A method for decoding the creep compliance of high-density and low-density calcium silicate hydrate (CSH) gels

Abstract

The present application relates to a method for decoding the creep compliance of high-density and low-density calcium-silicate-hydrate (C-S-H) gel, comprising the following steps: Step 1, quantitatively characterizing the microstructure evolution of cement paste due to hydration reaction according to the component properties of selected macro-cement paste and creep loading conditions, including the evolution of hydration degree with time, the evolution of volume fraction of each phase with hydration degree and with time; Step 2, constructing a correlation model from the creep compliance of C-S-H gel at the microscale to the creep compliance of cement paste at the macroscale based on the theory of composite mechanics, and inversely analyzing to obtain the creep compliance of C-S-H gel combined with the creep test data of cement paste; Step 3, constructing a correlation model from the creep compliance of high-density C-S-H gel and low-density C-S-H gel at the sub-micron scale to the creep compliance of C-S-H gel at the microscale based on the theory of composite mechanics, and inversely analyzing to obtain the creep compliance of high-density C-S-H gel and low-density C-S-H gel.

Description

TECHNICAL FIELD

[0001] The application discloses a method for decoding creep compliance of high-density and low-density calcium silicate hydrate (C-S-H) gel, and belongs to the technical field of cement-based material mechanical behavior research. BACKGROUND

[0002] The creep of cement paste is the main source of concrete creep, and accurately characterizing the creep of cement paste is the premise of studying concrete creep. Generally speaking, C-S-H gel is considered to be the origin of the creep of cement paste. Two types of C-S-H, i.e. high-density C-S-H and low-density C-S-H, are observed through experiments, and the elastic modulus measured by nanoindentation is 29.4±2.4GPa and 21.7±2.2GPa respectively, which are considered to be the cornerstone of the multi-scale modeling of the elastic behavior of cement composites. It is reported that the creep of high-density C-S-H and low-density C-S-H shows non-aging characteristics in the first few days. However, the nanoindentation test is difficult to capture the short-term creep behavior and characteristic time of high-density C-S-H and low-density C-S-H. In general, there is still a lack of identification work on the full creep behavior of high-density C-S-H and low-density C-S-H. SUMMARY

[0003] To solve the problems in the prior art, the application provides a method for decoding creep compliance of high-density and low-density calcium silicate hydrate (C-S-H) gel, which is based on the obtained creep compliance of high-density C-S-H gel and low-density C-S-H gel, and combines the mechanical theory of composites, so that the creep behavior of cement paste and concrete can be accurately predicted.

[0004] The technical scheme adopted by the application to solve the above technical problems is as follows: a method for decoding creep compliance of high-density and low-density calcium silicate hydrate (C-S-H) gel, which comprises the following steps:

[0005] Step 1) quantitatively characterizing the microstructure evolution of cement paste caused by hydration reaction according to the component properties of the selected macro-cement paste and the creep loading conditions: including the evolution of hydration degree with time, the evolution of the volume fraction of each phase with hydration degree and with time;

[0006] Step 2) constructing a correlation model from the creep compliance of C-S-H gel at the microscale to the creep compliance of macro-cement paste based on the mechanical theory of composites, and inversely analyzing the creep compliance of C-S-H gel in combination with the creep test data of cement paste;

[0007] Step 3) Based on the composite mechanics theory, a correlation model is constructed from the creep compliance of high-density C-S-H gel and low-density C-S-H gel at sub-micron scale to the creep compliance of C-S-H gel at micro scale, and the creep compliance of high-density C-S-H gel and low-density C-S-H gel is obtained by inverse analysis, wherein the high-density is 1750 kg / m 3 , and the low-density is 1440 kg / m 3 .

[0008] Further, the specific method of step 1) is as follows:

[0009] Step 1.1) The Parrot-Killoh cement hydration evolution model is used, the mass fraction ratio of the four clinkers of cement, the water-cement ratio and the temperature condition are input, and the evolution curve of the hydration degree of each of the four clinkers of cement and the total hydration degree over time is calculated by iteration; the four clinkers are tricalcium silicate C3S, dicalcium silicate C2S, tricalcium aluminate C3A and tetracalcium aluminoferrite C4AF;

[0010] Step 1.2) The Ulm model is used to calculate the evolution of the four clinkers of cement, high-density C-S-H gel, low-density C-S-H gel, calcium hydroxide crystal, aluminate hydrate, water and pore with the hydration degree;

[0011] Step 1.3) Combined with steps 1.1) and 1.2), the volume fraction of the four clinkers, high-density C-S-H gel, low-density C-S-H gel, calcium hydroxide crystal, aluminate hydrate, water and pore in the above cement paste is calculated to evolve over time.

