Modern methodologies for deformation measurements and landslide movement control

Transcription

1 Modern methodologies for deformation measurements and landslide movement control M. Caprioli & G. Strisciuglio Dipartimento di Vie e Trasporti, Politechnic of Bari, Italy Abstract The paper describes how to use the modern techniques of surveying founded on the GPS satellite systems and digital high precision levelling for the planning and the realization of control networks, as well as how to define a method to calculate deformations in the presence of small horizontal movements or vertical sinkings, based on the Bayesian inference and on the Kalman Filter. The Bayesian approach is finalized to the interpretation of the spatial and temporal variations of the deformations, the Kalman Filter to the measurement of the real time deformations of a network. Nowadays it is possible to realize the integration between digital high-precision levelling, useful in calculating altimetric variations in the control networks, and DGPS-RTK methods for planimetric surveying in real time. Keywords: landslide, deformations, GPS, DGPS-RTK, GSM, digital high precision levelling, Bayesian inference and on the Kalman Filter, error ellipse, control networks. 1 Introduction The problem of controlling some civil engineering works consists of evaluating any special movements of a certain number of points belonging to the work as accurately as possible. The aim is to remove the inevitable errors, which may be reduced and even eliminated by adopting operative/calculation methods. It will be appropriate to use methods which permit the influence of some causes of systematic error to be eliminated by difference in that they provide for the repetition of the measurements in the same conditions.

2 278 Risk Analysis IV According to their reference system the movements are divided into absolute (variation of position) and relative (shape changes or creeping ). Figure 1: Landslide surface. In the monitoring of the deformations it s necessary a double measurement, in the way to calculate the points position or the surface shape at the beginning and at the end of the considered period. The two survey operations must have conducted with such an accuracy to draw, from the mutual comparison, the measure of the movements. This is possible only when the value of the same overcomes the measurements uncertainty. The comparison of measurement campaigns carried out at different epochs leads to detecting of the movements field. The performance of a control campaign requires the following phases: planning the operation to acquire all the data in order to estabilish the fundamental parameters, performing the survey operations, data processing. It s important to verify, with opportune techniques, the reliability of the gotten results so that to give the opportune weight to the determined movements. In this way it s possible to avoid to consider as movement or deformation what it could be an error of measurements. In the calculation they are considered all the measurements, conducted during different epoches. 2 Theory In the phase of treatment of the observations it can result very useful to adjourn a least squares estimation, after the introduction of new observations effected during following surveys, without calculating again the whole system (Kalman Filter analysis). The Kalman Filter has been a useful tool for many years in geodetic field, but today it assumes great importance due to the development of the modern techniques for real time survey.

3 Risk Analysis IV 279 The Kalman Filter is born as a non-static approach unlike the least sequential squares: to every epoch, in fact, new observations and new unknown dependent parameters are added with a certain law by the preceding parameters. The updating consists in studying the variations of these parameters during the time. Figure 2: Error ellipse in a control network. The Filter results essential for the control of the data and the measurements in real time; in such way it s immediately possible: - to remove wrong measurements that could influence negatively final results; - to underline meaningful movements/deformations. The Filter foresees two procedures: - filtering: determination of the best value of the parameters at the current measurement epoch - smoothing: best value of the parameters of the preceding epoches. The first one allows to determine the parameters, actually, making use of all the information, beginning from the first epoch to the epoch in examination. The second, after having finished all the measurements, it allows to determine the solutions of the preceding epoches keeping in mind of all the finished measurements, reaching the solution that would be had using the least sequential squares. The filtering is fundamental for the control of the real time data, the smoothing for the post-processing ones. In the phase of treatment of the observations it can result very useful the insertion of an hypotetical direction for the movements (theorem of Bayes). The Bayesian approach, allows, advance in comparison to the traditional techniques:

4 280 Risk Analysis IV - to draw the deformations of the control network; - to remove the gros errors ; - to underline the movements of the same topographical network. It results essential to know previously a series of informations. We suppose to have a field of movements coming from the calculation of the network in different times effected with the method of the least squares estimation: from the theory we know that the field follows a normal distribution characterized by an average, by a variance and by a variance - covariance matrix. In the hypothesis of incorrelation of the information, this matrix results to be a diagonal matrix proportional to the identity. Initial information allows to define previously the model: this the starting point of the Bayesian theory. The final function, that represents the new level of knowledge after the effected measurements, is directly proportional to the first function, that represents the state of knowledge before the execution of the survey, and to a likelihood function representative of how the same observations influence the system parameters during the time. It s possible to suppose, therefore, that, after having individualized a group of points of homogeneous behavior, can be reached knowledge of the direction and the verse of the movement. In this way, unmeaningful movements of opposite verse could be eliminated. In the classical inferential methods, this is very complex: it s not simple to individualize a preferential direction of the movement. Increasing the number of dimensions of the known parameters, hypotheses are even stronger thin to reach the chance to evaluate the three-dimensional position of every single point in the select reference system. 3 Modern topographical methods The utility of the two methods could find maximum application in the elaboration and in the interpretation of the results coming from a geodetic control network realized for the monitoring of horizontal movement of landslide and/or static-structural deformations of large structures. Topographical methods to determine movements may be divided into determining vertical movements and/or horizontal ones with methodologies which mainly refer to one of them and also with appropriately decide upon techniques for determing both. The operational phases of the survey are the followings: - planning of network; - materialization of the points of station/control; - execution of the measurements (manuals / automatic); - calculation of coordinates; - average speed of the movement (only in the periods in which the landslide movement is sufficiently homogeneous). The project of network requests a defined accuracy and a defined reliability.

