Γεωστατιστική ανάλυση των μετρήσεων στη γεωτεχνική μηχανική

Abstract

Instrumentation for monitoring geotechnical projects during construction and operation is an interesting approach for geomechanics, since it contributes to a deeper understanding of field performance, especially the last decades that instrumentation is combined with continuous technical evolution. However, quite often, the restricted number of available measurements, the collapse of some instruments and the effect of measurement errors introduce uncertainties in the way the variable under study distributes in the field. The variable under study can be estimated in the field through the use of the principles of geostatistics. Indeed, geostatistical analysis estimates the spatial variable and the estimation error based on the measurements and thus, it can quantify the uncertainties. It is worth mentioning that, even though geostatistics can be applied to any spatial variable, this work is focused on ground movements, that is one of the most important and most commonly measured variable in geotechnical projects. So, the need for a profound study concerning the applicability of geostatistical analysis in geotechnical issues arise, regarding both the movement estimation on the field and the optimum layout of the movement monitoring network. The main test site for the study was landslide S2, a small size landslide in flysch, where the movements of the ground surface were recorded by topographic methods. The first part of the study concerned the necessity to treat the landslide field as a whole or to separate the field in areas of big and small movements. It was made certain that separating the field produced better results. The separation was based on the landslide limit, which is known from the field investigation. Also, a new method is proposed for determining the landslide limit, independently of the field investigation. The method consists of determining the point of greater change in the movement estimation along lines perpendicular to the landslide direction. Also, the ability to adopt geostatistical analysis in cases like S2, where the monitoring network is restricted, is tested. To face the measurement parsimony, two decision maps were compiled and applied. The geostatistical analysis in movement measurements in S2 in multiple time steps showed that the normalized variograms coincided. Indeed, variogram describes the relation among measurements and since the spatial variable in this case is ground movement, then the variogram reflects the relative movement among measurement locations. So, by definition, changes in the landslide mechanism can be traced through changes in the normalized variogram of ground movements. Lastly, the effect of different measurement errors on the movement estimation as well as on the optimum layout of the monitoring network was studied. The Monte Carlo technique was introduced to the geostatistical analysis (development of MC1 methodology) and applied to case S2. The two variogram models used (linear and Gaussian) showed small sensitivity to measurement errors. For the case of the linear variogram, small coefficients of variation of estimation and of MSE were observed in the majority of control points in the field. When the Gaussian model was adopted, the effect of measurement errors in both estimation and MSE increased. The small variability of the variogram parameters combined with the great computation cost of MC1 resulted in the development of the simplified methodology MC2, which is based on the assumption that the variogram remains constant - and equal to the variogram when no measurement errors are considered (analysis MC0) - throughout Monte Carlo iterations. According to this assumption, the equations that produce the estimation and the MSE are considerably simplified, leading to the result that these are equal to the estimation and the MSE of the MC0 analysis. So, the results of MC2 methodology are based on only one geostatistical analysis, eliminating the need for multiple time-consuming iterations. MC2 methodology can be used instead of MC1 when measurement errors do not affect variogram shape. Otherwise, MC2 results decline from MC1 results as the coefficients of variation of variogram parameters increase.