A Mesoscopic Modeling Method for Simulating the High-Temperature Performance of UHPC Considering the Heterogeneity of Mortar

Abstract

The present invention provides a mesoscopic modeling method for simulating the high-temperature performance of ultra-high performance concrete considering the heterogeneity of cement mortar. The method is as follows: Divide UHPC into heterogeneous mortar and inclusion components; Based on mercury intrusion test data, combine the random field distribution and generation algorithm to obtain the high-temperature porosity random field; Propose a relational expression between the overall high-temperature physical parameters of heterogeneous mortar and porosity; Obtain the value field of the high-temperature physical parameters of mortar; Use a geometric model to characterize the inclusion components and generate the mesoscopic geometric models of each inclusion component; Obtain the random field of the values of the high-temperature physical parameters of each inclusion component; Combine the high-temperature physical parameter random field of mortar and the high-temperature physical parameters corresponding to the random inclusion components described above to obtain a double-random thermo-mechanical coupling physical model. The present invention reasonably reflects the heterogeneous characteristics of cement mortar in UHPC materials, and at the same time greatly simulates the discreteness problem of material physical parameters caused by the heterogeneity of mortar in CA-UHPC materials.

Description

Technical Field

[0001] The present invention relates to the field of numerical analysis of material simulation, and specifically to a mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar. Background Art

[0002] Ultra-High Performance Concrete (UHPC) is a super-high-strength cement-based material with high strength, high toughness, and low porosity, which can effectively reduce the amount of concrete used in building structures and extend the service life, meeting the requirements of the full-life cycle use of current building structures. However, UHPC material is a heterogeneous composite material composed of mortar, pores, coarse aggregates, and steel fibers. The randomness of internal components and spatial structures makes it have heterogeneous characteristics. The physical properties of materials at high temperatures, including thermal parameters and mechanical properties, are the premise for calculating the temperature field of structures and the fire resistance performance at high temperatures. The heterogeneous characteristics of UHPC will cause the heat conduction path to be random, resulting in discreteness of the thermal parameters and mechanical parameters of the material. However, currently, when establishing the high-temperature heat transfer model of concrete, it is mostly assumed that concrete is a macroscopically homogeneous material. Some scholars have established high-temperature mesoscopic models from a mesoscopic perspective, but only considered the spatial random distribution of inclusion components such as steel fibers and coarse aggregates, while ignoring the heterogeneous characteristics of mortar itself. Summary of the Invention

[0003] To solve the above problems and aiming at the deficiencies of existing numerical models, the technical solution provided by the present invention is a mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar. The present invention uses the porosity to characterize the heterogeneity of mortar through a random field and uses random geometry to characterize the randomly distributed inclusion components, which more reasonably reflects the heterogeneous characteristics of mortar in concrete materials.

[0004] The technical solution provided by the present invention is as follows:

[0005] In a first aspect, the present invention provides a mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar, which is characterized by including the following steps:

[0006] Step 1: Divide UHPC into two parts: heterogeneous mortar and inclusion components. Among them, the heterogeneous mortar is characterized by the porosity through a random field, and the inclusion components include coarse aggregates and steel fibers, which are characterized by random geometry. For the heterogeneous mortar, conduct high-temperature mercury intrusion tests on mortar specimens to obtain the porosity evolution model of mortar at different temperatures with respect to temperature.

[0007] Step 2: Based on the porosity evolution model of mortar at different temperatures obtained from the mercury intrusion test, combine the random field distribution and generation algorithm to obtain the high-temperature porosity random field.

[0008] Step 3: Propose a mathematical expression for the relationship between the overall high-temperature physical parameters of the inhomogeneous mortar and the porosity.

[0009] Step 4: Combine the high-temperature porosity random field generated in Step 2 and the mathematical relationship expression in Step 3 to generate the high-temperature physical parameter value field of the mortar.

[0010] Step 5: For different inclusion components, use a geometric model to characterize the inclusion components, and generate the mesoscopic geometric models of each inclusion component through the grading, content, and random generation and placement algorithms of each group. On this basis, assign the corresponding high-temperature physical parameters to each component to obtain the high-temperature physical parameter value random field of each inclusion component.

[0011] Step 6: Combine the high-temperature physical parameter random field of the mortar in Step 4 and the high-temperature physical parameter value random field of each inclusion component in Step 5 to obtain a double-random thermo-mechanical coupling physical model of UHPC considering the inhomogeneity of the mortar, and then through the application of corresponding initial conditions, boundary conditions, and mesh division, obtain a double-random thermo-mechanical coupling numerical model of UHPC considering the inhomogeneity of the mortar.

