Yüzeysel temellerde düşey yatak katsayısı değerlerinin taşıma gücü değerleri ve diğer yöntemler kullanılarak elde edilmesi ve karşılaştırılması
Obtaining and comparing of the vertical modulus of subgrade reaction values for shallow foundations by using bearing capacity values and other methods
Yazar: MUSTAFA TALHA UÇAR
Danışman: PROF. DR. HÜSEYİN YILDIRIM
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

Özet:
Temel tasarımında üst yapıdan gelen yapı yükünün zemin taşıma gücünden büyük olmaması ve oturma değerlerinin sınırlandırılması, sağlanması gereken iki önemli şarttır. Gelişen bilgisayar teknolojisine paralel olarak artık yapı tasarımı bilgisayar desteği ile yapılmakla birlikte yapı analizlerinde kullanılan birçok programda ise yapı-zemin etkileşiminde kullanılan iki önemli parametre; taşıma gücü ve zemin yatak katsayısı değerleridir. Geoteknik mühendisliğinin temel konularından biri olan taşıma gücü değerinin elde edilmesi için birçok farklı yöntem mevcut olmakla birlikte, yatak katsayısı değerinin elde edilmesi hususunda da birçok farklı yöntem mevcuttur. 
Kesme kutusu, serbest basınç ve üç eksenli basınç gibi laboratuvar deneyleri kullanılarak elde edilebilen içsel sürtünme açısı ve kohezyon değerlerini kullanan; Terzaghi (1943), Meyerhof (1963), Hansen (1970) ve Vesic (1975) klasik taşıma gücü yöntemleri, taşıma gücü değeri elde edilmesi için kullanılan en bilinir yöntemlerdendir. Taşıma gücü değeri ayrıca SPT, CPT, plaka yükleme deneyi, presiyometre deneyi gibi arazi deneyleriyle de elde edilebilir. Bu yöntemler haricinde yine arazide uygulanan jeofizik yöntemler ile zemine ait sismik dalga hızlarından çeşitli yaklaşımlar yardımıyla taşıma gücü değerini elde etmek mümkündür.
Yatak katsayısı değerinin tahmini için ise Bowles?a ait zemin türüne göre yatak katsayısı değer aralıklarını veren tablo sıklıkla kullanılır. Bu tahmin yöntemi haricinde yine Bowles?a ait taşıma gücü değerinin 40 katı alınarak elde edilen yatak katsayısı değerlerinin kullanımı da oldukça yaygındır. Yatak katsayısı değerinin elde edilmesi için kullanılabilecek teorik olarak en makul deneylerden biriside plaka yükleme deneyidir. Bu yöntemler haricinde ise yatak katsayısı değeri elde edilmesi için zeminin elastik özelliklerini kullanan; Vesic(1961), Biot(1937) ve Bowles formülleri kullanılabilir. 
Türkiye?nin çeşitli yerlerinde, inşaat işleri için hazırlanan zemin etüt raporlarından elde edilen 50 adet veri kullanılarak yapılan bu çalışma kapsamında taşıma gücü değerleri değişik yöntemlerle elde edilip karşılaştırılmış olup ayrıca bu değerlerden yatak katsayısı değerlerinin elde edilmesi için Bowles?un taşıma gücünden yatak katsayısı bulunmasına yarayan ampirik formülü kullanılmıştır. Zemin elastik özelliklerinden yatak katsayısı değeri tayini için kullanılan Vesic, Biot ve Bowles yöntemlerinde, jeofizik deneylerden elde edilen zemin elastik parametreleri kullanılarak, yatak katsayısı değerleri elde edilmiştir. Bu yöntemler haricinde plaka yükleme deneyi ve standart penetrasyon deneyi verilerinden de yatak katsayısı değerleri belirlenmiş olup tüm bu yatak katsayısı değerleri Bowles?un zemin türüne göre yatak katsayısı değer aralıklarını veren tablosu ile karşılaştırılmıştır.
