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

Yıl 2020, Cilt: 35 Sayı: 3, 1353 - 1368, 07.04.2020

Mehmet Ulker

https://doi.org/10.17341/gazimmfd.528145

Öz

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

Öz

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.

Anahtar Kelimeler

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

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