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This paper presents mesoscale thermo-mechanical analyses of plain (unreinforced) concrete based on the discrete element method (DEM). The proposed discontinuum modelling strategy represents the aggregates and matrix as a system of deformable polyhedral blocks, interacting along their boundaries. The nodal velocities of each block are calculated via the explicit integration scheme of DEM, and contact stresses are computed based on the relative contact displacements of the adjacent blocks. To better predict the thermo-mechanical behaviour of concrete, fracture energy-based contact constitutive models are implemented by considering temperature dependency at the zone and contact properties. First, the discrete meso models are tested under uniaxial compression loading at room temperature. Then, transient thermo-mechanical tests are performed considering different load levels. The results of the computational models are compared with the macroscopic response quantities of concrete obtained from the available experimental studies in the literature. The results indicate that the developed DEM framework predicts the complex mesoscale thermo-mechanical response history and the typical damage progression observed in concrete. Furthermore, the fracture patterns, crack propagation with temperature, and the differential thermal expansion phenomena are studied in detail. © 2020 Elsevier Ltd

Department of Civil & Infrastructure Engineering

World University root node

Engineering Fracture Mechanics

A meso-scale discrete element method framework to simulate thermo-mechanical failure of concrete subjected to elevated temperatures

This paper presents a 2-D finite element (FE) based micro modelling framework for thermo-mechanical response history analysis of solid brick masonry structures subjected to fire. The 2-D FE framework considers geometric and material nonlinearities, and transient states of strain in conjunction with the temperature-dependent material properties. Material nonlinearity within the 2-D FE model is considered by the temperature-dependent total strain rotating crack model. The FE framework is validated against the thermo-mechanical response of a half-scale masonry wall subjected to one-sided fire exposure, and it is observed that the predictions of the FE framework are reasonably accurate. Utilizing the validated FE framework, thermo-mechanical response history characterization is performed on a full-scale masonry wall subjected to one-sided fire exposure. Critical physical phenomena which include thermal bowing, heat diffusion, unit-mortar thermo-mechanical interaction, cracking and stress profiles within the masonry structures are studied intricately. Furthermore, thermo-mechanics within representative volumes enclosing unit as well as mortar and their correlation with the global thermo-mechanical response is studied. Such 2-D micro-scale thermo-mechanical computations on masonry walls followed by a detailed discussion on their thermo-mechanics are one of the novel features of the present study. It is observed that thermal bowing resulted from a complex interaction between thermal dilation and cracking and crushing in the mortar and unit within the masonry structure. © 2020 Elsevier Ltd

Fulltext

Engineering Structures

Finite element based micro modelling of masonry walls subjected to fire exposure: Framework validation and structural implications

This article develops a temperature-dependent distributed plasticity model in a direct stiffness method (DSM) based formulation for coupled nonlinear thermo-mechanical analysis of steel space frames. The developed framework considers geometric and material nonlinearities, and performs coupled thermo-mechanical analysis by a two-level spatial discretization strategy. An isotropic hardening plasticity in combination with the von Mises yield criterion is considered, where the temperature-dependent yield function is derived from the stress-strain relations of Eurocode 3. The effects permanent plastic strains, large deformations and temperature-dependent material properties are directly incorporated in to the force deformation relations derived in a DSM based setting. Such a DSM based framework in conjunction with the distributed plasticity model facilitates higher computational efficiency. To ensure full coupling between mechanical and thermal solvers, thermodynamically consistent plastic heating term is added to the energy balance of the system. Also, connection flexibility is accounted for by developing a zero-length spring element integrated with 1-D beam-column elements. Five numerical examples are presented to demonstrate the efficacy of the developed framework. Within the numerical investigation, the importance of plastic heating coupling in the context of macro modelling based structural fire analysis of steel structures is quantified and the results indicate that such a coupling can be ignored in such macro scale structural fire computations. © 2019 Elsevier Ltd

Fire Safety Journal

Distributed plasticity model for analysis of steel structures subjected to fire using the direct stiffness method

High strength concrete (HSC) is predominantly used in high-rise reinforced concrete buildings. While excellent from strength point of view at room temperature, HSC is known to be prone to spalling, when exposed to high temperatures (e.g., in case of a fire). Fire resistance evaluated from building codes (CEN in Design of concrete structures. Part 1–2: general rules—structural fire design, Eurocode-2, Brussels, 2004; Bureau of Indian Standards in Indian code of practice for fire safety of buildings (General): details of construction code of practice. IS-1641, New Delhi, 1989) [1, 2] and simulation-based studies typically does not consider the effects of spalling. To alleviate these difficulties, a 2-D hydrothermal model has been developed for predicting the extent of spalling in HSC. The numerical model evaluates pore pressure inside the concrete as a function of time using the laws of thermodynamics. Spalling is said to occur when the pore pressure built-up within concrete exceeds its tensile strength. The model depends on several parameters such as permeability, initial moisture content, and thermomechanical properties of concrete. All of these parameters are considered by the model through a two-way coupling between the pore pressure analysis and thermal analysis, both implemented using the finite element method. Validity of the numerical example is established by comparing the spalling predictions obtained from the numerical model against standard experiments available in the literature. Parametric studies have also been performed using the numerical model to quantify the effects of model parameters such as permeability, grade of concrete, and type of fire scenario on the prediction of spalling. © 2019, Springer Nature Singapore Pte Ltd.