Yapılan analizler neticesinde klasik taşıma gücü formülleri ile elde edilen taşıma gücü değerlerinin kendi arasında Terzaghi

Abstract:
The main goal of the foundation, the lowest part of a structure, is to transfer the structure loads to the soil on which it is resting. A foundation must have transfers the load throughout soil without overstressing the soil because overstressing the soil can cause excessive settlements or shear failure of the soil. Therefore, it is obvious that in foundation design, the transfer of the superstructure loads to the soil safely is a crucial factor. 
Foundations can be classified with respect to their depth that the foundation with a depth greater than its width is referred as deep foundation, whereas the foundation with a depth lower than its width is referred as shallow foundation. A spread footing can simply explained as an enlargement of a load-bearing column or a wall that makes it possible to spread the load of the structure over a larger area of the soil. If the soil has a low bearing capacity value than the size of the spread footing increase drastically that the required area of the spread footing is become impracticably large that in this case it become more economical to construct a concrete pad, a mat foundation, under the area of the entire structure. 
In geotechnical engineering, bearing capacity value is the capacity of soil to support the loads applied from foundation to the ground. The bearing capacity value of the soil means the value of maximum contact pressure between the foundation and the soil which should not produce shear failure in the soil. Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure; on the other hand, allowable bearing capacity value can be calculated by dividing the ultimate bearing capacity value by a factor of safety.
Nowadays, the design period of structures is mostly accomplished by computer-aided analysis programs due to the development in technology. In these programs, structure-soil relationship is mostly described by the soil bearing capacity value and the value of the modulus of subgrade reaction of the soil which are crucial parameters in foundation design. Not only the bearing capacity values of the soil but also the subgrade modulus of the soil can be determined by various methods.
The study of Prandtl (1920) that inspects the adhesion and inner friction angle properties of metals, inspired Terzaghi (1943), Meyerhof (1963), Hansen (1970) and Vesic (1975)  and they all suggests their formulas, also known as classical bearing capacity methods. These methods, need angle of internal friction and the cohesion values of the soil which can be determined by lab experiments such as shear box test, unconfined compression test or triaxial load test, are the most common ways to obtain bearing capacity values. 
There are also some other ways to obtain bearing capacity value of the soil such as in-situ testing methods. Standard penetration test, conic penetration test, plate load test and pressuremeter test are popular in-situ methods to obtain the soil bearing capacity values of the soil. Geophysical studies, mostly performs to investigate dynamic properties of the soil, can be used to obtain bearing capacity values. Keçeli (2000), Türker (2004), Kurtuluş (2000) and Tezcan et al (2010) methods are common ways to derive the bearing capacity value from the shear wave velocity of the soil by using empirical equations.
Winkler model, where the behavior of the soil is simplified by means of fictitious springs placed continuously under the foundation, is a method to analyze beams and slabs resting on underneath the structure. 
The modulus of subgrade reaction value of the soil, can be thought as a spring constant, is based on this fictitious spring concept. In many computers aided structural analysis program the user has to determine a suitable modulus of subgrade reaction value to represent the soil. To determine this modulus of subgrade reaction value there are several methods using several kinds of data such as elastic properties of the soil or the bearing capacity value of the soil. However, it is not theoretically valid that the modulus of subgrade reaction value is dependent only elastic properties or the bearing capacity value of the soil. 
Modulus of subgrade reaction value can be used to determine the value of the possible differential settlement of the foundation that is also a factor for some design quantities such as bending moments and shear forces in the structure. 
One of the deficiencies of the Winkler model is there will be no differential settlement or bending moments or shear forces in the structure, in disregard of reality, if the Winkler model is used to analyze a uniformly distributed load on a slab. The reason for this deficiency is that in Winkler model, the fictitious springs representing the modulus of subgrade reaction are not related to each other?s.  
On the other hand, Winkler model can be used effectively when analyzing vertical piles or point loaded foundations. Thus, the modulus of subgrade reaction value is still quite popular. 
