Mechanism analysis of rock damage and failure based on the relation between deep chamber axial variation and in situ stress fields
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摘要: 針對深部地下硐室與地應力場之間的軸變關系及其對硐室圍巖損傷破裂的影響，建立了非均質圍巖統計損傷力學模型；分析了不同斷面形狀、地層側壓系數、構造應力場對硐室圍巖損傷破裂的作用機制和影響規律，定義了地層臨界側壓系數；開展了三山島金礦西嶺礦區埋深2000 m地層硐室損傷破裂數值模擬，得到了該礦區深部地下硐室設計與布置原則。研究結果表明，“等應力軸比”情況下硐室圍巖應力集中程度最小，損傷破裂區面積最小；地應力場是圍巖損傷破裂的根本原因，側壓系數越大，硐室頂、底板處應力峰值越大，圍巖以拉伸破裂為主，圍巖損傷破裂區面積隨側壓系數增大呈指數性增大；隨著地層深度的增加，硐室臨界側壓系數不斷減小并趨近于1，深部地下硐室對水平構造應力更加敏感；構造應力場誘使圍巖損傷破裂程度增大，損傷破裂區向構造應力場圍巖應力集中區轉移，使得硐室圍巖發生冒頂和巖爆風險升高。因此，深部地下硐室的設計與布置應結合實際地應力條件，硐室軸向、斷面形狀、軸比盡可能符合地應力條件，從而最大程度降低地應力場對硐室圍巖損傷破裂及穩定性的不利影響。Abstract: The demands for deep underground mining and construction are increasing with the continuing development of society and the economy. Deep underground chambers function as primary elements in deep underground mining and other subsurface facilities. Therefore, rational designs of such chambers would play a pivotal role in construction safety and economic efficiency. The primary goal of this study is to reveal the relation between the in situ stress field and axes of an elliptical cross section of an underground chamber. Based on the rock deformation and damage, a numerical model is developed to define the heterogeneous damage evolution near the chamber. In this parametric study, we characterized the damage evolution in response to the chamber’s cross-sectional shape, lateral stress coefficient, and tectonic stress azimuth, thus introducing the critical lateral stress coefficient to define the chamber stability. Furthermore, a case study of a ?2000 m chamber in the Sanshandao gold mine was conducted using the proposed model to optimize the shape, design, and location analysis of the underground mining chamber. Simulation outcomes show that the damaged area and stress concentration near the chamber are minimized when the axis ratio is equal to the lateral stress coefficient. The damaged area is determined by the in situ stress configuration; a high lateral stress coefficient sees a pronounced increment in the tension stress inside the roof and floor of the chamber, resulting in an exponential enlargement of the damaged area. Compared with the shallow underground chamber, the deep chamber is more sensitive to an increase in the lateral stress coefficient. With an increase in depth, the critical lateral stress coefficient gradually decreased to 1. The larger horizontal tectonic stress in the deep strata causes damage accumulation in the roof and the floor, encouraging rock outbursts in the damaged zones. To conclude, to optimize the design and minimize the outburst hazard for a deep underground chamber, the chamber’s cross-sectional shape, axes ratio, and direction must reasonably reflect the in situ stress field.
