Numerical modelling and its physical modelling support in Civil Engineering

Currently, there is a progressive divestment of some institutions with strong traditions and skills in physical modelling and their consequent impoverishment, to the detriment of numerical modelling. For many reasons, the economic imperatives and the exponential growth of computational means and numerical methods should certainly not be excluded. In this work, the author aimed to highlight the new requirements of the recent sophisticated developments in physical modelling, precisely due to the new needs imposed on them by mathematical and numerical modelling and the growing risks in civil construction works. In this context, reflections are reported, justified by scientific and real-world examples, on the need for maintenance and reinforcement of investments in physical modelling, both to support the scientific community and to design buildings of significant economic, social and environmental impact.

5 The complementarity of physical and numerical modelling is a very rich field to be explored in terms of teaching engineering, both in the laboratory and in the classroom. The information obtained from numerical models and experimental results is crucial for the development of an understanding of the behaviour of actual structures and methods to efficiently design them; therefore, the promotion of practical lessons based on physical and numerical models is critically important.
The use of physical models can help to improve our understanding of how structures work. It is important to remember that both physical models and numerical models are good options as long as they are an accurate representation of the actual structure (Saidani and Shibani, 2014). To illustrate various physical aspects of seepage in dams, Marques (2020) shows the advantages of numerical modelling in the geotechnical training of civil engineering students.
In this paper, the advantages and disadvantages of each of the physical and numerical Section 2 details and discusses the laboratory experiments used to validate semiempirical models and to assess the behaviour of large-scale structures, where physical modelling is useful to complement or improve the results of numerical modelling. Inefficient or inappropriate uses of numerical models and physical modelling to improve mathematical models, so that they can describe the most important phenomena with enough approximation, are shown in Section 3. A final discussion is provided in Section 4.

Materials and Methods
In general, a physical modelling test program needs a high number of experiments; however, physical modelling tests are time-consuming and expensive. Numerical modelling plays an important role in countering this requirement as they can help to interpret the experimental results and, thus, reduce the number of tests to be performed. In addition to physical modelling performed in the laboratory, a numerical model is a valuable tool for the analysis and explanation of phenomena in different fields.
In the field of soil mechanics, the use of physical modelling is common, especially to assess the soil-structure interaction phenomena and to validate semi-empirical models. Figure 1 Research Development, v. 9, n. 10, e5019108409, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i10.8409 6 provides a general view of an experiment of a study carried out in a laboratory by Carreiras et al. (2003) to investigate the scour-settlement process of vertical cylindrical piles of differing heights and densities. The horseshoe vortex and the vortex shedding generated at the bottom, around the cylinder, induced an erosion around it, promoting sediment transport and formation and propagation of ripples clearly shown in Figure 1.
Numerical modelling is not capable of reproducing the phenomena that occur in these circumstances in the way that physical modelling can. As reported in Carreiras et al. (2003), experiments on the local scour produced by regular and nonlinear waves around a single pile have shown a good fitting between the equilibrium scour depth S and the Keulegan-Carpenter number.
We found that it was possible to test and validate model (1), which seems to provide a good representation of the scour S. (1) where D is the diameter of the cylindrical pile, and KC is the Keulegan-Carpenter number, as defined in Carreiras et al. (2003). Development, v. 9, n. 10, e5019108409, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i10.8409 In the area of structural mechanics, it is mainly the construction of bridges and concrete and earth-fill dams that require complementary physical and numerical simulation approaches to assess specific aspects of design, construction, and structural behaviour of different types of actions/forcing. We refer the reader to the works of Chen and Chen (2014), Al-Janabi et al. (2020) and Ninot et al. (2015), among many others for more information on this topic.     Miyata and Yamaguchi, 1993;Miyata, 2002).
To analyse the bridge's response to wind action and ensure that it functions correctly under stress, an interesting description of the types of tests generally performed in a wind tunnel at the design stage is provided in (Diana et al., 2013;Diana et al., 2015). A comparison of the maximum static horizontal deflection of the Akashi bridge with that of the Messina Bridge (Italy) is also discussed.
The physical model of the no. 3 powerhouse-dam section of the Three-Gorges Dam is shown in Figure 5. After a complete geological study, which involved about 15 possible dam sites, the 3rd powerhouse-dam section was identified as the most unstable section (shown in Figure 5). This figure aims to show some of the various instruments and devices installed for the sliding stability tests.
Both the numerical and physical modelling tests of the Three Gorges Dam have demonstrated that the stability against sliding of the critical dam section (the no. 3 powerhouse-dam section) can meet the safety requirements (Liu et al., 2003a(Liu et al., , 2003b, and the following conclusion was drawn, "The integration of multiple methods is shown to be a more Research, Society and Development, v. 9, n. 10, e5019108409, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i10.8409 effective approach for the stability analyses of the Three-Gorges Dam foundation since no satisfactory individual method can be used alone to solve the problem".
Within the scope of fluid mechanics, there are several references for the need to complement different analysis methodologies, highlighting the phenomena of turbulence, fluid-structure interaction (Jabbari, 2014) and multiphase flows. It is thanks to high-speed computers and advanced algorithms that these important fields, particularly multiphase flow modelling, are areas of rapid growth. An example is a shallow angle plunging jet studied computationally and experimentally by Deshande et al. (2012), which reveals a typical occurrence of partially submerged air cavities formed at the plunging location of the jet onto a quiescent pool. Figure 6 shows the cavities formed intermittently in the impact zone. The formed cavities become separated from the jet and propelled downstream by the initial jet momentum. The process of formation, detachment and propulsion of cavities occurs periodically in the nearfield and as a result, distinct cavities are seen to occur at different streamwise locations, as is evident from Figure 6.
It is shown that, in addition to the high pressures expected from the theory of impact, the pressure on the body surface can later decrease to sub-atmospheric levels. The creation of a cavity due to such low pressures is considered. The cavity starts at the lowest point of the • Inefficient numerical formulation, or its implementation, to solve the mathematical model.

