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Constitutive models of HJC and RHT for different in-situ stress conditions were established by adopting ANSYS/LS-DYNA software, and the effects of blasting on effective stress and rock damage in different constitutive models were analyzed comparatively. The results show that the effective stress variation in the HJC model is more consistent with practical scenarios, while the rock damage in the RHT model can better reflect practical conditions. In-situ stress has a minor impact on effective stress in regions close to blast holes but a significant influence on effective stress in areas farther away. Additionally, in-situ stress has a smaller effect on rock damage in the HJC model, but substantially affects the damage variables in the RHT model.

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利用ANSYS/LS-DYNA软件建立不同地应力下的HJC本构模型和RHT本构模型，对比分析不同本构模型中爆破对模型有效应力、岩石损伤的影响。结果表明：HJC本构模型的有效应力变化更贴近实际情况，而RHT本构模型的岩石损伤更贴近实际情况；地应力对距离炮孔较近区域有效应力的影响较小，而对距离炮孔较远区域有效应力的影响较大；地应力对HJC本构模型的岩石损伤影响较小，对RHT本构模型的损伤变量影响较大。

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缪广红（1985—），男，安徽淮南人，博士，副教授，硕士研究生导师，主要从事爆炸力学相关研究。E-mail：

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缪广红（1985—），男，安徽淮南人，博士，副教授，硕士研究生导师，主要从事爆炸力学相关研究。E-mail：

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缪广红（1985—），男，安徽淮南人，博士，副教授，硕士研究生导师，主要从事爆炸力学相关研究。E-mail：

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Coal Science and Technology, 2023, 51(S1): 50-64., articleTitle=Study on initiation and propagation mechanism of internal cracks caused by dynamic and static action of shaped charge blasting under in-situ stress, refAbstract=null)], funds=[Fund(id=1241327696656003287, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, awardId=11902003, language=CN, fundingSource=国家自然科学基金(11902003), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241327686585479998, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, xref=1., ext=[AuthorCompanyExt(id=1241327686589674302, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, companyId=1241327686585479998, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Mechanics and Optoelectronic Physics, Anhui University of Science and Technology, Huainan 232001, Anhui, China), AuthorCompanyExt(id=1241327686602257216, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, companyId=1241327686585479998, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.安徽理工大学　力学与光电物理学院，安徽　淮南　232001)]), AuthorCompany(id=1241327686702920517, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, xref=2., ext=[AuthorCompanyExt(id=1241327686711309127, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, companyId=1241327686702920517, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, Anhui, China), AuthorCompanyExt(id=1241327686723892041, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, companyId=1241327686702920517, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.安徽理工大学　土木建筑学院，安徽　淮南　232001)])], figs=[ArticleFig(id=1241327692050657356, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Fig.1, caption=Strength model curve, figureFileSmall=mR34Ht3RikhzSOFAV8tSlw==, figureFileBig=ZMdr89PtwADf7QEsZs+VjA==, tableContent=null), ArticleFig(id=1241327692176486484, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=图1, caption=强度模型曲线, figureFileSmall=mR34Ht3RikhzSOFAV8tSlw==, figureFileBig=ZMdr89PtwADf7QEsZs+VjA==, tableContent=null), ArticleFig(id=1241327692314898526, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Fig.2, caption=Damage model curve, figureFileSmall=NKzLj+rbujx0018KWDwj4A==, figureFileBig=FMrf+uytFb5fGxZGhHO+4A==, tableContent=null), ArticleFig(id=1241327692398784609, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=图2, caption=损伤模型曲线, figureFileSmall=NKzLj+rbujx0018KWDwj4A==, figureFileBig=FMrf+uytFb5fGxZGhHO+4A==, tableContent=null), ArticleFig(id=1241327692499447910, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Fig.3, caption=Curve of equation of state, figureFileSmall=4rl8QlcuE3BRbR5URIs0kw==, figureFileBig=xnTG2+v7rqj2t7sFXu407A==, tableContent=null), ArticleFig(id=1241327692625277040, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=图3, caption=状态方程曲线, figureFileSmall=4rl8QlcuE3BRbR5URIs0kw==, figureFileBig=xnTG2+v7rqj2t7sFXu407A==, tableContent=null), ArticleFig(id=1241327692717551731, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Fig.4, caption=Curves in RHT constitutive model, figureFileSmall=Y8arU2Be+6w5YrILxmPpIA==, figureFileBig=m/8WMbddJGE+d3VeCfOiEg==, tableContent=null), ArticleFig(id=1241327692805632121, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=图4, caption=RHT本构模型曲线, figureFileSmall=Y8arU2Be+6w5YrILxmPpIA==, figureFileBig=m/8WMbddJGE+d3VeCfOiEg==, tableContent=null), ArticleFig(id=1241327692906295422, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Fig.5, caption=Effective stress of HJC constitutive model, figureFileSmall=JrjAxi6Vp2j4JpR9uWUz9g==, figureFileBig=tny2Mv2pSKA2nepXS2MYbw==, tableContent=null), ArticleFig(id=1241327693006958723, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=图5, caption=HJC本构模型有效应力图

