On the Friction Between Soil and Steel With Extension to Soft Materials and Geological Faults

ABSTRACT

A unified constitutive model for friction is developed using a generalised power‐law framework that captures rate, load, temperature and state dependencies across granular, cohesive, soft‐material interfaces and geological faults. Grounded in an energy‐balance derivation and state‐evolution tribology, the model defines the interface velocity (strain‐rate) as the fundamental constitutive property. The inverted kinetic friction formulation utilises a power‐law representation, successfully reproducing static‐to‐dynamic transitions, direct velocity‐strengthening effects and evolutionary velocity‐weakening behaviours. Representative systems: rock penetration, cohesive soil sliding, high‐speed machining and fault friction are systematically mapped. The explicit incorporation of Arrhenius temperature kinetics corrected to couple the activation energy with the rate‐and‐state exponent () proves that the model captures macroscopic thermal weakening. Furthermore, numerical sensitivity analyses of the real area of contact evolution confirm sublinear growth under confining pressure, successfully predicting pressure‐induced friction drops. This robust formulation bridges classical empirical laws with modern rate‐and‐state mechanics. The framework is parsimonious, physically coherent and demonstrates powerful predictive capabilities across tribological and Earth science contexts.