Stochastic Lattice Modelling of the Force-Displacement and Cracking Behaviour of the Steel Reinforced Tie

Darius Zabulionis,Rimantas Kačianauskas,Romualdas Kliukas,Liudas Tumonis,Ona Lukoševičienė

doi:10.1155/2019/6340656

Abstract

The stochastic modelling of the microcracking and the force-displacement behaviour of the tensile steel reinforced tie using the lattice model is presented in the current article. The three-dimension problem of the modelling of the tie is reduced to the two-dimensional so as the main stiffness parameters of the concrete and the reinforcement of the two-dimensional model would be the same as for the three-dimensional. The concrete and steel obey the Hook law. All elastic constants, as well as dimensions of the tie, were assumed as the deterministic quantities except for the critical concrete tensile strains which were treated as a two-dimensional stationary uncorrelated truncated Gaussian random field. The discrete element approach and the explicit integration scheme have been used for the modelling. The estimations of the main parameters of the force-displacement behaviour stochastic process and other statistical indexes were obtained using 72 realization of the force-displacement behaviour of a chosen model. Extra two stochastic realizations of the two different models, as well as three deterministic models, were modelled to compare stochastic and deterministic behaviour of the force-displacement behaviour. The analysis showed that the force-displacement behaviour of the tie under tensile force cannot be treated as a Gaussian stochastic process when the p value is 0.05 at the small displacements and within the interval when the cracking of the concrete is very intensive. However, at the bigger displacements, when the cracking becomes less intensive, the tensile force can be treated as a Gaussian random variable.

Highlights

The cracking and the force-displacement behaviour of the reinforced concrete structures is still under intensive consideration for several decades, see Hegemier, Murakami and Hageman [1], Balevicius and Augonis [2], Choi and Cheung [3], Yankelevsky, Jabareen and Abutbul [4], Stramandinoli and Rovere [5], Morelli et al [6]
The analysis showed that the force-displacement behaviour of the tie under tensile force cannot be treated as a Gaussian stochastic process when the p value is 0.05 at the small displacements and within the interval when the cracking of the concrete is very intensive
As majority phenomenon in nature, the behaviour of the reinforced tie subject to the tensile force is a stochastic phenomenon depending on various random factors: moduli of elasticity, Poison’s ratio, the compressive and tensile strength of the concrete and steel, and the bond between the concrete and the steel rod, etc

Summary

Introduction

The cracking and the force-displacement behaviour of the reinforced concrete structures is still under intensive consideration for several decades, see Hegemier, Murakami and Hageman [1], Balevicius and Augonis [2], Choi and Cheung [3], Yankelevsky, Jabareen and Abutbul [4], Stramandinoli and Rovere [5], Morelli et al [6]. Heterogeneous material is modelled as a web of connecting elements that undertake only axial force and represent particular volume consisting of different materials, said filler and binder, for instance, see Potyondy and Cundall [19], Rojek et al [20], Pilkavicius, Kacianauskas and Norkus [21], Zabulionis et al [22] According to this approach, the elastic constants of the connecting element, mainly only axial stiffness, are calculated by taking into account the interaction of the particles via the matrix and by taking into account different mechanical properties of the materials that constitute the representative volume of the connecting element of the lattice model. An advantage of the lattice method is the ability to model fracture process of the materials, see Kosteski, D’Ambra and Iturrioz [29], Braun and Fernandez-Saez [30]

Methods

Results

Conclusion