CN108279163B - Method for predicting cement-based material elastic modulus based on mercury intrusion test - Google Patents
Method for predicting cement-based material elastic modulus based on mercury intrusion test Download PDFInfo
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- CN108279163B CN108279163B CN201810108085.3A CN201810108085A CN108279163B CN 108279163 B CN108279163 B CN 108279163B CN 201810108085 A CN201810108085 A CN 201810108085A CN 108279163 B CN108279163 B CN 108279163B
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
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Abstract
The invention discloses a method for predicting the elastic modulus of a cement-based material based on mercury intrusion test, which comprises the following steps: obtaining a cement-based material sample, carrying out a mercury injection experiment on the dried sample, calculating the relation between the accumulated porosity and the pore diameter, converting the accumulated porosity into relative compactness, expressing the relative compactness and the pore diameter in a log-log coordinate system, determining a region in which the relative compactness and the pore diameter are linearly related, obtaining the slope of the region in which the relative compactness and the pore diameter are linearly related, determining characteristic parameters of a porous structure of the cement-based material according to the range and the slope of the linear correlation, and obtaining the elastic modulus of the cement-based material through iterative calculation based on an equivalent medium theory; the method solves the problem of excessive parameter setting in the prediction of the elastic modulus of the cement-based material based on hydration dynamics and mesomechanics, and thus, a simple analysis method for predicting the elastic modulus by using the characteristic parameters of the porous structure of the cement-based material is established.
Description
Technical Field
The invention relates to the technical field of analysis and characterization of inorganic non-metallic materials, in particular to a method for analyzing and characterizing cement-based material performance indexes based on mercury intrusion experiments.
Background
For cement-based materials, the elastic modulus (young's modulus, bulk modulus, shear modulus) plays an important role in structural design and analysis. In view of the importance of elastic modulus, the prior work on cement-based materials has led to various predictive methods. In general, current prediction methods can be divided into two broad categories: analytical method and numerical method. The analytic method establishes a proper mesomechanics method based on the geometrical and physical characteristics of the cement-based material; compared with an analytical method, the numerical method directly solves a basic rigid equation and relies on the powerful computing power of a computer. A number of research results have shown that the accuracy of various prediction methods depends mainly on the accuracy of the characterization of the porous structure of the cement-based material.
Cement-based material porous structures exhibit extremely complex heterogeneous characteristics, typically spanning multiple scales from nanometers to micrometers. On the nanometer scale, basic units with the size of about 5 nanometers are stacked to form hydrated calcium silicate gel with a porous structure; on the micrometer scale, the disordered stacking of hydrated products (calcium silicate hydrate gel, calcium hydroxide, ettringite) and unhydrated clinker forms a capillary pore structure. Therefore, for cement-based materials, accurate characterization of the porous structure and prediction of the elastic modulus requires fundamentally solving the multi-scale problem. For example, a two-scale homogenization method is a commonly used method that uses the Mori-Tanaka method and self-consistent theory for nano-scale calcium silicate hydrate gel and micro-scale cement slurry, respectively. Notably, the multi-scale method requires a large number of parameters to be set when performing cross-scale description from nano-scale to micro-scale, and the equivalent parameters are difficult to directly measure in experiments. In addition, the multi-scale method has the problems of low efficiency, poor operability and the like, particularly for cement-based composite materials doped with mineral admixtures.
In recent years, researchers have found that cement-based material porous structures have remarkable self-similar characteristics, and further, a geometric method is developed to describe and construct the porous structures of the cementing materials. The geometric method solves the problems of low efficiency, poor operability and the like of a multi-scale method, so that the porous structure of the cementing material is efficiently constructed. Therefore, by combining a mesomechanics method (such as an equivalent medium theory), the porous structure of the cement-based material constructed based on the geometric method also provides feasibility for predicting the elastic modulus of the cement-based material.