[0012] Further, the specific method of step 2) is as follows:

[0013] Step 2.1) The micro scale C-S-H gel creep compliance is correlated with the macro cement paste creep compliance by using a self-consistent format, at the micro scale, the cement paste is composed of a disordered structure including C-S-H gel, four clinkers of cement, calcium hydroxide crystal, aluminate hydrate, pore and water, the hydration degree curve obtained in step 1.1) is discretized, and it is assumed that the creep duration t c ≤t≤t end is composed of N constant hydration degree platform intervals, i.e. t i ≤t≤t i+1 , wherein 1≤i≤N, t1=t c and t N+1 =t endrespectively, represent the loading age and the end of creep age, respectively; in each hydration plateau interval, the microstructure of the cement paste is considered to be constant, and the hydrating reactants and the elastic hydrating products of the cement paste are assumed to be ellipsoidal inclusions, and the C-S-H gel is assumed to be spherical inclusion, and the hydrating reactants and the elastic hydrating products of the cement paste are four clinkers of cement, calcium hydroxide crystals, aluminate hydrates, pores and water; the elastic modulus of the C-S-H gel in the Laplace space is the Poisson's ratio is 0.24, and discretization is performed in the Laplace space, first, the complex variable s in the Laplace space is discretized numerically: s k = 10 -10+20(k-1) / (K-1) , wherein k = 1, 2, …, K, s k is the discrete value of the complex variable s, K represents the number of s k , K = 1000, and the variable s in the above equation is replaced by s k to obtain the elastic modulus of the C-S-H gel corresponding to s k in the Laplace space, denoted as According to the self-consistent scheme and the elastic-viscoelastic correspondence principle, the effective elastic stiffness tensor of the cement paste with a directional distribution of particle structure in s k and the i-th hydration degree plateau interval, i.e., t i ≤ t ≤ t i+1 , in the Laplace space is written as:

[0014]

[0015] wherein I represents a fourth-order unit tensor, r represents each component phase in the cement paste, and is taken as C3S, C2S, C3A, C4AF, C-S-H gel, calcium hydroxide crystals, aluminate hydrates, pores and water, represents the volume fraction of each phase corresponding to the i-th plateau interval, represents the elastic stiffness tensor of each phase in the Laplace space corresponding to s k and the i-th plateau interval; represents the Eshelby tensor of each phase;

[0016] The iteration solution of is performed An isotropic initial stiffness tensor is selected, substituted into on the right side of equation (1), the value of on the left side of equation (1) is calculated, when the difference between the input on the right side and the obtained on the left side is less than a preset threshold value, the iteration is ended, and the obtained is transversely isotropic, and the directionally averaged tensor of the effective elastic stiffness of the cement paste with randomly distributed phases in Laplace space is obtained The effective elastic modulus of the corresponding cement paste in Laplace space is further obtained All s k The corresponding After that, the two-mode fractional Maxwell model is used to fit The data, and the effective elastic modulus of the cement paste in Laplace space on the ith plateau interval is obtained The continuity condition of the creep curve of the cement paste in the ith and (i-1)th plateau intervals is considered for all N plateau intervals, that is, the creep compliance values at t=t i are the same, and the complete creep compliance J cem (t,t c ) of the cement paste is obtained

[0017]

[0018]

[0019]

[0020] wherein, is the difference between the creep compliance values of the cement paste at t=t i , L -1 represents the inverse Laplace transform, and s is a complex variable in Laplace space;

[0021] Step 2.2) Inverse calculation of the creep compliance of C-S-H gel, the appropriate elastic modulus of C-S-H gel in Laplace space is selected according to the creep test data of the cement paste Form, according to the properties of cement and the creep loading conditions, the volume fractions and evolution of the phases of the cement paste are calculated according to step 1), the creep of the cement paste is calculated according to step 2.1), and the following objective is optimized:

[0022]

[0023] wherein, RJ cem represents the relative error between the calculated value and the test value of the creep of the cement paste, J cem_c (t l ) and J cem (t l ) represent the calculated value and the test value of the creep of the cement paste at the t l time, respectively, n represents the number of test points, and when RJ cemThe elastic modulus of the corresponding C-S-H gel in Laplace space is obtained The creep compliance J of the C-S-H gel is obtained by Laplace inverse transform CSH (t) :

[0024]

[0025] Further, the specific method of step 3) is as follows:

[0026] Step 3.1) The creep compliances of the sub-micron scale high-density C-S-H gel and the low-density C-S-H gel are related to the creep compliance of the micro-scale C-S-H gel by using the Mori-Tanaka method, and the creep compliances of the high-density C-S-H gel and the low-density C-S-H gel are respectively characterized by the fractional order very slow constitutive relation:

[0027]

