Mechanical properties and crack evolution of interbedded cemented tailings backfill
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摘要: 在進行大尺寸采空區嗣后充填過程中，膠結充填體易出現分層等結構現象。為深入分析結構特征對膠結充填體力學特性及裂紋演化規律的影響，首先制作中間層高度比為0.2、0.4、0.6和0.8，灰砂比為1∶4、1∶6、1∶8和1∶10的分層膠結充填體試件，然后利用GAW–2000伺服試驗系統開展單軸壓縮試驗，最后借助二維顆粒流軟件（PFC–2D），分析膠結充填體內部裂紋分布規律。結果表明：（1）分層充填體單軸抗壓強度與高度比呈指數函數關系、與灰砂比呈多項式函數關系；彈性模量與高度比及灰砂比均呈多項式函數關系；單軸抗壓強度及彈性模量均隨高度比的增加而減小、隨灰砂比的增大而增大，且兩者對灰砂比敏感度更高。（2）充填體內部裂紋演化曲線先緩慢上升，達到單軸抗壓強度的80%左右時快速上升，且灰砂比越大、高度比越大，上升速度越快，拐點到來越早，充填體試件越易發生破壞，超過單軸抗壓強度后曲線開始迅速下降。（3）分層充填體主要表現為剪切破壞、張拉破壞及共軛剪切破壞，且破壞主要集中于中間軟弱層；高度比越大，試件內部裂紋越密集，灰砂比越大，裂紋越易向兩端演化。Abstract: In the process of filling a large-scale goaf, due to the limitations in the capacity of the mixing tank, it is difficult to completely filling the goaf all once, but multiple fillings of a goaf can easily produce a layered structure in the cemented tailings backfill. This layered structure has a significant effect on the mechanical properties of the cemented tailings backfill. To analyze the influence of these structural characteristics on the mechanical properties and evolution of cracks in cemented tailings backfill, the layered cemented tailings backfill specimens with height ratios of 0.2, 0.4, 0.6 and 0.8, and cement-tailing ratios of 1∶4, 1∶6, 1∶8 and 1∶10 were made, and then the uniaxial compression test was carried out by using a GAW–2000 servo test system, and finally the crack distribution inside the cemented tailings backfill were analyzed by using 2D particle flow software(PFC-2D). The results show that: (1) the relationship between the uniaxial compressive strength and the height ratio of the layered backfill can be represented by an exponential function, and the relationship between the uniaxial compressive strength and the cement-tailing ratio can be represented by a polynomial function. The relationship between the elastic modulus and the height ratio and the cement-tailing ratio can be represented by a polynomial function. The uniaxial compressive strength and the elastic modulus are found to decrease with increase in the height ratio, and increase with increase in the cement-tailing ratio, with both being more sensitive to the cement-tailing ratio. (2) The evolution curve of cracks in the cemented tailings backfill increases gradually at first, and then rapidly increases to about 80% of the peak strength, whereby the larger is the cement-tailing ratio, the lager is the height ratio. Furthermore, the earlier the fast-rising inflection point occurs, the more easily is the backfill specimen damaged, and the curve begins to decline rapidly after exceeding the peak strength. (3) The layered backfill fails primarily by mainly shear failure, tensile failure and conjugate shear failure, and the failure is mainly concentrated in the middle weak layer. The larger is the height ratio, the denser are the cracks, the bigger is the cement-tailing ratio, and the more easily the cracks evolve to both ends.
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圖 2 分層充填體試件制作與單軸壓縮試驗
Figure 2. Making and uniaxial compression test of layered backfill specimens
圖 3 高度比與單軸抗壓強度關系。（a）線性擬合；（b）指數擬合；（c）多項式擬合
Figure 3. Relationship between height ratio and uniaxial compressive strength: (a) linear fitting; (b) exponential fitting; (c) polynomial fitting
圖 4 灰砂比與單軸抗壓強度關系。（a）線性擬合；（b）指數擬合；（c）多項式擬合
Figure 4. Relationship between cement-tailing ratio and uniaxial compressive strength: (a) linear fitting; (b) exponential fitting; (c) polynomial fitting
圖 5 高度比與彈性模量關系。（a）線性擬合；（b）指數擬合；（c）多項式擬合
Figure 5. Relationship between height ratio and elastic modulus: (a) linear fitting; (b) exponential fitting; (c) polynomial fitting
圖 6 灰砂比與彈性模量關系。（a）線性擬合；（b）指數擬合；（c）多項式擬合
Figure 6. Relationship between cement-tailing ratio and elastic modulus: (a) linear fitting; (b) exponential fitting; (c) polynomial fitting
圖 8 分層充填體彈性模量敏感度曲線
Figure 8. Elastic modulus sensitivity curve of interbedded backfill
圖 9 尾砂真實粒徑分布與模擬顆粒對比
Figure 9. Comparison of the true grain-size distributions in tailings and the simulation particles
圖 10 分層充填體數值模型細觀結構（頂底層灰砂比為1∶4、中間層灰砂比為1∶8、中間層高度比為0.4）
Figure 10. Microstructure of numerical model of interbedded backfill (The cement-tailing ratio of top and bottom layer is 1∶4, the cement-tailing ratio of middle layer is 1∶8, and the height ratio of middle layer is 0.4)
圖 11 不同分層充填體裂紋演化規律。（a）高度比為0.4；（b）高度比為0.6；（c）灰砂比為1∶6；（d）灰砂比為1∶8
Figure 11. Cracks evolution of different interbedded backfills: (a) height ratio of 0.4; (b) height ratio of 0.6; (c) cemented-tailings ratio of 1∶6; (d) cemented-tailings ratio of 1∶8
