Method for predicting ultra-early elastic modulus of 3D printing set cement

Abstract

The invention discloses a 3D printing set cement ultra-early elastic modulus prediction method, and belongs to the field of cement-based material mechanical property research. The method comprises the following specific steps: carrying out an ultra-early elastic modulus test on a 3D printing set cement test piece by adopting a press-in method, and calculating an experimental value of the elastic modulus through mechanical response under a constant strain rate control condition; constructing a set cement ultra-early RVE model, and proposing a hydration degree quantitative calculation method based on a hydration reaction process; carrying out equivalent calculation on matrix phase elastic parameters forming the set cement based on a particle accumulation theory, and predicting a calculated value of the elastic modulus of the set cement by combining a micromechanics self-consistent model; the ultra-early rheological characteristics of set cement are considered, the model is corrected and optimized, and the precision of the prediction model is improved by combining indentation method data fitting. According to the method, the press-in method and the RVE model are combined, a set cement ultra-early time-varying elastic modulus prediction system is constructed, and technical support is provided for early mechanical research of 3D printing cement and building structure forming control optimization.

Description

Technical Field

[0001] The present invention relates to the field of research methods for the elastic modulus of building cement-based materials, and in particular to a method for predicting the ultra-early elastic modulus of 3D-printed cement stone. Background Art

[0002] In recent years, architectural 3D printing technology has become a research hotspot in civil engineering, owing to its sustainable advantages of increasing automated construction efficiency by over 50%, enabling the realization of complex geometries, and reducing material waste by 30%-40%. Cement-based materials, as the core medium in the printing process, have a dynamic rheological property, interlayer bond strength, and time-varying elastic modulus that directly determine the layer-by-layer stability and long-term service performance of printed structures. However, unlike traditional cast-in-place concrete, which relies on formwork for hardening, 3D-printed cement-based materials must rapidly develop a self-supporting elastic modulus in the ultra-early stage, from initial setting to the stage of stripping strength, to withstand the critical shear stress generated by the accumulation of overlying materials. This unique requirement makes accurately quantifying the evolution of the elastic modulus during this stage a key bottleneck in the controllability of the printing process. Traditional static compression testing requires removing standard specimens from the formwork and applying destructive loads, and is unable to capture the material's sudden changes in properties at ultra-early stages, on the minute-scale. Existing theoretical models for the ultra-early elastic modulus of cement paste fail to consider material composition and printing process parameters, hindering effective prediction of the elastic modulus of 3D-printed cement paste in the ultra-early stage.

[0003] Patent publications CN116186969A and CN117033850A both use micromechanics theory to partition ultra-high-performance concrete (UHPC) at multiple scales and predict its elastic modulus. However, the measured ages used in both applications are still conventional, and the composition of the RVE matrix and inclusion phases at the cement paste scale also follows the traditional division. Furthermore, the existing techniques do not provide a method for determining the key parameter, hydration, during the calculation process, and the predicted age does not reach the ultra-early stage. The prediction results rely on material input parameters, and the accuracy of these methods for 3D-printed cement paste has not been verified. Summary of the Invention

[0004] To address the deficiencies of the above-mentioned prior art, the present invention aims to provide a method for predicting the ultra-early elastic modulus of 3D-printed cement paste. First, a cement paste specimen is subjected to an indentation test using a press, and the elastic modulus of the cement paste specimen under constant strain rate loading is calculated using the indentation method. A representative volume element (RVE) model of the ultra-early age of cement paste is then reconstructed. The macroscopic and microscopic scales are linked in micromechanics, and the model is used for micromechanics calculation and analysis. The ultra-early age elastic modulus of cement paste is calculated based on particle packing theory and a self-consistent model in micromechanics. The elastic modulus E calculated from the self-consistent model is then corrected by nonlinear fitting based on the rheological properties of cement paste at ultra-early age. Finally, the experimental value of the ultra-early age elastic modulus of cement paste measured by the indentation method is compared with the value calculated using the self-consistent model in micromechanics to obtain the ultra-early age elastic modulus of cement paste. This method reduces the number of engineering tests, enhances operability, and provides theoretical and technical support for subsequent research on the elastic modulus of 3D-printed cement paste.

