Combining field and modelling techniques to assess rockfall dynamics on a protection forest hillslope in the European Alps

Adequate management of a mountain forest that protects downslope areas against impacts of rockfall requires insight into the dynamics of the hillslope environment. Therefore, we applied a combined approach, using field and modelling techniques, to assess the determining factors for rockfall source areas, rockfall tracks and rockfall runout zones on a forested slope in mountainous terrain. The first objective of this study was to understand why rockfall occurs in the study area. The second objective was to translate the knowledge obtained in the field into a model that simulates rockfall dynamics on a forested slope realistically. The third objective was to assess which hillslope characteristics primarily determine the distribution of active rockfall tracks. To achieve these objectives, we made a geomorphological map of the whole study area, and we measured the major discontinuity planes in the bedrock that are exposed in the rockfall source areas. Furthermore, a test site for simulation modelling within the larger study area was defined in which both a forest and a hillslope inventory were carried out. The available data and our developed rockfall simulation model allowed us to assess the slope characteristics that mainly determine the distribution of areas affected by rockfall. We found that in decreasing order of importance, both standing and felled trees, the surface roughness and rockfall resistant shrubs primarily determine the distribution of rockfall-affected areas. Simulation tests without a forest cover produced similar rockfall runout zones as fossil rockfall events identified in the field. We believe that the combined field and modelling approach is a prerequisite for understanding how forests can protect against rockfall.     

Humic substance charge determination by titration with a flexible cationic polyelectrolyte

The anionic charge of humic substances (HS) plays a major role in the interaction of HS with other components. Therefore, the potential of the polyelectrolyte titration technique to obtain the charge density of HS in simple 1-1 electrolyte solutions has been investigated. Titrations are carried out with an automatic titrator combined with the “Mütek particle charge detector” which allows determination of the Mütek potential and the pH as a function of the added amount of titrant which is a solution of poly-diallyldimethylammonium chloride (polyDADMAC), a cationic strong polyelectrolyte. When the Mütek potential reverses its sign the iso-electric point (IEP) of the polyDADMAC-HS complex is reached. The polyDADMAC/HS mass ratio at the IEP gives information on the HS charge density and from the pH changes in solution an estimate of the charge regulation in the HS-polyDADMAC complex can be obtained. In general, for polyDADMAC-HS complexes an increase in the dissociation of the acid groups of HS is found (charge regulation). The charge regulation decreases with increasing concentration of 1-1 background electrolyte. Cation incorporation can be neglected at 1-1 electrolyte concentrations ? 1 mmol L⁻¹ and a 1-1 stoichiometry exists between the polyDADMAC and HS charge. However, at these low salt concentrations the charge regulation is substantial. A detailed analysis of purified Aldrich humic acid (PAHA) at pH 5 and a range of KCl concentrations reveals that the anionic charge of PAHA in the complex increases at 5 mmol L⁻¹ KCl by 30% and at 150 mmol L⁻¹ KCl by 12%. On the other hand, increasing amounts of K⁺ become incorporated in the complex: at 5 mmol L⁻¹ KCl 5% and at 150 mmol L⁻¹ KCl 24% of the PAHA charge is balanced by K⁺. By comparing at pH 5 the mass ratios polyDADMAC/PAHA in the complex at the IEP with the theoretical mass ratios of polyDADMAC/PAHA required to neutralize PAHA in the absence of charge regulation and K⁺ incorporation, it is found that at 50 mmol L⁻¹ KCl the extra negative charge due to the interaction between polyDADMAC and PAHA is just compensated by K⁺ incorporation in the complex. Therefore, a pseudo 1-1 stoichiometry exists at about 50 mmol L⁻¹ 1-1 electrolyte concentration and only at this salt concentration polyDADMAC titrations and conventional proton titrations give identical results. Most likely this is also true for other HA samples and other pH values. For FA further study is required to reveal the conditions for which polyDADMAC and proton titrations give identical results.     

Mechanical resistance of coppice stems derived from full‐scale impact tests

Broadleaf coppice forests have the capacity to mitigate the threat posed by rockfall in many mountainous regions. Other forest types alike the rockfall protective effect is determined by the mechanical resistance of the coppice tree stems. In addition, the rockfall protective function of coppice forests is enhanced by specific stem aggregations (clumps) that have a rock interception and retention effect difficult to evaluate. The main objectives of this study are to quantify the mechanical resistance of small diameter coppice stems and to gain qualitative insight on breakage behavior. The aim is to supply data for more reliable assessments of the rockfall protective function of coppice forests with rockfall simulation models and to provide a basis for better estimating the rockfall protective effect of coppice clumps. To achieve these objectives we assessed the mechanical resistance of 73 beech (Fagus sylvatica L.) coppice stems using an impact pendulum device. We found an exponential relationship between the stem diameter at breast height (DBH) and mechanical resistance (loss of momentum or kinetic energy of the impactor during impact). Moreover, the results show that the high flexibility of the stems leads to relatively long lasting impacts and only negligible damage at the point of impact on the stem. As a result, the mechanical resistance of the stems is partly determined by impactor velocity and mass. These findings question the practicality of defining mechanical resistance by means of the change of momentum or energy of the impactor. Moreover, the results highlight the limits of upscaling or downscaling the data of this study to conclude for the mechanical resistance of beech trees of other than the tested dimensions. For the target DBH range the obtained dataset is nevertheless more reliable than data of previous studies, because the DBH specific impact process could be considered. Copyright © 2013 John Wiley & Sons, Ltd.     

