This work presents a comparative analysis between two model hierarchies commonly applied in tunnel structural design: continuum ground models and bedded-beam models. Firstly, the main characteristics of each model and the interfaces between them are discussed. Based on those evaluations a simple procedure is proposed for determining the bedded-beam model imposed loads which lead to results compatible to those of a given continuum model. Said procedure is then explored to estimate simplified compatibilization loads for basic and illustrative cases, where a reasonable compatibilization was achieved for a relatively simple applied load.

In the light of the complexity and interdisciplinarity of the phenomena involved in the construction of tunnels, hierarchical modelling is an important tool for the structural analysis and design practice of these structures. This work develops a study on two bidimensional model hierarchies commonly applied for the structural design of tunnels: models with the soil/rock mass as a continuous deformable solid and bedded beam models. The study focused on the evaluation and investigation of the potential combined use of those model hierarchies in the analysis and design practice, mainly regarding the comparison of representable physical phenomena and compatibility or compatibilization of computed results. To that end, inputs, outputs and hypotheses of the models were described, with the identification of the interface between the hierarchies. With these concepts as a baseline, a simple practical procedure for the case by case calculation of "ideal" compatibilization loads was formalized. Said loads, when applied to a bedded beam model lead to lining loads that are identical to those of the analogous continuous rock/soil mass model whose results are applied for the compatibilization. The procedure was applied to calibrate simplified compatibilization loads, and apply them to two studies. The first applied a case study to comparatively assess the loads imposed to a bedded beam model regarding the compatibility of the results with those of an analogous continuous rock/soil mass model. It was noticed that the compatibility of usual imposed loads from the bibliography and practice is generally low. On the other hand by calibrating loads based on the proposed "ideal" compatibilization procedure, even with higher simplification of the imposed load, a reasonable result compatibility may be obtained, especially for axial loads. That is, as long as the imposed loads bear magnitude and distribution that generally resemble the "ideal" compatibilization load, reasonable compatibility for internal beam loads may be obtained. Motivated by that observation, the second study performed a parametric analysis of the effects of variating hypotheses applied to the continuous rock/soil mass modelssuch as geometry, materials, cover, etc. -in the respective "ideal" compatibilization load for bedded beam models. A total of 93 scenarios of hypothesis combinations were evaluated, identifying the relative effect and importance of hypotheses in the magnitude and distribution pattern of the "ideal" compatibilization loads. The study foresees the possibility of estimating simplified compatibilization loads based on the physical problem definition, without the need of knowing beforehand the results of the continuous soul/rock mass model, as the calculation of the "ideal" compatibilization load would imply.

This work presents a study on the compatibilization of the lining load results between continuous ground mass and bedded beam models for tunnel design, through the calibration of the loads imposed to the bedded beam models. A review on compatibilization premises and the computation of “ideal” compatibilization loads, which yield identical results between model hierarchies is presented. A case study was developed, illustrating that even with significant simplification of the calibrated loads, if they bear magnitude and distribution that resembles those of the “ideal” compatibilization load, reasonable compatibility, potentially better than that of usual generic imposed loads, may be obtained. Motivated by this observation, a parametric study on the magnitude and distribution of the “ideal” compatibilization load was performed, yielding conclusions that foresee the estimation of simplified compatibilization loads directly from the physical problem definition.