CN111462839B - Multiscale prediction method for thermal expansion coefficient of hardened cement mortar - Google Patents
Multiscale prediction method for thermal expansion coefficient of hardened cement mortar Download PDFInfo
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- CN111462839B CN111462839B CN202010317379.4A CN202010317379A CN111462839B CN 111462839 B CN111462839 B CN 111462839B CN 202010317379 A CN202010317379 A CN 202010317379A CN 111462839 B CN111462839 B CN 111462839B
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- 239000011083 cement mortar Substances 0.000 title claims abstract description 56
- 238000000034 method Methods 0.000 title claims abstract description 47
- 239000004568 cement Substances 0.000 claims abstract description 30
- 239000000203 mixture Substances 0.000 claims abstract description 15
- 239000004576 sand Substances 0.000 claims abstract description 8
- 238000002156 mixing Methods 0.000 claims abstract description 7
- 239000000378 calcium silicate Substances 0.000 claims description 38
- 229910052918 calcium silicate Inorganic materials 0.000 claims description 38
- OYACROKNLOSFPA-UHFFFAOYSA-N calcium;dioxido(oxo)silane Chemical compound [Ca+2].[O-][Si]([O-])=O OYACROKNLOSFPA-UHFFFAOYSA-N 0.000 claims description 38
- 239000012071 phase Substances 0.000 claims description 23
- 238000012360 testing method Methods 0.000 claims description 23
- 238000000265 homogenisation Methods 0.000 claims description 14
- 239000007790 solid phase Substances 0.000 claims description 10
- 239000011148 porous material Substances 0.000 claims description 5
- AXCZMVOFGPJBDE-UHFFFAOYSA-L calcium dihydroxide Chemical compound [OH-].[OH-].[Ca+2] AXCZMVOFGPJBDE-UHFFFAOYSA-L 0.000 claims description 4
- 239000000920 calcium hydroxide Substances 0.000 claims description 4
- 229910001861 calcium hydroxide Inorganic materials 0.000 claims description 4
- 150000004645 aluminates Chemical class 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 claims description 3
- 230000007613 environmental effect Effects 0.000 claims description 3
- 239000002245 particle Substances 0.000 claims description 3
- 239000000463 material Substances 0.000 abstract description 14
- 239000000126 substance Substances 0.000 abstract description 7
- 238000004458 analytical method Methods 0.000 abstract description 4
- 238000011160 research Methods 0.000 abstract description 4
- 239000000470 constituent Substances 0.000 abstract description 3
- 238000004088 simulation Methods 0.000 abstract description 3
- 238000013461 design Methods 0.000 abstract description 2
- JLDKGEDPBONMDR-UHFFFAOYSA-N calcium;dioxido(oxo)silane;hydrate Chemical compound O.[Ca+2].[O-][Si]([O-])=O JLDKGEDPBONMDR-UHFFFAOYSA-N 0.000 description 5
- 239000011398 Portland cement Substances 0.000 description 4
- 230000007246 mechanism Effects 0.000 description 4
- 239000002131 composite material Substances 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- 230000036571 hydration Effects 0.000 description 2
- 238000006703 hydration reaction Methods 0.000 description 2
- 239000002994 raw material Substances 0.000 description 2
- 239000007787 solid Substances 0.000 description 2
- 238000010998 test method Methods 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 238000013329 compounding Methods 0.000 description 1
- 239000004567 concrete Substances 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000002389 environmental scanning electron microscopy Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000007789 gas Substances 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 230000000704 physical effect Effects 0.000 description 1
- 230000001737 promoting effect Effects 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
Abstract
The invention discloses a multi-scale prediction method of thermal expansion coefficient of hardened cement mortar, which comprises the steps of firstly carrying out multiphase multi-scale division on the hardened cement mortar; calculating the relative volume content of each constituent phase on different scales; homogenizing the elastic modulus parameter and the temperature stress coefficient of each scale gradually from the minimum scale to the large scale; the thermal expansion coefficient of the hardened cement mortar of the maximum dimension was calculated. According to the microstructure composition of the cement mortar and the elastic performance and thermal performance of each composition phase, the invention comprises the mixing proportion of the cement mortar, the chemical composition of the cement and the type of sand, adopts a multi-scale method to determine the thermal expansion coefficient, and provides accurate parameters for cement-based material mechanics, deformation performance research, numerical simulation analysis and structural design; a multi-scale prediction model of the thermal expansion coefficient of the hardened cement mortar is established, the prediction of the macroscopic performance of the cement mortar based on a microstructure is realized, and the problem of numerous influence factors of the thermal expansion coefficient of the cement mortar is solved.
Description
Technical Field
The invention belongs to the field of multi-scale calculation and analysis of cement-based materials, and particularly relates to a multi-scale prediction method for thermal expansion coefficients of hardened cement mortar.
