# Seismic Performance of Steel Structure-Foundation Systems Designed According to Eurocode 8 Provisions: The Case of Near-Fault Seismic Motions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Seismic Analysis of Steel Structure-Foundation Systems

^{2}and live loads 3 kN/m

^{2}. The steel buildings were designed as concentrically braced frames in association with the provisions of Eurocode 3 [17] and Eurocode 8 [11], assuming undeformable soil conditions. The steel type/grade used was S355 for columns and S275 for braces and beams. The connections for the interior-secondary beams that were not part of a frame were designed as pinned ones, while the rest of the connections involving beams and columns that were part of a frame were designed as moment-resisting ones. The steel braces intersected at their mid-length and were modeled as fixed in-plane and pinned out of plane [18]. The design earthquake forces were evaluated according to the design spectrum of Eurocode 8 [11], assuming peak ground acceleration (PGA) equal to 0.36 g, behavior factor equal to 3, and soil type B. Final sections for beams, columns, and braces are shown in Table 1. Column orientation follows Figure 2, which is commonly used for steel buildings designed as dual systems, i.e., MRF with concentric bracings [11].

_{s}are the shear modulus, Poisson’s ratio, and velocity of shear waves, respectively, of the soil medium, α is the half-length of an equivalent square foundation, m and m

_{v}are the mass of the foundation and a virtual soil mass, respectively. The soil shear modulus of soil categories C and D resulted from the corresponding velocity of shear waves, equal to 270 m/s and 180 m/s, while the soil density was assumed to be 1800 kgr/m

^{3}and 1900 kgr/m

^{3}, respectively. Taking into account the non-linear soil deformations for soil types C and D due to relatively large values of ground acceleration, the effective shear modulus resulted from reduced values (reduction 16%) of its initial value [11].

_{w}of these earthquakes is also mentioned in this table. These near-fault accelerograms were applied to the two normal/horizontal axes of Figure 2, examining three values for the angle of seismic incidence θ: 0°, 45°, and 90°. It should be noted that the accelerograms of Table 4 had been recorded in the vicinity of the fault, i.e., at a distance no more than 10 km and had been produced from earthquakes of magnitude six or greater. The components of the accelerograms of Table 4 all exhibited directionality, i.e., the fault normal component was stronger than the fault parallel one. Thus, the accelerograms had been used as-recorded, and no scaling procedure had been applied to them. This was in accordance with ASCE 7–16 [20], where it is explicitly mentioned that: ‘The fault normal and the fault parallel component of the recorded near-fault motions is maintained and applied to the corresponding orientation of the structures considered’. The 5%-damped response spectra of the fault normal component of the accelerograms of Table 4, as well as the mean values of these spectra, are displayed in Figure 3. For comparison purposes, the Eurocode 8 spectra for soil types B, C, and D [11] are also provided in Figure 3.

## 3. Seismic Performance Assessment

_{SSI}to R

_{FIX}, where R is the maximum value of the following structural parameters: interstorey drift ratio (IDR), residual interstorey drift ratio (RIDR), base shear (V

_{b}), and overturning moment (M

_{b}). It should be noted that for the cases of soil types C and D, the net interstory displacements of the steel structures in the direction of the two horizontal -normal axes X and Y of Figure 2 were calculated, i.e., rotation of the foundation was excluded.

_{b}and M

_{b}were provided for the two orthogonal structural axes X and Y of Figure 2. Due to the ‘Link element’ of SAP 2000 [14], the computed V

_{b}for the SSI cases was the summation of damping and elastic forces. For the fixed base case, the V

_{b}was the elastic force.

#### 3.1. 2-Story Steel Structure-Foundation Systems

^{−3}(soil type C), δ = 1.56 ∙ 10

^{−2}(soil type D), ω = 4.61 ∙ 10

^{−4}(soil type C), and ω = 8.77 ∙ 10

^{−4}(soil type D). Excluding the aforementioned failure cases, the maximum values of IDR and RIDR for the three values of θ are shown in Table 6, along with the corresponding values for the R index (R

_{IDR}, R

_{RIDR}). In Table 7, values for V

_{b}, M

_{b}, and the associated values of the R index (R

_{Vb}, R

_{Mb}) are presented. These V

_{b}, M

_{b}values were the largest ones observed for the 2-story steel structure-foundation system and came from seismic motion No.3 of Table 4 and θ = 45° incidence angle.

