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基于GNSS时序数据的西部矿区地表动态沉陷预测模型研究

Research on surface dynamic subsidence prediction model for western mining areas based on GNSS time series data

  • 摘要: 矿区GNSS连续监测站相比常规观测站能够更好地获取地表动态沉陷特征,但布设GNSS站点太多及费用过高制约了其实际应用。为了探讨基于少量站点GNSS连续观测数据构建地表动态沉陷模型的可行性,以黄土高原矿区地表沉陷监测工程为实例,通过绘制地表点动态下沉及其下沉速度与加速度变化曲线,发现其分布特征与Boltzmann角度函数及其一阶、二阶导数的变化曲线高度一致,因此选择具有“S”型分布特征的Boltzmann角度函数构建地表动态下沉模型,引入相对位置角x和偏心角y 两个参数描述监测站与工作面动态边界的相对位置关系,利用GNSS时序观测数据反演Boltzmann模型的4个参数(A1A2ab),并阐明了各参数的物理意义及其变化特征。基于此,利用工作面推进过程中获取的GNSS时序观测数据构建了地表动态沉陷Boltzmann模型,通过分析模型参数随工作面推进位置(参数x)的变化特征,发现这些参数的时序变化随地表沉陷量增大而趋于稳定值,利用该模型可实现后续沉陷量的精准预测。进一步分析发现,主断面上各GNSS站点Boltzmann模型参数的空间变化符合高斯函数分布特征,采用不少于5个GNSS站点的观测数据即可稳定拟合高斯函数参数,据此建立了地表任意点动态沉陷的Boltzmann预测模型。实测数据验证表明,上述基于少数(不少于5个)站点GNSS时序观测数据所构建的Boltzmann模型,具有很好的参数确定性及预测精度,这为西部矿区地表沉陷的动态监测和预测提供了有效手段。

     

    Abstract: Compared to conventional observation stations, continuous GNSS monitoring stations in mining areas can better capture dynamic subsidence characteristics of the ground surface. However, the practical application is constrained by the excessive number of GNSS stations required and the high associated costs. To explore the feasibility of constructing surface dynamic subsidence models using continuous GNSS observations from a limited number of stations, the surface subsidence monitoring project in the Loess Plateau mining area was used as a case study. By plotting dynamic subsidence curves and their corresponding velocity and acceleration variation curves, it was found that their distribution characteristics closely matched those of the Boltzmann angular function and its first-order and second-order derivatives. Therefore, the Boltzmann angular function with its “S-shaped” distribution characteristic was selected to construct the surface dynamic subsidence model. Two parameters−the relative position angle x and eccentricity angle y−were introduced to describe the relative positional relationship between monitoring stations and the dynamic boundary of the working face. The four parameters of the Boltzmann model (A1, A2, a, b) were inverted using GNSS time-series observation data, and the physical significance and variation characteristics of each parameter were elucidated. Based on this, a Boltzmann model for surface dynamic subsidence was constructed using GNSS time-series observation data acquired during the working face advancement. Analysis of how model parameters vary with the working face advancement position (parameter x) revealed that these parameters' temporal changes tend toward stable values as surface subsidence increases. This model enables precise prediction of subsequent subsidence. Further analysis revealed that the spatial variation of Boltzmann model parameters across GNSS stations on the main fault plane conforms to Gaussian distribution characteristics. Observation data from no fewer than five GNSS stations can stably fit Gaussian function parameters, enabling the establishment of a Boltzmann prediction model for dynamic subsidence at any surface point. Field data validation demonstrates that the Boltzmann model constructed from time-series observations at a small number of stations (no fewer than five) exhibits excellent parameter determinacy and prediction accuracy. This provides an effective approach for dynamic monitoring and prediction of surface subsidence in western mining areas.

     

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