Background
The thermal expansion coefficient is one of the most basic and important thermophysical characteristic parameters of cement-based materials, and directly determines the magnitude of temperature deformation. Research on the thermal expansion coefficient of cement mortar at home and abroad is focused on a macroscopic test method, and the given thermal expansion coefficient has larger discreteness due to raw materials, mixing ratio, environmental conditions, test equipment, test method, operation technology of testers and the like.
The overall properties of the composite material depend on the properties, geometry, and topology of the constituent materials. Cement mortar is a complex heterogeneous porous medium material, and has the advantages of various composition substances, coexistence of solid, liquid and gas phases, disordered distribution, wide scale range of the substance distribution, distribution from nanometer to micrometer and millimeter, and great change of the composition structure in the hydration process. The multi-scale method can consider the characteristics of the composition materials on different scales, realizes the simulation of the material performance from microscopic, microscopic and macroscopic, establishes the relationship among the composition performance, the microstructure and the macroscopic performance of the material, and fundamentally explains the change mechanism of the macroscopic performance of the material, thereby having great significance for promoting the research of the material.
Disclosure of Invention
The invention aims to provide a multi-scale prediction method for the thermal expansion coefficient of hardened cement mortar, aiming at the defects of the prior art. According to the parameters such as the mixing proportion of cement mortar, the cement chemical composition, the type of sand and the like, the thermal expansion coefficient can be determined by adopting a multi-scale method, so that accurate parameters are provided for cement-based material mechanics, deformation performance research, numerical simulation analysis and structural design.
The aim of the invention is realized by the following technical scheme: a multi-scale prediction method for the thermal expansion coefficient of hardened cement mortar comprises the following steps:
(1) The cement mortar is divided into different scales according to microstructure composition, and the different scales comprise different phases.
(2) And (3) respectively obtaining the volume percentage content of different phases in different scales divided in the step (1).
(3) Gradually adopting a homogenization method from the minimum scale to the top, and calculating the bulk modulus of each scale according to the volume percentage content of different phases in different scales obtained in the step (2)
wherein ,kr 、f r Bulk modulus, volume fraction, etc. of the r-th phase of dimension X, respectively;k 0 bulk modulus, g, of reference medium for dimension X 0 Shear modulus for scale X reference medium; finally obtaining the bulk modulus of the cement mortar>
(4) Gradually adopting a homogenization method from the minimum scale to the top, and calculating the temperature stress coefficient of each scale according to the volume percentage content of different phases in different scales obtained in the step (2)
wherein ,κr Temperature stress coefficient for dimension X r-th phase; finally obtaining the temperature stress coefficient of the cement mortar
(5) Bulk modulus of Cement mortar obtained according to step (3) and step (4)And temperature stress coefficientCalculating the thermal expansion coefficient alpha of cement mortar M ：
Further, the step (1) specifically comprises the following steps: dividing cement mortar into five scales of a scale I, a scale II, a scale III, a scale IV, a scale V and the like in sequence from small to large according to microstructure composition; the scale I comprises a basic block of calcium silicate hydrate and a nano-pore; the scale II comprises a hydrated calcium silicate solid phase and gel pores after the scale I is homogenized; the scale III comprises high-density hydrated calcium silicate homogenized by the scale II and low-density hydrated calcium silicate homogenized by the scale II; the scale IV comprises hydrated calcium silicate, calcium hydroxide, unhydrated cement particles, aluminate and capillary holes after the homogenization of the scale III; and the dimension V comprises cement paste and sand homogenized by the dimension IV.
Further, the cement mortar is obtained after the homogenization of the dimension V.
Further, the step (2) specifically comprises: the volume percentage of different phases on the scales I, II, III and IV is obtained by test or calculated by a Powers model, a Jennings-Tennis model or a CEMHYD3D model; the volume percentage of different phases on the scale V is obtained according to the mixing proportion of the cement mortar.
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, adopting a Self-consistency method to calculate homogenized high-density calcium silicate hydrate and low-density calcium silicate hydrate, wherein the reference medium is the high-density calcium silicate hydrate and the low-density calcium silicate hydrate; calculating homogenized calcium silicate hydrate on the scale III by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate; calculating homogenized cement paste on the scale IV by adopting a Self-consistency method, wherein a reference medium is cement paste; and on the scale V, the Mori-Tanaka method is adopted to calculate the homogenized cement mortar, and the reference medium is cement paste.
The beneficial effects of the invention are as follows: the invention establishes a prediction method of the thermal expansion coefficient of the hardened cement mortar based on the microstructure characteristics of the cement mortar, establishes a connection between the microstructure and macroscopic thermal expansion performance of the cement mortar, and fundamentally solves the problems of multiple influence factors of the macroscopic performance of cement-based materials and large dispersion of test data. According to the method, under the condition of inputting basic parameters, the thermal expansion coefficient of the hardened cement mortar can be conveniently determined, the testing device is not needed, and the precision level reaches the nanometer scale.