[0028] Wherein, E0 is the elastic modulus, β is the structure parameter, 0 < β ≤ 1; Γ(·) is the Gamma function, is the inverse Mittag-Leffler function, and the Mittag-Leffler function is expressed as The inverse Mittag-Leffler function is numerically calculated by the Mittag-Leffler function, the elastic modulus of the high-density C-S-H gel and the low-density C-S-H gel in Laplace space is characterized by the dual-mode fractional order Maxwell model, and is expressed as:

[0029]

[0030]

[0031] Wherein, s represents a complex variable of Laplace space, represents the modulus, characteristic time and fractional derivative in the first mode fractional order Maxwell model of the high-density C-S-H gel; represents the modulus, characteristic time and fractional derivative in the second mode fractional order Maxwell model of the high-density C-S-H gel; represents the modulus, characteristic time and fractional derivative in the first mode fractional order Maxwell model of the low-density C-S-H gel; represents the modulus, characteristic time and fractional derivative in the second mode fractional order Maxwell model of the high-density C-S-H gel; the modulus of the discrete C-S-H gel in Laplace space in step 2.1) is obtained, and here the modulus of the high-density C-S-H gel and the low-density C-S-H gel in sk Elastic modulus in Laplace space and Then, the Poisson's ratio of both is combined to derive s k Elastic stiffness tensor of corresponding high-density C-S-H gel and low-density C-S-H gel in Laplace space and According to Mori-Tanaka method, s k Effective elastic stiffness tensor of C-S-H gel containing high-density C-S-H gel inclusions with directional distribution in Laplace space

[0032]

[0033]

[0034]

[0035] where, represents the volume fraction of high-density C-S-H gel in C-S-H gel of the i-th plateau regime, and the volume fraction of low-density C-S-H gel in the i-th plateau regime and the volume fraction of low-density C-S-H gel The calculation is as follows: In formula (11), is s k Global strain concentration tensor of high-density C-S-H gel corresponding to the i-th plateau regime, where I represents a fourth-order unit tensor, and in formula (12), is s k Local strain concentration tensor of high-density C-S-H gel corresponding to the i-th plateau regime, where S HD represents the Eshelby tensor of high-density C-S-H gel in C-S-H gel, and the result is is transversely isotropic, and the directional average processing thereof can obtain the effective elastic stiffness tensor of C-S-H gel containing randomly distributed high-density C-S-H gel inclusions in Laplace space Thus, the corresponding effective elastic modulus E After obtaining all s k corresponding to The two-mode fractional Maxwell model is used to fit data, and thus the effective elastic modulus of C-S-H gel in Laplace space in the i-th plateau regime can be obtained The continuity condition of the C-S-H gel creep compliance curve in the i-th and (i-1)-th plateau interval is considered for all N plateau intervals, that is, the creep compliance value at t=t i , that is, the complete creep compliance J CSH (t,t c ) of the C-S-H gel is obtained.

[0036]

[0037]

[0038]

[0039] wherein formula (14) represents the effective creep compliance of the C-S-H gel in the i-th plateau interval , and s represents a complex variable in the Laplace space, by performing the inverse Laplace transform on . represents the difference between and J CSH (t i ,t c ).

[0040] Step 3.2) The creep compliances of the high-density C-S-H gel and the low-density C-S-H gel are inversely calculated, and the creep compliance forms of the two are set as formula (7), and the creep compliance J CSH_c (t) of the corresponding C-S-H gel is calculated according to step 3.1), and the creep parameters of the high-density C-S-H gel and the low-density C-S-H gel are optimized by determining the following objective:

[0041]

[0042] wherein RJ CSH represents the relative error between the calculated value and the inverse calculated value of the C-S-H gel creep, J CSH_c (t l ) and J CSH (t l ) respectively represent the calculated value of the C-S-H gel creep compliance at t l and the value of the C-S-H gel creep compliance at t l obtained by inversely calculating formula (6), when RJ CSH is the smallest, that is, the uniaxial creep compliances J HD (t) and J LD (t) of the high-density C-S-H and the low-density C-S-H are obtained.

[0043] Beneficial effects: Compared with the prior art, the technical scheme of the present application has the following beneficial effects:

[0044] 1. This invention considers cement hydration and the multi-level structure of cement paste. Through composite material mechanics methods, a quantitative correlation mechanism is established between the creep compliance of high-density CSH gel and low-density CSH gel at the submicron scale and the creep compliance of macroscopic cement paste. The creep compliance of high-density CSH gel and low-density CSH gel is obtained from macroscopic experimental data of cement paste through back analysis. For the first time, a method for obtaining the creep compliance of high-density CSH gel and low-density CSH gel is presented using back analysis. The method is simple to operate and has high calculation efficiency.

[0045] 2. Comparative verification confirms that this method has good accuracy.

