###### Abstract  
This study introduces a Multi-Depth Deflectometer (MDD) combined with a Global Navigation Satellite System (GNSS) which was developed for measuring the deformation of railway slab track layers. We newly designed the MDD with the addition of laser sensor modules for increasing precision in which the MDD head is fixed at the top of the track slab. The MDD/GNSS system can measure the relative deflection between each track layer as well as the total deflection at the top of the track slab, which makes it possible to evade the fixed condition problem of classical MDD. The new MDD/GNSS system was installed at the transition zone between a tunnel entrance and its embankment, which experienced high settlement levels prior to repair. The system was used to monitor whether the repaired concrete track foundation with pressurized cement grouting was stabilized effectively and what track layer position was most unstable so that it had the most influence. The GNSS system was designed and built for computing net settlement at each track layer even when the MDD could not be fixed firmly at the end point, which is a major drawback of classical MDD. The results obtained from MDD and GNSS measurements indicated significant potential in aiding railway track settlement measurements. multiple depth deflectometer; Global Navigation Satellite System; embankment settlement; trend model; virtual reference technique; prediction model +
Footnote †: journal: Applied sciences  
such as road pavement and railway track sites, to evaluate the stiffness and condition of the soil. Generally, MDD has been used as a device for accurately measuring the permanent deformation of each layer in a pavement system [10]. Effective elastic moduli of multilayered pavement structures can be back calculated from the measurements [8; 9]. [PERSON] et al. [11] used MDDs to measure pavement deflections under static loads. [PERSON] et al. [12] used MDDs to develop a mechanistic-empirical design method for an asphalt pavement putting model and to calibrate a laboratory rutting model. In a special case, MDDs were used as dynamic gauges to measure pavement deflection under a Heavy Vehicle Simulator (HVS) wheel load and as online gauges to measure induced displacements [13]. They are also used to measure track settlement and assess track stability. This is helpful in identifying areas of the track such as rail transition zone, which may be prone to settlement or failure, and in designing appropriate remediation measures [14]. A Global Navigation Satellite System (GNSS) is a system that uses satellite signals to determine the location of an object on Earth. There are several GNSS systems in operation around the world, including the Global Positioning System (GPS) used by the United States, the GLONASS system used by Russia, the Galileo system used by the European Union, and the BeiDou system used by China [15]. These systems use a network of satellites orbiting the Earth to transmit signals to receivers on the ground, which can then use the timing and strength of the signals to calculate the receiver's position and other information, such as altitude and velocity [16]. The GNSS is utilized in a wide range of applications, including navigation, mapping, surveying, and precision agriculture. [PERSON] et al. [17] developed a GPS technology to monitor the settlement of railway tracks by continuously observing real-time data to better understand the changes in railway track foundations at different stages and to ensure the safety of the railway. [PERSON] and his team proposed a method for monitoring rock displacements using the GPS [18]. [PERSON] et al. [19] used Kalman filtering techniques to achieve positioning accuracy of 2 to 3 mm for monitoring frost heave in railway track foundations using GPS technology.