5 Risk Analysis IV 281 Figure 3: GPS control network. The techniques to reach such results are various and they must be studied according to the objective, in such way to be optimized the survey and to get the pre-defined accuracy in the most economic way. Historically the measurement of the horizontal movements is made with triangulation, trilateration, poligonation and the other classical topographical operations, while the measurement of the vertical movements with the high precision levelling. Today, the development of the technology at support of the survey makes it possible the realization of one planimetric/altimetric network realized with traditional and satellite measurements and high precision levellings. The advantages in the use of the GPS are different, above all considering the: - worldwide availability of GPS signal; - increasing of baselines length; - the visibility is not requested; - chance to realize 3D networks; - chance of indipendence between the network configuration and the reference system; - elaboration in DGPS-RTK ; - support to the decision making (allarm signal). Above all, this last aspect could reveal innovative and of fundamental importance, after the last catastrophic events those have struck our territory. With DGPS is possible to transform the absolute positioning of a point (fixed or mobile) in a relative positioning in comparison with another that can be considered fixed and of known coordinates. With DGPS-RTK the correction is directly effected during the survey, using the connection between a GSM modem provided of a SIM card for data transmission and GPS device with external antenna, in this case the ambiguities are fixed in very small times with the attainment of sub-centimeter accuracy.

6 282 Risk Analysis IV Figure 4: GPS software for post-processing elaboration. Figure 5: DGPS-RTK system. The advantages, now consolidated, of the digital high precision levelling are instead: - sub-millimeter precision (tenths of amillimetre); - extreme accuracy; - simplicity of planning and realization of the network; - simplicity of execution of the measurements; - simplicity of the survey tools;

7 Risk Analysis IV simplicity of calculation and compensation due to the linearity of the mathematical model; - automatic recording and memorization of raw data during the survey. In levelling networks the measurements are always hyper determined in order to reach an evaluation of uncertainty and of the calculation of the rms of the measured sizes. Measuring vertical movements, for which the reference direction is already known, provides more simple than determine the direction which characterize horizontal movements. The limited distance between the points means that errors caused by atmospheric refraction can be kept down. At the end of all the survey operation, with an abundance of measurements and the consequent possibility of compensation, it s possible to know the error ellipses, the fundamental parameters, the vairations, and the uncertainty of measure. Figure 6: Digital high-precision level and coded staff. 4 Experimental test The experimental test has been conducted on the campaign of the landslide of Serra dell Acquara Vadoncello, Senerchia (Avellino), Campania region, South Italy. The zone is indicated in figure n.7 on the national cartography (IGM 1:25000). They are in course of elaboration and analysis the results coming from more GPS surveys conducted in two different periods (the second six months after the first). During the treatment of the observations, in the first phase, it has been defined the planimetric network and it has been conducted the post-processing elaboration of GPS data. The purpose is to determine the ellipses of error of all the network points of the two phases. After having imported the GPS data, it has been executed the baselines process and therefore the adjustment of the network. The gotten network is rapresented in figure n. 8. The scheme of the network is constituted by six points obtained with static GPS occupation and

8 284 Risk Analysis IV connected to a vertex of the IGM95 network (point indicated with the name IGM1, out of landslide area), considered of known coordinates. In a second phase, it will be effected the nework compensation with the purpose of monitoring the possible movements of the points, analyzing the data using the tools given by the exposed theories. Figure 7: IGM cartography 1:25000 with the landslide area. 5 Conclusions Figure 8: The experimental test network. The possiblity of integration between modern techniques of planimetric and altimetric survey and the elaboration using Bayesian approach and Kalman Filter allow to reduce the limits in 3D point positioning, obtaining sub-millimetric accuracy. The evaluation of control costs becomes secondary if compared to the safety of the works like viaducts, dykes, landslides.

9 Risk Analysis IV 285 References [1] Bagnaschi, L., Application of Adaptive Kalman Filter for the estimation of position, velocity and acceleration of a moving body from GPS measurements, ETH Zurich, [2] Barbarella, M. & Radicioni, F., Kalman Filtering in levelling: an application, Global and Regional Geodynamics, Springer-Verlag, NY, [3] Caprioli, M., Importance and role of the GPS permanent national network for topographic and professional application, ASI-CGS, Matera, [4] Caprioli, M., et al.,experimental test of GPS-RTK measurements with GPS-GSM network by T.I.M. (Telecom Italia Mobile), ISPRS WG VI/3 meeting, Zagreb, Croatia, [5] Gatti, M., GPS data processing in deformation monitoring networks, Bollettino di Geodesia e Scienze Affini, pp , [6] Gruendig, L., Adjustment and design methodology, Deformation Measurements Workshop, MIT, [7] Koch, K. R., Bayesian Inference with Geodetic Application, Springer- Verlag, Berlin, [8] Manzino, A. M., Introduzione al filtro di Kalman in Geodesia, Bollettino SIFET, n 2/2003. [9] Trizzino, R. & Sorgente, M., Ottimizzazione di una rete di controllo GPS per il monitoraggio di una frana, Proceedings of International Conference Prevention of Hydrogeological Hazards: the Role of Scientific Research, Alba, Italy, [10] Pinto, L., et al., Controllo delle deformazioni: un approccio statistico di tipo Bayesiano, Proceedings of ASITA Conference, [11] Radicioni, F., Testing a real-time GPS system for quasi-static deformation monitoring of ground surfaces and large structures, Perugia, [12] Remondi, W. B., Triple difference with Kalman Filtering: Making it work, GPS Solution Vol 3, 58-64, [13] Welch, G., and Bishop, G., An introduction to the Kalman Filter, Siggraph course 8, 2001.