# Lateral Load Capacity and p-Multiplier of Group Piles with Asymmetrical Pile Cap under Seismic Load

^{*}

## Abstract

**:**

## 1. Introduction

_{s}increases from 2.5 MPa to 30 MPa, the deflection does not increase significantly, and the pile tip displacement decreases with increasing E

_{s}[3]. Wang et al. [4] presented a numerical investigation to measure the effect of flexural stiffness on the load transfer curve (p-y curve) of a laterally loaded monopile in solid sand. As the flexural stiffness increases, the wedge failure mechanism regulates the pile behavior. However, due to the greater flexural stiffness, a larger soil zone is mobilized for the same deflection at the soil surface, and the depth of the effect of wedge failure also increases.

_{m}) remains constant throughout the load, and the entire pile depth range is critically examined. Overall observations show that the numerical model is reliable for the improvement of the soil-pile reaction while decreasing the overall flexural stiffness of the pile friction. The p

_{m}parameter considers the pile group effect [8].

## 2. Literature Review

#### 2.1. Piles under Seismic Load

_{h}W and k

_{v}W in the horizontal and vertical directions and can be defined as [10]:

_{ae}= active force per unit length of the wall in earthquake conditions, P

_{a}= active force per unit length of the wall in static conditions, K

_{ae}= coefficient of active earth pressure in earthquake conditions, and k

_{h}, k

_{v}= coefficient of horizontal and vertical ground acceleration in earthquake conditions.

_{DS}) D + 0.7E

_{h}

_{DS}) + 0.525E

_{h}+ 0.75L

_{DS}) D + 0.7E

_{h}

_{DS}= design acceleration spectral response parameter in a short period (2/3 × F

_{a}S

_{s}), E

_{h}= horizontal seismic load effect, L = live load, and F

_{a}= site coefficient (taken based on the value of the maximum seismic acceleration spectral response parameter that is considered risk-targeted (MCE

_{R}) is mapped in the short period, S

_{s}, and the 1 s period, S

_{1}, in SNI 1726 [11]).

#### 2.2. p-Multiplier

_{m}is used to modify a single pile lateral soil spring to obtain pile springs in a group. Usually, the p-multiplier is constant in the same row.

_{u}= lateral bearing capacity.

_{m}, where D is the diameter or width of the pile and s is the center-to-center distance between the piles in the direction of loading.

_{m}= p-multiplier, s = distance between piles, and D = diameter of the pile.

_{m}) is taken from the center-to-center distance of the pile in the loading direction group, expressed in multiples of the pile diameter (D). The calculation of group effects based on the American Association of State Highway and Transportation Officials [16] is shown in Table 1.

_{m}value to the other pile spacing values, interpolation between values must be carried out [16].

#### 2.3. Soil Stiffness

_{s}, then the shear modulus (small strain) G

_{max}is given as [17]:

_{max}= ρ V

_{s}

^{2}

_{max}= shear modulus of seismic conditions, and V

_{s}= shear wave velocity.

_{s}) can be related to the shear modulus of seismic conditions (G

_{max}) as follows [18]:

_{s}= 2 (1 + v) G

_{max}

_{s}values and N-SPT [19,20,21,22]. According to SPT implementation standards, N-SPT is the number of blows required to obtain the last 30 cm of sample tube penetration from a total of 45 cm at each test step. Sample penetration is obtained from a hammer weighing 63.5 kg dropping from a constant free fall height (76 cm) to the anvil mounted on the drill post. The test results cannot be separated from the influence of equipment features and procedures, including the energy content of the hammer. Some of these empirical equations are based on the number of SPT blows with corrected energy (N

_{60}), and the number of SPT blows corrected with energy and stress (overburden) (N

_{1})

_{60}[20,21].

_{s}correlation, constant regression coefficient, number of data pairs, and R

^{2}value. In general, the most suitable function for SPT-V

_{s}data regression is a function as shown in the following equation [21]:

_{s}= A × N

_{60}

^{B}

_{60}= corrected N-SPT with energy, and V

_{s}= wave shear velocity at the same depth at which the N-SPT value is measured.

