Abstract In the underground construction of tunnels, high precision of convergence and settlement measures are necessary, and the employment of the total station can attain this goal. The resultant errors of the precision of the total station are evaluated, considering its linear and angular precision in the horizontal and vertical line. The theoretical basis of error propagation and its calculation expressions are established. Error propagation for several distances in the function of the precision of the evaluated total station is calculated. Error propagation in the convergence and settlement is defined separately. Finally, procedures for minimization of the error propagation in the convergence measures in the underground excavations are listed. The eveloped methodology was applied in tunnels of the Yellow Line of the São Paulo subway and in a mining tunnel.
1 Introduction In the world today, the convergence measures in tunnels are made, fundamentally, with a total station. It could be cited among other countries, Germany, Australia, the United States, and Spain.
Figure 1 shows the convergence instrumentation scheme (relative displacement) and absolute displacement with a total station in a tunnel in Germany.
In Figure 1 according to Intermetric/Interfels (1994), the maximum measuring distance is 100 m. In this article as noted, we will propose a maximum measuring distance of 40 m, depending on the precision of the total station evaluated.
In Brazil, the convergence measures with a total station in tunnels were initiated in 1994 in the construction of the Ibirapuera tunnel in the city of São Paulo. The Polytechnic School of the University of São Paulo developed researches for the determination of convergence and vector displacement through a total station in a tunnel of the ring road of São Paulo (Hamze-Guilart 2002) as well as a methodology for interpretation of monitoring of underground excavations by modeling historical data of geotechnical instrumentation. Data obtained in three tunnels of different geomechanical and constructive characteristics were studied (Hamze-Guilart 2007).