[0046] 3. This invention can serve as the cornerstone of a multi-scale model for predicting the creep behavior of cement-based materials. Attached Figure Description

[0047] Figure 1 This is a flowchart of the present invention patent;

[0048] Figure 2 A schematic diagram of the multi-level structure of cement paste;

[0049] Figure 3 The results of this invention are compared with experimental data, including two sub-figures (a) and (b). Figure (a) shows the long-term basic creep of cement paste under various water-cement ratios calculated based on the obtained creep compliance of high-density CSH gel and low-density CSH gel, and compares it with the data. Figure (b) shows the early creep of cement paste at multiple ages calculated based on the obtained creep of high-density CSH gel and low-density CSH gel, and compares it with the data. Detailed Implementation

[0050] The technical solution of the present invention will now be further described in conjunction with the accompanying drawings and embodiments (the following embodiments are only descriptive and not limiting, and cannot be used to limit the scope of protection of the present invention).

[0051] This embodiment aims to demonstrate a method for obtaining the creep compliance of high-density CSH gels and low-density CSH gels. The flowchart is shown below. Figure 1As shown. First, based on the selected macroscopic cement paste data and corresponding cement composition and loading conditions, the volume fraction evolution of each phase in the cement paste over time is quantitatively calculated. Next, a correlation model is constructed from the creep compliance of CSH gel at the microscale to the creep compliance of cement paste at the macroscale. Combined with cement paste creep data, the creep compliance of CSH gel is obtained through back-analysis. Finally, a correlation model is constructed from the creep compliance of high-density and low-density CSH gels at the submicron scale to the creep compliance of CSH gel at the microscale. The creep compliance of high-density and low-density CSH gels is obtained through back-analysis. Specifically, the following steps are included:

[0052] Step 1) Based on the selected macroscopic cement paste component properties and creep loading conditions, quantitatively characterize the evolution of the cement paste microstructure caused by hydration reaction: including the evolution of hydration degree over time, and the evolution of the volume fraction of each phase with hydration degree and time.

[0053] Step 2) Based on the theory of composite material mechanics, construct a correlation model from the creep compliance of CSH gel at the microscale to the creep compliance of cement paste at the macroscale. Combine with the creep test data of cement paste, back-analyze to obtain the creep compliance of CSH gel.

[0054] Step 3) Based on the theory of composite material mechanics, construct a correlation model from the creep compliance of high-density and low-density CSH gels at the submicron scale to the creep compliance of CSH gels at the microscale. Inverse analysis is then used to obtain the creep compliance of high-density and low-density CSH gels, where the high density is 1750 kg / m³. 3 Low density is 1440 kg / m³ 3 .

[0055] The specific method for step 1) is as follows:

[0056] Step 1.1) Using the Parrot-Killoh cement hydration evolution model, input the mass fraction ratio of the four clinkers in the cement, the water-cement ratio, and the temperature conditions, and use iterative calculation to calculate the evolution curves of the hydration degree of each of the four clinkers and the total hydration degree over time; the four clinkers are tricalcium silicate C3S, dicalcium silicate C2S, tricalcium aluminate C3A, and tetracalcium aluminoferrite C4AF.

[0057] Step 1.2) The Ulm model was used to calculate the evolution of cement clinker, high-density CSH gel, low-density CSH gel, calcium hydroxide crystals, aluminate hydrates, water and pores with the degree of hydration.

[0058] Step 1.3) combined with steps 1.1) and 1.2) calculates the evolution of the volume fractions of the four types of clinker, high-density CSH gel, low-density CSH gel, calcium hydroxide crystals, aluminate hydrates, water and pores in the above cement paste over time.

[0059] The specific method for step 2) is as follows:

[0060] Step 2.1) A self-consistent scheme is used to correlate the creep compliance of CSH gel at the microscale with the creep compliance of the macroscale cement paste. At the microscale, the cement paste consists of a disordered structure including CSH gel, four types of cement clinker, calcium hydroxide crystals, aluminate hydrates, pores, and water. The hydration degree curve obtained in Step 1.1) is discretized, assuming a creep duration of t. c ≤t≤t end It consists of N constant hydration degree plateau intervals, i.e., t i ≤t≤t i+1 Where 1≤i≤N, t1=t c and t N+1 =t end These represent the loading age and the creep termination age, respectively. Within each hydration plateau interval, the microstructure of the cement paste is considered constant. The hydration reactants and elastic hydration products of the cement paste are assumed to be ellipsoidal inclusions, and the CSH gel is assumed to be a spherical inclusion. The hydration reactants and elastic hydration products of the cement paste are the four types of cement clinker, calcium hydroxide crystals, aluminate hydrates, pores, and water. The elastic modulus of the CSH gel in Laplace space is assumed to be... With a Poisson's ratio of 0.24, Discretization in Laplace space begins with numerical discretization of the complex variable s in Laplace space: s k =10 -10+20(k-1) / (K-1) Where k = 1, 2, ..., K, s k K represents the discrete values ​​of the complex variable s, where K represents s. k The number of [elements], K = 1000, will Replace the variable s in the text with s k Get s in Laplace space k The elastic modulus of the corresponding CSH gel is denoted as . Based on the self-consistent scheme and the elastic-viscoelastic correspondence principle, cement paste with oriented particle structure in s k and the i-th hydration plateau interval, i.e., t i ≤t≤t i+1 The corresponding effective elastic stiffness tensor in Laplace space Written as:

