## 1 Introduction
As a result, the application of stepped temporary support is limited to a specific range of roof conditions. To address the applicability requirements of stepped temporary support for the roof, this research employs numerical simulation methodology based on the principles of stepped temporary support. It investigates the repetitiveness of support for various roadway roofs and establishes the applicable scope of stepped temporary support for roof conditions. The outcomes of this study effectively address the essential challenge faced during the practical implementation of stepped temporary support. Currently, numerous researchers and institutions have conducted extensive studies on temporary support and numerical simulation of tunnels. Geological conditions in many coal-producing countries, including Europe and America, are generally favorable, displaying robust stability of tunnel roofs and floors. Consequently, the adoption of integrated cutting and anchoring units, which obviate the need for temporary support, has become commonplace, resulting in limited research regarding this aspect. Reverberating studies chiefly concentrate on China, which possesses tunnels characterized by distinctive features and intricate geological conditions. [PERSON] [9] proposed a self-moving auxiliary support device in which two brackets mutually provided support, and self-movement was achieved through a displacement cylinder. [PERSON] et al. [10] introduced a temporary support device that follows the tunneling machine, establishing contact with the tunnel roof through a staggered bracket work structure. It successfully accomplished tasks such as installing mesh anchors for permanent support. [PERSON] [11] presented a temporary support device suitable for fully mechanized drivage. By utilizing alternating main and auxiliary support groups, it effectively supported the tunnel roof and achieved autonomous movement in a step-like manner. [PERSON] et al. [12] presented a temporary support scheme specifically designed to meet the mechanical requirements of the surrounding rock support system in the working face. They conducted an analysis of the mechanical characteristics of a self-moving temporary support and designed it accordingly. [PERSON] et al. [13] proposed a collection of robotized self-moving anchor support units. They established a mechanical coupling model of the surrounding rock of tunnels and advanced support brackets, using the Qishan Mine as an exemplar. By employing the finite element method, they analyzed the stress distribution and strength of the self-moving advance support unit. [PERSON] et al. [14] studied the stress distribution, deformation, and failure characteristics of the surrounding rock at the tunneling face through numerical simulation. [PERSON] et al. [15] developed advanced non-repetitive mechanical movement support equipment and conducted an analysis on support timing and strength verification. Through analysis of existing research, several scholars have proposed temporary support equipment for tunneling faces using a stepping support approach. However, the reliability and practicality of this equipment are limited. Furthermore, while some scholars have conducted numerical simulations on roadways, there is a lack of research on the repeatability of roadway roof support in tunneling faces. To address these gaps, this study focuses on temporary support in tunneling faces. Firstly, we designed and developed a twin-link stepping temporary support equipment to establish a new process that integrates excavation, temporary support, and anchor support operations. Secondly, to assess the suitability of stepping temporary support for the roadway roof, we constructed a numerical model of the stepping temporary support operation based on the principles of stepping temporary support and utilized 3 DEC software.