A method for predicting the mechanical properties of c-s-h gel
Patent Information
- Application Number
- CN202611057531.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-16
- Publication Date
- 2026-10-16
AI Technical Summary
水泥基材料脆性大、抗拉强度低,对偏心加载极为敏感
(1)本发明通过理论计算途径从根本上规避了上述实验难题,无需制备狗骨头型试件、无需夹持加载、无需担心端部破坏,仅需分子动力学模拟获得的微观结构参数和粉末样品的孔隙率即可完成胶凝力预测。这一方法完全克服了现有技术中数据离散性大、试件要求高、试验破坏性的三大缺陷,属于C-S-H凝胶拉伸性能表征领域的方法论突破。
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of micromechanical property prediction technology of cement-based materials, specifically relating to a method for predicting the mechanical properties of CSH gel. Background Technology
[0002] Calcium-silicate-hydrate (CSH) gel is one of the most important cementitious phases in cement concrete and a key component determining the mechanical properties and durability of cement-based materials. The molecular structure of CSH gel is a layered structure composed of alternating Ca-Si layers, connected by interlayer adhesion forces (mainly hydrogen bonds and van der Waals forces). The strength of these interlayer adhesion forces largely determines the tensile properties of CSH gel, thus affecting the overall strength of cement concrete. Hou et al., through molecular dynamics simulations, found that the calcium silicate sheets of CSH gel are connected by stable ionic-covalent Ca-O and Si-O bonds, making them difficult to fracture under tensile loads, while the interlayer region contains an unstable hydrogen bond network, which is prone to failure under tensile loads. Therefore, accurately characterizing and predicting the macroscopic tensile properties (i.e., interlayer adhesion) of CSH gel is of fundamental importance for optimizing the performance of cement-based materials.
[0003] Currently, the testing methods for the macroscopic tensile properties of CSH gels mainly rely on direct macroscopic tensile testing, which faces the following fundamental difficulties in practical applications: (1) Large data dispersion. Cement-based materials are brittle and have low tensile strength, making them extremely sensitive to eccentric loading. Even with the use of spherical tension joints or flexible connection devices, small deviations between the specimen and the force axis of the testing machine will still generate additional bending moments and secondary stresses, resulting in the tested tensile strength being far lower than the true value.
[0004] (2) Destructive nature of the test and end failure issues. Even with clamping methods using embedded reinforcing bars or end-bonded rigid plates, premature failure often occurs due to stress concentration in the clamping area or at the connection point, rather than effective fracture within the gauge length. This "non-gauge length fracture" problem makes the test results unable to truly reflect the intrinsic tensile properties of the material. In addition, these methods are all destructive tests, making it impossible to track the performance of the same specimen or monitor the evolution of its microstructure.
[0005] (3) High requirements for specimen preparation. Dog bone-shaped (dumbbell-shaped) specimens are difficult to form by powder pressing, and internal defects (such as pores and microcracks) are difficult to control, which further aggravates the dispersion of test results. For CSH gel, a nanoscale gel phase, macroscopic specimen preparation can hardly achieve accurate characterization of its microstructure.
[0006] To overcome the limitations of experimental testing, researchers have recently begun to use molecular dynamics (MD) simulations to explore the mechanical behavior of CSH gels at the microscopic scale. However, existing MD simulations and multi-scale methods focus on calculating macroscopic elastic constants such as elastic modulus and shear modulus, and there is still a lack of direct calculation and theoretical prediction methods for the ultimate tensile strength (i.e., gelling force) of CSH gels.
