Exploring the limitations of applying ground reaction curve in hard rock

Excavation in underground construction causes changes in the stress of the ground which causes motion in the surrounding regions particularly the tunnel's ceiling and walls. It is imperative to perform a stability analysis for the mineral and tunneling industries during the excavation process, and the modern methods of tunneling rest on the ground reaction curve (GRC). While GRC is a good tool to visualize these displacements, there exist gaps between the analytical and numerical outcomes as analytical solutions do not extend beyond isotropic circumstances for tunnels that are deep. As a result, there is an increased demand for an equation which focuses on the numerical methods. This paper seeks to address this pressing question by looking into GSI=75 where K=0.5, 1, 1.5 and 2. GRC was used alongside numerical and analytical methods to see the ratio of maximum displacement on point. The purpose of the evaluation was to determine the boundaries of the analytical technique and its effectiveness; conditions that aren't suitable for use of the analytical method were also evaluated. FLAC2D was used for the numerical methods and Duncan-Fama' method was employed for the analytical approaches. The gap in tunnel wall displacement estimates between the analytical and numerical methods was acceptable under isotropic stress conditions. However, large discrepancies were revealed between the methods under anisotropic stress, and wall displacement results of the tunnel weren't overly influenced by the excavation depth. In particular, numerical and analytical displacement estimates for the tunnel crown diverged in shallow models. This was because previously, wall displacements were less affected than crown displacements by excavation depths. Finally, equations were presented for the tunnel ceiling and walls in elastic shapes, which compared favorably with numerical data as opposed to the method of analysis. The presented equations are said to be new especially due to their treatment of issues associated with non-isotropic stress analytical solutions but only for tunnels which are situated at shallow depths and that covers only the tunnel centroid. The equations render better performance in terms of alignment with numerical outcomes that is achieved over a wide range of stress ratios and depths as compared to the current methods in use; this increases the effectiveness of segments in real tunneling conditions.