Rockfall rebound: comparison of detailed field experiments and alternative modelling approaches

The accuracy of rockfall trajectory simulations mainly rests on the calculation of the rebound of fragments following their impact on the slope. This paper is dedicated to the comparative analysis of two rebound modelling approaches currently used in rockfall simulation using field experiments of single rebounds. The two approaches consist in either modelling the rock as a single material point (lumped mass approach) or in explicitly accounting for the fragment shape (rigid body approach). A lumped mass model accounting for the coupling between translational and rotational velocities and introducing a slope perturbation angle was used. A rigid body approach modelling the rocks as rigid locally deformable (in the vicinity of the contact surface) assemblies of spheres was chosen. The comparative analysis of the rebound models shows that both of them are efficient with only a few parameters. The main limitation of each approach are the calibration of the value of the slope perturbation (‘roughness’) angle, for the lumped mass approach, and the estimation of the rock length and height from field geological and historical analyses, for the rigid body approach. Finally, both rebound models require being improved in a pragmatic manner to better predict the rotational velocities distribution. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantifying the protective function of a forest against rockfall for past,present and future scenarios using two modelling approaches

Following a major rockfall event in 1987, two types of protection measures were taken in the village Saint Martin le Vinoux (French Alps). Firstly, technical measures using civil engineering were installed, and secondly, a forest management intervention to increase its protection was carried out. This study aims to assess whether this intervention was successful in the sense that it improved the protective function of the forest. We evaluated the rockfall risk for the situation of 1987 (before the intervention), today and the future, using model simulations with past, present and future vegetation cover scenarios. To increase the meaningfulness of our results, we used two different models, called Rockfor^.NET, which is a rapid one-dimensional rockfall forest evaluation tool, using simple slope and forest characteristics and RockyFor, a process based on three-dimensional rockfall simulation model that takes the barrier effect of individual trees explicitly into account. Both models correctly predicted that the forest was not capable of stopping rocks from the 1987 rockfall event. Further, both models indicate an increase of the number of rocks reaching the base of the slope from 1987 onwards. RockyFor shows an increase from 11% in 1987 to 19% in 2086. Rockfor^.NET shows an increase from 26% in 1987 to 56% in 2086. We conclude that a second attempt to increase the protective function of the forest should aim at restoring a dense coppice stand.     

Toward objective rockfall trajectory simulation using a stochastic impact model

The accuracy of rockfall trajectory simulations depends to a large extent on the calculation of the rebound of falling boulders on different parts of a slope where rockfalls could occur. The models commonly used for rebound calculation are based on restitution coefficients, which can only be calibrated subjectively in the field. To come up with a robust and objective procedure for rebound calculation, a stochastic impact model associated with an objective field data collection method was developed and tested in this study. The aims of this work were to assess the adequacy of this approach and to evaluate the minimum amount of field data required to obtain simulation results with a satisfactory level of predictability. To achieve these objectives, the rebound calculation procedure developed was integrated into a three-dimensional rockfall simulation model, and the simulated results were compared with those obtained from field rockfall experiments. For rocky slopes, the simulations satisfactorily predict the experimental results. This approach is advantageous because it combines precise modelling of the mechanisms involved in the rebound and of their related variability with an objective field data collection procedure which basically only requires collecting the mean size of soil rocks. The approach proposed in this study therefore constitutes an excellent basis for the objective probabilistic assessment of rockfall hazard.     

The use of ballistic trajectory and granular flow models in predicting rockfall propagation

The term rockfall is often used ambiguously to describe various mass movement processes. Here we propose more precise terminology based on the physical nature of the moving mass, differentiating between two distinct types of rockfall: fragmental rockfall and rock mass fall. For both rockfall types, the current knowledge of the mechanisms controlling propagation of the mass movement are described, showing how these mechanisms can be simulated with different modelling approaches. However, we point out that almost no development has been realized concerning dynamic behaviour of the transitional processes between these two end‐member rockfall types. Some simplified means of dealing with these complications are suggested, but we emphasize that a considerable amount of fundamental methodological development remains necessary. Copyright © 2012 John Wiley & Sons, Ltd.     

Error propagation in non-linear delay-time tomography

Delay-time tomography can be either linearized or non-linear. In the case of linearized tomography, an error due to the linearization is introduced. If the tomography is performed in a non-linear fashion, the theory used is more accurate from the physical point of view, but if the data have a statistical error, a noise bias in the model is introduced due to the non-linear propagation of errors. We investigate the error propagation of a weakly non-linear delay-time tomography example using second-order perturbation theory. This enables us to compare the linearization error with the noise bias. We show explicitly that the question of whether a non-linear inversion methods leads to a better estimation of the model parameters than a linearized method is dependent on the signal-to-noisc ratio. We also show that, in cases of poor data quality, a linearized inversion method leads to a better estimation of the model parameters than a non-linear method.