A Computational Framework for Reproducible Generation of Synthetic Grain-Size Distributions for Granular and Geoscientific Applications

Particle size distribution (PSD), also referred to as grain-size distribution (GSD), is a fundamental characteristic of granular materials, influencing packing density, porosity, permeability, and mechanical behavior across soils, sediments, and industrial powders. Accurate and reproducible representation of PSD is essential for computational modeling, digital twin development (i.e., virtual replicas of physical systems), and machine learning applications in geosciences and engineering. Despite the widespread use of classical distributions (log-normal, Weibull, Gamma), there remains a lack of systematic frameworks for generating synthetic datasets with controlled statistical properties and reproducibility. This paper introduces a unified computational framework for generating virtual PSDs/GSDs with predefined statistical characteristics and a specified number of grain-size fractions. The approach integrates parametric modeling with two histogram-based allocation strategies: the equal-width method, maintaining uniform bin spacing, and the equal-probability method, distributing grains according to quantiles of the target distribution. Both methods ensure statistical representativeness, reproducibility, and scalability across material classes. The framework is demonstrated on representative cases of soils (Weibull), sedimentary and industrial materials (Gamma), and food powders (log-normal), showing its generality and adaptability. The generated datasets can support sensitivity analyses, experimental validation, and integration with discrete element modeling, computational fluid dynamics, or geostatistical simulations.