The projected urban expansion rate is forecasted to reach 60% by 2030 and rise to 68.4% by 2050, as outlined in the 2018 World Urbanization Prospects report. The increasing urban population not only necessitates the development of efficient and sustainable transportation systems but also calls for the utilization of underground space due to limited available land area. Consequently, the utilization of underground space has emerged as a viable solution to mitigate traffic congestion. However, despite advancements in tunneling technology, such as Tunnel Boring Machines, aimed at ensuring safe, stable, and sustainable tunnel construction, tunneling in predominantly soft-ground conditions at shallow depths in urban environments presents a significant challenge, especially for accurately predicting the surface settlements to prevent damage to above-ground structures. The current study presents the results of numerical investigations aimed at evaluating ground settlements caused by shallow-depth tunneling in frictional soil using the three-dimensional finite element platform PLAXIS-3D. It explores variations in parameters such as the friction angle (φ), cover depth (C) from the tunnel center, and tunnel diameter (D) in relation to the prediction of surface settlements. Subsequently, settlement outcomes from the numerical analysis are compared with established analytical formulations proposed by Peck (7th International conference on soil mechanics and foundation engineering, pp 225–290 (1969)), Clough and Schmidt (Developments in geotechnical engineering, pp 567–634 (1981)), and Pinto and Whittle (J Geotech Geoenviron Eng 140:1–17 (2013)). This comparative analysis seeks to identify the most suitable formulation that closely aligns with the numerical findings, thereby assisting tunnel designers in making more precise predictions of tunneling-induced surface settlements.