CN110083879B - Concrete internal temperature and humidity field distribution calculation method based on grid structure - Google Patents

Abstract

The invention discloses a method for calculating the temperature and humidity field distribution inside concrete based on a grid structure. Corresponding parameters; finite element analysis and solution, establish the governing equation of concrete moisture-heat coupling, set the initial conditions and boundary conditions, use the Galerkin method to transform the governing equation into a system of equations with node temperature and humidity as unknown quantities, and use the finite difference method to solve the equations The group is discretized in the time domain, and the equations are solved iteratively; the post-processing work is performed, and the temperature and humidity distribution inside the concrete is obtained by analyzing the data obtained from the simulation of the heat and mass transfer model. The invention uses the one-dimensional rod unit in the Lattice structure as the heat and mass transfer medium, simplifies the three-dimensional heat and mass transfer problem into a local one-dimensional heat and mass transfer problem, and greatly reduces the calculation amount.

Description

A Calculation Method of Temperature and Humidity Field Distribution in Concrete Based on Grid Structure

technical field

The invention belongs to the field of numerical analysis of the concrete temperature and humidity field, and in particular relates to the establishment of a concrete mass and heat transfer model and the calculation of the temperature and humidity field in different environments.

Background technique

As the most widely used building material at present, concrete is widely used in various building structures, such as: highways, bridges, hydraulic structures, airport runways, military projects, etc. Usually, with correct construction and maintenance methods, a durable concrete structure can be obtained, and its service life can reach more than a hundred years. However, concrete will produce volume changes from the beginning of pouring, and the cracks produced by volume instability will affect the durability of concrete, so it has become a hot spot in the study of concrete durability.

In the absence of external forces, the main causes of deformation of concrete structures are: plastic shrinkage, drying shrinkage, autogenous shrinkage (internal drying), temperature shrinkage, carbonation shrinkage, creep, etc. The volume deformation caused by various reasons causes stress inside the concrete. When the concrete is subject to internal or external constraints, the internal stress will be more uneven, and cracking will occur when the local stress exceeds the tensile strength of the material itself. When concrete is in a variable temperature environment, it will be affected by temperature stress to a large extent. Repeated changes in ambient temperature will affect the temperature field distribution in the concrete structure, thereby causing changes in temperature stress. If the temperature stress exceeds the maximum load that the concrete can bear, microcracks will occur in the concrete. In addition, the change of environmental humidity is also an important factor for concrete to produce surface cracks. When the humidity of the surrounding environment is lower than the humidity of the concrete surface, the moisture contained in the concrete will be lost to the external environment, resulting in shrinkage effect, and may cause shrinkage cracks. Under the action of external force, these micro-defects undergo distributed growth and aggregation to form macroscopic main cracks, and the continuous expansion of subjective cracks leads to the final failure of concrete. Whether in the early cement hydration process after concrete pouring or during the service and operation of concrete structures, temperature and humidity changes are the most important factors affecting the deformation of concrete materials. The temperature and humidity in concrete often affect each other, the temperature gradient will accelerate the diffusion of water vapor, and the moisture will also take away part of the heat in the structure during the moisture transfer process, thus affecting the temperature distribution. When discussing such issues, we should Consider the coupling effect of the two. Many scholars monitor the temperature and humidity distribution of concrete by means of experiments, but the experimental conditions are often limited, and only a few measuring points can be obtained. Therefore, it is of great significance to study the temperature and humidity distribution inside concrete by means of simulation.

Lattice model is often used to simulate the failure process of concrete because of the introduction of simple element constitutive relations, and the macroscopic and complex failure phenomena can be reflected through the interaction between rod elements. If we use the Lattice structure to simulate the temperature and humidity distribution of concrete, we can also convert the three-dimensional heat and mass transfer problem into a simple one-dimensional transmission. For smaller structures, the influence of the aggregate distribution inside the concrete on the temperature and humidity distribution is also considered. , the temperature and humidity distribution data obtained from the simulation can be directly used to simulate the cracking of concrete structures under the action of temperature and humidity stress. Therefore, we invented a heat and mass transfer model based on Lattice structure, and used it to simulate the temperature and humidity distribution of concrete in different environments.

