Meso-energy evolution and rock burst proneness of the stress thresholds of granite under triaxial cyclic loading and unloading test
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摘要: 為研究三軸循環加卸載條件下三山島花崗巖細觀能量演化規律, 采用顆粒流理論確定了花崗巖的應力門檻值(起裂應力σci、損傷應力σcd和峰值強度σf), 研究了應力門檻值對應的邊界能、應變能(線性接觸應變能和平行黏結應變能)、耗散能(摩擦能和阻尼能)、動能隨圍壓變化的規律, 并從能量角度建立了巖爆傾向性評價指標Wx. 結果表明: 三山島花崗巖不同圍壓下相應的σci/σf位于37.0%~44.8%區間, σcd/σf位于81.2%~89.0%區間, 隨著圍壓的增大, 起裂邊界能、應變能和耗散能呈線性關系增加, 損傷(峰值)邊界能、應變能和耗散能呈指數關系增加; 其中耗散能受圍壓影響最為敏感, 增幅倍數最大, 其次是邊界能, 最后為應變能. 圍壓對起裂應變能比例影響不大, 損傷和峰值應變能比例隨圍壓增大緩慢減小, 峰值應變能比例下降幅度最大. 基于巖爆傾向性評價指標Wx可知, 當圍壓在20 MPa內, 三山島花崗巖巖爆傾向性相對較小; 當圍壓達到30 MPa時巖爆傾向性開始迅速增加. 研究成果為巖爆傾向性的評價提供了新的參考指標, 進一步為井下巖體工程的穩定性研究提供了新思路.Abstract: To study the meso-energy evolution of Sanshandao granite under triaxial cyclic loading and unloading, the stress thresholds (the crack initiation stress σci, crack damage stress σcd, and peak stress σf) of Sanshandao granite were determined; the variation law of the boundary energy, strain energy (linear contact strain energy and parallel bond strain energy), dissipation energy (friction energy and damping energy), and kinetic energy corresponding to each stress threshold with confining pressures was analyzed; and a new index Wx for evaluating the rock burst proneness was established from the perspective of energy based on a simulation using PFC3D. The results show that the corresponding σci/σf is in the range of 37.0% to 44.8%, and σcd/σf is in the range of 81.2% to 89.0% under different confining pressures. With the increase of confining pressure, the boundary energy, strain energy, and dissipation energy of the crack initiation increase linearly, and the boundary energy, strain energy, and dissipation energy of the crack damage and peak increase exponentially. Among them, the dissipation energy exhibits the maximum increment with the change in confining pressure, followed by the boundary energy, and then the strain energy. The confining pressure has little effect on the proportion of the strain energy of crack initiation. Moreover, with increasing pressure, the proportion of the crack damage and the peak strain energy decrease slowly; however, the proportion of peak strain energy decreases to a greater extent. According to the new index Wx for the evaluation of the rock burst proneness, when the confining pressure was less than 20 MPa, the rock burst proneness of Sanshandao granite was relatively small, and when the confining pressure reached 30 MPa, the rock burst proneness began to increase rapidly. This study provides a new reference index for the evaluation of rock burst proneness and further provides a new idea for the stability study of underground rock mass engineering.