Results of numerical applications that sufficiently clarify the examples mentioned
above are provided in the following section.

Results
Currently, numerical modelling is an essential tool in the design of the largest and most demanding civil construction works; however, on the one hand, the best principles for using this technology are not always observed; on the other hand, as the following examples show, theoretical knowledge and support for physical modelling are not always sufficient.
Experience and common sense are essential factors that need to be considered.

Use of Software as a 'Black Box'
The most common formulations of the water quality process consist of systems of differential equations resulting from the mass conservation of a group of substances that are considered the most significant for the water quality process; however, the mathematical formulations developed for water quality process modelling are not consensual, since drastic simplifications are used as there are no universal laws for the reactions of water quality indicators (Pinho et al., 2004b).
These equations depend on several coefficients/parameters that need to be specified a priori. These coefficients are site-dependent and depend also on the water's characteristics.
Thus, the establishment of mathematical formulations to characterize water quality processes (reactions) should always be questioned.
To account for the lack of sufficient local information, water quality models are often used with coefficients obtained and validated by default, possibly in very different conditions.

Imperfect Knowledge of Flow Interactions with the Bottom and Boundaries (Roughness Effects)
This is a big problem, especially in the field of fluid mechanics. The dynamics of the water flow over irregular bottoms and boundaries with different characteristics and roughness, Research, Society and Development, v. 9, n. 10, e5019108409, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i10.8409 13 which normally are difficult to simulate with sufficient accuracy, translates into spurious data that can significantly affect the final results. The simulation of a real case shown below is proof enough of this.
In terms of area A and flow Q, the Saint-Venant equations are written as: ( 2) ( 3) where A is area, Q is flow, g is acceleration of gravity, is flow depth, represents bathymetry, is hydraulic radius and K is the Manning-Strickler coefficient.    As this figure shows, the difference in arrival times of the wavefront at Penacova, in just 20 km, is very significant. There is a difference of about 13 minutes between both To reproduce this phenomenon, two numerical models were tested: The Saint-Venant model (Equations (2) and (3) above) and the standard Boussinesq model shown below (Equations (4) and (5)). (4) where u is depth-averaged velocity, is fluid density and represents friction stresses at bottom.
As in the Saint-Venant model (momentum Equation (3)), the Manning-Strickler approach was considered to compute the friction term (last term of Equation (5)). Figure 9 shows the same example of a dam break simulated by two different mathematical models (Saint-Venant and Boussinesq standard), under ideal conditions ( ).
When 0, Serre standard equations are recovered, and with and , a set of extended Serre equations with improved dispersive characteristics is obtained.    Development, v. 9, n. 10, e5019108409, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i10.8409 19 once again, the need to make a prior analysis of the physical phenomena that are intended to be reproduced before using a numerical model.

Model
The use of a given numerical method depends on the type of equations to be solved and on how the numerical method was implemented. In a scientific article, it is insufficient to simply state that "Method X was used". Variations in the implementation of "Method X" affect performance measures by factors of 2, 10 or more.
In physics, there are three types of partial differential equations: elliptic equations, such as Laplace and Poisson, which represent or describe the potential of force fields in a variety of physical contexts; parabolic equations, which model diffusion or heat conduction problems; hyperbolic equations, which model wave motion.
To solve elliptic equations, finite-difference methods are the simplest and most intuitive to implement; however, they are not the most efficient. The accuracy of Galerkin and least-squares methods is usually better, although the extra cost can negate this advantage for most problems. A current method of approximate solution of boundary value problems for elliptic partial differential equations is the method of boundary elements.
For parabolic equations, a variety of methods are commonly used. Among them are: Finite difference schemes, Lax-Friedrichs and Lax-Wendroff, which can be viewed as modifications of forward-time central-space and a variety of Crank-Nicolson methods.
Upwind schemes are also commonly used.
For hyperbolic equations, many methods are also used, including: Finite difference schemes, first order and higher order of finite volume schemes; however, the finite element method is more common today and mathematically more efficient than the previous methods.

Conclusions
To design a hydraulic system of significant dimensions, impact and costs, one or more of the following approaches are generally used: • Results of previous experimental studies and data measured in similar systems.
• Physical modelling, using spatial scales sometimes too small and often distorted.
• Computational models that solve increasingly complex mathematical formulations.
Despite the significant improvement of computational models in recent decades, and subsequently, the improvement and widespread adoption of numerical methods, for many real-world problems, there are no mathematical and numerical solutions powerful enough to dispense the first two approaches. Likewise, physical modelling alone does not solve many real-world problems either. As experience has shown, instead of alternatives, physical and numerical models should be seen as complementary approaches.
The need to maintain a strong investment in physical modelling is highlighted, together with the growth of numerical modelling and computational means, both to support the technical and scientific communities and to design and carry out projects that have significant impacts and costs.
As a final note, some critical points are highlighted: • Physical modelling is essential to describe and understand phenomena that are currently not possible to analyse in other ways.
• Numerical models should never be used without prior knowledge of their capabilities and limitations.
• The use of physical modelling in laboratory and field data are the best ways to calibrate and validate numerical models.
• Model results (physical and numerical) should never be used blindly; on the contrary, they must always be the object of analysis and critical consideration.