Lecture Notes in Civil Engineering

Numerical modeling of spalling in high strength concrete at high temperature

This article develops a fully coupled hydro-thermo-mechanical formulation based on the direct stiffness method for analysis of steel and reinforced concrete structural space frames. The superiority of the developed formulation lies in developing the direct stiffness method for fire analysis, which enables use of a much coarser spatial mesh when compared to existing fire analysis frameworks. Effects of temperature-dependent material properties, damage due to fire and pore pressure, nonlinear thermal gradients, and large deformations of structural members are directly integrated into the stability and bowing functions in the construction of the member stiffness matrix. This alleviates the need to perform element-level numerical quadrature, typically required by all existing finite element–based approaches. Full coupling between the pore pressure, thermal and mechanical solvers is considered through a two-level spatial discretization strategy with a staggered scheme for the numerical solution procedure. Five numerical examples are presented to demonstrate the accuracy and efficacy of the developed formulation in analysis of steel and reinforced concrete structural members and frames. © The Author(s) 2018.

Advances in Structural Engineering

Fully coupled multi-physics nonlinear analysis of structural space frames subjected to fire using the direct stiffness method

This article presents a framework based on the direct stiffness method for nonlinear thermo-mechanical analysis of reinforced concrete plane frames subjected to fire. It accounts for geometric nonlinearity, material nonlinearity, and nonlinear thermal gradients and incorporates two-way coupling between thermal and structural analyses. Force deformation relations are derived from classical Euler–Bernoulli beam theory and are expressed in terms of temperature-dependent stability and bowing functions. This is one of the unique features of proposed framework and allows a coarser spatial discretization to be used as opposed to full finite element–based approaches (such as SAFIR [registered trademark of the software SAFIR developed at the University of Liege]). The cross sections of the structural members are discretized with two-dimensional meshes for thermal analysis while structural analysis utilizes a line element based on direct stiffness method. Equivalent bending and axial rigidities of this line element are computed using several fibers along the length of the member, passing through the nodes of the two-dimensional mesh used for thermal analysis. The total strain at each fiber is decomposed into mechanical, thermal, creep, and transient thermal components. A discrete damage parameter is introduced at fiber level to ensure irreversibility of crushing and cracking in accordance with relevant constitutive laws. Five numerical examples are presented to demonstrate the accuracy and efficacy of the developed framework with respect to theoretical solutions, experimental observations, and some of the existing macro- and micro-finite element–based approaches. It is found that the developed framework can predict the response of reinforced concrete structures very well. © 2017, © The Author(s) 2017.

Nonlinear analysis of reinforced concrete plane frames exposed to fire using direct stiffness method

In this paper, a computationally efficient integrated frame-work is developed for coupled thermo-mechanical analysis of 3D frames. It can account for physical phenomena like large deformations, temperature dependent material degradation, permanent plastic deformations and fire induced spalling which are prevalent at elevated temperatures. The developed frame-work utilizes three way sequential coupling between thermal, mass transport and structural analysis. A two level discretization scheme is incorporated where 1D beam column elements are utilized for structural analysis, the cross-section of these beam-column elements are further discretized into matrix of segments. Aforementioned strategy entails sequential coupling of effects of non-uniform temperature and pore pressure across the cross-section into structural analysis. Subsequently structural analysis is performed with an updated Lagrangean based formulation with force deformation relationships deduced form classical Euler-Bernoulli beam column theory. Critical physical phenomena like cracking, crushing, spalling and transient states of strain in case of concrete and yielding in case of steel are duly accounted. Cross-sectional reduction due to spalling are accounted for by replacing the spalled segments with void segments in the subsequent time steps. Numerical examples of steel and concrete structures subjected to various fire scenarios are presented to demonstrate the accuracy of developed framework. Furthermore, progressive collapse analysis is carried out for concrete and steel 3D subjected to fire. © 2017 The Authors. Published by Elsevier Ltd.

Procedia Engineering

Efficient Three Dimensional Nonlinear Thermo-Mechanical Analysis of Structures Subjected to Fire

A novel coupled framework for analysis of reinforced concrete (RC) and steel planar frames subjected to fire is developed with three-way coupling between heat transfer, mechanical deformations and pore pressure build-up. Structural members are discretized in space using a two-level scheme where the mechanical solver utilizes 1D line elements, and the thermal and the pore pressure solvers work on 2D finite element (FE) meshes for each sub-span used by the mechanical solver. Such a strategy enables consideration of effects of large deformations, temperature-dependent material properties (thermal, moisture transport and mechanical), and spalling. None of the earlier developed frameworks considered a three-way coupling between mechanical, thermal and pore pressure solvers without employing a full-fledged 3D FE scheme. A matrix method type approach, developed herein, enables modeling of the three main physical processes taking place in RC members during fire without the need to consider full-fidelity 3D FEM. Several numerical examples are presented to demonstrate the accuracy and applicability of the developed framework in fire analysis of normal and high strength RC and steel structures. © 2017 Elsevier Ltd

Computers and Structures

An integrated framework for nonlinear analysis of plane frames exposed to fire using the direct stiffness method

Instability of pile foundations due to liquefaction of surrounding soil is considered as one of the vital cause of its failure. Many case studies are available, where pile foundations are subjected to severe damage due to liquefaction even though designed with good factor of safety. Assuming incorrect failure mechanism in design is probable reason for these failures. Earlier studies idealize pile as a column, and a buckling mode of failure is postulated as a failure mechanism. Lateral spreading during liquefaction can cause large lateral loads on the pile and induce a different failure mode. This is the focus of the present study. Here pile is idealized as a beam-column and failure analysis is performed against buckling as well as flexural instabilities. By considering flexural as well as buckling instabilities, a simplified approach to quantify the critical axial load on pile is formulated in the present paper. A case study is also presented to demonstrate the calculation of critical axial load. Results from the case study infer that, at certain level of lateral spreading piles fail in yielding rather than buckling, which needs to be given due consideration in the design of pile foundations in liquefiable soils. © ASCE.