Proposal of a Numerical Simulation Method for Elastic, Failure and Collapse Behaviors of Structures and its Application to Seismic Response Analysis of Masonry Walls

Abstract

We propose a dynamic analysismethod – a refined version of the DEM- that can simulate three-dimensional elastic, failure and collapse behaviors of structures. A structure is modeled as an assembly of rigid elements. Interaction between elements is modeled using multiple springs and multiple dashpots attached to surfaces of the elements. The elements are assumed to be rigid, but the method allows the simulation of structural deformation by permitting penetration between elements. There are two types of springs: one is a restoring spring to simulate elastic behavior before failure and the other is a contact spring for simulating contact and recontact between elements. A contact dashpot is also used to dissipate the energy of contact. Structural failure is modeled by replacing restoring springs with contact springs and dashpots. A method for determining spring constants is also proposed. The validity of the method is confirmed by the numerical simulation of masonry wall models. First, the elastic behavior induced by an impact force is calculated. It is found that the elastic behavior determined using the proposed method is in good agreement with that determined using the finite element method. Second, the seismic behaviors of masonry wall models with different laying patterns and a wall model with reinforcement are analyzed. It is found that the proposed method allows expression of the difference in behavior due to different laying patterns and reinforcement. The validity of the proposed method is thus confirmed. The proposed method is suitable for simulating seismic behavior of masonry structures.

A Discrete Macro-Element Method (DMEM) for the nonlinear structural assessment of masonry arches

“…The integration of Eq (12) has been performed according to a uniform fibre discretation of the adjacent elements, as depicted in Figure 5, where the masonry macroelements p and q, have been discretised according to The shear sliding behaviour of adjacent elements, along the interfaces, being associated to a single degree of freedom, has been characterised according to a uniaxial nonlinear behavior, as clarified in the next section. 13 It is worth to notice that, the choice to concentrate the mechanical properties of the connected elements in zero-thickness interfaces is common to other discrete numerical approaches such for example the applied element method [30]- [34] and the rigid body spring model [35]- [38], however these latter strategies do not operate at the macro-scale.…”

“…Influence of the tensile fracture energy: (a) mid-span load and (b) quarter of span load.The influence of the tensile strength has been investigated by considering the load scenarios for the values of the tensile strength , the results are reported inFigure 19. It can be observed how the tensile strength strongly influences the ultimate load capacity of the arch in both the load configurations 34. …”

Seismic Behavior Analysis of Masonry Structures Using

“…This segmentation of the surface allows the spring constant to be defined theoretically, which is the main improvement over earlier methods. For more details, see [7]. A restoring spring, which models the elasticity of the elements, is set between continuous elements ( Fig.…”

“…The total sum of the restoring and contact force for a certain element is obtained by summing up the restoring or contact force by springs and dashpots for all elements with which the element of interest is in contact. For more details, see [7]. The equation of motion for translational motion is written as…”

“…A refined DEM [7] was then proposed by Furukawa et al in 2011. In this scheme, a restoring spring resisting tension is included, the structure is modeled as an assembly of hexahedral elements, and the surface of each element is divided into many segments to which springs and dashpots are attached.…”