圖 12 分層充填體應力–應變曲線、裂紋累積曲線及裂紋增量曲線復合圖。（a）高度比0.4、灰砂比1∶4；（b）高度比0.4、灰砂比1∶8
Figure 12. Composite plots of stress-strain curve, crack cumulative curve and crack increment curve of interbedded backfills: (a) height ratio of 0.4 and cemented tailings ratio of 1∶4; (b) height ratio of 0.4 and cemented tailings ratio of 1∶8
表 1 尾砂和水泥化學成分（質量分數）
Table 1. Chemical composition of tailings and cement (mass fraction)
% Component SiO2 Al2O3 CaO MgO P S Fe Au Fe2O3 SO3 Tailing 65.7 14.3 1.88 0.49 3.05 0.13 0.08 <0.01 Cement 21.36 4.92 62.33 3.41 3.21 1.92 
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表 2 擬合復相關系數(R2)
Table 2. Fitting complex correlation coefficient (R2)
Function type Cement-tailing ratio Average value 1∶4 1∶6 1∶8 1∶10 Linear 0.808 0.802 0.850 0.919 0.845 Exponential 0.892 0.968 0.996 0.953 0.952 Polynomial 0.800 0.873 0.996 0.857 0.882
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表 3 擬合復相關系數(R2)
Table 3. Fitting complex correlation coefficient (R2)
Function type Height ratio Average value 0.2 0.4 0.6 0.8 Linear 0.942 0.931 0.945 0.968 0.947 Exponential 0.897 0.992 0.997 0.934 0.955 Polynomial 0.993 0.987 0.994 0.938 0.978
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表 4 擬合復相關系數(R2)
Table 4. Fitting complex correlation coefficient (R2)
Function type Cement-tailing ratio Average value 1∶4 1∶6 1∶8 1∶10 Linear 0.934 0.969 0.948 0.977 0.957 Exponential 0.999 0.937 0.909 0.998 0.961 Polynomial 0.999 0.938 0.999 0.998 0.984
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表 5 擬合復相關系數(R2)
Table 5. Fitting complex correlation coefficient (R2)
Function type Height ratio Average value 0.2 0.4 0.6 0.8 Linear 0.993 0.943 0.995 0.978 0.977 Exponential 0.989 0.979 0.996 0.988 0.988 Polynomial 0.989 0.998 0.997 0.998 0.996
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表 6 數值模型細觀力學參數
Table 6. Meso-mechanical parameters of numerical model
Type Parameter Value Tailings particles Density/(kg·m?3) 2700 Porosity 0.4 fric 0.5 Kn/(N?m?1) 6.0×109 Ks/(N?m?1) 6.0×109 Radii of particles/m 4.1×10?4?3.0×10?3 Cement particles Density/(kg?m?3) 3200 fric 0.5 Kn/(N?m?1) 6.0×109 Ks/(N?m?1) 6.0×109 Radii of particles/m 3.0×10?4 Parallel bond contact pb_emod/(N?m?1) 1.0×109 pb_coh/(N?m?1) 4.0×108 pb_ten/(N?m?1) 2.0×108 pb_radius 1.0 Smooth joint contact sj_Kn/(N?m?1) 200×109 sj_Ks/(N?m?1) 200×109 sj_fric 0.1 sj_large 1 Note: fric is friction coefficient; pb_ emod, pb_ coh, pb_ ten and Pb_ radius is the elastic modulus, cohesion, tensile strength and contact radius of parallel bonding contact. sj_ Kn，sj_ Ks，sj_ fric and sj_ large is the normal stiffness, tangential stiffness, friction coefficient and size of the smooth joint contact.
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表 7 分層充填體破壞模式
Table 7. Failure modes of interbedded backfill
Cement- tailings ratio Height ratio 0.2 Height ratio 0.4 Height ratio 0.6 Height ratio 0.8 Failure mode analysis 1∶4 
Keeping the tailing cement ratio at 4, when the height ratio is 0.2, it is mainly shown as tensile failure through the stratification plane; when the height ratio increases to 0.4, it is mainly shown as tensile shear failure; when the height ratio continues to increase to 0.6, it is mainly shown as tensile failure in the parallel loading section; when the height ratio increases to 0.8, it is mainly shown as tensile failure in the middle weak layer. 1∶6 
Keep the tailing cement ratio of 6, when the height ratio is 0.2, the failure mainly occurs in the middle weak layer and penetrates the upper and lower layers; when the height ratio is 0.4, the middle weak layer takes the lead in the occurrence of multiple tension cracks; when the height ratio is increased to 0.6, the specimen shows a large shear crack failure through the weak layer; when the height ratio is increased to 0.8, the middle weak layer presents conjugate shear failure. 1∶8 
When the height ratio is 0.2 and 0.4, the failure mode is basically similar, which mainly appears in the middle weak layer and is mainly tensile failure; when the height ratio increases to 0.6, it mainly appears as the main shear failure of the weak layer and accompanied by the secondary tensile crack failure; when the height ratio is 0.8, it mainly appears as the conjugate shear failure of the middle weak layer. 1∶10 
All the failures are concentrated in the middle weak layer, when the height ratio is 0.2 and 0.4, it is mainly tensile failure; when the height ratio is 0.6 and 0.8, it is mainly conjugate shear failure with secondary tensile crack. Note: Yellow indicates CPB and red indicates internal crack.
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