（a）t=40 μs；（b）t=80 μs；（c）t=120 μs

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（a）t=40 μs；（b）t=80 μs；（c）t=120 μs

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（a）t=50 μs；（b）t=100 μs；（c）t=150 μs

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（a）t=50 μs；（b）t=100 μs；（c）t=150 μs

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（a）HJC本构模型；（b）RHT本构模型

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（a）HJC本构模型；（b）RHT本构模型

, figureFileSmall=A86LOZ/h+HcEoj23HQ+2uQ==, figureFileBig=v/1hy+3aXTBL0m/efRICEA==, tableContent=null), ArticleFig(id=1241327695674536122, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Table 1, caption=

Parameters of HJC constitutive model

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项目数值项目数值项目数值
ρ岩石/（g·cm-3）2.66A0.79C0.007
G/GPa17B0.61D10.04
fc/MPa150N1.6D21.0
T/MPa4.0SFMAX5.0EFMIN0.01
Pc/MPa16Pl/MPa800K1/GPa85
μc0.001μl0.1K2/GPa-171
K3/GPa208
), ArticleFig(id=1241327695783588027, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=表1, caption=

HJC本构模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
项目数值项目数值项目数值
ρ岩石/（g·cm-3）2.66A0.79C0.007
G/GPa17B0.61D10.04
fc/MPa150N1.6D21.0
T/MPa4.0SFMAX5.0EFMIN0.01
Pc/MPa16Pl/MPa800K1/GPa85
μc0.001μl0.1K2/GPa-171
K3/GPa208
), ArticleFig(id=1241327695863279807, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Table 2, caption=

Parameters of RHT constitutive model

, figureFileSmall=null, figureFileBig=null, tableContent=
项目数值项目数值项目数值
ρ岩石/（g·cm-3）2.66α1.1Pel/GPa0.000 4
Pcomp0.06Np4.0A1/GPa0.867 1
A2/GPa1.456 7A3/GPa0.890 34T1/GPa43.87
T2/GPa0fc/MPa150 0.1
0.38G/GPa17D10.04
D21.0 0.012ξ0.5
A1.6N0.6Q00.64
B0.010 5 3.0×10-11 3.0×10-12
βc0.010 6βt0.014 4 3.0×1019
3.0×1019 0.4 0.7
Af1.62Nf0.6
), ArticleFig(id=1241327695934582978, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=表2, caption=

RHT本构模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
项目数值项目数值项目数值
ρ岩石/（g·cm-3）2.66α1.1Pel/GPa0.000 4
Pcomp0.06Np4.0A1/GPa0.867 1
A2/GPa1.456 7A3/GPa0.890 34T1/GPa43.87
T2/GPa0fc/MPa150 0.1
0.38G/GPa17D10.04
D21.0 0.012ξ0.5
A1.6N0.6Q00.64
B0.010 5 3.0×10-11 3.0×10-12
βc0.010 6βt0.014 4 3.0×1019
3.0×1019 0.4 0.7
Af1.62Nf0.6
), ArticleFig(id=1241327696001691845, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Table 3, caption=

Parameters of equation of state for air

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C0C1C2C3C4C5C6E0/MPaV0
00000.40.400.250
), ArticleFig(id=1241327696085577927, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=表3, caption=

空气状态方程参数

, figureFileSmall=null, figureFileBig=null, tableContent=
C0C1C2C3C4C5C6E0/MPaV0
00000.40.400.250
), ArticleFig(id=1241327696152686793, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Table 4, caption=

