The pore ratio is an important parameter affecting the stability and safety of tailings reservoirs; however, the relationship between the pore ratio and physical properties of tailings sand has not been researched in-depth. In this paper, using the tailings from a tungsten mine in southern Shaanxi as a case study, the correlation between the minimum void ratio and related parameters is analyzed, based on laboratory test data, and the optimal marginal distribution function of the parameters is determined. The Gumbel-Hougard copula function that best describes the correlation between parameters is identified, and it is used to establish the joint probability distribution model of the three parameters, and the guarantee rate is introduced to estimate and analyze the minimum void ratio. The results show that the optimal edge distribution of the fine particle content and specific gravity follows a truncated normal distribution, and the optimal edge distribution of the minimum void ratio follows a logarithmic normal distribution. According to AIC criterion, the Gumbel-Hougard copula is the best three-dimensional copula function to fit the minimum void ratio and related parameters. When the guarantee rate is 0.485, the joint probability distribution model achieves optimal performance in terms of estimating the minimum void ratio. The maximum error of the estimation is 1.99%, which is verified through data, and the estimation meets the requirements for practical engineering. The method proposed in this paper uses the existing measured data to establish a joint probability distribution model and combines the collected fine particle content and specific gravity data with the guarantee rate to estimate the minimum void ratio, providing a novel basis for the study of the physical properties of tailings.

中文翻译：

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基于 Copula 的尾矿矿床最小空隙率参数估计方法

孔隙比是影响尾矿库稳定性和安全性的重要参数；然而，尾矿砂的孔隙率与物性之间的关系尚未得到深入研究。本文以陕南某钨矿尾矿为例，结合室内试验数据，分析最小空隙率与相关参数的相关性，确定参数的最优边际分布函数。识别出最能描述参数间相关性的Gumbel-Hougard copula函数，用于建立三个参数的联合概率分布模型，保证率引入估计和分析最小空隙率。结果表明，细粒含量和比重的最优边缘分布服从截断正态分布，最小空隙率的最优边缘分布服从对数正态分布。根据 AIC 准则，Gumbel-Hougard copula 是拟合最小空隙率和相关参数的最佳三维 copula 函数。当保证率为 0.485，联合概率分布模型在估计最小空隙率方面达到最佳性能。估算最大误差为1.99%，经数据验证，估算满足实际工程要求。本文提出的方法利用已有的实测数据建立联合概率分布模型，将采集到的细颗粒物含量和比重数据与保证率相结合，估算出最小空隙率，为物理力学研究提供了新的依据。尾矿的特性。