_{60}) applies to indirect estimates of V

_{s}as follows:

_{60}

^{0.26}

_{s}is often not economical at all locations [23]. The correlation equation developed between V

_{s}(m/s) and N-SPT corrected with energy and suitable for all soils by simple regression analysis based on Maheswari et al. [23] are as follows [20]:

_{60}

^{0.304}

_{60}

^{0.266}

_{s}-N. The data evaluated refers to soft−hard clay soils (classified as CH, CL, and SC according to USCS), loose−very dense silty sand (SM), and loose−very dense silt (ML). Regression analysis was used to define the relationship between V

_{s}and penetration resistance. A regression procedure is used to adjust the curve through the points to minimize the squared deviation of the measured points. The relevant equations define the curves in the two-variable spaces, and the coefficient of determination (R

^{2}) value is calculated.

_{60}

^{0.327}

_{60}

^{0.365}

## 3. Methodology

_{p}), and pile stiffness (E

_{s}).

_{R}acceleration spectral response parameter by static equivalent method and mapped for a short period (S

_{s}) and 1.0 s period (S

_{1}); S

_{s}= 0.80 and S

_{1}= 0.40, S

_{s}= 1.00 and S

_{1}= 0.40, S

_{s}= 1.20 and S

_{1}= 0.50. Soil stiffness was compared using the value of shear wave velocity (V

_{s}) derived from N-SPT data (Table 2) values using methods from Hasancebi and Ulusuay in Hammam and Eliwa [22] in Equation (18), Maheswari et al. [23] in Equations (19) and (20), and Tsimbaos and Sabatakakis [24] in Equations (21) and (22), while the pile stiffness was appealed to the value of the concrete quality of K-250, K-350, and K-450.

#### 3.1. Site Characteristics

#### 3.2. Finite Element Method

_{inter}value should be less than 1 [26].

#### 3.3. Loads and Material Characteristics

_{s}) and 1.0 s period (S

_{1}) at Malang city, Indonesia (Figure 7) from the Indonesian Earthquake Zone Map, where the S

_{s}value occurs at 0.80–1.00 g (red color) and the S

_{1}value occurs at 0.30–0.50 g (yellow color). Therefore, the amplification factor for a short period (S

_{s}) and 1.0 s period (S

_{1}) in this research was taken as S

_{s}= 0.80 and S

_{1}= 0.40 for condition 1, S

_{s}= 0.90 and S

_{1}= 0.40 for condition 2, and S

_{s}= 1.00 and S

_{1}= 0.50 for condition 3. The amplification factor was used to determine the MCE

_{R}acceleration spectral response and design spectral acceleration parameters. The combination lateral load values of the group pile (P

_{G}) were 7051.887 kN for condition 1 (P

_{G1}), 8973.120 kN for condition 2 (P

_{G2}), and 10,690.011 kN for condition 3 (P

_{G3}). At once, the combination lateral load values of the single piles (P

_{S}) are calculated from the group pile divided by the number of piles; these values are 542.453 kN for condition 1 (P

_{S1}), 690.240 kN for condition 2 (P

_{S2}), and 822.309 kN for condition 3 (P

_{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.

_{r}(K

_{r}= E

_{p}I

_{p}/E

_{s}L

_{p}

^{4}). Where, I

_{p}is the inertia moment of the pile and L

_{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

_{p1}= 20.75 MPa, 52 $\times $ 10

^{−5}from E

_{p2}= 29.05 MPa, and 59 $\times $ 10

^{−5}from E

_{p3}= 37.35 MPa with E

_{s}from Tsimbaos and Sabatakakis [24] at 20.00 m depth. From this value, based on Li et al., 2014 [28], the piles are categorized as very flexible piles with a flexibility factor of 10

^{−5}.

_{s1}was the value of the young modulus using the shear wave velocity value approach from Maheswari et al. [23] and E

_{s2}used the modulus based on Hasancebi and Ulusuay in Hammam and Eliwa [22]. Meanwhile, E

_{3}was based on Tsimbaos and Sabatakakis [24], where the V

_{s}values used to determine the value of G

_{max}in Equation (14), in which the value of $\overline{\mathrm{N}}$ was in the range of 15 to 50 and V

_{s}was in the range of 175 to 350.

_{inter}), which has a value between 0.01 and 1.0 (Table 4). The lower limit value of 0.01 indicates no friction between the structural elements and the soil. The upper limit value of 1.0 means that the structural element and the soil are in contact and cannot slip over each other (rigid) [30]. R

_{inter}is taken by dividing the friction angle in the concrete pile by the soil friction angle at each depth. The concrete friction angle was approximated at 27.90° based on direct shear testing by Ilori et al. [31] to investigate the interaction between the soil and concrete in-situ concerning friction.