[0007] In fiber-reinforced cementitious composites, the interfacial bonding performance between the fiber and the matrix is crucial in determining the mechanical behavior of the composite. Single-fiber pull-out testing is a classic method for evaluating interfacial bonding performance. Li et al. conducted systematic single-fiber pull-out tests on nano-silica modified carbon fibers and cement matrices, finding that the formation of CSH gel near the fiber surface significantly improves interfacial bonding performance. In terms of theoretical models, researchers have established two types of debonding models—stress-controlled and energy-controlled—to describe the interfacial failure behavior during fiber pull-out. Zhao Xiangpeng et al. used lattice model theory to numerically simulate the single-fiber pull-out process, effectively reducing the requirements for instruments and operation in experimental testing. Patent CN115497580A constructs a correlation model from submicron-scale (HD CSH and LD CSH) creep compliance to macroscopic cement paste creep compliance, and obtains the creep performance of CSH gel through inverse analysis. This patent focuses on creep (time-dependent deformation) rather than the ultimate failure mechanism of "pull-out / slip," but provides a modeling approach from microscopic to macroscopic scales.
[0008] The above studies indicate a high degree of mechanical similarity between the fiber pull-out process from the matrix and the slip / pull-out process of silicate chains in the interlayer of CSH gel under tensile load. Both involve the relative displacement of the "reinforcement" (fibers or silica chains) from the "matrix" (cement matrix or Ca-Si layer) by overcoming interfacial bonding forces. However, no studies have yet systematically applied this analogy to the theoretical calculation of the macroscopic cementitious force of CSH gel.
[0009] Therefore, there is an urgent need to provide a method for predicting the mechanical properties of CSH gel based on the fiber pull-out analogy mechanism, so as to predict the macroscopic gelling force of CSH gel and overcome the technical defects of existing experimental testing methods, such as large data dispersion, high experimental difficulty, and stringent specimen requirements. Summary of the Invention
[0010] The technical problem this invention aims to solve is to provide a method for predicting the mechanical properties of CSH gel. It establishes a theoretical calculation model based on the silicon chain pull-out / slippage failure mechanism, directly calculating the gelling force (macroscopic tensile force) in the interlayer direction of CSH gel, thus avoiding data dispersion caused by differences in test specimens. Furthermore, it eliminates the need for destructive mechanical sample preparation, avoiding secondary damage such as microcrack propagation, and significantly improving the reliability of macroscopic tensile properties.
[0011] The technical solution adopted is as follows: A method for predicting the mechanical properties of CSH gel includes the following steps: (1) Establish a molecular dynamics CSH gel model and prepare CSH powder samples with the same variables; (2) Obtain the microstructure parameters of CSH gel under the target calcium-silicon ratio condition. The microstructure parameters include interlayer adhesion, average silicate chain length and number of silicate chains per unit area. (3) Obtain the porosity of a CSH gel powder sample with the same target calcium-silicon ratio conditions; (4) Substitute the interlayer adhesion force, the average chain length of the silicate chain, the number of silicate chains per unit area and the porosity into the pre-constructed gelation force theoretical calculation model to calculate the theoretical value of the macroscopic gelation force of CSH gel.
[0012] Preferably, the method for establishing the molecular dynamics CSH gel model in step (1) is as follows: using the target calcium-silicon ratio as a variable, by adjusting the number of interlayer calcium ions and water molecules in the Tobermorite configuration, molecular dynamics relaxation is performed using the ClayFF force field to obtain the CSH gel model.
[0013] Preferably, the method for preparing CSH powder samples under the same variables in step (1) is as follows: using chemical precipitation, synthesizing under the condition that the calcium-silicon molar ratio is consistent with the target calcium-silicon ratio, and obtaining powder samples by filtration and drying.
[0014] Preferably, the interlayer adhesion force, the average chain length of the silicate chain, and the number of silicate chains per unit area in step (2) are obtained by establishing and analyzing a CSH gel molecular dynamics model under the target calcium-silicon ratio condition; wherein, the interlayer adhesion force is obtained by simulating the peak stress of interlayer separation in the established molecular dynamics model, the average chain length of the silicate chain is obtained by averaging the number of silicon-oxygen tetrahedral connections, and the number of silicate chains per unit area is obtained by dividing the number of silicate chains on the model surface by the corresponding area.
