## 3 Geotechnical Analysis of the Dam
### Grain Size Distribution Analysis  
The grain size distribution curves (Figure 6a,b) show a consistent pattern across all samples: steep slopes in the fine-grained region (silt and clay sizes) and gentler slopes in the sand region. This shape indicates a well-graded distribution of fine particles but a more uniform distribution of sand particles. According to the unified soil classification system (USCS) in Table 1, the samples are categorized into four groups: sandy clay (SC), clay of low plasticity (CL), silt of (ML), and silty clay of (CL-ML). This classification reveals that the downstream area predominantly comprises fine-grained soils, with over half being low-plasticity clays. The absence of high-plasticity clays (CH) is noteworthy, suggesting that while the soils may exhibit some expansive behavior, they might not be as pronounced as in regions with CH soils. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Sample No** & \(\mathbf{D_{60}}\) & \(\mathbf{D_{30}}\) & \(\mathbf{D_{10}}\) & \(\mathbf{Cu}\) & \(\mathbf{Cc}\) & **UCSC Class** \\ \hline
1 & 0.1716 & 0.0674 & 0.0127 & 13.4582 & 2.0754 & CL-ML \\ \hline
2 & 0.1430 & 0.0268 & 0.0061 & 23.5049 & 0.8270 & CL \\ \hline
3 & 0.1157 & 0.0135 & 0.0043 & 27.0398 & 0.3659 & CL \\ \hline
4 & 0.5864 & 0.2790 & 0.0320 & 18.3029 & 4.1421 & SC \\ \hline
5 & 0.1285 & 0.0602 & 0.0071 & 18.1284 & 3.9752 & ML \\ \hline
6 & 0.0516 & 0.0243 & 0.0083 & 6.2478 & 1.3836 & CL \\ \hline
7 & 0.0562 & 0.0131 & 0.0039 & 14.5856 & 0.7921 & CL \\ \hline
8 & 0.0511 & 0.0142 & 0.0052 & 9.8145 & 0.7599 & CL \\ \hline
9 & 0.1087 & 0.0184 & 0.0049 & 22.2292 & 0.6344 & CL-ML \\ \hline
10 & 0.0750 & 0.0165 & 0.0038 & 19.8936 & 0.9655 & CL \\ \hline
11 & 0.0750 & 0.0134 & 0.0036 & 20.9759 & 0.6712 & CL \\ \hline
12 & 0.1280 & 0.0385 & 0.0080 & 16.0958 & 1.4560 & CL-ML \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grain size analysis and soil classification from the downstream area of the Tiga Dam. Figure 6: (**a**) Grain size analysis on 1–6 soil samples from the downstream area of the Tiga Dam in Kano State, Nigeria. (**b**) Grain size analysis on 7–12 soil samples from the downstream area of the Tiga Dam in Kano State, Nigeria. Two critical ratios assess the soil's gradation: Uniformity coefficient (Cu = D\({}_{60}\)/D\({}_{10}\)), ranging from 6.247 (sample 6) to 27.040 (sample 3), with a mean of 17.523 and std of 5.883. The coefficient of curvature (Cc = (D\({}_{30}\))\({}^{2}\)/(D\({}_{60}\)\(\times\) D\({}_{10}\))) ranges from 0.366 (sample 3) to 4.142 (sample 4), with a mean of 1.504 and std of 1.278. According to standard criteria [44], for well-graded soils, Cu > 4 for gravels, Cu > 6 for sands, and 1 \(\leq\) Cc \(\leq\) 3. All samples meet the Cu criterion for sands, indicating a wide range of particle sizes. However, Cc values vary significantly: well-graded samples 1, 4, 5, 6, 12 (41.67%) and poorly graded samples 2, 3, 7, 8, 9, 10, 11 (58.33%). This mix of well-graded and poorly graded soils has important geotechnical implications. Well-graded soils typically have better engineering properties--higher shear strength, lower compressibility, and reduced erosion susceptibility--as smaller particles fill the voids between larger ones. In contrast, poorly graded soils are more prone to erosion and piping, a critical concern for dam safety. Key statistical parameters from Table 2 further elucidate that D\({}_{60}\): mean = 0.140 mm, std = 0.145 mm, D\({}_{30}\): mean = 0.048 mm, std = 0.074 mm, and D\({}_{10}\): mean = 0.008 mm, std = 0.0079 mm. The high standard deviations relative to means, especially for D\({}_{60}\) and D\({}_{30}\), reflect significant variability in grain sizes across samples. This heterogeneity is visually apparent in the histograms (Figure 7a-e), which show right-skewed distributions, particularly pronounced for D\({}_{60}\) and D\({}_{30}\). Such variability suggests diverse sediment sources or differential sorting processes, which are common in alluvial environments downstream of dams.