[0005] Specifically, the present invention provides a method for predicting the ultra-early elastic modulus of 3D printed cement stone, and the specific implementation steps are as follows:

[0006] A method for predicting the ultra-early elastic modulus of 3D printed cement stone, characterized in that the implementation steps include:

[0007] S1. Prepare cement paste specimens, perform ultra-early elastic modulus tests on the cement paste specimens using the indentation method, and obtain the results;

[0008] S2. Obtaining the experimental value of the elastic modulus of the cement paste specimen under constant strain rate loading conditions;

[0009] S3. Based on the ultra-early structural characteristics of cement paste, an ultra-early RVE model of cement paste is established, and the calculated value of the ultra-early elastic modulus of cement paste is obtained. The specific process is as follows:

[0010] S31. Measuring the degree of hydration of the cement paste forming the cement paste at the initial setting time, 3 hours after the initial setting time, and the final setting time using a conductivity method to obtain the volume fractions of the unhydrated cementitious material, hydration products, and pore water forming the cement paste at any hydration time;

[0011] S32. Calculate the ultra-early elastic modulus E of the cement paste, taking into account the water-binder ratio, age, degree of hydration, and the volume fractions of the unhydrated cementitious materials, hydration products, and pore water that form the cement paste;

[0012] S4. Based on the ultra-early rheological properties of cement paste, the elastic modulus E obtained in S3 is corrected by nonlinear fitting. The expression of the corrected elastic modulus E(t) is:

[0013] E(t)=EAe f(t)

[0014] Where: E is the elastic modulus of cement paste, A is the dimensionless correction coefficient, and f(t) is the rheological function related to age t;

[0015]

[0016] Where T is the age-related parameter, t and t i are arbitrary age and initial setting time respectively;

[0017] S5. Compare the test result obtained in S1 with the corrected elastic modulus E(t) obtained in S4 to verify the accuracy.

[0018] Preferably, in step S2, the specific expression of the elastic modulus of the cement stone specimen is:

[0019]

[0020] Where, E r is the reduced elastic modulus of the cement paste specimen, E1 and v1 are the elastic modulus and Poisson's ratio of the cement paste specimen, E i and v i are the elastic modulus and Poisson's ratio of the indenter.

[0021] Preferably, in step S3, the ultra-early RVE model of cement stone includes a matrix phase and an inclusion phase, wherein the matrix phase is unhydrated cementitious material, and the inclusion phase is hydration products and pore water.

[0022] Preferably, the three-phase components forming the cement stone include unhydrated cementitious material, hydration product and pore water, and the specific expressions of the volume fractions of the unhydrated cementitious material, the hydration product and the pore water are:

[0023]

[0024]

[0025] f p =1-f c -f h

[0026] Where α represents the degree of cement hydration with age, W / C is the water-cement ratio, and f c 、f h 、f p They represent the volume fraction of cementitious materials, the volume fraction of hydration products and the volume fraction of pores in cement paste respectively.

[0027] Preferably, in step S31, the specific expression for calculating the degree of hydration by the conductivity method is:

[0028]

[0029] Where K0 represents the electrical conductivity of the cement paste forming cement paste at the initial setting time, K t Indicates the electrical conductivity of the cement paste forming cement paste 3 hours after initial setting, K ∞ It represents the electrical conductivity of the cement paste that forms cement stone after complete hydration, β is the time parameter, k is the shape parameter of the hydration degree curve, and t is the hydration time.

[0030] Preferably, in step S32, the equivalent bulk modulus K of the matrix phase is c and shear modulus G c It is obtained by equivalent conversion based on the particle packing theory after considering the structural characteristics and viscoelastic properties of ultra-early cement stone, and the elastic modulus E is calculated based on micromechanics.