Parameters of explosive materials

, figureFileSmall=null, figureFileBig=null, tableContent=
ρ炸药/（g·cm-3）D/（cm·μs-1）PCJ/GPaA/GPaB/GPaR1R2ωE0/GPa
1.50.512 29.53276.28.445.22.10.53.87
), ArticleFig(id=1241327696215601355, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=表4, caption=

炸药材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
ρ炸药/（g·cm-3）D/（cm·μs-1）PCJ/GPaA/GPaB/GPaR1R2ωE0/GPa
1.50.512 29.53276.28.445.22.10.53.87
), ArticleFig(id=1241327696278515918, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Table 5, caption=

Proportion of damage zones and fracture zones at 260 μs in HJC constitutive model

, figureFileSmall=null, figureFileBig=null, tableContent=
损伤区域地应力/MPa
01015202530
粉碎区（D>0.8）3.853.923.994.004.114.16
裂隙区（0.2≤D≤0.8）0.080.090.090.100.100.11
), ArticleFig(id=1241327696362402001, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=表5, caption=

260 μs时HJC本构模型岩石粉碎区与裂隙区占比

, figureFileSmall=null, figureFileBig=null, tableContent=
损伤区域地应力/MPa
01015202530
粉碎区（D>0.8）3.853.923.994.004.114.16
裂隙区（0.2≤D≤0.8）0.080.090.090.100.100.11
), ArticleFig(id=1241327696454676690, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=EN, label=Table 6, caption=

Proportions of damage zones and fracture zones at 260 μs in RHT constitutive model

, figureFileSmall=null, figureFileBig=null, tableContent=
损伤区域地应力/MPa
01015202530
粉碎区（D>0.8）5.093.603.463.092.792.76
裂隙区（0.2≤D≤0.8）8.366.505.003.913.442.39
), ArticleFig(id=1241327696513396948, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241321697702367327, language=CN, label=表6, caption=

260 μs时RHT本构模型岩石粉碎区与裂隙区占比

, figureFileSmall=null, figureFileBig=null, tableContent=
损伤区域地应力/MPa
01015202530
粉碎区（D>0.8）5.093.603.463.092.792.76
裂隙区（0.2≤D≤0.8）8.366.505.003.913.442.39
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不同本构模型下地应力对爆破效果的影响研究
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缪广红 1 , 张旭 2 , 孙伟波 1 , 孙文翔 2
矿冶工程杂志 | 采矿 2025,45(2): 13-19
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矿冶工程杂志 | 采矿 2025, 45(2): 13-19
不同本构模型下地应力对爆破效果的影响研究
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缪广红1 , 张旭2, 孙伟波1, 孙文翔2
作者信息
  • 1.安徽理工大学　力学与光电物理学院，安徽　淮南　232001
  • 2.安徽理工大学　土木建筑学院，安徽　淮南　232001

    • 缪广红（1985—），男，安徽淮南人，博士，副教授，硕士研究生导师，主要从事爆炸力学相关研究。E-mail：

Influence of In-situ Stress on Blasting Effects Under Different Constitutive Models
Guanghong MIAO1 , Xu ZHANG2, Weibo SUN1, Wenxiang SUN2
Affiliations
  • 1.School of Mechanics and Optoelectronic Physics, Anhui University of Science and Technology, Huainan 232001, Anhui, China
  • 2.School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, Anhui, China
出版时间: 2025-04-01 doi: 10.3969/j.issn.0253-6099.2025.02.003
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摘要
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利用ANSYS/LS-DYNA软件建立不同地应力下的HJC本构模型和RHT本构模型，对比分析不同本构模型中爆破对模型有效应力、岩石损伤的影响。结果表明：HJC本构模型的有效应力变化更贴近实际情况，而RHT本构模型的岩石损伤更贴近实际情况；地应力对距离炮孔较近区域有效应力的影响较小，而对距离炮孔较远区域有效应力的影响较大；地应力对HJC本构模型的岩石损伤影响较小，对RHT本构模型的损伤变量影响较大。

本构模型  /  地应力  /  爆破效果  /  数值模拟  /  损伤变量  /  有效应力  /  岩石损伤

Constitutive models of HJC and RHT for different in-situ stress conditions were established by adopting ANSYS/LS-DYNA software, and the effects of blasting on effective stress and rock damage in different constitutive models were analyzed comparatively. The results show that the effective stress variation in the HJC model is more consistent with practical scenarios, while the rock damage in the RHT model can better reflect practical conditions. In-situ stress has a minor impact on effective stress in regions close to blast holes but a significant influence on effective stress in areas farther away. Additionally, in-situ stress has a smaller effect on rock damage in the HJC model, but substantially affects the damage variables in the RHT model.