#### 3.2. 5-Story Steel Structure-Foundation Systems

^{−2}(soil type C), δ = 3.7 ∙ 10

^{−2}(soil type D), ω = 1.05 ∙ 10

^{−3}(soil type C), and ω = 2.25 ∙ 10

^{−3}(soil type D). Excluding the aforementioned failure cases, the maximum values of IDR and RIDR for the three values of θ are shown in Table 9, along with the corresponding values for the R index (R

_{IDR}, R

_{RIDR}). In Table 10, values for V

_{b}, M

_{b}, and the associated values of the R index (R

_{Vb}, R

_{Mb}) are presented. These V

_{b}, M

_{b}values were the largest ones observed for the 5-story steel structure-foundation system and came from seismic motion No.2 of Table 4 and θ = 90° incidence angle.

#### 3.3. 8-Story Steel Structure-Foundation Systems

^{−2}(soil type C), δ = 6.1 ∙ 10

^{−2}(soil type D), ω = 1.43 ∙ 10

^{−3}(soil type C), and ω = 3.16 ∙ 10

^{−3}(soil type D). Excluding the aforementioned failure cases, the maximum values of IDR and RIDR for the three values of θ are shown in Table 12, along with the corresponding values for the R index (R

_{IDR}, R

_{RIDR}). In Table 13, values for V

_{b}, M

_{b}, and the associated values of the R index (R

_{Vb}, R

_{Mb}) are presented. These V

_{b}, M

_{b}values were the largest ones observed for the 8-story steel structure-foundation system and came from seismic motion No.5 of Table 3 and θ = 90° incidence angle.

## 4. Discussion and Conclusions

_{b}and M

_{b}revealed either an increase or a decrease to the base shear and the overturning moment of the steel structures with SSI included (soil categories C and D) in comparison to steel structures founded on rigid soil. This variation on V

_{b}and M

_{b}should be further investigated in terms of an integrated performance-based seismic design approach for steel structure-foundation systems [24].