[0031] Preferably, in step S32, the water-binder ratio, age, hydration degree and volume fraction of unhydrated cementitious material, hydration product and pore water of cement paste are combined and the equivalent bulk modulus K is obtained. c and shear modulus G c On this basis, the bulk modulus K, shear modulus G and elastic modulus E in the micromechanics self-consistent model are obtained, and the specific expressions are:

[0032]

[0033] Where, f r , K r and G r They are volume fraction, bulk modulus and shear modulus respectively. a and b are parameters related to bulk modulus K and shear modulus G. n is the number of constituent phases of the material to be predicted, and r is one phase in the three-phase components of the material to be predicted.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1. This paper constructs a prediction model for the ultra-early elastic modulus of cement paste by comparing the experimental value of the ultra-early elastic modulus of cement paste measured by the indentation method with the calculated value of the ultra-early elastic modulus of cement paste using a micromechanics self-consistent model. The model is used to characterize the ultra-early elastic properties of 3D-printed cement paste, providing theoretical and technical support for subsequent research on the elastic modulus of 3D-printed cement paste.

[0036] 2. Based on the particle packing theory and the self-consistent model of micromechanics, the present invention reconstructs an RVE model suitable for calculating the ultra-early stage of cement stone, and proposes a calculation method for the key parameter hydration degree α in the cement stone hydration process. This method relies on conductivity technology and has the characteristics of short experimental cycle and strong operation convenience. Compared with finite element simulation, it significantly reduces the technical complexity and is suitable for rapid engineering applications.

[0037] 3. The present invention only needs to obtain three test values of the ultra-early elastic modulus of cement stone by the indentation method to predict the elastic modulus of cement stone at any ultra-early age, which greatly reduces the number of engineering tests and has strong operability. It has guiding significance for studying the relevant properties of 3D printed cement stone ultra-early material. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of the method for predicting the ultra-early elastic modulus of 3D printed cement stone according to the present invention;

[0039] Figure 2 This is a graph showing the elastic modulus-time curve of the indentation method for the preferred loading time of specimen 1 in the method for predicting the ultra-early elastic modulus of 3D printed cement stone of the present invention;

[0040] Figure 3 This is a graph showing the elastic modulus-time curve of the indentation method for the preferred indenter type of specimen 2 in the method for predicting the ultra-early elastic modulus of 3D printed cement stone of the present invention;

[0041] Figure 4 This is a graph showing the change of the rheological function f(t) over time in the method for predicting the ultra-early elastic modulus of 3D printed cement stone according to the present invention;

[0042] Figure 5 This is a curve diagram for verifying the ultra-early elastic modulus calculation model of cement stone specimens 1#, 2#, and 5# in the method for predicting the ultra-early elastic modulus of 3D printed cement stone of the present invention;

[0043] Figure 6 This is an error diagram of the calculation model for the ultra-early elastic modulus of cement paste specimens 1#, 2#, and 5# in the method for predicting the ultra-early elastic modulus of 3D printed cement paste of the present invention;

[0044] Figure 7 This is a curve diagram showing the verification of the calculation model for the ultra-early elastic modulus of cement paste No. 1, No. 8, and No. 9 at different initial setting times in the method for predicting the ultra-early elastic modulus of 3D printed cement paste according to the present invention;

[0045] Figure 8 This is an error diagram of the calculation model for the ultra-early elastic modulus of cement paste specimens 1#, 8#, and 9# in the method for predicting the ultra-early elastic modulus of 3D printed cement paste of the present invention;

[0046] Figure 9 This is a curve diagram for verifying the calculation model of the ultra-early elastic modulus of 6# and 7# 3D printed cement pastes in the method for predicting the ultra-early elastic modulus of 3D printed cement paste of the present invention. DETAILED DESCRIPTION

