Reliable estimates of the kinematic characteristics of movements are obtained by using a statistical model SSM. This model represents a useful tool for the management of alert and alarm systems.

L'elaboration des donnees du deplacement median d'un modèle statistique SSM opportun fournit des estimations fiables des caracteristiques cinematiques du mouvement. Le modèle peut être ainsi utilise pour la gestion des systèmes d'alarme.

Die Bearbeitung von Bewegungsdaten anhand eines geeigneten statistischen Modell SSM ergibt vertrauliche Abschatzungen der kinematischen Eigenschaften der Bewegung. Das Modell kann also fuer das Management von Alarmsystemen verwendet werden.

Introduction

The widespread use of automatic monitoring systems for the purpose of measuring slope displacements has been increasing with the development of electronic technology. Extensometers are usually set up to monitor ground displacement, while in-situ inclinometer probes as well as Time Domain Reflectometry (TDR) are largely used to detect the soil failure zone and to study the evolution of deep displacements with time. Measurement of displacements is pursued for two main objectives. Firstly to detect which are the triggering factors and how they govern the slope movement; secondly to design and manage alert and alarm systems needed to reduce the risk of human fatalities. Accordingly, the displacement monitoring systems are usually integrated with other devices capable of giving information on the triggering factors. For example, for rainfall induced landslides the most used devices are rainfall gauges and pore pressure transducers, as they provide useful data to evaluate the decrease/increase in pore pressures.

Displacements and displacement patterns of landslides are highly variable in time and space, and a unique approach cannot be defined to model landslide movements. Nevertheless, past analyses giving insight into the movement of reactivated landslides all assume nonlinear viscoplastic behaviour of the soil involved in the failure process [Skempton et al., 1969; Iverson, 1986; van Genuchten, 1990]. Accordingly, the shear strength depends on the shear strain rate that is strictly related to the velocity v of the landslide. For a one-dimensional problem it can be written as

(Equation in full paper)

The foregoing models of analyzing landslide evolution and predicting time of failure are based on a knowledge of the kinematic characteristics of the movement, such as displacement, velocity and acceleration. These could be determined through differentiation with respect to time of the displacement data recorded by an automatic monitoring system, but care is needed when the accuracy of the instrumentation is comparable to the size of the displacements. In fact, if this is the case, the calculation may provide unacceptable results, and a statistical analysis is preferable.

The aim of this paper is to propose a statistical approach using a State Space Model for analyzing the time series of displacements of slow landslides. An application to the in-place inclinometer data from the Castelrotto landslide in northern Italy is also given.

Processing of displacement data

Data recorded by automatic displacement monitoring systems generally consist in measures of an electrical signal, such as the voltage, which may be related to displacement through a calibration curve.

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