A power–exponential secant modulus model for the compression and settlement behavior of compacted loess fill

Uneven foundation settlement is a primary cause of various issues in high-fill engineering projects, arising from differences in the compressibility of fill materials associated with their inherent heterogeneity. Accurately characterizing these properties is therefore essential for ensuring engineering stability. This study proposes a novel nonlinear secant modulus model based on a composite power exponential model (CPE model), designed to overcome the limitations of existing models in consistently characterizing the entire consolidation process. Compared with traditional secant modulus models, the proposed model is more concise, requires fewer parameters, and captures the nonlinear evolution of soil mechanical properties during compaction. Its applicability and modeling advantages were validated through one-dimensional consolidation tests on field-compacted loess. The results demonstrate that the power–exponential composite evolution law of the proposed model reproduces the characteristic evolutionary trend of the secant modulus: a rapid increase at low stress, steady growth at intermediate stress levels, and gradual deceleration under high stress. The underlying physical mechanism of the model corresponds to key processes such as pore closure, structural weakening, and skeletal rearrangement, thereby accurately reflecting the stress-dependent evolution of the secant modulus. This demonstrates the model’s strong applicability for analyzing compressive deformation and predicting settlement in high-fill foundations under complex stress conditions.