[0012] Furthermore, in Step 2, the control equation of the high-temperature porosity random field is as follows:

[0013]

[0014] In the formula, x is the porosity value on the two-dimensional plane, 0 < x < 1; f(x) is the probability density of x; μ and σ are the logarithmic mean and logarithmic standard deviation, respectively.

[0015] Furthermore, Step 3 includes the following sub-steps:

[0016] Step 3-1: Regard the mortar as a two-phase model composed of pores and matrix. Through the Monte Carlo algorithm, generate random geometric pores in the mortar region, and at the same time assign different ratios of high-temperature physical parameters to the geometric pores and the matrix. Combine the corresponding boundary conditions and calculate the overall high-temperature physical parameters of the two-phase geometric model through finite element software.

[0017] Step 3-2: Based on the simulation results, summarize the mathematical expression for the relationship between the overall high-temperature physical parameters (i.e., equivalent parameters) of the two-phase system and the high-temperature physical parameters and porosity of each of the two-phase components (pores and matrix), and form a two-phase homogenization theory expression.

[0018] Step 3-3: Conduct thermal engineering parameter and mechanical property tests at high temperatures to obtain the evolution formulas of high-temperature thermal conductivity, specific heat, density, and elastic modulus with temperature. Then, combined with the mathematical expression in Step 3-2, back-calculate the high-temperature physical parameters of the matrix.

[0019] Further, in the step 3-2, the high-temperature physical parameters include the equivalent thermal conductivity k of the overall two-phase system m , the equivalent specific heat C p,m , the equivalent density ρ m , the equivalent coefficient of thermal expansion γ m and the equivalent elastic modulus E m , and their two-phase homogenization theoretical formulas are as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] In the formula, k p correspond to the thermal conductivities of the matrix and pores respectively; C p,p correspond to the specific heats of the matrix and pores respectively; ρ p correspond to the densities of the matrix and pores respectively; and γ p are the coefficients of thermal expansion of the matrix and pores respectively; E p correspond to the elastic moduli of the matrix and pores respectively, V p is the porosity; n k is the control coefficient of the equivalent thermal conductivity k m , n E is the control coefficient of the equivalent elastic modulus E m .

[0026] Further, in the step 5, the high-temperature physical parameters include thermal conductivity, specific heat, density, coefficient of thermal expansion and elastic modulus.

[0027] Further, in the step 6, the UHPC double-stochastic thermo-mechanical coupling numerical model considering the mortar heterogeneity is numerically solved by various general finite element solvers for predicting the equivalent material parameters of UHPC considering the mortar heterogeneity, constructing the temperature field, mechanical field and thermo-mechanical coupling simulation.

[0028] In a second aspect, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering mortar heterogeneity as described in the first aspect.

[0029] In a third aspect, the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, characterized in that when the computer program is executed by a processor, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar as described in the first aspect.

[0030] In a fourth aspect, the present invention provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar as described in the first aspect.

[0031] The beneficial effects of the present invention are as follows:

[0032] 1. The mesoscopic modeling method of the present invention can reasonably reflect the heterogeneous characteristics of mortar in concrete materials;

[0033] 2. The mesoscopic modeling method of the present invention can largely simulate the discreteness problem of the overall high-temperature physical parameters of concrete materials caused by the heterogeneity of mortar;

[0034] 3. The mesoscopic modeling method of the present invention can simulate the positive effect of coarse aggregate on the strength improvement of UHPC materials during the compression process. Description of the Drawings

[0035] Figure 1 is a flowchart of the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar of the present invention;

[0036] Figure 2 is a double-random characterization method for the micro-mesoscopic geometric structure of UHPC considering the heterogeneity of mortar of the present invention;

[0037] Figure 3 is a method for assigning high-temperature physical parameters of heterogeneous mortar of the present invention;

[0038] Figure 4 is a double-random physical model of UHPC considering the non-uniformity of mortar of the present invention (taking elastic modulus as an example);

[0039] Figure 5 is the implementation and verification of the double-random mesoscopic numerical model of the present invention;

[0040] Figure 6 is the thermal conductivity of UHPC with and without considering the heterogeneity of mortar of the present invention;

[0041] Figure 7 is the strength of UHPC with and without considering the heterogeneity of mortar of the present invention. Detailed Embodiments

[0042] The present invention will be further described below in conjunction with specific embodiments, and the content of the present invention is not limited thereto at all.

