In this study, the peridynamic Drucker-Prager plastic model with fractional order derivative is proposed to investigate the plastic behavior of surrounding rocks around tunnels, in which the Caputo fractional derivative is employed due to its mathematical simplicity. Instead of utilizing just one parameter for the typical nonassociated flow rule, such as dilation angle, multiple parameters, such as fractional order and interval of fractional derivative, are used to specify the direction of plastic deformation, and the fractional derivative based-typical flow rule is proposed. As a result, compared with the traditional peridynamic Drucker-Prager plastic model, the proposed method is a more generalized model including the typical nonassociated flow rule. Besides, based on the PD force density, the strategy of exertion of initial stress is proposed to simulate in-situ stress in rocks. Taking a block subjected to compression as an example, the impacts of various factors, such as fractional order and interval of fractional derivative, are investigated. A numerical simulation of tunnel excavation in rocks is carried out and the numerical results obtained by the proposed method are verified by comparing with FEM results.

中文翻译：

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具有分数阶导数的近场动力学 Drucker-Prager 塑性模型用于隧道开挖数值模拟

在这项研究中，提出了具有分数阶导数的近场动力学 Drucker-Prager 塑性模型来研究隧道周围围岩的塑性行为，其中由于其数学简单性而采用了 Caputo 分数导数。典型的非关联流动规则不是只使用一个参数，例如膨胀角，而是使用分数阶和分数导数区间等多个参数来指定塑性变形的方向，以及基于分数导数的典型流动规则被提议。因此，与传统的近场动力学 Drucker-Prager 塑性模型相比，所提出的方法是一个更广义的模型，包括典型的非关联流动规则。此外，基于 PD 力密度，提出了施加初始应力的策略来模拟岩石的地应力。以块体受压为例，研究了分数阶、分数阶导数区间等各种因素的影响。对岩石隧道开挖进行了数值模拟，并通过与有限元分析结果的比较验证了所提方法得到的数值结果。