## 2 Materials and Methods
### Testing Method  
A modified oedometer testing method was developed to capture the directionally dependent swelling behavior of the expansive soil. An automated unsaturated consolidation (UC) apparatus was constructed, incorporating controlled vertical load, lateral confinement, matric suction, and real-time displacement and pressure monitoring capabilities. The apparatus is illustrated in Figure 1.  
The apparatus comprised several integrated subsystems within a rigid reaction frame. At the base, a consolidated drained pressure chamber housed a high air-entry value ceramic disk (HAEV disk), which was designed to apply and measure the air and water pressures independently. Digital pressure transducers integrated in the air and water pump with \(\pm\)1 kPa accuracy can regulate the air (0-500 kPa) and water (0-50 kPa) pressures, and a pressure transducer with \(\pm\)1 kPa accuracy was equipped on the loading rod connected to the reaction frame to control the vertical load (0-500 kPa) applied through the reaction frame and the vertical movement of the pressure chamber. Extensive drainage lines and outlet valves facilitated the saturation of the disk and equipment using a Mariotte bottle, as well as water delivery and bubble flushing. A pressure regulator maintained a low upward gradient (<50 kPa) to remove bubbles and ensure the full saturation of the HAEV disk. The saturated HAEV disk then acted as an air-water interface, transmitting pore-water stresses to the specimen above. During testing, the water pressure always remains constant at 40 kPa to accelerate the saturation of the HAEV disk and ensure an unobstructed water supply path. After the vertical load (\(\sigma_{v}\)), air pressure (\(u_{a}\)), and water pressure (\(u_{w}\)) were all applied in the pressure chamber, and the soil specimen was ready to be inundated under the given net normal stress (\(\sigma_{v}-u_{a}\)) and matric suction (\(u_{a}-u_{w}\)). The linear variable displacement transducer (LVDT) for measuring axial strains was mounted on the loading rod and bracketed to the top of the pressure chamber, enabling precise measurements of the axial strains to a precision of 1 \(\times\) 10\({}^{-3}\) mm. Fine threaded rods connected the components and provided adjustability. Signals from the transducers interfaced with a data acquisition system, recording the pressures, vertical displacement, air pressures, and water pressures. Considering the fact that the permeability of expansive soil is extremely small, which results in quite a long period of time to achieve suction equilibrium, the frequency of the recording was set to 5 min intervals. The benchmark for the determination of suction equilibrium was also set as the changes in the readings for lateral pressure and vertical displacement were <1 kPa and 0.010 mm, respectively. A significant innovation was the integration of a \"retractable ring\" device for the lateral confinement of the soil specimens during testing. As depicted in Figure 2, it consisted of a stainless steel ring with a 61.8 mm inner diameter and 30 mm height, housing a miniature pressure transducer (0-1000 kPa, \(\pm\)1 kPa accuracy), thin acrylic spacer, and a curved plate. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Description** & \(w_{L}\) **(\%)** & \(I_{P}\) & \(G_{s}\) & **Sand (\%)** & **Silt (\%)** & **Clay (\%)** & **USCS** & **MDUW (kN/m\({}^{3}\))** & **OMC (\%)** \\ \hline Expansive soil & 56.3 & 34.9 & 2.75 & 0 & 52.1 & 47.9 & CH & 17.2 & 17.9 \\ \hline \hline \end{tabular} Note: \(w_{1}\): liquid limit; \(I_{P}\): plasticity index; \(G_{s}\): specific gravity; USCS: unified soil classification system; MDUW: maximum dry unit weight; and OMC: optimum moisture content.  
\end{table} 
Table 1: Index properties of the testing soil. An adjustable tightening mechanism joined the halves of the ring, enabling it to close down in discrete steps to maintain the laterally confined state.