## Author Contributions

## Funding

## Conflicts of Interest

## References

- EN1998-5. Eurocode 8: Design of Structures for Earthquake Resistance—Part 5: Foundations, Retaining Structures and Geotechnical Aspects; European Committee for Standardization (CEN): Brussels, Belgium, 2005. [Google Scholar]
- Stone, W.C.; Yokel, F.Y.; Celebi, M.; Hanks, T.; Leyendecker, E.V. Engineering Aspects of the September 19, 1985 Mexico Earthquake—No. Building Science Series-165; National Institute of Standards and Technology NIST: Washington, DC, USA, 1987. [Google Scholar]
- Minasidis, G.; Hatzigeorgiou, G.D.; Beskos, D.E. SSI in steel frames subjected to near-fault earthquakes. Soil Dyn. Earthq. Eng.
**2014**, 66, 56–68. [Google Scholar] [CrossRef] - Fernández Sola, L.R.; Tapia Hernández, E.; Dávalos Chávez, D. Respuesta inelástica de marcos de acero con interacción inercial suelo-estructura. Rev. Ing. Sísmica
**2015**, 92, 1–21. [Google Scholar] [CrossRef] [Green Version] - Ayough, P.; Mohamadi, S.; Seiyed Taghia, S.A.H. Response of steel moment and braced frames subjected to near-source pulse-like ground motions by including soil-structure interaction effects. Civ. Eng. J.
**2017**, 3, 15–34. [Google Scholar] [CrossRef] - Flogeras, A.K.; Papagiannopoulos, G.A. On the seismic response of steel buckling-restrained braced structures including soil-structure interaction. Earthq. Struct.
**2017**, 12, 469–478. [Google Scholar] [CrossRef] - Ghandil, M.; Behnamfar, F. Ductility demands on MRF structures on soft soils considering soil-structure interaction. Soil Dyn. Eart Hquake Eng.
**2017**, 92, 203–214. [Google Scholar] [CrossRef] - Shakib, H.; Homaei, F. Probabilistic seismic performance assessment of the soil-structure interaction effect on seismic response of mid-rise setback steel buildings. Bull. Earthq. Eng.
**2017**, 15, 2827–2851. [Google Scholar] [CrossRef] - Farhadi, N.; Saffari, H.; Torkzadeh, P. Estimation of maximum and residual inter-storey drift in steel MRF considering soil-structure interaction from fixed-base analyses. Soil Dyn. Earthq. Eng.
**2018**, 114, 85–96. [Google Scholar] [CrossRef] - Shahbazi, S.; Mansouri, I.; Hu, J.W.; Karami, A. Effect of soil classification on seismic behavior of SMFs considering soil-structure interaction and near-field earthquakes. Shock Vib.
**2018**. [Google Scholar] [CrossRef] [Green Version] - EN1998-1. EEurocode 8: Design of Structures for Earthquake Resistance—Part 1: General Rules, Seismic Actions and Rules for Buildings; European Committee for Standardization (CEN): Brussels, Belgium, 2005. [Google Scholar]
- EN1997-1. Eurocode 7: Geotechnical Design—art 1: General rules; European Committee for Standardization (CEN): Brussels, Belgium, 2004. [Google Scholar]
- Tartaglia, R.; D’Aniello, M.; De Martino, A.; Di Lorenzo, G. Influence of EC8 rules on P-delta effects on the design and response of steel MRF. Inegneria Sismica Int. J. Earthq. Eng.
**2018**, 35, 104–120. [Google Scholar] - SAP 2000. Static and Dynamic Finite Element Analysis of Structures: Version 19.0; Computers and Structures (CSI): California, CA, USA, 2016. [Google Scholar]
- McCormick, J.; Aburano, H.; Ikenaga, M.; Nakashima, M. Permissible residual deformation levels for building structures considering both safety and human elements. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. [Google Scholar]
- Nakano, Y.; Maeda, M.; Kuramotio, H.; Murakami, M. Guideline for post-earthquake damage evaluation and rehabilitation of RC buildings in Japan. In Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, 1–6 August 2004. [Google Scholar]
- EN1993-1. Eurocode 3: Design of Steel Structures—Part 1: General Rules and Rules for Buildings; European Committee for Standardization (CEN): Brussels, Belgium, 2009. [Google Scholar]
- Costanzo, S.; D’Aniello, M.; Landolfo, R. Proposal for design rules for ductile X-CBFS in the framework of Eurocode 8. Earthq. Eng. Struct. Dyn.
**2019**, 48, 124–151. [Google Scholar] [CrossRef] [Green Version] - Mulliken, J.S.; Karabalis, D.L. Discrete model for dynamic through-the-soil coupling of 3-d foundations and structures. Earthq. Eng. Struct. Dyn.
**1998**, 27, 687–710. [Google Scholar] [CrossRef] - ASCE 7-16. Minimum Design Loads and Associated Criteria for Buildings and Other Structures; American Society of Civil Engineers (ASCE): Reston, WV, USA, 2017. [Google Scholar]
- ASCE 41-17. Seismic Evaluation and Retrofit of Existing Buildings; American Society of Civil Engineers (ASCE): Reston, WV, USA, 2017. [Google Scholar]
- Azad, S.K.; Topkaya, C.; Astaneh-Asl, A. Seismic behavior of concentrically braced frames designed to AISC341 and EC8 provisions. J. Constr. Steel Res.
**2017**, 133, 383–404. [Google Scholar] [CrossRef] - Costanzo, S.; Tartaglia, R.; Di Lorenzo, G.; De Martino, A. Seismic behavior of EC8-compliant moment resisting and concentrically braced frames. Buildings
**2019**, 9, 196. [Google Scholar] [CrossRef] [Green Version] - Millen, M.D.L.; Pampanin, S.; Cubrinovski, M.; Carr, A. Integrating soil-structure interaction within performance-based design. In Proceedings of the Annual Technical Conference of the New Zealand Society for Earthquake Engineering, Auckland, New Zealand, 21–23 March 2014. [Google Scholar]

