Evaluating the Role of Earthquake Early Warning

Therefore, we can consider that the influence of in IDR is low, therefore, following results are obtained by adopting a value of =30. In order to evaluate the importance of Repi, the analysis of GIDS was distributed in four groups. Figure 5.4(a) presents the GIDS for ground motion records with Repi 50 km, the MIDR is 0.82% for T= 0.75 s and it is reasonable that the mean has small values since the vast majority of records have low magnitudes. Figure 5.4(b) display the MIDR ratio for different Repi, the distribution occurs as expected, the response attenuates as Repi increases. The response for IDR with Repi 150 represents 20% of Repi 50, for fundamental periods greater than 2s. The response for IDR with 100 Repi 150 and 50 Repi 100 become similar at approximately 40% of Repi

Likewise, the relevance of soil type in MIDR was evaluated for =30. Figure 5.5(a) present the MIDR for stiff soil, the graphics turn out to be almost identical to Figure X.XX(a) which implies that MIDR happens in stiff soil and Repi 50. Figure 5.5(b) shows MIDR ratio normalized by MIDR for stiff soil, as expected, the response with rock soil was considerably less in the range of 30%. On the other hand, stiff and soft soil present similar response with a maximum difference of 10%.

For buildings where flexural deformations (=0.1) govern, maximum interstorey drift demands occurred near the top as shown in Figure 5.6(a). In contrast, Figure 5.6(b) presents structures that combine shear and flexural deformations (=8) where larger IDR are experienced near mid height. While, buildings in which shear deformations (=30) dominated, IDR happen near the bottom as display in Figure 5.6(c). These results are consistent with plots presented by Miranda (1999) and Galasso (2013). The estimation of seismic demands given by a linear-MDOF model are expected to remain on the elastic range or with controlled levels of nonlinearity. The Federal Emergency Management Agency (FEMA) earthquake loss estimation methodology, commonly known as Hazus, has developed the estimation of various damage states for structural and non-structural components for 36 generic model buildings types that are classified in terms of their structural systems. The average IDR of structural damage states can be found in the Table 5.9a through 5.9d in Hazus-MH 2.1 Technical Manual and are presented as thresholds for the aforementioned figures. In this study, =30 and =8 correspond to Concrete Moment Frame (C1M) and =0.1 correlated to Concrete Shear Walls (C2M) both mid-rise buildings with moderate code design level. It can be observed that building response with moderate damage represent less than 1% of the total database and only one ground motion record, Friuli (1976), presents complete damage. Consequently, the building response of the flat file remains on the elastic range and the use of a linear-MDOF model is valid. Furthermore, a comparison for different values of is presented in Figure 5.6 (d). From base to mid-height of the building, IDR analysed with =0.1 and =8 is less than IDR computed with =30. On the contrary, from mid height to the top IDR ratio with =0.1 and =8 are up to 4 and 2 times greater, respectively.

Multiple non-structural components and building contents, necessary for the functionality of critical facilities, are damaged as a result of large floor acceleration demands which represent a considerable cost for buildings operation. PFAs, estimated by the simplified model, are expected to remain in the elastic range when subjected to moderate earthquakes. Default threshold values of PFA for each of the damage states are summarized in Table 6.3 of Hazus-MH 2.1 Technical Manual. Figure 5.7 shows PFA vs normalised height for different and display the thresholds for each damage state which remain constant for all building types. A considerable amount of ground motion records still present slight damage, however, an increase of building responses with moderate damage has occurred. It is evident that buildings with smaller values of develop larger acceleration demands as height increases. The use of a linear-MDOF model is reasonable for non-structural components but the implementation of a non-linear model should be taken into consideration if the analysis had shown stronger non-linearity and severe structural damage. Figure 5.7(d) shows the influence of the fundamental period for PFA along the height, the accelerations are amplified as the period decreases and the height increases and regardless the value of , small periods present higher floor accelerations. Additionally, the thresholds of human comfort discussed in Table 2.1 are presented, where the acceleration on the roof for small periods start to be annoying and the elevators should be shut down for acceleration greater than 0.08g as has been recommended.

