Çok sıra ankrajlı iksa sistemlerinde hesap yöntemlerinin karşılaştırılması
Comparison of calculation methods on multiple row of anchored walls
Yazar: SAFA ÇEVİK
Danışman: PROF. DR. MUSAFFA AYŞEN LAV
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Zemin Mekaniği ve Geoteknik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2017
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Günümüzde şehirleşmenin önemli ölçüde gelişmesine paralel arsa fiyatlarının artması çok bodrum katlı yapıların inşasına sebep olmuştur. Bu sebeple derin temel kazılarına ihtiyaç duyulmaktadır. Derin temel kazılarının yapılabilmesi için iksa sistemleri gerekmektedir.
Bu çalışma kapsamında, çok sıra ankrajlı iksa sistemlerin tasarımı için Microsoft Excel ortamında, sonlu elemanlar yöntemiyle çözüm yapan Zemank isimli bir bilgisayar programı geliştirilmiştir.
Tez çalışmasının birinci bölümünde, çalışmanın amacı veliteratürde konu ile ilgili daha önce yapılmış çalışmalara yer verilmiştir.
İkinci bölümde, yanal toprak basınçları hesabında kullanılan Rankine ve Coulomb terorileri ayrıntılı olarak açıklanmıştır. Sükunet, aktif ve pasif durumlar için toprak basıncı katsayısı hesaplarına değinilmiştir. Çok sıra ankrajlı iksa sistemlerine gelen ve çeşitli araştırmacılar Terzaghi- Peck, Tschebotarioff, Lehmann, Klenner tarafından çok sıra ankrajlı sistemler için önerilen toprak basıncı dağılımları irdelenmiştir.
Üçüncü bölümde, kazıklı perdeler ve zemin ankrajları ile ilgili bilgiler verilmiştir. Kazıklı perdeler ve zemin ankrajlarına ait inşa yöntemleri açıklanmıştır. Zemin ankrajlarının yapısal kısımları tanıtılmış olup imalat yöntemlerine göre ankrajlar anlatılmıştır. Zemin ankrajı taşıma gücü hesabı ve ankraj tahkikleri de irdelenmiştir.
Dördüncü bölümde, yatak katsayısı ve sonlu elemanlar (maatris) yöntemi anlatılmıştır. Yatay yatak katsayısı tanımlanmış ve iksa sistemlerine uygulanış şeklinden bahsedilmiştir. Bowles tarafından geliştirilen sonlu elemanlar (matris) yöntemi elastik zemine oturan bir kiriş baz alınarak anlatılmıştır. Daha sonra bu matris yöntemi kullanarak 2 sıra ankrajlı bir iksa kesiti çözülmüş ve kazıkta oluşan yatay deplasman, moment ve kesme kuvveti diyagramları verilmiştir.
Beşinci bölümde, sonlu elemanlar (matris) yöntemi ile çok sıra ankrajlı iksa analiz ve tasarımını yapan "Zemank" isimli bilgisayar programı tanıtılmıştır. Programa ait veri girişi ve sonuç ekranları tanıtılmıştır. Program kazıkta meydana gelen yatay deplasman, moment ve kesme kuvvetini hesaplar ve elde edilen sonuçlara göre ankraj boyutlandırması, kazık ve kuşak kirişinin betonarme hesabı TS 500 kuralları çerçevesinde otomatik olarak yapılmaktadır.
Altıncı bölümde, parametrik bir çalışma olarak, içsel sürtünme açısı ve zemin birim hacim ağırlığı değiştirilerek iki farklı iksa yüksekliği için sırasıyla Zemank, SAP2000 ve Plaxis 2D (2016) programları ile analizler yapılmıştır.
Yedinci bölümde, analizler sonucu, kazık elemanda meydana gelen yatay deplasman, moment ve kesme kuvveti değerleri karşılaştırılmıştır. Zemank ile SAP2000 programları karşılaştırıldığında neredeyse aynı sonuçlar verdiği, Zemank ile Plaxis 2D (2016) programları karşılaştırıldığında ise sonuçların bir miktar farklılık gösterdiği görülmüştür. Bulunan küçük farklar, çözüm aşamasında yapılan kabullerden kaynaklanmaktadır.

Abstract:
Nowadays, urbanization has developed considerably and increase of the land prices has caused to built the basement stories. For this reason, deep base excavations are needed. Supporting systems are required for deep base excavations.
