Oyuk genişlemesi probleminin sonlu elemanlar yöntemi ile iki boyutlu sayısal analizi
Two dimensional numerical analysis of cavity expanison problem with finite element methods
Yazar: EMİN ŞENGÜN
Danışman: PROF. DR. METE İNCECİK ; DOÇ. DR. MEHMET BERİLGEN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Zemin Mekaniği ve Geoteknik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2013
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Sonlu elemanlar yöntemi = Finite element method

Özet:
Oyuk genişlemesi teorisinin temelini oluşturduğu oyuk genişlemesi analizleri geoteknik mühendisliğinde karşılaşılan birçok problemin çözümünde kullanılmaktadır. Özellikle son yirmi yılda kazıklı temellerin ve zemin ankrajlarının kapasitelerinin araştırılmasında, arazi deneylerinin yorumlanmasında, tünellerin ve yeraltı kazılarının davranışlarının analizlerinde ve kuyu stabilitesinde oyuk genişlemesi yaklaşımları oldukça yararlı sonuçlar vermiştir.Bu çalışma kapsamında killi bir zemin içerisinde drenajsız koşullar altında oyuk genişlemesi analizleri ele alınmış olup zemin içerisinde var olan bir oyuğun çapının iki katına çıkartılması suretiyle oyuk genişlemesi sırasında ve konsolidasyon sonrasında oyuk çevresinde meydana gelen gerilme, şekil değiştirme ve boşluk suyu basıncı değişimi araştırılmıştır. Bu amaç doğrultusunda oyuk çevresini oluşturan zemin, Boston Mavi Kili (Boston Blue Clay) olduğu kabul edilerek Plaxis 2011 2D kullanılarak ve Modified Cam Clay (MCC), Soft Soil (SS) ve Hardening Soil (HS) malzeme bünye modelleri ile sonlu elemanlar analizleri yapılarak incelenmiştir. Konsolidasyon analizlerinde iki boyutlu bütünleşik analizler kullanılarak minumum boşluk suyu basıncı elde edilmiştir. Ayrıca oyuk genişlemesi sırasında oyuk çevresindeki zeminin gerilme geçmişi ile boşluk suyu basıncını arasındaki ilişki de araştırılmıştır. Oyuk genişlemesi probleminin incelenmesi için gerçekleştirilen sayısal analizlerde aksi simetrik geometrik idealizasyonu yapılmış ve problem iki boyutlu olarak ele alınmıştır. İlk olarak oyuk çapının iki katına çıkartılması suretiyle oyuk genişlemesi sırasında oluşan zemin deformasyonları teorik ve ölçüme dayalı sonuçlarla karşılatırılmış ve sonuçların birbiriyle çok uyumlu olduğu görülmüştür. Bir sonraki aşamada yapılan analizler sonucunda oyuk çevresinde meydana gelen gerilme, şekil değiştirme ve boşluk suyu değişimleri ile zemin gerilme geçmişi ve boşluk suyu basıncı ilişkisi elde edilerek literatürde yapılan benzer çalışma sonuçları ile karşılaştırılmıştır. MCC ve SS ve HS bünye modülleri için oyuk genişlemesi hemen sonrasında elde edilen gerilmeler literatür çalışmalarıyla uyumlu dağılımlar gösterirken oyuk çevresinde oluşan plastik bölge alanı HS model için daha geniş alan kapladığı görülmüştür. Ayrıca SS ve HS bünye modülü için oyuk genişlemesi sonrasında aşırı konsolidasyon oranının artması ile boşluk suyu basıncında önemli bir değişim görülmezken, MCC bünye modelinde aşırı konsolidasyon oranının artması ile elde edilen boşluk suyu basıncında önemli düşüş görülmüş ve bu sonuç literatürde görülen teori ve ölçüme dayalı sonuçlarla uyum göstermiştir.Killi bir zemin içerisindeki drenajsız oyuk genişlemesi problemi üzerine gerçekleştirilen iki boyutlu sayısal analiz çalışma sonuçları literatürde yapılan benzer teorik ve ölçüme dayalı çalışmalarla uyumlu sonuçlar verirken aynı zamanda benzer problemler için daha hızlı ve pratik çözüm olanakları sağlamıştır ve ayrıca sayısal modellemeler için seçilen malzeme bünye modüllerinin de önemini bir kez daha göstermiştir.

