Stochastic dynamic analysis of box-girder bridges

Abstract

In this study, under the effect of strong ground motions for bridges which have multi spans, and continuous box-girders with elastomer bearings, the finite element method and dynamic analysis steps are combined and dynamic behavior of viaduct is determined depending on various soil types and damping ratios by stochastic analysis method based on random vibration. Furthermore, based on recorded ground motion, the calculations performed by stochastic methods, are obtained in order to simulate earthquake acceleration for each soil types and at bedrock level based on white noise model depending on seismic activity of zone. By the stochastic dynamic analyses of the viaduct system, the structural responses such as displacements, bending moments and shear forces are calculated. The results in frequency domain are compared with those of made by deterministic methods in time domain. Stochastic dynamic procedure is applied to the analysis of viaduct system, thus stiffness and mass matrices are obtained to establish the finite element model and to carry out dynamic analysis. The computer code BRIFEAP is developed to discreatize the viaduct system, for dynamic analyses BRIDAP, for simulation of ground motion SIMEARTHP and BRISTOCAP is developed to perform the stochastic analysis of viaduct system. In stochastic analyses, filtered white noise model is taken as basis to consider the variation of ground motions. Simulated ground motions are generated at the bedrock level for three soil types and for twenty relevant components of recorded strong ground motions for each. Programs are developed for a small viaduct model and dynamic analyses are carried out by constituting substructure procedures at the beginning. Having carried out the analyses by using developed computer programs for the system, the displacements of the nodal points and the dynamic characteristics are obtained and compared with those of the computer package SAP2000 to verify the program developed. Later, the analyses of an actual box-girder viaduct having elastomeric bearings are carried out by making additions and improvements to the programs to represent the structural system as accurately as possible. The stiffness of elastomeric bearings decreases inertia forces due to ground motion by providing flexibility to the superstructure of the viaduct. The analysis includes the governing equations and specifications of the elastomeric bearing stiffness depending on its mechanical properties. An equivalent (or reduced) model of viaduct is developed by considering the elements that only connect the selected reference nodal points to reduce the computation volume and time. A second reduction is done in the mass and stiffness matrices for decreasing the number of the freedom which governs the free vibration of the system. By performing the dynamic analysis with reduced dynamic stiffness matrices is showed that the reduced model of the system can represent the actual system with an acceptable accuracy. Since ground motions have several types of uncertainties due to their random properties, a deterministic analysis of the system is not realistic. In the present thesis, random variations are considered for the ground motions. Stochastic analysis is carried out by using the power density function of the ground motion recorded at local site. They are filtered by adopting the transfer functions of Tajimi and Penzien. For this purpose, the corresponding power spectral density functions and the constant power spectral magnitudes are obtained for various types of soils. Having performed stochastic and deterministic dynamic analyses for the viaduct without making any simplification, a simple model representing one of the middle piers is developed and the corresponding stochastic analyses are carried out. In these analyses, the single pier with elastomeric bearings at the supports is considered. The pier is assumed to be subjected to horizontal and vertical ground motions simultaneously and the recorded and simulated ground motions are taken into consideration. The variances and average values of the base shear forces and the overturning moments are obtained for various ratios of damping and for soil types. The results are compared with those of the deterministic analysis as well. By carrying out the analyses, the stochastic methods have given results compatible with those of deterministic dynamic analysis and also have been observed as its economical and procedure superiority of the prediction of randomness.

Özet

Bu çalışmada çok açıklıklı değişken kutu kesitli kirişleri olan elastomer mesnetli köprüler için sonlu eleman yöntemi ile dinamik analiz adımları birleştirilerek kuvvetli yer hareketleri etkisindeki viyadüğün dinamik davranışı, farklı zemin tipleri ve sönüm oranlarına bağlı olarak rasgele titreşim kuramına dayalı stokastik analiz yöntemi ile belirlenmektedir. Ayrıca, kaydedilmiş bir yer hareketi esas alınarak stokastik yöntemlere dayalı hesaplamalar ile her zemin grubu için ve beyaz gürültü modeli esas alınarak anakaya seviyesinde benzeştirilmiş deprem ivmeleri bölgenin sismik aktivitesine bağlı olarak elde edilmektedir. Stokastik dinamik analizler ile viyadük sisteminde yerdeğiştirme, eğilme momenti ve kesme kuvvetleri gibi yapısal tepkiler için frekans ortamında hesaplanan sonuçlar, deterministik dinamik yöntemlerle zaman ortamında yapılan analizlerden elde edilen değerlerle karşılaştırılmıştır. Stokastik dinamik çözümleme yönteminin uygulanabilmesi için köprü sisteminde sonlu eleman modelinin kurulması ve dinamik analizleri gerçekleştirmek üzere bilgisayar programları geliştirilmiştir. Viyadük sisteminin ayrıklaştırılarak sonlu elemanlarla modellenmesi için BRIFEAP, dinamik analizleri için BRIDAP, kaydedilmiş bir yer hareketinin beyaz gürültü ile anakaya seviyesinde ve farklı zemin tiplerine göre benzeştirilmesi için SIMEARTHP ve viyadük sisteminin stokastik analizleri için BRISTOCAP adlı bilgisayar programları geliştirilmiştir. Stokastik analizlerde yer hareketinin değişimi, filtrelenmiş beyaz gürültü modeli ile göz önüne alınmaktadır. Kaydedilmiş kuvvetli yer hareketinin ilgili bileşeni için anakaya seviyesinde ve 3 zemin türünde 20 şer adet benzeştirilmiş yer hareketleri türetilmektedir. Yapılan çözümlemelerden stokastik yöntemlerin deterministik dinamik yöntemlerle uyumlu sonuçlar vermesinin yanısıra stokastik yöntemin rasgeleliğin tahmininde üstünlüğü ve ekonomikliği gözlenmiştir.