Simulation of Rockfall protection nets with hard
frictional constraints and elastoplastic elements

The importance of rockfall protection barriers, such as ring nets, is increasing significantly in the context of the ongoing climate crisis and global warming. Rising temperatures lead to a growing risk of rockfall, as seen in catastrophic events like those in Blatten or Brienz, but also in smaller-scale incidents such as rocks sliding down meadows. At the same time, alpine regions are being used more intensively for tourism, agriculture, industry, and infrastructure development. This intensified use contrasts with the growing effort required to ensure the safety of railways, roads, settlements, and hiking paths—without even considering large-scale events in which entire mountain slopes are literally collapsing due to melting permafrost, water freezing in rock fissures, glacier retreat, and the resulting changes in the alpine ecosystem.

Among other necessary and sensible protective measures, rockfall protection nets represent a practical and environmentally compatible solution. They can be installed with relatively little intervention in the ecosystem, as they do not block natural water flows, while effectively protecting people and infrastructure from rockfall events.

Developing a reliable simulation framework for modeling these nets supports both research and practical engineering applications. Such simulations can reduce the number and cost of largescale physical tests, improve understanding of energy absorption and structural requirements, and support optimized net design. It is therefore desirable that the underlying model achieves a high level of accuracy while maintaining acceptable computation times.
An established approach to achieve these objectives, is a four node discretization of the rings, consisting of nodes and scalar force elements. This discretization offers the advantage that contact interactions between rock and net simplify to well-defined and computationally efficient cases, depending only on the modeled rock geometry—for instance, phere-to-node or convexbody-to-node contacts. These interaction types are well known and widely used in contact mechanics and physics-based simulation.

The one-dimensional force elements must represent the dissipative effects of the net deforming elastoplastically under load. To ensure a reliable and efficient evaluation, a formulation based on nonsmooth dynamics is implemented, supplementing the normal and frictional contact laws with corresponding impulse formulations. In its simplest form, such an elastoplastic element consists of a spring in series with a friction element, yielding ideal elastoplastic behavior. Extensions of this model include isotropic hardening behavior and unilateral element formulations.
Additional components of ring net systems that must be considered include the overall suspension structure, typically consisting of supports or rods to which the net is fastened with cables or ropes, as well as dissipative elements such as braking devices. These braking elements are installed between the cables and their anchoring points on the ground, further enhancing the system’s energy absorption capacity and overall performance.