## 3 Results
### Assessment of the Mechanical Behavior (Strength and Stiffness) of Novel Geomaterials
Compared to their compressive strength results, the XG-based mixtures showed proportionally greater gaps in stiffness relative to GG and GY. This suggests that while biopolymers improve strength through cohesive effects, their influence on stiffness remains limited, potentially due to the absence of cementitious mineral bonding phases. Still, the reduced variability and repeatable response of these mixtures highlight their potential for specific engineering applications where high stiffness is not the primary requirement. The relationship between stiffness and strength is shown in Figure 11. The general correlation obtained for all mixtures was expressed as \(\mathrm{G_{o}}\) = 3354.7\(\mathrm{q_{u}}\), with a determination coefficient of \(R^{2}\) = 0.74. Although this represents a moderate fit, it highlights the limitation of applying a grouped regression model across different stabilization strategies. The variability in composition and behavior among the mixtures suggests that individual regression analyses are more appropriate. This observation aligns with the findings of [PERSON] et al. [12], who reported a much stronger correlation for CLW-based mixtures alone, reaching \(\mathrm{G_{o}}\) = 4828.8\(\mathrm{q_{u}}\) with a coefficient of determination of \(R^{2}\) = 0.96. Such results reinforce the importance of disaggregated modeling when dealing with diverse materials and stabilization mechanisms. Figure 11: The direct relationship between the UCS and stiffness. Application of the Porosity/Binder Index in Predicting the Compressive Strength and Stiffness of Novel Geomaterials  
The porosity/binder index (\(\eta/B_{iv}\)), originally developed by [PERSON] et al. [39] (3), has become a key tool in the rational design of soil-binder mixtures. By establishing a relationship between the void content of compacted soils and the absolute volume of binder, this index provides a robust physical foundation for predicting mechanical behavior--including unconfined compressive strength (\(q_{\text{u}}\)) and small-strain stiffness (\(\text{G}_{\text{o}}\))--through the power-type relationship shown in Equation (1). \[q_{u}\ \text{V}\ G_{\text{o}}=A_{\text{f}}\left[\frac{\eta}{\left(B_{iv}\right)^{ x}}\right]^{-C} \tag{1}\]  
The model considers the combined effects of soil matrix density and effective binder availability, while the exponent x allows for adjusting the relative influence of each variable depending on the material type and stabilization mechanism [40]. Although originally conceived for soil-cement mixtures, the applicability of this approach has been successfully extended to systems using lime [35,41], pozzolans [42], and more recently, biopolymers such as xanthan gum (XG) [25,26]. In recent studies, [PERSON] et al. [25,26] successfully adapted the \(\eta/B_{iv}\) index to account for the inclusion of XG and PPF, modifying the traditional porosity calculation to incorporate their volumetric contributions. This reformulation enabled accurate modeling of both strength and stiffness in mixtures stabilized with sustainable binders, achieving determination coefficients above 0.9 for \(q_{\text{u}}\) and above 0.8 for \(G_{\text{o}}\) under optimal conditions. Furthermore, it was identified that the optimal exponent x for XG-treated systems is approximately 0.04, significantly lower than the 0.28 commonly used in Portland cement mixtures, indicating a dominant influence of porosity in these biopolymer-based systems [25]. These findings reinforce the versatility and relevance of the \(\eta/B_{iv}\) index as a rational criterion for designing innovative geomaterials. In this study, the \(\eta/B_{iv}\) index is applied to a set of eight novel mixtures composed of construction residues (CLW, GY, GG), biopolymers (XG), and fiber-reinforced systems (XG-PPFs). This work compiles and extends the index-based models previously developed by [PERSON] et al. [6,25,26] and [PERSON] et al. [12], with the aim of comparing and unifying the dosage curves corresponding to each stabilization strategy.