阅读说明：本技术 一种混凝土早龄期热膨胀系数多尺度模型的预测方法 (Prediction method of concrete early-age thermal expansion coefficient multi-scale model ) 是由 曹秀丽 叶罡 李强 李蓓 孙平平 于 2020-04-21 设计创作，主要内容包括：本发明公开了一种混凝土早龄期热膨胀系数多尺度模型的预测方法,该方法首先对混凝土进行多尺度划分；分别计算不同尺度上各组成相的相对体积含量；从最小尺度开始,逐步向大尺度均匀化各尺度的弹性模量参数和温度应力系数；计算最大尺度的热膨胀系数边值；分阶段建立早龄期的混凝土热膨胀系数预测模型。本发明根据混凝土的微观结构组成及各组成相的弹性及热学性能,建立了混凝土早龄期热膨胀系数的多尺度预测模型,模型考虑了配合比、龄期、水泥、粗、细骨料种类及性能、温、湿度等影响因素,实现了基于微观结构对混凝土宏观性能的预测,从根本上解决了混凝土热膨胀系数影响因素众多的问题。(The invention discloses a method for predicting a multiscale model of a thermal expansion coefficient of concrete in an early age, which comprises the following steps of firstly carrying out multiscale division on the concrete; respectively calculating the relative volume content of each composition phase on different scales; from the minimum scale, homogenizing the elastic modulus parameters and the temperature stress coefficients of all scales gradually to the large scale; calculating the edge value of the thermal expansion coefficient of the maximum scale; and establishing a concrete thermal expansion coefficient prediction model in an early age stage by stages. According to the invention, a multi-scale prediction model of the early-age thermal expansion coefficient of the concrete is established according to the microstructure composition of the concrete and the elasticity and thermal properties of each composition phase, and the model considers the influence factors such as the mix proportion, the age, the cement, the coarse and fine aggregate types and properties, the temperature and the humidity, so that the prediction of the macroscopic property of the concrete based on the microstructure is realized, and the problem of numerous influence factors of the thermal expansion coefficient of the concrete is fundamentally solved.)

1. A prediction method of a concrete early-age thermal expansion coefficient multi-scale model is characterized by comprising the following steps:

(1) the concrete is divided into different scales according to the microstructure composition, and the different scales contain different phases.

(2) And (3) respectively obtaining the volume percentage of different phases in different scales divided by the step (1).

(3) Gradually adopting a homogenization method from the minimum scale to the upper part, and calculating the thermal expansion coefficient of drainage of each scale according to the volume percentage content of different phases in different scales obtained in the step (2)And coefficient of thermal expansion without drainage

Wherein f is_φPorosity in the dimension X, α_f,XIs the coefficient of thermal expansion, K, of pore water of dimension X_fIs the bulk modulus of the pore water,is the bulk modulus of the dimension X,is the temperature stress coefficient of the dimension X,is the Biot coefficient for the scale X,the Biot modulus for the scale X,thermal porosity coefficient of variation for scale X;the equal parts are calculated according to the following formulas respectively:

wherein k is_r、f_rRespectively, the bulk modulus, volume fraction, kappa, of the r-th phase of the dimension X_rTemperature stress coefficient, k, of the r-th phase of dimension X₀The bulk modulus of the reference medium is the dimension X,shear modulus at the scale X;calculated according to the following formula:

wherein, g_rShear modulus of the r < th > phase at dimension X;g₀the shear modulus of the reference medium is dimension X; the volume modulus of the concrete is finally obtainedThermal expansion coefficient without drainageAnd coefficient of thermal expansion of drainage

(4) Obtaining the bulk modulus of the concrete at each early age according to the steps (2) to (3)Thermal expansion coefficient without drainageAnd coefficient of thermal expansion of drainageCalculating the thermal expansion coefficient α (t) of the concrete at the early age t:

wherein, t_iInitial setting time, t_fα for final setting time_a(t) is the additional thermal expansion coefficient at time t, calculated according to the following formula:

wherein S is the saturation coefficient of concrete, Delta T represents the change of temperature, K_sIs the bulk modulus of the concrete solid-phase skeleton, and Δ p is the change due to temperature and relative humidityThe capillary pressure p caused by the formation changes.

