![Material parameters of the HCP paste used in simulations of experiments of Lura et al. [10]](https://www.researchgate.net/profile/Francesco-Pesavento/publication/225101253/figure/tbl1/AS:393686232911874@1470873520088/Material-parameters-of-the-HCP-paste-used-in-simulations-of-experiments-of-Lura-et-al_Q320.jpg)
![Dependence of av s ws (S w ) identified in [6] for OC and HPC concretes using experimental data of BaroghelBouny et al. [9]](https://www.researchgate.net/profile/Francesco-Pesavento/publication/225101253/figure/fig7/AS:668678769094663@1536436850920/Dependence-of-av-s-ws-S-w-identified-in-6-for-OC-and-HPC-concretes-using_Q320.jpg)
![Material parameters of a C-30 concrete used in simulations of tests of L'Hermite et al. [12]](https://www.researchgate.net/profile/Francesco-Pesavento/publication/225101253/figure/tbl2/AS:393686232911875@1470873520116/Material-parameters-of-a-C-30-concrete-used-in-simulations-of-tests-of-LHermite-et-al_Q320.jpg)
![Comparison of theoretical, Eq. (8), and values of shrinkage strains measured by Baroghel-Bouny et al. [9] for OC and HPC concretes at various relative humidity levels](https://www.researchgate.net/profile/Francesco-Pesavento/publication/225101253/figure/fig8/AS:668678769094665@1536436850944/Comparison-of-theoretical-Eq-8-and-values-of-shrinkage-strains-measured-by_Q320.jpg)
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Modelling creep and shrinkage of concrete by means of effective stresses
Abstract and Figures
A novel model of mechanical performance of concrete at early ages and beyond, and in particular, evolution of its strength properties (aging) and deformations (shrinkage and creep strains), described in terms of effective stress is briefly presented. This model reproduces such phenomena known from experiments like drying creep or some additional strains, as compared to pure shrinkage, which appear during autogenous deformations of a maturing, sealed concrete sample. Creep is described by means of the modified microprestress-solidification theory with some modifications to take into account the effects of temperature and relative humidity on concrete aging. Shrinkage strains are modelled by using effective stresses giving a good agreement with experimental data also for low values of relative humidity. Results of four numerical examples based on the real experimental tests are solved to validate the model. They demonstrate its possibilities to analyze both autogenous deformations in maturing concrete, and creep and shrinkage phenomena, including drying creep, in concrete elements of different age, sealed or drying, exposed to external load or without any load.
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... Hydrating cementitious system is a partially saturated porous media and the status of the pore fluids in pore structure, including water and moist air, will change with the drop of internal relative humidity. According to Gray et al. and Gawin et al. [70,71], the changed pore fluids will exert pressure on the solid skeleton of cementitious system, which is the internal driving force of autogenous shrinkage and can be expressed: ...
... where σ tot [MPa] is the total pressure exerted by the pore fluids on the solid skeleton; σ gas [MPa] is the gas pressure; S [-] is the degree of saturation; κ [-] is the Biot coefficient; σ wat [MPa] is the total pressure exerted by the water. According to Gawin et al. [71], the total pressure exerted by the water σ wat is mainly made up by three parts: σ wat = σ cap + σ dis + σ sur (2) where σ cap [MPa] is capillary tension; σ dis [MPa] is the disjoining pressure and σ sur [MPa] is the surface tension of solid gel particles. ...
... Among these different kinds of pressure exerted by the pore fluids, the gas pressure σ gas is negligible compared with others [71]. In earlyage sealed cement paste, the relative humidity is always above 75% [72], while the surface tension σ sur only plays a significant role when relative humidity is lower than 50% [73]. ...
