Deciphering Soil-Plant and Soil-Insect Interactions: A Mathematical Modeling Approach

Abstract

Abstract The Pev and Rv functions were introduced as a way of summarizing the mechanical phenomenon of root-soil interactions and the effect of root growth on soil volume. The Mohr-Coulomb criterion was applied to the Rv function to demonstrate the relationship between root morphology, soil mechanical properties, and soil stability. The theory of elasticity and plasticity was applied in the analysis of the Bio-Geo Interface, which showed that the force F generated by the roots increased with time due to the growth of the roots and the increase in their volume. The forces acting on the Bio-Geo Interface were represented mathematically through the use of vector arithmetic, which helped to calculate the direction of the forces acting on the system. The Pev function was used to study the evolution of the plant and how it affected the Rv function. The results showed that the interplay between plant growth and soil mechanics is crucial in understanding the behavior of the Bio-Geo Interface, and can provide valuable insights into the interactions between plants and soil in natural and engineered systems. In the study of soil-insect interaction, a mathematical function, Iev, was proposed to represent the insect’s evolution in the soil environment. The function takes into account factors such as food sources and void ratio, which are important indicators of the biological and geotechnical aspects of the soil respectively. Despite the potential impact of insects on the soil environment, it has been concluded that their force resulting from their movement and behavior is negligible according to theories of elasticity and plasticity. This means that the impact of insects on the soil is minimal and does not significantly affect the soil’s mechanical properties. However, the biological aspects of the soil, such as food sources, remain important factors in the study of insect evolution in the soil environment.