# Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Nonlinear Modeling of the Inelastic Behavior

## 3. Energy-Related Parameters

_{Ia}or relative input energy E

_{Ir}, which reads as follows:

_{ka}and E

_{kr}are the kinetic energies representing the difference between the absolute and relative input energy, respectively, E

_{ξ}is the damping energy, E

_{s}is the elastic strain energy and E

_{H}is the hysteretic energy. Based on Equation (1) the following parameters are therefore considered in the present study:

- -
- inelastic absolute E
_{Ia}_{μ}and relative E_{Ir}_{μ}input energy for the given ductility demand μ; - -
- input energy reduction factors, R
_{Ea}= E_{Ia}/E_{Ia}_{μ}and R_{Er}= E_{Ir}/E_{Ir}_{μ}(i.e., the ratio between the elastic input energy and the inelastic value corresponding to a given ductility demand μ); - -
- the hysteretic energy dissipation demand E
_{H}; - -
- the hysteretic energy reduction factors, R
_{Ha}= (E_{H}/E_{Ia})_{μ}and R_{Hr}= (E_{H}/E_{Ir})_{μ}(i.e., the ratio between the hysteretic energy dissipation demand and the inelastic input energy value corresponding to a given ductility demand μ); - -
- the parameter η that quantifies the plasticity level in terms of dimensionless cumulative plastic deformation ratio, i.e., η = E
_{H}/(R_{y}δ_{y}), where R_{y}and δ_{y}are the elastic limit strength and displacement, respectively.

## 4. Database of Horizontal Fault-Normal Pulse-like Seismic Ground Motion Records

_{f}) less than 30 km, moment magnitudes (M

_{w}) greater than 5.0 and soil preferred shear-velocities (V

_{S}

_{30}) between 160 m/s and 1000 m/s. It is highlighted, however, that the largest part of the selected records belonged to two soil classes only, namely B and C according to the Eurocode 8 soil classification. It is also pointed out that the maximum closest site-to-source distance within the final dataset was slightly larger than the limit distances commonly considered in similar studies, and it was meant to possibly take into account the pulse-like seismic ground motions induced by very large magnitude earthquakes. Moreover, only records with moment magnitudes larger than 5.0 were used in order to focus on the range of magnitude values that generally dictates the hazard in medium-to-high seismicity regions. The full set of values of the most relevant seismological parameters is provided in Figure 2. Herein, the pulse period (T

_{p}) was estimated according to the methodology illustrated in [14]. As already pointed out in previous studies (see for instance [6,9,14]), it is especially highlighted that near-fault pulse-like earthquakes can exhibit very high values of T

_{p}.

## 5. Sensitivity Analysis

#### 5.1. Clustering of Seismic Records

#### 5.2. Influence of Seismological Parameters

_{Ia}

_{μ}and relative E

_{Ir}

_{μ}input energy are shown in Figure 3.

_{S}

_{30}only, namely less than 180 m/s. Otherwise, no significant effects are produced, since the mean spectra for V

_{S}

_{30}larger than 180 m/s are very close to each other and almost overlap for period values larger than 4 s. This evidence, however, is not conclusive and might be affected by statistical distortion, since the number of seismic records with V

_{S}

_{30}less than 180 m/s is low and much less than the number of those available for V

_{S}

_{30}between 180 m/s and 360 m/s or between 360 m/s and 800 m/s.

_{Ea}and R

_{Er}for a given ductility demand μ. To this end, the spectra related to R

_{Ea}only are shown in Figure 4 because they have similar results as those carried out for R

_{Er}. It can be noted from Figure 4 that the mean spectra of the absolute input energy reduction factor R

_{Ea}in terms of earthquake magnitude and site-to-source distance were not too far each other for period values less than 4 s. On the other hand, mean spectra of the absolute input energy reduction factor in terms of soil type were closer to each other for almost the whole range of period values.

_{H}provided no enlightening new evidence about the role of seismological parameters on the energy demand with respect to the conclusions already drawn from the analysis of absolute E

_{Ia}

_{μ}and relative E

_{Ir}

_{μ}input energy spectra, as can be concluded by comparing Figure 3 and Figure 5.

