# Reinforced Drapery Meshes: A Design Method Accounting for Retaining Ropes Contribution
## 1 Introduction  
Rockfall constitutes one of the most hazardous landslide phenomena and can cause fatalities and damages [1, 2, 3]. For this reason, preventive and protective structures are installed to reduce rockfall risk in inhabited areas. Among them, reinforced drapery meshes, subdivided into secured or pinned draperies, represent an effective solution for minimizing rockfall risk, especially for vertical rock faces overhanging road infrastructures [4, 5]. The system consists of steel wire mesh panels and a systematic anchoring pattern, which directly acts on the stability of the rock surface [6, 7]. In secured Drapery, the anchors, whose pattern can be squared or quincunx-like, are connected to each other and to the net through ropes, forming a rhomboidal or square rope grid. The ropes are generally connected to the heads of the anchors, equipped with eyebolds or plates, proceeding from top to bottom, as seen in Figure 0(a). Alternatively, if no ropes are installed (pinned drapery systems), spike plates, which fasten the anchors and the mesh to the rock, are used, as shown in Figure 0(b). This structure is able to control the movement of rock blocks and fragments by confining small detached fragments into delimited sections of the mesh. The net can be made up of single-torsion or double-twisted steel wire mesh or of several types of fabric, such as a cable net, in which the cables are fixed to each other with studs or wire threads. As a result of the increasing usage of this system due to its low cost and ease of installation, recent studies have aimed to investigate the most appropriate design method [8, 9, 10], either with numerical methods [11, 12, 13, 14] or with real-scale tests [15, 16, 17, 18]. The scientific literature also includes numerical studies on the net component only [19, 20, 21, 22]. Despite being widely used, no universally recognized guidelines or technical standards exist for the design of reinforced drapery systems [15], and the mechanisms of preventive/protective rockfall mitigation measures are still debated today [8]. As an example, [PERSON] and [PERSON] [14] subdivided reinforced drapery systems into two categories according to the scope: the prevention of the detachment of unstable single rock blocks, and the retention/stabilization of shallow portions of weathered rock or soil slopes. The former task is generally achieved by using rock bolts, i.e., a passive system; in the framework of the latter case, [PERSON] et al. [10] assumed that the system is active, i.e., that the mesh can exert pressure normal to the slope, and the anchors have an initial pretension. Focusing on rock slopes, a different approach was proposed by [PERSON] et al. [23]: the anchors, acting as a passive system, should prevent the destabilization of a shallow superficial layer of weathered rock (thickness \(\leq\) 3 m), considering that, even if a tightened force is applied to the anchors, this force does not usually exceed 50 kN. This system adopts membranes that are not pretensioned during installation. Furthermore, uncertainties linked to the utilization of an encoded design procedure are also related to the loading conditions [24], i.e., snow and debris, to the influence of the mesh, to the friction at the interface between the slope and the mesh, and to the possibility of the accumulation of rock fragments [6; 17]. It is worth mentioning that current engineering practice adopts the limit equilibrium for the design of either active or passive reinforced drapery systems. The present paper focuses on secured drapery systems specifically for rock slopes, with particular reference to the effectiveness of the ropes. The mesh retaining action is progressively activated, and its stabilizing action is strongly related to its deformation [25], whose value is a function of the load induced by the detached rock fragments or small blocks. Consequently, the mechanical resistance of the mesh is linked to its puncturing (i.e., punching) force-displacement behavior.