## 4. Results and Discussion

#### 4.1. Group Pile Lateral Load Capacity

_{ult}) happens at a load of 1000 kN.

_{s}increases [3,4]. Soil stiffness has a negative correlation with deflection and lateral loads (Figure 11), where both factors will decrease with increasing soil stiffness. With an increase in the soil stiffness effect, the deflection decreases by 1.00–2.00 mm (15–20%) and increases the lateral resistance to 1–20 kN (1–5%) (Table 5 and Table 6). Zhou et al. [3] found the deflection did not rise significantly when E

_{s}increased.

#### 4.2. p-Multiplier

_{m}) parameter was used to consider group pile effects. The p-multiplier is calculated using the single pile p-y curve divided by the p-y curve for each pile group row. The p-y curve obtained with the help of finite difference software for the single pile and the group pile is calculated using the API [7] method approach with ultimate soil resistance, p

_{u}, from the first row to the fourth row also being obtained based on numerical calculations based on the finite difference method (Figure 13a). Pile modeling with the finite difference method is the same with the 3D finite element method and the relationship between soil resistance and deflection (p-y curve) was taken at a depth of 0.00 m to match the pile group’s deflection output from the 3D finite element analysis.

_{m}decreases gradually with y, revealing that the pile group effect depends on the pile deflection. As the pile deflection increases, the protective effect becomes more significant and causes a considerable decrease in p

_{m}. This difference may occur due to the diversity of methodology, soil type, and geometric parameters used between studies to derive the p-multiplier. Other reasons that can cause this difference in results are the reduction of the earth pressure limit, group effect, and inconstant depth [36].

_{m}values for the three variables, followed by Reese and Impe [15] and FEMA P-751 [14]. This may be because AASHTO [16] used data from most of the tests in the 3 × 3 pile group, and there were no fixed-head conditions in the AASHTO [16] database. Reese and Impe [15] generally matches or approaches the p

_{m}value from the 3D finite element method obtained in this study. This is appropriate because Reese and Impe [15] not only considers the effects of the adjacent, parallel piles but also considers misaligned piles concerning the applied load.

_{m}value, and its value continues to decrease as the row of piles increases. This is in accordance with the behavior of the lateral load capacity, where the farther the pile is from the lateral load, the lower the p

_{m}will be. Zhou and Tokimatsu [11] also revealed that the p-multiplier decreases approximately from the leading row to the last row in the subgroup, whereas the p-multiplier of the leading row in the final subgroup is equal to or even greater than the last row in the front group.

## 5. Conclusions

- Lateral load capacity of group piles:
- Asymmetrical pile caps and pile configurations do not affect the behavior of lateral resistance and deflection, only producing different lateral resistance values with a difference of 1–50% and 60–70% for deflection values compared to the finite element 3D single pile analysis. On the effect of combination lateral loads, pile stiffness, and soil stiffness, the analysis of lateral resistance and deflection of group piles with 3D finite elements is in good agreement with single pile 3D finite elements.
- In addition, the asymmetrical shape of the pile cap and pile configuration affects the location of the greatest lateral resistance. The slope of the pile cap can increase the shear zone, thus increasing the lateral resistance so that the most remarkable overlap occurs in the direction opposite to the loading direction.

- p-multiplier:
- In this study, the proposed method is less effective with asymmetrical pile configurations, where the value of the p-multiplier increases with an increasing deflection. In future research, it is necessary to not solely divide the lateral resistance of the pile group by a single pile to get the p-multiplier value. In this case, further studies are required to be carried out with the possibility of adding another multiplying or dividing factor.
- Results from Reese and Impe [15] generally match or approach the p
_{m}value from the 3D finite element method obtained in this study. This is appropriate because Reese and Impe [15] not only considers the effects of adjacent, parallel piles, but also considers misaligned piles concerning the applied load. The 3D finite element method was within the range suggested by the design recommendations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Indonesian Earthquake Zone Map (

**a**) amplification factor for a short period (S

_{s}), (

**b**) amplification factor for 1.0 s period (S

_{1}).

**Figure 9.**Lateral load capacity vs. deflection (

**a**) P

_{S1}, P

_{G1}, (

**b**) P

_{S2}, P

_{G2}, (

**c**) P

_{S3}, P

_{G3}.