[0015] Preferably, the porosity of the CSH gel powder sample in step (3) is obtained by water saturation method, nitrogen adsorption method or mercury porosimetry.
[0016] Preferably, the theoretical calculation model for cementitious force in step (4) is as follows: × ; Where F is the macroscopic tensile load, N, i.e., the theoretical cementing force; f is the interlayer adhesion force, N, obtained through molecular dynamics simulation; L is the average chain length, dimensionless, obtained through solid-state silicon spectroscopy or molecular dynamics simulation; B is the proportionality conversion coefficient, obtained through fitting, dimensionless; ρ is the porosity, %, and s is the cross-sectional area of the specimen, nm. 2 The value is calculated based on the size of the test block required for macroscopic tensile testing; n is the number of silicon chains per square nanometer, in nm. -2 The cell parameters were calculated using molecular dynamics simulations; 2 / π is the cosine of the angle between the silicon chain pull-out and tensile failure, with the angle ranging from 0 to 90°.
[0017] The formula for fiber pull-out failure is as follows: ; In the formula, P max τ is the maximum pull-out force of the fiber (N), τ is the average interfacial bond shear stress (MPa), and d is the fiber diameter (mm). The fiber embedding length (mm) is used; if the fiber has end anchoring (such as end hook steel fiber), the additional strength contributed by the end anchoring must also be added.
[0018] Preferably, the cementitious force theoretical calculation model uses the mathematical expectation of the cosine projection direction to geometrically approximate the randomly stacked silicate chain structure inside CSH. The processing procedure is as follows: Assuming the silicon chains are uniformly distributed, and applying a highly approximated approach to the randomly stacked structure within the CSH, the expected value of the cosine projection direction is: .
[0019] Preferably, the fitting process for B is as follows: The synthesized CSH gel powder was subjected to different degrees of decalcification and then pressed into cylindrical specimens. The splitting tensile strength was obtained by Brazilian splitting test. According to the FIB Model Code 2010 standard, the macroscopic tensile strength is 0.9 times the splitting tensile strength. The macroscopic tensile strength (MPa) is calculated, then divided by the initial cross-sectional area (mm²), which is calculated based on the required size of the actual test block.2 The macroscopic tensile force (N) is obtained. Substitute all parameters except B obtained from molecular dynamics simulations and tests into the formula: × ; Then, a linear fit was performed to obtain the value of B.
[0020] Preferably, the formulas and parameters required for the fitting process are as follows: The Brazilian split tensile strength formula is: ; In the formula, f tsp The tensile strength is the splitting tensile strength in MPa; P is the failure load in N; D is the diameter of the cylinder and H is the height of the cylinder, both in mm. The formula for macroscopic tensile strength is: ; In the formula, f t The tensile strength is the macroscopic tensile strength, i.e., the direct tensile strength, in MPa; P is the failure load, in N; and A is the initial cross-sectional area of the specimen failure section, both in mm². 2 ; The intensity conversion formula is: ; In the formula, f t This refers to the macroscopic tensile strength, i.e., the direct tensile strength, measured in MPa; f tsp The splitting tensile strength is expressed in MPa. The least squares formula used to fit B is: ; The forced fitted line passes through the origin (0,0); the numerator is x and... The sum of products has a denominator that is the sum of the squares of x.
[0021] Preferably, the prediction method is applicable to the prediction of mechanical properties of CSH gels with a calcium-to-silicon ratio in the range of 0.5 to 2.1.
[0022] This invention also provides a prediction system for a theoretical prediction method of macroscopic gelling force of CSH gels, comprising: The molecular dynamics simulation module can establish a CSH gel model under the target calcium-silicon ratio condition and output the interlayer adhesion force F, the average silicon chain length L, and the number of silicon chains per unit area n. The porosity testing module is used to obtain the porosity ρ of CSH gel powder samples under the same calcium-silicon ratio. The calculation module is used to substitute the above parameters into the formula to calculate the macroscopic cementitious force T; The output module is used to output the gelling strength prediction results.