[0047] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0048] The present invention discloses a method for predicting the ultra-early elastic modulus of 3D printed cement stone. The ultra-early elastic modulus of cement stone is tested by an indentation method, and an RVE model of the ultra-early elastic modulus of cement stone is established. The test value of the ultra-early elastic modulus of cement stone measured by the indentation method is compared and fitted with the calculated value of the ultra-early elastic modulus of cement stone calculated by using a micromechanics self-consistent model to obtain the ultra-early elastic modulus of cement stone. The indentation head of the universal testing machine used in the indentation method is a cone with a semi-cone angle of 45°, a height of 10 mm, a depth of 5 mm, and a material of low carbon steel. The elastic modulus E i 206×10 3 MPa, Poisson's ratio v i The loading pressure accuracy of the universal testing machine indenter is 0.1~0.5N, and the loading speed accuracy is 0.001~0.005mm / m. During the entire loading process, the universal testing machine indenter is loaded at a uniform speed of 5mm / min, and the loading time is 1min. The specific implementation steps are as follows: Figure 1 As shown:

[0049] S1. Prepare cement paste specimens according to the mix ratio of the cement paste's ultra-early-age elastic modulus. After the cement paste specimens reach initial setting, perform an ultra-early-age elastic modulus test on the cement paste specimens using the indentation method. Record the indentation depth-time curves and load-indentation depth curves of the cement paste specimens at different ultra-early-age times. The relationship between the load F and the indentation depth h of the cement paste specimens at different ultra-early-age times is expressed as follows:

[0050]

[0051] Where E and v are the elastic modulus and Poisson's ratio of the cement paste specimen, respectively. is the half angle of the indenter.

[0052] S2. Based on the test results obtained in S1, calculate the elastic modulus of the cement stone specimen under constant strain rate loading conditions. The specific process is as follows:

[0053] The loading process of the indentation method in step S1 produces elastic and plastic deformation. The unloading curve represents the process of elastic recovery. By analyzing the unloading curve, the elastic modulus of the ultra-early cement paste can be calculated. The slope of the unloading segment of the indentation load-depth curve is defined as the contact stiffness S, and its fitted expression is:

[0054]

[0055] Where P is the indentation load, h is the indentation depth, B and m are fitting parameters, and h max is the maximum indentation depth, h f is the residual indentation depth.

[0056] Thus, the relationship between contact stiffness and reduced modulus is obtained, and the relationship expression is as follows:

[0057]

[0058] Where S is the contact stiffness, A(h o&p ) is the contact area. The contact area of the conical indenter selected here is circular in cross section, so the constant η=1, h o&p The calculation method for the indentation depth is as follows:

[0059]

[0060] Through the above analysis, according to the definition of reduced elastic modulus, the elastic modulus of cement paste at ultra-early stage can be solved, and the expression is as follows:

[0061]

[0062] Where, E r is the reduced elastic modulus of the cement paste specimen, E1 and v1 are the elastic modulus and Poisson's ratio of the cement paste specimen, E i and v i are the elastic modulus and Poisson's ratio of the indenter.

[0063] S3. Establish an ultra-early RVE model for cement paste. Specifically, it includes a matrix phase and an inclusion phase. The matrix phase is the unhydrated cementitious material, and the inclusion phase is the hydration product and water filling the pores. The hydration kinetic parameter hydration degree is measured, the elastic parameters of the unhydrated cementitious material in the matrix phase are corrected, and the elastic modulus of the multi-phase composite ultra-early cement paste is calculated. The specific steps include:

[0064] S31. The conductivity method is used to measure the hydration degree of the cement paste that forms the cement stone at the initial setting time, 3 hours after the initial setting time, and the final setting time. Based on the three-parameter model, the regular characteristics of the evolution of the hydration degree with time are revealed. Finally, the volume fractions of the three-phase components of the cement paste of the cement stone at any hydration time, namely, unhydrated cementitious material, hydration products, and pore water, are obtained, where the unhydrated cementitious material is the cementitious material remaining from the hydration reaction.

