## 2 Materials and Methods  
### Proposed Procedure, Objective, and Scope  
According to the classical Mohr-Coulomb failure theory, the specimens exhibited visible failure angles \(\theta\) during unconfined compression tests, as shown in Figure 6a. By measuring this angle, the internal friction angle \(\phi\) can be determined in terms of the total stress using Equation (4):  
\[\phi=2\cdot(\theta-45) \tag{4}\]  
Figure 5: Site location on the groundwater level map (modified from Aviles [39]). On the other hand, Figure 6b shows the maximum compressive stress \(\mathrm{q}_{u}\) obtained from the stress-strain curve. Regarding the stress state according to the Mohr-Coulomb criterion, as shown in Figure 6c, the shear strength \(\tau_{\mathrm{f}}\) and normal stress \(\sigma_{\mathrm{f}}\) at failure can be determined using Equations (5) and (6), respectively:  
\[\tau_{\mathrm{f}}=(\cos\phi)\cdot\frac{\phi}{2} \tag{5}\]  
\[\sigma_{\mathrm{f}}=(1-\mathrm{sen}\phi)\cdot\frac{\mathrm{q}_{u}}{2} \tag{6}\]  
According to [PERSON] and [PERSON]. [3], the concept of \"estimation procedures\" emerges as a strategy to reduce the high costs and complexities associated with the classical application of unsaturated soil mechanics. Widely accepted models, such as those developed by [PERSON] and [PERSON], require direct and controlled measurement of matric suction, but this is a technically demanding and costly process. In this context, the development of simplified methodologies to estimate shear strength in unsaturated soils without active suction control is particularly valuable. [PERSON] and [PERSON] [44] conducted footing model tests on a statically compacted fine-grained unsaturated soil with five distinct matric suction profiles. They proposed a Modified Total Stress Approach (MTSA), which circumvents direct suction measurement by indirectly incorporating suction effects through the unconfined compressive strength of unsaturated samples. The equations derived in their study proved effective for estimating shear strength under total stress conditions, showing good agreement with in situ plate load tests, despite the absence of direct suction measurements. Additionally, the authors  
Figure 6: (**a**) Measurements of the shear angle \(\theta\) in different tested specimens; (**b**) stress–axial strain of the UCS graph; (**c**) Mohr circles of the UCS test. emphasized the practicality of conventional sampling procedures, positioning the MTSA as a feasible alternative when suction control is not achievable. [PERSON] and [PERSON] [27] investigated the mechanical behavior of an unsaturated silly clay from Jiyuan, China, through CU triaxial tests on specimens with water contents ranging from 15% to 27%, and subjected to confining pressures of 100, 200, and 300 kPa. The tests were conducted under total stress conditions without direct suction measurements. The results indicated that the shear strength decreased quadratically with increasing water content, with reductions of up to 48.47% observed at 300 kPa. In contrast, the internal friction angle exhibited a linear decline. Higher confining pressures partially mitigated the weakening effect of the increased water content, enhancing the shear strength by up to 89.15%. The authors highlighted the need for further validation across other soil types, as the findings were specific to silly clays from a single region and a limited moisture content range. [PERSON], [PERSON], and [PERSON] [26] investigated the shear strength of an unsaturated red clay through UU and CD triaxial tests on reconstituted samples with moisture contents ranging from 10% to 45%, under confining pressures of 100, 200, and 300 kPa, without direct suction measurements. Their results revealed a significant increase in cohesion in terms of the total stress, which was attributed to the implicit suction effect. The friction angle remained relatively constant up to 20% moisture content and decreased thereafter.