Disclosure of Invention
Aiming at the existing problems, the invention aims to provide a simple analysis method for establishing the elastic modulus of the cement-based material, which solves the problems that the assumed conditions are unreasonable and the parameters are difficult to measure in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a method for predicting the elastic modulus of a cement-based material based on a mercury intrusion test comprises the following steps:
1) manufacturing a cement-based material sample according to requirements, and freeze-drying the cement-based material sample for later use;
2) carrying out mercury injection experiment on the sample obtained in the step 1), gradually applying pressure P to obtain the accumulated porosity f, and calculating the relation between the accumulated porosity f and the diameter of the pore d;
3) converting the accumulated porosity f of the sample into relative compactness chi, and representing the relative compactness chi and the pore diameter d in a double logarithmic coordinate system;
4) determining the relative compactness chi and the area (d) linearly related to the pore diameter d1～d2)，d1<d<d2Wherein d is1Denotes the lower limit of the diameter, d, which is linearly related2Expressing the upper diameter limit of linear correlation, and calculating the slope A of the linear correlation region of the relative compactness chi and the pore diameter d by applying a least square method;
5) according to the range of linear correlation (d)1～d2) Determining mathematical parameters (n, i, b) for constructing the porous structure with the slope A, wherein n represents the total number of pore phases and solid phases of the iteration element in one-dimensional direction, i represents the iteration number, and b represents the number of the solid phases in the iteration element;
6) based on equivalent medium theory, the porous structure characteristic parameters (n, i, b) and the solid-phase elastic modulus (shear modulus G)0Bulk modulus K0) And obtaining the elastic modulus of the cement-based material through iterative calculation.
In the operation process of the step 2), the pores of the cement-based material are regarded as cylinders with different diameters, and the calculation formula between the cumulative porosity f and the diameter of the pores d is as follows:
wherein, γsSurface tension of mercuryForce, θ, represents the contact angle of mercury with the pore surface.
In the operation process of the step 3), the calculation formula for converting the accumulated porosity f of the sample into the relative compactness x is as follows: χ ═ 1-f.
In the operation process of the step 4), the calculation formula for calculating the slope A of the linear correlation region of the relative compactness chi and the pore diameter d by using a least square method is as follows:
where ∑ denotes the sum and S denotes the number of samples.
In the operation process of the step 5), n, i and b are all positive integers.
In the operation process of step 5), the calculation method of the mathematical parameters n and i for constructing the porous structure comprises the following steps:
in the operation process of the step 5), the calculation method of the mathematical parameter b for constructing the porous structure comprises the following steps: (b ═ n)3-A)。
In the operation process of the step 6), the shear modulus G of the solid phase is obtained by a nano indentation test experiment0The modulus of change of the solid body is measured to be K0。
In the operation process of step 6), the solid phase is regarded as a matrix phase and the pore phase is regarded as a distribution phase, and the volume fraction c of the pore phase is 1-b/n3. After one iteration, the elastic modulus calculation formula of the iteration phase is as follows:
wherein G is1，K1The shear modulus and the bulk modulus of the iteration phase after 1 iteration.
Based on the equivalent medium theory, the iterative phase is regarded as the matrix phaseThe pore phase is regarded as a distribution phase, and the volume fraction c of the pore phase is 1-b/n3. After i iterations, the elastic modulus calculation formula of the iteration phase is as follows:
wherein G isi，KiThe shear modulus and the volume change modulus of an iteration phase after i iterations; gi-1，Ki-1The shear modulus and the bulk modulus of the iterative phase after i-1 iterations.
After i iterations, the iteration phase represents the integral structure of the porous structure of the cement-based material to be researched, and the shear modulus and the bulk modulus of the integral cement-based material are respectively Gi，Ki。
The invention has the advantages that: compared with the problem of excessive parameter setting in the prior art based on hydration dynamics and mesomechanics methods, the analytical method for predicting the elastic modulus is established on the basis of efficiently constructing the porous structure of the cement-based material.
The mercury intrusion test applied by the method is a general technical means in the research of cement-based materials, theoretical data of the elastic modulus of the cement-based materials are finally obtained by processing the data according to the experimental data measured by the mercury intrusion test, and the theoretical data of the elastic modulus of the cement-based materials are basically the same as the finally measured data by comparing the data with the finally measured test value, so that the workload of final measurement is greatly reduced.
The method adopts a unified mathematical formula to carry out iterative calculation in the whole process, does not contain any unreasonable assumed conditions or experiment parameters which are difficult to measure, and has important significance for developing an efficient construction method of a porous structure and establishing a simple analysis method of the elastic modulus for the performance research of the cement-based material.
Drawings
FIG. 1 is a graph of experimental data for mercury intrusion into a cement slag slurry according to an embodiment of the present invention;
FIG. 2 is a graph showing data analysis of a mercury intrusion test of cement slag slurry according to an example of the present invention;
FIG. 3 is a diagram showing mathematical parameters for constructing a porous structure of a cement slag slurry in an example of the present invention;
FIG. 4 is a diagram showing a model for constructing a porous structure of a cement slag slurry in an example of the present invention;
FIG. 5 is an iterative graph showing prediction of the modulus of elasticity of a cement slag slurry in an example of the present invention;
FIG. 6 is a comparison of a predicted value of the modulus of elasticity of the cement slag slurry in the example of the present invention with that of the ultrasonic test.