[0023] The method for predicting the mechanical properties of CSH gel according to the present invention can be applied in the mix design of cement-based materials, optimization of mineral admixture dosage, or evaluation of the chemical erosion durability of CSH gel.
[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention fundamentally avoids the above-mentioned experimental difficulties through theoretical calculation. It eliminates the need for preparing dog bone-shaped specimens, clamping and loading, and end damage. The gelling force can be predicted using only the microstructure parameters obtained from molecular dynamics simulation and the porosity of the powder sample. This method completely overcomes the three major defects of existing technologies: large data dispersion, high specimen requirements, and destructive testing. It represents a methodological breakthrough in the field of CSH gel tensile property characterization.
[0025] (2) This invention systematically transfers the mechanical analysis framework of fiber pulling to the description of the pull-out behavior of silicate chains in the CSH gel interlayer for the first time, establishes the theoretical connection of "the sum of silicon chain pulling force = macroscopic gelling force", and processes the geometric approximation of the random stacked structure inside CSH through the mathematical expectation of the projection direction of the cosine value, realizing the cross-scale theoretical calculation from molecular scale parameters to macroscopic mechanical properties.
[0026] (3) The estimation method provided by this invention only requires basic data from molecular dynamics simulation and conventional powder porosity testing to obtain the macroscopic gelling force of CSH gel under different calcium-silicon ratios. Experimental verification shows that the calculated tensile force is close to the tensile force value after empirical conversion from the Brazilian splitting test and the trend of change is consistent, proving that the method has reliable prediction accuracy and can significantly reduce experimental costs and testing cycle.
[0027] (4) The theoretical calculation method proposed in this invention can directly deduce the gelation force evolution trend based on the changes in molecular dynamics model parameters (such as different microstructures corresponding to different decalcification degrees), providing a non-destructive evaluation tool for studying the performance degradation of CSH gel under environmental factors such as chemical erosion and temperature changes.
[0028] In summary, this invention establishes a theoretical prediction method for the macroscopic gelling force of CSH gel through interdisciplinary theoretical analogy innovation and cross-scale parameter correlation modeling. In terms of technical effect, it realizes a paradigm shift from "difficult to measure accurately" to "theoretically calculable", providing a brand-new theoretical tool for the precise design and optimization of cement-based material performance. Attached Figure Description
[0029] Figure 1 This is a linear fitting graph of the proportional conversion coefficient B of the present invention; where the horizontal axis X is the product of the independent variables other than the empirical coefficient B in the theoretical calculation formula. Detailed Implementation
[0030] The accompanying drawings are for illustrative purposes only. The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments are only preferred examples of the present invention and do not represent all the technical contents of the present invention.
[0031] Example 1 A prediction system for a theoretical prediction method of macroscopic gelling force of CSH gels, comprising: The molecular dynamics simulation module can establish a CSH gel model under the target calcium-silicon ratio condition and output the interlayer adhesion force F, the average silicon chain length L, and the number of silicon chains per unit area n. The porosity testing module is used to obtain the porosity ρ of CSH gel powder samples under the same calcium-silicon ratio. The calculation module is used to substitute the above parameters into the formula to calculate the macroscopic cementitious force F; The output module is used to output the gelling strength prediction results.
[0032] A method for predicting the mechanical properties of CSH gel includes the following steps: (1) Establish a molecular dynamics CSH gel model and prepare CSH powder samples with the same variables.
[0033] The method for establishing the molecular dynamics CSH gel model is to use the target calcium-silicon ratio as a variable, adjust the number of interlayer calcium ions and water molecules in the Tobermorite configuration, and perform molecular dynamics relaxation using the ClayFF force field to obtain the CSH gel model.
