Model Description

Context

This repository contains the reference implementation of the Bitumen Black Space Model (B2SM), a mathematical framework developed to describe the rheological behaviour of bituminous binders in Black Space Diagrams derived from Dynamic Shear Rheometer (DSR) measurements. The model provides a continuous, bounded representation of the relationship between complex shear modulus (|G*|) and phase angle (δ), enabling quantitative analysis of unmodified and polymer-modified binders.

The software accompanies the associated research publication and provides the implementation used for model development, parameter estimation, and validation.

Purpose

The repository provides an open-source implementation of the B2SM methodology described in the accompanying publication. It enables researchers to

• fit the Bitumen Black Space Model to experimental DSR data;
• analyse unmodified, polymer-modified, and highly modified binders;
• generate Black Space diagrams and fitted model responses;
• construct rheological master curves using the implemented temperature-shift methodology; and
• reproduce the analyses presented in the associated publication.

Detailed instructions for installation, data formatting, workflow, and execution are provided in the repository README.

The repository serves as the reference software implementation accompanying the associated publication and archived research dataset.

Model Overview

The software implements three related Black Space models:

• the original B2SM for unmodified binders;
• a single polymer-dip extension for polymer-modified binders (PMB); and
• a two polymer-dip extension for highly modified binders (PMB2).

In addition, the repository contains routines for constructing rheological master curves using Kaelble temperature shift factors and a modified CAM modulus model, allowing simultaneous prediction of complex modulus and phase angle over a wide reduced-frequency range.

Intended Use

The implementation is intended as a transparent research reference rather than a general-purpose engineering software package. It is designed to support reproducible research, comparison of alternative modelling approaches, and future development of Black Space modelling methodologies.

Limitations

The B2SM is a descriptive rheological model rather than a constitutive material model. Consequently, the fitted parameters should be interpreted as descriptors of Black Space curve geometry rather than intrinsic material properties. Model quality depends on the quality and coverage of the experimental DSR data and assumes measurements are obtained within the linear viscoelastic region.

Related Resources

In addition to the software, the repository includes a small set of representative example DSR datasets that demonstrate the required input format and allow users to reproduce the analysis workflow. The complete experimental dataset used in the accompanying publication is archived separately in the associated research data repository.

Other

The GNU General Public License holds for the python script. The Creative Commons Attibution is here for the dataset provided with exemplary data for the model.