# A Modified Pressure-Sinkage Model for Studying the Effect of a Hard Layer in Sandy Loam Soil
## 3 Deformation under Pressure Plate as a Function of Depth  
Deformation refers to compaction. The deformation in the plate sinkage test involved vertical and lateral compaction, along with soil movement under the plate [34]. There are typically two deformation zones in the field. The first is the build-up zone that has an increasing resistance, and the second is the stationary zone with constant resistance. To identify the soil density distribution in the deeper layers of sandy loam soil, [PERSON] [33] used the cone penetrometer in a field. [PERSON] also specified the two deformation zones and explained them in another study's results [24]. The pressure in the build-up zone can elevate to severe relative depth (z\({}_{\text{o}}\)/d). In the stationary zone, the pressure remains constant to an extent. The plat sinkage test can help observe this phenomenon. Figure 2 illustrates a plate sinkage test's schematic diagram. Once loading begins in the build-up zone, soil aggregates and particles rearrange while air becomes expelled, which increases the density of the dry bulk. Thus, sinkage mainly results from compaction below the plate. If the plate keeps sinking and the load is increased, then the soil immediately under the plate can no longer compact at the critical relative depth. Because of this, a conical mass is developed that moves by the plate and leads to lateral deformation and compaction; that is, sinkage is largely caused by soil becoming laterally displaced [34]. According to [PERSON] et al. [24], however, if a hard layer is present at a certain depth under the footing (circular or rectangular), it can have a substantial effect on the pressure distribution, as well as the load-bearing capacity, of the soil. The hard layer mainly alters the soil's pressure distribution because the pressure is 60% greater compared to that in a homogeneous half-space. As a result, the interaction of the compact zone with the effect of a rigid layer increases compaction and pressure. Moreover, this pressure distribution can be altered as a function of relative depth. Figure 3 presents the assessment of [PERSON]'s measurements, where the critical relative depth as the soil density function was plotted. Their z\({}_{\text{o}}\)/d measured 2-7 cm in depth. This value is based on the soil density and moisture content. As can be seen from Figure 3, the critical relative depth (z\({}_{\text{o}}\)/d) strongly decreases at high moisture content levels, as the soil tends to exhibit plastic flow behavior. Hence, the experiments conducted in this study considered moisture content levels between 7% and 9%. This study primarily aimed to determine the critical relative sinkage (z\({}_{\text{o}}\)/D), called the breaking point, by assessing the plate sinkage test's characteristics. Based on the experimental results, Equation (2) presents the breaking point, (z\({}_{\rm o}\)/D). \[\frac{z_{\rm o}}{D}-\frac{H}{D}=1.05-1.07 \tag{2}\]  
where z\({}_{\rm o}\) is the vertical deformation, D is the sinkage plate diameter, and H is the soil thickness. Figure 3: Relative depth (z\({}_{\rm o}\)/d), with soil density at a moisture content level of 9% and 15% for a penetrometer cone of 1.6 cm in diameter. Figure 2: Schematic of the plate sinkage test. Table 2 presents the critical relative sinkage (z\({}_{\rm o}\)/D) values of sinkage plates, gathered from the experiments involving varied soil thickness. Figures 4 and 5 present the results of pressure-sinkage on a logarithmic scale for 30 and 40 cm soil thickness levels, respectively, considering a 20 cm sinkage plate diameter. The measurements were carried out at three initial bulk densities (\(\rho\)) of 1.3, 1.4, and 1.5 g/cm\({}^{3}\). The curves clearly exhibited the transition zone before and after the breaking point for the plate sinkage test. As shown in the figures, the pressure-sinkage curves include two parts. The first part is prior to the breaking point that conveys the build-up zone.