[0034] The process of preparing CSH powder samples under the same variables is as follows: using chemical precipitation method, synthesizing under the condition that the calcium-silicon molar ratio is consistent with the target calcium-silicon ratio, and obtaining powder samples by filtration and drying (2) obtaining the microstructure parameters of CSH gel under the target calcium-silicon ratio condition, the microstructure parameters include interlayer adhesion force, average chain length of silicate chain and number of silicate chains per unit area.
[0035] (2) Obtain the microstructure parameters of CSH gel under the target calcium-silicon ratio condition. The microstructure parameters include interlayer adhesion force, average chain length of silicate chain and number of silicate chains per unit area. The interlayer adhesion force, average chain length of silicate chain and number of silicate chains per unit area are obtained by establishing a molecular dynamics model of CSH gel under the target calcium-silicon ratio condition and analyzing it. They are obtained by simulating the peak stress of interlayer separation of the established molecular dynamics model, by calculating the average value of the number of silicon-oxygen tetrahedral connections, and by dividing the number of silicate chains on the model surface by the corresponding area.
[0036] (3) Obtain the porosity of a CSH gel powder sample with the same target calcium-silicon ratio conditions. The porosity of the CSH gel powder sample is determined by the water saturation method.
[0037] (4) Substitute the interlayer adhesion force, the average chain length of the silicate chain, the number of silicate chains per unit area and the porosity into the pre-constructed gelation force theoretical calculation model to calculate the theoretical value of the macroscopic gelation force of CSH gel.
[0038] The theoretical calculation model for cementitious force is as follows: × ; Where F is the macroscopic tensile load, N, i.e., the theoretical cementing force; f is the interlayer adhesion force, N, obtained through molecular dynamics simulation; L is the average chain length, dimensionless, obtained through solid-state silicon spectroscopy or molecular dynamics simulation; B is the proportionality conversion coefficient, obtained through fitting, dimensionless; ρ is the porosity, %, and s is the cross-sectional area of the specimen, nm. 2 The value is calculated based on the size of the test block required for macroscopic tensile testing; n is the number of silicon chains per square nanometer, in nm. -2 The cell parameters were calculated using molecular dynamics simulations; 2 / π is the cosine of the angle between the silicon chain pull-out and tensile failure, with the angle ranging from 0 to 90°.
[0039] The tensile failure mechanism of CSH gel can be analogized to fiber pull-out failure in fiber-reinforced composites. When CSH gel is subjected to tensile load, silicate chains undergo relative slippage or pull-out between layers. The resistance essentially stems from interlayer bonding, and the pull-out or slippage behavior of the silicate chains reflects the failure process of this interlayer bond. Therefore, the sum of all silicate chain pull-out forces equals the theoretical cementitious force of the CSH gel. If the fibers have end anchorages (such as hooked steel fibers), the additional strength contributed by the end anchorages must also be added. End anchorages are not considered in this embodiment.
[0040] The cementitious force theoretical calculation model uses the mathematical expectation of the cosine projection direction to geometrically approximate the randomly stacked silicate chain structure inside CSH. The processing procedure is as follows: Assuming the silicon chains are uniformly distributed, and applying a highly approximated approach to the randomly stacked structure within the CSH, the expected value of the cosine projection direction is: .
[0041] The fitting process for B is as follows: The synthesized CSH gel powder was subjected to different degrees of decalcification, washed and dried, and then pressed into cylindrical specimens. The splitting tensile strength was obtained by Brazilian splitting test.