_{Ha}and R

_{Hr}for a given ductility demand μ. Assuming the hysteretic energy reduction factor R

_{Ha}as a reference parameter, Figure 6 shows that it was strongly affected by the earthquake magnitude and to a lesser extent by soil type, whereas the site-to-source distance did not produce very large effects. Specifically, the increment of the earthquake magnitude caused a shifting on the right of the period at which the peak of the hysteretic energy reduction factor was attained. In addition, the larger the earthquake magnitude was, the lower was the slope of the post-peak branch of the hysteretic energy reduction factor R

_{Ha}spectrum. Note, however, that the peak value of the hysteretic energy reduction factor R

_{Ha}spectrum did not seem much affected by the earthquake magnitude, and its variability decreased when the earthquake magnitude increased. Regarding the influence of the soil type, it appeared evident for rather low values of V

_{S}

_{30}only, but it might be possible that this evidence could have been corrupted by the low number of seismic records available for V

_{S}

_{30}less than 180 m/s.

_{H}alone cannot provide a proper assessment of the structural behavior, particularly for reinforced concrete structures. In fact, the hysteretic energy associated with structural systems having small strength and undergoing a large cyclic response can be similar to that experienced by structural systems having large strength but undergoing a small cyclic response.

_{H}. As a matter of fact, the mean spectra of the cumulative plastic deformation ratio η differed significantly only for very large earthquake magnitude values and period values less than 4 s.

#### 5.3. Influence of Hysteretic Model and Ductility Level

_{Ia}

_{μ}and relative E

_{Ir}

_{μ}input energy as well as those for input energy reduction factors R

_{Ea}and R

_{Er}and hysteretic energy dissipation demand E

_{H}. The observed differences became larger and larger for increasing values of the ductility level μ. On the other hand, the spectra of the hysteretic energy reduction factors R

_{Ha}and R

_{Hr}as well as those for the cumulative plastic deformation ratio η were affected to a rather larger extent by hysteretic behavior and/or the ductility level μ (see Figure 8 and Figure 9). Particularly, these plots emphasized that large differences can arise in the spectra of the hysteretic energy reduction factor and the cumulative plastic deformation ratio if non-degrading systems (i.e., EPP and HYST1) or degrading ones (i.e., HYST2, HYST3, HSYT4 and HYST5) are compared. These differences were also amplified for increasing values of the ductility level.

## 6. Closed-Form Approximation of Energy-Related Spectra

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{Ha}, can be formulated in a fully closed-form fashion. In fact, recalling that the regression model for R

_{Ha}is

**Table A1.**Numerical values of the constants involved in the closed-form approximation of the mean spectrum of the hysteretic energy reduction factor R

_{Ha}(NDHYST: non-degrading hysteretic behavior; DHHYST: degrading hysteretic behavior).

μ | a_{2} | ${\overline{\mathit{T}}}_{2}$ | n_{2} | ||||
---|---|---|---|---|---|---|---|

A | B | C | D | E | F | ||

NDHYST | 1.5 | −0.0214 | 0.6475 | 3.3569 | −19.1032 | −0.2048 | 2.6237 |

2 | −0.0241 | 0.7816 | 1.7847 | −9.9522 | −0.1780 | 2.451 | |

3 | −0.0269 | 0.8712 | 0.7283 | −3.7004 | −0.1503 | 2.2863 | |

4 | −0.0265 | 0.8904 | 0.5117 | −2.4956 | −0.1393 | 2.2247 | |

6 | −0.0236 | 0.8791 | 0.3522 | −1.6454 | −0.1410 | 2.2614 | |

DHYST | 1.5 | −0.0280 | 0.6092 | 1.5008 | −7.9736 | −0.1858 | 2.5178 |

2 | −0.0303 | 0.7304 | 1.1577 | −6.1035 | −0.1816 | 2.4935 | |

3 | −0.0310 | 0.7926 | 1.3923 | −7.7803 | −0.1985 | 2.6131 | |

4 | −0.0308 | 0.8027 | 1.1361 | −6.3390 | −0.2009 | 2.6494 | |

6 | −0.0309 | 0.7957 | 0.4391 | −2.1689 | −0.1872 | 2.5922 |

**Table A2.**Numerical values of the constants involved in the closed-form approximation of the mean plus one standard deviation spectrum of the hysteretic energy reduction factor R

_{Ha}(NDHYST: non-degrading hysteretic behavior; DHHYST: degrading hysteretic behavior).

