Effect of cleavage characteristics of mineral grains on the failure process of hard rock based on UDEC-GBM modeling
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摘要: 基于塊體離散單元數值模擬方法（UDEC-GBM），以鉀長石礦物顆粒為例，詳細研究了礦物晶粒解理傾角、解理傾角圍壓效應及解理間距對硬質巖石力學性質、微觀開裂過程及機理的影響，并探討了解理特征在工程實際中可能帶來的影響。數值研究結果表明：（1）晶粒解理具有明顯傾角效應，當解理傾角由0°增加到90°時，巖石的彈性模量、單軸壓縮強度及峰后脆延特征都會發生變化，穿晶總裂紋數受影響明顯，主要體現在鉀長石張拉穿晶裂紋顯著增加，鉀長石剪切裂紋數量在60°增加到最大值后減少，石英穿晶張拉裂紋數量也有明顯變化，總體而言不斷增加，而沿晶裂紋數量呈減少趨勢，整個開裂過程仍以張拉沿晶主導；（2）晶粒解理傾角效應受圍壓影響，圍壓會導致沿晶裂紋和穿晶裂紋數量和二者比值發生變化，但不同傾角下圍壓對沿晶裂紋和穿晶裂紋數量和比值變化影響不一樣；（3）當解理間距由2 mm增加到4 mm時，穿晶裂紋數量有增加趨勢，而沿晶裂紋數量減少，總剪切和張拉裂紋數量比值不變，對巖石微觀張拉、剪切破壞機制無明顯影響。此外，具有解理結構的礦物晶粒含量較高且礦物晶粒本身性質對巖石性質及響應影響顯著時，解理特征對板裂、巖爆等破壞的影響應給予重視。Abstract: Based on the UDEC (Universal distinct element code) modeling and grain-based model (UDEC-GBM), the effects of mineral’s (e.g., feldspar) cleavage angle, the confining effect of the cleavage angle and cleavage spacing on mechanical properties, microcracking process and mechanism of hard rocks, and the resulting problems in engineering were investigated in the present study. Numerical results show that: (1) Mineral cleavage has a considerable angle effect. As the cleavage angle increases from 0° to 90°, the elastic modulus, uniaxial compressive strength, and post-peak characteristics of the rock are affected. The total number of transgranular cracks is obviously affected, which is mainly reflected by the increase in the number of feldspar tensile cracks and the number of feldspar shear cracks increases to a maximum at 60° and then decreases, and the number of quartz tensile cracks changes considerably. In general, the number of transgranular cracks increases, while the number of intergranular cracks decreases. However, tensile and intergranular cracking dominate the cracking process. (2) The cleavage effect is affected by the confining pressure. The confining pressure will cause the number and proportion of intergranular cracks and transgranular cracks to change. However, the confining pressure at different angles has different effects on the number and proportion of intergranular cracks and transgranular cracks. (3) As the cleavage spacing increases from 2 to 4 mm, the number of transgranular cracks increases and the number of intergranular cracks decreases. However, the ratio of the total shear and tensile cracks remains constant, indicating that microscopic tensile and shear cracking mechanisms are almost unaffected. In addition, when the proportion of minerals with cleavage characteristics is high and the type of mineral has a considerable influence on the rock properties, the influence of cleavage characteristics on rock failures, such as spalling and rockburst, should be given attention.
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圖 2 Voronoi模型和Trigon模型破壞路徑比較
Figure 2. Comparison of potential failure paths between the Voronoi model and Trigon model
圖 6 破壞結果。（a）數值試件；（b）微觀裂紋；（c）物理試驗
Figure 6. Failure results: (a) numerical specimen; (b) microcracks; (c) physical test
圖 7 數值模型。（a）數值試件；（b）內部礦物晶粒；（c）解理傾角和間距定義
Figure 7. Numerical model: (a) numerical specimen; (b) mineral grains; (c) definition of cleavage angle and spacing
圖 8 不同解理傾角下單軸應力–應變曲線
Figure 8. Uniaxial stress–strain curves at different cleavage angles
圖 10 90°解理傾角下總裂紋演化過程（T和S分別代表張拉和剪切開裂）
Figure 10. Evolution of the total crack at the 90° cleavage angle (T and S indicate tensile cracking and S cracking, respectively)
圖 13 不同類型穿晶裂紋數量（T和S分別代表張拉和剪切開裂）
Figure 13. Number of different transgranular cracks (T and S indicate tensile cracking and S cracking, respectively)
圖 14 不同解理傾角下宏觀破壞。（a）0°；（b）20°；（c）40°；（d）60°；（e）90°；（f）單軸壓縮試驗結果
Figure 14. Macroscopic failure at different cleavage angles: (a) 0°; (b) 20°; (c) 40°; (d) 60°; (e) 90°; (f) test result under uniaxial compression
圖 18 0 MPa時不同類型穿晶裂紋占總穿晶裂紋比例
Figure 18. Ratio of different types of transgranular cracks to the total transgranular cracks at 0 MPa
圖 19 3 MPa時不同類型穿晶裂紋占總穿晶裂紋比例
Figure 19. Ratio of different types of transgranular cracks to the total transgranular cracks at 3 MPa
圖 22 不同解理間距下單軸應力–應變曲線
Figure 22. Uniaxial stress–strain curves at different cleavage spacings
表 1 基本物理與力學參數
Table 1. Basic physical and mechanical parameters
Density/
(kg·m?3)Uniaxial compressive
strength/MPaElastic modulus/
GPaP, wave
velocity/(km·s?1)2687 115 32.2 4.5 
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表 2 礦物晶粒物理、力學參數
Table 2. Physical and mechanical parameters of grains
Grain type Percentage/% ρ/(g·cm–3) Sh/GPa Bu/GPa υ Q 27 2,650 44.0 37.0 0.08 B 5 2,850 12.4 41.1 0.36 K 58 2,560 27.2 53.7 0.28 P 10 2,630 29.3 50.8 0.26 Note: Q, B, K and P represent quartz, biotite, K-feldspar and plagioclase respectively; υ represents Poisson's ratio; Bu, Sh and ρ represent bulk modulus, shear plane modulus and density respectively.
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表 3 加載鋼板參數
Table 3. Properties of the loading platens
Bu/GPa Sh/GPa ρ/(kg·m?3) 15715 11785 7800
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表 4 接觸微觀參數
Table 4. Microparameter of contacts
Contact type Microparameter of contacts kn/
(GPa·m–1)ks/
(GPa·m–1)cp/
MPaφp/
(o)$ {\tau _{{\text{max}}}} $/MPa Q-Q 72000 36000 80 35 48 B-B 41740 20870 52 35 35 K-K 52175 26087 70 35 40 P-P 62610 31305 75 35 44 Intergranular contact 34870 17392 50 42 14 Note: Intergranular parameters are uniformly set between grains, and different parameters are set inside grains (such as Q-Q); the residual cohesion, friction angle and tensile strength of intracrystalline and intergranular contact are set to 0.
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久色视频表 5 參數校核結果
Table 5. Calibrated results of properties
Item E/GPa UCS/MPa σT σci/UCS σcd/UCS υ UDEC-GBM 33.5 116.5 — 0.36 0.86 0.25 Tests 32.7 115.4 6.7 — — 0.24 Error/% 2.45% 0.95% — — — 4.17% Note: E, UCS σT, σci and σcd represent the elastic modulus, uniaxial compressive strength, crack initiation stress and damage stress of granite specimens respectively.
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