[0042] According to the FIB Model Code 2010 standard, the macroscopic tensile strength is 0.9 times the splitting tensile strength. The macroscopic tensile strength (MPa) is calculated, then divided by the initial cross-sectional area (mm²). 2 The macroscopic tensile force (N) is obtained. Substitute all parameters except B obtained from molecular dynamics simulations and tests into the formula: × Then, linear fitting was performed, and the final result was B=0.000185. The formula and parameters required for fitting the data are as follows: The Brazilian splitting tensile strength formula is: ; In the formula, f tsp The tensile strength is the splitting tensile strength in MPa; P is the failure load in N; D is the diameter of the cylinder and H is the height of the cylinder, both in mm. The formula for macroscopic tensile strength is: ; In the formula, f t The tensile strength is the macroscopic tensile strength, i.e., the direct tensile strength, in MPa; P is the failure load, in N; and A is the initial cross-sectional area of the specimen failure section, both in mm². 2 The intensity conversion formula is: ; In the formula, f t This refers to the macroscopic tensile strength, i.e., the direct tensile strength, measured in MPa; f tsp The splitting tensile strength is expressed in MPa. The least squares formula used to fit B is: ; The forced fitted line passes through the origin (0,0); the numerator is x and... The sum of products has a denominator that is the sum of the squares of x, so there is no need to subtract the mean.
[0043] After different degrees of decalcification, the resulting calcium-to-silicon ratios were 1.58, 1.36, 1.18, 1.07, 0.76, 0.70, and 0.62, respectively. The macroscopic tensile forces and curves obtained through testing and calculation are shown in Table 1 and Table 2, respectively. Figure 1 As shown.
[0044] Table 1. Comparison of macroscopic tensile forces at different Ca / Si ratios Non-porosity is obtained by acquiring porosity (1-ρ). See Table 1 and... Figure 1 It can be seen that with different degrees of decalcification treatment, the calcium-silicon ratio of hydrated calcium silicate decreases, and the tensile force first decreases and then increases. The calculated macroscopic tensile force results are basically consistent with the Brazilian splitting test results, therefore, the reliability is higher.
[0045] Comparative Example 1, direct tensile test.
[0046] Experimental method: Direct tensile tests were conducted on CSH gel-molded specimens using dog bone-shaped specimens.
[0047] Ten specimens were prepared, but only three fractured effectively within the gauge length, resulting in a valid data rate of 30% and a coefficient of variation of 27.4%. The remaining seven specimens failed prematurely at the fixture bonding points or specimen ends, rendering their data invalid.
[0048] The effective data rate of direct tensile testing is only 30%, and the data dispersion is as high as 27%, making it difficult to obtain stable and reliable cementitious force values. However, the method of this invention does not require the preparation of dog bone-shaped specimens, clamping and loading, or large-scale destructive tensile tests, and can obtain stable prediction results. It fundamentally overcomes the defects of high data dispersion and high specimen requirements of direct tensile testing, and significantly reduces research and development costs and time.
[0049] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.
Claims
1. A method for predicting the mechanical properties of CSH gel, characterized in that, Includes the following steps: (1) Establish a molecular dynamics CSH gel model and prepare CSH powder samples with the same variables; (2) Obtain the microstructure parameters of CSH gel under the target calcium-silicon ratio condition. The microstructure parameters include interlayer adhesion, average silicate chain length and number of silicate chains per unit area. (3) Obtain the porosity of a CSH gel powder sample with the same target calcium-silicon ratio conditions; (4) Substitute the interlayer adhesion force, the average chain length of the silicate chain, the number of silicate chains per unit area and the porosity into the pre-constructed gelation force theoretical calculation model to calculate the theoretical value of the macroscopic gelation force of CSH gel.
2. The method for predicting the mechanical properties of CSH gel according to claim 1, characterized in that, The method for establishing the molecular dynamics CSH gel model in step (1) is as follows: using the target calcium-silicon ratio as a variable, by adjusting the number of interlayer calcium ions and water molecules in the Tobermorite configuration, molecular dynamics relaxation is performed using the ClayFF force field to obtain the CSH gel model.
3. The method for predicting the mechanical properties of CSH gel according to claim 1, characterized in that, The method for preparing CSH powder samples under the same variables in step (1) is as follows: chemical precipitation method is used to synthesize the samples under the condition that the calcium-silicon molar ratio is consistent with the target calcium-silicon ratio, and the powder samples are obtained by filtration and drying.
