The recently developed framework for modeling grain breakage in granular materials is shown to be valid for saturated/unsaturated conditions. The model describes the initiation, development, and stabilization of breakage using three parameters, all depending on the strength of a representative particle size. When water is introduced, the strength of the soil's particles is expected to weaken, which leads to increased breakage intensities. The model is able to predict the early onset of crushing and the increase in particle breakage rate, both considered characteristic behaviors of a crushable granular medium in wet conditions. Initially dry and saturated model lines limit the evolution of the model parameters in the intermediate saturation states. A mid-loading change in the saturation of the granular medium results in an increased rate of particle breakage. The experimental data available in the literature is analyzed in light of the proposed model, which allows a better understanding of the development of particle breakage under the influence of water.

The Soil Water Retention Curve (SWRC) is a critical property for understanding water movement in unsaturated soils, influencing hydraulic conductivity and shear strength. While empirical models like those of Brooks and Corey and van Genuchten are widely used, they often lack a direct connection to soil microstructure. This study introduces shape parameters $$\nu$$ ν (for particle size distribution, PSD) and $$\mu$$ μ (for SWRC) to establish a direct correlation between soil grading and water retention. Using the UNSODA database, we analyzed 301 soil samples across various textures and void ratios. Results show a strong correlation between $$\nu$$ ν and $$\mu$$ μ , particularly in soils with lower void ratios, where denser packing enhances the influence of PSD on water retention. Coarser soils exhibited stronger correlations, while finer soils showed more complex behavior due to additional hydraulic mechanisms. The proposed empirical formula provides a practical tool for predicting SWRC based on PSD, offering a balance between simplicity and physical relevance. Validation using independent datasets confirmed the model’s robustness for granular soils but highlighted limitations in fine-grained soils, where clay content introduces divergence. This study advances the understanding of soil–water interactions and provides a valuable framework for geotechnical and hydrological applications.

This paper examines the parameter ν, a shape factor of the particle size distribution (PSD) in granular materials, and its broad applications in geotechnical engineering. Defined as the slope of the PSD in a log-log plot, ν provides a funda-mental measure of distribution shape, capturing the evolution of granular materials under varying conditions. While initially developed to quantify particle break-age, ν has proven to be a versatile tool with applications extending to the modeling of PSD evolution, micromechanical analysis, and the influence of environ-mental factors such as moisture. The paper explores the theoretical foundation of ν, its connections to fractal theory, and its role in describing granular transformations under mechanical and hydraulic influences. Additionally, the relationship between ν and other PSD-based breakage parameters, such as those proposed by Marsal, Hardin, and Einav, is examined, highlighting its advantages as a unifying descriptor of grain size evolution. By synthesizing these perspectives, this study underscores the value of ν as a robust and adaptable parameter for advancing the understanding of granular mechanics and geotechnical engineering.

In this paper, hybridization is proposed as an alternative approach to sustainable tourism development in Morocco’s southeastern cities. Hybridization refers to the integration of multiple elements, such as traditional and modern, to create a new synthesis that incorporates the aspects required from a modern building. The evolutionary approach adopted helps to balance between short-term requirements and long-term sustainability, while also preserving cultural heritage and promoting innovation. By implementing sustainable and culturally sensitive strategies, a positive future can be secured for architectural and urban systems like Ksours and Kasbahs.