A series of cyclic triaxial tests were conducted on marine soft clay deposits to establish and validate a predictive model for cumulative plastic strain. Additionally, a numerical model of particle flow code in cyclic triaxial tests was developed. The effects of confining pressure, moisture content, and dynamic stress ratio on the dynamic properties of marine soft clay were examined, considering factors such as volume deformation and microscopic failure patterns. The results indicated that both the predictive model and numerical model showed strong consistency with the experimental data. The plastic strain of marine soft clay was influenced by moisture content, stress ratio, and confining pressure in a consistent manner, with moisture content being the primary factor. A predictive model for the cumulative plastic strain of marine soft clay was successfully established, allowing for the evaluation of dynamic properties from the perspective of cumulative plastic strain. During the loading process in the numerical model, microcracks within the soil structure gradually compacted, and the main displacement of the specimen extended from the vertical center axis to the sides, ultimately resulting in shear damage.

Several studies have explored the potential of waste marble powder (WMP) and lime (LM) as solutions for issues associated with clayey soils. While WMP enhances mechanical properties and addresses environmental concerns, LM effectively improves soil characteristics. This research investigates the efficacy of LM and WMP, both individually and in combination, in addressing challenges specific to clayey soils in Bouzaroura El Bouni, Algeria. These soils typically exhibit low load-bearing capacity, poor permeability, and erosion susceptibility. LM demonstrates promise in enhancing soil properties, while WMP not only addresses environmental concerns but also enhances mechanical characteristics, providing a dual benefit. The study utilizes a three-variable experiment employing Response Surface Methodology (RSM) Box-Behnken Design, with variations in clay content (88%-100%), LM treatment (1.5%-9%), and WMP inclusion (1.5%-9%). Statistical analysis, including ANOVA, reveals significant patterns with p-values <5%. Functional relationships between input variables (clay, LM, and WMP) and output variables (cohesion, friction angle, and unconfined compressive strength) are expressed through high determination coefficients (R-2 = 99.84%, 77.83%, and 96.78%, respectively). Numerical optimization identifies optimal mixtures with desirability close to one (0.899-0.908), indicating successful achievement of the objective with 88% clay content, 3% LM, and 6% WMP. This study provides valuable insights into optimizing clay soil behavior for environmental sustainability and engineering applications, emphasizing the potential of LM and WMP as strategic additives.