μ | a_{2} | ${\overline{\mathit{T}}}_{2}$ | n_{2} | ||||
---|---|---|---|---|---|---|---|

A | B | C | D | E | F | ||

NDHYST | 1.5 | −0.0194 | 0.6978 | 1.8259 | −9.9142 | −0.1292 | 2.0273 |

2 | −0.0175 | 0.7984 | 1.6756 | −9.1343 | −0.1207 | 1.9585 | |

3 | −0.0216 | 0.8996 | 0.4226 | −2.0704 | −0.0716 | 1.6473 | |

4 | −0.0238 | 0.9356 | 0.3371 | −1.6183 | −0.0814 | 1.723 | |

6 | −0.0179 | 0.9084 | 0.1269 | −0.4014 | −0.0891 | 1.7948 | |

DHYST | 1.5 | −0.0200 | 0.6151 | 1.7104 | −9.4731 | −0.1325 | 2.0556 |

2 | −0.0213 | 0.7275 | 1.2304 | −6.6671 | −0.1231 | 1.9848 | |

3 | −0.0305 | 0.8451 | 1.0438 | −5.7996 | −0.1085 | 1.8823 | |

4 | −0.0313 | 0.8656 | 0.8527 | −4.7955 | −0.1178 | 1.9639 | |

6 | −0.0351 | 0.8852 | 1.2214 | −7.1531 | −0.1431 | 2.1494 |

**Table A3.**Numerical values of the constants involved in the closed-form approximation of the mean minus one standard deviation spectrum of the hysteretic energy reduction factor R

_{Ha}. (NDHYST: non-degrading hysteretic behavior; DHHYST: degrading hysteretic behavior).

μ | a_{2} | ${\overline{\mathit{T}}}_{2}$ | n_{2} | ||||
---|---|---|---|---|---|---|---|

