Effect of in-situ stress on fracture formation process of rock mass in presplit blasting
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摘要: 基于弹性力学平面应变问题假设，建立了地应力下岩体预裂爆破理论模型。通过Laplace变换和数值反演的方法分析了爆炸应力波的衰减规律，讨论了地应力对岩体预裂爆破应力场分布的影响。此外，采用显式动力学有限元方法，模拟了静水压力和非静水压力条件下岩体预裂爆破的压力演化过程和裂纹扩展行为，并通过Hough变换的方法定量表征了爆炸裂纹的分布特征。研究结果表明：深部岩体预裂爆破成缝困难主要是由于地应力削弱了爆炸引起的切向拉应力作用，孔间岩体质点因切向位移受限而无法形成拉伸破裂面，拉伸破裂成缝机制通过切向拉应力演化和质点位移矢量变化得以验证。基于应力波叠加破坏理论提出的预裂爆破孔间成缝准则可以预测岩体孔间裂纹是否贯穿，得到不同地应力条件下装药直径和孔距的关系可用于指导预裂孔布置方式，从而为深部岩体预裂爆破提供理论指导。Abstract: The evolution and distribution characteristics of cracks in presplit blasting can be significantly affected by the in-situ stress, often leading to issues such as over or under excavation in deep rock masses. In this paper, a theoretical model for presplit blasting under in-situ stress in rock engineering was developed based on the assumption of plane-strain problem of elastic mechanics. The propagation and attenuation of explosion stress waves were analyzed using a combination of Laplace transforms and numerical inversion. Furthermore, the impact of initial static stress on the blasting-induced dynamic stress field distribution in presplitting was examined and discussed. The Riedel-Hiermaier-Thoma (RHT) model in LS-DYNA code was employed to investigate the dynamic mechanical behavior of rock mass, and its material parameters were calibrated by comparing blasting crack patterns and the explosion pressure attenuation curves. Then, the validated model was used to simulate the damage features of rock presplit blasting under both hydrostatic and anisotropy pressure conditions, thereby analyzing the effects of the static stress and the dynamic pressure on the crack extension behavior. In addition, the distribution characteristics of blasting cracks are quantitatively characterized by the Hough transform method. The results indicate that the difficulty in crack coalescence for deep rock presplit blasting is primarily attributed to the reduction of tangential tensile stress caused by the in-situ stress. This prevents the formation of tensile fracture planes between boreholes due to restricted tangential displacements, which was demonstrated by the evolution of circumferential tensile stress and particle displacement vectors. Moreover, a crack coalescence criterion in presplit blasting was proposed to predict whether inter-borehole cracks penetrate based on the damage theory of stress wave superposition, and the relationship between charge diameter and hole spacing under various in-situ stress can guide the arrangement of boreholes, thus improving the presplit blasting effectiveness for deep rock.
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Key words:
- presplit blasting /
- in-situ stress /
- crack coalescence mechanism /
- theoretical model /
- deep rock
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图 1 预裂爆破理论模型示意图
Figure 1. Schematic diagram of theoretical model for presplit blasting
图 2 地应力作用下炮孔周边切向应力分布
Figure 2. Tangential stress distribution around the borehole under in-situ stress
图 3 炮孔中心连线方向上静态应力分布
Figure 3. Static stress distribution along the center line of two boreholes
图 4 不同爆破荷载下动态切向应力演化
