Assessment of change to gravity field due to underground railroad tunnel construction

Abstract

Tunnel Ober-/Untertürkheim is an underground railroad tunnel that was constructed between 2015 and 2019. The tunnel crosses obliquely below Nähterstraße in Wangen, Baden-Württemberg, at a depth of circa 22 m. The 2014 Diplomarbeit of Benjamin Efinger involved a gravimetric survey of a set of points situated along Nähterstraße, near the site of the at that time still unbuilt tunnel. In 2020 I have resurveyed those points, in addition to which I have surveyed several additional points situated along the same line, near where the survey line crosses above the tunnel. The coordinates of all gravimetric survey points are known via SAPOS augmented GNSS survey. The purpose of this thesis is to compare the pre- and postconstruction gravitation fields. The first task of survey data postprocessing is to apply corrections to each gravimetric observation; the applied corrections account for the centrifugal component as well as the component that is height of instrument times free-air gradient. Next a survey least squares adjustment is implemented in such a way that partitions every corrected gravimetric observation between a constant component common to all observations, time dependent bias of the gravimeter response variable, difference of magnitude of gravitation relative to a reference value, and random error. According to predictive modelling contained in the 2014 Diplomarbeit of Efinger, the endpoints of the survey line are sufficiently far from the tunnel that there is at most negligible change of gravitation there due to tunnel construction. Except for the two endpoints of the survey line: for all points observed both pre- and postconstruction, the least squares survey adjustment distinguishes preconstruction relative gravitation from postconstruction relative gravitation. The known, one-dimensional coordinates of the survey points together with their adjusted relative gravitation values constitutes a dataset that supports simultaneous least squares estimation of two Legendre series: one corresponding to preconstruction state of gravitation, the other corresponding to postconstruction state of gravitation. The difference between the two Legendre series is a stochastic function that is denoted as F; it is a model of the change of gravitation from preconstruction to postsconstruction. At the point where the survey line crosses above the underground railroad tunnel, Efinger’s predicted change of gravitation is approximately F - 1.618 √var(F).