Steel Structure | Beams | Braces | Columns |
---|---|---|---|

2-story | IPE 450 | CHS 219.1 × 5.0 | HEM 320 |

5-story | IPE 500 | CHS 273.0 × 5.6 | HEM 600 |

8-story | IPE 500 | CHS 355.6 × 6.3 | HEM 700 |

**Table 2.**Formulae for mass, springs, and dashpots (after [19]).

Mass (Inertia) Ratio, β | Equivalent Radius, r_{0} | Virtual Soil Mass (Inertia), m_{v} | Static Stiffness K | Damping C | |
---|---|---|---|---|---|

Vertical | $\frac{\left(1-\nu \right)}{4}\frac{m}{\rho {r}_{0}^{3}}$ | $\frac{2a}{\sqrt{\pi}}$ | $\frac{0.27m}{\beta}$ | $\frac{4.7Ga}{1-\nu}$ | $\frac{0.8a}{{V}_{s}}K$ |

Horizontal | $\frac{\left(7-8\nu \right)}{32\left(1-\nu \right)}\frac{m}{\rho {r}_{0}^{3}}$ | $\frac{2a}{\sqrt{\pi}}$ | $\frac{0.095m}{\beta}$ | $\frac{9.2Ga}{2-\nu}$ | $\frac{0.163a}{{V}_{s}}K$ |

Rocking | $\frac{3\left(1-\nu \right)}{8}\frac{m}{\rho {r}_{0}^{5}}$ | $\frac{2a}{\sqrt[4]{3\pi}}$ | $\frac{0.24m}{\beta}$ | $\frac{4.0G{\alpha}^{3}}{1-\nu}$ | $\frac{0.6a}{{V}_{s}}K$ |

Torsion | $\frac{m}{\rho {r}_{0}^{5}}$ | $\frac{2a}{\sqrt[4]{3\pi}}$ | $\frac{0.045m}{\beta}$ | $8.31G{\alpha}^{3}$ | $\frac{0.127a}{{V}_{s}}K$ |

Steel Structure | 1st Mode (s) | 2nd Mode (s) |
---|---|---|

2-story, soil type B (fixed base) | 0.254 | 0.236 |

2-story, soil category C | 0.569 | 0.546 |

2-story, soil category D | 0.600 | 0.578 |

5-story, soil type B (fixed base) | 0.523 | 0.474 |

5-story, soil category C | 1.264 | 1.169 |

5-story, soil category D | 1.342 | 1.283 |

8-story, soil type B (fixed base) | 0.800 | 0.749 |

8-story, soil category C | 1.289 | 1.180 |

8-story, soil category D | 1.429 | 1.333 |

No. | Earthquake, Location, Year | Recording Station | M_{w} |
---|---|---|---|

1. | San Fernando, (Calif.), 1971 | Pacoima Dam | 6.6 |

2. | Superstition Hills, (Calif.), 1987 | Parachute Test Site | 7.3 |

3. | Loma Prieta, (Calif.), 1989 | Los Gatos | 6.5 |

4. | Cape Mendocino, (Calif.), 1992 | Petrolia | 7.0 |

5. | Landers, (Calif.), 1992 | Lucerne Valley | 7.3 |

6. | Northridge, (Calif.), 1994 | Rinaldi Receiving St. | 6.7 |

7. | Northridge, (Calif.), 1994 | Newhall | 6.7 |

8. | Northridge, (Calif.), 1994 | Sylmar Converter St. | 6.7 |

9. | Kobe, Japan, 1995 | Takatori | 6.9 |

10. | Christchurch, New Zealand, 2011 | Resthaven | 6.3 |

Steel Structure-Foundation, θ | Number of Failures - Steel Structure | Number of Failures - Foundation |
---|---|---|

