This work aims to improve the turbulence modeling in RANS simulations for particle-laden flows. Using DNS data as reference, the errors of the model assumptions for the Reynolds stress tensor and turbulence transport equations are extracted and serve as target data for a machine learning process called SpaRTA (Sparse Regression of Turbulent Stress Anisotropy). In the present work, the algorithm is extended so that additional quantities can be taken into account and a new modeling approach is introduced, in which the models can be expressed as a scalar polynomial. The resulting corrective algebraic expressions are implemented in the RANS solver SedFoam-2.0 for cross-validation. This study shows the applicability of the SpaRTA algorithm to multi-phase flows and the relevance of incorporating sediment-related quantities to the set of features from which the models are assembled. An average improvement of ca. thirty percent on various flow quantities is achieved, compared to the standard turbulence models.