[0061]

[0062] Where I represents the fourth-order unit tensor, and r represents the constituent phases in the cement paste, taken as C3S, C2S, C3A, C4AF, CSH gel, calcium hydroxide crystals, aluminate hydrates, pores, and water. This represents the volume fraction of each phase corresponding to the i-th platform interval. s k The elastic stiffness tensors of each phase corresponding to the i-th platform interval in Laplace space; Represents the Eshelby tensor of each phase;

[0063] Iterative solution Choose an isotropic initial stiffness tensor and substitute it into the right side of equation (1). In the middle, calculate and obtain the left side of equation (1) The value, when the input on the right The result obtained from the left side If the difference is less than a preset threshold, the iteration ends, and the obtained value is... It is transversely isotropic. By directional averaging, we obtain the effective elastic stiffness tensor of the randomly distributed cement paste phases in Laplace space. This allows us to obtain the effective elastic modulus of the corresponding cement paste in the Laplace space. After obtaining all s k corresponding Then, a two-mode fractional Maxwell model was used for fitting. The data yields the effective elastic modulus of the cement paste in Laplace space on the i-th platform interval. Considering the continuity condition of the cement paste creep curve in the i-th and (i-1)-th plateau intervals for all N plateau intervals, i.e., t = t i The creep compliance value is the same at the same time, that is, the complete creep compliance J of the cement paste is obtained. cem (t,t c )

[0064]

[0065]

[0066]

[0067] in, The i-th and (i-1)-th platform intervals are at t=t i The difference in creep flexibility of cement paste at each location, L -1 Let represent the inverse Laplace transform, where s is a complex variable in the Laplace space;

[0068] Step 2.2) Back-calculate the creep compliance of CSH gel, and select an appropriate elastic modulus of CSH gel in Laplace space based on the creep test data of cement paste. Based on the cement properties and creep loading conditions, the volume fraction and evolution of each phase in the cement paste are calculated according to step 1), and the creep of the cement paste is calculated according to step 2.1). The process is then optimized through the following objectives:

[0069]

[0070] Among them, RJ cem J represents the relative error between the calculated and experimental values ​​of cement paste creep. cem_c (t l ) and J cem (t l ) represent the creep of cement paste at time t. l The calculated and experimental values ​​at time n, where n represents the number of test points, are given by RJ. cem The minimum value yields the corresponding elastic modulus of the CSH gel in Laplace space. The creep compliance J of CSH gel can be obtained by using the inverse Laplace transform. CSH (t):

[0071]

[0072] The specific method for step 3) is as follows:

[0073] Step 3.1) The Mori-Tanaka method was used to correlate the creep compliance of submicron-scale high-density and low-density CSH gels with the creep compliance of micro-scale CSH gels. Fractional-order extremely slow constitutive relations were used to characterize the creep compliance of high-density and low-density CSH gels respectively:

[0074]

[0075] Where E0 is the elastic modulus, β is the structural parameter, 0 < β ≤ 1; Г(·) is the Gamma function. It is the inverse Mittag-Leffler function, which is represented as: The inverse Mittag-Leffler function is numerically calculated using the Mittag-Leffler function. A two-mode fractional Maxwell model is employed to characterize the elastic modulus of high-density and low-density CSH gels in Laplace space, expressed as:

[0076]

[0077]

[0078] Where s represents a complex variable in the Laplace space, The modulus, characteristic time, and fractional derivative are represented in the first-mode fractional Maxwell model of high-density CSH gel. The modulus, characteristic time, and fractional derivative are represented in the second-mode fractional Maxwell model of high-density CSH gel. The modulus, characteristic time, and fractional derivative are represented in the first-mode fractional Maxwell model of low-density CSH gel. This represents the modulus, characteristic time, and fractional derivative in the second-mode fractional Maxwell model of the high-density CSH gel; similar to step 2.1), the modulus of the discretized CSH gel in Laplace space is obtained here, where the modulus of the high-density and low-density CSH gels in s... k Elastic modulus in Laplace space and Then, combining the Poisson ratios of the two, s is derived. k The corresponding elastic stiffness tensors of high-density CSH gel and low-density CSH gel in Laplace space and The si of CSH gels containing oriented, high-density CSH gel inclusions was calculated using the Mori-Tanaka method. k The effective elastic stiffness tensor in Laplace space corresponding to the i-th platform interval

