In this study, we investigate the impact of topological disorder on liquid distribution and transport phenomena in three-dimensional unsaturated granular media using the Shan-Chen lattice Boltzmann method. Distinct samples of disordered media are generated, characterized by the disorder index $I_v$. Under different $I_v,$ varied liquid cluster distributions are demonstrated in a gravity-driven vapour-liquid system. Gradually increasing the initial liquid phase in the simulation domain allows the full range of saturation. The focuses are placed on the liquid cluster statistics from the connectivity, total cluster number, largest cluster and mean cluster volume at an increasing saturation. Meanwhile, the interfacial area, liquid retention curves and relative permeability-saturation curves are produced at diverse $I_v$ and wettability. It is found that the slopes of retention curves are well correlated with the proposed capillary index $I_c$ that unifies both disorder and wettability. The proposed generalized correlation between capillary index and slope index is useful in terms of determining the capillary pressure-saturation curve and relative permeability-saturation curve for a given granular system at varied contact angles. Additionally, the cohesive strength-saturation curves are also obtained with the aid of the interfacial area and negative capillary pressure, which elucidates that a packing with a higher $I_v$ experiences a relatively larger cohesive strength. These results enhance the understanding of disorder effect and will be beneficial for the exploration of many retention curves-related phenomena such as liquid transfer and stress-strain relation for wet granular media.

在这项研究中，我们使用Shan-Chen格子Boltzmann方法研究了拓扑混乱对三维不饱和粒状介质中液体分布和传输现象的影响。生成了无序媒体的不同样本，其特征在于无序索引${\mathrm{一世}}_v$。下不同${\mathrm{一世}}_v，$在重力驱动的蒸气-液体系统中证明了各种液体簇的分布。在模拟域中逐渐增加初始液相可以实现整个饱和范围。重点放在连通性，总簇数，最大簇和平均簇体积（饱和度不断增加）的液态簇统计上。同时，界面面积，液体保留曲线和相对渗透率-饱和度曲线在不同的条件下产生。${\mathrm{一世}}_v$和润湿性。发现保留曲线的斜率与建议的毛细管指数有很好的相关性${\mathrm{一世}}_C$兼顾了无序性和润湿性。在确定给定颗粒系统在变化的接触角下的毛细管压力-饱和度曲线和相对渗透率-饱和度曲线方面，建议的毛细管指数和斜率指数之间的广义相关性很有用。此外，还可以通过界面面积和负毛细管压力获得内聚强度-饱和度曲线，这说明填料具有较高的填充度。${\mathrm{一世}}_v$具有相对较大的内聚强度。这些结果增进了对无序效应的理解，并将有助于探索许多与保留曲线有关的现象，例如湿颗粒介质的液体转移和应力-应变关系。