2-story, fixed, 0° | 4/10 | - |

2-story, fixed, 45° | 4/10 | - |

2-story, fixed, 90° | 5/10 | - |

2-story, soil type C, 0° | 0/10 | 0/10 |

2-story, soil type C, 45° | 0/10 | 0/10 |

2-story, soil type C, 90° | 0/10 | 0/10 |

2-story, soil type D, 0° | 0/10 | 0/10 |

2-story, soil type D, 45° | 0/10 | 0/10 |

2-story, soil type D, 90° | 0/10 | 0/10 |

Steel Structure-Foundation, θ | IDR (%) | RIDR (%) | R_{IDR} | R_{RIDR} |
---|---|---|---|---|

2-story, fixed, 0° | 0.62 | 0.28 | - | - |

2-story, fixed, 45° | 0.52 | 0.13 | - | - |

2-story, fixed, 90° | 0.52 | 0.07 | - | - |

2-story, soil type C, 0° | 3.22 | 0.25 | 5.19 | 0.89 |

2-story, soil type C, 45° | 3.33 | 0.25 | 6.40 | 1.92 |

2-story, soil type C, 90° | 2.50 | 0.16 | 4.81 | 2.29 |

2-story, soil type D, 0° | 3.50 | 0.39 | 5.64 | 1.39 |

2-story, soil type D, 45° | 3.41 | 0.23 | 6.56 | 1.77 |

2-story, soil type D, 90° | 2.46 | 0.13 | 4.73 | 1.86 |

Steel Structure-Foundation | V_{b} (kN) | M_{b} (kNm) | R_{Vb} | R_{Mb} |
---|---|---|---|---|

2-story, fixed | 7222 (X) 6923 (Y) | 34,740 (X) 36,950 (Y) | - | - |

2-story, soil type C | 6720 (X) 7633 (Y) | 47,220 (X) 48,740 (Y) | 0.93 (X) 1.10 (Y) | 1.36 (X) 1.32 (Y) |

2-story, soil type D | 5575 (X) 8219 (Y) | 51,130 (X) 38,750 (Y) | 0.77 (X) 1.19 (Y) | 1.47 (X) 1.05 (Y) |

Steel Structure-Foundation, θ | Number of Failures - Steel Structure | Number of Failures - Foundation |
---|---|---|

5-story, fixed, 0° | 9/10 | - |

5-story, fixed, 45° | 9/10 | - |

5-story, fixed, 90° | 9/10 | - |

5-story, soil type C, 0° | 5/10 | 0/10 |

5-story, soil type C, 45° | 6/10 | 0/10 |

5-story, soil type C, 90° | 6/10 | 0/10 |

5-story, soil type D, 0° | 7/10 | 0/10 |

5-story, soil type D, 45° | 7/10 | 0/10 |

5-story, soil type D, 90° | 7/10 | 0/10 |

Steel Structure-Foundation, θ | IDR (%) | RIDR (%) | R_{IDR} | R_{RIDR} |
---|---|---|---|---|

5-story, fixed, 0° | 0.51 | 0.08 | - | - |

5-story, fixed, 45° | 0.67 | 0.05 | - | - |

5-story, fixed, 90° | 0.73 | 0.04 | - | - |

5-story, soil type C, 0° | 2.10 | 0.25 | 4.12 | 3.13 |

5-story, soil type C, 45° | 2.22 | 0.44 | 3.31 | 8.80 |

5-story, soil type C, 90° | 2.69 | 0.33 | 3.68 | 8.25 |

5-story, soil type D, 0° | 3.17 | 0.18 | 6.22 | 2.25 |

5-story, soil type D, 45° | 2.38 | 0.24 | 3.55 | 4.80 |

5-story, soil type D, 90° | 2.57 | 0.41 | 3.52 | 10.25 |

Steel Structure-Foundation | V_{b} (kN) | M_{b} (kNm) | R_{Vb} | R_{Mb} |
---|---|---|---|---|