[0079]

[0080]

[0081]

[0082] in, This represents the volume fraction of high-density CSH gel in the CSH gel of the i-th plateau region, based on the volume fraction of low-density CSH gel in the i-th plateau region. Volume fraction of low-density CSH gel calculate: In equation (11), For s in Laplace space kThe global strain concentration tensor of the high-density CSH gel corresponding to the i-th platform interval, where I represents the fourth-order unit tensor, in equation (12), It is a high-density CSH gel in Laplace space s k The corresponding local strain concentrated tensor, where S HD The Eshelby tensor of the high-density CSH gel in the CSH gel is obtained. It is transversely isotropic. By directional averaging, the effective elastic stiffness tensor of CSH gels with randomly distributed high-density CSH gel inclusions in Laplace space can be obtained. Thus, the corresponding effective elastic modulus can be obtained. In obtaining all s k corresponding Then, a two-mode fractional Maxwell model was used for fitting. The data can be used to obtain the effective elastic modulus of the CSH gel in Laplace space on the i-th plateau interval. Considering the continuity condition of the CSH gel creep compliance curve in the i-th and i-1-th plateau intervals for all N plateau intervals, i.e., t = t i The creep compliance value is the same at the same time, that is, the complete creep compliance J of CSH gel is obtained. CSH (t,t c );

[0083]

[0084]

[0085]

[0086] Equation (14) represents the effective creep compliance of the CSH gel in the i-th plateau interval. Through the The inverse Laplace transform is performed to obtain s, which represents a complex variable in the Laplace space; express and J CSH (t i ,t c The difference between )

[0087] Step 3.2) Back-calculate the creep compliance of high-density CSH gel and low-density CSH gel, and set the creep compliance of the two as Equation (7). According to Step 3.1), calculate the creep compliance J of the corresponding CSH gel. CSH_c(t), the creep parameters of high-density CSH gel and low-density CSH gel were optimized by determining the following objectives:

[0088]

[0089] Among them, RJ CSH J represents the relative error between the calculated and inverse values ​​of CSH gel creep. CSH_c (t l ) and J CSH (t l ) represent the CSH gel creep compliance at t l The calculated value at time t and the CSH gel creep compliance obtained by back calculation through equation (6) at t l The value at time RJ CSH At its minimum, the uniaxial creep compliance J of high-density CSH and low-density CSH is obtained. HD (t) and J LD (t).

[0090] 4. Verification through examples:

[0091] To verify the accuracy of this method, we first selected two sets of cement paste creep data for back analysis to obtain the creep parameters of high-density CSH gel and low-density CSH gel, as shown in Table 1. Based on the creep parameters obtained in Table 1, according to the multi-level model of creep compliance from high-density CSH gel and low-density CSH gel to CSH gel and then to cement paste, we predicted the creep data of several other independent cement pastes. The prediction results are shown in Table 1. Figure 3 As shown in a and b in the figure.

[0092] Table 1. Creep parameters of high-density and low-density CSH gels obtained from back analysis

[0093]

[0094] 5. Method Application Guidelines:

[0095] Once the macroscopic cement paste creep data is selected, the volume fraction evolution of each phase of the cement paste over time is first calculated based on the mass fraction ratio of cement clinker and the loading conditions. Then, based on the multi-level creep model of cement paste, the creep compliance of high-density CSH gel and low-density CSH gel is obtained through back-analysis of the macroscopic cement paste creep data at each scale through CSH gel.

[0096] In summary, the method proposed in this patent can guarantee sufficient accuracy and is simple to operate, thus having good promotional value.