To sum up, a number of different analyses and comparisons have been done in order to show the complex seismic response of different building typologies. The models analyses show different acceleration propagation (reduction or amplification) and inter-storey deformations along the height. These estimates vary in magnitude and location (along the height of the building) due to the fundamental period, structural typology and soil type. Therefore, it is not possible to use a single performance indicator (e.g. PGA) to assess potential real-time damages during an earthquake and the indicators shown above will be tested on the next sections.

earthquake features, an empirical non-linear regression analysis based on the ITACA database was developed to determine the coefficients, residuals and standard deviations. The equation was formulated for IDR(x), MIDR and PFA(x) for three different lateral resisting systems with fundamental periods ranging from 0.05 to 5 s. The seismic features considered in the functional form need be rapidly predicted in real time, since they are going to be incorporate in an EEW framework. For that reason, only earthquake magnitude, epicentral distance and soil type were considered as dependent variables. The verification of the results are compared with historical data and validated by econometric tests. Additionally, a comparison with two additional complex models is performed in order to evaluate the influence of the fault mechanism type in the model.

The equation selected to perform the empirical regression is the model adopted by Bindi (2009) where Y relates to magnitude FM(M), distance FD(R,M), and soil amplification FS. The function is as follows:

• Y=YxYY represent the geometric mean of both EDP horizontal components such as IDR(x) and IDRmax expressed in percentage and PFA(x) expressed in m/s2
• bi regression coefficients to be computed
• FMM= b2∙MMagnitude scaling
• FDR,M= b3log10Repi2+b62 Distance function
• FS= b9Ss+b10SA Soil amplification

is the fractional number of standard deviations and is standard deviations Koleva et al. (2008) derived an equation to estimate IDRmax only for shear wall structures the analysis was done with Mw ranging from 5.0 to 7.6 and Rjbm 100 km. Nonetheless, the residual plots showed slightly biased trends for increasing magnitude at longer distance

In the performance prediction equation, earthquake features represent predictor variables (independent) and EDP constituted response variables (dependent), as can be observed in equation 3.2, the relationship between these variables are not linear. In order to determine the coefficients a non-linear regression analysis was performed in Matlab, the scripts are presented in Section A.6 to A.8 of the Appendix. In the following paragraphs, the goodness of fit will be evaluated by statistical parameters obtained from the model. For example, standard deviation (σ) represents how the calculated values are spread out from the mean. Consequently, the variation of standard deviation versus the fundamental period is analysed for each EDP and different . Figure 5.8(a) shows σ associated with MIDR. Figure 5.8(b), Figure 5.8(c) and Figure 5.8(d), presents σ associated with IDR(x=0.05), IDR(x=0.30), IDR(x=1.00), where the maximum response happens for =30, =8 and =0.1,respectively. Figure 5.8(e) and Figure 5.8(f) shows σ associated with PFA(x=0.50) and PFA(x=1.00) where larger acceleration has been found. In general, the aforementioned standard deviation plots display a stable trend for fundamental periods larger than 1 s with an average value of 0.35, as a result it can be concluded that the standard deviation is not affected by fundamental periods or lateral stiffness ratio. In a similar work, Neam and Taghikhany (2016) derived a new prediction equation for MIDR considering near-fault ground motions where the standard deviations vary from 0.5 to 0.6 and σ also remains constant for different fundamental periods and .

The stochastic error from the model is represented by residual values which indicate the difference between the observed and predicted values. In order to assess the appropriateness of the model, residual values are plotted versus independent variables. Due to space constraints, only relevant responses are shown below, Section A.9 of the Appendix shows a summary table of residuals associated with MIDR, IDR(x) and PFA(x) for different fundamental periods, and normalized height. Figure 5.9 and Figure 5.10 present the distribution of residual values against Mw and Repi for T=0.75 s. considering (a) GIDS =8 (b) IDR(x=1) =8 (c) PFA(x=1) =30. As can be observed, the scatter plot is equally and randomly spread around the horizontal axis throughout the range of fitted values. This indicates that the derived equation has produced unbiased estimates. Additionally, a linear trend of the residual plot has been computed and the output shows that the scatter is normally distributed with a symmetrical pattern around zero. Several ground motions records have Repi 50 km and it is expected that Figure 5.10 display more data on the left side. It is worth mentioning that similar results have been obtained for other fundamental periods, and normalized height. A summary table containing residual values corresponding to ground motion records is presented in Section A.XX of Appendix

