## 2 Background of Scale Model Similitude Theories  
The relation between a scaled model and the analogous prototype behaviour can be characterised using the theory of \"scale model similitude\". Ref. [3] described three different approaches with varying levels of sophistication, including \"dimensional analysis theory\", \"similitude theory\", and \"governing equations method\". Dimensional analysis theory is based on the principle of dimensional homogeneity [4]. This theory involves transforming the homogeneous equations dimensionally, comprising the quantities physically, and defining a physical circumstance as a corresponding equation involving dimensionless products of powers of the physical quantities. Dimensional analysis theory can be employed to understand the problem-solution form without the direct application of scale modelling. Similitude theory, on the other hand, involves setting up the necessary and appropriate conditions for correlation between phenomena. This approach can accurately predict the behaviour of a prototype by using scaling laws related to the prototype through similarity conditions, as schematically illustrated in Figure 1[5; 6; 7]. \"Similitude theory\" pinpoints the forces functioning in a system and employs dimensional analysis to form and associate the dimensionless terms for the scale model and full-scale prototype [8]. The prediction equations are commonly referred to as the scaling relationships that exist between the model and the prototype. Finally, the governing-equations method comprises changing the differential equation characterizing the process to a nondimensional equation and developing similarity between the model and the prototype variables, including the initial and boundary conditions of the system. In addition, it  
Figure 1: Flowchart for forecasting the structural behaviour of full-scale prototypes using a physical test of a scale model. is imperative to establish similarity variables for the initial and boundary conditions that govern the system. Scale models of dynamic loading and soil-structure interaction (SSI) conditions can be described as those involving geometric, kinematic, and dynamic similarities to the prototype [9]. Geometric similarity describes a situation wherein the model and the prototype have analogous physical dimensions. Kinematic similarity refers to a phenomenon in which the model and the prototype have analogous particles at similar points and times, whilst dynamic similarity defines a circumstance in which corresponding components of both the model and prototype undergo analogous forces. Scale models may fulfil the criteria of similarity to the prototype with different degrees of accuracy. The terms \"distorted\", \"adequate\", and \"true\" are sometimes used to describe the degree of accuracy with regard to meeting the requirements of similitude [10]. A \"distorted\" model is a scale model in which the prediction equation is distorted due to a significant deviation in similitude requirements. Compensating distortions are introduced to preserve the prediction equation in other dimensionless products. A scale model is \"adequate\" when the primary features of the phenomenon are correctly scaled with minor deviation consequences and the equation of prediction is not considerably influenced. A \"true\" model refers to a scale model that fulfils all similitude requirements. Dimensional analysis essentially intends to reduce the number of parameters in a model to the fundamental \"measures of nature\", i.e., mass, length, and time, while developing a scale factor for all three quantities. For instance, the modulus of elasticity is a stress indicator with units of force/area and corresponding dimensions of \(ML^{-1}T^{-2}\), which represent the mass (\(M\)), length (\(L\)), and time (\(T\)) dimensions. Therefore, the scale factors for mass \(\mu\), length \(\lambda\), and time \(\tau\) can be combined to develop a scaling relation of \(\mu\lambda^{-1}\tau^{-2}\), which correlates the model-prototype stress response.