Claims

1. A method of decoding the creep compliance of high density and low density calcium-silicate-hydrate (C-S-H) gels, characterized by, The method comprises the following steps: Step 1) quantitatively characterizing the microstructure evolution of the macro-cement paste caused by the hydration reaction according to the component properties of the selected macro-cement paste and the creep loading conditions: including the evolution of the hydration degree with time, the evolution of the volume fraction of each phase with the hydration degree and with time; Step 2) constructing a correlation model from the creep compliance of the C-S-H gel at the microscale to the creep compliance of the macro-cement paste based on the composite mechanics theory, and combining the creep test data of the cement paste to obtain the creep compliance of the C-S-H gel by inverse analysis; Step 3) Based on the composite mechanics theory, a correlation model is constructed from the creep compliance of high-density C-S-H gel and low-density C-S-H gel at the sub-micron scale to the creep compliance of C-S-H gel at the micro scale, and the creep compliance of high-density C-S-H gel and low-density C-S-H gel is obtained by inverse analysis, wherein the high density is 1750 kg / m 3 , and the low density is 1440 kg / m 3 ; The specific method of step 3) is as follows: Step 3.1) the creep compliances of the sub-micron scale high-density C-S-H gel and the low-density C-S-H gel are correlated with the creep compliance of the C-S-H gel at the microscale by using the Mori-Tanaka method, and the creep compliances of the high-density C-S-H gel and the low-density C-S-H gel are respectively characterized by using the fractional order special slow constitutive relation: where E0is the elastic modulus, β is a structural parameter, 0 < β ≤ 1; Γ(·) is the Gamma function, is the inverse Mittag-Leffler function, the Mittag-Leffler function is expressed as The inverse Mittag-Leffler function is numerically calculated by the Mittag-Leffler function, and a dual-mode fractional Maxwell model is used to represent the elastic modulus of high-density C-S-H gel and low-density C-S-H gel in Laplace space, which is expressed as: where s denotes the complex variable in Laplace space, denote the modulus, characteristic time and fractional derivative in the first mode fractional Maxwell model in high density C-S-H gel; denote the modulus, characteristic time and fractional derivative in the second mode fractional Maxwell model in high density C-S-H gel; denote the modulus, characteristic time and fractional derivative in the first mode fractional Maxwell model in low density C-S-H gel; denote the modulus, characteristic time and fractional derivative in the second mode fractional Maxwell model in high density C-S-H gel; the modulus of the discrete C-S-H gel in Laplace space in step 2.1), here in obtaining the elastic modulus of high density C-S-H gel and low density C-S-H gel in Laplace space at s k and Afterwards, the Poisson's ratio of both is combined to derive the elastic stiffness tensor of high density C-S-H gel and low density C-S-H gel in Laplace space k and According to the Mori-Tanaka method, the s k and the effective elastic stiffness tensor in Laplace space corresponding to the i-th plateau interval ​​ wherein, represents the volume fraction of high-density C-S-H gel in the C-S-H gel in the i-th plateau regime, and is calculated according to the volume fraction of low-density C-S-H gel in the i-th plateau regime and the volume fraction of low-density C-S-H gel is calculated as: In formula (11), is the s k and the global strain concentration tensor of high-density C-S-H gel corresponding to the i-th plateau regime, wherein I represents a fourth-order unit tensor, and in formula (12), is the s k corresponding to the local strain concentration tensor, wherein S HD represents the Eshelby tensor of high-density C-S-H gel in the C-S-H gel, and the obtained is transversely isotropic, and after directional averaging processing, the effective elastic stiffness tensor of the C-S-H gel with randomly distributed high-density C-S-H gel in the Laplace space is obtained , so as to obtain the corresponding effective elastic modulus After obtaining all s k corresponding to , the two-mode fractional Maxwell model is used to fit data, so as to obtain the effective elastic modulus of the C-S-H gel in the Laplace space in the i-th plateau regime The continuity condition of the C-S-H gel creep compliance curve in the i-th and i-1-th plateau regimes is considered for all N plateau regimes, that is, the creep compliance values at t=t i are the same, that is, the complete creep compliance J CSH (t,t c ) of the C-S-H gel is obtained. wherein formula (14) represents the effective creep compliance of C-S-H gel in the i-th plateau interval By taking the Laplace transform of where s is a complex variable in Laplace space; represents and J CSH (t i ,t c ) represents the difference between Step 3.2) Back-calculate the creep compliance of the high density C-S-H gel and the low density C-S-H gel, set the form of the creep compliance of both as (7) formula, according to step 3.1), the creep compliance of the corresponding C-S-H gel J is calculated CSH_c (t), the creep parameters of the high density C-S-H gel and the low density C-S-H gel are optimized by determining the following objectives: where RJ CSH represents the relative error between the calculated and back-calculated values of C-S-H gel creep, J CSH_c (t l ) and J CSH (t l ) represent the calculated value of C-S-H gel creep compliance at time t l and the value of C-S-H gel creep compliance at time t l back-calculated from (6), respectively, when RJ CSH is at a minimum, i.e. the uniaxial creep compliances J HD (t) and J LD (t) for high density C-S-H and low density C-S-H, respectively.

2. The method of decoding the creep compliance of high density C-S-H gel and low density C-S-H gel according to claim 1, characterized in that, The specific method of step 1) is as follows: Step 1.1) the Parrot-Killoh cement hydration evolution model is used, the mass fraction ratio of the four kinds of clinker of cement, the water-cement ratio and the temperature condition are input, and the evolution curves of the hydration degree of the four kinds of clinker of cement and the total hydration degree with time are calculated by using iteration; the four kinds of clinker are tricalcium silicate C3S, dicalcium silicate C2S, tricalcium aluminate C3A and tetracalcium aluminoferrite C4AF; Step 1.2) the Ulm model is used to calculate the evolution of the four kinds of clinker of cement, the high-density C-S-H gel, the low-density C-S-H gel, the calcium hydroxide crystal, the aluminate hydrate, the water and the pore with the hydration degree; Step 1.3) combining steps 1.1) and 1.2), the volume fractions of the four kinds of clinker of cement, the high-density C-S-H gel, the low-density C-S-H gel, the calcium hydroxide crystal, the aluminate hydrate, the water and the pore in the above cement paste are calculated to evolve with time.

