İki parametreli zeminler üzerine oturan yapı sistemlerinin dinamik analizi
Dynamic analysis of structures resting on two parameter elastic foundation
Yazar: MEHMET AKİF HAMARAT
Danışman: PROF. ENGİN ORAKDÖĞEN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2012
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Deprem yükü = Earthquake load ; Dinamik analiz = Dynamic analysis ; Yapı analizi = Structure analysis ; Yapı-zemin etkileşimi = Soil-structure interaction ; Zemin = Soil

Özet:
Bu çalışmada iki parametreli zeminler üzerine oturan yapı sistemleri, dinamik etkiler altında incelenmiştir. Yapılan analizlerde SAP2000 programından ve SAP2000 ile etkileşimli çalışan excel makrosundan yararlanılmıştır. Excel makrosu yardımıyla zemine ait zemin yüzey parametresi , ? parametresi, SAP2000 programı da kullanılarak ardışık yaklaşımla belirlenebilmektedir.Tez beş bölümden oluşmaktadır. Birinci bölümde zemin modelleri verilip çalışmanın amaç ve kapsamı sunulmuştur.İkinci bölümde iki parametreli zeminde, zemin karakteristiklerinin tanımı yapılarak, iki parametreli zemine ait formülasyonlar sunulmuştur. Zemin yüzey parametresinin nasıl elde edilebileceği gösterilmiştir.Üçüncü bölümde iki parametreli zeminin SAP2000 programında nasıl modellendiği gösterilmiştir. Excel makrosu yardımıyla zemin yüzey parametresinin hesabı anlatılmıştır.Dördüncü bölümde dört adet sayısal örnek yapılmıştır. Bu örneklerden ilk ikisi, iki parametreli zemin ortamının SAP2000'de modellenebilirliğini göstermektedir. Üçüncü örnekte, daha önceki çalışmalarda karşılaştırma amacıyla yapılan, iki parametreli zemine oturan tekil yük ve düzgün yayılı yükle yüklü plak, SAP2000 programı ve excel makrosu yardımıyla çözülmüş ve bulunan sonuçlar önceki çalışmalardaki sonuçlarla karşılaştırılmıştır. Dördüncü örnekte iki parametreli zemine oturan üç ve sekiz katlı iki bina ele alınmış ve bu iki bina arasındaki mesafe değiştirilerek çeşitli sıkışabilir zemin derinliklerinde deprem yüklemesi altında dinamik analizleri gerçekleştirilmiştir. Dinamik yüklemeden önce, sisteme ait zemin yüzey parametresi, düşey yükler altında excel makrosu kullanılarak ardışık yaklaşımla belirlenmiş ve bu parametreye bağlı olarak da zemin yatak katsayısı, C ve zemin kayma parametresi, CT elde edilmiştir. Çeşitli durumlar için elde edilen yatak katsayısı ve kayma parametresinin dinamik yükler altında değişmediği kabul edilerek her bir durum için üç ve sekiz katlı binanın bulunduğu yapı sisteminin dinamik analizleri gerçekleştirilmiştir. Deprem yüklemesi olarak Kocaeli depreminin doğu-batı ivme kaydının yanı sıra aynı anda düşey ivme kaydı da kullanılmıştır. Zeminin düşey kütlesi olarak, sıkışabilir tabaka kalınlığının üçte birinin zeminin yoğunluğu ile çarpılması sonucu elde edilen değer kullanılmıştır. Yapılan analizler sonucunda, binaların serbest titreşim periyotlarının, binalara ait çeşitli düğüm noktalarındaki deplasmanların, belirli kolonların kesme kuvvetlerinin ve binaların en alt katına ait toplam kesme kuvvetlerinin zamana bağlı olarak farklı yapılar arası mesafe ve sıkışabilir tabaka kalınlığı için değişimleri grafikler halinde sunulup yorumlanmaya çalışılmıştır.Beşinci bölümde çalışma kapsamında elde edilen sonuçlara ve değerlendirmelere yer verilmiştir. Yapılacak başka çalışmalar için önerilerde bulunulmuştur.

