Energy absorption of trees in a rockfall protection forest

In mountain areas rockfalls are frequent events. Their unpredictability, in terms of frequency and magnitude, determines the potential hazard for humans, settlements, and infrastructure in these areas. Different artificial protection methods against rockfall exist, such as barriers and restraining nets. However, a natural form of protection is provided by the forest growing on mountain slopes. The difficulty when regarding the forest stand as a protection barrier against rockfall is to assess and predict its protective effect. The aim of this study is to develop a numerical model that can be used to estimate the energy absorption capacity Ecap of a single tree during a rockfall. These values can thereafter be implemented in a coupled rockfall singletree model, which can then be used to study the protective effect of the forest. The rock-tree interaction was investigated with full-scale impact tests, which simulated a rock impact on a Norway spruce tree (Picea abies (L.) Karst. ) in its natural environment. Every test was monitored with high-speed cameras and accelerometers and provided information about the behaviour of the tree structure during a rock impact. The complex interaction between a rock and a single Norway spruce tree was then simulated using the finite element method. Despite the large natural variations in the wood and the soil material properties, as well as the complex interaction between single roots and the surrounding soil; the numerical singletree model (NSTM) developed gave results, which agreed well with the full-scale impact tests. These tests were performed with a lower energy than the one required for a rock to penetrate through the tree stem. In order to validate NSTM for higher energy levels, full-scale rockfall experiments performed at Cemagref in Grenoble on Silver fir trees (Abies alba) growing on a natural slope were used. Even though these trees are much related to Norway spruce trees, neither the material properties nor the size of the root-soil plate are the same. However, comparing the experimentally obtained energy absorption capacity Ecap with the calculated values, an excellent agreement was obtained. Using NSTM and performing parameter studies with a spherical rock, the energy absorption capacity Ecap could be predicted as a function of diameter at breast height DBH and the position of the impacting rock in terms of impact height above ground level Himp, eccentricity with respect to the tree center line χ, and impact angle αimp. Using only the size of the tree in terms of DBH as previously done to define Ecap is insufficient as Ecap also depends on the position of the impacting rock. Furthermore, the tree stem and the root-soil system absorbed different amounts of energy. When simulating the full-scale impact tests, it was found that about 2/3 of the initial kinetic energy was absorbed by the tree stem and ∼1/3 by the root-soil system. However, this relationship seems to be dependent upon the impact velocity vimp and the shape of the impacting object. For a spherical rock with diameter 1.45 m impacting the tree with 24 m/s, about 4/5 of the energy was absorbed in the tree stem. Both cases show that the tree stem is the most important factor for the energy absorption capacity. In order to study the protective effect of damaged trees, a series of computations were carried out assuming the inner part of the stem to be hollow. Removing a circular inner part of the tree stem with a diameter corresponding to 50% of the tree stem diameter