Abstract:
The cavity expansion methods forming the basis of theory of cavity expansion is widely used to solve the problems encountered in geotechnical engineering. In recent decades, cavity expansion methods have given beneficial results in the areas of soil testing and the main soil properties cab specifically be obtained such as shear modulus, total horizontal in-situ stress, undrained shear strength and coefficient of horizontal consolidation thanks to similar mechanical action formed by cavity expansion and cone penetration and pressumeter expansion. Cavity expansion theory is used with considerable success in the interpretation of these types of in-situ soil tests. Moreover, cavity expansion methods are used in the prediction of end-bearing and shaft capacities of a driven pile in soils and can also be used to estimate the pull-out capacity of earth anchors. They are also applied to the design and construction of tunnels and underground excavations in order to provide stability and serviceability and, furthermore, they are used to estimate ground settlements due to tunneling and designing tunnel support systems to maintain stability. Cavity expansion method also provides a useful prediction of borehole instability.For the first time, cavity expansion analysis emerged to figure out the problems of metal indentation, which became more important when the industrial revolution intensified in the late 19th century and early 20th century. After metal indentation, the concerns were related to explosions within the ground and how the stress waves generated by these explosions would propagate.As a result of these improvements, geomechanics with more of a geotechnical engineering property followed notably with works by Ladanyi (1972), Palmer (1972), Vesic (1972) who attempted to capture the important feature of soil stress-strain nonlinearity. The next generation of cavity expansion analyses appeared in the 1980s, 1990s, and 2000s (notably, Randolph et al. 1979; Yu and Houlsby 1991; Collins et al. 1992 and Salgado et al. 1997).Cavity expansion processes can be divided into two basic types, firstly expansion from a finite radius and secondly expansion from zero initial radius. Although different types of analyses can be used to solve each of these problems, this study presents numerical analysis that provides the solution to both problems simultaneously.The expansion of cavity in soil is a one-dimensional boundary value problem. To solve it using the principles of continuum mechanics, a mathematical constitutive model is needed to describe the stress-strain behavior of soil. However, soil is some of the oldest and most complex construction materials and, therefore, a description of soil behavior can only be achieved by developing a constitutive model. The most widely used theories for developing soil models are the assumptions of elasticity and plasticity. Linear or nonlinear elastic models, viscoelastic or viscoelastic-plastic models or elastic-plastic models (perfectly plastic or strain hardening/softening) may be used to adequately describe the stress-strain behavior of soils. In this study, cavity expansion analysis was used in Plaxis finite element code?s soil models to describe the stress-strain behavior of soils. Some of them are Modified Cam Clay (MCC), Soft Soil (SS) and Hardening Soil (HS). The Modified Cam Clay model (Roscoe and Burland, 1968; Schofield and Wroth, 1968) represents the hardening behavior of the elasto-plastic materials based on the critical state concept and involves logarithmic relationship between the mean effective stress and void ratio. Yield surface of the MCC is described by an ellipse and therefore the plastic strain increment vector (which is vertical to the yield surface) for the largest value of the mean effective stress is horizontal, and hence no incremental deviatoric plastic strain takes place for a change in mean effective stress. The Soft Soil is based on the modified Cam Clay model especially meant for primary near-normally consolidated clays, clayey silts and peat also to describe the non-linear stress-strain behavior of soils, beside the Cam Clay model, the pseudo-elastic (hypo-elastic) type of model has been developed. Soft Soil model also provides some features in Plaxis such as stress dependent stiffness, memory of preconsolidation stress, failure behavior based on Mohr- Coulomb criterion. The Hardening Soil model is an advanced model for simulation of soil behavior such as different types of soil both soft soils and stiff soils and well known hyperbolic model (Duncan and Chang, 1970). Basic feature of the Hardening soil model is the stress dependency of soil stiffness so that all stiffnesses increase with pressure.In the concept of this study, the cavity expansion methods were studied and the changes in stresses, pore-water pressures and displacements caused by the undrained expansion of cylindrical cavity were investigated during and subsequent consolidation by doubling initial radius of the cavity existing in a clayey soil. For this purpose, the surrounding soil of cavity, which is assumed Boston Blue Clay, was investigated by using Plaxis 2011 2D and Modified Cam Clay (MCC), Soft Soil (SS) and Hardening Soil (HS) constitutive models and by making finite element analysis. In addition, the relation between the surrounding soil stress history and the pore-water pressure during the expansion of the cavity was explored.In the numerical analysis of the cavity expansion problem, modelled as