煤炭资源的地下开采会造成地表沉陷，对地表生态环境及建(构)筑物的安全使用造成一定威胁，在采前获知开采过程中的地表沉陷动态预计值，是进行开采沉陷区生态环境动态修复设计的重要基础，是该领域亟待解决的问题之一。为实现煤炭地下开采导致地表沉陷动态过程的准确预计，根据地表沉陷动态规律总结出理想时间函数模型的形态，据此引入Boltzmann时间函数模型，从下沉量、下沉速度、下沉加速度3个方面对该模型进行分析，发现其能够满足地表沉陷动态趋势；探究该时间函数模型各参数对模型图像的影响，确定其物理意义并分别定义为最终下沉量A、最大下沉速度出现时间t₀、下沉急缓程度系数B，从而构建基于Boltzmann时间函数的动态预计模型参数体系；通过对单点实测下沉量进行拟合发现该模型拟合精度较传统动态预计模型更高，拟合优度R²达到0.998 8；对矿区地表监测点实测下沉量进行参数反演，根据反演结果建立了沉陷盆地内任意点动态预计参数与地表最大下沉量、回采速度及覆岩岩性系数的相关关系，给出了该模型各动态预计参数在地表任意点的计算方法，并利用收集的6个工作面数据验证其精度可靠；构建了融合Boltzmann时间函数与概率积分法的地表沉陷动态预计模型，可实现对沉陷盆地内任意点任意时间的地表沉陷预计；运用该预计模型求得多时期下沉量并对其进行精度验证，结果显示开采过程中的动态预计相对误差保持在6.0%以内，相对误差最小值为2.7%。

The underground extraction of coal resources can induce surface subsidence, posing a potential threat to both the ecological environment and the structural stability of buildings. Anticipating the dynamic subsidence values prior to mining is crucial for establishing a foundation for dynamic restoration designs in mining subsidence areas. This represents a pressing concern within the field. In order to precisely predict the dynamic progression of surface subsidence resulting from underground coal mining, an optimal time function model is synthesized based on the dynamic principles governing surface subsidence. Subsequently, the Boltzmann time function model is introduced to comprehensively analyze the model in terms of subsidence value, subsidence velocity, and subsidence acceleration. The analysis reveals that the model aligns with the dynamic trends of surface subsidence. Through an exploration of the influence of various parameters on the model’s representation, their physical significance is determined, and defined as the final subsidence value A, the time of maximum subsidence rate t₀, and the coefficient of the degree of urgency of subsidence B, leading to the establishment of a dynamic prediction model parameter system based on the Boltzmann time function. Fitting the measured subsidence values at a singular point demonstrates that the accuracy of this model surpasses that of traditional dynamic prediction models, achieving a fitting disturbance R² of 0.998 8. Parameter inversion is conducted on the measured subsidence values at monitoring points within the mining area. Based on the inversion results, correlations are established between the dynamic predicted parameters of any point in the subsidence basin and the maximum subsidence value on the surface, mining speed, and overlying rock lithology coefficient. A calculation method for determining the dynamic predicted parameters of the model at any surface point is provided, and its accuracy is verified to be reliable by utilizing the data collected from six working faces. A dynamic prediction model for surface subsidence, integrating the Boltzmann time function and probability integration method, is formulated, enabling predictions at any point and time within the subsidence basin. The model is employed to obtain subsidence values for multiple periods, and its accuracy is validated. Results indicate that the dynamic prediction relative error during the mining process is less than 6.0%, the minimum is 2.7%.