[0065] The specific expression for calculating the degree of hydration by the conductivity method is:

[0066]

[0067] Where K0 represents the electrical conductivity of the cement paste forming cement paste at the initial setting time, K t Indicates the electrical conductivity of the cement paste forming cement paste 3 hours after initial setting, K ∞ It represents the electrical conductivity of the cement paste forming cement stone after complete hydration, β is the time parameter, and k is the shape parameter of the hydration degree curve.

[0068] The time it takes for different cement pastes to fully hydrate varies, but generally exceeds 28 days. The relationship between the maximum hydration degree and the specific water-binder ratio in the cement paste is expressed as follows. This expression, combined with the conductivity measurement data, can further determine K ∞ The numerical value can be used to accurately calculate the degree of hydration.

[0069]

[0070] Based on S31, the hydration degree of cement paste at any age with a specific water-binder ratio is obtained, and the specific expression for calculating the volume fraction of the three phases is:

[0071]

[0072] f p =1-f c -f h

[0073] Where α represents the degree of cement hydration with age, W / C is the water-cement ratio, and f c 、f h 、f p They represent the volume fraction of cementitious materials, the volume fraction of hydration products and the volume fraction of pores in cement paste respectively.

[0074] S32. Through the calculation of the main influencing parameters in S31, the elastic properties of the unhydrated cementitious material are first corrected based on the particle packing theory. Then, the elastic modulus of the cement paste at an ultra-early stage is calculated using the micromechanics self-consistent model. The specific calculation process is as follows:

[0075] The main mineral components of the unhydrated cementitious materials in the ultra-early RVE model of cement paste are C3S, C2S, C3A and C4AF. The ultra-early cement particles do not produce too many hydration products with strong bonding effects. It is believed that the strength is mainly the stacking strength of the particles. Therefore, according to the particle stacking theory, the elastic properties of the unhydrated cementitious materials in the ultra-early RVE model of cement paste are corrected to obtain the corrected bulk modulus K of the gel particles. c and shear modulus G c , the corrected expression is:

[0076]

[0077] σ=0.5γH

[0078] Where, v c is the Poisson's ratio of the unhydrated cementitious material in the RVE model, v c The value is 0.30, G i represents the original shear modulus of the unhydrated cementitious material, σ is the effective confining compressive stress, P a is the standard atmospheric pressure, γ is the cement bulk density, and H is the effective compressive stress depth, which is 5 mm.

[0079] The bulk modulus K after correction of the cementitious material c and shear modulus G c On the basis of the micromechanics, considering the influencing factors such as water-binder ratio, age, hydration degree and volume fraction of each component of cement paste, the elastic modulus E of cement paste at ultra-early stage is obtained, and the specific expression is:

[0080]

[0081] Where, f r , K r and G r They are volume fraction, bulk modulus and shear modulus respectively. Since the cement stone components are regarded as three phases, f r , K r and G r Each includes three categories, namely f c 、f h 、f p , K c , K h , K p , G c , G h , G p The subscripts c, h, and p represent the three phases of cement paste, namely, unhydrated cementitious material, hydration products, and pore water, respectively. E is the ultra-early elastic modulus of cement paste obtained by micromechanical calculations. a and b are parameters related to the bulk modulus K and shear modulus G, respectively. The specific expressions are as follows:

[0082]

[0083]

[0084] The calculation results of step S4 and step S3 assume that the ultra-early-stage cement paste is an elastic material. In reality, the ultra-early-stage cement paste has rheological properties. Therefore, the elastic modulus E obtained in step S3 needs to be corrected by nonlinear rheological fitting to obtain the ultra-early-stage elastic modulus of the cement paste. The corrected elastic modulus E(t) is expressed as:

[0085] E(t)=EAe f(t)

[0086] Where: E is the elastic modulus of cement paste, A is the dimensionless correction coefficient obtained through nonlinear regression analysis, f(t) is the rheological function related to age t, and the specific expression of the rheological function is:

[0087]

[0088] Where f(t) is the rheological function related to age t, and the age-influencing parameters T are obtained by fitting, t and t i are arbitrary age and initial setting time respectively, t i The parameters f(t) are obtained by nonlinear regression analysis.

