Investigation on cracking behavior and influencing factors of jointed rock masses under the coupling effect of confining pressure and blasting
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摘要: 为了深入研究围压与爆破耦合作用下节理岩体的动力响应及损伤机制，采用显式动力学数值模拟方法，并结合任意拉格朗日-欧拉算法和流固耦合技术，对节理岩体的破裂过程进行模拟。基于时域递归理论，分别计算了爆炸应力波穿过节理面时的透射与反射系数。通过爆炸光弹性试验，分析了爆炸应力波在节理岩体中的传播过程与特征。此外，利用Riedel-Hiermaier-Thoma (RHT) 损伤模型，讨论了不同节理角度及不同围压对爆破裂纹扩展行为的影响，并结合FracPaQ程序定量描述了爆破裂纹的分布规律。最后，通过分析节理尖端的主应力分布及动态应力强度因子变化规律，揭示了节理岩体的爆破损伤机制。结果表明：节理面与非静水压力对爆破裂纹扩展均有导向作用，且非静水压力的导向效应会因节理面的存在而减弱；非静水压力下，应力波透、反射系数随着水平方向压力的增加分别呈减小和增大的趋势。由节理面两侧法向与切向位移变化规律，发现剪切应力是尖端翼裂纹扩展的主要原因。根据动态应力强度因子判断，拉伸裂纹在爆破初期主导节理尖端的损伤，而剪切裂纹在后期占主导地位。Abstract: Propagation features of blast-induced stress waves undergo substantial alterations as they traverse heterogeneous interfaces. In rock engineering, the prevalence of discontinuous structural planes, such as joints and fissures, becomes increasingly pronounced with increasing burial depth. To gain a comprehensive insight into the dynamic response and damage mechanism, an explicit dynamics numerical method incorporating the ALE algorithm and fluid-solid coupling technology was adopted, which allows for precise simulation of the fracture process within jointed rock mass under the combined effects of confining pressure and blasting load. Based on the time-domain recurrence theory, the transmission and reflection coefficients of the stress wave were calculated, and the propagation process and features of the stress wave were then analyzed by the explosion photoelasticity test using an epoxy resin plate. Additionally, the Riedel-Hiermaier-Thoma (RHT) damage model was used to investigate the influence of different joint angles and confining pressures on cracking behavior. Furthermore, the cracks were quantitatively assessed using the FracPaQ program. Finally, the damage mechanism of the jointed rock mass was revealed by analyzing the principal stress distribution and displacement change as well as the dynamic stress intensity factors (DSIFs) of the joint tip. The results show that both the joint and the anisotropic pressure have a guiding effect on crack extension, and the effect of the anisotropic pressure will be weakened by the presence of the joint. For the anisotropic pressure condition, the stress wave transmission and reflection coefficients tended to decrease and increase, respectively, with increasing pressure in the horizontal direction. From the change rule of normal and tangential displacement on both sides of the joint surface, it is found that shear stress is the main cause of tip-wing crack expansion. An analysis of the DSIFs reveals that tensile cracks predominantly contribute to damage at the joint tip during the initial phase of blasting, with shear cracks becoming the dominant form of damage in the later stages.