constitutive model  /  in-situ stress  /  blasting effect  /  numerical simulation  /  damage variable  /  effective stress  /  rock damage
缪广红, 张旭, 孙伟波, 孙文翔. 不同本构模型下地应力对爆破效果的影响研究. 矿冶工程杂志, 2025 , 45 (2) : 13 -19 . DOI: 10.3969/j.issn.0253-6099.2025.02.003
Guanghong MIAO, Xu ZHANG, Weibo SUN, Wenxiang SUN. Influence of In-situ Stress on Blasting Effects Under Different Constitutive Models[J]. Mining and Metallurgical Engineering, 2025 , 45 (2) : 13 -19 . DOI: 10.3969/j.issn.0253-6099.2025.02.003
正文
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深部岩体爆破工程中，岩体通常处于复杂地应力环境中，地应力对爆破效果影响显著，直接关系到爆破破岩效率、围岩稳定性以及工程安全[1]。
现有岩石爆破效果研究主要集中在岩石爆破试验和数值模拟两个方面。在试验研究方面，学者们通过缩比模型试验探讨了爆破荷载下岩石的破坏特征，但由于试验成本高、危险性大，且难以真实反映大规模工程的实际响应，其应用受到限制[2-5]。在数值模拟方面，有限元法、离散元法等数值模拟方法得到了广泛应用，其中LS-DYNA软件因其高效性和准确性成为主流工具[6-9]。然而，不同本构模型（如HJC、RHT和JH2本构模型）在描述岩石爆破过程时存在显著差异。例如，HJC本构模型仅采用一个弹性极限面来描述材料的屈服准则，相较于RHT本构模型，它较为片面；但在破坏形态的描述方面，RHT本构模型表现不理想[10-13]。
准确可靠的本构关系是开展相关岩石爆破效果研究的关键，然而，目前国内外学者对地应力作用下岩石爆破能量分布特征及爆破损伤机制的研究仍不深入，尤其在不同本构模型下地应力对爆破效果的影响方面，尚未形成系统性的理论体系。因此，本文基于LS-DYNA软件，分别采用HJC和RHT本构模型研究地应力对爆破效果的影响，旨在为岩体爆破工程提供参考。
1　损伤本构模型
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1.1　HJC本构模型
HJC（Holmquist-Johnson-Cook）本构模型用于描述岩石的本构及其参数[14]，将岩石等效强度表示为压力、应变率和损伤的函数，其中压力表示为体应变的函数，且考虑了永久粉碎影响；损伤累积是塑性体积应变、等效塑性应变及压力的函数。HJC本构模型综合考虑了这三个方面对强度的影响，被广泛应用于数值计算。
HJC本构模型包括强度模型、损伤模型和状态方程[15]3部分。强度模型曲线如图1所示，强度模型等效强度表达式见式（1）。
式中：σ*为无量纲等效应力，，为最大归一化无量纲强度极限；A为材料归一化内聚强度；D为损伤度，0≤D≤1；B为归一化压力硬化系数；P*是根据fc归一化后的压力；N为压力硬化指数；C为应变率硬化系数；为无量纲应变率；σ为实际等效应力；fc为静态单轴压缩强度；P为压力；为应变率；为参考应变率，。
损伤模型曲线如图2所示。损伤度D是塑性体积应变、等效体积应变和压力的函数，其表达式见式（2）。
式中：Δεp和Δμp分别为一个循环积分计算中的等效塑性应变增量和塑性体积应变增量；D1和D2均为材料损伤常数；T为抗拉强度；T*为归一化最大拉伸静水压力。
状态方程曲线如图3所示，分为线弹性阶段（OA）、塑性阶段（AB）、压密阶段（BC）3部分。
P≤Pc时，材料处于线弹性阶段，弹性体积模量为：
式中：Pc为单轴压缩试验中材料破碎临界压力；μc为单轴压缩试验中材料临界应变。
Pc<P<Pl时，材料处于塑性阶段，随着压力及塑性体积应变增加，岩石内部的气孔逐渐变小，变成密实介质。
式中：μ为体积应变；Pl为单轴压缩试验中材料压实时的临界压力；μl为单轴压缩试验中材料压实时的体积应变；ρ为岩石瞬时密度；ρ0为原始密度。
