Doygun kumların statik ve dinamik davranışlarının bünyesel modellenmesine yönelik geliştirilen sayısal formülasyonların karşılaştırmalı çalışması: Yeni bir pekleşme kuralı önerisi

Günümüze kadar pek çok çalışma kumların bünye davranışlarını modellemek üzere teoriler önermiş, klasik deneylerle bu teoriler belli ölçüde doğrulanmıştır. Kumların gözlenen tipik gerilme-şekil değiştirme davranışını yakalayabilen teoriler, sonrasında geliştirilen sayısal yazılımlara aktarılarak birçok geoteknik mühendisliği probleminin çözümünde kullanılmıştır. Bu hedeften uzaklaşmadan, halen yeni modeller geliştirilmekte, kaydedilen ilerlemeler daha çok ilgili sayısal formülasyonların en efektif nasıl integre edileceği ya da en geniş yelpazede zemin davranışının daha az model parametresiyle nasıl modelleneceğine odaklanmaktadır. Bu çalışmada suya doygun kumların statik ve dinamik davranışları teorik olarak modellenmiştir. Genelleştirilmiş Plastisite Teorisi kapsamında, modelde kullanılan bir akma ve potansiyel yüzeyiyle yapılan analizler, hiçbir yüzey tanımı yapmadan alınan analiz sonuçlarıyla karşılaştırılmıştır. Kumlarda elastik ve plastik davranışları ayıran ve plastik deformasyonların hesabında kullanılan yüzey fonksiyonlarına olan ihtiyaç burada sorgulanmıştır. Çalışmada önce kum zeminin plastik davranışı birim vektörlerle hesaplanmıştır. Ardından birim vektörlerin integrasyonu ile akma yüzeyi ve potansiyel fonksiyonu çıkartılmış, zemine ait bünye ilişkileri, üç eksenli deney simülasyonlarıyla, iki farklı formülasyon için karşılaştırmalı olarak sunulmuştur. Çalışmanın ikinci bölümünde, yüzey tanımlı formülasyonda kullanmak üzere yeni bir pekleşme kuralı geliştirilmiştir. Beraberinde önerilen yeni bir interpolasyon kuralı ile de plastik yükleme modülü güncellenmiş ve gevşek kumların sıvılaşma davranışı yeniden modellenmiştir. Model sonuçları mevcut statik ve dinamik üç eksenli deneylerle doğrulanmıştır.

Anahtar Kelimeler:

Bünye modellemesi, genelleştirilmiş plastisite, kumlar, statik ve dinamik davranış, pekleşme kuralı

Comparative study of numerical formulations developed for constitutive modeling of static and dynamic behavior of saturated sands: A newly proposed hardening law

To date, many studies have proposed theories to model the load-induced behavior of sands which have been verified, to some extent, by classical experiments. Theories that can capture the typical stress-strain relationship of sands were then transferred into numerical softwares used in the solution of many geotechnical engineering problems. Without ever moving on from this goal, new models are still being developed, and the progress that has been made thus far now focuses more on how to integrate relevant numerical formulations in the most effective manner or to model the broadest range of soil behavior with fewer model parameters. In this study, the static and dynamic constitutive behaviors of saturated sands are modeled. Within the scope of the Generalized Plasticity Theory, analyses conducted by using a flow and a potential surface in the model are compared with the results obtained without any reference to a surface definition. The need for including such surface functions, which distinguishes the elastic behavior from that of the plastic behavior of sands and which are used to calculate plastic deformations, is questioned here. In this research, firstly the unit vectors for loading and plastic flow directions are defined and the static and dynamic behaviors of sands are calculated. Then, yield and potential surfaces are derived by integrating these unit vectors and the constitutive relations of sand are presented comparatively for the two formulations in terms of a number of triaxial test simulations. In the second part of the study, a new hardening law is proposed to be utilized within the formulation with the surface definitions. The plastic loading modulus is also updated with a newly proposed kinematic interpolation rule and the liquefaction behavior of loose sands is remodeled. The model results are subsequently verified with the static and dynamic triaxial tests.

Keywords:

Constitutive modeling, generalized plasticity, sands, static and dynamic behavior, hardening law,

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