Use of earthquake accelerograms

Introduction

Earthquakes are one of the most damaging natural disasters known to mankind. They cause the deaths of thousands of lives, destruction of properties and terrible financial damages. Since what causes the deaths of people and the destruction of valuable properties is the reaction of the structure to the cyclic loads of the earthquakes. As a consequence, earthquake engineers should design structures which are earthquake resistance. One way of doing this is to use accelerogram.

In this project the use of earthquake accelerograms in structural analysis will be investigated. Accelerograms are recorded through accelerograph, they are recording of acceleration as a function of time during earthquakes.

In order to carryout analysis of a structure under earthquake conditions a representation of the earthquake loading is essential. In such situation based on which design code is being followed a dynamic analysis of the structure will be required in which case accelerograms will be used given that they offer detailed representation of the ground motions during earthquakes at the same time they provide the nature of the earthquake ground shaking.

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When caring out an accelerogram based analysis selection of suitable earthquake ground motion is necessary. This can either be real or artificial depending on the requirements of the analysis. Selecting recorded accelerograms is good basis for the realistic design of structures to resist earthquake loads given that they fit in to the required scenario of the earthquakes or some detailed features of the earthquake ground motion. On the other hand, artificially generated earthquake accelerograms can be used for the analysis since the generated accelerograms can be made to perfectly fit with the required design spectra.

Once, a recorded earthquake accelerogram is selected it will be necessary to scale with the intention that it matches the target spectrum, to achieve this there are different types of scaling procedures to choose.

In this project two types of accelerograms will be discussed, these are recorded accelerograms and artificial accelerograms. As well as this the selection and scaling procedures which are covered in the literature will be discussed in the literature review chapter.

Aims.

The main aim of this project is to find out how the desired intensity of an earthquake loading can be represented by selecting the appropriate accelerograms and using the right scaling procedures.

To find out the type of accelerogram that could be used for this project and also which selection and scaling procedures will be adopted for the project?

In order to achieve this aims the following objects are undertaken.

Objectives.

• Explore the use of acelerograms in structural analysis.
• Explore the main types of accelerograms i.e. real and artificial accelerograms and find out the advantages and limitations of each so that the appropriate type accelerogram for the project is selected.
• Investigate different selection procedures of accelerograms. Consequently, workout which selection procedure is suitable for the project.
• Investigate the different scaling procedures there are, which scaling procedure will be used for the project and the problems associated with scaling accelerograms.
• Carryout numerical analysis based on modelling accelerograms.

Organisation of the dissertation.

The dissertation is organised into four main chapters. The first chapter contains the introduction, aims and objectives as well as the organisation of the dissertation.

The theoretical background which states the necessary theory for this dissertation is presented in chapter two.

Chapter three presents literature review which is central to this dissertation since it contains the evaluation and comparison of works by specialists in the field of earthquake engineering.

Chapter four presents the comprehensive methodology of how the analysis is carried out and how the data will be analyst and the criteria for.

The detailed discussion of the findings from the structural response analysis is contained in Chapter five.

Chapter six which is the final chapter contains conclusion sections and the major highlights of the project with some future recommendations.

Theoretical background.

In this chapter the necessary theory for this project will be stated. Ways of obtaining information from the time history, how to record accelerograms and also how to generate artificial accelerograms will be discussed. As well as all of these the definitions of important parameters and their usefulness is going to be stated.

Definitions of parameters.

Peak ground acceleration (PGA) is the parameter that is most frequently used to describe the severity of the ground motion. It is the highest absolute value of the acceleration in the record data.

PGA=maximum |Acceleration (time)| (1)

Although PGA is a parameter which is often used by engineers to characterise the damage of the earthquake on the structure (Sen, Tapan K.), some researchers identify it as a poor parameter compared to other parameters (Acevedo, 2003).