[0043] Figure 1 is the specific flowchart of the present invention. The core point of the present invention is to use the porosity to characterize the heterogeneity of the mortar through a random field, and use random geometry to characterize the randomly distributed inclusion components (see Figure 2 ). In order to further explain the technical solution of the present invention, the present invention will be elaborated in detail below with specific examples, including the following steps:

[0044] Step 1: Divide the UHPC into two parts, namely heterogeneous mortar and inclusion components. Among them, the heterogeneous mortar is characterized by the porosity through a random field, and the inclusion components include coarse aggregates and steel fibers, and the randomly distributed inclusion components are characterized by random geometry. For the heterogeneous mortar, a high-temperature mercury intrusion test is carried out on the mortar specimens to obtain the porosity evolution model of the mortar at different temperatures (see formula (1)).

[0045]

[0046] p(T) is the porosity, and T is the temperature (°C).

[0047] Step 2: Based on the average porosity measured by the mercury intrusion test and referring to the value range of the random porosity field parameters in the previous patent (Patent No.: ZL201810339476.6), the correlation length is taken as 0.005 m, and the coefficient of variation (CV p (T)) at different temperatures is taken according to formula (2), and a high-temperature porosity random field is generated in combination with the random field theory.

[0048]

[0049] CV p (T) is the coefficient of variation of the porosity at different temperatures; T is the temperature (°C).

[0050] Among them, the control equation of the porosity random field model is:

[0051]

[0052] In the formula, x is the porosity value on the two-dimensional plane, 0 < x < 1; f(x) is the probability density of x; μ and σ are the logarithmic mean value and logarithmic standard deviation of the porosity value x, respectively.

[0053] Step 3: Propose a mathematical expression for the relationship between the overall high-temperature physical parameters of the heterogeneous mortar and the porosity, including the following sub-steps:

[0054] Step 3-1: Consider mortar as a two-phase model composed of pores and matrix. By using the Monte Carlo algorithm, randomly geometric pores are generated within the mortar region. Meanwhile, different ratios of high-temperature physical parameters are assigned to the geometric pores and the matrix. Combining with the corresponding boundary conditions, the high-temperature physical parameters of the overall two-phase geometric model can be calculated through finite element software.

[0055] Step 3-2: Based on the simulation results, mathematical expressions for the high-temperature physical parameters (i.e., equivalent parameters) of the overall two-phase system in relation to the high-temperature physical parameters of the two-phase components (pores and matrix) and the porosity are derived, forming the two-phase homogenization theory.

[0056] Among them, the equivalent thermal conductivity k m , the equivalent specific heat C p,m , the equivalent density ρ m , the equivalent coefficient of thermal expansion γ m , and the equivalent elastic modulus E m of the two-phase homogenization theory are respectively shown in formulas (4) to (8) as follows:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] In the formulas, k p respectively correspond to the thermal conductivities of the matrix and the pores; C p,p respectively correspond to the specific heats of the matrix and the pores; ρ p respectively correspond to the densities of the matrix and the pores; and γ p are respectively the coefficients of thermal expansion of the matrix and the pores; E p respectively correspond to the elastic moduli of the matrix and the pores, V p is the porosity; n k is the control coefficient of the equivalent thermal conductivity k m , n E is the control coefficient of the equivalent elastic modulus E m . In this embodiment, n k = 1.83 and n E = 1.35.

[0063] Step 3-3: Conduct thermal engineering parameters (including thermal conductivity, density, specific heat, and thermal expansion) and mechanical property tests at high temperatures to obtain the evolution formulas of high-temperature thermal conductivity, specific heat, density, and elastic modulus with temperature. Then, combined with the mathematical expressions in Step 3-2, inversely calculate the high-temperature physical parameters of the matrix.

[0064] The inversely calculated high-temperature physical parameters are as follows:

[0065] (1) Thermal conductivity W / (m·K):

[0066] Mortar:

[0067] Matrix:

[0068] (2) Specific heat J / (kg·K):

[0069] Mortar:

[0070]

[0071] Matrix:

[0072]

[0073] (3) Density kg / m 3 :

[0074] Mortar:

[0075] Matrix: ρ m = 2980

[0076] (4) Coefficient of expansion

[0077] Mortar:

[0078]

[0079] Matrix:

[0080]

[0081] (5) Elastic modulus GPa:

[0082] Mortar:

[0083]

[0084] Matrix:

[0085]

[0086] Note: The relevant parameter values of the above high-temperature physical parameters are reference values, and the relevant values can be determined according to specific test results.

