Discrete element simulation of the mechanical properties of shale with different bedding inclinations under conventional triaxial compression
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摘要: 頁巖作為頁巖氣儲層，在沉積過程中形成部分弱面，在力學特性上表現出各向異性特征。所以，使用離散元軟件從微細觀層面探討深部頁巖力學各向異性特征具有重要實踐意義。基于頁巖室內常規三軸壓縮試驗結果，采用離元程序PFC2D對常規三軸壓縮下不同層理傾角頁巖進行了顆粒流模擬研究，分析了層理傾角及圍壓對頁巖力學特性的影響規律。結果表明：（1）頁巖峰值強度與黏聚力隨層理傾角的增加整體呈“U”形變化，但峰值強度在不同圍壓下的變化趨勢有所區別；而內摩擦角隨層理傾角的增大呈非線性變化。（2）層理傾角對頁巖周圍顆粒的位移方向及大小的影響隨著層理面與軸向應力的夾角的增大而減小。（3）同一層理傾角試樣最終破壞時的微裂紋總數隨著圍壓的升高有所增加；同一圍壓下，試樣最終破壞時的微裂紋數目，隨著層理傾角的增加呈現先減少后增多的趨勢。（4）同一層理傾角頁巖的脆性隨圍壓的增長整體呈下降趨勢;低圍壓情況下，頁巖脆性隨層理傾角的增加呈兩端大中間小的變化規律。Abstract: With the growth in energy demand, shale gas has attracted considerable attention as an unconventional clean and efficient energy source. In addition, the recoverable reserves of deep shale gas in China far exceed those with a depth less than 3500 m. Thus, deep shale gas is an important replacement field for shale gas production in China. Shale, as a shale gas reservoir, forms many weak surfaces in the deposition process and shows different degrees of anisotropy in the mechanical properties. Therefore, it is of great importance to use particle flow code (PFC) to explore anisotropy of shale from the perspective of micro-level for deep shale gas production in China. Based on the experimental results obtained from the shale specimens under conventional triaxial compression, PFC2D was used to simulate the triaxial mechanical properties of shale with different bedding inclinations. The effects of bedding inclination and confining pressure on the mechanical properties of shale specimens were analyzed. The following results are obtained. (1) With the increase of bedding inclination, the peak strength and cohesion of shale all display a "U"-type variation, but the trend of peak strength is different under different confining pressures and the internal friction angle varied nonlinearly with the bedding inclination increases. (2) The effects of bedding inclinations on the displacement direction and size of surrounding particles decrease with the increase of the angle between the bedding inclination and axial stress. (3) At constant bedding inclination, the number of microcracks at the final failure of the specimen increases with the increase of confining pressure. Under the same confining pressure, the number of microcracks in the final failure of the specimen first decreases and then increases with the increase in bedding inclination. (4) With increased confining pressure, the brittleness of shale with the same bedding angle decreases as a whole. Under low confining pressure, shale brittleness is larger at both ends and smaller in the middle with the increased bedding inclinations.
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Key words:
- shale /
- bedding inclinations /
- failure mode /
- brittleness index /
- discrete element simulation
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圖 2 層理頁巖室內試驗與模擬峰值強度對比。（a）β=0°；（b）β=90°
Figure 2. Comparison between the experimental and numerical peak strength of the bedding shale: (a) β = 0°; (b) β = 90°
圖 3 頁巖峰值強度參數與層理傾角的關系。（a）峰值強度隨層理傾角的變化；（b）黏聚力、摩擦角隨層理傾角的變化
Figure 3. Relationship between the peak strength parameters of shale and bedding inclinations: (a) peak strength variation vs bedding inclinations; (b) cohesion variation C and internal friction angle φ vs bedding inclinations
圖 4 不同圍壓層理頁巖最終破裂模式 (β=15°)
Figure 4. Ultimate failure modes of the bedding shale in different confining pressures (β=15°)
圖 5 不同圍壓層理頁巖最終破裂模式 (β = 30°)
Figure 5. Ultimate failure modes of the bedding shale in different confining pressures (β = 30°)
圖 6 不同圍壓層理頁巖最終破裂模式 (β = 45°)
Figure 6. Ultimate failure modes of the bedding shale in different confining pressures (β = 45°)
圖 7 不同圍壓層理頁巖最終破裂模式（β=60°）
Figure 7. Ultimate failure modes of the bedding shale in different confining pressures (β = 60°)
圖 8 不同圍壓層理頁巖最終破裂模式（β = 75°）
Figure 8. Ultimate failure modes of the bedding shale in different confining pressures (β = 75°)
圖 9 不同層理傾角試樣位移場示意圖。（a）β=15°；（b）β=45°；（c）β=75°
Figure 9. Diagram of the displacement field of specimens with different bedding inclinations: (a) β=15°; (b) β=45°; (c) β=75°
圖 10 層理頁巖微裂紋演化曲線。（a）不同圍壓下β=0°頁巖微裂紋演化規律；（b）不同層理傾角頁巖微裂紋演化規律（σ3=60 MPa）
Figure 10. Evolution curves of the number of microcracks of the bedding shale: (a) evolution law of shale microcrack at β=0° under different confining pressures; (b) evolution law of microcracks in shale with different bedded inclination angles (σ3=60 MPa)
圖 12 不同層理傾角下脆性指標隨圍壓的變化
Figure 12. Variation of brittleness index with confining pressure under different bedding dip angles
圖 13 不同圍壓下脆性指標隨層理傾角的變化
Figure 13. Variation of brittleness index with bedding dip under different confining pressures
表 1 頁巖PFC2D細觀參數
Table 1. Micro-parameters of shale in PFC2D
pb_emod/
GPapb_krat pb_ten/
MPapb_coh/
MPasj_kn/
GPasj_ks/
GPasj_ten/
MPasj_coh/
MPa43 1.7 132 57 12000 2000 18 7 
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表 2 常規三軸壓縮下層理頁巖試驗與模擬破壞模式對比
Table 2. Comparison between experimental and numerical failure modes of the bedding shale specimens underconventional triaxial compression
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