Dirichlet Series Creep Function for Aging Concrete

Bažant, Zdeněk P.; Wu, Spencer T.

doi:10.1061/jmcea3.0001741

Cited by 76 publications

(17 citation statements)

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“…The least squares method can be applied to obtain the values of the 𝐷𝐷 𝜇𝜇 functions. To this end, the values of the retardation time 𝜏𝜏 𝜇𝜇 , the age at loading 𝑡𝑡 ′ and the time increment 𝑡𝑡 − 𝑡𝑡 ′ must be chosen properly to ensure both that the system is not ill-conditioned, and that the solution has good accuracy (Bazant and Wu, 1973). The value of 𝑚𝑚 is a function of the time interval for which the viscoelastic response is desired.…”

Section: Constitutive Laws Of the Materials (A) Concretementioning

confidence: 99%

Soil-structure interaction with time-dependent behaviour of both concrete and soil

Alexandre

Mansur

Maria³

2022

Lat. Am. j. solids struct.

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As the consideration of soil-structure interaction is increasingly being incorporated into design practice, there is a need for solutions that consider the most relevant aspects of the behaviour of both the concrete and the soil, some of which are time-dependent. The present work introduces a model that suits both the structure and the foundation -including the supporting soil -allowing the coupled analysis of hardening on cure, creep, shrinkage and cracking of concrete, and consolidation of soil. Both the structure and the foundation are modeled as one-dimensional finite elements. The timedependent behaviour of the concrete and soil is modeled using Kelvin chains. For the structural elements, a mixed finite element formulation is used. Validation tests were conducted in the proposed modeling, comparing its results with available experimental and analytical data. The study of a reinforced concrete continuous beam supported by foundations on consolidating clay considering the time-dependent behaviour of the materials showed considerable changes in the effects of the soil-structure interaction.

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Section: Constitutive Laws Of the Materials (A) Concretementioning

confidence: 99%

Soil-structure interaction with time-dependent behaviour of both concrete and soil

Alexandre

Mansur

Maria³

2022

Lat. Am. j. solids struct.

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“…The method proposed by Gilbert is modified in this paper as significant improvement of computational efficiency can be obtained if the compliance function J ( t , t ′) which reflects the time evolution of strain in a creep test at the unit stress level is approximated by a Dirichlet series corresponding to a Kelvin rheological chain. The expressions for S i can be derived for example, based on the Dirichlet series approximation The analysis is performed by converting the integral type constitutive creep law to an equivalent rate‐type creep law by incorporating Dirichlet series in which the effects of the stress history can be taken into account by using internal variables that are updated after each step . The rate‐type law is beneficial in the solution of structural problems by allowing an efficient and exact integration of the stress history using only a limited number of history variables.…”

Section: Numerical Modelingmentioning

confidence: 99%

Influence of long‐term creep on prestressed concrete beams in relation to deformations and structural resistance: Experiments and modeling

Reybrouck

Mullem

Taerwe

et al. 2020

Structural Concrete

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Realistic structural models incorporating the time‐dependent effects of concrete are essential in order to make accurate predictions of the time‐dependent deflections at any time of the service life. Experimental databases are used to calibrate and validate existing models for creep and shrinkage available in international standards. However, extensive research campaigns on large‐scale prestressed beams are scarce. In 1967–1985, a research program comprising a unique set of long‐term experimental data on concrete beams was conducted in joint collaboration with four Belgian research institutes to determine the influence of creep and shrinkage on the long‐term behavior of reinforced and prestressed concrete members. The main aim of the final part of the research campaign was the determination of the long‐term behavior of prestressed and partially prestressed beams subjected to permanent loads, considering the influence of the magnitude of the loads, the degree of prestressing, the shape of the cross‐section, the type of prestressing and the stress conditions. This paper reports on the obtained unique set of long‐term tests. Additionally, also information related to the creep and shrinkage data of prisms and the results of the static tests in a four‐point bending configuration until failure at the age of 28 days and 5 years are presented in this paper. The measurements of the prestressed members are compared with a simplified calculation method based on the direct stiffness method, which accounts for aging, creep, and shrinkage. The proposed simplified calculation model allows fast and accurate predictions of strains, stresses, and deflections as a function of time. The results show that the direct stiffness method in combination with the current models of EN1992‐1‐1 and fib Model Code 2010 can predict the long‐term behavior of concrete beams in good agreement with the available experimental data. The research allows to develop more accurate calculation guidelines with respect to the evolution of deflections, concrete deformations and stresses of prestressed beams as function of the prestress‐degree, shape of the cross‐section, and the type of prestressing.

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“…Based on the formulation derived by [34], the biaxial creep strain tensor given by the integral of Eq. ( 4) is determined through a fitted series of Dirichlet as…”

Section: Creepmentioning

confidence: 99%

“…Also, considering the main goal of this work-evaluate the influence of time-dependent strains in the nonlinear shear structural response-MC90 expressions are acceptable and will not affect the main conclusions related to shear behavior. The approximation of the Dirichlet series is performed by means of the hidden variables formulation [34]; constants k i set as 10 -i (k 1 = 0.1, k 2 = 0.01; k 3 = 0.001) and 3 series are considered (m = 3), which does not require the storage of all previous stress states for the determination of the creep strain increment in a time step. The algorithm used to compute creep strains through a Dirichlet series is described in detail in Annex A.…”

Section: Creepmentioning

confidence: 99%

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Influence of time-dependent restrained strains in the shear response of RC frames

2016

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The final publication is available at Springer via http://dx.doi.org/10.1617/s11527-016-0875-8Time-dependent strains, when restrained, can lead to important tensile forces and damage, affecting, among other aspects, the shear response and ultimate load carrying capacity of shear-critical RC frames. This paper presents a detailed study of this problematic by means of an extension of a shear-sensitive fibre beam model to time dependent behaviour of concrete. The model is firstly validated with experimental tests on diagonally pre-cracked beams under sustained loads. From these analyses, the contributions of shear distortions and bending curvatures to the total long-term deflection of the beams are discerned. Afterwards, the model is applied to study the influence of restraining strains due to long-term creep and shrinkage in the service and ultimate shear response of frames. In contrast with flexural resistant mechanisms, delayed strains may influence the latter shear resistance of integral structures by reducing the concrete contribution to shear resistance and leading to a sooner activation of the transversal reinforcement. These aspects can be relevant in assessing existing structures and this model, due to its relative simplicity, can be advantageous for practical applications.Peer ReviewedPostprint (author's final draft

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Dirichlet Series Creep Function for Aging Concrete

Cited by 76 publications

References 0 publications

Soil-structure interaction with time-dependent behaviour of both concrete and soil

Soil-structure interaction with time-dependent behaviour of both concrete and soil

Influence of long‐term creep on prestressed concrete beams in relation to deformations and structural resistance: Experiments and modeling

Influence of time-dependent restrained strains in the shear response of RC frames

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