P≥Pl时，材料处于压密阶段，此时岩石可以看成连续密实介质，岩石所受压力与体积的关系为：
式中：为修正后的体积应变，；K1、K2、K3均为常量。
1.2　RHT本构模型
RHT本构模型考虑了压力硬化、应变硬化、应变率硬化、压缩、偏应力张量的第三不变量、损伤效应、体积压缩、裂纹软化等效应[16]。基于HJC本构模型引入弹性极限面、失效面和残余强度面，分别描述材料初始屈服强度、失效强度及残余强度的变化规律，RHT本构模型曲线如图4所示。
失效面定义为压力P、应力洛德角θ和应变率的函数：
式中：σfail为失效面应力；YTXC（P）为压缩子午线上等效应力；R3（θ）为角隅函数；为应变率强化因子；A为失效面常数；为归一化层裂强度；Nf为失效面指数；ft为单轴拉伸强度。
由失效面确定弹性极限面，弹性极限面应力定义为：
式中：σelastic为弹性极限面应力；Felastic为弹性强度与失效面强度之比，可根据单轴拉伸强度ft和单轴压缩强度fc确定；FCAP（P）为弹性极限面帽子函数，用于限制静水压力下弹性偏应力。
残余强度面应力定义为：
式中：σresidual为残余强度面应力；B为残余强度面常数；M为残余强度面指数。
2　数值模型
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2.1　建模
利用ANSYS/LS-DYNA软件建立2D数值模型，模型厚度为一个单元，在z轴上施加约束，限制模型变形。单元类型选择3D SOLID164，模型尺寸为1 000 mm×1 000 mm×1 mm，单元长度设置为5 mm；网格划分时，对模型切割处理使得每个单元为六面体单元，炸药和炮孔周围单元网格细化处理，炮孔直径和炸药直径均为60 mm。后处理阶段岩石采用Lagrange算法，空气和炸药采用Euler算法，通过关键字*CONSTRAINED_LAGRANGE_IN_SOLID实现流固耦合；地应力采用dynain文件法[17]实现应力初始化。
2.2　材料参数设置
HJC本构模型由关键字*MAT_JOHNSON_HOLMGUIST_CONCRETE定义，RHT本构模型由关键字*MAT_RHT定义。炸药材料由关键字*MAT_HIGH_EXPLOSIVE_BURN定义，炸药状态方程为JWL状态方程[18]：
式中：PCJ为爆轰产物的压力；E0为单位体积内能；V为相对体积；A、B、R1、R2、ω均为常数，通常采用炸药圆筒试验[19]确定。
空气材料使用*MAT_NULL模型，密度为1.29 kg/m3，采用*LINEAR_POLYNOMIAL关键字定义空气状态方程：
式中：Pa为气体压力；γ为相对体积；C0、C1、C2、C3、C4、C5、C6均为常数，理想气体C0=C1=C2=C3=C6=0。
模型参数详见表1～4，采用g-cm-μs单位制。
3　模拟结果分析
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3.1　无地应力作用下的爆破效果
ANSYS/LS-DYNA模拟一般采用有效应力表征岩石应力特性，反映炸药起爆后岩体介质中爆炸应力场的动态变化过程。无地应力状态下2种本构模型在40、80、120 μs时的有效应力云图如图5～6所示。炸药爆炸后产生的冲击波在炮孔周围均匀分布，爆炸初期的冲击波在极短时间内达到峰值，迅速作用于岩体，形成粉碎区，而后继续对岩体做功，能量逐渐损耗，冲击波衰减为应力波。相较而言，RHT本构模型的应力传播速度和衰减速度更快，作用于粉碎区的有效应力范围更广。
2种本构模型在50、100、150 μs时的损伤云图如图7～8所示。作用时间越久，岩体损伤范围越大。HJC本构模型中的岩体损伤集中在炮孔周围，没有呈现裂纹扩展现象；而RHT本构模型中的岩体损伤范围较大，以裂纹形式向外扩散。与文献[20]的试验结果相比，本文模拟的HJC本构模型没有形成裂纹，结果相差较大，这可能与HJC本构模型的损伤累积与等效塑性应变及压力有关，无法捕捉模型的拉伸破坏行为；RHT本构模型的模拟结果与文献[20]的裂纹扩展基本一致。
3.2　不同地应力作用下的爆破效果
为了探究不同地应力作用下的爆破效果，选取A、B两点，如图9所示。A点位于爆心距10 cm处，处于爆炸冲击波作用范围；B点位于爆心距40 cm处，此处冲击波衰减为应力波。