**Figure 10.**Lateral load capacity vs. deflection (

**a**) E

_{p1}= 20.75 MPa, (

**b**) E

_{p2}= 29.05 MPa, (

**c**) E

_{p3}= 37.35 MPa.

**Figure 12.**Pile configuration, (

**a**) pile configuration, (

**b**) deflection surface, (

**c**) overlapping of failure zones.

**Table 1.**p-multiplier according to AASHTO [16].

Pile Space | p-Multiplier, p_{m} | ||
---|---|---|---|

Row 1 | Row 2 | Row 3 and Upper | |

3D | 0.8 | 0.4 | 0.3 |

5D | 1 | 0.85 | 0.7 |

Parameters | Methods | Unit | MH | MH | SC-SM | SC-SM | CL |
---|---|---|---|---|---|---|---|

Depth | M | 0.00–5.50 | 5.50–8.50 | 8.50–11.50 | 11.50–14.50 | 14.50–17.50 | |

$\overline{\mathrm{N}}$_{60} | 12 | 11 | 14 | 28 | 34 | ||

V_{s} | Maheswari et al., 2010 [23] | m/s | 176.67 | 172.18 | 194.68 | 233.75 | 243.14 |

Hasancebi and Ulusuay, 2006 in Hammam and Eliwa [22] | 204.80 | 200.34 | 208.53 | 249.35 | 269.12 | ||

Tsimbaos and Sabatakakis, 2011 [24] | 237.39 | 230.90 | 209.41 | 269.15 | 334.70 | ||

Parameters | Methods | Unit | MH | SM | SM | MH | CL-ML |

Depth | M | 17.50–20.00 | 20.00–23.50 | 23.50–26.50 | 26.50–29.50 | 29.50–30.00 | |

$\overline{\mathrm{N}}$_{60} | 44 | 68 | 55 | 54 | 55 | ||

V_{s} | Maheswari et al., 2010 [23] | m/s | 263.66 | 296.06 | 279.39 | 279.36 | 241.78 |

Hasancebi and Ulusuay, 2006 in Hammam and Eliwa [22] | 288.43 | 314.14 | 296.83 | 303.06 | 305.09 | ||

Tsimbaos and Sabatakakis, 2011 [24] | 365.18 | 372.23 | 343.76 | 388.62 | 456.36 |

Parameters | Symbol | Unit | MH | MH | SC-SM | SC-SM | CL |
---|---|---|---|---|---|---|---|

Depth | M | 0.00–5.50 | 5.50–8.50 | 8.50–11.50 | 11.50–14.50 | 14.50–17.50 | |

Shear Modulus | G_{max1} | kN/m^{2} | 31,512.89 | 30,168.81 | 54,463.84 | 58,647.40 | 62,843.00 |

G_{max2} | kN/m^{2} | 42,346.40 | 40,843.44 | 62,487.42 | 66,734.39 | 76,989.80 | |

G_{max3} | kN/m^{2} | 56,897.20 | 54,258.68 | 63,015.42 | 77,752.24 | 119,082.54 | |

Modulus of Elasticity | E_{s1} | kN/m^{2} | 80,257.83 | 76,107.67 | 141,750.84 | 157,208.03 | 172,158.08 |

E_{s2} | kN/m^{2} | 107,848.87 | 103,036.85 | 162,633.48 | 178,885.72 | 210,913.15 | |

E_{s3} | kN/m^{2} | 144,907.24 | 136,879.86 | 164,007.69 | 208,419.75 | 326,226.01 | |

Parameters | Symbol | Unit | MH | SM | SM | MH | CL-ML |

Depth | M | 17.50–20.00 | 20.00–23.50 | 23.50–26.50 | 26.50–29.50 | 29.50–30.00 | |

Shear Modulus | G_{max}1 | kN/m^{2} | 71,347.32 | 137,818.78 | 132,539.58 | 81,007.64 | 66,740.49 |

G_{max}2 | kN/m^{2} | 85,382.60 | 155,159.96 | 149,607.27 | 95,333.66 | 106,266.07 | |

G_{max}3 | kN/m^{2} | 136,865.04 | 217,852.44 | 200,658.77 | 156,762.39 | 237,768.36 | |

Modulus of Elasticity | E_{s1} | kN/m^{2} | 199,772.48 | 385,892.57 | 371,110.81 | 226,821.40 | 186,873.38 |

