# A Modified Pressure-Sinkage Model for Studying the Effect of a Hard Layer in Sandy Loam Soil
## 2 Materials and Methods  
As shown in Figure 1a, a bevameter (plate sinkage test) was utilized to carry out the experiments. The equipment's design, construction, and function are explained in other published research [31]. A hydraulic cylinder was used to apply the necessary load. The experiment included a soil bin that was 200 cm in length, 100 cm in width, and had a changeable thickness of 70 cm. Three circular sinkage plates of 10 cm, 15 cm, and 20 cm are connected to the hydraulic cylinder and are in contact with the soil. A known force is applied to this soil. The applied vertical load is measured through using a stainless-steel S-beam load cell (HBM, Germany) with a 30 kN capacity. To measure the vertical deformation (sinkage), an analog displacement encoder (MLO-POT-0360-TLF, FESTO, Germany) with a 30 cm stroke was used. This displacement sensor's slider was connected to the hydraulic cylinder rod end and was simultaneously moving. The hydraulic cylinder could move transversely as well as longitudinally through the rail to test all points in the soil bin's soil surface. The soil bin's bottom was a hard layer in a field. The tilling of agricultural soils is performed until 30-40 cm of depth, which is similar to the contact diameter of tires [24]. The soil thickness can be assessed because the soil bin's height can be changed. To prepare the soil: first, the soil (from a field belonging to the Szent Istvan Campus, MATE University, Hungary) was transferred to the laboratory; then, a 5 mm mesh was used to sieve this soil and remove any coarse parts and plant roots; and the soil was then stored where it would not dry up. Previous studies have used this same soil [32; 33], which is a sandy loam with a composition of sand (2-0.05 mm), mud (0.05-0.002 mm), and clay (<0.002 mm). The soil's bulk density and moisture content can be established using the sampling method, which involves taking different soil samples during and after the tests. The soil samples were dried for 24 h in the oven at 110 \({}^{\circ}\)C. The weight of the samples was noted before and after drying them to establish the moisture content and bulk density. Table 1 presents the soil examination results, along with the angle of shearing resistance and the cohesion that was determined based on the direct shear test results. The tests were conducted in a laboratory under controlled conditions. For the tests, two soil thicknesses of 30 cm and 40 cm were used with diverse bulk densities. The soil bin was first filled with 30 cm thickness of soil in layers, with each layer being 5 cm thick. A wood plate was used to compress all layers and obtain the initial bulk density of 1.3 g/cm\({}^{3}\) \begin{table}
\begin{tabular}{c c} \hline \hline
**Feature** & **Value** \\ \hline Cohesion & 58.07 kPa \\ Angle of shearing resistance & 37.59\({}^{\circ}\) \\ Water content & 7-9\% dry basis \\ Bulk density & 1.3, 1.4, and 1.5 g/cm\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of sandy loam soil used in the experiments. Figure 1: (a) Plate sinkage test (bevameter device); (b) soil surface leveling. To avoid the concentration of stress on conglomerated points at the soil surface under the loading plate, the soil surface was specifically leveled, as shown in Figure 1b. To apply the load, a sinkage plate with a 20 cm diameter was used, as this size offers more realistic conditions that would be comparable to the soil's behavior under a tire. Next, the sinkage plate was connected to the force sensor and moved closer to the soil surface through the bevameter. The S-beam load cell was used to measure the vertical force, and the analog displacement encoder was used to measure the displacement. These steps were conducted at the sinkage plate's 3 cm/s penetration rate. The penetration points were obtained where the soil bin walls would not impact the data. The force and displacement sensors transferred the signals to a strain gauge measurement device, called Spider 8, which then sent this measured data to a computer.