## 1 Introduction
\[i=0.5z_{0} \tag{8}\]  
All these relationships were derived from [PERSON]'s hypothesis, which does not provide any theoretical background. To find an explanation to this problem, many experimental programs have been carried out involving centrifuge modelling and physical modelling tests [29; 32; 36; 37; 38; 39]. [PERSON] et al. [38] studied various parameters affecting the ground settlement, such as tunnel depth, tunnel size, and volume loss on greenfield settlement. The authors concluded that Gaussian curves do not provide satisfactory results for sands with higher volume loss. They suggested the use of a modified Gaussian curve for such problems. Mathematical equations were proposed to incorporate the effect of the three parameters (tunnel depth, tunnel size, and volume loss on greenfield settlement). Various researchers carried out further analysis [23; 40]. [PERSON] [41] analyzed parameters such as tunnel depth and dimensions, overburden pressure, and face pressure [41]. [PERSON] et al. [37] used small-scale physical modelling to study the effect, on ground settlement, of tunnels constructed side-by-side; the authors concluded that the existing Gaussian curve does not provide accurate measurement of ground settlement for tunnels constructed in close proximity. A modified Gaussian curve suggested by [PERSON] [32] provides better results for the same case as reported by the authors. [PERSON] et al. [36] performed an axisymmetric trap-door test using centrifuge modelling facilities under 1g speed. Analysis was done with variable depth to diameter ratios. Moreover, displacements and earth pressure around the trap door were recorded. [PERSON] [42] performs centrifuge tests for different geotechnical problems. Numerical analysis was also performed after validation using test results. [PERSON] et al. [39] studied greenfield ground settlement through a physical modelling technique. The analysis was done for variation in cover depth to tunnel diameter ratios and at different relative densities for sand. Results showed a decrease in the surface settlement as the relative density increased and vice-versa. Apart from above-mentioned experimental approaches, numerical techniques were also adopted in some research. [PERSON] et al. [43] studied a finite-difference model generated through the FLAC package. They compared the results with previously available empirical and analytical methods to propose a set of K values for practical utilization based on tunnel dimensions and soil strengths. [PERSON] et al. [44] analyzed a three-dimensional numerical model generated through Plaxis-3D; results obtained showed the slightest deviation from observed field data. Still, there is a lack of experimental and numerical approaches for cohesionless soils. Our study explores the effects of ground settlement due to tunnelling in cohesionless soils. In our study experimental and numerical approaches were carried out. A physical model of a cubic tunnel box made up of mild steel plates and having dimensions of 1 m was developed. Tunnels with 0.30 m in the centre of the cubic box were used in the experiment. The results of the experimental analysis were back-analyzed to validate our numerical model. We developed a 2D finite-element model to expand the research on a real-life scale. We performed a full-scale 2D elastoplastic study for five tunnel openings: circular, horseshoe, arch, square, and elliptical. The study was aimed at finding proper design recommendations for all these shapes by accurate prediction of ground settlement.