2. The method for predicting the multiscale model of early-age thermal expansion coefficients of concrete according to claim 1, wherein the step (1) is specifically as follows: dividing concrete into six scales of a scale I, a scale II, a scale III, a scale IV, a scale V, a scale VI and the like from small to large according to the composition of a microstructure; the dimension I comprises basic blocks of hydrated calcium silicate and nanopores; the dimension II comprises a calcium silicate hydrate solid phase and a gel hole after the dimension I is homogenized; the scale III comprises high-density calcium silicate hydrate after being homogenized by the scale II and low-density calcium silicate hydrate after being homogenized by the scale II; the dimension IV comprises calcium silicate hydrate, calcium hydroxide, unhydrated cement particles, aluminate and capillary pores after the homogenization of the dimension III; the scale V comprises the cement paste and sand after the scale IV is homogenized; and the dimension VI comprises the cement mortar and the coarse aggregate after the homogenization of the dimension V.

3. The method for predicting the multiscale model of early-age thermal expansion coefficients of concrete according to claim 2, wherein the concrete is obtained after the scale VI is homogenized.

4. The method for predicting the multiscale model of early-age thermal expansion coefficients of concrete according to claim 3, wherein the step (2) is specifically as follows: the volume percentage contents of different phases on the scales I, II, III and IV are obtained by tests, or calculated by a Powers model, a Jennings-Tennis model or a CEMHYD3D model; the volume percentage content of different phases on the scales V and VI is obtained according to the mixing proportion of the concrete.

5. The method for predicting the multiscale model of early-age thermal expansion coefficients of concrete according to claim 4, wherein the test is an environmental scanning electron microscope test.

6. The method for predicting the multiscale model of the early-age thermal expansion coefficient of concrete according to claim 3, wherein the homogenization method in the step (3) and the step (4) is specifically as follows: calculating a homogenized calcium silicate hydrate solid phase on the scale I by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate solid phase; on the scale II, the homogenized high-density calcium silicate hydrate and low-density calcium silicate hydrate are calculated by adopting a Self-consistency method, and reference media are high-density calcium silicate hydrate and low-density calcium silicate hydrate; calculating homogenized calcium silicate hydrate on a scale III by adopting a Self-consistency method, wherein a reference medium is calcium silicate hydrate; calculating homogenized cement paste on a scale IV by adopting a Self-consistency method, wherein a reference medium is the cement paste; calculating homogenized cement mortar on a scale V by adopting a Mori-Tanaka method, wherein a reference medium is cement paste; and calculating homogenized concrete in a scale VI by adopting a Mori-Tanaka method, wherein the reference medium is cement mortar.

7. The method for predicting the multiscale model of early-age thermal expansion coefficient of concrete according to claim 1, wherein in the step (4), the saturation coefficient S-V of the concrete_ew/V_p(ii) a Wherein, V_ewIs the volume content of evaporable water per unit volume of set cement, V_pWater-saturated porosity.

8. The method for predicting the multiscale model of early-age thermal expansion coefficients of concrete according to claim 1, wherein in the step (4), the capillary pressure is measuredWherein RH is relative humidity, R is an ideal gas constant, T is absolute temperature, and v' is the molar volume of water.

Technical Field

The invention belongs to the field of multi-scale calculation and analysis of cement-based materials, and particularly relates to a prediction method of a multi-scale model of a thermal expansion coefficient of concrete in an early age.

Background

The coefficient of thermal expansion is one of the main thermophysical parameters of concrete and is also an important parameter for characterizing the volume stability of concrete. The research on the thermal expansion coefficient of the concrete in the early age at home and abroad is mostly carried out by a macroscopic test method, and a prediction model is obtained based on the fitting of test results. Due to the reasons of raw materials, mixing ratio, environmental conditions, testing equipment, testing methods, operation techniques of testers and the like, the discreteness of the given thermal expansion coefficient is large, the model usually takes the age as a main parameter, the consideration factors are few, the thermal expansion mechanism cannot be revealed, and the model is limited in practical application; in addition, experimental studies require long continuous tests, which are time-consuming and energy-consuming.

