Issue 73

U. De Maio et alii, Fracture and Structural Integrity, 73 (2025) 59-73; DOI: 10.3221/IGF-ESIS.73.05

turbulence in the flow, and the turbulent dissipation rate, ε , which quantifies the rate at which the turbulent kinetic energy ( k ) is dissipated into thermal energy due to the viscous effects . The transport equations for k and ε read, respectively:

  

  

 t



   x x   k x x       i



k

k

   u

  P



i

k





t

x

     k j

j

(2)

 t













2

   u



 C P C



 

 





i

1

k

2





t

x

k

k

    j

i

j

where k P represents the production of turbulent kinetic energy due to the mean flow gradients and quantifies how much energy from the mean flow is transferred into turbulence through shear or strain in the flow,  t is the turbulent viscosity and expressed by the following form:

2

k

    t C

(3)



Eqns. (2) and (3) also consist of some empirical constants, i.e.,  k ,   ,  C 1 ,

 C whose values have been obtained

 C 2 , and

by a combination of theoretical analysis, calibration, and experimental data fitting [21]. To track the evolution of the interface between the two different fluid flows, air and water, a level set method is employed, able to represent the interface implicitly through a continuous function  defined over the computational domain. The method adds the following equation, called level set function:

     

      















      x x



x











 

  1

i

(4)

u

i

  t

 

 

x

i

i

i

 

x x

j

j

where γ is the reinitialization parameter, and ε is the numerical interface thickness controlling parameter set proportional to the maximum finite element size in the component. The density is a function of the level set function. If  1 and  2 are the constant densities of water and air, respectively, water corresponds to the domain where  < 0.5, and air corresponds to the domain where  > 0.5. Meso-scale model for structural response simulation The proposed numerical framework relies on a coupled damage-plasticity model, proposed by [22], to investigate the structural response of buildings subjected to flash floods. With respect to available discrete fracture models based on cohesive approach [11,23–25], the model combines damage mechanics and plasticity theory for an accurate description of the mechanical behavior of the material under various loading conditions, capturing both softening behavior due to the tensile cracking and the inelastic deformations caused by compressive stress. The theoretical framework is based on the following constitutive equations:               t un c un un e p d d 1 1 :       C (5) according to which the current stress tensor  depends on the positive and negative part of the effective stress tensor un  obtained by a spectral decomposition in order to account for the different mechanical responses of masonry under tensile and compressive loading conditions and reduced by the isotropic damage variables t d and c d in tension and compression

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