Guidelines for Gaussian curve-fitting to settlement data

Fitting a Gaussian curve to real settlement data is of practical use because the parameters that describe the curve, namely volume loss, maximum settlement and trough width, are conceptually easy to understand and can be compared at different locations and for different tunnel sizes, depths and construction methods. Where the magnitude of surface settlements is small, it can be difficult to obtain the Gaussian curve parameters because the magnitude of the measurement error is approaching the magnitude of the surface settlements themselves. Other factors influencing the accuracy of curve-fitting are the number of monitoring points and their spacing relative to the trough width, and the curve-fitting method used. This paper presents the results of a Monte Carlo analysis, which are then used to provide guidance on the reliability of Gaussian curve parameter determination for different error ratios, trough widths, transverse settlement monitoring array layouts and curve-fitting methods.