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Describes a set of numerical techniques which implement the rate‐dependent multi‐mechanism deformation (M‐D) constitutive model for rock salt in a finite element code for use in three‐dimensional, finite strain simulations of creep closure in deeply buried salt excavations. Presents essential details of the numerical implementation. The constitutive model is exercised in a three‐dimensional closure simulation of a large underground field experiment. Compares results from the simulation against actual closure measurements taken from the experiment.

Creep behavior of concrete at high temperature has become a major concern in building structures, such as factories, bridges, tunnels, airports and nuclear buildings. Therefore, a simple and accurate prediction model for the high-temperature creep behavior of concrete is crucial in engineering applications.

In this paper, the variable-order fractional operator is introduced to capture the high-temperature creep behavior of concrete. By assuming that the variable-order function is a linear function with time, the proposed model benefits from the advantages of both formal simplicity and the physical significance for macroscopic intermediate materials. The effectiveness of the model is demonstrated by data fitting with existing experimental results of high-temperature creep of two representative concretes.

The results show that the proposed model fits well with the experimental data, and the value of order is increasing with the increase of the applied stress levels, which meets the fact that higher stress can accelerate the rate of creep. Furthermore, the relationship between the model parameters and loading conditions is deeply analyzed. It is found that the material coefficients are constant at a constant temperature, while the order function parameters are determined by the applied stress levels. Finally, the variable-order fractional model can be further written into a general equation of time and applied stress.

This paper provides a simple and practical variable-order fractional model for predicting the creep behavior of concrete at high temperature.

This dictionary is divided into three parts. The first contains technical terms arranged in groups concerned with the various branches of engineering (e.g. welding equipment, transport, etc.), each item being illustrated. The second part consists of a vocabulary of basic terms not included in the first. The third part consists of indexes in the eight languages covered (English, German, French, Italian, Portuguese, Spanish, Polish and Russian), each being in two parts. Of these the first is the index of terms and the second an index of the illustrations, not giving each term separately, but each illustration which usually occupies a whole page and may show forty or more components.

The purpose of this paper is to present an analysis of the effect of the temperature on the creep deformation during vertical well drilling in salt rocks in selected cases.

The authors performed numerical simulations by Finite Element Method, using non-linear viscoelastic models and weak thermomechanical coupling. The authors evaluated, in selected cases, the effect of temperature during salt rock vertical well drilling. Numerical examples were performed to validate the studies. More specifically, the authors considered the problem of vertical well drilling for oil exploration below these salt layers.

The authors concluded that the biggest reduction in the wellbore closure rate occurs when the wellbore is at low temperature with respect to the rock initial. This is due to two factors, namely, a reduced salt viscous strain rate and the thermal strain contrary to the well radial closure caused by the temperature variation. Beyond the creep effect, the thermal strain also affects the stress in the creep constitutive equation.

With recent oil discoveries in deep water, for example, in the pre-salt, where temperatures are high, the study of the influence of temperature is important, since it contributes to the increase of the creep. The results here presented are relevant, although the engineering aspects of a practical solution for reducing the wellbore displacement based on temperature variation is challenging. Such approach requires cooling mechanisms that delay the heating of the drilling fluid, which is surrounded by rocks at high temperature.

The main contribution of this paper is to present a numerical study, in selected cases, of the effect of temperature on the creep deformation during vertical well drilling in salt rocks, analyzing a possible reduction of these deformations when subjected to a temperature variation.

In literature, previous studies have focused on analyzing rienforced concrete (RC) columns with idealized end conditions when subjected to fire. In nature, full fixity or free rotation at column ends is not attained. Such ends may be considered partially restrained in rotation. This paper aims to shed a new light on the effect of different degrees of rotational restraint on the lateral deformation behavior of slender heated RC columns subjected to non-linear strain distributions produced by a time-dependent temperature history.

To find the strain distribution on the cross section, an iterative technique is adopted using Newton–Raphson method. By introducing a reliable calculation procedure, the lateral deformational behavior is expressed using numerical and searching techniques. A methodology is presented to calculate the effective length factor for RC columns at elevated temperature.

The results of the proposed model showed good agreement with available experimental test results. It was also found that the variation of rotational end restraint level has a considerable effect on the lateral deformation behavior of heated slender RC columns. In addition, the effectiveness and the validity of an analytical model should be verified by simultaneously validating the axial and lateral deformations. Moreover, the effective length factor for heated column is higher than that for the corresponding column at ambient temperature.

This paper shows the impact of different boundary conditions on the behavior of heated slender RC columns. It suggests powerful techniques to determine the lateral deflection and the effective length factor at high temperatures.

Concrete arch structures are commonly constructed for various civil engineering applications. Despite their frequent use, there is a lack of research on the response and performance of concrete arches when subjected to fire loading. Hence, this paper aims to investigate the response and in-plane failure modes of shallow circular concrete arches subjected to mechanical and fire loading.

