Impact of mapping strategies on rockfall frequency-size distributions

doi:10.1016/j.enggeo.2020.105639

Engineering Geology

Volume 272, July 2020, 105639

https://doi.org/10.1016/j.enggeo.2020.105639 Get rights and content

Highlights

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Rockfall frequency-size distributions are used in Austria for the definition of a design block
•
Mapping strategies have an impact on rockfall frequency-size distributions
•
Comparing rock types, the variations of ECDF within and among the catalogues become evident for larger percentiles
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Frequency-size distribution for design block analysis have to be used with caution, especially for the larger percentiles
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Inferential statistical parametric and non-parametric tools are needed to cope with small datasets and close data gaps

Abstract

Rockfall frequency size distributions are used in Austria for the definition of a design block for the planning of technical rockfall protection. Rockfall size datasets are often incomplete. Here, we study fifteen catalogues of rockfall size in Austria, Italy, and the USA to analyse the impact of the data collection and mapping methods on the representativeness of the catalogues and on the estimates of frequency-size statistics. To describe and compare the catalogues of rockfall size, we first use Empirical Cumulative Distribution Functions (ECDFs), followed by parametric distribution estimates in the form of Probability Density Functions (PDFs), and Cumulative Distribution Functions (CDFs). We discuss the output of Kolmogorov-Smirnov tests, the position of the frequency-size distribution rollover, and the p-value and the standard errors associated to the distribution parameters estimates to determine the reliability of our model results. In addition, we analyse the variations in the modelled CDFs for different percentiles of the frequency-size distributions to describe and discuss the representativeness of the rockfall catalogues. Our results show that different mapping strategies may affect the estimates of frequency-size distribution of rock fall volume, a relevant information when evaluating the possible impacts of rockfall processes. We conclude offering recommendations for rockfall mapping, and the use and of a non-parametric statistical method being capable to deal with small datasets, which is very typical when dealing with rockfall data. Such recommendations help for a correct dimensioning of designing rockfall mitigation measures.

Introduction

A rockfall is a type of extremely rapid mass movement characterized by a potentially long travel distance from the release (source) to the deposition area. Local rock properties and slope geometry condition the rockfall behaviour, making it difficult to prepare rockfall inventories with consistent and comprehensive spatial and temporal information. Methods used to collect information on rockfalls depend on the size and complexity of the study area, and on the scope and the resources available for the investigation, and include (i) field mapping, (ii) systematic search of archives, chronicles, newspapers and technical and event reports, (iii) visual inspection and in-situ monitoring of rock cliffs, (iv) interpretation of remote sensing imagery or photogrammetry, and (v) rockfall dating techniques.

In the literature, different statistical methods were proposed to analyse spatial, temporal, and size information of rockfalls. Implicitly or explicitly, all methods require “completeness” and “representativeness” of the rockfall catalogues and series (Corominas et al., 2017a; De Biagi et al., 2017b, De Biagi et al., 2017b; Malamud et al., 2004; Rossi et al., 2010). However, determining the level of completeness or the representativeness of the catalogues and time series is not trivial, and this can jeopardize the significance of the statistical analyses performed on the rockfall records.

Published rockfall statistics are rare, covering mostly small areas (slope scale) and short time periods, and are focused mainly on volume-frequency analysis or for the definition of a “design block” (Agliardi et al., 2009; Brunetti et al., 2009; Corominas et al., 2017a, Corominas et al., 2017b; Crosta et al., 2015; De Biagi et al., 2017b; Dussauge et al., 2003; Dussauge-Peisser et al., 2002; Guzzetti et al., 1994; Lambert and Bourrier, 2013; Lari et al., 2014; Macciotta, 2014; Malamud et al., 2004).

In this work, we analyse 15 catalogues with information on the size of rockfalls obtained using different mapping methods for seven study areas in Austria, Italy, and the USA. We compare the rockfall information, and we discuss the impact of the different mapping methods on the quality, representativeness, and completeness of the size distributions of the rockfalls.

Different statistical approaches are introduced and exploited to estimate frequency-size rock fall statistics. The advantages and limitations of the different approaches are presented and discussed providing a guidance for their proper usage and promoting standard and comparable procedures to analyse frequency-size rock fall statistics for the definition of a design block, which is a fundamental part when it comes to the planning of technical rockfall protection measures.

