The combined discrete-finite element method is often used for dynamic interaction simulations, in which contact detection is the most time-consuming but critical constituent. Therefore, it is significant to develop an accurate and efficient contact detection algorithm. In this study, an efficient contact detection algorithm termed TSC (tire-sand contact) is developed for dealing with the interactions between spherical discrete elements and hexahedral finite elements. The global search of TSC is suitable for the contact detection of tire-sand interaction. In the global search phase, according to the contact characteristics of tire movement on granular terrain, the potential contact pairs are quickly determined by using the method of dynamically changing the slave nodes and master segments within a moving contact region. The local search is based on the principle of inside-outside algorithm, and the contact region is divided into three types, i.e. surface contact region, edge contact region and node contact region. In the local search phase, the invalid contact pairs and repeated contact pairs can be quickly excluded from the multiple potential contact pairs of one particle according to the relevant judgment conditions. And the Hertz-Mindlin contact model is used in corresponding contact force calculation. As a result, the quick contact search and accurate evaluation of contact force are accomplished. Finally, several numerical examples are presented to validate the accuracy and efficiency of the TSC algorithm in 3D contact analysis, which also demonstrates the advantages of the proposed algorithm in tire-sand interaction simulations. (C) 2019 Elsevier B.V. All rights reserved.