Figure 4. Evolution of the tangential stress under different blasting loads
图 5 动态切向应力的比较与孔间峰值应力分布
Figure 5. Dynamic tangential stresses and distribution of maximum stress in adjacent holes
图 6 相邻炮孔间应力波传播和叠加示意图
Figure 6. Diagrams of stress wave propagation and superposition in adjacent holes
图 7 不同地应力下孔距与装药直径之间的关系
Figure 7. Relationship between hole spacing and charge diameter under different in-situ stresses
图 9 爆破荷载下岩石压力和损伤过程
Figure 9. Explosion pressure and damage evolution of rock mass under blasting load
图 11 预裂爆破数值模型及炮孔附近局部网格
Figure 11. Numerical model of presplit blasting and local mesh near the borehole
图 13 不同方法得到的静态应力分布的比较
Figure 13. Comparison of static stress distributions obtained by different methods
图 15 不同工况下中点O处动态切向应力的时程曲线
Figure 15. Dynamical tangential stress-time curves at the middle point O under different conditions
图 16 地应力下岩体预裂爆破裂纹扩展模式
Figure 16. Fracture patterns in presplit blasting under in-situ stress
图 17 爆破裂纹及位移矢量演化
Figure 17. Evolution of blasting cracks and corresponding displacement vectors
图 19 岩石预裂爆破优化设计（单位：m）
Figure 19. Optimal design scheme for rock presplit blasting (unit in m)
图 20 不同方案下岩石爆炸压力演化过程
Figure 20. Evolution of explosion pressure in different design schemes for rock blasting
图 21 不同方案中岩石爆破块体分布特征
Figure 21. Distribution characteristics of rock fragmentation induced by blasting in different schemes
参数名称 取值 参数名称 取值 参数名称 取值 密度ρroc/(kg·m−3) 2620 状态方程参数B0 1.22 剪切模量减小因子ξ 0.50 抗压强度fc/MPa 162 状态方程参数B1 1.22 参考压缩应变率$ {\dot{\varepsilon }}_{0}^{\mathrm{c}} $/s−1 3.0×10−5 初始孔隙度φ0 1.00 侵蚀塑性应变$ {\varepsilon }_{\mathrm{s}}^{\mathrm{f}} $ 2.00 参考拉伸应变率$ {\dot{\varepsilon }}_{0}^{\mathrm{t}} $/s−1 3.0×10−6 损伤因子D1 0.04 压缩屈服面参数$ {G}_{\mathrm{c}}^{\mathrm{*}} $ 0.50 破坏压缩应变率$ {\dot{\varepsilon }}_{\mathrm{c}} $/s−1 3.0×1025 损伤因子D2 1.00 拉伸屈服面参数$ {G}_{\mathrm{t}}^{\mathrm{*}} $ 0.70 破坏拉伸应变率$ {\dot{\varepsilon }}_{\mathrm{t}} $/s−1 3.0×1025 破坏面参数A 2.48 洛德角相关因子B 0.05 最小损伤残余应变$ {\varepsilon }_{\mathrm{p}}^{\mathrm{m}\mathrm{i}\mathrm{n}} $ 0.012 破坏面参数N 0.79 洛德角相关因子Q0 0.68 孔隙坍塌压力pcrush/MPa 108 残余面参数Af 1.62 压缩应变率指数βc 0.008 孔隙压实压力pcomp/GPa 6.00 残余面参数Nf 0.62 拉伸应变率指数βt 0.011 拉伸体积塑性应变分数$ {f}_{\mathrm{t}}^{\mathrm{p}} $ 0.001 相对抗剪强度$ {F}_{\mathrm{s}}^{\mathrm{*}} $ 0.18 弹性剪切模量G/GPa 21.9 Hugoniot多项式系数A1/GPa 33.95 相对抗拉强度$ {F}_{\mathrm{t}}^{\mathrm{*}} $ 0.06 状态方程参数T1/GPa 33.95 Hugoniot多项式系数A2/GPa 41.42 孔隙度指数Npor 3.0 状态方程参数T2/GPa 0.00 Hugoniot多项式系数A3/GPa 8.71 
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ρpol/(kg·m−3) cpol/(m·s−1) S1 S2 S3 γpol αpol V0 915 2901 1.481 0.0 0.0 1.64 0.0 1.0
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参数 值 参数 值 参数 值 密度ρcop/(kg·m−3) 8330 材料常数ncop 0.31 EOS常数S1 1.49 杨氏模量Ecop/GPa 110 材料常数mcop 1.09 EOS常数S2 0.0 泊松比μcop 0.35 材料常数wcop 0.025 EOS常数S3 0.0 熔化温度T/K 1357 材料常数Acop/GPa 0.089 EOS常数αcop 0.47 初始内能E0/(m·s−1) 0.0 材料常数Bcop/GPa 0.292 EOS常数Ccop 4430
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表 4 地应力加载条件
Table 4. In-situ stress conditions used in the numerical study
应力
状态工况 σhor/MPa σv/MPa 应力
状态工况 σhor/MPa σv/MPa 静水
压力H1 10 10 非静水
压力A1 0 20 H2 20 20 A2 10 20 H3 30 30 A3 30 20 H4 40 40 A4 40 20
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