Within the scope of this study, a computer program named "Zemank" was developed for the design of multiple row of  anchored walls using Microsoft Excel with finite element method.
In first chapter of study, a brief summary of purpose of the study given and the previous work on the subject was included in literature. These studies are about multiple row of anchored walls and behavior of them for different cases. Such as, Sefi (2014) investigated that the effect of semi top- down construction method on anchored systems. Alkaya and Yesil (2010) investigated that unbraced, single row of anchored and multiple row of anchored systems are compared for economically with various wall heights. Researchers Alkaya and Yesil noticed that, unbraced and single row anchored systems are economic for 8-9 m. wall heights and multiple row of anchored walls are economic for 9 m. and higher wall heights.
In second chapter of study, information about the calculation of lateral earth pressures is given. Rankine and Coulomb theories used in the calculation of lateral earth pressures are described. Calculations for coefficients of at rest, active and passive cases are given. A forward movement (deformation) of about 0.002*H is reqired to create active case. An inward movement (deformation) of 0.08*H is required to create passive case. If soil is under water table, the influence of water pressure added to calculations. Pratically, soil friction angle ϕ is taken same for natural and saturated soil. If there is a curved surface behind the wall, the earth pressure is calculated taking this slope into consideration. If there is a surcharge load, the earth pressure calculated taking into account the effect of the surcharge load. 
Some researcher Terzaghi- Peck, Tschebotarioff, Lehmann and Klenner have made various studies for the calculation of earth pressures affecting multi row anchoring systems. Terzaghi- Peck suggested that rectangular distribution for sandy soil and also suggested that trapezoidal distribution for clayey soil. Tschebotarioff suggested that trapezoidal distribution for sandy soil and also suggested that triangular distribution for clayey soil. Lehmann suggested that trapezoidal distribution for sandy and clayey soils. Klenner suggested that rectangular distribution for sandy and clayey soils. SIA-191 (Switzerland Ground Anchor Code) suggested that rectangular distribution for sandy and clayey soils.
In third chapter of study, piled walls and ground anchors were examined. An excavation pit opened in the grouund will lead to reduction of the stress in the excavation area. If the horizontal stress reduction due to the excavation is large to enough to disrupt the stability of the ground, the strain loss that occurs in this case is covered by the excavation system. When selecting the system to be used, the duration of the excavation pit will be opened, the ground profile and properties and the bearing systems of the neighboring structures must be taken into account.
If the height of the ground is too high, but if the ground properties are insufficient, pile walls are applied. Usually fore piles are used. Pile construction is done in there ways. These are examined as intermittend alignment piles, tangent piles and intersecting piles.
Anchors are used to transfer the loads from deep excavation to the rock or the earth and to minimize the horizontal movement of the wall. Ground anchors transfer the prestressing load to the stable ground behind the slip surface. Basically, the ground anchor has three components. These are anchoring head, anchor free length and anchor bond length. Ground anchors can be classified temporarily and permandntly according to their usage time. Ground anchors can be classified type A, type B, type C and type D to their consturuction methods.
The construction phases ground anchor are, opening anchor hole, placement of anchor tendons, injection and prestressing tendons. For calculating anchor bearing capacity there are some cases. These are, soil or rock properties about anchor bond, geological load on anchor bond, contsturuction method of anchor bond, length and diameter of anchor bond and injection pressure. Uniform distirubition is accepted for calculating anchor bearing capacity. There are various formulas for rocks, granular soils and cohesive soils.
In fourth chapter of study, subgrade modulus which was developed by Winkler (1867) and finite element (matrix) method which was developed by Bowles for calculating multiple row of anchor systems were examined. Subgrade modulus (ks) allows modelling of the structure-ground interaction and is widely used in practices. Basically, proportional representation of displacement (Δ) that occurs at the same point as the stress (q) at a ponit on the ground. In the case of solutions based on elastic theory using subgrade modulus, ground is defined by independent springs close to each other. If piles are considered vertical beams, lateral subgrade modulus (kh) is defined. If change of lateralsubgrade modulus is known for depth of pile, displacements, bending moments and shear forces are calculated for pile.
