TITLE:
Modelling of Soil Compression Curve with Hysteresis in Void Ratio-Effective Stress Relation
AUTHORS:
Ippei Iiyama
KEYWORDS:
Compressibility Index, Consolidation Test, Normal Consolidation, Overconsolidation, Preconsolidation Stress
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.10,
October
27,
2026
ABSTRACT: Soil compression curve is used for predicting land subsidence associated with a consolidation process. It is often described as a relationship between void ratio e [m3∙m−3] of the soil and effective stress σ' [N∙m−2] exerted on the soil, and the trajectory of it depends on stress history. A mathematical model of soil compression curve is useful for reproducing and predicting purposes when it is concise and able to formulate hysteretic behaviours in e-σ' relation. This study aimed at developing a mathematical model to describe a compression curve and enabling the model to predict hysteretic behaviours in e-σ' relation. The model was developed based on the geometrical features of a compression curve commonly observed on the e-log10σ' relation. The expansion and recompression processes were also modelled for predicting hysteresis of e-σ' relations by introducing the concept of potential expansion curve and assuming the geometrical similarity between compression curves and expansion curves on the e-log10σ' plane. The proposed model performed well for reproducing and predicting various kinds of measured e-σ' relations, and enables to predict any hysteretic behaviours found along repetitions of expansion-compression processes.