.54 | 11.38 | 6.56 | 11.11 | 6.55 | 11.25 | 6.66 | 9.76 |
| 5.81 | 23.62 | 5.82 | 23.83 | 5.82 | 23.83 | 5.68 | 20.85 |
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