Drawings
FIG. 1 is a schematic diagram of a multiphase, multi-scale compounding process for cement mortar;
FIG. 2 is a graph showing comparison between the thermal expansion coefficient test value and the predicted value of cement mortar.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings:
according to the multi-scale prediction method for the thermal expansion coefficient of the hardened cement mortar, the thermal expansion coefficient of the cement mortar is deduced according to the microstructure composition of the cement mortar and the related performance of each composition material.
The invention relates to a multi-scale prediction method for the thermal expansion coefficient of hardened cement mortar, which specifically comprises the following steps:
step 1, dividing cement mortar into five scales in sequence from small to large according to microstructure composition: scale i, scale ii, scale iii, scale iv, scale v.
Because the occurrence mechanisms of the microcomponents on the performances of different materials are different, the cement mortar is divided into the following scales from the point of view of thermal expansion mechanism as shown in fig. 1:
dimension I includes basic blocks of calcium silicate hydrate (C-S-H basic building block) and nanopores (nanoposities); scale ii includes calcium silicate hydrate solid phase (C-S-H solid) and gel pore (gel porosity); scale iii includes high density calcium silicate hydrate (HD C-S-H) and low density calcium silicate hydrate (LD C-S-H); scale iv includes homogenized calcium silicate hydrate (C-S-H), calcium Hydroxide (CH), unhydrated cement particles, aluminates, and capillaries; dimension v includes homogenized cement paste and sand. The minimum dimension of the dimension dividing method is a hydrated calcium silicate solid phase, and the characteristic dimension is in a nano dimension, so that the occurrence mechanism of thermal expansion performance and the essential attribute of the cement-based material are reflected; the maximum dimension is cement mortar.
And 2, respectively calculating the relative volume contents of the constituent phases with different scales.
The volume fractions of the different phases on scales I, II, III, IV were obtained from experiments (environmental scanning electron microscopy) or from the calculation of Powers model (Powers T.C., brownyard T.L.Studies of the Physical Properties of Hardened Portland Cement Pat.5. Studies of the Hardened Paste by Means of Specific-Volume Measurements [ J ]. Journal of American Concrete Institute,1947,18 (6): 669-711.), jennings-Tennis model (Jennings H.M., tennis P.D.model for the Developing Microstructure in Portland Cement Pastes [ J ]. Journal of the American Ceramic Society,1994,7 (12): 3161-3172 ]), CEMHYD3D model (A Three-Dimensional Cement Hydration and Microstructure Development Modeling Package, version3.0, national Institute of Standards and Technology, 2005.); the volume fractions of different phases on the scale V are obtained according to the mixing proportion of the cement mortar.
Step 3, starting from the minimum scale, gradually adopting a homogenization method upwards; the homogenization method calculates a homogenized calcium silicate hydrate solid phase on a scale I by adopting a Self-consistency method (see [ Eshelby J.D. the Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems [ C ]. Proceedings of the Royal Society of London Series A,1957 ], and the reference medium is the calcium silicate hydrate solid phase itself; on the scale II, calculating homogenized high-density and low-density hydrated calcium silicate by adopting a Self-consistency method, wherein a reference medium is the high-density and low-density hydrated calcium silicate; calculating homogenized calcium silicate hydrate on the scale III by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate; on the scale IV, calculating homogenized cement paste by adopting a Self-consistency method, wherein reference mediums are cement paste per se respectively; the homogenized cement mortar was calculated on scale V using the Mori-Tanaka method (see [ Mori T., tannaka K.average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions [ J ]. Acta Metallurgica,1973,21 (5): 571-574 ]) with reference to cement paste and sand as inclusions.
The bulk modulus of each scale was calculated according to the following formula
Wherein, the superscript hom represents homogenization, and the subscript X represents a dimension X; k (k) r 、f r Bulk modulus, volume fraction, k, of the r-th phase of the scale 0 For the bulk modulus of the scale reference medium, α 0 Calculated according to the following formula:
in the formula ,g0 For this scale the shear modulus of the medium is referenced.
Step 4, starting from the minimum scale, gradually adopting a homogenization method upwards, wherein the homogenization method adopted by each scale and the reference medium are consistent with the step 3; the temperature stress coefficient of each scale is calculated according to the following formula
wherein ,κr Temperature stress coefficient for the r-th phase of the scale
Step 5, on the scale of cement mortar, according to the bulk modulusAnd temperature stress coefficient>The homogenized thermal expansion coefficient alpha is calculated using the following formula M ：
According to the invention, monitoring through a testing device is not needed, and computer software can be programmed according to the steps by adopting languages such as MATLAB and the like to carry out quick solving.
