## 3 Geotechnical Analysis of the Dam
### Permeability  
The permeability values for twelve soil samples were collected from the downstream area of the Tiga Dam in Nigeria. Hydraulic conductivity, often called permeability in geotechnical engineering, is a critical parameter that quantifies a soil's ability to transmit water through its pore spaces. This property significantly influences seepage patterns, pore water pressures, and, consequently, the stability of earth dams. The permeability values range from 3.40 \(\times\) 10\({}^{-9}\) m/s (sample 6) to 1.49 \(\times\) 10\({}^{-7}\) m/s (sample 4), spanning nearly two orders of magnitude. This substantial variability (coefficient of variation = 152.17%) suggests a highly heterogeneous hydraulic environment downstream of the dam. To better interpret these results, we can categorize the samples based on their permeability ranges [44]: 1. Very low permeability (k \(<\) 10\({}^{-8}\) m/s): samples: 2, 3, 6, 7, 8, 9, 10, 12 (66.67% of samples), range: 3.40 \(\times\) 10\({}^{-9}\) to 9.18 \(\times\) 10\({}^{-9}\) m/s, and mean: 6.02 \(\times\) 10\({}^{-9}\) m/s, std: 2.07 \(\times\) 10\({}^{-9}\) m/s; 2. Low permeability (10\({}^{-8}\)\(\leq\) k \(<\) 10\({}^{-7}\) m/s): samples: 1, 5, 11 (25% of samples), range: 2.95 \(\times\) 10\({}^{-8}\) to 9.32 \(\times\) 10\({}^{-8}\) m/s, and mean: 5.20 \(\times\) 10\({}^{-8}\) m/s, std: 3.33 \(\times\) 10\({}^{-8}\) m/s; 3. Moderate permeability (10\({}^{-7}\)\(\leq\) k \(<\) 10\({}^{-6}\) m/s): sample: 4 (8.33% of samples), and value: 1.49 \(\times\) 10\({}^{-7}\) m/s. Comparing these results with standard soil classifications [44], samples 2, 3, 6, 7, 8, 9, 10, and 12 fall within the \"clay\" category (k \(<\) 10\({}^{-8}\) m/s), samples 1, 5, and 11 are at the lower end of \"silty clay\" (10\({}^{-8}\)\(\leq\) k \(<\) 10\({}^{-6}\) m/s), and sample 4 is firmly in the \"silty clay\" range in Figure 10. These classifications align well with the USCS designations from the grain size analysis. The one discrepancy is sample 4, classified as SC by USCS but showing higher permeability than its grain size would suggest. This difference likely stems from its non-plastic nature and high silt content, allowing more efficient water flow despite its fine-grained composition. The predominantly very low to low permeability values suggest that most downstream areas act as a natural hydraulic barrier. According to [PERSON] et al. (2010), soils with k \(<10^{-8}\) m/s are often used as dam core materials to minimize seepage. However, the heterogeneity in permeability poses challenges. Even with most soils being \"tight,\" more permeable zones (samples 4, 5) can create preferential flow paths, leading to concentrated seepage and potential piping issues. In low-permeability soils, excess pore water pressures dissipate slowly. [PERSON]'s consolidation theory shows that the time for 90% consolidation (t\({}_{90}\)) is inversely proportional to permeability. For the very low permeability samples (k \(\approx 6\times 10^{-9}\) m/s), t\({}_{90}\) could be in the order of months or even years, depending on drainage path length. This slow dissipation means that during rapid drawdown events or heavy rains, high pore pressures can persist, reducing effective stress and potentially triggering slope instability. [PERSON] and [PERSON] showed that high hydraulic gradients can develop in earth dams with low-permeability cores (k \(<10^{-7}\) m/s), especially near the upstream face. If similar low-permeability soils exist in the dam's core, there is a risk of hydraulic fracturing. This phenomenon occurs when seepage forces exceed the soil's tensile strength, creating cracks that dramatically increase permeability, potentially leading to dam failure ([PERSON] et al., 2016). The permeability result corroborates the erosion concerns raised by the grain size and Arterberg limits analyses. [PERSON] et al. found that in soils with k \(>10^{-7}\) m/s, the critical hydraulic gradient for piping initiation is lower ([PERSON] et al., 2016). Thus, sample 4 is particularly susceptible to internal erosion.