## 3 Geotechnical Analysis of the Dam
### Shear Strength Characteristics  
The comprehensive shear strength data for twelve soil samples collected from the downstream area of the Tiga Dam in Kano State, Nigeria, is presented in Figure 11. Shear strength, a soil's ability to resist shear stresses without failure, is paramount in geotechnical engineering, particularly in earth dam design, which governs slope stability, bearing  
Figure 10: Permeability on twelve soil samples from the downstream area of the Tiga Dam in Kano State, Nigeria. capacity, and erosion resistance [11]. Table 4, obtained through direct shear tests, presents three key shear strength parameters: 1. Cohesion (c): the shear strength at zero normal stress: range: 1.4 kN/m\({}^{2}\) (sample 4) to 17.9 kN/m\({}^{2}\) (sample 1), mean: 9.72 kN/m\({}^{2}\), standard deviation: 4.22 kN/m\({}^{2}\), and coefficient of variation: 43.42%; 2. Angle of internal friction (\(\varphi\)): the rate at which shear strength increases with normal stress: range: 4.6\({}^{\circ}\) (sample 2) to 24.7\({}^{\circ}\) (sample 4), mean: 12.74\({}^{\circ}\), standard deviation: 5.63\({}^{\circ}\), and coefficient of variation: 44.19%; 3. Dry unit weight (yd): not a shear strength parameter but influences shear behavior: range: 13.05 kN/m\({}^{3}\) (sample 7) to 19.44 kN/m\({}^{3}\) (sample 4), mean: 15.40 kN/m\({}^{3}\), standard deviation: 1.75 kN/m\({}^{3}\), and coefficient of variation: 11.36%. The shear box test results (Figure 11a-l) display linear Mohr-Coulomb failure envelopes, indicating that the soil behavior adheres well to this classical shear strength model within the tested stress range. However, the wide dispersion in envelope slopes (\(\varphi\)) and \(y\)-intercepts (c) underscores the substantial variability in shear strength characteristics across the downstream area. Based on classification by [PERSON] and [PERSON] [48]: low cohesion (c \(<\) 5 kN/m\({}^{2}\)): sample 4 (8.33%), medium cohesion (5 \(\leq\) c \(<\) 10 kN/m\({}^{2}\)): samples 2, 3, 5, 6, 7, 8, 9, 10, 12 (75%), and high cohesion (c \(\geq\) 10 kN/m\({}^{2}\)): samples 1, 11 (16.67%). Most samples exhibit medium cohesion, typical of inorganic clays (CL), as identified in earlier grain size and Atterberg limits analyses. Sample 1's high cohesion (17.9 kN/m\({}^{2}\)) is noteworthy. Despite its low plasticity (PI = 4%), its cohesion exceeds that of more plastic clays. This suggests the presence of cementation agents like iron oxides or carbonates, which are common in tropical soils [10]. Such cements enhance cohesion but can dissolve during prolonged saturation, leading to strength loss--a critical concern during wet seasons. Conversely, sample 4's low cohesion (1.4 kN/m\({}^{2}\)) aligns with its non-plastic, sandy nature. This low cohesion makes it highly susceptible to surface erosion, mainly where runoff concentrates, like dam abutments or along preferential flow paths. Using [PERSON] and [PERSON]'s guidelines [44]: low \(\varphi\) (\(<\) 10\({}^{\circ}\)): sample 2 (8.33%), medium \(\varphi\) (10\({}^{\circ}\)\(\leq\)\(\varphi\)\(<\) 15\({}^{\circ}\)): samples 3, 6, 7, 8, 9, 10, 11, 12 (66.67%), high \(\varphi\) (15\({}^{\circ}\)\(\leq\)\(\varphi\)\(<\) 20\({}^{\circ}\)): sample 5 (8.33%), and very high \(\varphi\) (\(\varphi\)\(\geq\) 20\({}^{\circ}\)): sample 4 (8.33%). Most samples show medium friction angles, consistent with their claye nature. However, sample 4 stands out with \(\varphi\) = 24.7\({}^{\circ}\), a value more typical of clean sands. This high friction angle and low cohesion confirm its classification as a sandy clay (SC) with dominant sand behavior. While its high shear strength benefits slope stability, its erosion resistance relies almost entirely on interlocking rather than cohesive bonds, making it vulnerable to seepage forces. Sample 2's low friction angle (\(\varphi\) = 4.6\({}^{\circ}\)) is concerning.