Technical Note A method for estimating the accuracy of tunnel convergence measurements using tape distometers Lucia Simeoni à , Luca Zanei Dipartimento di Ingegneria Meccanica e Strutturale, Universita ` degli Studi di Trento, via Mesiano 77, 38100 Trento, Italy article info Article history: Received 23 April 2008 Received in revised form 28 October 2008 Accepted 8 November 2008 Available online 31 December 2008 1. Introduction A 60 km railway near Bolzano in Northern Italy has been re- opened after 15 years of disuse. The railway passes through three tunnels that were built at the beginning of the twentieth century, and were consistently being repaired up until the 1980s. Since 2004, convergence measurements using a tape distometer have been carried out once a year in those tunnels in order to check their stability. Because the movements were quite minimal, a method to assess the accuracy of the convergence measures was needed for recognizing the actual changes in length of the reference points. The accuracy was estimated as the total error calculated by introducing the measurement error, the calibration error and the frame error. When the frame error was calculated for each day of measurements, it was possible to detect changes in line length as small as 0.25 mm. This value is about one half of the change in length that can be measured by using other techniques, such as the Total Station or the digital camera. 2. Importance of accuracy and precision of convergence measurements When planning a monitoring programme, the instrument type and the measurement procedure should be established with reference to the required degree of accuracy and precision. In this paper, following Dunnicliff [1], accuracy is defined as ‘‘the closeness of approach of a measurement to the true value of the quantity measured’’, and precision defined as ‘‘the closeness of approach of each of a number of similar measurements to the arithmetic mean’’. Accuracy is synonymous with degree of correctness; thus it is mathematically equal to error. The measurement may differ from the true value because gross, systematic or random errors have occurred. Precision is synon- ymous with reproducibility and repeatability. If an instrument is not precise a number of measurements should be taken in order to use their mean value; otherwise the error of the measurement will increase. Any measurement should be known with the error it involves, and the error (i.e. the required degree of accuracy and precision) must be less than the minimum level of change of the physical quantity that is monitored. The convergence measurements in tunnels are carried out on cross sections and detect the changes in position of set points on the excavation or lining surface to ascertain whether a state of stable equilibrium has already been reached, will be reached or if instabilities are to be expected [2]. The monitoring data can simply provide information about the tunnelling conditions [3], or may be used in the back analyses to model the soil behaviour and to design the tunnel lining by comparing measurements to the computed behaviour [4–7]. Alternatively, Vardakos and Gutierrez [8] process the convergence measurements with a statistical framework based on the Markov estimator to calibrate the analytical or numerical models. This method requires knowing the value of error (accuracy) for each convergence measurement, and it may be seen as a first and approximate back analysis. The convergence measurements represent the simplest and least expensive operation because no sophisticated instruments need to be installed in the rock. Only simple and inexpensive bolts or targets are fixed to the surface. The three principal instruments used for performing convergence measurements are: the tape or wire distometer, the Total Station and the digital camera. The Total ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijrmms International Journal of Rock Mechanics & Mining Sciences 1365-1609/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2008.11.004 à Corresponding author. Tel.: +39 461882585; fax: +39 461882599. E-mail address: lucia.simeoni@ing.unitn.it (L. Simeoni). International Journal of Rock Mechanics & Mining Sciences 46 (2009) 796–802