The addition of supplementary cementitious materials (SCMs), which is an effective method to reduce the CO 2 emission during the cement production, will change the autogenous shrinkage of early-age hydrating cementi-tious systems. In this paper the effect of different SCMs, i.e., silica fume and fly ash, on the physical properties and autogenous shrinkage of cement paste is studied, both experimentally and numerically. The experiment results show that autogenous shrinkages of cement pastes reduce significantly with the increase of water-binder ratio. The addition of fly ash will lead to smaller autogenous shrinkage while the influence of the dry densified silica fume on the autogenous shrinkage is not pronounced. A numerical simulation model, in which autogenous shrinkage is split up into an elastic part and a time-dependent part is proposed in this paper. The two parts are calculated separately. The simulation of the visco-elastic response of the cement paste to the internal driving force was performed by using a solidification theory model that takes the aging into consideration. The physical properties of different kinds of cement paste are experimentally investigated and the measured results are taken as input parameters of the simulation model. The simulated autogenous shrinkage of different kinds of cement pastes are compared with the measured results to verify the prediction of the proposed model.
... As changes in temperature and humidity cause disturbances in the equilibrium of disjointed pressure, this theory can consider the influences of temperature and humidity on concrete creep [31]. Well-known creep models, such as the BP [30], BKX [32], B3 Model [33], and their improved ones [34][35][36][37][38], based on the solidification-microprestress theory, have been proposed. ...
... By substituting the fitted values of ξ t and ξ ω, and the short-term strength into Eqs. (36) and (37), the long-term shear strength parameters of concrete can be determined, as listed in Table 1. Then parameter identification was conducted by Eqs. ...
The influence of moisture content and overstress on the creep of concrete was investigated from the perspective of damage rheology theory. The weakening effects of moisture and overstress were characterized by a time-independent and a time-dependent damage functions, respectively, and then combined and applied to a modified creep model that can represent the elasto-visco-plastic creep deformation of concrete. Hence, a damage creep model is proposed to describe the creep behavior of water-bearing concrete. Theoretical and statistical analyses, as well as a comparison with the ACI-209 model were performed to examine the validity and superiority of the proposed model. Further analyses showed that not only the deformation parameters, but also the long-term strength parameters degraded with time and increasing moisture. Experiments were then conducted on saturated cement mortar with different static moisture holding durations to investigate the time correlation of moisture-induced damage on the mechanical properties of the material. The experimental results proved that moisture-induced damage was independent of time.
... The above formulas represent the resultant temperature and water vapour pressure inserted into motion equations for the mechanical part through the terms τ P avg and α T avg . Although some researchers have J. Zhang et al proposed that the stress state and the deformation of high-temperature concrete should additionally take into account the effect of capillary pressure P c as well as solid pressure P s , and further details see Gray and Schrefler [46], Pesavento et al. [47], Gray et al. [48], and Gawin et al. [49]. Currently, there are still many researchers whose work has yielded valid simulation results by considering only the effects of temperature and vapour pressure, e.g. ...
In this study, a fully coupled hygro-thermo-mechanical bond-based Cosserat peridynamic model is formulated to simulate the complex crack propagation and multi-field interaction process in concrete under fire. This model can consider the effect of the size and the independent rotation of cement particle. A numerical solution with a multi-rate explicit integration strategy is adopted for the complex multi-field interaction. The proposed model and the numerical solution are verified by the experimental results and finite element solutions. Numerical examples focus on the influence of fracture on mass transfer and heat conduction, and the effects of cement particle size on the temperature, water vapour pressure and crack propagation. Numerical results demonstrate the model's effectiveness in simulating the hygro-thermo-mechanical behaviours and crack propagation processes in concrete subjected to high temperatures.
... To resolve the problem, some macroscopic approaches are proposed to simulate the 80 shrinkage and swelling behavior of porous materials based on the notion of effective stress 81 (e.g., Coussy et al. 1998Coussy et al. , 2004Gawin et al. 2007). In these approaches, the interfacial tension 82 on the fluid-air interface is considered the driving force for the soil shrinkage (Reichenbauer et shrinkage. ...