The concrete is a non-uniform porous medium material, the distribution of the micro components of the concrete spans the scales of nanometer, micrometer, millimeter and the like, and the prediction of the physical and mechanical properties of the concrete can be essentially reduced into a plurality of scales. The multi-scale method can consider the structural characteristics of different scales of the material, and achieves the purpose of obtaining the macroscopic effectiveness performance based on the microstructure information. The multi-scale method is introduced into the research of the thermal expansion coefficient of the concrete, and has important significance for predicting and controlling the early temperature crack of the concrete structure and evaluating the early cracking risk.

Disclosure of Invention

The invention aims to provide a method for predicting a multiscale model of thermal expansion coefficients of early-age concrete aiming at the defects of the prior art. According to the mixing proportion of the concrete, the type of the cement, the types of the coarse aggregate and the fine aggregate and performance parameters, the thermal expansion coefficient of the concrete can be determined by adopting a multi-scale method, so that accurate parameters are provided for controlling and evaluating the temperature cracks of the concrete in the early age.

The purpose of the invention is realized by the following technical scheme: a prediction method of a concrete early-age thermal expansion coefficient multi-scale model comprises the following steps:

(1) the concrete is divided into different scales according to the microstructure composition, and the different scales contain different phases.

(2) And (3) respectively obtaining the volume percentage of different phases in different scales divided by the step (1).

(3) Gradually adopting a homogenization method from the minimum scale to the upper part, and calculating the thermal expansion coefficient of drainage of each scale according to the volume percentage content of different phases in different scales obtained in the step (2)And coefficient of thermal expansion without drainage

Wherein f is_φPorosity in the dimension X, α_f,XIs the coefficient of thermal expansion, K, of pore water of dimension X_fIs the bulk modulus of the pore water,is the bulk modulus of the dimension X,is the temperature stress coefficient of the dimension X,is the Biot coefficient for the scale X,the Biot modulus for the scale X,thermal porosity coefficient of variation for scale X;the equal parts are calculated according to the following formulas respectively:

wherein k is_r、f_rRespectively, the bulk modulus, volume fraction, kappa, of the r-th phase of the dimension X_rTemperature stress coefficient, k, of the r-th phase of dimension X₀The bulk modulus of the reference medium is the dimension X,shear modulus at the scale X;calculated according to the following formula:

wherein, g_rShear modulus of the r < th > phase at dimension X;g₀the shear modulus of the reference medium is dimension X; the volume modulus of the concrete is finally obtainedThermal expansion coefficient without drainageAnd coefficient of thermal expansion of drainage

(4) Obtaining the bulk modulus of the concrete at each early age according to the steps (2) to (3)Thermal expansion coefficient without drainageAnd coefficient of thermal expansion of drainageCalculating the thermal expansion coefficient α (t) of the concrete at the early age t:

wherein, t_iInitial setting time, t_fα for final setting time_a(t) is the additional thermal expansion coefficient at time t, calculated according to the following formula:

wherein S is the saturation coefficient of concrete, Delta T represents the change of temperature, K_sΔ p is the change in capillary pressure p due to changes in temperature and relative humidity, which is the bulk modulus of the concrete solid framework.

Further, the step (1) is specifically: dividing concrete into six scales of a scale I, a scale II, a scale III, a scale IV, a scale V, a scale VI and the like from small to large according to the composition of a microstructure; the dimension I comprises basic blocks of hydrated calcium silicate and nanopores; the dimension II comprises a calcium silicate hydrate solid phase and a gel hole after the dimension I is homogenized; the scale III comprises high-density calcium silicate hydrate after being homogenized by the scale II and low-density calcium silicate hydrate after being homogenized by the scale II; the dimension IV comprises calcium silicate hydrate, calcium hydroxide, unhydrated cement particles, aluminate and capillary pores after the homogenization of the dimension III; the scale V comprises the cement paste and sand after the scale IV is homogenized; and the dimension VI comprises the cement mortar and the coarse aggregate after the homogenization of the dimension V.

Further, homogenizing the scale VI to obtain the concrete.

Further, the step (2) is specifically: the volume percentage contents of different phases on the scales I, II, III and IV are obtained by tests, or calculated by a Powers model, a Jennings-Tennis model or a CEMHYD3D model; the volume percentage content of different phases on the scales V and VI is obtained according to the mixing proportion of the concrete.

Further, the test is an environmental scanning electron microscope test.

