## 2 Materials and Methods
### Method
The average of the two readings were used as displacement values. The required steps such as resetting the gauge readings and verifying the uniformity of the applied loads were followed throughout all the testing procedures. Loads were implemented in a vertical and static manner onto the model footing. Load and displacement values were then transferred to a data collection device with 32 conduits. Afterwards, they were transformed into numeric values by means of geotechnical software (DS7 DataSystem 7.3). The values of vertical loads, settlements and stress values were acquired for all the conducted tests. The boundary effect was also considered for the testing case by mounting strain gauges onto the edges of the case, resetting them all to zero and observing them as the loads were applied--all the reading values in the gauges stayed constant [11]. The experimental configuration developed for this study is presented in detail in Figure 2. The setup was specifically designed to evaluate the settlement behavior of soil samples subjected to vertical loading, simulating shallow foundation conditions. The system is constructed on a rigid steel frame with bolted joints to ensure structural stability and to prevent horizontal or torsional displacement during loading operations. At the top of the frame, a servo-controlled vertical load motor is installed to apply monotonically increasing static loads to the test specimen. The load is transmitted through a vertical loading rod to a rigid steel foundation plate placed on the surface of the soil sample. The motor's load application is displacement-controlled to enable fine-tuned loading sequences and ensure gradual settlement response capture. To measure the applied load with high accuracy, a strain-gauge-based load cell (model: ESIT LCT series) is positioned in-line between the motor and the loading rod. The load cell continuously records the applied vertical force and transmits data to the acquisition unit for real-time monitoring and analysis. The foundation plate used to represent a shallow footing is fabricated from stainless steel, with dimensions of 100 mm \(\times\) 100 mm \(\times\) 20 mm (width \(\times\) length \(\times\) thickness). The base of the plate is machined flat to ensure uniform load distribution across the contact area. The plate rests directly on the prepared surface of the clay specimen, which is compacted in a cylindrical mold with dimensions of 600 mm diameter and 600 mm height to simulate field conditions under controlled laboratory parameters. To capture vertical settlements accurately, two high-sensitivity Linear Variable Differential Transformers (LVDTs) (model: ELE International) are symmetrically installed on either side of the foundation plate. These transducers are mounted on independent fixed frames isolated from the loading system to eliminate measurement errors due to system vibration or lateral movement. The LVDTs provide redundant readings to increase the reliability of displacement measurements and to detect potential tilt or eccentric loading during the test. The load and displacement signals are collected through a 32-channel data acquisition system (sampling frequency:10 Hz, voltage range: \(\pm\)10 V) that allows simultaneous monitoring of all measurement channels. The system is equipped with signal conditioning modules, analog-to-digital converters, and software-based data logging capabilities. This allows for the real-time graphical output of load versus settlement behavior, as well as post-test processing and numerical analysis. Throughout the test, the system operates under room temperature (20 \(\pm\) 2 \({}^{\circ}\)C) and a controlled relative humidity of approximately 60-65% to minimize environmental effects on material behavior. Soil specimens are conditioned for 24 h prior to testing, and tests are repeated three times for each mix design to ensure statistical reliability. All mechanical components and sensor placements were calibrated prior to testing.