, Volume 17, Issue 1, pp 231–240 | Cite as

Sinusoidal wave fit indexing of irreversible displacements for crackmeters monitoring of rockfall areas: test at Pietra di Bismantova (Northern Apennines, Italy)

  • Marco MulasEmail author
  • Martin Marnas
  • Giuseppe Ciccarese
  • Alessandro Corsini
Technical Note


Temperature changes affect crackmeters monitoring on a daily and a seasonal basis. This is due to rock mass thermal dilatancy and to instrumental matters. The consequent widening closing cycles can mask small irreversible displacements that might be precursors of rock failures. Recently, Weber et al. (Cryosphere 11:567–583, 2017) have proposed a linear fit method between temperature and fracture opening in order to compute the irreversibility index as a metrics to rank irreversible displacements. However, such an approach requires temperature sensors coupled to crackmeters. In order to overcome these limits, we propose an alternative method for deriving a normalised Z-score irreversibility index. It is based on sinusoidal wave fit of cracks opening time series only; thus, it does not require temperature monitoring. The methodology has been tested using data recorded by a wireless sensor network installed at La Pietra di Bismantova rock slab composed of 14 crackmeters and thermometers monitoring potentially unstable rock masses. A comparison of results obtained using the method of Weber et al. (Cryosphere 11:567–583, 2017) and the sinusoidal approach shows that the latter is much less sensitive to the duration of the moving window used to derive the irreversibility index, making it a much more flexible tool for indexing irreversible displacements over short time periods. Moreover, as rapid high–magnitude temperature changes can also be the causal factor of irreversible displacements, their statistical relation with peaks of the Z-score irreversibility index has been investigated. Results have shown that, depending on which crack is examined, correlations between irreversibility peaks and antecedent extreme temperature variations are more or less relevant. In conclusion, we believe that the Z-score sinusoidal wave fit irreversibility index (ZSFI) can represent a useful metrics for indexing irreversible displacements in unstable blocks using crackmeters’ datasets affected by temperature cycles at the daily and seasonal scale.

Graphical Abstract


Rockfall Crackmeters Irreversible displacements index Sinusoidal wave fit Northern Apennines 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Chemical and Geological SciencesUniversity of Modena and Reggio EmiliaModenaItaly
  2. 2.Ecole des Mines de NancyUniversité de LorraineNancy cedexFrance

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