Further, the homogenization method in the step (3) and the step (4) specifically comprises the following steps: calculating a homogenized calcium silicate hydrate solid phase on the scale I by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate solid phase; on the scale II, the homogenized high-density calcium silicate hydrate and low-density calcium silicate hydrate are calculated by adopting a Self-consistency method, and reference media are high-density calcium silicate hydrate and low-density calcium silicate hydrate; calculating homogenized calcium silicate hydrate on a scale III by adopting a Self-consistency method, wherein a reference medium is calcium silicate hydrate; calculating homogenized cement paste on a scale IV by adopting a Self-consistency method, wherein a reference medium is the cement paste; calculating homogenized cement mortar on a scale V by adopting a Mori-Tanaka method, wherein a reference medium is cement paste; and calculating homogenized concrete in a scale VI by adopting a Mori-Tanaka method, wherein the reference medium is cement mortar.

Further, in the step (4), the saturation coefficient S ═ V of the concrete_ew/V_p(ii) a Wherein, V_ewIs the volume content of evaporable water per unit volume of set cement, V_pWater-saturated porosity.

Further, in the step (4), the capillary pressureWherein RH is relative humidity, R is an ideal gas constant, T is absolute temperature, and v' is the molar volume of water.

The invention has the beneficial effects that: the invention establishes a multi-scale prediction method of the concrete early-age thermal expansion coefficient based on the common rule that the concrete thermal expansion coefficient changes along with the age and the essential attributes that the composition and the characteristics of the concrete microstructure evolve along with the age, establishes the relation between the concrete microstructure and the macroscopic thermal expansion performance, and fundamentally solves the problems of a plurality of influence factors on the macroscopic performance of the cement-based material and large dispersion of test data. By the method, the thermal expansion coefficient of the concrete at any age moment can be conveniently obtained, a set of testing device is not needed for real-time monitoring, and the precision level reaches the nanoscale; the method can predict the thermal expansion coefficient of the concrete at each age in the early age, can also predict the thermal expansion coefficients of the concrete at other ages after the early age, and has wide applicability.

Drawings

FIG. 1 is a schematic diagram of a concrete multiphase multi-scale composite process;

FIG. 2 is a graph comparing the test value and the predicted value of the thermal expansion coefficient of concrete.

Detailed Description

The technical scheme of the invention is explained in detail in the following with the accompanying drawings:

the method is based on the evolution rule of the concrete microstructure along with the age and the influence mechanism on the thermal expansion coefficient, establishes a multi-scale prediction model of the thermal expansion coefficient of the concrete in the early age according to the composition phase and the essential attributes of each phase of the concrete microstructure, and accurately predicts the development rule of the thermal expansion coefficient of the concrete in the early age according to the model.

Concrete is a heterogeneous material whose composition is related to multiple scales, such as high and low density hydrated calcium silicate on the nanometer scale, hydrated products such as calcium hydroxide, unhydrated cement particles, large capillary pores on the micrometer scale, cement paste, aggregate on the millimeter scale. The multi-scale method can consider the cross-scale and cross-level material mechanics characteristics of space and time, and is an important method for predicting material performance. The homogenization theory is an effective multi-scale calculation method, has the advantages of strict theory and easiness in numerical value realization of macroscopic equivalent performance of the material, and is an important method for designing the composite material, predicting the performance and optimizing the structure. On the scales of high-density calcium silicate hydrate, low-density calcium silicate hydrate, calcium hydroxide, unhydrated cement particles, coarse aggregate and fine aggregate, the thermal expansion coefficients of the composition phases on different scales are the inherent properties of the phases, and are not related to conditions such as water-cement ratio, age and the like, and the distribution and the content of the basic phases are changed only, so that the thermal expansion coefficients of the concrete scales and the like are changed along with the age. By adopting a multi-scale method and combining the evolution of the microstructure of the concrete in the early age, the development and the change of the thermal expansion coefficient of the concrete in the early age can be essentially predicted.