Lateral subgrade modulus was created from subgrade modulus parameters by Bowles. For calculating lateral subgrade modulus, we need some components. These components are pile diameter B, soil coheion c, soil friction angle ϕ, Terzaghi bearing capacity factors Nc- Nq- N and shape factors s1- s2. There ara some values for lateral subgrade modulus suggested by Bowles. Such as, for soft clay lateral subgrade modulus is changing range of 2- 40 MN/m3, for silty sand lateral subgrade modulus is changing range of 80- 200 MN/m3, for dense sandy soil lateral subgrade modulus changing range of 220- 400 MN/m3.
Newmark (1942) spcified that the value of subgrade modulus is not constant, it changes parabolically with depth. If the value of subgrade modulus is known each point, spring constant is calculated at same point.
Bowles (1974), developed finite element (matrix) method using the notion of subgrade modulus. With this method displacement, bending moments and shear forces can be calculated easily. In this method, there are some matrix solutions. "A" and "S" matrices are coefficient matrices, "AT" matrix is transpose of "A" matrix, "P" matrix is load (axial forces and moments) matrix. From these matrices displacements, bending moments and shear forces are calculated for pile. In this chapter, detailed solution of 2 row of anchored wall is done. Acceptions are, wall height H=5 m, soil friction angle 30º, soil cohesion c= 1 kPa, soil unit weight = 18 kN/m3, surcharge load q=5 kN/m2. Earth pressure is calculated with Terzaghi- Peck method for granular soils. Construction of matrices were shown. At the end of calculation, displacement, bending moment and shear force diagrams were shown for pile.
In fifth chapter of study, "Zemank" computer program which is developed for study is introduced. Computer program "Zemank" uses finite element (matrix) method for calculate the multi row of anchored walls. Program developed by using Microsoft Excel.
With developed program "Zemank" uses earth pressure distributions which were developed by varius researchers as Terzaghi-Peck, Tschebotarioff, Lehmann, Klenner and SIA-191 code. As a result of analysis, the horizontal displacement, moment and shear force diagrams generated for pile are graphically displayed, also anchor calculations are made. After static analysis, concrete design of pile and crossbeam are made with TS 500 code.
In sixth chapter of study, there is a parametric study for multiple row of anchored walls. Analyzes were performed with Zemank, SAP2000 and Plaxis 2D (2016). The parameters are wall height H, soil friction angle ϕ, soil cohesion c and soil unit weght . In all analysis cohesion value is accepted constant 5 kPa also elasticity modulus of soil is taken E= 50 000 kN/m2 in Plaxis, diameter of pile is 60 cm, horizontal pile spacing is 1.5 m and concrete is C30. For analysis 1, wall height is 8 m, soil friction angle ϕ= 30º and soil unit weight = 18 kN/m3. For analysis 2, wall height is 12 m, soil friction angle ϕ= 30º and soil unit weight = 18 kN/m3. For analysis 3, wall height is 8 m, soil friction angle ϕ= 35º and soil unit weight = 19 kN/m3. For analysis 4, wall height is 12 m, soil friction angle ϕ= 35º and soil unit weight = 19 kN/m3. For analysis 5, wall height is 8 m, soil friction angle ϕ= 40º and soil unit weight = 20 kN/m3. For analysis 6, wall height is 12 m, soil friction angle ϕ= 40º and soil unit weight = 20 kN/m3. The results of the analyzes are compared with the values of horizontal displacement, moment and shear force for pile.
In seventh chapter of study, there are some comments, results and suggestions. With compare Zemank and Sap2000, there is almost the same results for displacements, bending moments and shear forces for pile. With compare Zemank and Plaxis, the results are somewhat different. The small differences are due to the acceptence made during the solution phase. The results of displacements for Terzaghi- Peck and Tschebotarioff solutions by using Zemank and SAP2000 are close which are calculated by Plaxis. The results of bending moments by using Zemank and SAP2000 are smaller which are calculated by Plaxis. This difference is due to modelling of soil. The results of shear forces for Terzaghi- Peck and Tschebotarioff solutions by using Zemank and SAP2000 are close which are calculated by Plaxis. When soil friction angle increase, horizontal displacements of pile are decrease.
For future studies, there are some suggestions. "Zemank" program modelling earth pressure for one soil layer, program can be developed for multiple of soil layers. "Zemank" program calculates only static case, program can be developed for siesmic case with added siesmic parameters. In this study, parametric study is made for soil friction angle ϕ and soil unit weight . Cohesion value c can be used other studies.