R2 or coefficient of determination measures the strength of the relationship between the model and the dependent variable, it represents the percentage of the variance and how good the data fit the regression model. The values fluctuate between 0 and 100% where higher values of R2 indicate that greater variation is accounted for and the data points are closer to the regression line. The overall R2 is in the range of 70 to 75%, which indicates a good fit of the data. The standard errors, the residual plots and R2 indicate a good fit for the non-linear regression and now it is possible to evaluate the statistical output in order to estimate the reliability of the function. The coefficients explain the relationship between the independent and dependent variables (); on the other hand, p-values show whether these relationships are statistically significant in a larger population. It is calculated by comparing the goodness of fit of the entire model to the goodness of fit when that independent variable is omitted. The null hypothesis tests indicate that no correlation exists between the independent and each of the dependent variables, in other words, that the coefficients of each of the variables have no effects in the equation and are cumulatively zero (0). In case the p-value is less than the significance level, the null hypothesis is rejected and the variable is considered statistically significant and a meaningful addition to the fit of the model. However, a larger p-value indicates that there is not sufficient evidence to conclude that a correlation exists at the population level. The significance level is a measure of the strengths of the evidence that must be obtained in order to reject the null hypothesis, in this case, a value of 0.05 (5%) was taken. Table 5.6 presents P-values for the coefficients from the regression analysis for EDP, it can be seen that all values are less than the significance level near zero, so in general, the coefficients improve the fit of the model.

The regression coefficients, standard deviation and R2 corresponding to the main response of MIDR, IDR(x=1.00) and PFA(x=1.00) for =0.1,8,30 are presented in table 5.7. The evaluation of the normalized height has been computed with an increment of 0.1 and the associated coefficients are presented in Section A.XX to Section A.XX. of Appendix.

A comparison is performed between the new prediction equations characterized with different lateral resisting system and the building response parameters subjected to historical earthquake data for different soil types. The analysis is evaluated for a fundamental period of 0.75 s. where the higher response have been found. In order to validate the equation, the following seismic events with relevant data are selected:

• Friuli Third Shock 1976 Mw=5.9 Stiff Soil
• Irpinia 1980 Mw=6.9 Stiff Soil
• Umbria-Marche Second Shock 1997 Mw=6.0 Soft Soil
• L’Aquila 2009 Mw=6.3 Rock Soil

for different heights where the maximum drift happens and Figure 5.13 displays the trend for PFA (x) for the roof where the acceleration is higher. The building response is well captured for data with epicentral distance greater than 10 km; however, due to the lack of data, it is complicated to be reproduced with accuracy, a seismic event with small epicentral distance. Moreover, the error given by prediction equations and building responses for historical data identified with the same soil type is minimum. On the other hand, historical data identified with different soil type follows the prediction equation trend and often fall within the mean ± σ zone. The prediction equation trend happens as expected, the building response decreases as the distance increases. In general terms, the comparison suggests that the predictive model captures with reliability the building response of historical data with different soil conditions

A commonerror is to develop a model too complex to fit a particular set of data points or for a particular application. Sometimes, the size of the sample limits the number of variables that can be added to ensure reliable results. Overfitting can conduct to misleading R2 and regression coefficients; as a result, the model is improbable to describe the relationship between variables for a whole population. For that reason, two more complex functional forms are investigated and statistical parameters are compared with the previous model. Bommer (2003) is presented in eq. 4-3 and includes the fault mechanism type on the other hand, Akkar and Bommer (2010) has been shown in eq. 4-4 and neglects the effect of M and Repi coupling terms.

The main statistical parameters and R2 are presented in table 5.16 and Table 5.17, respectively. The two complex models have more variables to analyse, it is expected that the standard deviation and R2 presents higher values; however, the difference between them is less than 3% which indicates that the models are reliable. Furthermore, Table 5.18 displays the p-values obtained for both complex models, the p-value for fault mechanism type (coefficient b8) indicates a low contribution to the model and a high probability that it does not belong to the equation and that there is a possibility that multicollinearity ihas been occurring. The results suggest that an overfitting problem has been taking place as well. In order to improve the p-values presented for the new equation model, more historical data that include different fault type mechanism is needed. To sum up, the new performance prediction equation presents reliable statistical parameters and predicts with accuracy the response of historical data. The analysis for the three prediction models was performed for historical seismic events where the highest response occurred for MIDR, IDR(x) and PFA(x) and it is presented in Figure 5.14. Akkar and Bommer (2003) overestimated the response and some historical data falls outside the mean ± σ zone. The building response is well captured specially for the prediction equation of Bindi (2009).

