# Novel Nature-Inspired Hybrids of Neural Computing for Estimating Soil Shear Strength
## 3 Data Collection and Statistical Analysis  
The data used in the present work is provided from a vast geotechnical assessment from the Royal City project located in Hanoi city of Vietnam [31]. The construction area is nearly 120,950 m\({}^{2}\). The main point was to explore the situation of the sub-surface soil using the boring sampling method. A total of 28 boreholes were constructed using a so-called mixture of water and bentonite \"slurry\", where the minimum and maximum depths were 55 and 75 m, respectively. Notably, piston samplers were used to obtain soil samples with 91-mm diameter. Finally, 154 soil specimen were tested to measure the shear strength by taking into consideration 12 influential factors, including depth of sample (DOP), percentage of sand, percentage of loam, percentage of clay, percentage of moisture content (MC), wet density (WD), dry density (DD), void ratio (VR), liquid limit (LL), plastic limit (PL), plastic Index (PI), and liquidity index (LI). Figure 6 addresses the graphical relationship between the SSS and soil variables. Besides, Table 1 denotes the descriptive statistics of the dataset.  
Figure 4: The humpback whales bubble-net feeding.  
Figure 5: The seed reproduction of the invasive weed optimization (IWO) algorithm.  
Figure 6: Distribution of shear strength values versus soil parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Features**} & \multicolumn{8}{c}{**Descriptive Index**} \\ \cline{2-10}  & **Mean** & **Standard Error** & **Median** & **Mode** & **Standard Deviation** & **Sample Variance** & **Skewness** & **Minimum** & **Maximum** & **Count.** \\ \hline Depth of sample (m) & 24.72 & 1.21 & 31.20 & 38.00 & 15.06 & 226.83 & \(-\)0.57 & 1.20 & 47.00 & 154 \\ Sand (\%) & 16.26 & 1.11 & 13.00 & 10.00 & 13.83 & 191.16 & 2.95 & 0.00 & 70.80 & 154 \\ Lomb (\%) & 55.18 & 0.92 & 57.95 & 55.90 & 11.50 & 132.33 & \(-\)2.47 & 0.00 & 69.20 & 154 \\ Clay (\%) & 28.10 & 0.62 & 26.80 & 24.60 & 7.68 & 59.01 & 0.28 & 9.10 & 48.00 & 154 \\ Moisture content (\%) & 33.23 & 0.70 & 31.60 & 25.80 & 8.69 & 75.99 & 1.00 & 20.80 & 69.20 & 154 \\ Wet density (gcm\({}^{3}\)) & 1.82 & 0.01 & 1.85 & 1.89 & 0.10 & 0.01 & \(-\)0.90 & 1.52 & 1.95 & 154 \\ Dry density (gcm\({}^{3}\)) & 1.38 & 0.01 & 1.41 & 1.41 & 0.16 & 0.02 & \(-\)0.68 & 0.90 & 1.60 & 154 \\ Void Ratio & 0.97 & 0.02 & 0.91 & 1.20 & 0.23 & 0.05 & 0.98 & 0.67 & 1.81 & 154 \\ Liquid limit (\%) & 40.87 & 0.70 & 40.70 & 46.00 & 8.69 & 75.55 & 0.77 & 25.60 & 74.20 & 154 \\ Plastic limit (\%) & 25.38 & 0.40 & 25.00 & 21.00 & 5.01 & 25.12 & 1.01 & 17.90 & 48.70 & 154 \\ Plastic Index (\%) & 15.49 & 0.35 & 15.10 & 15.70 & 4.42 & 19.80 & 0.79 & 6.50 & 36.30 & 154 \\ Liquidity index & 0.49 & 0.02 & 0.47 & 0.45 & 0.19 & 0.04 & 0.06 & \(-\)0.03 & 0.88 & 154 \\ Shear strength (kg/cm\({}^{3}\)) & 0.38 & 0.01 & 0.38 & 0.29 & 0.10 & 0.01 & \(-\)0.21 & 0.18 & 0.57 & 154 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Descriptive statistics of the used dataset.  
The aforementioned factors are used as input data for estimating the SSS as the desired variable (i.e., the output). In other words, the intelligent models of this study are applied to analyze the relationship between the SSS and these factors. To this end, two sets of data are required: (i) the first group called training data are used to train the models, and (ii) the second group called testing data are specified as unseen soil conditions to evaluate the integrity of the developed networks. Similar to many previous studies [12; 32], 80% of the dataset (i.e., 123 samples) were randomly selected for the training data, and the remaining 20% (i.e., 31 samples) were used as testing data.