## 3 Methodology
### Loads and Material Characteristics  
The combination lateral loads (P) consist of equivalent static earthquake loads based on SNI 1726 [11], and lateral earth pressure on semi-basement walls according to [PERSON] [10] using [PERSON]'s theory in Equation (1). The earthquake load by the static equivalent method was taken based on the amplification factor for a short period (S\({}_{\text{s}}\)) and 1.0 s period (S\({}_{\text{1}}\)) at Malang city, Indonesia (Figure 7) from the Indonesian Earthquake Zone Map, where the S\({}_{\text{s}}\) value occurs at 0.80-1.00 g (red color) and the S\({}_{\text{1}}\) value occurs at 0.30-0.50 g (yellow color). Therefore, the amplification factor for a short period (S\({}_{\text{s}}\)) and 1.0 s period (S\({}_{\text{1}}\)) in this research was taken as S\({}_{\text{s}}\) = 0.80 and S\({}_{\text{1}}\) = 0.40 for condition 1, S\({}_{\text{s}}\) = 0.90 and S\({}_{\text{1}}\) = 0.40 for condition 2, and S\({}_{\text{s}}\) = 1.00 and S\({}_{\text{1}}\) = 0.50 for condition 3. The amplification factor was used to determine the MCE\({}_{\text{R}}\) acceleration spectral response and design spectral acceleration parameters. The combination lateral load values of the group pile (P\({}_{\text{G}}\)) were 7051.887 kN for condition 1 (P\({}_{\text{G1}}\)), 8973.120 kN for condition 2 (P\({}_{\text{G2}}\)), and 10,690.011 kN for condition 3 (P\({}_{\text{G3}}\)). At once, the combination lateral load values of the single piles (P\({}_{\text{S}}\)) are calculated from the group pile divided by the number of piles; these values are 542.453 kN for condition 1 (P\({}_{\text{S1}}\)), 690.240 kN for condition 2 (P\({}_{\text{S2}}\)), and 822.309 kN for condition 3 (P\({}_{\text{S3}}\)). The input load used in condition 3 was used in the analysis of the effects of pile stiffness and soil stiffness. The axial input load for a single pile is 956.495 kN, which is taken from the axial ultimate bearing capacity. For the case of the group piles, they consist of 5 axial loads generated based on column reactions due to service loads, where the first axial load with coordinates (0.00, \(-\)2.00, 0.00) is 3088.864 kN, the second axial load with coordinates (\(-\)1.20, 0.00, 0.00) is 949.60 kN, the third axial load with coordinates (2.418, 0.00, 0.00) is 970.236 kN, the fourth axial load with coordinates (\(-\)1.20, 2.40, 0.00) is 1297.65 kN, and the fifth axial load with coordinates (2.418, \(-\)2.40, 0.00) is 1190.500 kN. [PERSON] and [PERSON] [27] proposed a method for classifying piles into different categories based on the flexibility factor, K\({}_{\text{r}}\) (K\({}_{\text{r}}\) = E\({}_{\text{P}}\)I\({}_{\text{P}}\)/E\({}_{\text{s}}\)L\({}_{\text{p}}\)\({}^{4}\)). Where, I\({}_{\text{P}}\) is the inertia moment of the pile and L\({}_{\text{P}}\) is the pile length. The classification of the bored pile at Brawijaya University consists of a flexibility factor of 44 \(\times\) 10\({}^{-5}\) from E\({}_{\text{P1}}\) = 20.75 MPa, 52 \(\times\) 10\({}^{-5}\) from E\({}_{\text{P2}}\) = 29.05 MPa, and 59 \(\times\) 10\({}^{-5}\) from E\({}_{\text{P3}}\) = 37.35 MPa with E\({}_{\text{s}}\) from Tsimbaos and Sabatakakis [24] at 20.00 m depth. From this value, based on [PERSON] et al., 2014 [28], the piles are categorized as very flexible piles with a flexibility factor of 10\({}^{-5}\). There were three values of modulus of elasticity used in this study calculated by Equations (16)-(22) (Table 3), where E\({}_{\rm s1}\) was the value of the young modulus using the  
Figure 7: Indonesian Earthquake Zone Map (**a**) amplification factor for a short period (S\({}_{\rm s}\)), (**b**) amplification factor for 1.0 s period (S\({}_{\rm l}\)). shear wave velocity value approach from [PERSON] et al. [23] and E\({}_{\rm S2}\) used the modulus based on [PERSON] and [PERSON] in Hammam and Eliwa [22].