[0089] S5. Compare the test result obtained in S1 with the corrected elastic modulus E(t) obtained in S4 to verify the accuracy of the ultra-early elastic modulus of cement paste obtained in S4.

[0090] The following is a detailed description of a method for predicting the ultra-early elastic modulus of 3D printed cement stone according to the present invention with reference to examples:

[0091] The implementation process of the specific example is achieved as follows:

[0092] S1. Design the mix ratio for testing the ultra-early elastic modulus of cement paste. Prepare two cement paste specimens, ordinary cement paste and 3D-printed cement paste. The ordinary cement paste mix ratio is used for comparison with the 3D-printed cement paste mix ratio. The specific mix ratios are shown in Table 1.

[0093] Table 1

[0094]

[0095] According to the mix ratio of S1, the raw materials were mixed and placed into a cylindrical mold with a diameter of 160 mm and a height of 70 mm to make cement stone specimens.

[0096] Four groups of 1# cement stone specimens were prepared, and the loading times of the four groups were set to 0.5 min, 1 min, 2 min and 5 min respectively. The relationship curve between the elastic modulus and time of the cement stone specimens was recorded 3 to 8 h after pouring to determine the loading time of the indentation method.

[0097] Since cement paste has viscous characteristics in the early stage, the pressing method does not consider creep and relaxation. Therefore, it is necessary to determine a reasonable loading time first. The experimental instrument of this specific embodiment adopts INSTRON-5848 press, which adopts a loading rate of 0.5mm / s. Six ages are selected for the 1# cement paste specimen, that is, the loading time is set to 0.5min, 1min, 2min, and 5min 3 to 8h after pouring. The measured elastic modulus and time relationship curve is shown in Fig. Figure 2 .from Figure 2 It can be seen that the measurement results for the three loading times other than 5 minutes are relatively close, indicating that the loading time within 2 minutes has little effect on the ultra-early elastic modulus. The measurement results are unstable when the loading time is 5 minutes, indicating that with the increase of loading time and the improvement of hydration degree, the ultra-early elastic modulus of cement paste is more affected by its viscous deformation. Based on the above analysis, and considering that the loading time should not be too short, a loading time of 1 minute is selected.

[0098] The initial setting time of 1#, 8# and 9# cement stone specimens was controlled to 2h, 4h and 7h by retarding setting, and the influence of initial setting time on the test results was obtained.

[0099] Six groups of 2# cement stone specimens were prepared to determine the type of indenter used in the INSTRON-5848 press in the indentation method. The first and second groups were determined to use a conical indenter based on the indentation load-depth curve. The third, fourth, fifth, and sixth groups used conical indenters with semi-cone angles of 70.3°, 45°, 30°, and 15°, respectively. The ultra-early elastic modulus and time relationship curves at the same time point were measured and compared with the results of the traditional stress-strain method test. The traditional stress-strain method test was performed using a dial indicator and a WDW-50 micro-controlled electronic universal testing machine. The relationship curves of the ultra-early elastic modulus and time obtained for different indenters are shown in Figure 2. Figure 3 ,from Figure 3 It can be seen that the indenter with a semi-cone angle of 45° is closer to the results obtained by the traditional stress-strain method and is more suitable for indentation measurement.

[0100] S2. Based on the test results obtained in S1, calculate the elastic modulus of the cement stone specimen under constant strain rate loading conditions.

