A ground motion record selection procedure utilizing a vector-valued intensity measure for optimized incremental dynamic analysis

Aris I. Theophilou & Marios K. Chryssanthopoulos

University of Surrey, Faculty of Engineering and Physical Sciences, Civil Engineering, Guildford, UK

IDA progresses by increasing the yield reduction factor Ry, within a range of intensity levels.

A vector-valued intensity measure (IM) is con-sidered, comprised of the spectral deformation S_d(T1), the yield reduction factor Ry, and the ‘Nor-malized Spectral Area’ (NSA) parameter, symbol-ized as shown below

S_d R_y S

( )

^T^T^T^T RR^R_y^y SSS_dN_dN

(

^{T T}^T^T¹^T^T²

)

⁽²⁾

NSA is evaluated by integration of the deforma-tion spectral area and normalizadeforma-tion to the spec-tral deformation S_d(T₁) at the fundamental period.

It is therefore independent of the response spec-trum intensity. As a result, it has the potential to capture the effect of the record frequency content and period elongation on the response. The NSA parameter, denoted as S_dN(T₁,T₂), is given by

where T1 is the fundamental period of the system, T_N= 1.0 sec is the unit period, and Sd(T1) is the response spectrum deformation at T1.

The DM investigated is the ductility fac-tor μd. It is defined as the maximum inelastic 1 INTRODUCTION

The objective of the present study is to predict the ductility demand of a multi-storey building, within a range of ground motion intensity levels, through incremental dynamic analysis (IDA) (Vamvatsikos and Cornell, 2002). A procedure is developed for optimizing IDA by selecting records from a given dataset. The procedure utilizes a vector-valued intensity measure (IM) which incorporates the normalized spectral area parameter. In the context of performance based earthquake engineering, structural performance is evaluated in terms of damage measures (DMs).

The procedure leads to the same level of accuracy in response prediction for a smaller number of records used, compared to random selection. Conversely, it results in a more accu-rate response prediction, for the same number of records used.

2 RECORD SELECTION PROCEDURE The procedure is applied to a single-degree-of-freedom (SDOF) system, which could act as a proxy to a multi-degree-of-freedom system repre-senting the actual structure.

The SDOF system has an elasto-perfectly-plastic force-deformation relationship fff_S

( )

^u,u , shown in Figure 1. The yield strength is denoted as fy, and the maximum deformation response as um. Also shown in Figure 1 is the corresponding linear sys-tem defined as an elastic syssys-tem with the same stiffness, together with the maximum elastic defor-mation u0, i.e. the spectral deformation Sd(T1), and the elastic strength f0. The deformation capacity of the bilinear system is assumed to be unlimited, as the purpose is to evaluate the maximum defor-mation um. The yield strength fy and the elastic strength f0 are related through the yield reduction factor Ry, given by

Figure 1. SDOF system force-deformation relationship.

48 deformation u_m divided by the yield deformation u_y, expressed as

Having defined both IM and DM to be con-sidered, regression analysis is conducted in order to quantify their functional relationship, includ-ing the standard error and the correlation coeffi-cient. For the relationship between ln(S_dN(T₁,T₂)) and ln(μd), the simple linear regression model was found to be suitable.

As observed in Figure 2, the sample correlation coefficient r is seen to increase, as the yield reduc-tion factor R_y increases from 2 to 6, which implies that the proposed IM becomes more efficient.

Another observation is that for different yield reduction factors R_y, the peak sample correlation coefficient r corresponds to different integration ranges for the NSA parameter S_dN(T₁,T₂).

The initial step in developing the procedure for record selection is to form a suite of records from available databases, according to the design earth-quake scenario. Records are then allotted into bins on the basis of their NSA parameter S_dN(T₁,T₂).

Optimized suites, comprised of a reduced number of records, are then identified from the bins.

3 EXAMPLE

The proposed record selection procedure was applied to a SDOF system of fundamental period T₁= 1.0 sec, which could be considered typical of the fundamental period of a ten storey reinforced concrete frame building. The structure is assumed to be first mode dominated with viscous damping ratio 5%.

In order to compare bin selection to random selection, datasets of a large number of suites were formed using each procedure. The rigorous solu-tion was obtained using a suite comprising of all 34 records. Statistical analysis of the datasets was then carried out, the resulting statistics of which were used in the comparison.

Figure 3 shows the IDA curves for the ductil-ity factor 95% percentile, expressed as a two-sided 95% prediction interval. The ductility factor μd is plotted against the intensity measure R_y. For this specific example, the proposed selection procedure based on bin discretization has resulted in predic-tion intervals up to 35–45% narrower than random selection.

4 CONCLUSIONS

In the present study, IDA was applied in the pre-diction of the ductility demand of a SDOF system, which is taken as a proxy to a multi-storey building, for a range of ground motion intensity levels. The proposed record selection procedure resulted in a more accurate prediction of structural perform-ance due to future earthquake events, as a result of the higher correlation of DM to the proposed vector-valued IM, compared to random selection.

REFERENCE

Vamvatsikos, D. & Cornell, C.A. 2002. Incremental Dynamic Analysis, Earthquake Engineering and Struc-tural Dynamics, Vol. 31, 491–514.

Correlation Between ln(SdN(T1,T2)) - ln(μ^d)

0.0

SdN(1.0,1.4) SdN(1.0,1.6) SdN(1.0,1.8) SdN(1.0,2.0) SdN(1.0,2.2)

Figure 2. Correlation between ln(S_dN(T₁,T₂)) – ln(μd).

Ductility Factor 95% Percentile - 95% Prediction Interval - N = 5

Figure 3. IDA curves for ductility factor 95% percen-tile, 95% prediction interval, N = 5.

ICASP Book I.indb 48

ICASP Book I.indb 48 6/22/2011 12:41:32 AM6/22/2011 12:41:32 AM

GS_328 — Applications (5)

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Applications of Statistics and Probability in Civil Engineering – Faber, Köhler & Nishijima (eds)

Reliability level of structures designed according to the design

In document Applications of Statistics and Probability in Civil Engineering (Page 86-90)