# Seismic Response of Adjacent Unequal Buildings Subjected to Double Pounding Considering Soil-Structure Interaction

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Impact Elements

_{L}is the stiffness and C

_{L}is the damping coefficient (Anagnostopoulos [1], Shakya and Wijeyewickrema [19]). Numerical simulation performed by Jankowski [34] showed that for concrete to concrete impact, K

_{L}= 9350 t/m provides good correlation between experimental results provided by Van Mier et al. [35] and theoretical results. In the present study, the same value of K

_{L}is used.

_{G}is considered as 100 K

_{L}to avoid errors in convergence and to ensure that it works as nearly rigidly when the gap is closed.

## 3. Model Description

## 4. Results and Discussion

#### 4.1. Adjacent Buildings with Equal Foundation Levels

#### 4.2. Adjacent Buildings with Unequal Foundation Levels

#### 4.3. Soil Response

## 5. Conclusions

- The top lateral displacement in the single and the two adjacent buildings is bigger in the SSI effect case than in the fixed base case.
- When considering the SSI effect, the top acceleration of the short building in the two adjacent buildings decreases with the decrease of its height, while the top acceleration in the tall building is not strongly affected by the height of the short building.
- The base shear forces, the bending moments and the base normal forces in the two adjacent buildings are bigger when considering the SSI effect than in the fixed base case.
- The shear force in the column in the basement level is bigger than in the floor levels for the different heights of the two adjacent buildings.
- The results of the straining actions on the two adjacent buildings subjected to earthquake considering SSI reveal the double pounding at top of the low building and at foundation level.
- The importance of equal foundation levels should be considered for adjacent buildings even if they have not the same number of floors.
- The soil-structure interaction (SSI) and the double pounding effects should be taken into consideration in the building design and the seismic analysis of adjacent buildings especially those with different heights and different foundation levels.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**The buildings with soil mesh of modelled representation. (

**a**) The two adjacent buildings with unequal foundation levels; (

**b**) Single 12-floor building (with foundation at −5 m); (

**c**) Single 6-floor building (with foundation at −3 m).

**Figure 10.**Stress in the soil in x direction around the foundation of the single and adjacent buildings.

**Figure 11.**Stress in the soil in z direction around the foundation of the single and adjacent buildings.

**Figure 12.**Lateral normal force at the foundation for the two adjacent and single buildings with SSI.

**Figure 14.**Points distributed around the foundations of the single building and the two adjacent buildings with unequal foundation levels. (

**a**) Single building basement foundation; (

**b**) The foundations with unequal levels of the two adjacent buildings.

**Figure 15.**Comparison for top displacement and acceleration between the single and the two adjacent buildings with unequal foundation levels and SSI.

**Figure 16.**Straining actions at the base of the single and the two adjacent buildings with unequal foundation levels and SSI.

**Figure 18.**Lateral normal force at the foundation of the single and the two adjacent buildings with unequal foundation levels and SSI.

**Figure 19.**Shear force over the height of the tall building in the two adjacent buildings with unequal foundation levels and SSI.

**Figure 20.**Lateral soil stresses (KN/m

^{2}) for the two adjacent buildings with equal foundation levels.

**Figure 21.**Vertical soil stresses (KN/m

^{2}) for the two adjacent buildings with equal foundation levels.

**Figure 22.**Lateral soil stresses (KN/m

^{2}) for the two adjacent buildings with unequal foundation levels.

**Figure 23.**Vertical soil stresses (KN/m

^{2}) for the two adjacent buildings with unequal foundation levels.

Elastic Modulus, E (KN/m^{2}) | 30,000 |

Soil shear modulus, G (KN/m^{2}) | 14,350 |

Poisson’s ratio, ν | 0.40 |

Weight per unit volume, γ (KN/m^{3}) | 16 |

Symbol | Definition | Symbol | Definition |
---|---|---|---|

F.L. | Foundation Level. | s | Building considering SSI. |

G.L. | Ground Level. | S | Single building considering SSI. |

12-12 | Two adjacent buildings: both with 12 floors. | f | Fixed base building. |

12-10 | Two adjacent buildings: one with 12 floors and the other with 10 floors. | F | Fixed base single building. |

12-8 | Two adjacent buildings: one with 12 floors and the other with 8 floors. | U | Displacement. |

12-6 | Two adjacent buildings: one with 12 floors and the other with 6 floors. | a | Acceleration. |

12-4 | Two adjacent buildings: one with 12 floors and the other with 4 floors. | Q | Base shear force. |

12-2 | Two adjacent buildings: one with 12 floors and the other with 2 floors. | M | Base bending moment. |

h | High (tall) building with 12 floors. | N | Base normal force. |

s | Short (low) building. | Sx | Lateral soil stress. |

alone | Single building. | Sz | Vertical soil stress. |

SSI | Soil Structure Interaction effect. | N L | Lateral normal force at foundation. |

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**MDPI and ACS Style**

Kontoni, D.-P.N.; Farghaly, A.A.
Seismic Response of Adjacent Unequal Buildings Subjected to Double Pounding Considering Soil-Structure Interaction. *Computation* **2018**, *6*, 10.
https://doi.org/10.3390/computation6010010

**AMA Style**

Kontoni D-PN, Farghaly AA.
Seismic Response of Adjacent Unequal Buildings Subjected to Double Pounding Considering Soil-Structure Interaction. *Computation*. 2018; 6(1):10.
https://doi.org/10.3390/computation6010010

**Chicago/Turabian Style**

Kontoni, Denise-Penelope N., and Ahmed Abdelraheem Farghaly.
2018. "Seismic Response of Adjacent Unequal Buildings Subjected to Double Pounding Considering Soil-Structure Interaction" *Computation* 6, no. 1: 10.
https://doi.org/10.3390/computation6010010