Study on the calculation model of mutually embedded displacement between miscellaneous fill and soft soil

With the overlying load, soft soil particles with high water content can easily embed into miscellaneous fill with large pores, resulting in mutually embedded displacement. This displacement significantly contributes to the total settlement, making its prediction crucial. Considering the final state of mutually embedded displacement as the research object, and taking into account the overlying load, particle size and porosity of the miscellaneous fill, and friction force, a conceptual model based on static equilibrium theory was developed to derive the calculation formula for mutually embedded displacement. The calculation formula indicates that mutually embedded displacement increases with increasing external load, particle size and porosity of the miscellaneous fill, while it increases with decreasing friction coefficient. Furthermore, parameter determination methods in the calculation formula were illustrated using a soft soil moisture content of 40.15% and concrete ball miscellaneous fill. The results indicate that for spherical miscellaneous fill particles, the path coefficient (K) and force coefficient (M) exhibit a linear relationship with particle size, while the lateral friction force (τ) shows a linear relationship with the load. Comparing between the formula's calculations and laboratory tests, it was found that the maximum error is 15.8%, indicating the model's reasonableness and the formula's high predictive accuracy. The derived formula is both convenient and simple, providing theoretical guidance for calculating or predicting the settlement of composite foundations comprising miscellaneous fill and soft soil.