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圖 1 試驗設備. (a) WEP-600試驗機；(b) MTS810試驗機
Figure 1. Test equipments: (a) WEP-600; (b) MTS810
圖 2 混合顆粒黏結模型.(a) 單軸模型；(b) 三軸模型；(c) 巴西劈裂模型
Figure 2. Mixed bonded particle model: (a) uniaxial compression model; (b) triaxial compression model; (c) Brazilian splitting model
圖 3 花崗巖巴西劈裂試驗和模擬結果對比
Figure 3. Results of Brazilian splitting test of granite obtained from numerical simulation and experiments
圖 4 花崗巖單軸壓縮試驗和模擬結果對比
Figure 4. Results of uniaxial compression test of granite obtained from numerical simulation and experiments
圖 5 不同圍壓下模擬和試驗的強度包絡線對比
Figure 5. Comparison of the strength envelopes of simulations and tests under different confining pressures
圖 6 三軸循環加卸載條件下裂紋不同發展階段的應力-應變曲線(σ3=5 MPa)
Figure 6. Stress-strain diagram obtained from triaxial cyclic loading and unloading showing different stages of crack development(σ3=5 MPa)
圖 7 不同細觀能量動態變化曲線(σ3=5 MPa). (a) 邊界能；(b) 線性接觸應變能；(c) 平行黏結應變能；(d) 摩擦能；(e) 阻尼能；(f) 動能
Figure 7. Different meso-energy dynamic curves(σ3=5 MPa): (a) boundary energy; (b) linear contact strain energy; (c) parallel bond strain energy; (d) friction energy; (e) damping energy; (f) kinetic energy
圖 8 巖石變形破壞過程中能量與應力變化曲線(σ3=5 MPa)
Figure 8. Energy and stress curves of rock deformation and failure process(σ3=5 MPa)
圖 9 不同圍壓下應力門檻值細觀能量變化曲線. (a) 邊界能；(b) 應變能；(c) 耗散能
Figure 9. Energy evolution curves of stress thresholds under different confining pressures: (a) boundary energy; (b) strain energy; (c) dissipation energy
圖 10 不同圍壓下應力門檻值應變能比例變化曲線
Figure 10. Strain energy ratio curves of stress thresholds under different confining pressures
圖 11 不同圍壓循環加卸載下Wet指標變化曲線
Figure 11. Variation of Wet under different confining pressures
圖 12 不同圍壓循環加卸載下Wcf指標變化曲線
Figure 12. Variation of Wcf under different confining pressures
圖 13 不同圍壓循環加卸載下Wx指標變化曲線
Figure 13. Variation of Wx under different confining pressures
表 1 三山島花崗巖試驗力學特性
Table 1. Mechanical properties of Sanshandao granite test
密度/(kg·m-3) 單軸抗拉強度/MPa 拉伸彈性模量/GPa 單軸抗壓強度/MPa 壓縮彈性模量/GPa 單軸起裂應力/MPa 單軸損傷應力/MPa 泊松比 拉壓比 摩擦角/(°) 內聚力/MPa 2686 12.40 40.99 94.37 43.98 37.75 81.16 0.20 0.13 49.96 17.19 
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表 2 混合顆粒黏結模型細觀力學參數
Table 2. Meso-mechanical parameters of the mixed bonded particle model
礦物名稱 Rmin/mm Rmax/mm ρ/(kg·m-3) μ E*/GPa kr E*/GPa λ n σc/MPa c/MPa ?/(°) 斜長石 1.5 2.5 2560 0.5 96.41 1.33 137.64 1 0.36 224 224 12.5 鉀長石 1.5 2.5 2630 0.5 105.93 1.33 151.23 1 0.36 252 252 15.0 石英 1.5 2.5 2650 0.5 103.42 1.33 147.64 1 0.36 235.2 235.2 13.5 黑云母 1.5 2.5 3050 0.5 32.83 1.33 46.86 1 0.36 196 196 10.0
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表 3 巖爆傾向性評價指標
Table 3. Evaluation indexes for rock burst proneness
評價指標 計算公式 指標分類標準 Wet Wet=ER/ED
ER為卸載時恢復的彈性應變能,
ED為加卸載循環中耗散的能量.Singh[19]的硬巖分類標準：
Wet < 10，弱巖爆傾向；
10≤Wet < 15，中等巖爆傾向；
Wet≥15，強烈巖爆傾向.Wcf Wcf=E1/E2
E1為峰前總能量,
E2為峰后總能量.Wcf≤1，無巖爆傾向；
1 < Wcf≤2，弱巖爆傾向；
2 < Wcf≤3，中等巖爆傾向；
Wcf>3，強烈巖爆傾向.
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