Constitutive Modeling of Monotonic Behavior of Clays: Mathematical Formulation, Numerical Implementation and Experimental Verification

Year 2020, , 361 - 369, 01.06.2020

Mehmet Barış Can Ülker

https://doi.org/10.2339/politeknik.516345

Abstract

Foundations constitute a significant part of the design of civil engineering systems. Geotechnical considerations are particularly important in identifying the conditions leading to instability of shallow and deep foundations under various loadings. In the case the foundation layer is clay, one should identify the conditions leading to failure of clay soil upon loading. The most common way of doing so is to theorize the constitutive behavior of the soil using mathematical equations. In this study, constitutive modeling of clays under monotonic loadings is presented using the Generalized Plasticity Theory. Numerical formulation is summarized in terms of governing equations which are solved for each load step by an explicit integration method which is implemented into a computer program. Elasto-plastic constitutive matrix is derived based upon the inversion of strain-stress relationship without using a yield or a potential function in the model which is used to get the stress-strain incremental relationship. Plastic strains are then calculated using a non-associative flow rule. Subsequently, a number of drained and undrained strain-controlled triaxial tests are simulated to verify the model and its implementation. The related tests are also simulated using the well-known modified Cam Clay model to highlight the capabilities of the Generalized Plasticity model. Simulation results demonstrate the effectiveness and the capability of the model to capture static behavior of normally and overconsolidated clays.

Keywords

Clays, constitutive modeling, generalized plasticity, monotonic loading, numerical analysis

Constitutive Modeling of Monotonic Behavior of Clays: Mathematical Formulation, Numerical Implementation and Experimental Verification

Abstract

Foundations constitute a significant part of the
design of civil engineering systems. Geotechnical considerations are
particularly important in identifying the conditions leading to instability of shallow
and deep foundations under various loadings. In the case the foundation layer
is clay, one should identify the conditions leading to failure of clay soil upon
loading. The most common way of doing so is to theorize the constitutive
behavior of the soil using mathematical equations. In this study, constitutive
modeling of clays under monotonic loadings is presented using the Generalized
Plasticity Theory. Numerical formulation is summarized in terms of governing
equations which are solved for each load step by an explicit integration method
which is implemented into a computer program. Elasto-plastic constitutive
matrix is derived based upon the inversion of strain-stress relationship
without using a yield or a potential function in the model which is used to get
the stress-strain incremental relationship. Plastic strains are then calculated
using a non-associative flow rule. Subsequently, a number of drained and
undrained strain-controlled triaxial tests are simulated to verify the model
and its implementation. Simulation results demonstrate the effectiveness and
the capability of the model to capture static behavior of normally and
overconsolidated clays.

Keywords

Clays, constitutive modeling, generalized plasticity, monotonic loading, numerical analysis

References

• [1]. Balasubramaniam AS, Chaudhry AR. “Deformation and strength characteristics of soft Bangkok clay”, ASCE J. Geotech. Eng. Div., 104 GT9: 1153-1167, (1978).
• [2]. De Borst R. and Heeres OM, “A unified approach to the implicit integration of standard, non-standard and viscous plasticity models”, Int. J. Numer. Anal. Mthd Geomech., 26: 1059-1070, (2002).
• [3]. Henkel DJ., “The effect of overconsolidation on the behaviour of clays during shear”. Geotechnique, VI: 139-150, (1956).
• [4]. Pastor M., Zienkiewicz OC, Leung KH., “Simple model for transient soil loading in earthquake analysis: II. Non-associative models for sands”, Int. J. Num. Anal. Mthd. Geomech., 9: 477-498, (1985).
• [5]. Pastor M., Zienkiewicz OC., “A generalized plasticity hierarchical model for sand under monotonic and cyclic loading”, Proceedings of the 2nd Int. Conf. on Num. Models in Geomech., 31 March-4 April; Ghent, Belgium: M. Jackson and Son Pub., 131-150, (1986).
• [6]. Pastor M, Zienkiewicz OC, Chan AC., “Theme/feature paper: Generalized plasticity and the modeling of soil behavior”, Int. J. Numer. Anal. Mthds Geomech., 14: 151-190, (1990).
• [7]. Rahman MS, and Ulker MBC., “Modeling and Computing for Geotechnical Engineering: An Introduction”, CRC Press-Taylor & Francis, ISBN 9781498771672, Boca Raton, NJ, (2018).
• [8]. Tatlioglu E., Ulker MBC, Lav A., “Effect of mean stress dependency of elastic soil moduli on the constitutive behavior of sand through UBCSAND”, Proc. 26th European Young Geotechnical Engineers Conference, Sept. 11-14, Graz, Austria, (2018).
• [9]. Ulker MBC., “Constitutive modeling of static behavior of clays using the generalized plasticity theory”, Proc. 16th National Soil Mechanics and Foundation Engineering Conference, October 13-14, Atatürk University, Erzurum, (2016).
• [10]. Ulker MBC, “A new hardening interpolation rule for the dynamic behavior of soils using generalized plasticity framework”, Proc. of the 19th Int. Conf on Soil Mechanics and Geotech. Engg. (ICSMGE), 17-22 Sept., Seoul, South Korea, (2017).
• [11]. Zienkiewicz OC, and Mroz Z., “Generalized plasticity formulation and applications to geomechanics”, Desai CS, Gallagher RH, editors, Mechanics of Engineering Materials. Wiley; Ch. 33: 655-679, (1984).
• [12]. Zienkiewicz OC, Leung KH, Pastor M., “Simple model for transient soil loading in earthquake analysis: I. Basic model and its application”, Int. J. Numer. Anal. Methods Geomech., 9: 453-476, (1985).