In order to verify the predictive effect of the method of the invention, the following experimental verification was performed:
the method predicts the thermal expansion coefficient of the hardened cement mortar which adopts ordinary Portland cement, has the water cement ratio of 0.35,0.40,0.45,0.50, adopts river sand as aggregate and adopts standard curing for 28 days, and carries out comparison analysis with the test value. The test contents are specifically as follows:
1. overview
1.1 test raw materials
The cement used was Type I Portland Cement, the chemical composition of which is shown in Table 1.
TABLE 1 content of major chemical components of cements
1.2 test protocol
And placing the test piece into a standard curing room for curing after pouring, wherein the test piece is 100mm multiplied by 500mm in size. After curing for 28 days, the test piece is put into an oven for testing, and the thermal expansion coefficient of the test piece is tested by adopting a thermal expansion coefficient testing system.
1.3 coefficient of thermal expansion of the Main phase
Table 2 coefficients of thermal expansion of the components
2. Model verification and evaluation
The test values of the thermal expansion coefficients of the hardened cement mortars with different cement ratios and the predicted values of the invention are compared with each other as shown in figure 2. It can be seen that the fit between the predicted value and the test value is better, which indicates that the model can have better prediction precision.
The invention adopts a multi-scale method to establish a connection between the microstructure and the macroscopic performance of the cement mortar, and the thermal expansion coefficient of the hardened cement mortar can be predicted according to the chemical composition of the cement, the mixing proportion of the cement mortar and the sand type, which is difficult to realize in the prior art.
Claims (3)
1. A multi-scale prediction method for the thermal expansion coefficient of hardened cement mortar is characterized by comprising the following steps:
(1) Dividing the cement mortar into different scales according to microstructure composition, wherein the different scales comprise different phases;
(2) Respectively obtaining the volume percentage content of different phases in different scales divided in the step (1);
(3) Gradually adopting a homogenization method from the minimum scale to the top, and calculating the bulk modulus of each scale according to the volume percentage content of different phases in different scales obtained in the step (2)
wherein ,kr 、f r Bulk modulus and volume fraction of the r-th phase of the scale X;k 0 bulk modulus, g, of reference medium for dimension X 0 Shear modulus for scale X reference medium; finally obtaining the bulk modulus of the cement mortar>
(4) Gradually adopting a homogenization method from the minimum scale to the top, and calculating the temperature stress coefficient of each scale according to the volume percentage content of different phases in different scales obtained in the step (2)
wherein ,temperature stress coefficient for dimension X r-th phase; finally obtaining the temperature stress coefficient of the cement mortar>
(5) Bulk modulus of Cement mortar obtained according to step (3) and step (4)And temperature stress coefficient>Calculation of thermal expansion System of Cement mortarNumber alpha M ：
The step (1) specifically comprises the following steps: dividing cement mortar into five dimensions of a dimension I, a dimension II, a dimension III, a dimension IV and a dimension V in sequence from small to large according to microstructure composition; the scale I comprises a basic block of calcium silicate hydrate and a nano-pore; the scale II comprises a hydrated calcium silicate solid phase and gel pores after the scale I is homogenized; the scale III comprises high-density hydrated calcium silicate homogenized by the scale II and low-density hydrated calcium silicate homogenized by the scale II; the scale IV comprises hydrated calcium silicate, calcium hydroxide, unhydrated cement particles, aluminate and capillary holes after the homogenization of the scale III; the scale V comprises cement paste and sand homogenized by the scale IV;
the step (2) specifically comprises the following steps: the volume percentage of different phases on the scales I, II, III and IV is obtained by test or calculated by a Powers model, a Jennings-Tennis model or a CEMHYD3D model; the volume percentage of different phases on the dimension V is obtained according to the mixing ratio of the cement mortar;
the homogenization method in the step (3) and the step (4) 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, adopting a Self-consistency method to calculate homogenized high-density calcium silicate hydrate and low-density calcium silicate hydrate, wherein the reference medium is the high-density calcium silicate hydrate and the low-density calcium silicate hydrate; calculating homogenized calcium silicate hydrate on the scale III by adopting a Self-consistency method, wherein a reference medium is the calcium silicate hydrate; calculating homogenized cement paste on the scale IV by adopting a Self-consistency method, wherein a reference medium is cement paste; and on the scale V, the Mori-Tanaka method is adopted to calculate the homogenized cement mortar, and the reference medium is cement paste.
2. The method for multi-scale prediction of thermal expansion coefficient of hardened cement mortar according to claim 1, wherein said scale v is homogenized to obtain cement mortar.
3. The method of claim 1, wherein the test is an environmental scanning electron microscope test.
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