Seismic Analysis of Masonry Buildings: A Macro-Element-Based Approach with 3DMacro 

 

 

The structural assessment of historic masonry buildings is unquestionably one of the most complex challenges in structural engineering. Unlike modern materials, masonry exhibits a highly nonlinear response and a significant discrepancy between tensile strength, which is considerably lower and difficult to assess accurately, and compressive strength.
In this article, based on the video tutorial above, we explore the challenges involved in modeling masonry structures and how the macro-element strategy implemented in 3DMacro provides a solution that balances technical accuracy with computational efficiency. 
 

The Challenge of Masonry Modeling 

To understand and simulate the collapse behavior of masonry buildings, engineers face three major obstacles: 

  1. Material and Mechanical Uncertainties: Strength and ductility vary significantly depending on the wall type and the degradation mechanisms associated with static, cyclic, or dynamic loading. 
  2. Geometric Uncertainties: Identifying the exact structural layout of historic buildings is difficult, and engineers often have to deal with highly irregular geometries. 
  3. Choice of Numerical Strategy: If the model or data input is inaccurate, the results will be misleading regardless of the complexity or computational cost of the selected method. 

Although nonlinear dynamic analysis is the most realistic method for simulating a building’s behavior during an earthquake, its computational cost is very high for masonry buildings. For this reason, pushover analysis, or nonlinear static analysis, has become an extremely useful and efficient tool, clearly showing the distribution of damage at different load levels in terms of strength and ductility. 

 

Limitations of Traditional Models 

Historically, engineers have chosen between nonlinear Finite Element Models (FEM) and simplified macro-models. The Equivalent Frame Model has been the most popular choice in engineering practice, representing a planar wall as a frame made of nonlinear elements. 

However, this model has considerable limitations in real buildings. Historic masonry rarely forms a perfect grid; when walls have irregular shapes or openings, such as doors and windows, are not perfectly aligned, deciding where to place the frame “beams” and “columns” requires too many simplifications, which can introduce significant errors into the analysis. 

 

The Solution: 3DMacro’s Macro-Element Strategy 

To address the issue of irregularity, 3DMacro uses a macro-element strategy. In this method, each wall is subdivided into equivalent elements represented by an articulated quadrilateral. 

 

The in-plane collapse behavior of the wall is captured through a system of nonlinear links: 

  • Flexural Failure: Simulated through interface links normal to the plane, representing the wall’s flexural deformability and axial deformability. 
  • Diagonal Shear Failure: Captured by two nonlinear diagonal links connecting the vertices of the quadrilateral. 
  • Shear Sliding: Managed by interface links parallel to the plane, allowing the sliding that occurs along mortar joints to be simulated. 

 

From an efficiency standpoint, each macro-element is governed by only four degrees of freedom, three for rigid-body motion and one to describe shear deformability, which keeps computation time fully manageable. 

 

Workflow and Integrated Modeling 

3DMacro was designed with an intuitive interface that makes it easier to create a reliable model. The software is divided into two main environments for building the geometric model: the plan editor and the wall editor. 

Some of the main workflow features include: 

  • Code Definition: Users can select the Structural Eurocodes, which automatically affects the generation of elastic response spectra and several design parameters based on soil type, importance factor, and peak ground acceleration. 
  • Structural Versatility: In addition to fully masonry buildings, either existing or new, the software enables the modeling of slabs, lintels, and reinforced concrete elements such as bond beams, which can be configured with 2D beam behavior. It also allows users to manage the global behavior of the model between 2D and 3D in the advanced options. 
  • Seismic Strengthening: Modern retrofit interventions can be simulated, from composite materials such as FRP, including glass, carbon, or aramid fibers, and the CAM system, consisting of stainless steel strips, to steel jacketing and reinforced masonry. 
  • Detailed Results: After running a pushover analysis, the software generates a capacity curve and allows users to visualize the damage pattern in 3D. Each symbol appearing on the walls is associated with a specific failure event, such as flexure, shear, and so on. Finally, users can export a technical report with the seismic vulnerability assessment and safety checks. 

 

Conclusion 

Ensuring accuracy when modeling masonry buildings, while meeting the requirements of modern codes such as the Structural Eurocodes, requires specialized tools. The macro-element model available in 3DMacro represents a highly recommended evolution compared with equivalent frame models, enabling engineers to overcome the architectural irregularities of historic buildings and reliably and efficiently assess their seismic performance.