Detailed Description
The invention is described in further detail below with reference to the following description of the drawings and the detailed description.
The cement-based materials mentioned in the examples of the present invention are mainly formulated by mixing cement and mineral admixtures (e.g. granulated blast furnace slag) with water. The cement-based material porous structure after curing and hardening comprises gel pores and capillary pores. The pores of the cement-based material are represented by complex geometric shapes and random spatial distribution. The mercury intrusion test is widely applied to the pore distribution characterization of cement-based materials due to the simple principle and equipment, and is a conventional test means in the field of cement-based material research.
Example 1: a method of constructing a porous structure of a cement-based material, as illustrated in figures 1, 2, 3 and 4, comprises the following:
1) obtaining a cement-based material sample, and freeze-drying the cement-based material sample:
mixing the cement, the slag powder and water, and maintaining in a standard curing room for 28 days. Taking cured cement slag slurry small blocks (about 0.5 cm)3) And a plurality of the dried powder are placed in a liquid nitrogen atmosphere for freezing (about 2-3 min), and then placed in a vacuum drying oven for vacuumizing, the weight of water loss is recorded every 24h until the weight reaches 0.01%/day, and the whole drying process lasts for about 1 week.
2) Taking the dried sample to carry out mercury injection experiment, gradually applying pressure, and calculating the relationship between the accumulated porosity and the pore diameter:
taking the dried sample to carry out mercury injection experiment, and obtaining the accumulated porosity f (f) (P) with the applied pressure P ranging from 0 MPa to 206 MPa; regarding the pores of the cement-based material as cylinders with different diameters, and calculating the relationship between the cumulative porosity f and the pore diameter d of the sample, namely f (d), wherein the calculation method comprises the following steps:
wherein gamma iss0.48N/m represents the surface tension of mercury, and θ 140 ° represents the contact angle of mercury with the pore surface.
Mercury intrusion data (cumulative porosity versus pore diameter) were obtained for the cement slag slurry samples measured as shown in fig. 1.
3) Converting the accumulated porosity into relative compactness, and expressing the relative compactness and the pore diameter in a log-log coordinate system:
the cumulative porosity f of the sample was converted to a relative solidity χ, i.e., χ ═ 1-f. The relative solidity χ and the pore diameter d are represented in a log-log coordinate system.
4) Determining a region in which the relative compactness and the pore diameter are linearly related, and calculating the slope of the region in which the relative compactness and the pore diameter are linearly related by applying a least square method:
determining the region (d) in which the relative compactness is linearly related to the pore diameter1～d2) I.e. log χ ═ Alogd + B, d1<d<d2Wherein d is1Represents the lower limit of the diameter (d) in linear dependence1＝5nm)，d2Represents the upper diameter limit (d) of the linear dependence2320nm) as shown in fig. 2. Calculating the linear correlation area (d) of the relative compactness and the pore diameter by using a least square method1～d2) The calculation method of the slope A is as follows:
calculating to obtain: and A is 0.0608.
5) According to the linear correlation range (d)1～d2) And slope AMathematical parameters (n, i, b) for constructing the porous structure are determined, wherein a positive integer n represents the number of phases (including pore phases and solid phases) in one-dimensional direction of the iteration element (composed of pore phases and solid phases), a positive integer i represents the iteration number, and a positive integer b represents the number of solid phases in the iteration element, as shown in fig. 3.
6) Determining mathematical parameters n and i for constructing the porous structure, wherein the calculation method comprises the following steps:
wherein d is15nm denotes the lower limit of the linearly dependent diameter, d2320nm represents the upper diameter limit of the linear dependence, and a 0.0608 represents the slope of the region of the linear dependence of relative solidity on pore diameter. The calculation result is as follows: n is 4, i is 3.
7) Determining a mathematical parameter b for constructing the porous structure, wherein the calculation method comprises the following steps:
(b＝n3-A)
wherein a-0.0608 represents the slope of the region of linear correlation of relative solidity to pore diameter, and b-60, and the porous structure visualization was achieved based on MAT L AB software, as shown in fig. 4.
8) After i-3 times of iterative calculation, the calculation method is as follows:
wherein the shear modulus G011.2GPa, bulk modulus K031.3GPa, the parameter c is 1-b/n 35/64; the iterative process is shown in figure 5.
9) The prediction result of the elastic modulus of the cement slag slurry sample is as follows: young's modulus is 20.1GPa, shear modulus is 7.7GPa, and bulk modulus is 17.0 GPa. Meanwhile, the ultrasonic method is adopted to test and verify the method of the invention, and the result is shown in figure 6.