... Modern theories take into account a variety of factors that affect the rates of concrete creep and shrinkage. The influences of various factors on concrete agingsuch as temperature (Gernay, 2012) and relative humidity (Gawin et al., 2007) are considered separately. ...
Long-term strength investigations of construction elements made of reinforced concrete (RC) under creep conditions are considered. A calculation method that allows determination of the load-bearing capacity and long-term strength of RC thin-walled elements under short- and long-term loading is proposed. The method is based on a combination of the finite-element method for solving boundary value problems at each time step and the finite-difference method for integrating the initial value problems. The numerical results are compared with experimental data obtained in the loading–unloading mode during long-term deformation. An example of creep and damage calculations in the RC coating and recommendations for parameter selections are given.
Prediction of time-dependent deformation such as shrinkage and creep are of utmost interest in terms of long-term
13 serviceability of a concrete structure. However, owing to highly heterogeneous nature of concrete, existing
14 macroscopic prediction models lack in terms of its general applicability. Hence, in this study, a multi-scale
15 description is used to simulate the shrinkage and creep of concrete where the heterogeneity and associated
16 physical-chemical processes are modelled in a mathematical framework. A hierarchical homogenisation technique
17 is used to link across different scales. Model predicated shrinkage and creep are then validated with the
18 corresponding experimental data. Model prediction is also compared with few national codes and popular
19 macroscopic models to highlights the associated gaps in these models that can be overcome with the present
20 developed multi-scale approach
For concrete with low water-to-binder ratio, the autogenous shrinkage often takes up most of the total shrinkage. In restrained structures, this kind of shrinkage will produce tensile stress. Once the tensile stress exceeds the tensile strength, it will lead to cracks and seriously endanger the durability of the structure. In this paper, the updated autogenous shrinkage prediction models of concrete in recent years are reviewed in detail. By comparing and analyzing these models, the latest research progress of autogenous shrinkage models is understood, and a direction for the subsequent research of autogenous shrinkage models of concrete is provided. Finally, the problems existing in current autogenous shrinkage models are summarized and prospected.
Models for thermo-hydro-mechanical behavior of saturated/unsaturated porous media are reviewed. The necessary balance equations are derived using averaging theories. Constitutive equations are obtained using the Coleman-Noll procedure and thermodynamic equations for the model closure are introduced. A particular form of the governing equations is then solved numerically and the numerical properties are discussed. Application examples conclude the paper. There are 165 references in this review article.
Creep and shrinkage testing of two sets of specimens is described. For the size and shape tests, the specimens modeled 100 to 400 mm section square columns, 100 to 400 mm thick slabs, and sealed specimens. For the age at loading tests the specimens modeled 150 mm square columns, 150 mm thick slabs, and sealed specimens that were loaded at concrete ages ranging from 8 to 182 days. Strains were monitored while the specimens were kept in a constant environment room. The experimental results form an extensive and consistent series that can be used to calibrate or validify creep and shrinkage prediction methods. The experimental results are compared with predictions based on the method recommended by ACI Committee 209 and a simple method for an improvement of predictions is presented.
The paper presents a new general constitutive law for creep in which the aging due to continuing hydration of cement is taken into account in a manner that is both simpler and physically better justified than in existing theories. Micromechanical analysis of the solidification process is used to show that the aging may be modeled as a growth of the volume fraction of load-bearing solidified matter (hydrated cement), which itself is treated as nonaging and thus is describable as a nonaging viscoelastic material. The analysis shows that a history integral should be used to express the rate, rather than the total value, of the viscoelastic strain component. Material functions can be chosen in a way that yields previously established simple laws, i.e., the double power law, logarithmic law and log-double power law, as special asymptotic cases. The creep strain is obtained as a sum of aging and nonaging viscoelastic strains and an aging viscous strain (flow). Nonlinearity is introduced by modifying the current creep rate as a function of the current stress. Verification by test results and numerical application is left to Part II, which follows.