Zeminlerin endeks ve mukavemet özelliklerinin istatistiksel analizi

Abstract

Bu çalışma, 1972-92 yılları arasında ÎTÜ Zemin Mekaniği Laboratuvarı «nda yapılmış olan çeşitli deneylere ait sonuçların bir veri bankası oluşturacak şekilde biraraya getirilmesini ve deney verilerinin istatistiksel anali2İni içermektedir. Çalışmanın ilk bölümünü deney sonuçlarının toplanması oluşturmaktadır. Deney verileri daha sonra alt gruplara bölünerek her grup için yapılan istatistiksel analis kapsamında zeminlerin endeks ve mukavemet öselliklerine ait istatistiksel parametreler ve olasılık dağılım fonksiyonları belirlenmiştir. Dağılım modellerinin uygunluğu Kolmogorov- Smirnov testi ile incelenmiş ve birçok semin öselligindeki değişkenliğin normal yada lognormal dağılımla açıklanabile ceği saptanmıştır. Çalışmanın son bölümünü korelasyon ve regresyon analisi oluşturmaktadır. Bu bağlamda seminlerin mukavemet öcellikleri ile endeks ösellikleri arsında korelasyon türü ilişkiler irdelenmiş ve korelasyon matrisleri belirlenmiştir. Bir sonraki aşamada, semin değişkenliğinin temel bileşenleri nin belirlenmesi için faktör analisi yapılmıştır. Son olarak, seminlerin mukavemet ösellikleri ile basit endeks öselliklerinin ilişkilendirilmesi amacıyla regresyon analisi yapılarak çeşitli regresyon eşitlikleri elde edilmiş ve bunların uygunluğu ve anlamlılığı çeşitli istatistiksel yöntemlerle belirlenmiştir.

The application of statistical and probabilistic concepts in r.ieotechnical engineering has been the concern of many researchers in recent decades. This is not so surprising especially when the existence of uncertainties in soil engineering is considered. This fact builds up the main reason in using probabilistic approaches in geotechnical problems. The variability of physical characteristics determining the mechanical behaviour of soils does not permit a precise system and mathematical modelling of soil behaviour. This variability is attributable to the random characteristics of natural phenomena during deposition, physical changes during exploration and measurement- errors during testing. As a result, considering the physical characteristics of soils as random variables will be a proper assumption which makes the way to probabilistic approaches. If also the actions, loads etc. are taken as random variables, risk analysis and safety factor calculations will also be possible. In geotechnical engineering, an important default in utilising deterministic approach is that the uncertainties existing in soil properties can not be taken into account except the safety factor. Deterministic methods, formulations and modellings, by definition, are based on some assumptions and idealised conditions. So it can be said that deterministic approaches must be questionable. In development of engineering designs, decisions are often required regardless of the state of quality of inf'ormatio n * n d t h u s, mu s t b e f o r ıru j late d u n d e r c o n d i t i o n s of uncertain! ty in the sense that the consequences of a given decision can't be determined with complete confidenc In other words, there exists a finite amount of risk associated with every engineering decision. A con ventional deterministic design procedure may not adress the problem adequately. From the above discussion, it is clear that the application of probability concepts in geotechnical problems is not only desirable but necessary for a systematic treatment of the uncertainties existing. If properly used, probability concepts may help to quantify experience or judgmental information thus filling the gap between the deterministic and subjective approaches. As it has been mentioned before, considering a variable as a randomly behaviouring parameter makes the probabilistic analysis of the variable possible. So it is obvious that mathematical description of the variable will be necessary for the statistical evaluation. A random variable can be described mathematically by a distribution model. By proposing a distribution model the randomness character of the variable can be represented in the form of some probability distribution function. For the appropriate probabilistic description of a random variable, some parameters or statistics need to be evaluated or estimated on the basis of a set of observed data obtained from a population. Among the most important statistical parameters are the mean which denotes the average or expected value of the random variable and the standart deviation which represents the dispersion of the variable with respect to the mean value. The mean value and variance ( square of the standart deviation ) can be interpreted as, respectively, the centroidal distance and the central moment of inertia of the density function. For most engineering problems, the absolute dispersion about the mean value may not be as important as the ratio of degree of dispersion to the mean value. Hence the coefficient of variation which is the ratio of standart deviation and mean value, is often preferred.