## 1 Introduction
A structural design optimization method was also proposed based on the elastoplastic behavior of the structure [11]. Figure 1: Illustration of the difference between typical QRST and column-free QRST. However, given the inherent limitation of physical tests to cover only specific working conditions, investigations into structural behavior under a broader range of loading scenarios necessitate the use of analytical or numerical modeling [15; 16; 17]. In order to determine the internal force distribution of the DOT tunnel structure, the unbalanced force transition method was combined with the force method to obtain the structural response. The applicability of the proposed method was verified through finite element (FE) numerical models and on-site experiments [18]. For DOT tunnels, the adverse effects on the structure caused by the correction process during the construction phase were investigated with the help of FE numerical models. The corresponding construction recommendations have been provided, as well [19; 20]. For a special-shape shield tunnel lining, a shell-spring numerical model combined with prototype experiments was used to effectively reveal the structural behavior and stagger effect under self-weight conditions and design conditions, providing accurate design parameters [13; 21]. Moreover, in practical engineering applications, designers seek assurance about the ability of simple models, such as the ESHR (equivalent stiffness homogeneous ring) model or the beam spring (BS) model, to yield simulation results with sufficient accuracy to meet design specifications. There is also a growing demand for a thorough evaluation of key design parameters [22]. On the other hand, it is worth noting that an increasing number of constructed tunnels are now exposed to environmental disturbances, such as ground surface surcharge [23; 24], lateral unloading [25], top unloading [26], and adjacent construction activities [27; 28]. Hence, an applicable numerical model can assist operators with evaluating structural performance when confronted with such emergencies. Therefore, in this study, the mechanical behavior of column-free QRST structures is investigated using a combination of prototype experiments and numerical simulations. The subsequent sections of this paper are structured as follows: In Section 2, the test specimen and test setup are introduced; primary experimental results are presented and analyzed; and several optimization methods are also proposed. In Section 3, three numerical models, including the equivalent stiffness homogeneous ring model (ESHR model), beam spring model (BS model), and modified beam spring model (MBS model) are used to simulate structural behavior. A model-based hybrid analysis method is also proposed for analyzing the deformation mechanism of the column-free QRST structure. Finally, in Section 4, the design methodology is investigated using the ESHR model, taking the construction process using a temporary column into consideration. A sensitivity analysis of three load parameters of the structure is conducted, including lateral pressure coefficient, offset load, and buried depth. Some engineering recommendations are also proposed.