Image2Block: An automated pipeline for rigid block modeling of rubble masonry walls

Overview

This repository provides image-based pipelines for analyzing masonry walls under shear-compression loading using limit analysis and pushover analysis. Models are derived from binary images of wall structures.

The modeling method is optimization-based rigid block modeling. Please refer to these publications for detailed explanation:

Wang, Q., dos Santos, K. R., & Beyer, K. (2025). Geometric planning for masonry wall construction with natural stones using discrete convolution. Engineering Structures, 329, 119695.

Wang, Q., Haindl, M., dos Santos, K. R., & Beyer, K. (2024). Applying a 2D variational rigid block modeling method to rubble stone masonry walls considering uncertainty in material properties. International Journal of Architectural Heritage, 1-23.

The image below illustrates an example analysis showing the failure mode of a rubble stone masonry wall:

Table of Contents

• Environment Setup

• Limit Analysis Workflow

  • Config Parameters

• Pushover Analysis Workflow

  • Config Parameters

• Examples

• Citation

• Contact

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Environment Setup

Tested on Ubuntu 20.04.6 LTS.

Step 1: Build Virtual Environment

python -m venv ./venv/
source ./venv/bin/activate

Step 2: Configure Virtual Environment

cd path/to/source
python setup.py install
pip install -r requirements.txt

Step 3: Obtain MOSEK License

Free academic and trial licenses are available at MOSEK.

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Limit Analysis Workflow

Directory: Workflows/LA_2D_image

Step 1: Understand the Input Files

The input for an example analysis is in Workflows/LA_2D_image/data

• Binary wall image: Stones in white, mortar in black.
• config.json: Contains geometry, material properties, boundary conditions, and plotting parameters.

Config File Parameters Limit Analysis

Geometry Parameters:

• scale_img_to_height, scale_img_to_width, wall_thickness: Wall dimensions in mm (height = vertical, width = horizontal, thickness = out-of-plane).
• point_grid_size: Integer controlling shape simplification during edge detection. Higher = more simplification. Min = 1.
• mesh_size: Integer for mortar discretization mesh size.

Material Parameters:

• Mortar properties:

  • mortar_mortar_fc: Compressive strength (MPa)
  • mortar_mortar_ft: Tensile strength (MPa)
  • mortar_mortar_cohesion: Cohesion (MPa)
  • mortar_mortar_mu: Friction coefficient

• Stone–mortar interface:

  • mortar_stone_fc, mortar_stone_ft, mortar_stone_cohesion, mortar_stone_mu: Same properties as above

• Ground/Beam interface:

  • ground_beam_fc, ground_beam_ft, ground_beam_cohesion, ground_beam_mu: Usually set to high values to prevent failure at these interfaces

• Density:

  • unit_density, mortar_density: Density of stone and mortar (kg/m³)

Boundary Conditions:

• boundary: Type of loading condition ("cantilever" or "double_bending")
• vload: Vertical axial load (MPa)
• hload_direction: Direction of horizontal load (1 or -1)

Plot Parameters:

• plot_max_disp: Max displacement in mm when plotting the failure mode

Step 2: Generate Rigid Block Model

python 01_generate_model.py -i ./data -r ./result

• -i: Directory with wall image and config file
• -r: Output directory for results

Step 3: Run Limit Analysis

python 02_run_limit_analysis.py -i ./data -r ./result

Step 4: Plot Failure Mechanism

python 03_plot_failure_mode.py -i ./data -r ./result

Step 5: Review Results

• Max Load: ./result/***/run_limit_analysis/load_multiplier.txt (last column, MPa)
• Failure Mode: ./result/***/run_limit_analysis/***/displacement.png
• Discretization Visualization: Open ./result/***/kmodel/mortar.msh in ParaView

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Pushover Analysis Workflow

Directory: Workflows/PO_2D_image

Step 1: Understand the Input Files

The input for an example analysis is in Workflows/PO_2D_image/data

• Same binary wall image and geometry/material/boundary parameters as the limit analysis.
• Additional pushover-specific parameters in config.json.

Config File Parameters Pushover Analysis

Pushover-Specific Material Parameters:

• crack_gap: Gap threshold (m) to zero tensile strength and cohesion
• E_stone, E_mortar: Young's modulus for stone and mortar
• Poisson_stone, Poisson_mortar: Poisson's ratio for stone and mortar

Pushover Protocol Parameters:

• force_step: Load increment in pre-peak phase (kN)
• disp_step: Displacement step in post-peak phase (m)
• max_iterations_pushover: Max analysis steps
• element_id_control: ID of element controlling post-peak displacement, or false to use beam element

See configuration for limit analysis for other parameters.

Step 2: Generate Rigid Block Model

python 01_generate_model.py -i ./data -r ./result

Step 3: Run Pushover Analysis

python 02_run_pushover.py -i ./data -r ./result

Step 4: Plot Pushover Curve

python 03_plot_pushover_curve.py -i ./data -r ./result

Step 5: Review Results

• Deformed Models (Each Step): ./result/***/run_pushover/***/sample0/
• Force–Displacement Curve: Located in result directory
• Discretization Visualization: Open ./result/***/kmodel/mortar.msh in ParaView

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Examples

• Additional examples for limit analysis are in ./LA_2D_image/examples.
• Additional examples for pushover analysis are in ./PO_2D_image/examples.

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Citation

If you use this toolkit in your research or publications, please cite the following papers:

Wang, Q., Haindl, M., dos Santos, K. R., & Beyer, K. (2024). Applying a 2D variational rigid block modeling method to rubble stone masonry walls considering uncertainty in material properties. International Journal of Architectural Heritage, 1-23.

Contact

For questions and feedback, please contact:

Qianqing Wang at Earthquake Engineering and Structural Dynamics (EESD)

📧 Email: [qianqing.wang@epfl.ch]