The invention discloses a multiscale prediction method for early-age thermal expansion coefficient of concrete, which specifically comprises the following steps:

step 1, dividing concrete into six scales from small to large according to microstructure composition: a scale I, a scale II, a scale III, a scale IV, a scale V and a scale VI;

the multi-scale division of the concrete can be flexibly carried out according to actual conditions, the minimum scale is divided into the nanometer scale, the minimum scale is determined based on the current research level at home and abroad and can reflect the thermal expansion mechanism of the cement-based material from the nanometer scale, the maximum scale is the concrete, and the following division method is preferably adopted from the perspective of the thermal expansion coefficient:

the concrete is prepared by homogenizing dimension I, dimension II, dimension IV, dimension V and dimension VI, wherein dimension I comprises basic calcium silicate hydrate blocks (C-S-H basic building blocks) and nano-pores (nanoporosity), dimension II comprises solid calcium silicate hydrate (C-S-H solid) and gel pores (gel porosity) after homogenizing dimension I, dimension III comprises high-density calcium silicate hydrate (HD C-S-H) after homogenizing dimension II and low-density calcium silicate hydrate (L D C-S-H) after homogenizing dimension II, dimension IV comprises calcium silicate hydrate (C-S-H), Calcium Hydroxide (CH), unhydrated cement particles, aluminate and capillary pores after homogenizing dimension III, dimension V comprises cement paste and sand after homogenizing dimension IV, dimension VI comprises cement mortar and coarse aggregate after homogenizing dimension V, and dimension VI is homogenized to obtain the concrete.

Step 2, respectively calculating the relative volume contents of the composition phases of different scales at different times of each age, and expressing the relative volume contents by volume percentage:

the Volume fractions of the different phases on the scales I, II, III, IV can be obtained by experiments (environmental scanning electron microscope experiments) or by the Powers model (Powers T.C., Brownyard T. L. Studies of the Physical Properties of the Hardened Portland and center paste.Part5.Studies of the Hardened Paste by Meanso Specific-Volume measures [ J ] Journal of the American Concrete Institute,1947,18(6): MH669. supplement), Jennings-Tennis model (Jennings H.M., Tennis P.D.model for the same Concrete in the Portland and center Paste [ J ] model of the Concrete, model of the Concrete model, Cement 3, model of the Concrete model, Cement 3, 3172, Cement 3, 313, 3121, 313, 3121, 3, 313, 3172, 313, 3, 313, 3, respectively;

step 3, starting from the smallest scale, progressively applying a homogenization method upwards, said homogenization method applying a Self-Consistent method (see [ Eshelby J.D. the Determination of the Elastic Field of an Elastic ingredient and a Related formulation [ C ] the proceedings of the Royal Society of L on Series A,1957 ]) on the scales I, II, III, IV, the reference medium corresponding to each scale being itself, respectively, and on the scales V, VI, the Mori-Tanaka method (see [ Mori T., Tannaka K. Average in-and-inherent of Materials with cement mortar, in particular cement mortar, the reference medium corresponding to each scale J.Acurra, 1973, 19721, 571) respectively:

calculating a homogenized calcium silicate hydrate solid phase on a scale I by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate solid phase per se; on the scale II, a Self-consistency method is adopted to calculate homogenized high-density and low-density calcium silicate hydrate, and a reference medium is the high-density and low-density calcium silicate hydrate; calculating homogenized calcium silicate hydrate on a scale III by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate; calculating homogenized cement paste on a scale IV by adopting a Self-consistency method, wherein reference media are the cement paste per se; adopting a Mori-Tanaka method to calculate homogenized cement mortar on the scale V, wherein the reference medium is cement paste, and sand is inclusion; and (3) calculating homogenized concrete on a scale VI by adopting a Mori-Tanaka method, wherein a reference medium is cement mortar, and coarse aggregate is mixed.

The coefficient of thermal expansion for each dimension is calculated according to the following formula:

in which the upper index hom represents the homogenized, and the lower index X represents the dimension X;is the coefficient of thermal expansion of the drainage water in this dimension,coefficient of thermal expansion for non-drainage of this scale, f_φPorosity of this scale, α_f,XIs the coefficient of thermal expansion, K, of pore water of this scale_fIs the bulk modulus of pore water;is the bulk modulus of this scale and,is the temperature stress coefficient of this scale and,for a porous elastic Biot coefficient of this scale,the porous elastic Biot modulus of this scale,the thermal porosity coefficient of change for this scale,respectively according to the following formula:

in the formula, k_r、f_rThe volume modulus, volume fraction, kappa, of the r-th phase of the scale_rTemperature stress coefficient, k, of the r-th phase of the scale₀Referencing the bulk modulus of the medium for the scale;the shear modulus for this scale is calculated according to the following formula:

wherein, g_rShear modulus of the r-th phase of this scale, α₀Calculated according to the following formula:

in the formula, g₀The shear modulus of the medium is referenced for this scale.