The results from the examples show that: the theoretical data of the elastic modulus of the cement-based material is basically the same as the final data measured by ultrasonic waves, in the actual operation process, the elastic modulus of the final product can be obtained by the method, the final measurement work is not needed, the measurement work is time-consuming and labor-consuming, and the measurement cost is high, so that the final measurement workload is greatly reduced.
It should be noted that the above-mentioned embodiments are merely preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and any combination or equivalent changes made on the basis of the above-mentioned embodiments are also within the scope of the present invention.
Claims (5)
1. A method for predicting the elastic modulus of cement-based material based on mercury intrusion test includes such steps as preparing the sample of cement substrate to obtain the characteristic parameters of porous structure, and features that the characteristic parameters (n, i, b) of porous structure and the elastic modulus (G) of solid phase are used0，K0) Obtaining the elastic modulus of the cement-based material through iterative calculation;
wherein n represents the total number of pore phases and solid phases in one-dimensional direction of the iteration element, i represents the iteration number, b represents the number of solid phases in the iteration element, G0And K0All obtained from nanoindentation test experiments, G0Denotes the shear modulus, K0Represents the bulk modulus;
the method comprises the following steps:
1) manufacturing a cement-based material sample according to requirements, and freeze-drying the cement-based material sample for later use;
2) carrying out mercury injection experiment on the sample obtained in the step 1), gradually applying pressure P, and obtaining accumulated porosity f (f) (P); calculating the relationship between the accumulated porosity f and the pore diameter d, regarding the pores of the cement-based material as cylinders with different diameters, and calculating the relationship between the accumulated porosity f and the pore diameter d of the sample, namely f (d), wherein the calculation method comprises the following steps:
wherein, γsRepresents the surface tension of mercury, and θ represents the contact angle of mercury with the pore surface;
3) converting the accumulated porosity f of the sample into relative compactness chi, and representing the relative compactness chi and the pore diameter d in a double logarithmic coordinate system;
4) determining the relative compactness chi and the area (d) linearly related to the pore diameter d1～d2)，d1<d<d2Wherein d is1Denotes the lower limit of the diameter, d, which is linearly related2Expressing the upper diameter limit of linear correlation, and calculating the slope A of the linear correlation region of the relative compactness chi and the pore diameter d by applying a least square method;
5) according to the range of linear correlation (d)1～d2) Determining characteristic parameters (n, i, b) of the porous structure of the cement-based material together with the slope A,
the method for calculating the characteristic parameters n and i of the porous structure of the cement-based material comprises the following steps:
the method for calculating the characteristic parameter b of the porous structure of the cement-based material comprises the following steps: (b ═ n)3-A)；
6) Based on equivalent medium theory, the porous structure characteristic parameters (n, i, b) and the solid-phase elastic modulus (G)0，K0) Obtaining the elastic modulus of the cement-based material through iterative calculation;
regarding the solid phase as a matrix phase and regarding the pore phase as a distribution phase, the volume fraction c of the pore phase is 1-b/n3，
After one iteration, the elastic modulus calculation formula of the iteration phase is as follows:
wherein G is1，K1The shear modulus and the volume change modulus of the iteration phase after 1 iteration;
after i iterations, the elastic modulus calculation formula of the iteration phase is as follows:
wherein G isi，KiThe shear modulus and the volume change modulus of the iteration phase after i iterations; gi-1，Ki-1The shear modulus and the volume change modulus of the iteration phase after i-1 iterations;
wherein G is0，G1，Gi，Gi-1The unit of (a) is GPa; ko，K1，Ki，Ki-1The unit of (a) is GPa; p is in MPa and θ is in °; the unit of d is nm; gamma raysThe unit of (1) N/m.
2. The method for predicting the elastic modulus of a cement-based material based on mercury intrusion test according to claim 1, wherein during the operation of step 3), the calculation formula for converting the cumulative porosity f of the sample into the relative compactness χ is as follows: χ ═ 1-f.
3. The method for predicting the elastic modulus of the cement-based material based on the mercury intrusion test according to claim 1, wherein during the operation of the step 4), a calculation formula for calculating the slope a of the linear correlation region of the relative compactness χ and the pore diameter d by using a least square method is as follows:
where ∑ denotes the sum and S denotes the number of samples.
4. The method for predicting the elastic modulus of a cement-based material based on mercury intrusion experiments as claimed in claim 1, wherein n, i and b are positive integers during the operation of the step 5).
5. The base of claim 1The method for predicting the elastic modulus of the cement-based material in the mercury intrusion test is characterized in that after i iterations, the iteration phase is the integral structure of the researched porous structure of the cement-based material, and finally the shear modulus G of the cement-based material is obtainediAnd bulk modulus Ki。
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