Assessment of the EEWS Application to Campania

The Performance-based Earthquake Early Warning framework, displayed in Figure X.XX, presents the ground motion prediction equation and structural model to describe two separate stages comprising the hazard and structural analysis. As a result, a new performance prediction equation that merges these two stages and connects the corresponding seismic features with the structures characteristics of a building was created in the previous chapter. For decision making and seismic risk management purposes, a representative measure of the earthquake potential has to be obtained. At a given time t, real-time information of magnitude (Mw) and distance (R) is issued by EEWS, the probability that a ground motion intensity measure (e.g. PGA) is exceeded during the service life of the structure is calculated via a Real-time Probabilistic Seismic Hazard Analysis (RTPSHA). The prediction process is based on a Bayesian framework in which the posterior probabilistic density function f1,2,...,n represents the magnitude calculated at a given time by the triggering sequence of a developing earthquake in a seismic network via the Bayes theorem. The Gutenberg-Richter recurrence relationship incorporates data from past earthquakes where the seismic features of the Campania region are described by {β=1.69, Mmin=4, Mmax=7} . The seismic stations provide a vector (τ) with information of the predominant period from the first four seconds of P-waves records which are analysed in the frequency domain and the maximum amplitude of the record is extracted with the associated frequency. (Convertito et. al, 2008). Since the magnitude is a selected parameter, the posterior PDF was obtained with an inverse procedure and the vector have been generated by a Monte Carlo approach using the function elaborated by Allen and Kanamori (2003), presented in equation X. XX. However the parameters are computed for California, a further research is recommended to implement this approach in Italy.

The posterior PDF is presented in equation 2-3 It can be observed that, is time dependent and the quantity of data process will increase with time as the earthquake triggers more seismic stations. Figure X.XX(b) shows the real-time PDF of M and how the prediction become stable on the magnitude simulated.

Likewise, the PDF of source-to-site distance is calculated at a given time by the triggering sequence of a developing earthquake given by a vector {S1, S2,.., Sn}. The RTLoc algorithm developed by Satriano (2008) is used for the real-time localisation of the hypocentre, this approach creates a dense grid point located inside the region where the network works. In order to obtain the probability that the hypocentre match that grid point, a volume that is likely to contain the hypocentre is calculated known as the Voronoi cell of that station. In this case, the PDF for the source-to-site distance was considered a deterministic parameter, because the analysis was performed for a target site with a known epicentre. Iervolino et al. (2009) investigated the uncertainty of the parameters used in a real-time hazard analysis and conclude that the dominating variability was associated with the ground motion prediction equations, the new performance prediction equation helps to reduce the uncertainty by simplifying the process. A new real-time hazard analysis have been computed in terms of building response in the hybrid EEWS for the Campania region using equation X.XX.

In this chapter a simulation of the development of an EEWS on the Campania region was carried out and real-time hazard curves in terms of building response are derived. The classical approach of setting alarms using the PGA as an intensity measure was compared with different performance parameters or EDPs such as Peak Floor Acceleration (PFA) and Maximum Interstorey Drift (MIDR). Given that the simulation is focused on mid-rise to high-rise buildings, the analysis has been carried out for the two biggest urban areas in Campania, Naples capital of the Campania region and Salerno. Saint Angelo De Lombardi, a small town affected by the Irpinia earthquake, was also considered for comparison reasons even though only small buildings are expected to be located in the town as shown in Table 6.1. Figure 6.1 (a) presents the target sites, the epicentre location and the geographical distribution of 29 seismic stations from the ISNet network. In order to obtain the RTPSHA, the analysis was performed in the Matlab script provided by the supervisor of this investigation, Dr. Carmine Galasso. Three seismic events were simulated with a Mw= 5, 6 and 7.The seismic event follows this triggering sequence: 2 stations (t=7 s.), 9 stations (t=9 s.), 18 stations (t=13 s.), 29 stations (t=18 s.), if 4 s. have passed from its trigger, the station is considered in the simulation process. The simulation evaluates three different earthquake scenarios by comparing real-time hazard curve in terms of PGA and performance parameters with an alarming decisional rule focus on elevator failure, non-structural damage and human comfort. There is an important branch of the literature discussing the issue of setting thresholds in order to prevent a significative number of false alarms and missed alarms, which is called the crywolf effect (Iervolino et.al., 2007; Grasso et.al., 2007). This issue becomes of importance when the cost of implementing a warning is high, for instance, when a critical infrastructure such as a nuclear plant or energy generator is shut down. However, in the proposed cases of setting early warning in buildings, the cost of alarming is considered not significant. Therefore, the alarming decision was set based on a 10% probability of exceedance. A more refined threshold can be estimated based on a cost-benefit analysis (including expected loss and expected utility) as done in Iervolino et.al (2007). This potential improvement is an area of further research.

