## 3 Results and Discussion  
### Load Test Database  
[PERSON] [34] collected 58 results of load tests on aggregate piers and discussed that such data should fulfill several criteria to form a reliable database for statistical analysis. These criteria mainly include: adequate soil characterization, adequate description of load test and pier geometry, uniformity of the soil, proper shear response of the matrix soil, loading in a rapid manner, and the possibility of bearing capacity extrapolation from the measured displacements. Consequently, the 30 individual load tests that satisfied the previous criteria were selected to analyze the ultimate bearing capacity by [PERSON] and [PERSON] [18]. Recently, [PERSON] et al. [35] added seven new load test data by [36]: these additional data satisfied the same criteria for updating a load test database. Accordingly, 37 footing loading tests were used for the application of MLR and DNN in this study, as summarized in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Load Test** & **Footing** & **Compaction** & **s\({}_{u}\)** & **\({}_{d}\)\({}_{p}\)** & **B** & **\({}_{d}\)\({}_{p}\)** & **\({}_{d}\)\({}_{p}\)** & **\({}_{p}\)** & **\({}_{p}\)** & **Bearing** & **Fier** \\
**Designation** & **Shape** & **Method** & **(k/Pa)** & **(\%)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **Configuration** \\ \hline B0.30 & Circular & Drop ram & 30 & 100 & 0.30 & 0.00 & 0.30 & 8.00 & 26.67 & 722 & SP \\ B0.45 & Circular & Drop ram & 30 & 44.4 & 0.45 & 0.00 & 0.30 & 8.00 & 26.67 & 396 & ISP \\ B0.60 & Circular & Drop ram & 30 & 25 & 0.60 & 0.00 & 0.30 & 8.00 & 26.67 & 559 & ISP \\ B0.75 & Circular & Drop ram & 30 & 16 & 0.75 & 0.00 & 0.30 & 8.00 & 26.67 & 482 & ISP \\ BBS & Circular & Vibrated & 12 & 46.8 & 1.37 & 0.00 & 1.00 & 5.00 & 5.00 & 189 & ICP \\ G1 & Square & Vibrated & 99 & 30.2 & 2.74 & 0.00 & 0.74 & 4.57 & 6.18 & 552 & GP \\ G2 & Square & Vibrated & 54 & 24.2 & 2.74 & 0.00 & 0.74 & 4.57 & 6.18 & 532 & GP \\ G4 & Square & Vibrated & 59 & 30.2 & 2.74 & 0.00 & 0.74 & 3.05 & 4.12 & 645 & GP \\ G5 & Square & Tamped & 75 & 30.2 & 2.74 & 0.00 & 0.76 & 4.57 & 6.01 & 624 & GP \\ G6 & Square & Vibrated & 65 & 30.2 & 2.74 & 0.00 & 0.74 & 4.57 & 6.18 & 615 & GP \\ GS & Circular & Vibrated & 44 & 40.1 & 0.91 & 0.61 & 0.61 & 2.90 & 4.75 & 399 & ISP \\ HW & Circular & Vibrated & 22 & 122 & 0.66 & 0.00 & 0.73 & 10.00 & 13.70 & 628 & SP \\ HYII & Square & Vibrated & 12 & 36 & 1.25 & 0.00 & 0.85 & 14.00 & 16.47 & 177 & ISP \\ HYIII & Square & Vibrated & 12 & 36 & 1.25 & 0.00 & 0.85 & 14.00 & 16.47 & 252 & ISP \\ HYIV & Circular & Vibrated & 12 & 100 & 0.85 & 0.00 & 0.85 & 14.00 & 16.47 & 378 & SP \\ LS & Circular & Rammed & 100 & 100 & 0.61 & 0.00 & 0.61 & 3.05 & 5.00 & 1346 & SP \\ PWG1 & Square & Rammed & 30 & 34.6 & 2.29 & 0.46 & 0.76 & 2.33 & 3.07 & 338 & GP \\ PWG2 & Square & Rammed & 30 & 34.6 & 2.29 & 0.46 & 0.76 & 4.64 & 6.11 & 477 & GP \\ PWP1 & Circular & Rammed & 30 & 100 & 0.76 & 0.46 & 0.76 & 2.33 & 3.07 & 604 & SP \\ PWP2 & Circular & Rammed & 30 & 100 & 0.76 & 0.46 & 0.76 & 4.64 & 6.11 & 664 & SP \\ T10U & Circular & Tamped & 65 & 100 & 0.76 & 0.61 & 0.76 & 3.05 & 4.01 & 1096 & SP \\ T10V & Circular & Tamped & 69 & 100 & 0.76 & 0.61 & 0.76 & 3.05 & 4.01 & 1006 & SP \\ T15U & Circular & Tamped & 67 & 100 & 0.76 & 0.61 & 0.76 & 4.57 & 6.01 & 1132 & SP \\ T15W & Circular & Tamped & 70 & 100 & 0.76 & 0.61 & 0.76 & 4.57 & 6.01 & 1202 & SP \\ V10 PU & Circular & Vibrated & 57 & 95 & 0.76 & 0.61 & 0.74 & 3.05 & 4.12 & 1115 & SP \\ V10 PW & Circular & Vibrated & 61 & 100 & 0.76 & 0.61 & 0.76 & 3.05 & 4.01 & 1093 & SP \\ V10u & Circular & Vibrated & 63 & 88 & 0.76 & 0.61 & 0.71 & 3.05 & 4.30 & 1067 & SP \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of footing load test database. The footings consisted of 17 square footings and 21 circular footings.