A | B | C | D | E | F | ||

NDHYST | 1.5 | −0.0284 | 0.6322 | 1.8462 | −9.9993 | −0.2316 | 3.0642 |

2 | −0.0302 | 0.7707 | 1.3410 | −7.1059 | −0.2167 | 2.9499 | |

3 | −0.0311 | 0.8532 | 0.8433 | −4.3001 | −0.1731 | 2.6424 | |

4 | −0.0279 | 0.8527 | 0.6123 | −3.0186 | −0.1420 | 2.4353 | |

6 | −0.0236 | 0.8290 | 0.4360 | −2.0789 | −0.1412 | 2.4537 | |

DHYST | 1.5 | −0.0308 | 0.5767 | 1.4665 | −7.6810 | −0.2164 | 2.9881 |

2 | −0.0335 | 0.7065 | 1.5794 | −8.6345 | −0.2171 | 2.9481 | |

3 | −0.0357 | 0.7786 | 0.9515 | −4.9649 | −0.2303 | 3.0589 | |

4 | −0.0342 | 0.7772 | 0.7070 | −3.6003 | −0.2108 | 2.9318 | |

6 | −0.0298 | 0.7392 | 0.4812 | −2.3486 | −0.2026 | 2.9057 |

## References

- Archuleta, R.J.; Hartzell, S.H. Effects of fault finiteness on near-source ground motion. Bull. Seism. Soc. Am.
**1981**, 71, 939–957. [Google Scholar] - Somerville, P.G.; Graves, R.W. Conditions that give rise to unusually large long period ground motions. In Proceedings of the Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control, Applied Technology Council, San Francisco, CA, USA, 11–12 March 1993; pp. 83–94. [Google Scholar]
- Hall, J.F.; Heaton, T.H.; Halling, M.W.; Wald, D.J. Near-source ground motion and its effects on flexible buildings. Earthq. Spectra
**1995**, 11, 569–605. [Google Scholar] [CrossRef] - Somerville, P.G.; Smith, N.F.; Graves, R.W.; Abrahamson, N.A. Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity. Seism. Res. Lett.
**1997**, 68, 199–222. [Google Scholar] [CrossRef] - Menun, C.; Fu, Q. An analytical model for near-fault ground motions and the response of SDOF systems. In Proceedings of the 7th U.S. National Conference on Earthquake Engineering, Boston, MA, USA, 21–25 July 2002. [Google Scholar]
- Mavroeidis, G.P.; Papageorgiou, A.S. A mathematical representation of near-fault ground motions. Bull. Seism. Soc. Am.
**2003**, 93, 1099–1131. [Google Scholar] [CrossRef] - Bray, J.D.; Rodriguez-Marek, A. Characterization of forward-directivity ground motions in the near-fault region. Soil Dyn. Earthq. Eng.
**2004**, 24, 815–828. [Google Scholar] [CrossRef] - Mollaioli, F.; Bruno, S.; Decanini, L.D.; Panza, G.F. Characterization of the dynamic response of structures to damaging pulse-type near-fault ground motions. Meccanica
**2006**, 41, 23–46. [Google Scholar] [CrossRef] [Green Version] - Baker, J.W. Quantitative classification of near-fault ground motions using wavelet analysis. Bull. Seism. Soc. Am.
**2007**, 97, 1486–1501. [Google Scholar] [CrossRef] - Lu, Y.; Panagiotou, M. Characterization and representation of near-fault ground motions using cumulative pulse extraction with wavelet analysis. Bull. Seism. Soc. Am.
**2013**, 104, 410–426. [Google Scholar] [CrossRef] - Mukhopadhyay, S.; Gupta, V.K. Directivity pulses in near-fault ground motions—I: Identification, extraction and modeling. Soil Dyn. Earthq. Eng.
**2013**, 50, 1–15. [Google Scholar] [CrossRef] - Chang, Z.; Sun, X.; Zhai, C.; Zhao, J.X.; Xie, L. An improved energy-based approach for selecting pulse-like ground motions. Earthq. Eng. Struct. Dyn.
**2016**, 45, 2405–2411. [Google Scholar] [CrossRef] - Dabaghi, M.; Der Kiureghian, A. Simulation of orthogonal horizontal components of near-fault ground motion for specified earthquake source and site characteristics. Earthq. Eng. Struct. Dyn.