Abstract:
In modern design and analysis of structures, the superstructure-foundation-soil interaction has to be taken into account in a sophisticated way, which is sufficiently accurete but simple enough for practical purposes. The concept of a plate resting on an elastic foundation has been an important tool for the modeling and analysis of structural, highway, geotechnical and railroad engineering problems. Extensive research in this area has been reported in the literature.In order to model soil behavior, several approaches have been developed in the past. The oldest, most famous and most frequently used soil model is the one devised by Winkler (1867), in which the beam-supporting soil is modelled as a series of closely spaced, mutually independent, linear elastic vertical springs. The Winkler model has been extensively used to solve many soil-foundation interaction problems and has given satisfactory results for many practical problems. In that method, it is assumed that deflection at each point is proportional to the pressure applied at the point and completely independent of the pressures or deflections occuring at the neighbouring points along foundation. In the Winkler model, the properties of soil are described only by the parameter k, which represents the stiffness of the vertical spring. One of the major disadvantages of this model is that a plate undergoes rigid body displacements without any bending moments and shear forces in it when subjected to uniform loads. Moreover, the use of the Winkler model involves difficulties in determining the value of k.Discontinuous nature of Winkler?s model gives rise to the development of various forms of two-parameter elastic foundation models. Some of the major two-parameter elastic foundation models are Filonenko-Borodich model (1940), Hetenyi model (1946, 1950), Pasternak model (1954), Vlasov model (1966). Filonenko-Borodich, Hetenyi, Pasternak and Vlasov have attempted to make the classical Winkler model more realistic by postulating a two-parameter model. Their model takes into account the effect of shear interaction among adjacent points in the foundation. In these models, the first parameter represents the stiffness of the vertical spring, as in the Winkler model, whereas the second parameter is introduced to account for the coupling effect of the linear elastic springs. It is worth mentioning that the interaction enabled by this second parameter also allows the consideration of influence of the soil on either side of plate. In this model, the first and second parameters have to be determined experimentally.Vlasov and Leont?ev (1966) have introduced another arbitrary parameter, ?, dependent on soil material and thickness of the soil layer. However, they did not report the method of determining this parameter. In the work of Vallabhan and Daloglu (1999), it has been shown how the soil parameter , ?, can be estimated using an iterative computational procedure for plates. These three-parameter models constitute a generalization of two-parameter models, the third parameter being used to make them more realistic and effective. When the ? parmeter is determined, the first and second parameters of soil can be easily calculated. One of the basic features of the three-parameter models is the flexibility and convenience that they offer in the determination of the level of continuity of the vertical displacements at the boundaries between the loaded and unloaded surfaces of the soil.In this study, dynamic analysis of structures resting on two parameter elastic foundation are examined and their interactions are observed. SAP2000 program and excel macro are used to perform analysis. A soil surface parameter ? is obtained by excel macro with iterative procedure method. Excel macro is coded with VBA language and linked to SAP2000 program with SAP2000 open application programming interface (OAPI). The SAP2000 open application programming interface is powerful tool that allows users to automate many of processes required to build, analyze and design models and to obtain customized analysis and design results.The study is composed of five sections. In the first section, informations about one and two parameter foundation models are given. Content and aim of this study are explained at the end of the first section.In the second section, the characteristics of two parameter foundation are explained. Then, the formulations of two parameter foundation are given. The iterative procedure method that are used to obtain soil surface parameter ? is explained in this section.In the third section, how the two parameter foundation is modelled at SAP2000 program is shown and then the soil surface parameter calculation with excel macro is explained. The first parameter of soil, soil elastic bedding coefficient C, is represented by springs at SAP2000 model. The springs are created by area springs feature at SAP2000 program and soil elastic bedding coefficient is entered as the spring coefficient. The second