[0101] S3. Based on the structural characteristics of cement paste in its ultra-early stage, only trace amounts of hydration products exist in the cement paste, and the spatial structure formed between them does not have a strong bonding effect. Therefore, drawing on the particle packing density theory, it is believed that the strength contribution of cement paste in its ultra-early stage mainly comes from the cementitious materials, and the strength depends on the stacking strength of the cementitious materials. The RVE model of cement paste in its ultra-early stage is established, and the elastic modulus of cement paste in its ultra-early stage is obtained. The specific steps include:

[0102] S31. The conductivity method is used to measure the hydration degree of the cement paste that forms cement stone at the initial setting time, 3 hours after the initial setting, and the final setting time. Based on the three-parameter model, the regular characteristics of the evolution of the hydration degree with time are revealed, and finally the volume fraction of each component of the cement paste that forms cement stone at any hydration time is obtained.

[0103] S32. Considering the influencing factors such as water-binder ratio, age, hydration degree and volume fraction of each component of cement paste, the elastic modulus of cement paste at ultra-early stage is calculated based on particle packing theory and micromechanics self-consistent model.

[0104] S4. According to the ultra-early rheological properties of cement paste, the pressure injection method is compared with the initial setting time t i The test values of cement paste specimens were measured and the calculated values of cement paste at ultra-early stage were calculated using the self-consistent model of micromechanics. The micromechanics calculation method was modified. In order to explore the variation law of the dimensionless correction coefficient A in the correction model of ultra-early stage elastic modulus of cement paste and the rheological function f(t) related to age t, the elastic modulus of 1#, 2# and 5# cement paste specimens were tested by the elastic modulus indentation method from 2.5h to 9.0h after pouring. Then, the ultra-early stage elastic modulus of cement paste was obtained by combining the particle stacking theory and the calculated values of micromechanics. Finally, the values of A and the rheological function f(t) related to age t were obtained by fitting the modified model, as shown in the figure. Figure 4 .

[0105] S5. Compare the test result obtained in S1 with the corrected elastic modulus E(t) obtained in S4 to verify the accuracy of the ultra-early elastic modulus of cement paste obtained in S4.

[0106] Figure 5 This is a validation curve diagram of the calculation model for the ultra-early elastic modulus of cement paste specimens 1#, 2# and 5#. The figure reflects the degree of fit between the experimental values of the indentation method and the micromechanical calculation values of the three specimens, indicating that the model proposed in this patent can better predict the ultra-early elastic properties of cement paste specimens. Figure 6 This is the error diagram of the calculation model for the ultra-early elastic modulus of 1#, 2# and 5# cement stone specimens. The errors between the experimental values of the indentation method and the calculated values by micromechanics are both within 20%, proving the accuracy of the prediction model. Figure 7The curve diagram shows the validation of the calculation model for the ultra-early elastic modulus of cement paste specimens 1#, 8# and 9# at different initial setting times. The experimental data in the figure are consistent with the calculation results of the micromechanics model, verifying the effective prediction ability of the RVE model proposed in this method for the ultra-early elastic properties of cement paste specimens. Figure 8 This is the error diagram of the calculation model for the ultra-early elastic modulus of 1#, 8# and 9# cement stone specimens. The relative error between the measured data of the indentation method and the calculated value of the micromechanics model is less than 20%, which effectively verifies the high-precision characteristics of this model. Figure 9 This is a validation curve of the calculation model for the ultra-early elastic modulus of 6# and 7# 3D printed cement paste. The experimental comparison results of 3D printed cement paste with two different water-binder ratios show that the measured data are in good agreement with the model predictions, verifying the universality and prediction accuracy of this model.