Elevator failure

Failure is understood as the potential trapping of occupants during an earthquake or the malfunctioning of the system and slow restoration afterwards. These risks can be mitigated by implementing an automated early warning system that provides enough time to stop or shutdown an elevator depending on the available warning time. In Japan, 50% of the elevators Otis are equipped with earthquake detectors so passengers can exit safely, also during the Tohoku-Oki earthquake; several elevators performed an emergency shutdown. (Layne,2011). A threshold of 0.08g has been selected for the warning based on the Japanese Regulation (Cheng, 2014), and the differences in the EEWS outcome was evaluated with two parameters: PGA and PFA. In this case, the warning will be twofold: an automated system to stop the elevator in the nearest floor so passengers can exit; and a warning message to the occupants of the elevator saying: “An earthquake is expected to arrive in x seconds, the elevator will stop at the nearest floor”. As can be seen in Table 6.1, neither the PGA nor the PFA activates a warning for a seismic event of Mw=5 in the 3 target sites. On the other hand, a Mw=6 earthquake does not activate the alarm for any parameter in Naples, but both parameters (PGA and PFA) exceed the threshold in Saint Angelo di Lombardi. More important, 4 missed alarms are presented in Salerno, this means that a warning that should have been activated (based on PFA) was not triggered by the use of PGA. For the stronger Mw=7 event, both

parameters activate the warning for Salerno and Saint Angelo di Lombardi, however 5 missed alarms occurred in Naples. To sum up, from the 28 cases analized for Mw=6 and 7, PGA was able to activate the warning correctly in 19 cases (67%) but failed in the other 9 (33%).

Non-structural components collapse hazard

Non-structural components can pose threat on the occupants if the seismic shaking is strong, therefore, an early warning to shelter or go to a safety zone is proposed. These components are classified in drift-sensitive components which are affected by building displacement with a corresponding MIDR threshold of 0.4%; also, acceleration-sensitive components which are affected by building shaking with a corresponding PFA threshold of 0.25g. Both thresholds were selected as aslight damage level based on Table 6.4 of Hazus-MH 2.1 In this case the warning will be a message to the occupants of the building saying: “An earthquake is expected to arrive in x seconds, stay away from windows and look for a safe area on your floor”.

The occupants’ comfort during an earthquake.

Several studies have demonstrated a relation between peak accelerations and human comfort (Griffis, 1993). Therefore, a strong shaking can cause an important level of distress and fear even though the structural integrity of the building is not compromised. A threshold of 0.05g has been selected for a “very annoying” comfort level (Cheng, 2014), a comparison was performed in terms of PGA and PFA regarding the outcomes of the EEWS. In this case the warning will be a message to the occupants of the building saying: “An earthquake is expected to arrive in x seconds, the structure of the building is safe so please remain calm”. As shown in Table 6.3, a Mw=5 earthquake do not activate the alarm for any parameter in Salerno and Naples; but 2 missed alarms are presented in Saint Angelo di Lombardi. None of the parameters exceeds the alarming threshold for a seismic event of Mw=6 in Naples, however, both of them exceed the threshold in Saint Angelo di Lombardi and Salerno except a case in which a false alarm was found in the later. Both parameters are activated for all target sites for Mw=7 event. To sum up, from the 42 cases analysed, PGA was able to activate the warning correctly in 39 cases (93%) and had failed in the remaining 3 (7%).