parameter of soil, soil shear parameter 2CT, is represented by layered/nonlinear shell elements that have orthotropic material features at SAP2000 program. Soil shear coefficient 1.2×2CT is entered at shear modulus section of orthotropic material property form and the other sections at material property form is entered as a zero. The soil finite element nodes are restrainted to make only vertical displacements at SAP2000 program. The plate finite element and soil finite element are modelled very close to each other and then vertical displacements of their nodes are equalized by weld constraint feature of SAP2000 program.Excel macro has been developed in order to obtain soil surface parameter ?. It consists of two pages. The first value of soil surface parameter ?_i, modulus of elasticity of soil Es, poisson raito of soil ?s, and compressible soil depth H, size of soil finite element a×b, and number of soil finite elements are entered on the first page of excel macro. Shear modulus of soil Gs, soil elastic bedding coefficient C and soil shear parameter 2CT is calculated by excel macro.New soil surface parameter ?_(i+1) is calculated using these values on the second page of excel macro. Excel macro interacts SAP2000 program on second page. It enters soil elastic bedding coefficient C and soil shear parameter 2CT which are calculated by first soil surface parameter on related places of SAP2000 program. Then, it starts SAP2000 program analysis and gets displacement results di of nodes of soil finite elements. New soil surface parameter ? is calculated by using displacement results di of nodes of soil finite elements. [CT] stiffness matrice is calculated by unit displacement loading on nodes of soil finite element with using SAP2000 program and excel macro. When ?_i is close enough to ?_(i+1), iteration is terminated and soil surface parameter is obtained.In the fourth section, four numerical examples are given.In the first two examples illustrate two parameter foundation that is correctly modelled on SAP2000. A circular foundation which is solved previous studies is solved in the first example. The results are shown graphically to compare with previous studies. An arbitrarily shaped foundation is solved in the second example and then results are compared graphically with previous studies.In the third example a plate which is solved in previous studies is considered. This plate is subjected to uniformly distributed and concentrated loading cases. The problem is solved with SAP2000 program for different value of the thickness of the compressible soil layer. The results are compared with previous studies.In the fourth example, three and eight storey building which are resting on two parameter elastic foundation are considered and then dynamic analysis of this structure system is performed with SAP2000 program under earthquake loading by changing the distance between buildings and compressible soil depth. Before dynamic analysis of structure system, the soil surface parameter of system is obtained under vertical static loads by using excel macro and SAP2000 program. Then, soil elastic bedding coefficient C and soil shear parameter 2CT are obtained depending on soil surface parameter ?. Soil elastic bedding coefficient C and soil shear parameter 2CT which are obtained depending on different distance between buildings and compressible soil depth are considered constant during dynamic analysis. East-west and vertical acceleration records of Kocaeli Earthquake are used at the same time as dynamic loading. The value which is calculated by mutiplying one-third of compressible soil thickness to mass density of the soil is used as vertical mass of the soil. Dynamic analysis is performed by using linear time history direct integration method on SAP2000 program. Output time step size is selected as ?s=0,005 seconds. Hiber-Hughes-Taylor method is used for time history direct integration. After dynamic analysis, free vibration periods of buildings, displacements of various nodes of buildings, shear forces of certain columns of buildings and base shear forces of buildings are compared depending on time with different distance between buildings and different compressible soil depth.In the fifth section, the general results and conclusions are presented.In this study modelling of two parameter foundation at SAP2000 program are shown. Thus more complex structural system can be examined under static and dynamic loads and their interactions can be observed.Impact of eight storey building on three storey building are obviously seen in the fourth example. Their interactions are shown graphically with different distance between buildings and different compressible soil depth in the fourth example graphics.Linear behavior of structure systems resting on two parameter elastic foundation are observed under eartquake load in this study. In another work, non-linear behavior of structure systems resting on two parameter elastic foundation can be observed under eartquake load.