E_{s2} | kN/m^{2} | 239,071.29 | 434,447.88 | 418,900.34 | 266,934.24 | 297,544.98 | |

E_{s3} | kN/m^{2} | 383,222.10 | 609,986.82 | 561,844.55 | 438,934.70 | 665,751.40 |

Parameters | Symbol | Unit | MH | MH | SC-SM | SC-SM | CL |
---|---|---|---|---|---|---|---|

Depth | 0.00–5.50 | 5.50–8.50 | 8.50–11.50 | 11.50–14.50 | 14.50–17.50 | ||

Material model | Mohr–Coulomb | Mohr–Coulumb | Mohr–Coulumb | Mohr–Coulumb | Mohr–Coulumb | ||

Behavior type | Undrained | Undrained | Drained | Drained | Undrained | ||

Density above water table | γ_{unsat} | kN/m^{3} | 9.901 | 9.980 | 14.092 | 10.526 | 10.424 |

Density below water table | γ_{sat} | kN/m^{3} | 15.532 | 15.417 | 18.159 | 16.092 | 15.918 |

Effective density | γ′ | kN/m^{3} | 5.725 | 5.61 | 8.352 | 6.285 | 6.111 |

Poisson ratio | v | 0.273 | 0.261 | 0.301 | 0.340 | 0.370 | |

Cohesion | c | kN/m^{2} | 35.598 | 17.162 | 4.021 | 1.177 | 15.789 |

Friction angle | φ | ^{o} | 30.45 | 25.62 | 44.26 | 44.29 | 31.75 |

R_{inter} | 0.901 | 1.00 | 0.543 | 0.543 | 0.856 | ||

Parameters | Symbol | Unit | MH | SM | SM | MH | CL-ML |

Depth | M | 17.50–20.00 | 20.00–23.50 | 23.50–26.50 | 26.50–29.50 | 29.50–30.00 | |

Material model | Mohr–Coulumb | Mohr–Coulumb | Mohr–Coulumb | Mohr–Coulumb | Mohr–Coulumb | ||

Behavior type | Undrained | Drained | Drained | Undrained | Undrained | ||

Density above water table | γ_{unsat} | kN/m^{3} | 10.065 | 15.419 | 16.652 | 10.179 | 11.196 |

Density below water table | γ_{sat} | kN/m^{3} | 15.614 | 19.191 | 20.252 | 16.288 | 16.349 |

Effective density | γ’ | kN/m^{3} | 5.807 | 9.384 | 10.445 | 6.482 | 6.543 |

Poisson ratio | V | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | |

Cohesion | C | kN/m^{2} | 19.221 | 9.12 | 0.588 | 21.673 | 3.825 |

Friction angle | φ | ^{o} | 18.8 | 40.9 | 51.75 | 17.19 | 40.9 |

R_{inter} | 1.00 | 0.611 | 0.417 | 1.00 | 0.611 |

Lateral Resistance (kN) | The Difference of Lateral Resistance with the Single Pile (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Single Pile | 1st Row | 2nd Row | 3rd Row | 4th Row | 1st Row | 2nd Row | 3rd Row | 4th Row | |

Combination Lateral Loads Effect | |||||||||

P_{S1}, P_{G1} | 304.663 | 541.442 | 299.494 | 255.588 | 149.534 | 43.731 | 1.697 | 16.108 | 50.918 |

P_{S2}, P_{G2} | 414.567 | 711.253 | 389.264 | 333.519 | 197.712 | 41.713 | 6.103 | 19.550 | 52.309 |

P_{S3}, P_{G3} | 524.270 | 861.389 | 488.142 | 415.128 | 248.422 | 39.137 | 6.891 | 20.818 | 52.616 |

Pile Stiffness Effect | |||||||||

E_{p1} | 524.270 | 861.389 | 488.142 | 415.128 | 248.422 | 39.137 | 6.891 | 20.818 | 52.616 |

E_{p2} | 525.274 | 875.012 | 500.002 | 427.055 | 252.604 | 39.970 | 4.811 | 18.699 | 51.910 |

E_{p3} | 526.043 | 885.202 | 509.006 | 436.031 | 255.516 | 40.574 | 3.239 | 17.111 | 51.427 |

Soil Stiffness Effect | |||||||||

E_{s1} | 524.270 | 861.389 | 488.142 | 415.128 | 248.422 | 39.137 | 6.891 | 20.818 | 52.616 |

