Understanding how contaminants travel through soil and groundwater is essential for protecting ecosystems and managing pollution. In many real-world environments, substances such as heavy metal ions, electrically charged metal atoms dissolved in water that can be toxic, and suspended particles, tiny solid materials carried within flowing water, migrate together through porous geological materials. Porous materials are soils or rocks that contain many small interconnected spaces where water can move. Their movement is influenced not only by water flow but also by mechanical stress, meaning physical pressure applied to the soil, and temperature changes within the soil. Yet capturing all these interacting processes in a single predictive framework has long been a challenge for researchers studying subsurface environments, the regions below the ground surface where soil, rock, and groundwater interact.

Famous Professor Bing Bai and Haiyan Wu, Rui Zhou, Nan Wu, and Bixia Zhang from Beijing Jiaotong University, together with Nan Wu from Suzhou City University, developed a creative theoretical framework to address this complexity. Their research introduces a coupled multiphase-substance flow model designed to simulate the joint movement of water, solid particles, and dissolved contaminants in porous materials. A multiphase system refers to a mixture containing different forms of matter, such as solids and liquids moving together. The work is published in the peer-reviewed journal Journal of Rock Mechanics and Geotechnical Engineering. By integrating multiple physical processes into a unified thermodynamic structure, a framework based on the laws that govern energy and heat in physical systems, the model achieves an accurateprediction of how pollutants migrate underground.

The researchers built the model on principles of granular thermodynamics, a scientific approach that studies how collections of small particles behave when they interact, move, and exchange energy. Their framework considers the combined effects of deformation, meaning the change in shape or volume of soil under stress, seepage flow, the slow movement of water through soil pores, and the migration of suspended substances. As Professor Bai explained, “This model introduced the new concepts, such as granular temperature and granular entropy, to describe energy dissipation at meso-level.” Granular temperature refers to the energy associated with the motion and rearrangement of particles, while entropy entropy describes how disordered or randomly distributed those particles become. The meso-level refers to an intermediate scale between microscopic particle behavior and large-scale soil movement. These concepts allow scientists to account for energy changes that occur as particles rearrange, collide, or move through soil pores during transport processes.

Results show that the model can capture the complex interplay between physical forces and chemical transport. Chemical transport refers to the movement of dissolved substances carried by water through soil and rock. When external pressure compresses soil, the pore spaces, the tiny openings between soil grains that store water, shrink, trapping more suspended particles and altering the migration path of contaminants. The simulations also reveal that temperature gradients, differences in temperature between two locations, can accelerate the movement of pollutants by driving thermal diffusion, the tendency of particles to move from warmer areas toward cooler areas, and enhancing particle motion. These findings highlight how environmental conditions such as mechanical loading, the pressure exerted on soil by external forces, and temperature variations can strongly influence the speed and pattern of contaminant transport.

One of the major strengths of the framework is its ability to combine multiple processes into a single system of equations, mathematical expressions used to describe how physical quantities change and interact. As Professor Bai noted, “This viewpoint unifies the deformation, seepage, and suspended substance migration of geotechnical materials under the framework of granular thermodynamics.” Geotechnical materials refer to natural earth materials such as soils and sediments that engineers study when designing foundations or environmental systems. By linking mechanical deformation, fluid flow, the movement of liquids such as groundwater, and chemical migration, the approach provides a more realistic representation of how porous materials behave in natural and engineered settings.

To test the model, the team compared its predictions with laboratory experiments involving the coupled transport of heavy metal ions and suspended particles in a soil column. A soil column is an experimental setup where a vertical tube is filled with soil to reproduce how water and contaminants move through ground layers. The results closely matched the observed breakthrough curves, graphs showing how the concentration of a substance leaving the column changes over time, and deposition patterns measured in experiments. Deposition refers to particles becoming trapped or settling within the soil pores. The model successfully reproduced how changes in injection concentration, the amount of contaminant entering the system, flow velocity, the speed of moving water, and particle size affect pollutant movement, demonstrating its reliability for practical simulations.

Beyond theoretical insights, the research has practical applications in environmental engineering, the field focused on protecting natural resources and reducing pollution. Accurate predictions of contaminant migration are crucial for designing remediation strategies, methods used to clean polluted soils and groundwater, evaluating landfill safety, and managing groundwater resources. Groundwater refers to water stored beneath the surface in soil and rock layers that supply wells and springs. By incorporating factors such as temperature gradients and soil deformation, the new framework provides a tool for studying complex subsurface processes that traditional models often oversimplify.

Overall, the study offers a unified way to understand how pollutants travel through porous geological systems under combined physical forces. This research work is at a leading level internationally. As environmental challenges grow and contamination risks increase, models that capture the full complexity of subsurface transport could become essential for both scientific research and engineering practice.

Journal Reference

Bai B., Wu H., Zhou R., Wu N., Zhang B. “A granular thermodynamic framework-based coupled multiphase-substance flow model considering temperature driving effect.” Journal of Rock Mechanics and Geotechnical Engineering, 2025. DOI: https://doi.org/10.1016/j.jrmge.2024.11.017

About the Author

Bai Bing was born in October 1966, and is a professor at Beijing Jiaotong University, Beijing, China. His research interests include geo-environmental engineering, thermal consolidation theory, contaminant transport theory and control methods. He devoted himself to the advances in soil pollution, solid waste treatment and geotechnical environment. He developed a theory describing the cotransport of heavy metals and suspended particles considering temperature in porous media and proposed a nonlinear attachment-detachment model with hysteresis suitable for the substances with sizes ranging from ions to large particles, which is of great significance in groundwater pollution mechanism and purification technology. He developed a series of high-performance red mud-based geopolymer materials, providing important research ideas and technologies for solid waste utilization.

He has published more than 200 academic papers in international academic journals and edited 10 academic monographs and textbooks. In 2023, he was granted the Beijing Natural Science Award and the Natural Science Prize of the Ministry of Education of the People’s Republic of China in 2022 for his outstanding scientific research as a first-completion recipient. He has been named to Stanford University’s career list of the “World’s Top 2% Scientists” for consecutive years. He won the “Scott Sloan Award for best paper in 2021” named by the Fellow of the Royal Society. He was nominated for the Eni Award, an internationally authoritative award in the field of energy and environment, in 2023. He was awarded the 15th Scientist Medal by the International Association for Advanced Materials (IAAM) and was admitted as a Fellow of IAAM in 2024. He serves as an editorial board member of the Journal of Geotechnical Engineering and Rock and Soil Mechanics of China. He is the member of several professional committees, such as the director of the China Soil Mechanics and Engineering Branch.