# A Modified Pressure-Sinkage Model for Studying the Effect of a Hard Layer in Sandy Loam Soil
## 5 Conclusions  
This study examined the conventional pressure-sinkage models' limitations when assessing the effect of the rigid layer in soil. To accomplish this, an empirical investigation was conducted to determine the hard layer's impact on the pressure-sinkage relationship for plate sinkage that has a diameter similar to the vehicle tier. The study also explored the interaction zone between the rigid and compacted layers, and determined the critical relative sinkage (z\({}_{\text{o}}\)/D), which is also called the breaking point. The soil deformation under the plate was also identified. Two zones were outlined by the pressure-sinkage curves, which are the build-up zone with constant deformation and the other zone following the breaking point, which has exponential and non-constant deformation. The study further discussed modifying a simple conventional pressure-sinkage model to examine the hard layer. To accomplish this, a model parameter was improved upon, which is the sinkage modulus (k; the load-bearing capacity factor), resulting in a new parameter, kapp (the apparent sinkage modulus). According to the results, the rigid layer increased the compaction, thereby increasing the pressure and kapp. In the kapp equation, constants B and c were measured from two points on the experimental pressure-sinkage curve. The equation was further simplified both to make it implicit and to ensure that it could be solved numerically. To avoid calculation errors, the \(\Delta\)k model with \(\Delta\)(z/D) was put forth. In this model, different B and c values were used to determine coherent values of \(\Delta\)k at \(\Delta\)(z/D) = 0.5. Hence, this point was selected as a fixed point for determining the best range of B and c constants. A model used to determine the relationship between B and c was also presented, which showed coherent values regarding the constants at \(\Delta\)k = 20, 30, and 50 N/cm\({}^{2}\). The optimum range for B was thus determined to be between 10 and 20, and between 1 and 3 for c. The present model of the pressure-sinkage equation was thus found to reflect the rigid layer effect in soil with high fidelity through the new sinkage modulus equation.  
In the current study, the new modification of the load-bearing capacity factor (k) and the new pressure-sinkage model have been proposed and have been used to represent the affection of a hard layer in the soil. In future work, the authors plan to generalize the pressure-sinkage model and transform it into a full dimensionless form while considering the effect of the soil density and the finite depth.  
Conceptualization, N.D.S.; methodology, N.D.S. and G.P.; validation, N.D.S., G.P., and M.M.H.; formal analysis, N.D.S. and G.P.; investigation, N.D.S., G.P., and M.M.H.; resources, P.K. and G.P.; data curation, N.D.S. and G.P.; writing--original draft preparation, N.D.S.; writing--review and editing, N.D.S. and M.M.H.; visualization, N.D.S.; supervision, P.K.; funding acquisition, P.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Not applicable. This work was supported by the Stipendium Hungaricum Programme and by the Mechanical Engineering Doctoral School, Szent Istvan Campus, MATE University, Godollo, Hungary. The authors declare no conflict of interest.