5-story, fixed | 9216 (X) 8192 (Y) | 96,750 (X) 102,100 (Y) | - | - |

5-story, soil type C | 8588 (X) 12,960 (Y) | 112,300 (X) 86,640 (Y) | 0.93 (X) 1.58 (Y) | 1.16 (X) 0.85 (Y) |

5-story, soil type D | 5920 (X) 12,820 (Y) | 111,500 (X) 71,460 (Y) | 0.64 (X) 1.56 (Y) | 1.15 (X) 0.70 (Y) |

Steel Structure-Foundation, θ | Number of Failures - Steel Structure | Number of Failures - Foundation |
---|---|---|

8-story, fixed, 0° | 9/10 | - |

8-story, fixed, 45° | 9/10 | - |

8-story, fixed, 90° | 10/10 | - |

8-story, soil type C, 0° | 6/10 | 0/10 |

8-story, soil type C, 45° | 6/10 | 0/10 |

8-story, soil type C, 90° | 6/10 | 0/10 |

8-story, soil type D, 0° | 5/10 | 0/10 |

8-story, soil type D, 45° | 7/10 | 0/10 |

8-story, soil type D, 90° | 7/10 | 0/10 |

Steel Structure-Foundation, θ | IDR (%) | RIDR (%) | R_{IDR} | R_{RIDR} |
---|---|---|---|---|

8-story, fixed, 0° | 0.69 | 0.05 | - | - |

8-story, fixed, 45° | 0.70 | 0.06 | - | - |

8-story, fixed, 90° | 0.70 | 0.06 | - | - |

8-story, soil type C, 0° | 2.10 | 0.12 | 3.04 | 2.40 |

8-story, soil type C, 45° | 2.19 | 0.21 | 3.13 | 3.50 |

8-story, soil type C, 90° | 2.62 | 0.31 | 3.74 | 5.17 |

8-story, soil type D, 0° | 3.35 | 0.21 | 4.86 | 3.50 |

8-story, soil type D, 45° | 3.35 | 0.38 | 4.79 | 6.33 |

8-story, soil type D, 90° | 3.27 | 0.49 | 4.67 | 8.17 |

Steel Structure-Foundation | V_{b} (kN) | M_{b} (kNm) | R_{Vb} | R_{Mb} |
---|---|---|---|---|

8-story, fixed | 17,280 (X) 8748 (Y) | 121,800 (X) 240,900 (Y) | - | - |

8-story, soil type C | 18,000 (X) 7868 (Y) | 80,650 (X) 170,700 (Y) | 1.04 (X) 0.90 (Y) | 0.66 (X) 0.71 (Y) |

8-story, soil type D | 15,450 (X) 6024 (Y) | 58,780 (X) 173,500 (Y) | 0.89 (X) 0.69 (Y) | 0.48 (X) 0.72 (Y) |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Katsimpini, P.; Konstandakopoulou, F.; Papagiannopoulos, G.; Pnevmatikos, N.; Hatzigeorgiou, G.
Seismic Performance of Steel Structure-Foundation Systems Designed According to Eurocode 8 Provisions: The Case of Near-Fault Seismic Motions. *Buildings* **2020**, *10*, 63.
https://doi.org/10.3390/buildings10040063

**AMA Style**

Katsimpini P, Konstandakopoulou F, Papagiannopoulos G, Pnevmatikos N, Hatzigeorgiou G.
Seismic Performance of Steel Structure-Foundation Systems Designed According to Eurocode 8 Provisions: The Case of Near-Fault Seismic Motions. *Buildings*. 2020; 10(4):63.
https://doi.org/10.3390/buildings10040063

**Chicago/Turabian Style**

Katsimpini, Panagiota, Foteini Konstandakopoulou, George Papagiannopoulos, Nikos Pnevmatikos, and George Hatzigeorgiou.
2020. "Seismic Performance of Steel Structure-Foundation Systems Designed According to Eurocode 8 Provisions: The Case of Near-Fault Seismic Motions" *Buildings* 10, no. 4: 63.
https://doi.org/10.3390/buildings10040063