Peak ground velocity (PGV) is parameter which is considered to be good indicator of the severity of the earthquake (Akkar and Bommer, 2007). PGV is obtained by the integration of the ground acceleration time history.

PGV = maximum |Velocity (time)| (2)

Peak ground displacement (PGD) is the highest absolute value of the displacement in the in the time-history. PGD is obtained by integrating the ground velocity time history. It is the parameter which is mostly used when the design of the structure is displacement-based.

PGD= maximum |Displacement (time)| (3)

An important parameter which is used to predict the structural response of a structure during an earthquake is e. By definition e is the difference between the spectral acceleration of the record and the spectral acceleration which is obtained for the attenuation equation (Baker and Cornell, 2005).

How to get response spectrum from the time history.

Response spectrum for a given time history is obtained by placing the peak value of the time history (PGA, PGV, PGD) into different single degree of freedom (SDOF) systems at varying natural periods or frequency(Matheu et al , 2005). Level of damping is also considered. From this a plot of a given peak value (PGA, PGV or PGD) against the natural period or frequency is formed, which is the response spectrum of that is given time history.

It is helpful to use response spectrum for design as it makes the analysis easier since the problem is reduces from dynamic to static which is more straightforward to handle.

How accelerograms are recorded.

Accelerograph is an instrument that records the ground acceleration during an earthquake. These recordings from the accelerograph are what are called accelerogram.

There are three transducers in the accelerograph from which three components of the motion are recorded. One transducer records the vertical motion while the two remaining transducers record the horizontal motions (Trifunac and Todorovska, 2001).

The earliest accelerographs in the world were developed in the 1930s; from then on the numbers accelerograms which were recorded throughout the world has increased. Thus, there are advances in earthquake engineering in most of the developed world.

Analog accelerographs were the first to be used which were recorded on films. This procedure was costly and time consuming as it required digitations (Boore and Bommer, 2005). Advances in technology in the decades to follow resulted in the introduction of the first digital accelerographs in the late 1970s.

Digital accelerographs are easier to operate and the outputs from them are good representation of the earthquakes compared to analog accelerographs. In addition to this digital accelerographs do not require the digitations process and fewer errors.

Generation of artificial accelerograms.

Artificial accelerogram are generated to match the target response spectrum. Groups of accelerograms are used to generate artificial accelerograms. Superposition of sinusoidal waves is used to generate artificial accelerograms (Nguyen, VB, 2006). Computer programs such as SIMQKE are used to generate artificial records.

Literature review

Introduction.

This chapter covers studies carried out by specialists in the field of earthquake engineering and research case studies undertaken by researchers. This literature review is conducted to facilitate this research by providing the required background information. It focuses on four different areas which form the main themes of this research. These are: scaling and biased response, scaling and selection procedures and comparison of advantages and disadvantages of real and artificial accelerograms.

Selection procedures.

The selection of the appropriate accelerograms for the given structural design condition or analysis is necessary, as this forms the basis for realistic design of structures which resist earthquakes loads that may possibly occur at the specified site. Selection of accelerograms is usually based on earthquake scenarios such as magnitude, distance and site classifications (Bommer and Scott, 2000).

The magnitude of an earthquake is important information as it is a measure of the size of an earthquake in relation to the amount of energy that is released during the earthquake. The duration and the frequent content of the accelerogram are dependent on the magnitude of the accelerograms (Stewart et al. 2001). Since the duration of an earthquake is how long it takes for the fault area to rupture, earthquakes with large fault area have large magnitudes. Thus, the duration and the magnitude of an earthquake are related as that they both associate with the fault area.

Selection of accelerograms according to site classification requires a site which has similar geological characteristics to the site under consideration.

When selecting recorded accelerograms it is very important that the fault-site distance is used. Accelerograms which are recorded at near-fault distance have different characteristics from accelerograms which are recorded at a distance far from the fault-site. This results from the fact that rupture fault influences the characteristics of the accelerogram. Accelerogram which is recorded near the earthquake source is often influenced by rupture of fault effect, such as rupture directivity and fling step (Stewart et al., 2001).