[0107] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for predicting the ultra-early elastic modulus of 3D printed cement stone, characterized in that: Implementation steps include: S1. Prepare cement paste specimens, perform ultra-early elastic modulus tests on the cement paste specimens using the indentation method, and obtain the results; S2. Obtaining the experimental value of the elastic modulus of the cement paste specimen under constant strain rate loading conditions; S3. Based on the ultra-early structural characteristics of cement paste, an ultra-early RVE model of cement paste is established, and the calculated value of the ultra-early elastic modulus of cement paste is obtained. The specific process is as follows: S31. Measuring the degree of hydration of the cement paste forming the cement paste at the initial setting time, 3 hours after the initial setting time, and the final setting time using a conductivity method to obtain the volume fractions of the unhydrated cementitious material, hydration products, and pore water forming the cement paste at any hydration time; S32. Calculate the ultra-early elastic modulus E of the cement paste, taking into account the water-binder ratio, age, degree of hydration, and the volume fractions of the unhydrated cementitious materials, hydration products, and pore water that form the cement paste; S4. Based on the ultra-early rheological properties of cement paste, the elastic modulus E obtained in S3 is corrected by nonlinear fitting. The expression of the corrected elastic modulus E(t) is: E(t)=EAe f(t) Where: E is the elastic modulus of cement paste, A is the dimensionless correction coefficient, and f(t) is the rheological function related to age t; Where T is the age-related parameter, t and t i are arbitrary age and initial setting time respectively; S5. Compare the test result obtained in S1 with the corrected elastic modulus E(t) obtained in S4 to verify the accuracy.

2. The method for predicting the ultra-early elastic modulus of 3D printed cement stone according to claim 1, wherein: In step S2, the specific expression of the elastic modulus of the cement stone specimen is: Where, E r is the reduced elastic modulus of the cement paste specimen, E1 and v1 are the elastic modulus and Poisson's ratio of the cement paste specimen, E i and v i are the elastic modulus and Poisson's ratio of the indenter.

3. The method for predicting the ultra-early elastic modulus of 3D printed cement stone according to claim 1, wherein: In step S3, the ultra-early RVE model of cement stone includes a matrix phase and an inclusion phase, wherein the matrix phase is unhydrated cementitious material, and the inclusion phase is hydration products and pore water.

4. The method for predicting the ultra-early elastic modulus of 3D printed cement stone according to claim 1, wherein: In step S31, the specific expressions of the volume fractions of unhydrated cementitious materials, hydration products and pore water are: f p =1-f c -f h Where α represents the degree of cement hydration with age, W / C is the water-cement ratio, and f c 、f h and f p They represent the volume fraction of cementitious materials, the volume fraction of hydration products and the volume fraction of pores in cement paste respectively.

5. The method for predicting the ultra-early elastic modulus of 3D printed cement stone according to claim 1 or 4, characterized in that: In step S31, the specific expression for calculating the hydration degree using the conductivity method is: Where K0 represents the electrical conductivity of the cement paste forming cement paste at the initial setting time, K t Indicates the electrical conductivity of the cement paste forming cement paste 3 hours after initial setting, K ∞ It represents the electrical conductivity of the cement paste that forms cement stone after complete hydration, β is the time parameter, k is the shape parameter of the hydration degree curve, and t is the hydration time.

6. The method for predicting the ultra-early elastic modulus of 3D printed cement stone according to claim 1 or 5, characterized in that: In step S32, the equivalent bulk modulus K of the matrix phase c and shear modulus G c It is obtained by equivalent conversion based on the particle packing theory after considering the structural characteristics and viscoelastic properties of ultra-early cement stone, and the elastic modulus E is calculated based on micromechanics.

7. The method for predicting the ultra-early elastic modulus of 3D printed cement stone according to claim 1, characterized in that: In step S32, the water-binder ratio, age, hydration degree and volume fraction of unhydrated cementitious materials, hydration products and pore water of cement paste are combined and the equivalent bulk modulus K is obtained. c and shear modulus G c On this basis, the bulk modulus K, shear modulus G and elastic modulus E in the micromechanics self-consistent model are obtained, and the specific expressions are: Where, f r , K r and G r They are volume fraction, bulk modulus and shear modulus respectively. a and b are parameters related to bulk modulus K and shear modulus G. n is the number of constituent phases of the material to be predicted, and r is one phase in the three-phase components of the material to be predicted.

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