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Key words:
- in-situ stress /
- jointed rock mass /
- explosion stress wave /
- crack extension /
- damage mechanism
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图 1 不同算法下材料及单元网格变化关系示意图
Figure 1. Schematics of material and element mesh variation for different algorithms
图 3 节理岩体爆破数值模型
Figure 3. Numerical model of jointed rock mass induced by blasting load
图 4 爆炸应力波在节理处的传播示意图
Figure 4. Illustration of propagation of the blast stress wave at the joint
图 5 节理岩体的透反射系数变化
Figure 5. Variations of transmission and reflection coefficients for jointed rock mass
图 6 不同方法下爆炸应力波传播对比
Figure 6. Comparison of stress wave propagation using various methods
图 7 水平和竖直方向上爆炸压力时程曲线
Figure 7. Time histories of explosion pressure in horizontal and vertical directions
图 8 围压作用下节理岩体爆破裂纹扩展过程
Figure 8. Expansion process of blasting cracks for jointed rock mass under confining pressure
图 9 节理岩体爆破裂纹分布特征
Figure 9. Distribution characteristics of blasting crack in jointed rock mass
图 10 FracPaQ程序识别爆破裂纹特征流程图
Figure 10. Flow chart for characteristics recognition of blasting cracks in FracPaQ program
图 11 节理岩体爆破裂纹的量化统计
Figure 11. Quantitative statistics of blasting cracks in jointed rock mass
图 12 45°节理尖端周围的测点布置
Figure 12. Arrangement of measurement points around the tip of joint with 45°
图 13 爆破400 µs后节理尖端周围的主应力分布
Figure 13. Principal stress distribution around the tip of joint after 400 µs under blasting load
图 14 节理尖端位移变化曲线
Figure 14. Displacement variation around the tip of the 45° joint for the case of 45-0-0
图 15 节理尖端局部极坐标系变换示意图
Figure 15. Diagram of the local polar coordinate system transformation at the joint tip
图 16 不同围压下节理尖端动态应力强度因子
Figure 16. DSIFs of joint tip under various confining pressures
表 1 花岗岩的RHT模型参数
Table 1. Parameters of RHT model for granite
参数名称 符号 取值 参数名称 符号 取值 参数名称 符号 取值 损伤因子 D1 0.04 密度 ρr 2620 kg/m−3剪切模量减小因子 ξ 0.50 损伤因子 D2 1.00 侵蚀塑性应变 $ {\varepsilon }_{\mathrm{s}}^{\mathrm{f}} $ 2.00 参考压缩应变率 $ {\dot{\varepsilon }}_{0}^{\mathrm{c}} $ 3.0×10−5 s−1 初始孔隙度 α0 1.00 抗压强度 fc 162 MPa 参考拉伸应变率 $ {\dot{\varepsilon }}_{0}^{\mathrm{t}} $ 3.0×10−6 s−1 失效面参数 A 2.48 压缩屈服面参数 $ {G}_{\mathrm{c}}^{\mathrm{*}} $ 0.50 破坏压缩应变率 $ {\dot{\varepsilon }}_{\mathrm{c}} $ 3.0×1025 s−1 失效面参数 N 0.79 拉伸屈服面参数 $ {G}_{\mathrm{t}}^{\mathrm{*}} $ 0.70 破坏拉伸应变率 $ {\dot{\varepsilon }}_{t} $ 3.0×1025 s−1 残余面参数 Af 1.62 洛德角相关因子 B 0.05 最小损伤残余应变 $ {\varepsilon }_{\mathrm{p}}^{\mathrm{m}} $ 0.012 残余面参数 Nf 0.62 洛德角相关因子 Q0 0.68 孔隙坍塌压力 pcrush 108 MPa 孔隙度指数 NP 3.00 压缩应变率指数 βc 0.008 孔隙压实压力 pcomp 6.00 GPa 状态方程参数 B0 1.22 拉伸应变率指数 βt 0.011 拉伸体积塑性应变分数 $ P_{\mathrm{t}}^{\mathrm{f}} $ 0.001 状态方程参数 B1 1.22 弹性剪切模量 G 21.9 GPa Hugoniot多项式系数 A1 33.95 GPa 相对抗剪强度 $ {F}_{\mathrm{s}}^{\mathrm{*}} $ 0.18 状态方程参数 T1 33.95 GPa Hugoniot多项式系数 A2 41.42 GPa 相对抗拉强度 $ {F}_{\mathrm{t}}^{\mathrm{*}} $ 0.06 状态方程参数 T2 0.00 GPa Hugoniot多项式系数 A3 8.71 GPa 
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ρe/(kg·m−3) DJ/(m·s−1) PCJ/GPa $ {E}_{0}^{\mathrm{J}} $/(kJ·m−3) AJ/GPa BJ/GPa R1 R2 ωJ 1320 6690 16.0 7.38×106 586 21.6 5.81 1.77 0.282
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表 3 空气模型材料参数
Table 3. Parameters for the air material
ρa/(kg·m−3) C0 C1 C2 C3 C4 C5 C6 $ {E}_{0}^{\mathrm{a}} $/(kJ·m−3) V0 1.29 0.0 0.0 0.0 0.0 0.4 0.4 0.0 250 1.0
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表 4 节理模型材料参数
Table 4. Parameters for the joint material
ρj/(kg·m−3) Ej/GPa μj Et/MPa σ0/MPa βj VP 2200 28 0.24 25 250 0.5 0.0
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表 5 围压加载条件
Table 5. Confining pressure conditions in numerical simulation
应力状态 工况 σx/MPa σy/MPa 应力状态 工况 σx/MPa σy/MPa 静水压力 α-10-10 10 10 非静水压力 α-20-10 20 10 α-30-30 30 30 α-30-10 30 10
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