Baker et al., (2001) stated that the energy content and the duration of the accelerogram are influenced by the type of rupture directivity which is present in the location the accelerogram is recorded at. For that reason in the selection process there should be a check for the type of rupture directivity present.

If the rupture directivity is a forward directivity the recorded accelerogram will have high amplitude and short duration. A characteristic of forward directivity is that the fault rupture velocity will be near as large as the velocity of the shear wave for the given site. Thus, there will be a wave front of the earthquake which arrives as a large pulse of motion at the start of the recording (Baker, 2009). This results in the structure being damaged. This occurs when the site is away from the epicentre.

On the other hand if the rupture directivity is a backward directivity which takes place when the accelerogram recorded on a site that is close to the epicentre, the recorded acclerogram will have small amplitude and long duration.

Another effect which is not often discussed in the literature is fling-step. This takes place when the ground that is subjected to the earthquake deforms statically and as a consequence the accelerogram will have unidirectional velocity pulse (Stewart. et al., 2001).

Considering the affects of the distance and directivity on the accelerogram in this manner makes sure that the most influential effects of the distance which are likely to affect the accelerogram are taken into account. For example if the forward directivity is not considered in the selection and the recording for the site had forward directivity the structure will be damaged in case an earthquake occurs.

Although most researchers have agreed for many years that the parameters that should be considered when selecting appropriate accelerogram for a given site are magnitude, distance and site classifications, with greater emphasis given to the magnitude and the distance. In contrast to this conservative view Baker and Cornell (2005, 2006) consider the effect of epsilon (the difference of Sa of the recorded accelerograms from the predicted Sa from the ground motion predicted equation) on the structural response to be greater than the effect of distance and magnitude. Thus, indicating that for selection e is the most significant parameter of the accelerogram. Since, e is a good indicator of the value of spectral acceleration on the spectrum if it is a peak value or not.

This new concept could be considered to be controversial as there are not a lot of researches which are conduct that prove this point stated above. This will be a good point to consider for this project.

Scaling procedures and biased response due to scaling.

Accelerograms are scaled on condition that the required intensity levels could not be achieved by the selection of a given accelerogram. This results from the fact that when selecting an accelerogram only limited characteristics are taken into account, such as the magnitude, distance, site classifications and at times e. Thus, scaling the selected accelerogram ensures that the characteristics which were not considered or could not be considered (since there is a limit to the recorded accelerograms from the data bank for a particular location) match that of the design spectrum.

There are numerous ways of scaling accelerograms which are considered in the literature. Study by Acevedo (2003) considers scaling accelerograms according to: Peak ground acceleration, peak ground velocity, Arias intensity (AI), Root-mean-square (RMS), spectral acceleration (Sa) and various parameters of the accelerogram. Most of scaling parameters are not of great use since some have more advantage in representation of the hazard than others. Out of all the scaling parameters the one which is often applied and recommended by codes is scaling to the spectral acceleration (Sa) which is an intensity measure.

Scaling factor is multiplied to the time history when the accelerogram is being scaled in terms of amplitude. The amplitude of the time history is scaled up or down so that it meets the requirements. In this method of scaling the frequent content of the accelerogram is not altered (Bommer and Scott 2000).

Bommer and Scott (2000) addressed that scaling accelerograms by a factor which is not close to one is more likely to bring about unrealistic earthquake ground motion as a result of increased in energy while the duration and the frequent content of the accelerogram stay unadjusted. When the accelerogram is scaled the resulting time history should have the features which are expected of a real earthquake, since if there is a great difference between the two, the scaled time history will not be of any use as it is unrealistic. For that reason scaling accelerograms should not be done if accelerograms that meet the design spectrum could not be found.

