Genetic programming-based closed-form solutions for predicting the compressive strength of cement-treated soils

This study presents closed-form predictive models for estimating the unconfined compressive strength (UCS) of cement-treated soils using two genetic programming techniques i.e., Gene Expression Programming (GEP) and Multi Expression Programming (MEP), addressing the limitations of existing closed-form predictive models that are often overly simplified, rely on a narrow set of input variables, or are tailored to specific soil types, thereby restricting their general applicability. An extended dataset comprising 328 data points was compiled from existing literature, covering both coarse- and fine-grained soils and incorporating key geotechnical and treatment-related parameters such as liquid limit (LL), fine content (FC), normalized compaction parameters (ρ norm , w norm ), cement dosage (C), curing time (T), and porosity-to-volumetric cement ratio (η/C iv ). The dataset was pre-processed using min–max normalization and split evenly into training and testing sets. Through a systematic trial-and-error process, optimal configurations for GEP and MEP were identified. The optimal GEP and final MEP models demonstrated high predictive accuracy, achieving coefficients of determination (R 2 ) of 0.86 and 0.92, respectively, and were further corroborated by low error room-mean-squared error, and mean absolute error. Closed-form mathematical expressions were derived from both models. Performance evaluation, including monotonicity and sensitivity analyses, confirmed the physical relevance of the models, with GEP showing higher physical consistency than MEP. Notably, feature importance varied between models: ρ norm was most influential in MEP, while FC had the highest impact in GEP. Overall, the developed models offer accurate and physically meaningful tools for predicting UCS in cement-stabilized soils, contributing to improved design practices in cement-soil stabilization applications.