Step 4, repeating the steps 2 to 3 for each early age moment to obtain the thermal expansion coefficient of the concrete at each early age moment, including the thermal expansion coefficient without water drainageAnd coefficient of thermal expansion of drainageAnd can further draw the change curve of the thermal expansion coefficient of the concrete along with the age, which is specifically as follows:

the thermal expansion coefficient of the concrete at initial setting is changed from the thermal expansion coefficient without water drainageDetermining and reflecting the influence of the concrete raw material and the pores on the thermal expansion coefficient; the thermal expansion coefficient of the concrete at final setting is determined by the thermal expansion coefficient of the drainageDetermining; the thermal expansion coefficient of the concrete is determined by a linear interpolation method of the thermal expansion coefficients during initial setting and final setting between the initial setting and the final setting; the thermal expansion coefficient of the finally set concrete consists of a drainage thermal expansion coefficient and an additional thermal expansion coefficient, and the influence of the factors such as the type and the performance of the raw materials of the concrete, the mixing proportion, the age, the temperature, the humidity and the like on the thermal expansion coefficient is quantitatively reflected; the common law that the thermal expansion coefficient of common concrete develops along with the age is as follows: after mixing, it reaches a maximum at initial setting and then decreases rapidly, reaches a minimum at final setting, and then increases gradually with age orTends to be stable; calculating the thermal expansion coefficient of the concrete at the early age t by using the following formula:

wherein t is age, t_iInitial setting time, t_fFor final setting time, α_a(t) is the additional thermal expansion coefficient at the age t, and is calculated according to the following formula:

wherein S is the saturation coefficient of concrete, and S is-V_ew/V_pCalculation of where V_ewIs the volume content of evaporable water per unit volume of set cement, V_pWater-saturated porosity; Δ T represents a change in temperature;bulk modulus of homogenized concrete; k_sDelta p is the change of capillary pressure p caused by the change of temperature and relative humidity, and the capillary pressure p is calculated according to the Kelvin-L aplace equation:

in the formula, RH is relative humidity, R is an ideal gas constant, T is absolute temperature, and v' is the molar volume of water.

The method does not need to monitor by a set of testing device, and can adopt MAT L AB and the like to compile computer software according to the steps to carry out rapid solution, adopt concrete with different mix proportions, different types of cement and different types of coarse and fine aggregates, repeat the steps 2 to 4, and obtain the change curve of the thermal expansion coefficient of the corresponding different concrete along with the age.

In order to verify the prediction effect of the method of the invention, the following tests were carried out:

the method of the invention is used for predicting the thermal expansion coefficient of the concrete which adopts the ordinary portland cement, has the water cement ratio of 0.45, the river sand as the fine aggregate and the limestone as the coarse aggregate in the early age, and carries out comparative analysis with the test value. The test contents are as follows:

1. overview

1.1 test stock

The cement is ordinary portland cement, and the chemical composition of the cement is shown in table 1.

Table 1: cement main chemical component content

1.2 protocol

The size of the test piece is 100mm × 100mm × 500mm, the test piece is placed in an oven for testing after pouring, and a thermal expansion coefficient testing system is adopted to test the thermal expansion coefficient.

1.3 coefficient of thermal expansion of the principal phase

Table 2: coefficient of thermal expansion of each component

2. Model validation and evaluation

The experimental values of the coefficient of thermal expansion of concrete in the early stage and the predicted values of the present invention are shown in FIG. 2. It can be seen that the predicted value is well matched with the test value, which shows that the model can better predict the precision.

The invention adopts a multi-scale method, establishes the relation between the microstructure and the macroscopic performance of the concrete, and can predict the thermal expansion coefficient of the early-age concrete according to the cement components, the mixing proportion of the concrete, the types of coarse and fine aggregates, which is difficult to realize by the prior art.