Analytical and Semi-Analytical Solutions for Describing Tunneling-Induced Transverse and Longitudinal Settlement Troughs

Pin Zhang, Zhen Yu Yin, Ren Peng Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


It is an ongoing problem to develop a solution to predict ground deformation induced by shallow tunnels construction in dry soils. This study proposes a closed-form elastic analytical solution and a plastic analytical solution for calculating the longitudinal settlement trough. Meanwhile, a semi-analytical solution is further developed for better fitting tunneling-induced ground deformation, where the metaheuristics optimization algorithm particle swarm optimization (PSO) is employed to identify the empirical parameters of the proposed semi-analytical solution. A uniform formulation with the combination of analytical and semi-analytical solutions accounting for tunnel uniform convergence and ovalization deformation modes is proposed. A 3-dimensional numerical model and centrifuge test results are used to validate the prediction capability of the proposed solutions in predicting longitudinal and transverse settlement troughs, respectively. The results indicate the proposed semi-analytical solution can overcome the deficiency of analytical solutions, and the predicted results show great agreement with actual tunneling-induced transverse and longitudinal settlement troughs. A simple linear relationship is discovered between coefficients of the proposed semi-analytical solution identified by PSO and their influential factors that assign physical meaning to these empirical coefficients and also provides a straightforward method to estimate coefficients effectively.

Original languageEnglish
Article number0001748
JournalInternational Journal of Geomechanics
Issue number8
Publication statusPublished - 1 Aug 2020


  • Analytical solution
  • Centrifuge modelling
  • Numerical modelling
  • Optimization
  • Settlement
  • Tunnel

ASJC Scopus subject areas

  • Soil Science

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