undrained expansion of an existing cavity with an initial radius 1 m, and a length of 10 m, axisymmetric geometric idealization was assumed and the surrounding soil (Boston Blue Clay) using 15 node triangular elements was generated in Plaxis 2D. During the modeling of cavity expansion, the expansion took place by assigning prescribed displacement in the radial direction along the side of the initial cavity. Plastic calculation was used to carry out elastic-plastic deformation analysis for undrained behavior in the expansion step. The modeling of undrained behavior based on effective stiffness parameters was available for all materials in plaxis such as Undrained (A), Undrained (B) and Undrained (C). During the plastic phase, Undrained (A) that enables modelling undrained behavior using effective parameters for stiffness and strength was used in all material models in this study. During the cavity expansion, assuming sufficient time for excess pore pressure dissipation, soil behaviour was arranged to undrained. Subsequently, the soil modelling was allowed to consolidate until the excess pore pressure at any point dissipated below 1.0 kPa. Consolidation (EPP) coupled two-dimensional analysis was used to in consolidation phase.First of all, the cylindrical cavity expansion analysis showed good agreement with measurements of radial soil displacement around a cavity mid-depth in the field (Cooke and Price, 1973; Pestana et al., 2002) and in the laboratory model tests (Randolph et al., 1979a; Randolph et al., 1979b; Steenfelt et al., 1981) and cavity expansion analytical solutions. At the second stage, as a result of the analysis carried out in this thesis, the change of stresses, pore-water pressures and displacements in soil, the relation between the surrounding soil stress history and the pore-water pressure were obtained. These results were compared with the results of the similar studies of the literature made in the mentioned area such as Randolph et al. (1979a) who provided numerical analysis for an undrained expansion of a cylindrical cavity by using BBC parameters and MCC constitutive model and presented the changes of stresses, displacements and pore pressures in the surrounding soil of cavity during cavity expansion and after subsequent reconsolidation as a function of radial distance. When compared with the results provided by Randolph et. al. (1979a) , SS and HS constitutive models show an acceptable level whereas MCC Model results obtained match quite well results for the stress distributions during radial expansion. However, after the subsequent consolidation, the change of stresses, pore water pressures in surrounding soil of cavity results were compared with the results of Randolph et al. (1979a) and these results were seen to be different from each other. The reason for this is that Randolph et al. (1979a) used Tergazhi?s one-dimensional consolidation analysis whereas this study used two-dimensional coupled consolidation analysis as a more realistic method. Moreover, when compared with the other constitutive models, the plastic zone around the cavity for HS constitutive model was observed to be occupying larger area. Furthermore, when the relation between the excess pore pressure near the cavity face and the overconsolidation was concerned, no significant change was observed in SS and HS models with respect to the excess pore pressure depending on the increase of overconsolidation ratio. However, in the MCC constitutive model, a significant decrease was observed in the increasing overconsolidation ratio and excess pore water pressure. Nonetheless, Coop and Wroth (1989) at Oxford University and Bond and Jardine (1991) at Imperial College measured pore water pressures generated at the pile soil interface during pile installation in clay and they observed a decrease ,to a considerable extent, in pore pressure along the pile (assume cavity) for overconsolidation clays. That is why, numerical solution is in agreement with the theory and based on the measurement results.In particular, in agreement with the field-testing, the results of numerical analysis were consistent with the results of the similar studies of the literature made in the mentioned area and numerical modeling also demonstrated the importance of constitutive models selected for the description of soil behavior.Despite some restrictions and simplifications in geometric idealizations and soil properties during the cavity expansion approaches and related numerical modelling solutions dealt within the context of this thesis, the study hopefully aims to contribute to the efficient and effective solutions of the cavity expansion problems as quite many problems encountered in geotechnical engineering have been closely associated with the problems of cavity expansion. Since the related studies carried out in Turkey are limited in number, this study is bound to play a vital role in this field to a considerable extent. If some recent researches carried on interpretation of in-situ soil testing and investigation of capacity of pile foundations are taken into account, the current numerical solutions might be improved on sandy soil analysis.Finally, numerical analyses developed for the cavity expansion problems presented matching results with the similar studies and findings based on measurement as well as producing rapid and effective solutions for the similar problems, and the materials selected for numerical modelling once more showed the importance of constitutive models.