Nuclide transport in fractured media involves the advection, dispersion, adsorption, etc. The dispersion and adsorption properties of the rock matrix have spatial variability, which results in an anomalous transport of nuclides. In this study, a time-fractional advection-diffusion equation (t-FADE) model is utilized to capture the sub-diffusion transport behavior with heavy-tail property, including the breakthrough curves (BTCs) of uranium and thorium transport in granite plates. Moreover, hydrodynamic dispersion of tritiated water, strontium and cesium in granite fractures are also studied. The results indicate that BTCs of nuclides transport in the granite fractures are unimodal and asymmetric. The decrease of the fractional order $\alpha$ reflects the stronger sub-diffusion. Furthermore, small initial velocity enhances sub-diffusion effect of nuclides and lengthens the breakout time of BTCs, which results in obvious heavy-tail phenomena. The analysis results demonstrate that the t-FADE model can accurately describe sub-diffusion behavior of nuclides transport. At last, the advantages of the t-FADE model in prediction and remediation of nuclides contamination are put forward.

核素在裂隙介质中的输运涉及平流、弥散、吸附等。岩石基质的弥散和吸附特性具有空间变异性，从而导致核素输运的异常。在这项研究中，利用时间分数平流扩散方程（t-FADE）模型来捕获具有重尾特性的次扩散输运行为，包括花岗岩板中铀和钍输运的突破曲线（BTC）。此外，还研究了氚水、锶和铯在花岗岩裂缝中的流体动力分散。结果表明，花岗岩裂隙中核素输运的BTC是单峰且不对称的。分数阶的减少$\alpha$反映了更强的子扩散。此外，较小的初速度增强了核素的亚扩散效应，延长了BTC的爆发时间，导致明显的重尾现象。分析结果表明，t-FADE模型能够准确描述核素输运的亚扩散行为。最后提出了t-FADE模型在核素污染预测和修复方面的优势。