在地应力分别为0、10、15、20、25、30 MPa条件下，分析2种本构模型在A点的有效应力时程曲线，如图10所示。RHT本构模型的应力传播速度和衰减速度比HJC本构模型快，冲击波从产生到衰减仅40 μs左右，而HJC本构模型的应力时程曲线更为平滑，衰减时间更长，为100 μs左右。与文献[21]研究结果对比发现，HJC本构模型的有效应力时程曲线更符合实际情况。与文献[22]研究结果相互验证发现，不同工况下，2种本构模型应力达到峰值的时间基本一致，HJC本构模型应力曲线波形基本相同，即地应力对爆炸冲击波和应力波的传播影响较小。
2种本构模型在B点的有效应力时程曲线如图11所示。结合A点的有效应力时程曲线可知，距离炮孔较近的区域，由于爆破冲击波远大于初始地应力，地应力对有效应力峰值没有太大影响。距离炮孔较远时，冲击波衰减成为应力波，与地应力处于相同数量级时，地应力对有效应力峰值影响较大。
3.3　不同地应力下岩石损伤结果分析
文献[23]指出，若某损伤区域损伤变量D>0.8，则为粉碎区；损伤变量分布在0.2～0.8之间，则为裂隙区。基于本文模拟结果，通过后处理软件LS/PREPOST计算各单元的损伤变量，分析不同地应力对岩石粉碎区和裂隙区的影响。统计损伤变量稳定时刻260 μs时2种模型岩石粉碎区与裂隙区在整体岩石中的占比，结果如表5～6所示。
由表5～6可知，随着地应力增大，RHT本构模型中岩石粉碎区和裂隙区占比均逐渐减小，说明地应力可有效抑制爆破对岩石的损伤，且随着地应力增大，这种抑制效果逐渐增强；而HJC本构模型中岩石粉碎区和裂隙区占比均增大，说明HJC本构模型对裂隙区的模拟不理想，RHT本构模型能较好模拟裂纹扩展的效果。
文献[24]研究发现，钻孔爆破中，炮孔周围受地应力作用影响，会产生应力集中。对于HJC本构模型，岩石损伤集中在炮孔周围，爆炸产生的冲击波与因地应力产生的应力集中共同作用，形成粉碎区，随着初始地应力增加，应力集中更加严重，使得粉碎区变大。对于RHT本构模型，岩石损伤不仅集中在炮孔周围，还会以裂纹形式向外扩展，文献[23]指出，地应力主要对后期爆生气体静作用阶段的裂纹扩展起抑制作用，故地应力从10 MPa增大到30 MPa时，RHT本构模型中岩石粉碎区占比仅降低了0.84百分点，裂隙区占比降低了4.11百分点，说明地应力对RHT本构模型中岩石粉碎区影响不大，对裂隙区影响较大。
4　结论
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1）在爆破模拟过程中，HJC本构模型对于爆炸产生的冲击波和应力波传播的模拟结果更贴近工程实际，而RHT本构模型对爆炸产生的损伤结果模拟得更好。
2）分别在爆炸冲击波作用范围和应力波作用范围内取A、B两点，发现在冲击波作用范围内，地应力对峰值应力没有太大影响；在应力波作用范围内，地应力对峰值应力有较大影响。
3）对比不同地应力下岩石损伤结果发现，在RHT本构模型中地应力对损伤变量有明显抑制作用，随着地应力增大，对岩石损伤变量的抑制效果会逐渐减弱。
4）不同初始地应力在不同本构模型中对岩石损伤变量影响不同，初始地应力对HJC本构模型整体影响较小，对RHT本构模型的粉碎区影响较小，对裂隙区影响较大。
基金
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  • 国家自然科学基金(11902003)
文献
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2025年第45卷第2期
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doi: 10.3969/j.issn.0253-6099.2025.02.003
  • 接收时间：2024-10-22
  • 首发时间：2026-03-19
  • 出版时间：2025-04-01
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  • 收稿日期：2024-10-22
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    1.安徽理工大学　力学与光电物理学院，安徽　淮南　232001
    2.安徽理工大学　土木建筑学院，安徽　淮南　232001
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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