**2018**, 47, 1369–1393. [Google Scholar] [CrossRef] - Quaranta, G.; Mollaioli, F. Analysis of near-fault pulse-like seismic signals through Variational Mode Decomposition technique. Eng. Struct.
**2019**, 193, 121–135. [Google Scholar] [CrossRef] - Makris, N. Rigidity-plasticity-viscosity: Can electrorheological dampers protect base-isolated structures from near-source ground motions? Earthq. Eng. Struct. Dyn.
**1997**, 26, 571–591. [Google Scholar] [CrossRef] - Alavi, B.; Krawinkler, H. Behavior of moment-resisting frame structures subjected to near-fault ground motions. Earthq. Eng. Struct. Dyn.
**2004**, 33, 687–706. [Google Scholar] [CrossRef] - Rupakhety, R.; Sigbjörnsson, R. Can simple pulses adequately represent near-fault ground motions? J. Earthq. Eng.
**2011**, 15, 1260–1272. [Google Scholar] [CrossRef] - Alonso-Rodríguez, A.; Miranda, E. Assessment of building behavior under near-fault pulse-like ground motions through simplified models. Soil Dyn. Earthq. Eng.
**2015**, 79, 47–58. [Google Scholar] [CrossRef] - Mazza, M. Effects of near-fault ground motions on the nonlinear behaviour of reinforced concrete framed buildings. Earthq. Sci.
**2015**, 28, 285–302. [Google Scholar] [CrossRef] [Green Version] - Quaranta, G.; Mollaioli, F.; Monti, G. Effectiveness of design procedures for linear TMD installed on inelastic structures under pulse-like ground motion. Earthq. Struct.
**2016**, 10, 239–260. [Google Scholar] [CrossRef] - MacRae, G.A.; Morrow, D.W.; Roeder, C.W. Near-fault ground motion effects on simple structures. J. Struct. Eng.
**2001**, 127, 996–1004. [Google Scholar] [CrossRef] - Cuesta, I.; Aschheim, M.A. Inelastic response spectra using conventional and pulse R-factors. J. Struct. Eng.
**2001**, 127, 1013–1020. [Google Scholar] [CrossRef] - Mavroeidis, G.P.; Dong, G.; Papageorgiou, A.S. Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom (SDOF) systems. Earthq. Eng. Struct. Dyn.
**2004**, 33, 1023–1049. [Google Scholar] [CrossRef] - Kalkan, E.; Kunnath, S.K. Effects of fling-step and forward directivity on the seismic response of buildings. Earthq. Spectra
**2006**, 22, 367–390. [Google Scholar] [CrossRef] - Tong, M.; Rzhevsky, V.; Junwu, D.; Lee, G.C.; Jincheng, Q.; Xiaozhai, Q. Near-fault ground motion with prominent acceleration pulses: Pulse characteristics and ductility demand. Earthq. Eng. Eng. Vib.
**2007**, 6, 215–223. [Google Scholar] [CrossRef] - Hatzigeorgiou, G.D.; Pnevmatikos, N.G. Maximum damping forces for structures with viscous dampers under near-source earthquakes. Eng. Struct.
**2014**, 68, 1–13. [Google Scholar] [CrossRef] - Makris, N.; Black, C. Evaluation of peak ground velocity as a good intensity measure for near-source ground motions. J. Eng. Mech.
**2004**, 130, 1032–1044. [Google Scholar] [CrossRef] - Mollaioli, F.; Bruno, S. Influence of site effects on inelastic displacement ratios for SDOF and MDOF systems. Comput. Math. Appl.
**2008**, 55, 184–207. [Google Scholar] [CrossRef] [Green Version] - Donaire-Ávila, J.; Benavent-Climent, A.; Lucchini, A.; Mollaioli, F. Energy-based seismic design methodology: A preliminary approach. In Proceedings of the 16th World Conference on Earthquake Engineering, 16WCEE 2017, Paper N° 2106. Santiago, Chile, 9–13 January 2017. [Google Scholar]
- Kalkan, E.; Kunnath, S.K. Relevance of absolute and relative energy content in seismic evaluation of structures. Adv. Struct. Eng.
**2008**, 11, 17–34. [Google Scholar] [CrossRef]