4. The method for predicting the mechanical properties of CSH gel according to claim 1, characterized in that, In step (2), the interlayer adhesion force is obtained by simulating the peak stress of interlayer separation in the molecular dynamics model, the average chain length of the silicate chain is obtained by averaging the number of silicon-oxygen tetrahedral connections, and the number of silicate chains per unit area is obtained by dividing the number of silicate chains on the model surface by the corresponding area.
5. The method for predicting the mechanical properties of CSH gel according to claim 1, characterized in that, The porosity of the CSH gel powder sample in step (3) was obtained by water saturation method, nitrogen adsorption method or mercury porosimetry.
6. The method for predicting the mechanical properties of CSH gel according to claim 1, characterized in that, The theoretical calculation model for cementitious force in step (4) is as follows: × ; Where F is the macroscopic tensile load, N, i.e., the theoretical cementing force; f is the interlayer adhesion force, N, obtained through molecular dynamics simulation; L is the average chain length, dimensionless, obtained through solid-state silicon spectroscopy or molecular dynamics simulation; B is the proportionality conversion coefficient, obtained through fitting, dimensionless; ρ is the porosity, %, and s is the cross-sectional area of the specimen, nm. 2 The value is calculated based on the size of the test block required for macroscopic tensile testing; n is the number of silicon chains per square nanometer, in nm. -2 The cell parameters were calculated using molecular dynamics simulations; 2 / π is the cosine of the angle between the silicon chain pull-out and tensile failure, with the angle ranging from 0 to 90°.
7. The method for predicting the mechanical properties of CSH gel according to claim 6, characterized in that, The cementitious force theoretical calculation model uses the mathematical expectation of the cosine projection direction to geometrically approximate the randomly stacked silicate chain structure inside CSH. The processing procedure is as follows: Assuming the silicon chains are uniformly distributed, and applying a highly approximated approach to the randomly stacked structure within the CSH, the expected value of the cosine projection direction is: 。 8. The method for predicting the mechanical properties of CSH gel according to claim 6, characterized in that, The fitting process and data proof for B are as follows: The synthesized CSH gel powder was subjected to different degrees of decalcification and then pressed into cylindrical specimens. The splitting tensile strength was obtained by Brazilian splitting test. The macroscopic tensile strength is 0.9 times the splitting tensile strength. The macroscopic tensile strength is calculated and then divided by the initial cross-sectional area to obtain the macroscopic tensile force. Substitute all parameters except B obtained from molecular dynamics simulations and tests into the formula: × ; Then, a linear fit was performed to obtain the value of B.
9. The method for predicting the mechanical properties of CSH gel according to claim 8, characterized in that, The formulas and parameters required for the fitting process are as follows: The Brazilian split tensile strength formula is: ; In the formula, f tsp The tensile strength is the splitting tensile strength in MPa; P is the failure load in N; D is the diameter of the cylinder and H is the height of the cylinder, both in mm. The formula for macroscopic tensile strength is: ; In the formula, f t The tensile strength is the macroscopic tensile strength, i.e., the direct tensile strength, in MPa; P is the failure load, in N; and A is the initial cross-sectional area of the specimen failure section (mm²). 2 ; The intensity conversion formula is: ; In the formula, f t This refers to the macroscopic tensile strength, i.e., the direct tensile strength, measured in MPa; f tsp The splitting tensile strength is expressed in MPa. The least squares formula used to fit B is: ; The forced fitted line passes through the origin (0,0); the numerator is x and... The sum of products has a denominator that is the sum of x squared.
10. The method for predicting the mechanical properties of CSH gel according to claim 1, characterized in that, The prediction method is applicable to the prediction of mechanical properties of CSH gels with a calcium-to-silicon ratio in the range of 0.5 to 2.1.
Citation Information
Patent Citations
Method for decoding creep compliance of high-density and low-density hydrated calcium silicate (C-S-H) gel
CN115497580A