In addition, another point which must also be considered is scaling the time axis of the accelerogram which is used to adjust the frequent content. This is not often carried out since it increases the duration and the energy content of the accelerogram. Thus impractical accelerogram is produced (Bommer and Scott, 2000). Compared to scaling of the amplitude it is more difficult to scale the time axis of the accelerogram from the fact that there is greater care to be taken when doing time axis scaling.

However, there is a further vital element in the discussion about scaling which is the biased response that results from scaling and what solutions there are in place that ensures unbiased response. Bias structural response due to scaling of accelerograms has been a topic of discussion and research for nearly a decade. The question is how the bias arises and what contributes to it.

Response is said to be bias if there is a systematic difference between the responses of a scaled record compared to unscaled record at the same intensity measure.

Research findings by Luco and Bazzuro (2007) show whether the response of the structure is degree of biased of a randomly selected records for a given magnitude and distance, as well as scaling dependant on: the scaling factor, strength of the structure, the structure's fundamental period of vibration and also the magnitude and the distance of the accelerogram.

From this it is clear that the scaling factor which is used is not the only factor that contributes to the existence of the bias response after scaling. This study implies that if all the factors which contribute to the response being biased after scaling are considered carefully during the scaling bias response could be avoided.

The findings of the above research also show that the bias response can be avoided if records are chosen carefully to have spectral shapes which are near enough to the spectral shape of the target. One particularly striking aspect of this is that the magnitude and the distance of the accelerogram are not of significance under this condition.

Furthermore, Baker and Cornell (2006) conducted a study which argued that bias response of a structure can be reduced by selecting the records according to Conditional mean spectrum (CMS-e) or e instead of magnitude and distance. Given that the structural response is to a great extent affected by the spectral shape (which e is an indirect measure of).

These studies indicate that bias response of a structure can be avoided or reduced by selecting accelerograms which have similar spectral shape to the target spectral shape. In addition, it is stressed that when selecting accelerograms the main emphasis should not be on the magnitude or the distance as they do not influence the spectra shape.

Recorded and Artificial accelerograms.

In this section of the literature review real accelerograms will be compared with artificial accelerograms at the same time the benefits and limitations of each will be discussed. Finally the type of accelerogram that will be used in this project will be stated with reasons.

There is more useful information about the earthquake for a particular site that is contained in a recorded accelerogram. These include the accelerogram characteristics such as amplitude, duration and frequency. As well as this, recorded accelerograms contain useful information on the factors affecting the accelerogram such as directivity, rupture mechanism and source to site distance.

In addition, recorded accelerograms have the characteristics which are expected of real earthquakes in contrast artificial accelerograms can sometimes have unrealistic characteristic which could result in impractical design, although there are technologies to limit this impracticalities this days. For that reason real accelerograms are often selected in the design of structures (Bommer et al., 2003).

The number of accelerograms which are recorded across the world has increased over the past few years at the same time these databanks do not cover all the seismically active areas. The reason for this is that some of these places do not have accelerographs in place to record the earthquakes. Consequently, it is very difficult to find recorded accelerograms that have the necessary magnitude, distance and soil type for a site which is located in a region with few or no accelerographs to record the accelerograms (Bommer et al., 2003).This is clearly a disadvantage of recorded accelerograms.

Meanwhile, the benefit of artificial accelerograms when compared with real accelerograms is that few records are needed to create artificial acclerogram which almost always matches the design spectra (Priestly, 2006). On the other hand, unlike artificial records real accelerograms can be scaled to match the design spectrum without affecting the essential characteristics such as the frequency content.

In trying to examine the many aspects of real and artificial accelerograms it is clear that both have their advantages and disadvantages for that reason it is always up to the engineer to select whichever is most suited for the design. For that reason the decision reached for this project is to use real accelerograms as they present less serious limitations than artificial accelerograms.

Summary of the literature review.