Discussion and Further Research

While the reliable estimation of M and Repi is a source of variability, the GMPE has been proved as the main source of uncertainty (Iervolino,2009) for RTPSHA in EEWS. In the current effort of linking directly EDPs and seismic features on the source through performance prediction equations, this study carried the risk of increasing the uncertainty in EEWS and therefore losing reliability. However, the standard deviations calculated for the prediction equations developed herein are similar to the ones of the traditional GMPEs. Therefore, the uncertainty of the prediction has not increased and two stages (seismological prediction and structural modelling) in the EEW framework have been successfully merged.

Furthermore, the goodness of fit of the prediction equations were demonstrated, therefore automatized estimation of building performance can be carried out with seismic parameters estimated in real-time.

Some further refinements for the prediction equations remain as a further area of research. For instance, the inclusion of the fault mechanism as a relevant variable has been discarded due to their poor significance indicators in the regression model. This finding can mean that the data, on fault type, is not large enough to fit the model and a synthetic strong-motion database might provide better insights.

On the topic of intensity prediction using the first P-wave seconds, it is important to point out that the parameter is based on California data. The question of whether or not this parameter can become representative for the Italian case remains as a source of uncertainty and future studies for the Italian case are needed.

The implementation of the EEWS for buildings was used for Naples and Salerno, the two biggest cities of Campania. The location of these cities allows warning time of 5 to 10 seconds in Salerno and 15 to 20 seconds in Naples (Iervolino et.al., 2011) which are large enough to implement the proposed measures. However, nearest cities such as Saint Angelo have insignificant warning times or are located in the denominated blind zone. The development of warning measures for these sites can be possible if the lead-time is increased at the cost of losing reliability (usage of only a couple of stations). The evaluation of this important trade-off remains as a further area of research.

The EEWS simulation was based upon the selection of thresholds from the literature. However, these thresholds can vary depending on the specific features of each building. For instance, some elevators and windows can be more or less resistant by design and some building components might me more acceleration or drift sensitive. Therefore, a real application should rely on a proper estimation of thresholds for the particular case. The results showed in this study can vary if these thresholds change, so, they should be seen as a specific case and not as a demonstrated generalization.

The implementation of EEWS on buildings can be costly and take an important adaptation time for the occupants. However, mid-rise and high-rise buildings may have the financial capacity to undertake such infrastructure improvements. On the other hand, these buildings normally have automatized systems and communication systems (e.g. speakers) on each space, so, the implementation of the warnings described in this study can take advantage of this existing infrastructure. Furthermore, the wording of the warnings and the way of communicating them (lights, verbal, sms, etc) might be refined for each particular application.

Given that mid-rise and high-rise buildings are an important economic component of the city, the cost of interrupting their activities can be not negligible. Therefore, a cost-benefit analysis on the alarming decision remains as an area for further research. This is even more important for critical buildings such as hospitals in which elevators are certainly a life-safety component and should remain operational specially after an earthquake hit.

Conclusions

This dissertation has shown the importance of using appropriate EDPs for the seismic performance of buildings by finding a wide and complex variation of performance along their height. This performance cannot be predicted by the PGA and more refined EDPs, as has been proposed in the previous study, are required to be utilised.

In order to estimate these EDPs in real-time, this study has developed and validated performance prediction equations for Italy. These equations have shown a good fit and an acceptable level of variability.

The performance prediction equations have been used to simulate real-time hazard curves in the region of Campania for different structural typologies and earthquake magnitudes.

One important conclusion of this study is the evaluation of the warning reliability by using EDPs. Iervolino (2011) proposed 18 stations out of 29 as the number in which the PGA prediction stabilizes and there is no need to include subsequent stations. This study proposes the same number of 18 stations until stabilization for the studied EDPs.

Furthermore, three potential early warning cases for non-structural damage in buildings were proposed based on available warning times and thresholds from the literature.

This study has demonstrated the poor performance of using an intensity measure, as the PGA, instead of EDPs for early warning systems in buildings. EDPs are much better correlated with structural and non-structural damages and therefore its real-time estimation and implementation in EEWS is a big improvement to prevent missed and false alarms. The case of elevator failure and its 33% of missed alarms are eloquent and shows an inadmissible performance by the PGA as a EEWS predictor. Furthermore, in the cases in which the alarming decision based on PGA is correct, the usage of EDPs shows a reduced alarming time and is therefore, more efficient.

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