3. A method of decoding the creep compliance of high density C-S-H gel and low density C-S-H gel according to claim 2, characterized in that, The specific method of step 2) is as follows: Step 2.1) A self-consistent scheme is used to correlate the creep compliance of CSH gel at the microscale with the creep compliance of the macroscale cement paste. At the microscale, the cement paste consists of a disordered structure including CSH gel, four types of cement clinker, calcium hydroxide crystals, aluminate hydrates, pores, and water. The hydration degree curve obtained in Step 1.1) is discretized, assuming a creep duration of t. c ≤t≤t end It consists of N constant hydration degree plateau intervals, i.e., t i ≤t≤t i+1 Where 1≤i≤N, t1=t c and t N+1 =t end These represent the loading age and the creep termination age, respectively. Within each hydration plateau interval, the microstructure of the cement paste is considered constant. The hydration reactants and elastic hydration products of the cement paste are assumed to be ellipsoidal inclusions, and the CSH gel is assumed to be a spherical inclusion. The hydration reactants and elastic hydration products of the cement paste are the four types of cement clinker, calcium hydroxide crystals, aluminate hydrates, pores, and water. The elastic modulus of the CSH gel in Laplace space is assumed to be... With a Poisson's ratio of 0.24, Discretization in Laplace space begins with numerical discretization of the complex variable s in Laplace space: s k =10 -10+20(k-1) / (K-1) Where k = 1, 2, ..., K, s k K represents the discrete values ​​of the complex variable s, where K represents s. k The number of [elements], K = 1000, will Replace the variable s in the text with s k Get s in Laplace space k The elastic modulus of the corresponding CSH gel is denoted as . Based on the self-consistent scheme and the elastic-viscoelastic correspondence principle, cement paste with oriented particle structure in s k and the i-th hydration plateau interval, i.e., t i ≤t≤t i+1 The corresponding effective elastic stiffness tensor in Laplace space Written as: where I represents the fourth-order identity tensor, r represents each constituent phase in the cement paste, and is taken as C3S, C2S, C3A, C4AF, C-S-H gel, calcium hydroxide crystals, aluminate hydrates, pores, and water, represents the volume fraction of each phase corresponding to the i-th plateau interval, represents the volume fraction of each phase corresponding to the i-th plateau interval, k and the elastic stiffness tensor of each phase in the i-th plateau interval in Laplace space; represents the Eshelby tensor of each phase; Iterative solution Choose an isotropic initial stiffness tensor and substitute it into the right side of equation (1). In the middle, calculate and obtain the left side of equation (1) The value, when the input on the right The result obtained from the left side If the difference is less than a preset threshold, the iteration ends, and the obtained value is... It is transversely isotropic. By directional averaging, we obtain the effective elastic stiffness tensor of the randomly distributed cement paste phases in Laplace space. This allows us to obtain the effective elastic modulus of the corresponding cement paste in the Laplace space. After obtaining all s k corresponding Then, a two-mode fractional Maxwell model was used for fitting. The data yields the effective elastic modulus of the cement paste in Laplace space on the i-th platform interval. Considering the continuity condition of the cement paste creep curve in the i-th and (i-1)-th plateau intervals for all N plateau intervals, i.e., t = t i The creep compliance value is the same at the same time, that is, the complete creep compliance J of the cement paste is obtained. cem (t,t c ) wherein is the difference between the creep compliance values of the cement paste in the i-th and i-1-th plateau interval at t = t i L -1 denotes the inverse Laplace transform, s is a complex variable of the Laplace space; Step 2.2) Inverse calculation of the creep compliance of C-S-H gel, selection of the appropriate elastic modulus of C-S-H gel in Laplace space from the creep test data of the cement paste Form, according to the cement properties and the creep loading conditions, calculation of the volume fractions and evolution of the phases of the cement paste according to step 1), calculation of the creep of the cement paste according to step 2.1), and optimization by the following objective: where RJ cem represents the relative error between the calculated and experimental values of the cement paste creep, J cem_c (t l ) and J cem (t l ) represent the calculated and experimental values of the cement paste creep at the t l time, respectively, and n represents the number of experimental points, when RJ cem is the minimum, the corresponding elastic modulus of the C-S-H gel in Laplace space is obtained The creep compliance J CSH (t) of the C-S-H gel is obtained by the inverse Laplace transform.

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