From reviewing different studies it can be said that for selection of accelerograms even though the standard method is to select according to magnitude, distance and site classification. There are some specialists such as Barker and Cornell who argue that selecting according to e is a more appropriate method for selection than magnitude and distance.

Furthermore, when selecting an accelerogram it is a good practice to take into consideration the rupture directivity which is present in the record and the fault-site distance of the record as these have an effect of the characteristics of the time history.

Taking into account all that is stated above the selection parameter which is chosen for this project is e as there is not a lot of research material which covers this. Since, selection according to magnitude, distance and site classification have a lot of research done on them.

There are varies methods of scaling accelerograms but the scaling procedure which is commonly in use is scaling in terms of the amplitude. This is found to a good practice as the frequency content of the time history is not altered.

Problem that is associated with scaling of accelerograms was found to be bias response of the scaled time histories. It found that there are other factors which contribute to the bias of the response rather than the scaling factor by alone. Finding from Baker and Cornell (2006) and also Luco and Bazzuro (2007) indicate that the bias response could be avoided by appropriate selection of accelerograms which have spectral shape similar to the target spectral shape.

The scaling procedure which will be used for this project is scaling in terms of the amplitude as it is easier to carryout and has fewer complications than some of the other methods.

From the literature review it was found that both real and artificial accelerograms have there own advantages and limitations. A major setback of artificial accelerograms was found to the fact that it can have unrealistic characteristics which could jeopardise the design. From the reason stated above and others which are covered in great depth in the literature review the decision that was reached for this project is to use real accelerograms as the associated problems are less serious.

Methodology

Introduction.

The main aim in conducting this research is to determine whether epsilon (e), is a good indicator of structural response. Various researches have been done in the past to show that magnitude and distance are good indicators of structural response. On the other hand there is considerable less research that shows that e can be used as a good indicator of structural response. Baker and Cornell (2005, 2006) stated that selection based on e is more effective in predicting structural response than selection based on magnitude and distance.

The studies done by Baker and Cornell (2005, 2006) focused on the effect of e on the structural response when the accelerogram is scaled to same Sa (T) value. Furthermore, this maximum interstorey drift has been used as the structural response parameter. In contrast to these studies in this research the effect of e on the structural response when the accelerogram is unscaled will be investigated to rule out bias in the response and also to give true response. Furthermore, more than one structural response parameters will be used these are maximum inter-storey drift and the demand capacity ratios these are maximum plastic rotation (?p), shear resistance contributed by the concrete, axial load and transverse reinforcement (VR3), and shear resistance to web crushing (VR2) where the maximum of these will represent the overall element damage index, Id,el (Kappos and Dymiotis, 2000).

Analytical procedure for determining the structural response.

Numerical analysis has to be carried out in order to find out if e is as good in indicating structural response as magnitude and closest distance.

This will be examined by applying 40 un-scaled accelerograms to a bare frame structure. The structural response of the bare frame structure to the 40 different time histories will be observed and the parameters stated previously will be used to assess the significance of e as a predictor of structural response.

The unscaled earthquake time histories will be applied to the bare frame structure only as a base acceleration at a constant time step. The structural responses of the structure are calculated using the Newmark. Although the time step of each accelerogram was different the adopted time step for the analysis is 0.02 seconds.

The program which is used to do the dynamic analysis in order to find the structural response of the bare frame structure is Drain 2000. This program is more advanced version of Drain-2D/96 which is a program which is used to work out the dynamic response of inelastic 2D structure. It is developed by Andreas J. Kappos and Christiana Dymiotis (2000).

Before any analysis was carried out modification are done to the bare frame to make it applicable with the specific input time history. These modifications are:

• The number of integration time steps to be considered in the dynamic analysis NSTEPS are specified for the given input time history.
• The magnification factor to be applied to the input time history in the x-direction, FACAXH is set to 10 to get the input file which is in g to m/s2.
• KEQINP=4 is used so that the input acceleration is at constant ?t with arbitrary format.

