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基于多项式混沌展开和物质点法的采空区注浆运移敏感性分析

Sensitivity analysis of grout migration in goaf grouting based on polynomial chaos expansion and material point method

  • 摘要: 针对采空区注浆通道复杂、浆液运移非线性及多参数计算量大的问题,结合物质点法(MPM)与非侵入式多项式混沌展开(PCE),建立浆液前沿推进速度的代理模型。选取浆液密度、体积模量、塑性黏度、屈服应力、固相体积分数和注浆压力为输入,设置单采空区和复杂分支采空区两类算例。采用MPM计算浆液速度场,以168组建模样本拟合PCE系数,并用独立样本比较代理预测值与MPM计算值。结果表明,单采空区中较高速度区域由竖直导浆通道向水平通道延伸,复杂采空区各分支的速度分布差异明显。复杂工况一阶、二阶和三阶PCE的建模样本CVRMSE分别为24.91%、11.37%和3.05%,三阶模型的拟合误差最小。系数分组结果中,两类工况的注浆压力总效应指标均最高,复杂工况中密度的总效应排序由第三升至第二。现场流态化充填试验采用粉煤灰∶矸石∶水为2∶5∶3的配比,实现了连续泵送,未观察到明显管路堵塞或浆体外泄。MPM与PCE相结合,可用于分析给定参数范围内的浆液速度响应;现场试验表明,所用配比和充填工艺满足本次试验的泵送要求。

     

    Abstract: To address the challenges of complex grouting channels in goafs, nonlinear grout migration, and the high computational cost of multi-parameter analysis,a surrogate model for the grout front advancement velocity is established by combining the material point method (MPM) with non-intrusive polynomial chaos expansion (PCE). Grout density, bulk modulus,plastic viscosity, yield stress, solid volume fraction, and grouting pressure are selected as input variables, and two cases—a single goaf and a complex branched goaf—are considered. MPM is used to calculate the grout velocity field. A total of 168 modeling samples are used to fit the PCE coefficients, and independent samples are used to compare the surrogate predictions with the MPM results. The results show that in the single goaf,high-velocity zones extend from the vertical grout-conducting channel to the horizontal channel, whereas in the complex goaf, the velocity distributions among branches differ markedly. For the complex case, the in-sample CVRMSE values of the first-, second-, and third-order PCE models are 24. 91%, 11. 37%, and 3. 05%, respectively, with the third-order model yielding the smallest fitting error. The coefficient grouping results show that grouting pressure has the highest total-effect index in both cases,while in the complex case,the total-effect ranking of grout density rises from third to second. In a field fluidized backfill trial,a fly ash ∶ gangue ∶ water ratio of 2 ∶ 5 ∶ 3 was adopted;continuous pumping was achieved,and no obvious pipeline blockage or grout leakage was observed. The combination of MPM and PCE can be used to analyze the grout velocity response within the given parameter ranges;the field trial indicates that the mix proportion and backfilling process used meet the pumping requirements of the trial.

     

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