# Effect of the Umbrella Arch Technique Modelled as a Homogenized Area above a Cross Passage
## 1 Introduction  
Cross passages are an important component of an underground structure: they are built at regular intervals for requirements such as safety, maintenance, emergency, passenger evacuation, and ventilation. These structures have a small cross-section, shorter length, and lower stiffness. Nevertheless, several studies have shown that the opening of these galleries frequently causes displacements and deformations in the main tunnel lining as well as in the ground surface. Maintaining the stability of the cross passages is of paramount importance. Therefore, it is often necessary to reinforce the soil prior to excavation. Depending on the geological conditions, various soil reinforcement techniques can be incorporated. In particular, the use of pre-support methods, including the umbrella arch method (UAM), jet grouting, mechanical pre-cutting and sub-horizontal fibreglass face reinforcement could keep the tunnel face stable in soft grounds. This paper focuses only on the implementation of the Umbrella Arch Method (UAM) pre-support in cross-passages, and other reinforcement techniques are outside the scope of this research. The umbrella arch technique or the pipe roof support system Figure 1 can be defined as an implementation of steel pipes or fibreglass pipes from the actual tunnel face to the front in an umbrella or canopy shape around the area to be excavated [1]; the pipes have an average length of 12 to 15 m, and an outer diameter varying from 70 to 200 mm. Steel pipes are typically installed at a 5 to 10 degree angle to create a sort of \"umbrella\" over the ground to be excavated [2]. The pipes will eventually be executed with advances that guarantee the necessary overlap for the stability of the tunnel face. The pipe umbrella method is installed in two different ways: predrilling and cased drilling [3]. Regarding the design parameters associated with the umbrella arch elements, numerical simulations using 2D and 3D models, in addition to analytical models, were performed by some research studies to better understand the influence of design parameters on the forepole elements used in an umbrella arch system. [PERSON] et al. [4] have contributed to the understanding of the influence of design parameters on umbrella vault elements. The authors used 2D finite element software using a homogeneous reinforced zone, and 3D finite difference software using structural elements to capture the behaviour of the tunnel front failure as a function of the following parameters: spacing, length, overlap, coverage angle, size, and angle of installation. Another study using an analytical approach was presented by [PERSON] et al. [5], the authors concluded that the diameter of a single umbrella element is more effective than the adjacent distance between elements to control tunnel displacement. In reviewing the literature that covers the umbrella arch method (UAM), it is notable that the performance of this type of pre-support has been consistently discussed by many authors, many of whom agree that the UAM has an efficient effect on the stability of the tunnel face in difficult ground conditions. [PERSON] and [PERSON] [3] proved that tunnel excavation under the umbrella support results in lower settlements, especially at the beginning of each pipe roof umbrella field. In the same context, an interesting study was conducted by [PERSON] and [PERSON] [6] by performing a series of centrifuge tests in unsaturated sands. The analysis of the results obtained showed that the application of the umbrella vault pre-support reduces the maximum settlement of excavated ground by full face to about a quarter of the non-pre-supported value under the same experimental conditions. Another study using the same type of analysis was conducted by [PERSON] et al. [7] and proved that the length of the forepole element has an influence on the tunnel stability. By comparing the numerical analysis with the results of real measurements, ref.