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圖 1 不同地應力場作用下橢圓形硐室應力計算簡圖
Figure 1. Stress calculation diagram of an oval chamber under various in situ stress fields
圖 2 等應力軸比硐室應力集中系數變化
Figure 2. Stress concentration factor for a chamber where the axial ratio equals the stress ratio
圖 4 硐室斷面軸比對圍巖損傷破裂影響。（a）Z=1/2；（b）Z=2/3；（c）Z=1；（d）Z=3/2；（e）Z=2
Figure 4. Effect of the chamber axial ratio on the damage of country rock: (a) Z=1/2; (b) Z=2/3; (c) Z=1; (d) Z=3/2; (e) Z=2
圖 5 硐室斷面軸比對圍巖彈性模量的影響。（a）Z=1/2；（b）Z=2/3；（c）Z=1；（d）Z=3/2；（e）Z=2
Figure 5. Effect of the chamber axial ratio on the elastic modulus of country rock: (a) Z=1/2; (b) Z= 2/3; (c) Z=1; (d) Z=3/2; (e) Z=2
圖 6 不同軸比硐室X方向應力分布情況。（a）拱頂處；（b）水平中線處
Figure 6. Stress distribution in the X direction of the chamber with various axial ratios: (a) chamber roof; (b) middle route of the chamber
圖 7 圍巖損傷破裂區與硐室軸比條件關系
Figure 7. Relationship between the damaged zone and chamber axial ratio
圖 8 硐室斷面形狀對圍巖損傷破裂影響。（a）橢圓形；（b）矩形；（c）圓形；（d）馬蹄形；（e）正方形
Figure 8. Effect of the chamber shape on the extent of damage of country rock: (a) ellipse; (b) rectangle; (c) circle; (d) horseshoe; (e) square
圖 9 硐室斷面形狀對圍巖彈性模量影響。（a）橢圓形；（b）矩形；（c）圓形；（d）馬蹄形；（e）正方形
Figure 9. Effect of the chamber shape on the elastic modulus of country rock: (a) ellipse; (b) rectangle; (c) circle; (d) horseshoe; (e) square
圖 10 不同形狀硐室X方向應力分布情況。（a）拱頂處；（b）水平中線處
Figure 10. Stress distribution in the X direction of a chamber with various shapes: (a) chamber roof; (b) middle route of the chamber
圖 11 圍巖損傷破裂區與硐室形狀條件關系
Figure 11. Relationship between the damaged zone and chamber shape
圖 12 側壓系數對圍巖損傷破裂影響。（a）λ=1；（b）λ=1.5；（c）λ=1.75；（d）λ=2；（e）λ=2.2
Figure 12. Effect of the lateral pressure coefficient on the damage of country rock: (a) λ=1; (b) λ=1.5; (c) λ=1.75; (d) λ=2; (e) λ=2.2
圖 13 側壓系數對圍巖彈性模量影響。（a）λ=1；（b）λ=1.5；（c）λ=1.75；（d）λ=2；（e）λ=2.2
Figure 13. Effect of the lateral pressure coefficient on the elastic modulus of country rock: (a) λ=1; (b) λ=1.5;(c) λ=1.75; (d) λ=2; (e) λ=2.2
圖 14 不同側壓系數硐室X方向應力分布情況。（a）拱頂處；（b）水平中線處
Figure 14. Stress distribution in the X direction of a chamber with various lateral pressure coefficients: (a) chamber roof; (b) middle route of the chamber
圖 15 圍巖損傷破裂區面積與地應力側壓系數條件關系
Figure 15. Relationship between the damaged zone and in situ stress lateral pressure coefficient
圖 16 不同地應力條件下對應的臨界側壓系數
Figure 16. Critical lateral pressure coefficient under various in situ stress conditions
圖 17 構造應力角對圍巖損傷破裂影響。（a）β=0°；（b）β=15°；（c）β=30°；（d）β=45°；（e）β=60°
Figure 17. Effect of the tectonic stress dip on the damage of country rock: (a) β=0°; (b) β=15°; (c) β=30°; (d) β=45°; (e) β=60°
圖 18 構造應力角對圍巖彈性模量影響。（a）β=0°；（b）β=15°；（c）β=30°；（d）β=45°；（e）β=60°
Figure 18. Effect of the tectonic stress dip on the elastic modulus of country rock: (a) β=0°;(b) β=15°;(c) β=30°;(d) β=45°;(e) β=60°
圖 19 不同構造應力角硐室X方向應力分布情況. (a)拱頂處;(b)水平中線處
Figure 19. Stress distribution in the X direction of a chamber with different tectonic stress dips: (a) chamber roof; (b) middle route of the chamber
圖 20 圍巖損傷破裂區面積與構造應力角度關系
Figure 20. Relationship between the damaged zone area and tectonic stress dip
圖 21 三山島金礦設計巷道圍巖損傷破裂。（a）圓形；（b）三心拱形
Figure 21. Damage to a roadway in the Sanshandao gold mine: (a) circle; (b) three-centered arch
圖 22 三山島金礦設計巷道圍巖彈性模量。（a）圓形；（b）三心拱形
Figure 22. Elastic modulus of the roadway in the Sanshandao gold mine: (a) circle; (b) three-centered arch
圖 23 三山島金礦設計巷道Mises應力分布情況。（a）圓形；（b）三心拱形
Figure 23. The von mises stress distribution in a roadway in the Sanshandao gold mine: (a) circle; (b) three-centered arch
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