Bowles?s subgrade reactions table values can be used to determine the value of the modulus of the subgrade reaction with respect to the soil type. Although this method is commonly used to estimate the subgrade reaction values of the soils, bearing capacity values can also be used to determine the modulus of subgrade reaction values. Bowles suggests that modulus of subgrade reaction value can be determined if bearing capacity value is multiplied by forty. Plate load test which is theoretically appropriate to determine the modulus of subgrade reaction value, is an in-situ alternative to obtain vertical modulus of subgrade reaction. There are also some formulas such as Vesic, Bowles and Biot that can be used to obtain modulus of subgrade reaction values by the use of elastic properties of the soil.
In this study fifty different data, based on soil investigations reports from all over the Turkey, are used to determine the relations between the ultimate bearing capacity values which are determined by various methods, are compared. The modulus of subgrade reaction values are obtained from these bearing capacity values by the use of Bowles empirical formula. Using the same data, the modulus of subgrade reaction values are also obtained from other methods such as Vesic, Bowles, Biot formulas, plate load test and SPT values. All these modulus of subgrade reaction values are compared with the Bowles?s modulus of subgrade reaction table values.   
According to analysis of the data, it is noticed that the results of the classical bearing formulas are mostly alike and the values has a pattern of Terzaghi < Meyerhof < Hansen < Vesic. Modulus of subgrade reaction values, obtained by Bowles empirical formula, are compatible with the Bowles table values. 
Not only the bearing capacity values obtained from Tezcan et all method fit with the mean values of classical bearing capacity methods, but also the modulus of subgrade reaction values derived from Tezcan et al method are compatible with Bowles?s table values. Therefore, for geophysical data, Tezcan et al method is the most suitable method for both bearing capacity values and the modulus of subgrade reaction values.
Like Tezcan et al method, bearing capacity values obtained from Bowles SPT method fits with the mean values of classical bearing capacity methods better than the other SPT method. Moreover, subgrade reaction values obtained by Bowles SPT method are compatible with Bowles table values, therefore; Bowles SPT method is the most suitable method for both bearing capacity values and the modulus of subgrade reaction values based on SPT data.
The modulus of subgrade reaction values, which are obtained by the elastic properties of the soil, are much higher than the Bowles?s table expected values. The reason of this higher modulus of subgrade reaction values is that the modulus of elasticity values calculated from geophysical data are also higher than expected values. Therefore, this study proves that the modulus of subgrade reaction values, derived from geophysical data on the basis of the theory of elasticity, are not suitable for the Vesic, Biot and Bowles formulas which can derive modulus of subgrade reaction values from elastic properties of the soil. 
A foundation with a length of three meters, a width of three meters and a height of fifty centimeters is modeled for different modulus of subgrade reaction values in SAP2000. Analysis results proves that the modulus of subgrade reaction value has a little effect on moment values of the foundation which means it has also a little effect on design of the foundation. 
The goals of this study are to understand the concepts of the soil bearing capacity and the modulus of subgrade reaction generally and investigate the possible ways to obtain the soil bearing capacity and modulus of subgrade reaction values. Thus, this paper does not probe the theory of the soil bearing capacity and the modulus of subgrade reaction nor the calculation analysis of these values. Therefore, this study is much more like a guide to effective ways to obtain the soil bearing capacity and modulus of subgrade reaction values based on soil investigation data.
In Conclusion, this study proves that it is possible to guess the modulus of subgrade reaction value from Bowles table of modulus of subgrade reaction values with respect to soil type. In addition, if the soil investigation report has enough data to obtain soil bearing capacity values from classical bearing capacity formulas, it is also possible to use bearing capacity values derived from Terzaghi, Meyerhof, Hansen and Vesic methods to obtain modulus of subgrade reaction value by the use of Bowles empirical formula. On the other hand if the soil investigation report has only SPT data, it is possible to check Bowles table values by the use of Bowles SPT and Bowles empirical formula. Moreover, if the soil investigation report has only geophysical data, it is possible to check Bowles table values with the Tezcan et al bearing capacity values by the use of Bowles empirical formula.