TUNNEL REACTION TO GROUND MOVEMENT USING A SIMPLIFIED MODEL
Authors: Yudenko Dmytro 
Published: December 2022

Purpose: the analysis is performed by modal superposition of the response of a simplified model containing connected bending and shear beams supported by Winkler-type springs.
Objective: to present a simplified model using coupled Bernoulli and shear beams supported by Winkler-type springs for the systematic identification of tunnels subject to earthquake-induced ground motions. A model formulation is introduced and closed-form solutions for the modal characteristic equation and mode shape are derived.
Research methods: the formulation of the model is introduced and closed-form solutions are derived for the equation of modal characteristic and mode shape. The latter are checked by the results of numerical models. A system identification algorithm is then presented, demonstrating its ability to recover the model parameters when the recorded acceleration time intervals along the tunnel are perturbed by noise and sensor locations change. The presented framework can be used for initial and simple recovery of tunnel response in the presence of monitoring data or for planning monitoring campaigns in newly constructed or existing tunnels.
Main results: using a simple genetic algorithm and the proposed simplified model, it was shown that system identification can be performed for variable conditions. The model was tested for two different earthquakes of different frequencies, and the influence of the distribution of sensors along the length of the tunnel was also parametrically investigated. The test results were intentionally compromised by adding white Gaussian noise with a variance equal to that observed during ground motion. It was observed that for values ​​of α >3.0 (ie, when the effect of the shear beam is significant), the model parameters can be successfully recovered. Therefore, for such conditions, the proposed approach can be used to recover important tunnel dynamic properties (e.g., T1 or α) as well as soil-structure interaction by tracking kb changes after earthquakes. For values ​​< 3, a Bernoulli beam with a Winkler basis is a valid representation, while observing differences with a model involving a Pasternak basis are marginal.
Scientific novelty: another approach to parametric system identification using simplified models. For tunnels, such models usually consist of beams on independent Winkler-type springs, including both numerical and analytical schemes. However, the seismic response of the continuum (i.e., soil) can be better modeled by including a transverse beam above the Winkler foundation, which allows interaction between individual springs, rather than using a single layer of independent springs. In geotechnical seismic resistance, a similar approach was used to assess the seismic response of pile foundations and retaining walls.
Conclusions and practical challenge: different sensor distributions and reduced number of sensors did not lead to significant differences in the final results. This first shows that sensor position is not the dominant parameter for the case of five sensors along the length of the tunnel, fixed at both ends, and uniform soil conditions and other assumptions made in the paper. Further tests should be performed on real data and sensors to examine the impact of other aspects such as sensor noise.
Key words: winkler springs, soil; soil; model; system identification algorithm is presented.