E_{s2} | 522.476 | 837.790 | 465.483 | 391.661 | 242.058 | 37.636 | 10.908 | 25.038 | 53.671 |

E_{s3} | 520.390 | 812.899 | 443.048 | 367.568 | 237.664 | 35.983 | 14.862 | 29.367 | 54.333 |

_{S1}, P

_{G1}= 542.453 kN, 7051.887 kN; P

_{S2}, P

_{G2}= 690.240 kN, 8973.120 kN; P

_{S3}, P

_{G3}= 822.309 kN, 10,690.011 kN. E

_{p1}= 20.75 MPa; E

_{p2}= 29.05 MPa; E

_{p3}= 37.35 MPa. E

_{s1}= Maheswari et al. [23]; E

_{s2}= Hasancebi and Ulusay in Hammam and Eliwa [22]; E

_{s3}= Tsimbaos and Sabatakakis [24].

Deflection (mm) | The Difference of Deflection with Single Pile (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Single Pile | 1st Row | 2nd Row | 3rd Row | 4th Row | 1st Row | 2nd Row | 3rd Row | 4th Row | |

Earthquake Combination Load Effect | |||||||||

P_{S1}, P_{G1} | 2.417 | 7.466 | 7.361 | 7.199 | 6.555 | 67.622 | 67.165 | 66.426 | 63.127 |

P_{S2}, P_{G2} | 3.532 | 11.114 | 10.938 | 10.662 | 9.572 | 68.220 | 67.709 | 66.873 | 63.101 |

P_{S3}, P_{G3} | 4.972 | 16.257 | 15.977 | 15.539 | 13.824 | 69.416 | 68.880 | 68.003 | 64.034 |

Pile Stiffness Effect | |||||||||

E_{p1} | 4.972 | 16.257 | 15.977 | 15.539 | 13.824 | 69.416 | 68.880 | 68.003 | 64.034 |

E_{p2} | 4.808 | 15.367 | 15.101 | 14.690 | 13.090 | 68.712 | 68.161 | 67.270 | 63.270 |

E_{p3} | 4.692 | 14.756 | 14.500 | 14.108 | 12.588 | 68.203 | 67.641 | 66.742 | 62.726 |

Soil Stiffness Effect | |||||||||

E_{s1} | 4.972 | 16.257 | 15.977 | 15.539 | 13.824 | 69.416 | 68.880 | 68.003 | 64.034 |

E_{s2} | 3.939 | 13.852 | 13.616 | 13.241 | 11.768 | 71.564 | 71.071 | 70.251 | 66.528 |

E_{s3} | 3.140 | 11.964 | 11.763 | 11.438 | 10.154 | 73.755 | 73.306 | 72.548 | 69.0.76 |

_{S1}, P

_{G1}= 542.453 kN, 7051.887 kN; P

_{S2}, P

_{G2}= 690.240 kN, 8973.120 kN; P

_{S3}, P

_{G3}= 822.309 kN, 10,690.011 kN. E

_{p1}= 20.75 MPa; E

_{p2}= 29.05 MPa; E

_{p3}= 37.35 MPa. E

_{s1}= Maheswari et al. [23]; E

_{s2}= Hasancebi and Ulusay in Hammam and Eliwa [22]; E

_{s3}= Tsimbaos and Sabatakakis [24].

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## Share and Cite

**MDPI and ACS Style**

Munawir, A.; Harimurti; Sumarsono, Q.A.R.P.
Lateral Load Capacity and p-Multiplier of Group Piles with Asymmetrical Pile Cap under Seismic Load. *Appl. Sci.* **2022**, *12*, 8142.
https://doi.org/10.3390/app12168142

**AMA Style**

Munawir A, Harimurti, Sumarsono QARP.
Lateral Load Capacity and p-Multiplier of Group Piles with Asymmetrical Pile Cap under Seismic Load. *Applied Sciences*. 2022; 12(16):8142.
https://doi.org/10.3390/app12168142

**Chicago/Turabian Style**

Munawir, As’ad, Harimurti, and Queen Arista Rosmania Putri Sumarsono.
2022. "Lateral Load Capacity and p-Multiplier of Group Piles with Asymmetrical Pile Cap under Seismic Load" *Applied Sciences* 12, no. 16: 8142.
https://doi.org/10.3390/app12168142