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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Creep and shrinkage of concrete ： ウィキペディア英語版 Creep and shrinkage of concrete Creep and shrinkage of concrete are two physical properties of concrete. The creep of concrete, which originates from the calcium silicate hydrates (C-S-H) in the hardened Portland cement paste (which is the binder of mineral aggregates), is fundamentally different from the creep of metals and polymers. Unlike the creep of metals, it occurs at all stress levels and, within the service stress range, is linearly dependent on the stress if the pore water content is constant. Unlike the creep of polymers and metals, it exhibits multi-months aging, caused by chemical hardening due to hydration which stiffens the microstructure, and multi-year aging, caused by long-term relaxation of self-equilibrated micro-stresses in the nano-porous microstructure of the C-S-H. If concrete is fully dried, it does not creep, but it is next to impossible to dry concrete fully without severe cracking. Changes of pore water content due to drying or wetting processes cause significant volume changes of concrete in load-free specimens. They are called the shrinkage (typically causing strains between 0.0002 and 0.0005, and in low strength concretes even 0.0012) or swelling (< 0.00005 in normal concretes, < 0.00020 in high strength concretes). To separate shrinkage from creep, the compliance function $J(t,\; t\text{'})$, defined as the stress-produced strain $\backslash epsilon$ (i.e., the total strain minus shrinkage) caused at time t by a unit sustained uniaxial stress $\backslash sigma\; =\; 1$ applied at age $t\text{'}$, is measured as the strain difference between the loaded and load-free specimens. The multi-year creep evolves logarithmically in time (with no final asymptotic value), and over the typical structural lifetimes it may attain values 3 to 6 times larger than the initial elastic strain. When a deformation is suddenly imposed and held constant, creep causes relaxation of critically produced elastic stress. After unloading, creep recovery takes place, but it is partial, because of aging. In practice, creep during drying is inseparable from shrinkage. The rate of creep increases with the rate of change of pore humidity (i.e., relative vapor pressure in the pores). For small specimen thickness, the creep during drying greatly exceeds the sum of the drying shrinkage at no load and the creep of a loaded sealed specimen (Fig. 1 bottom). The difference, called the drying creep or Pickett effect (or stress-induced shrinkage), represents a hygro-mechanical coupling between strain and pore humidity changes. Drying shrinkage at high humidities (Fig. 1 top and middle) is caused mainly by compressive stresses in the solid microstructure which balance the increase in capillary tension and surface tension on the pore walls. At low pore humidities (<75%), shrinkage is caused by a decrease of the disjoining pressure across nano-pores less than about 3 nm thick, filled by adsorbed water. The chemical processes of Portland cement hydration lead to another type of shrinkage, called the autogeneous shrinkage, which is observed in sealed specimens, i.e., at no moisture loss. It is caused partly by chemical volume changes, but mainly by self-desiccation due to loss of water consumed by the hydration reaction. It amounts to only about 5% of the drying shrinkage in normal concretes, which self-desiccate to about 97% pore humidity. But it can equal the drying shrinkage in modern high-strength concretes with very low water-cement ratios, which may self-desiccate to as low as 75% humidity. The creep originates in the calcium silicate hydrates (C-S-H) of hardened Portland cement paste. It is caused by slips due to bond ruptures, with bond restorations at adjacent sites. The C-S-H is strongly hydrophilic, and has a colloidal microstructure disordered from a few nanometers up. The paste has a porosity of about 0.4 to 0.55 and an enormous internal surface area, roughly 500 m2/cm3. Its main component is the tri-calcium silicate hydrate gel (3 CaO · 2 SiO3 · 3 H20, in short C3-S2-H3). The gel forms particles of colloidal dimensions, weakly bound by van der Waals forces. The physical mechanism and modeling are still being debated. The constitutive material model in the equations that follow is not the only one available but has at present the strongest theoretical foundation and fits best the full range of available test data. ==Stress-strain relation at constant environment== In service, the stresses in structures are < 50% of concrete strength, in which case the stress-strain relation is linear, except for corrections due to microcracking when the pore humidity changes. The creep may thus be characterized by the compliance function $J(t,\; t\text{'})$ (Fig. 2). As $t\text{'}$ increases, the creep value for fixed $t\; -\; t\text{'}$ diminishes. This phenomenon, called aging, causes that $J$ depends not only on the time lag $t\; -\; t\text{'}$ but on both $t$ and $t\text{'}$ separately. At variable stress $\backslash sigma(t)$, each stress increment $\backslash mbox\backslash sigma(t\text{'})$ applied at time $t\text{'}$ produces strain history $\backslash mbox\; \backslash epsilon(t)\; =\; J(t,\; t\text{'})\; \backslash mbox\; \backslash sigma(t\text{'})$. The linearity implies the principle of superposition (introduced by Boltzmann and for the case of aging, by Volterra). This leads to the (uniaxial) stress-strain relation of linear aging viscoelasticity: Here $\backslash epsilon^0$ denotes shrinkage strain $\backslash epsilon\_$ augmented by thermal expansion, if any. The integral is the Stieltjes integral, which admits histories $\backslash sigma\; (t)$ with jumps; for time intervals with no jumps, one may set $\backslash mbox\; \backslash sigma\; (t\text{'})\; =$ (\sigma (t') / \mbox t' ) \mbox t' to obtain the standard (Riemann) integral. When history $\backslash epsilon(t)$ is prescribed, then Eq.(1) represents a Volterra integral equation for $\backslash sigma\; (t)$. This equation is not analytically integrable for realistic forms of $J(t,\; t\text{'})$, although numerical integration is easy. The solution $\backslash sigma\; (t)$ for strain $\backslash epsilon\; =\; 1$ imposed at any age $\backslash hat$ (and for $\backslash epsilon^0\; =\; 0$) is called the relaxation function $R(t,\; \backslash hat\; )$. To generalize Eq. (1) to a triaxial stress-strain relation, one may assume the material to be isotropic, with an approximately constant creep Poisson ratio, $\backslash nu\; \backslash approx\; 0.18$. This yields volumetric and deviatoric stress-strain relations similar to Eq. (1) in which $J(t,\; t\text{'})$ is replaced by the bulk and shear compliance functions: At high stress, the creep law appears to be nonlinear (Fig. 2) but Eq. (1) remains applicable if the inelastic strain due to cracking with its time-dependent growth is included in $\backslash epsilon^0\; (t)$. A viscoplastic strain needs to be added to $\backslash epsilon^0\; (t)$ only in the case that all the principal stresses are compressive and the smallest in magnitude is much larger in magnitude than the uniaxial compressive strength $f\_c\text{'}$. In measurements, Young's elastic modulus $E$ depends not only on concrete age $t\text{'}$ but also on the test duration because the curve of compliance $J(t,\; t\text{'})$ versus load duration $t\; -\; t\text{'}$ has a significant slope for all durations beginning with 0.001 s or less. Consequently, the conventional Young's elastic modulus should be obtained as $E(t\text{'})\; =\; 1/J(t\text{'}+\backslash delta,\; t\text{'})$, where $\backslash delta$ is the test duration. The values $\backslash delta\; \backslash approx\; 0.01$ day and $t\text{'}\; =\; 28$ days give good agreement with the standardized test of $E$, including the growth of $E$ as a function of $t\text{'}$, and with the widely used empirical estimate $E\; =\; 57,000\; \backslash mbox$ $\backslash sqrt\; =\; 6895\; \backslash mbox\; ,\; f\_c\text{'}\; =\; \backslash mbox)$. The zero-time extrapolation $q\_1\; =\; J(t\text{'},t\text{'})\; =\; \backslash lim\_\; J(t\text{'}+\backslash delta,t\text{'})$ happens to be approximately age-independent, which makes $q\_1$ a convenient parameter for defining $J(t,\; t\text{'})$. For creep at constant total water content, called the basic creep, a realistic rate form of the uniaxial compliance function (the thick curves in Fig. 1 bottom) was derived from the solidification theory: ,~~~\theta=t-t',~~~1/\eta_f = q_4 /t |}} where $\backslash dot\; x\; =\; \backslash partial\; x\; /\backslash partial\; t$; $\backslash eta\_f$ = flow viscosity, which dominates multi-decade creep; $\backslash theta$ = load duration; $\backslash lambda\_0$ = 1 day, $m\; =\; 0.5$, $n=\; 0.1$; $v(t)\backslash rm\; MPa^$ = volume of gel per unit volume of concrete, growing due to hydration; and $q\_2,\; q\_3,\; q\_4$ = empirical constants (of dimension $\backslash rm\; MPa^$). Function $C\_g(\backslash theta)$ gives age-independent delayed elasticity of the cement gel (hardened cement paste without its capillary pores) and, by integration, $C\_g(\backslash theta)\; =\; \backslash mbox()$. Integration of $\backslash dot\; J(t,\; t\text{'})$ gives $J(t,\; t\text{'})$ as a non-integrable binomial integral, and so, if the values of $J(t,\; t\text{'})$ are sought, they must be obtained by numerical integration or by an approximation formula (a good formula exists). However, for computer structural analysis in time steps, $J(t,\; t\text{'})$ is not needed; only the rate $\backslash dot\; J(t,\; t\text{'})$ is needed as the input. Eqs. (3) and (4) are the simplest formulae satisfying three requirements: 1) Asymptotically for both short and long times $\backslash theta$, $\backslash dot\; J(t,\; t\text{'})$, should be a power function of time; and 2) so should the aging rate, given by $(t)/\backslash mbox\; t\}$) (power functions are indicated by self-similarity conditions); and 3) $\backslash partial^2\; J(t,t\text{'})\; /\backslash partial\; t\; \backslash partial\; t\text{'}\; >\; 0$ (this condition is required to prevent the principle of superposition from giving non-monotonic recovery curves after unloading which are physically objectionable). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Creep and shrinkage of concrete」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.