[0087] Step 4: Combine the high-temperature porosity random field generated in Step 2 with the mathematical relation expression in Step 3 to generate high-temperature physical parameter fields such as the thermal engineering parameter field and the elastic modulus field (including the thermal engineering parameter field and the mechanical parameter field). At the same time, combine the empirical relationship between the elastic modulus and other mechanical parameter fields (such as strength, peak strain, and descending section parameters). Based on the elastic modulus field, generate the high-temperature mechanical property field through the mechanical parameter conversion model. The process is as Figure 3 shown.

[0088] The mechanical parameter conversion model is specifically as follows:

[0089]

[0090]

[0091]

[0092] In the formula, E m，0 , f m，0 , β m，0 , σ m，0 , ε m，0 , ε m,p,0 ρ m,0 are the elastic modulus, strength, descending section parameter, stress, strain, peak strain, and density of the mortar at normal temperature.

[0093] The conversion relationship between the mechanical parameters at high temperature and those at normal temperature is specifically as follows:

[0094]

[0095]

[0096]

[0097]

[0098] In the formula, E m,T , f m,T , β m,T , ε m,T are the elastic modulus, strength, descending section parameter, and peak strain of the mortar at high temperature.

[0099] Step 5: For different inclusion components, use geometric models to characterize the coarse aggregate and steel fiber, and generate the mesoscopic geometric models of each inclusion component through the grading, content, and random generation and placement algorithms of each group. On this basis, assign the corresponding high-temperature physical parameters to each component. The high-temperature thermodynamics parameters of each inclusion component are shown in Table 1. Thus, the random field of the high-temperature physical parameter values of each inclusion component is obtained.

[0100] Table 1 High-temperature Thermodynamic Parameters of Inclusion Components

[0101]

[0102]

[0103] Note: The relevant parameter values in the table are reference values, and the relevant values can be determined according to specific test results.

[0104] Step 6, as Figure 4 shown, adopt the direct superposition method to combine the high-temperature physical parameter random field of the mortar in Step 4 and the high-temperature physical parameter value random field of each inclusion component in Step 5 to obtain a UHPC double-random thermo-mechanical coupling physical model considering the mortar heterogeneity. Then, by applying the corresponding initial conditions, boundary conditions, and mesh generation, a UHPC double-random thermo-mechanical coupling numerical model considering the mortar heterogeneity is obtained. Finally, numerical solutions are carried out through various general finite element solvers for predicting the equivalent material parameters of UHPC considering the mortar heterogeneity, constructing the temperature field, mechanical field, and thermo-mechanical coupling simulation, etc. For specific implementation cases, see Figure 5 .

[0105] Figure 6 By comparing the thermal conductivity coefficients considering and not considering the mortar heterogeneity, it can be seen that the present invention can simulate to a large extent the discreteness problem of the material thermodynamic parameters caused by the mortar heterogeneity in concrete materials. Figure 7 By comparing the change of the material strength with the volume fraction of coarse aggregate considering and not considering the mortar heterogeneity, it can be seen that when considering the mortar heterogeneity, the positive strengthening effect of the coarse aggregate on the UHPC strength during the compression process can be simulated.

[0106] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the mortar heterogeneity as described above.

[0107] The present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. The computer program, when executed by a processor, implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the mortar heterogeneity as described above.

[0108] The present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the mortar heterogeneity as described above.

[0109] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains may make various modifications or supplements to the described specific embodiments, or use similar means for substitution, without departing from the spirit of the present invention or exceeding the scope defined by the appended claims.

[0110] As described above, the above are only the preferred specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, improvements, etc. made by those skilled in the art within the technical scope disclosed by the present invention shall all be included within the scope of protection of the invention.