Section snippets

Definitions

In this work, we define a “primary rockfall” a rock that detaches from a rock wall or rock outcrop by sliding, toppling or falling, and a “secondary rockfall” the remobilization of a previously deposited (rockfall) boulder, typically on a slope. After detachment, a rock either falls along a rock wall or moves along a slope by bouncing and flying along ballistic trajectories, or by rolling and sliding. A rock may fragment into individual rockfall boulders impacting the ground and/or trees. The

Rockfall data sets

We used 15 catalogues listing rockfall volume in Austria, Italy, and the USA, to analyse the impact of the mapping methods on the quality, representativeness, and completeness of the size distribution of the rockfalls. Some of the catalogues are parts of comprehensive rockfall inventories comprising detailed information about other relevant rockfall features. Different mapping methods and strategies were adopted to collect the rockfall data in the different catalogues (Table 1).

Statistical analysis

We first use the

Results

To identify the factors influencing the volume size distribution we considered factors such as (i) lithology and the structural setting (catalogues C_UM, C_BB, C_OM, C_BT, C_H, C_YV), (ii) the position of the rockfalls on the slope (catalogues C_H4, C_H6 and C_H7), (iii) topographic factors, including slope geometry, and the presence of lakes and rivers at the bottom of the slope (catalogues C_H2 and C_H4), and (iv) possible human influences, including e.g., removal of boulders by local habitants.

Discussion and conclusions

We analysed fifteen catalogues listing information on rockfall size in Austria, Italy, and the USA with respect to the impact of mapping strategy i.e., choice of mapping method and data source. Results showed that specific factors have an impact on frequency-size distributions of the rockfalls. These factors should be considered when planning and conducting data collection campaigns i.e., the definition of a “boulder scenario” (or design block). The main results of this work can be summarized

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The Geological Survey of Austria is thanked for supporting S.M. during the paper completion also after leaving the Geological Survey. Special thanks to the National Park Service, CA, for the Yosemite rockfall dataset.

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They are often based on one or several scenarios which represent estimates of different event magnitudes (release volumes) and return periods, based on geological surveys of the rock cliff and (scarce) inventory data. In the past, a few analyses of rockfall frequencies based on long-term historical inventories have been published (e.g., Hungr et al., 1999; Dussauge-Peisser et al., 2002; Eckert et al., 2020; Melzner et al., 2020). De Biagi et al. (2017) combined the analysis of available historical data with a survey of detached blocks in a probabilistic method to determine the rockfall magnitude-frequency relationship.
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Magnitude may vary in a wide range of volumes, from cubic decimeters to millions of cubic meters (Hungr et al., 1999). Melzner et al. (2020) also investigated frequency–size distributions, finding a dependence on the method used to map rockfalls and, similarly to Corominas et al. (2018), recommended caution when considering the large–size region of the distributions. We did not consider the magnitude of rockfalls, here, as the model STONE does not directly account for that.
Rockfalls pose a substantial threat to ground transportation, due to their rapidity, destructive potential and high probability of occurrence on steep topographies, often found along roads and railway routes. Approaches for the assessment of rockfall susceptibility range from purely phenomenological methods and statistical methods, suitable for modeling large areas, to purely deterministic ones, usually easier to use in local analyses. A common requirement is the need to locate potential detachment points, often found uphill on cliffs, and the subsequent assessment of the runout areas of rockfalls stemming from such points.
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Impact of mapping strategies on rockfall frequency-size distributions

Highlights

Abstract

Introduction

Section snippets

Definitions

Rockfall data sets

Statistical analysis

Results

Discussion and conclusions

Declaration of Competing Interest

Acknowledgments

Earth Sci. Rev.

Eng. Geol.

Eng. Geol.

Technical Protection Against Rockfall - Terms and Definitions, Effects of Actions, Design, Monitoring and Maintenance. (Technical Guide)

Integrating rockfall risk assessment and countermeasure design by 3D modelling techniques

Nat. Hazard. Earth Syst. Sci.

Pareto Distributions

Chapter 7: Pareto and generalized Pareto distributions

Probability distributions of landslide volumes

Nonlinear Process. Geophys. Gottingen

Assessment of the hazard from rock fall on a highway

Can. Geotech. J.

Magnitude and frequency relations: are there geological constraints to the rockfall size?

Landslides

Rockfall occurrence and fragmentation

Key issues in rock fall modeling, hazard and risk assessment for rockfall protection