**Figure 2.**Variability of moment magnitude M

_{w}, closest site-to-source distance D

_{f}and soil preferred shear-velocities V

_{S}

_{30}as function of the pulse period T

_{p}within the considered dataset.

**Figure 3.**Spectra of the absolute E

_{Ia}

_{μ}and relative E

_{Ir}

_{μ}input energy for the hysteretic model HYST1 and ductility level μ equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 4.**Spectra of the absolute input energy reduction factor R

_{Ea}for the hysteretic model HYST1 and ductility level μ equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 5.**Spectra of the hysteretic energy dissipation demand E

_{H}for the hysteretic model HYST1 and ductility level μ equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 6.**Spectra of the hysteretic energy reduction factor R

_{Ha}for the hysteretic model HYST1 and ductility level μ equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 7.**Spectra of the cumulative plastic deformation ratio η for the hysteretic model HYST1 and ductility level μ equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 8.**Influence of the hysteretic model on the spectra of absolute input energy reduction factor R

_{Ea}for a ductility level μ equal to 2 (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 9.**Influence of the hysteretic model on the spectra of elastic limit strength R

_{y}and cumulative plastic deformation ratio η for a ductility level μ equal to 4 (filled area: envelope of the spectra; solid line: mean spectrum).

**Figure 10.**Comparison between calculated absolute input elastic energy E

_{Ia}spectra (mean and mean plus/minus one standard deviation) and proposed approximation (thin solid line: single spectrum; thick solid line: calculated spectrum; thick dashed line: proposed approximation).

**Figure 11.**Comparison between calculated absolute input energy reduction factor R

_{Ea}spectra (mean and mean plus/minus one standard deviation) and proposed approximation (thin solid line: single spectrum; thick solid line: calculated spectrum; thick dashed line: proposed approximation).

**Figure 12.**Comparison between calculated hysteretic energy reduction factor R

_{Ha}spectra (mean and mean plus/minus one standard deviation) and proposed approximation (thin solid line: single spectrum; thick solid line: calculated spectrum; thick dashed line: proposed approximation).

**Figure 13.**Comparison between calculated cumulative plastic deformation ratio η spectra (mean and mean ± one standard deviation) and proposed approximation (thin solid line: single spectrum; thick solid line: calculated spectrum; thick dashed line: proposed approximation).

**Figure 14.**Constants involved in the regression analysis of the mean spectra of the hysteretic energy reduction factor R

_{Ha}for hysteretic non-degrading behaviors (dots: regression results; line: proposed closed-form relationship), together with the regression error chart.

**Figure 15.**Constants involved in the regression analysis of the mean spectra of the hysteretic energy reduction factor R

_{Ha}for hysteretic degrading behaviors (dots: regression results; line: proposed closed-form relationship), together with the regression error chart.

Model Tag | Model Description |
---|---|

EPP | Elastic-perfectly plastic model including Bauschinger effect |

HYST1 | Elastoplastic model with hardening |

HYST2 | Bilinear model with stiffness and low strength degradation, and pinching effect |

HYST3 | Bilinear model with stiffness and high strength degradation, and pinching effect |

HYST4 | Takeda’s model |

HYST5 | Bilinear model with strain softening and stiffness degradation |

**Table 2.**Values of the parameters controlling the cyclic behavior of the analyzed systems (EPP: elastic-perfectly plastic model; HYST: hysteretic model).

Model Tag | p | α | β | γ | ρ |
---|---|---|---|---|---|

EPP | 0 | 100 | 0 | 1 | - |

HYST1 | 0.1 | 100 | 0 | 1 | 0.8 |

HYST2 | 0.05 | 2 | 0.1 | 0.5 | 0.8 |

HYST3 | 0.05 | 2 | 0.1 | 0.5 | 0.5 |

HYST4 | 0.1 | 2 | 0 | 1 | 0.8 |

HYST5 | −0.01 | 1 | 0.05 | 1 | 0.5 |

**Table 3.**Definition of the subsets of seismic records for the sensitivity analysis (the number of records is indicated within brackets).

Moment Magnitude M_{w} | Closest Site-to-Source Distance D _{f} (km) | Soil Type V _{S}_{30} (m/s) |
---|---|---|

5–6 (14) | 0–5 (31) | <180 (10) |

6–7 (64) | 5–15 (63) | 180–360 (66) |

>7 (49) | 15–30 (24) | 360–800 (51) |

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**MDPI and ACS Style**

AlShawa, O.; Angelucci, G.; Mollaioli, F.; Quaranta, G.
Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions. *Appl. Sci.* **2020**, *10*, 7578.
https://doi.org/10.3390/app10217578

**AMA Style**

AlShawa O, Angelucci G, Mollaioli F, Quaranta G.
Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions. *Applied Sciences*. 2020; 10(21):7578.
https://doi.org/10.3390/app10217578

**Chicago/Turabian Style**

AlShawa, Omar, Giulia Angelucci, Fabrizio Mollaioli, and Giuseppe Quaranta.
2020. "Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions" *Applied Sciences* 10, no. 21: 7578.
https://doi.org/10.3390/app10217578