Issue 43

A. Luciani et alii, Frattura ed Integrità Strutturale, 43 (2018) 241-250; DOI: 10.3221/IGF-ESIS.43.19 243 The behavior of the cable connected to the energy dissipating device is complex due to the behavior of the energy dissipating device. The cable withstands the force until the activation force of the dissipating device is reached (at about 45 kN in the studied case), then the deformation of the material composing the device starts, and the constitutive relationship is governed by this phenomenon. Once the maximum displacement of the energy dissipating device is reached, the system follows again the cable behavior. To simulate this behavior a tri-linear law was assigned to the material of energy dissipating devices. The first part had Young’s modulus of 63 GPa, the second one had Young’s modulus of 1.4 GPa and the last part had same behavior of the cables, with Young’s modulus of 150 GPa and ultimate stress of 1770 MPa. Also the numerical simulation of the ring net behavior is complex, due to the high number of interactions between the rings that slide and deform during the impact. Therefore, following Nicot et al. [18], the net was modelled with an equivalent hexagonal net, with hexagon sides of 350 mm. Each vertex of the hexagon is the center of one of the six rings connected to the central ring. The interaction between two rings is modelled by the truss elements connecting the vertices. The material assigned to the elements composing the equivalent net had tri-linear behavior, described by three different Young’s moduli. The Young’s modulus of the first part was of 170 GPa, till a strain of 0.001 is reached. The Young’s modulus of the second part was of 4GPa, until a strain of 0.25, and the Young’s modulus of the final part was of 170 GPa. This constitutive behavior was assessed numerically simulating the real scale tests reported by Gentilini et al. [24]. The block impacting the net was simulated as a polyhedral non-deformable element, with the same geometry of that foreseen ETAG 027 standards and the impact speed was of 25 m/s. In the numerical model, the posts were restrained at the base by a cylindrical hinge allowing rotation on the longitudinal axis while spherical hinges simulated anchorages of the cables to the ground and to the top of the posts. The longitudinal cables were free to slide on the top and on the basis of the posts in the longitudinal direction but were constrained in the other directions. In the model, the net was not allowed to slide on the longitudinal cables, differently to what happen in the real net fence. This simplification was necessary in order to reduce computational complexity of the simulation. Fig. 2 illustrates the general sketch of the model. Figure 2: Drawing of the modelled rockfall protection net fence. MEL Test SEL Test Real scale test Numerical model Real scale test Numerical model Breaking time (s) 0.30 0.32 0.26 0.22 Maximum elongation (m) 5.35 5.38 3.90 3.73 Final elongation (m) 4.80 5.05 3.20 3.35 Residual height (m) 3.55 3.34 3.95 3.71 Table 1: Comparison between the real scale test and the results of the numerical simulation. In the simulation the energy level foreseen by ETAG027 standard MEL and SEL tests were performed and the results of the simulations were compared to the data obtained by real scale tests reported by Gottardi and Govoni [11]. As can be seen from Tab. 1, the numerical model well reproduced the results of the real scale tests. In the simulation, the breaking time is evaluated as the first time the velocity of the block becomes zero and the maximum elongation is the maximum distance between the initial position of the net and the position of the net at the breaking time measured parallel to the slope. The final elongation was the same distance evaluated at the end of the test, i.e. at 6 s from the first contact of the block with the net. The residual height is the minimum distance between the lower and the upper longitudinal cables at the end of the test.