采煤沉陷与岩体力学参数的响应关系和反演

Response relationship and inversion of coal mining subsidence and rock mechanics parameters

  • 摘要: 岩体力学参数的合理取值是煤炭开采覆岩移动与地表沉陷规律数值模拟法研究的关键。为解决数值模拟法精准度高度依赖岩石力学参数的问题,研究构建了一种融合“正交试验−真三维数值模拟−响应面法”的参数反演系统方法。以黄玉川煤矿12403-2回采工作面为例,系统分析了弹性模量、泊松比、黏聚力、内摩擦角和抗拉强度等力学参数对采煤沉陷与覆岩移动规律的敏感性及显著性;研究引入了中心复合设计响应面法,针对分区反演关键参数设计了包含±1、0、± r 水平的试验方案,建立了最大沉陷值 W_\max 、顶板形变 h_\mathrmc 、底板底鼓 h_\mathrmb 、采空形变 \Delta h 、最大水平移动值 U_\max 和主要影响范围 B 与开采区、未采区岩体力学参数的多元回归响应函数。通过给定响应目标下的优化,反演获得了可靠的分区岩体力学参数取值,并对其有效性进行了验证。结果表明:开采区弹性模量 \overlineE 与抗拉强度 \overline\sigma _\mathrmt 是控制 W_\max 、 h_\mathrmc 、 h_\mathrmb 、 \Delta h 、 U_\max 及 B 指标的主控因素,其影响高度显著;未采区弹性模量 \overlineE' 对 U_\max 和 B 指标高度显著,未开采区抗拉强度 \overline\sigma _\mathrmt' 对 B 指标影响同样高度显著。与现场实测数据对比,基于响应函数与反演参数所得的数值模拟结果,其关键响应值与实测值的偏差集分别为0.86%, 3.57%, 1.79%, 0.94%和1.26%, 0.29%, 2.94%, 3.36%,充分验证了反演结果的可靠性。最后,通过与概率积分法对比,发现基于参数反演的数值模拟法在 B 指标预测偏差率仅为2.34%,远低于概率积分法的68.49%,说明在采煤沉陷盆地主要影响边界划定方面显著优于概率积分法。本研究方法明确了研究区采煤沉陷与岩体力学参数之间的定量响应关系,为煤炭开采中岩体力学参数的科学取值提供了可靠的解决方案,也为其他工程领域数值模拟参数反演提供有益借鉴。

     

    Abstract: The reasonable determination of rock mechanics parameters is crucial for the numerical simulation method of overlying rock movement and surface subsidence in coal mining. To address the issue that the accuracy of numerical simulation methods is highly dependent on rock mechanics parameters, this study developed a parameter inversion system method that integrates “orthogonal test−true 3D numerical simulation−response surface method”. Taking the 12403-2 mining face of the Huangyuchuan coal mine as an example, the study systematically analyzed the sensitivity and significance of mechanical parameters such as elastic modulus, Poisson’s ratio, cohesion, internal friction angle, and tensile strength to mining subsidence and overlying rock movement. The study introduced the central composite design response surface method, and designed experimental schemes with ±1, 0, and ±r levels for key parameters in the zonal inversion. Multiple regression response functions for mechanical parameters of rock in mining areas and non-mining areas were established for the maximum subsidence value ( W_\mathrm\max ), roof deformation ( h_\mathrmc ), floor heaving ( h_\mathrmb ), goaf deformation ( \Delta h ), maximum horizontal displacement ( U_\mathrm\max ), and major influence range ( B ) and these parameters. Optimization under given response objectives was performed to invert reliable rock mechanics parameter values, and their validity was verified. The results show that elastic modulus \overlineE and tensile strength \overline\sigma _\mathrmt are the primary controlling factors for W_\mathrm\max , h_\mathrmc , h_\mathrmb , \Delta h , U_\mathrm\max , and B , with highly significant effects. The elastic modulus \overlineE' in the unmined area has a highly significant effect on the U_\mathrm\max and B indicators, while the tensile strength \overline\sigma _\mathrmt' in the unmined area also exhibits a highly significant influence on the B indicator. Compared with field-measured data, the deviations between the key response values obtained through numerical simulations based on the response functions and inverted parameters and the measured values are 0.86%, 3.57%, 1.79%, 0.94% and 1.26%, 0.29%, 2.94%, 3.36%, respectively, which fully validates the reliability of the inversion results. Finally, by comparing with the probability integral method, it was found that the prediction deviation rate for the B indicator using the numerical simulation method based on parameter inversion is only 2.34%, significantly lower than the 68.49% deviation of the probability integral method. This indicates that the numerical simulation method based on parameter inversion is significantly superior to the probability integral method in delineating the major influence boundary of mining-induced subsidence basins. This research method clarifies the quantitative response relationship between mining subsidence and rock mechanics parameters, providing a reliable solution for the scientific determination of rock mechanics parameters in coal mining and offering valuable insights for numerical simulation parameter inversion in other engineering fields.

     

/

返回文章
返回