Simulation study of top coal caving and conveying process based on smoothed particle hydrodynamics
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摘要: 目前针对综放开采中顶煤放出规律的数值模拟研究中，对于顶煤运动的连续−非连续性问题需复杂的耦合算法，必须解决煤岩界面信息精确交互问题，且忽略了刮板输送机输送过程。针对该问题，基于光滑粒子动力学构建了无网格数值计算模型，通过建立连续介质力学控制方程的光滑粒子动力学离散方程，并引入弹塑性土体本构模型和Drucker−Prager屈服准则，实现了顶煤坍塌、运移、放出过程的动态模拟。考虑采场实际放煤和输煤过程，构建了刮板输送机模型，模拟沿工作面水平方向顶煤放出和底煤输送过程，得到不同刮板输送机运行速度（0~1.5 m/s)下的煤岩界面和煤流速度变化规律。仿真结果表明：弹塑性土体本构模型可有效模拟颗粒的流动行为，通过设定摩擦角、弹性模量等材料参数，避免了传统离散元法模型的参数不定问题；煤流速度稳定后，放煤口附近的顶煤应力分布呈 “双峰”形态；刮板输送机运行速度对放煤时间影响较大，但对终止的煤岩界面和放出体形状影响较小；多支架同时放煤需考虑刮板输送机的输送能力，不同支架之间的底煤输送干涉可能导致放煤口的堵塞效应； “见矸关门”准则导致不同放煤口放煤量存在差异，40个放煤口顶煤放出量的标准差（7.52 m2）高于自动放煤的标准差（1.93 m2）。Abstract: Currently, in the numerical simulation research on the release laws of top coal during fully mechanized mining, complex coupling algorithms are required to address the continuity-discontinuity issues of top coal movement and ensure precise interaction of coal-rock interface information. However, the conveying process of scraper conveyors is typically neglected in these simulations. To address this problem, a meshless numerical computation model was constructed based on smoothed particle hydrodynamics (SPH). The discrete equations of SPH, derived from the control equations of continuous medium mechanics, were established. An elastic-plastic soil constitutive model along with the Drucker-Prager yield criterion were introduced to achieve dynamic simulation of the caving, movement, and release processes of the top coal. Considering the actual coal release and conveying processes in the mining area, a scraper conveyor model was constructed to simulate the release of top coal and the conveying of bottom coal along the working face, obtaining the variations in coal-rock interface and coal flow velocity at different scraper conveyor operating speeds (0-1.5 m/s). The simulation results indicated that the elastic-plastic soil constitutive model effectively simulated the flow behavior of particles. By setting parameters such as friction angle and elastic modulus, the issue of uncertain parameters commonly found in traditional discrete element models was avoided. After stabilization of the coal flow velocity, the stress distribution of the top coal near the coal drawing outlet exhibited a "double peak" pattern. The operating speed of the scraper conveyor significantly impacted the coal drawing time, while its effect on the coal-rock interface at termination and the shape of the released body was minimal. When multiple supports released coal simultaneously, the conveying capacity of the scraper conveyor needed to be considered, as interference in bottom coal transportation between different supports could lead to blockage effects at the release port. The "gangue closing" rule resulted in variations in the amount of coal drawing at different coal drawing outlets, with the standard deviation of top coal drawing amount from 40 coal drawing outlets (7.52 m²) being greater than that of automatic coal drawing (1.93 m²).
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图 1 SPH计算域离散化及粒子支持域
Figure 1. Smoothed particle hydrodynamics (SPH) computational domain discretisation and particle support domains
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图 3 铝颗粒床在重力作用下坍塌过程的模拟和实验结果对比
Figure 3. Comparison between simulation and experiment results of aluminum particle bed collapse process under influence of gravity
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图 4 单个放煤口放煤SPH模型
Figure 4. SPH model of top coal caving with a single coal drawing outlet
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图 5 放煤终止时的煤岩界面及放出体形状
Figure 5. Coal-rock interface and shape of released body at the end of coal caving
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图 6 不同放煤时刻标记颗粒的位置
Figure 6. The positions of marked particles at different coal drawing times
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图 8 顶煤放出和底煤输送过程的SPH模拟结果（$ {V}_{{\mathrm{c}}}=1.0 $ m/s）
Figure 8. SPH simulation results of top coal drawing and bottom coal conveying process ($ {V}_{{\mathrm{c}}}=1.0 $ m/s)
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图 9 放煤口监测的煤流速度−时间曲线
Figure 9. Coal flow velocity-time curve monitored at the coal drawing outlet
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图 10 不同刮板输送机运行速度下煤岩界面和底煤输送距离（t=9.0 s）
Figure 10. Coal-rock interface and bottom coal conveying distance at different scraper conveyor operating speeds (t=9.0 s)
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图 11 不同时刻刮板输送机运行速度对煤岩界面形貌的影响
Figure 11. The impact of scraper conveyor speed at different times on the morphology of coal-rock interface
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图 12 2个放煤口同时放煤时的模拟结果（t=11.4 s）
Figure 12. Simulation results of coal being released simultaneously from two coal outlets （t=11.4 s）
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图 14 不同放煤技术下每个放煤口的顶煤放出量
Figure 14. Amount of top coal drawing from each coal drawing outlets under different coal drawing techniques
表 1 SPH模型参数设定
Table 1 Parameters seting in SPH model
参数 取值 参数 取值 初始粒子间距
$ {d}_{{\mathrm{ini}}} $/m取决于具体算例 声速$ {s} $/(m·s−1) $ \mathrm{ }s=\sqrt{\dfrac{K}{\rho}} $ 光滑长度$ {h}_{i} $/m $ h_i=1.2d_{\mathrm{ini}} $ 人工黏性力系数
$ {\mathrm{\alpha }}_{\mathrm{\Pi }},\;{\mathrm{\beta }}_{\mathrm{\Pi }} $$ {\mathrm{\alpha }}_{\mathrm{\Pi }}=0.1,{\mathrm{\beta }}_{\mathrm{\Pi }}=0.1 $ 时间步长$ \Delta t $/s $ \Delta t\leqslant C_{\mathrm{cour}}\left(\dfrac{h_i}{s}\right) $ 
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表 2 铝颗粒崩塌模拟采用的材料参数
Table 2 Material parameters used for aluminum particle collapse simulations
参数 数值 参数 数值 密度$ \rho $/(kg·m3) 2 004.0 弹性模量$ E $/MPa 5.84 摩擦角$ \phi $/（°） 21.9 泊松比$ \upsilon $ 0.3 黏聚力$ C $/Pa 0
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