Physical modeling has played an important role in studies related to complex tunnel geometries. This method is still used despite the high investment costs for experimental facilities and in the contrary, declining numerical modeling costs. Because of limitations in numerical models for correct implementation of soil and rock behavior (e.g. non linear response, strength anisotropy, accumulation of damage within cemented materials etc.) physical models still can be used to calibrate numerical models. A variety of modeling techniques have been developed by researchers to study ground response due to in-situ stress field. These techniques range from simple two-dimensional models to miniature tunnel boring machines that simulate the process of tunnel excavation and lining installation in a centrifuge setup. Physical modeling utilizes similarity theory and dimensional analysis. The rules of these theories dictate material and model properties, the manner of applying forces and field stresses, method of model construction, boundary conditions, monitoring and so on. In this paper, methods of making various physical models and their conditions together with the parameters that need to be determined accurately are discussed. Also, a circular tunnel is modeled and tested in the laboratory the results of which is presented and discussed.


In the period of 70's to 80's, research works related to rock foundation and underground engineering projects benefited a lot from physical modeling (Li et al. 2005). This method is still used despite the high investment costs for experimental facilities and contrasting declining numerical modeling costs.

There are several reasons why physical modeling might be undertaken either for research purpose or in a design situation. These include:

  1. Complexity of numerical modeling construction in some cases such as complex material behavior, complex geometry and excavations interactions etc.;

  2. Creep or secondary consolidation phenomena especially in rock pillars which requires complex numerical procedures;

  3. Cyclic loading effect, e.g. earthquake, cyclic wetting and drying causing liquefaction etc.;

  4. Limitation in numerical models for soil response, e.g. non-linear behavior, strength anisotropy, accumulation of damage within cemented materials etc.;

  5. Getting a better insight of the structural behavior while loading.

This list is not intended to be exhaustive, but to illustrate typical complexities of geotechnical engineering problems, and to encourage researchers and practitioners to evaluate the best approach for any given problem, balancing the relative advantages and disadvantages of physical and numerical models is necessary (Randolph et al. 2001).

The aims of model test are simulation of the prototype in the laboratory and solve problems about underground complexes in real conditions. Note that the main disadvantages of physical modeling are being time consuming and requiring higher costs.


Dimensional analysis which is a branch of applied mathematics is a research tool available to the design engineers. In any dimensional analysis, it is tried to find functional relationships between the measurable parameters which can simplify the problem of studying large problems in a smaller scale. These relations dictate the relative properties and size of the small model to represent the full scale problem accurately.

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