After each input time history was applied to the bare frame structure the output files were saved individually.

Input accelerograms.

The 40 unscaled accelerograms are adopted from Baker research group at Stanford University; these are for Peer Transportation Systems Research Program. This data is collected by Nirmal Jayaram, Shrey Shahi and Jack Baker in early 2010. This data can be found at the PEER website (http://peer.berkeley.edu/transportation/gm_peer_transportation.html).

The data which is obtained from this website includes the e values for the 40 records. These e values are calculated at different periods that range from 0.01 (s) to 10 (s). The attenuation relationship used to calculate the e values is Boore & Atkinson (2008) ground motion prediction equation.

From the databank of the accelerograms only the fault parallel records from soil site are downloaded for use in this research. For these records all the important parameters for each recorded are listed in Table 6. These include PGA, PGV, PGD, e, Magnitude, Hypocentral distance and closest distance. Some of these data which correspond to the specific time histories are taken from PEER NGA Database which can be downloaded from (http://peer.berkeley.edu/nga/flatfile.html).

The structural model.

The structure that is used in this analysis is design as a bare framed building with 10 stories. This structure was used by Dr. Christiana Dymiotis-Wellington for other projects but was also used in this project as the design of such structure is beyond the scope of this project. The bare frame structure whose layout and dimensions are shown in Figure 13, is a three bay structure which is designed for medium ductility and according to EC8 (Chyssanthopoulos et al. 2000).

The fundamental period of the bare frame structure is T=0.93 (s), for that reason when the analysis was complete the e values used to carry out the comparison is from the closest period to the period of the bare frame structure this is found to be T=0.95 (s).

The design of the bare frame structure is strong column weak beam design. Column failure is taken as global failure; column failure is taken as critical since it results in the structure losing stability. Whereas beam failure is not considered to be significant as beam failure will not result in the frame collapsing. This is due to fact that beams dissipate the energy consequently the damage is only concentrated in the beams.

The outer columns of the bare frame structure are modeled as beam-column elements with elasto-plastic response (Chyssanthopoulos et al. 2000). On the other hand, the internal columns and beams are modelled as beam elements.

For this research the response values which are taken into account are the responses from the outer and inner columns of the structure. The maximum interstorey drift and the Id,el values are all from the columns of the bare frame structure the structural response results for the beams are not considered.

Criteria for measuring the effect of ε.

After the computation is complete the output data will be analysed. The resulting maximum damage index, Id,el and maximum interstorey drift for each input time history are put into a spreadsheet. From these data scatter graphs are plotted for e values for the corresponding Id,el and maximum interstorey drift values, the same is done for magnitude and distance. These is done to see if there is any relationship between e and the structural response also to compare this to the relationships of distance and magnitude with the structural response.

Furthermore, the correlation coefficients between the e values and the corresponding structural response for the time histories are calculated. Also, the magnitude and the distance correlation for the structural response are calculated, as well as this the correlation coefficients of the e and magnitude and e and distance are calculated to see if any relationship exists between this variables and if there is, the strength of this relationship.

Typically, a +1 value for the correlation coefficient shows a strong positive correlation where as -1 correlation coefficient represents a strong negative correlation.

Discussion

In this chapter the findings from the structural response and how they relate to the ground motion parameters will be discussed. Detailed analysis will be done in which the mean focus will be on the relationship between e and structural response and how this compares with relationships that magnitude and distance have with structural response.

From the graphs of e against maximum damage index, Id,el for the inner and outer columns of the bare frame structure which are shown in Figures 6-7, there is positive correlation between maximum damage index, Id,el and e. This relationship is not strong enough as is evident from the correlation coefficients on Table 1, but from the correlation coefficients the relationship between e and Id,el for the outer columns is greater than that of e and Id,el for inner columns which means that the relationship between e and the maximum damage index, Id,el is greater. Furthermore, on av