## 2 Materials and Method
### Specim Preparation
A constant strain rate of 0.076% per minute was applied until failure occurred, allowing for the determination of the unconfined compressive strength and stress-strain behavior of the stabilized soil. Figure 2 shows the triaxial machine. The consolidation characteristics of lime-cement stabilized clay soil were comprehensively evaluated through a systematic experimental program employing ASTM D2435 [21] one-dimensional consolidation testing as the primary methodology, supplemented by auxiliary characterization tests following ASTM D7263 [23], D854 [19], and D2216 [24] standards. This test was crucial in determining the stabilized soil's pre-cons  
Figure 2: Laboratory triaxial testing machine setup showing loading frame, pressure cell, and control panel used for measuring the UCS of soil specimens. compression index, and compressibility characteristics. Specimens were carefully trimmed to fit the consolidation ring and then subjected to incremental loads (25, 50, 100, 200, 400, 800 and 1600 kPa). Each load was maintained for 0, 1, 2, 4, 8, 15, 30, 60, 120, and 1440 min or until primary consolidation was deemed complete, as indicated by the log-time method. Figure 3 shows the consolidation test apparatus. The consolidation testing methodology followed ASTM D2435 protocol using precision oedometer apparatus with 63.5 mm diameter and 25 mm height specimens, yielding a cross-sectional area of 3166.92 mm\({}^{2}\). Initial porosity (n\({}_{0}\)) was calculated using n\({}_{0}=1-(\mathrm{M_{s}}/(\mathrm{V_{0}}\times\mathrm{Gs}\times\mathrm{\rho_{w}}))\), where the mass of solids (M\({}_{\mathrm{s}}\)), initial volume (V\({}_{0}\)) of 0.000079 m\({}^{3}\), specific gravity (G\({}_{\mathrm{s}}\)), and water density (\(\mathrm{\rho_{w}}\)) of 1000 kg/m\({}^{3}\) were measured parameters. The corresponding initial void ratio was determined through the dry density method as e\({}_{0}=(\mathrm{Gs}\times\mathrm{\rho_{w}}\times\mathrm{V_{0}})/\mathrm{Ms}-1\). Gravimetric water content determinations followed ASTM D2216 procedures, incorporating precise mass measurements including ring weight (w\({}_{1}\)), wet soil plus ring weight before testing (w\({}_{2}\)), dry soil plus ring weight after testing (w\({}_{3}\)), and final soil plus ring weight (w\({}_{4}\)). Specific gravity determination adhered to ASTM D854 protocols. Pre-consolidation pressure (\(\mathrm{\sigma_{P}}^{\prime}\)) was determined through rigorous application of the Casagrande graphical method on the e-log \(\mathrm{\sigma^{\prime}}\) consolidation curve, involving systematic plotting of void ratio against the logarithm of effective stress and identification of maximum curvature points on the virgin compression line. The method's precision was validated through careful examination of the transition from recompression to virgin compression behavior, ensuring accurate demarcation of the yield stress threshold. The compression index (C\({}_{\mathrm{c}}\)) was quantified from the slope of the linear portion of the virgin compression line in e-log \(\mathrm{\sigma^{\prime}}\) space, calculated as C\({}_{\mathrm{c}}=\Delta\mathrm{e}/\Delta\mathrm{log}\)\(\mathrm{\sigma^{\prime}}\) through linear regression analysis of the virgin compression portion while excluding recompression and transitional regions. The reduction in compression index compared to unstabilized clay reflects the constraining effect of cementitious bonds formed through pozzolanic reactions between lime, cement, and clay minerals. The constrained modulus (M) was evaluated from consolidation data using M = \(\Delta\mathrm{\sigma^{\prime}}/\Delta\mathrm{\epsilon}\), where \(\Delta\mathrm{\epsilon}\) represents axial strain increment corresponding to applied stress increment \(\Delta\mathrm{\sigma^{\prime}}\). This parameter relates directly to the coefficient of volume compressibility (m\({}_{\mathrm{v}}\)) through M = 1/m\({}_{\mathrm{v}}\), where m\({}_{\mathrm{v}}=\Delta\mathrm{e}/((1+\mathrm{e_{0}})\Delta\mathrm{\sigma^{\prime}}\).