Claims

1. A mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar, characterized in that, it includes the following steps: Step 1: Divide UHPC into two parts, namely heterogeneous mortar and inclusion components. Among them, the porosity of the heterogeneous mortar is characterized by a random field, and the inclusion components including coarse aggregates and steel fibers are characterized by random geometry. For the heterogeneous mortar, conduct high-temperature mercury intrusion tests on mortar specimens to obtain the porosity evolution model of mortar at different temperatures; Step 2: Based on the porosity evolution model with temperature obtained from the mercury intrusion test, combine the random field distribution and generation algorithm to obtain the high-temperature porosity random field; Step 3: Propose a mathematical expression for the relationship between the overall high-temperature physical parameters of the heterogeneous mortar and the porosity; Step 3 includes the following sub-steps: Step 3-1: Regard the mortar as a two-phase model composed of pores and matrix. Through the Monte Carlo algorithm, generate random geometric pores in the mortar region, and at the same time assign different ratios of high-temperature physical parameters to the geometric pores and the matrix. Combine the corresponding boundary conditions and calculate the overall high-temperature physical parameters of the two-phase geometric model through finite element software; Step 3-2: Based on the simulation results, summarize the mathematical expression between the overall high-temperature physical parameters of the two-phase system and the high-temperature physical parameters and porosity of each of the two-phase components to form a two-phase homogenization theory expression; Step 3-3: Conduct thermal engineering parameter and mechanical property tests at high temperatures to obtain the evolution formulas of high-temperature thermal conductivity, specific heat, density, and elastic modulus with temperature. Then, combined with the mathematical expression in Step 3-2, back-calculate the high-temperature physical parameters of the matrix; Step 4: Combine the generated high-temperature porosity random field in Step 2 with the mathematical relationship expression in Step 3 to generate the high-temperature physical parameter value field of the mortar; Step 5: For different inclusion components, use geometric models to characterize the inclusion components, and generate the mesoscopic geometric models of each inclusion component through grading, content, and random generation and placement algorithms. On this basis, assign the corresponding high-temperature physical parameters to each component to obtain the high-temperature physical parameter value random field of each inclusion component; Step 6: Combine the high-temperature physical parameter random field of the mortar in Step 4 with the high-temperature physical parameter value random field of each inclusion component in Step 5 to obtain a double-random thermo-mechanical coupling physical model of UHPC considering the heterogeneity of mortar. Then, through applying the corresponding initial conditions, boundary conditions, and mesh division, obtain a double-random thermo-mechanical coupling numerical model of UHPC considering the heterogeneity of mortar.

2. The mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar according to claim 1, characterized in that, in Step 2, the control equation of the high-temperature porosity random field is: Wherein, x is the porosity value on a two-dimensional plane, ; f ( x ) is the x probability density; μ and σ are the logarithmic mean and the logarithmic standard deviation respectively.

3. The mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar according to claim 1, characterized in that, In the said step 3-2, the high-temperature physical parameters include the equivalent thermal conductivity of the overall two-phase system , the equivalent specific heat , the equivalent density , the equivalent coefficient of thermal expansion and the equivalent elastic modulus , and their two-phase homogenization theoretical formula is as follows: Wherein, and correspond to the thermal conductivities of the matrix and the pores, respectively; and correspond to the specific heats of the matrix and the pores, respectively; and correspond to the densities of the matrix and the pores, respectively; and are the thermal expansion coefficients of the matrix and the pores, respectively; and correspond to the elastic moduli of the matrix and the pores, respectively, is the porosity; is the equivalent thermal conductivity is the control coefficient of is the equivalent elastic modulus is the control coefficient of.

4. The mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the heterogeneity of mortar according to claim 1, characterized in that, in Step 5, the high-temperature physical parameters include thermal conductivity, specific heat, density, coefficient of thermal expansion, and elastic modulus.

5. The mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the inhomogeneity of mortar according to claim 1, characterized in that, in step 6, the UHPC double-stochastic thermo-mechanical coupling numerical model considering the inhomogeneity of mortar is numerically solved by various general finite element solvers to predict the equivalent material parameters of UHPC considering the inhomogeneity of mortar, and to conduct the coupled simulation of the constructed temperature field, mechanical field and thermo-mechanics.

6. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, when the processor executes the program, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the inhomogeneity of mortar according to any one of claims 1 to 5.

7. A non-transitory computer-readable storage medium, on which a computer program is stored, characterized in that, when the computer program is executed by a processor, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the inhomogeneity of mortar according to any one of claims 1 to 5.

8. A computer program product, comprising a computer program, characterized in that, when the computer program is executed by a processor, it implements the mesoscopic modeling method for simulating the high-temperature performance of UHPC considering the inhomogeneity of mortar according to any one of claims 1 to 5.

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