This study is conducted through the development of a three-dimensional finite element (FE) model in ANSYS. The FE model is verified by comparison to a non-discretisation numerical model derived herein and the reduced modulus buckling theory, both used for the non-linear inelastic analysis of shallow concrete arches subjected to uniformly distributed radial loading and uniform temperature field. Both anti-symmetric and symmetric buckling modes are examined, with analysis of the former requiring geometric imperfection obtained by an eigenvalue buckling analysis.

The FE results show that anti-symmetric bifurcation buckling is the dominant failure mode in shallow concrete arches under mechanical and fire loading. Additionally, parametric studies are presented which illustrate the influence of various parameters on fire resistance time.

Fire response of concrete arches has not been reported in the open literature. The authors have previously investigated the stability of shallow concrete arches subjected to mechanical and uniform thermal loading. It was found that temperature greatly reduced the buckling loads of concrete arches. However, this study was limited to the simplifying assumptions made which include elastic material behaviour and uniform temperature loading. The present study provides a realistic insight into the fire response and stability of shallow concrete arches. The findings herein may be adopted in the fire design of shallow concrete arches.

The purpose of this study is to develop an analytical model that is capable of predicting the behavior of shear endplate beam-column assemblies when exposed to fire, taking into account the thermal creep effect.

An analytical model is developed and validated against finite element (FE) models previously validated against experimental tests in the literature. Major material and geometrical parameters are incorporated in the analysis to investigate their influence on the overall response of the shear endplate assembly in fire events.

The analytical model can predict the induced axial forces and deflections of the assembly. The results show that when creep effect is considered explicitly in the analysis, the beam undergoes excessive deformation. This deformation needs to be taken into account in the design. The results show the significance of thermal creep effect on the behavior of the shear endplate assembly as exposed to various fire scenarios.

However, the user-defined constants of the creep equations cannot be applied to other connection types. These constants are limited to shear endplate connections having the material and geometrical parameters specified in this study.

The importance of the analytical model is that it provides a time-effective, simple and comprehensive technique that can be used as an alternative to the experimental tests and numerical methods. Also, it can be used to develop a design procedure that accounts for the transient thermal creep behavior of steel connections in real fire.

The paper aims to give an insight into the behaviour of reinforced concrete columns during and after the cooling phase of a fire. The study is based on numerical simulations as these tools are frequently used in structural engineering. As the reliability of numerical analysis largely depends on the validity of the constitutive models, the development of a concrete model suitable for natural fire analysis is addressed in the study.

The paper proposes theoretical considerations supported by numerical examples to discuss the capabilities and limitations of different classes of concrete models and eventually to develop a new concrete model that meets the requirements in case of natural fire analysis. Then, the study performs numerical simulations of concrete columns subjected to natural fire using the new concrete model. A parametric analysis allows for determining the main factors that affect the structural behaviour in cooling.

Failure of concrete columns during and after the cooling phase of a fire is a possible event. The most critical situations with respect to delayed failure arise for short fires and for columns with low slenderness or massive sections. The concrete model used in the simulations is of prime importance and the use of the Eurocode model would lead to unsafe results.

The paper includes implications for the assessment of the fire resistance of concrete elements in a performance‐based environment.

The paper provides original information about the risk of structural collapse during cooling.

A solution algorithm for the transient analysis of bodies undergoing creep under constant or time varying loads is presented. The constitutive equation adopted is of the form: έc=γσm. The finite element formulation is carried out in terms of displacements and creep strains as internal variables. The time discretization is achieved with a trapezoidal time integration scheme. The creep strains are condensed out to give an equation for displacement increments involving a modified stiffness matrix and force vector. A Newton—Raphson iterative scheme is used for the non‐linear creep strain rate‐stress relation, and creep strains are updated at the end of the time step. The algorithm has been implemented in NOSTRUM for two‐dimensional structural and plane continuum problems, with a von Mises type potential function governing the multiaxial creep constitutive relationship. Numerical results are presented.

Previous works in constructing interaction diagrams have only focused on incorporating transient creep strain implicitly in the ultimate limit strain. The present paper aims to use different approaches to define concrete ultimate limit strain (failure strain) envelops at high temperatures for preloaded and unloaded, confined and unconfined, columns during heating are proposed. These approaches are chosen to understand the effect of using different techniques to determine transient creep strain on the resulted N_u–M_u diagrams.

Transient creep strain is included within the concrete ultimate limit strain relationships, implicitly and explicitly, by four different ways, and accordingly, four different failure criteria are suggested. To define the concrete ultimate limit strain, studies are conducted to evaluate the compression strain corresponding to the maximal flexural capacity at elevated temperatures. In the analysis, the thermal and structural analyses are decoupled and, based on the resulted ultimate limit strain, the N_u – M_u diagrams are constructed at different fire exposures.

The validity of the proposed model is established by comparing its predictions with experimental results found in the literature. Finally, comparative calculations regarding interaction diagrams obtained by the proposed model and by other methods found in the literature are performed. It was found that the proposed model predictions agree well with experimental results. It was also found that the suggested approaches, which include simplifications, reasonably predicted the exact column capacity.

The model.