Contents of the invention

Based on the existing problems of concrete and the limitations of traditional experimental methods, the problem to be solved by the present invention is to provide a modeling and analysis method capable of effectively calculating the distribution of temperature and humidity fields inside concrete.

A method for calculating the temperature and humidity field distribution inside concrete based on a grid structure, comprising steps:

(1) The continuous concrete medium is discretized into a Lattice grid structure in which spatial rod units are connected to each other, and corresponding performance parameters are assigned to the rod units;

(2) Finite element analysis and solution, establishing the governing equation of concrete moisture-heat coupling, setting the initial conditions and boundary conditions, using the Galerkin method to transform the governing equation into a system of equations with node temperature and humidity as unknown quantities, and using the finite difference method to analyze the The equations are discretized in the time domain, and the equations are solved iteratively;

(3) Obtain the distribution law of the temperature and humidity field inside the concrete according to the result of iteratively solving the equations.

Further, the step (1) specifically includes:

(11) First, divide the concrete mesoscopic structure graph obtained by simulation or experiment into several square grids with the same size and side length s, and generate small squares with side length a in each grid, and finally in the small squares Randomly generate a node, each node represents a phase in the concrete structure, s/a is defined as the random degree of Lattice, which is used to represent the heterogeneity of the material;

(12) Use Delaunay triangulation to construct the Delaunay triangular grid in the Lattice grid structure, and connect the three nearest nodes with beams or rods to obtain the Lattice grid structure;

(13) Overlay the generated Lattice grid structure with the concrete mesoscopic structure diagram, and the rod elements are given corresponding performance parameters.

Further, the rod unit of the Lattice grid structure includes: a rod unit with two nodes located in the mortar phase, a rod unit with both nodes located in the coarse aggregate, and two nodes located in the mortar phase and the coarse bone respectively. Rod units in the material phase, different rod units are given different performance parameters.

Further, described step (2) specifically includes:

(21) Establish the governing equation of concrete moisture-heat coupling:

Among them, H is the moisture content of concrete; D _m is the moisture diffusion coefficient considering Knudsen diffusion; ρ is the density of concrete; C _ρ is the specific heat capacity of concrete; λ is the thermal conductivity of concrete; T is temperature; r is phase change factor; h _lv is the latent heat of evaporation; δ is the thermal gradient coefficient.

(22) Set initial conditions and boundary conditions according to the external environment;

(23) Use the Galerkin method to obtain the weak form of the moisture-heat coupling governing equation:

Among them, N _i is the shape function of node i

Substituting the boundary conditions to obtain the balance matrix equation of each bar element, assembling the element stiffness matrix and node flux, and obtaining a system of equations with node temperature and humidity as unknown quantities:

和

是温度和湿度对时间的导数向量，[C]、[K]、[P]、[M]、[L]、[N]均为杆单元相关的系数矩阵，{f1}和{f2}是驱动力向量。where {T} and {H} are temperature and humidity vectors,

and

is the derivative vector of temperature and humidity with respect to time, [C], [K], [P], [M], [L], [N] are coefficient matrices related to rod elements, {f1} and {f2} are driving force vector.

(24) Use the finite difference method to discretize the system of equations in the time domain:

([C]+0.5Δt[K]){T} ⁿ⁺¹ ＝([C]-0.5Δt[K]){T} ⁿ +[P]({u} ⁿ⁺¹ -{u} ⁿ ) +0.5Δt{f1}

([M]+0.5Δt[L]){H} ⁿ⁺¹ ＝([M]-0.5Δt[L]){H} ⁿ -0.5Δt[N]({T} ⁿ⁺¹ +{T} ⁿ )+0.5Δt{f2}

Among them, Δt is the selected iteration time step.

Substituting the given initial conditions to iteratively solve the matrix equations in matlab.

Further, described step (3) includes:

The temperature field distribution and the humidity field distribution of the concrete at a certain moment are obtained according to the result analysis of the iterative solution to the equation group;

According to the result of iteratively solving the equations, the temperature and humidity of the nodes at different positions change with time.

Compared with the prior art, the present invention divides the analysis object into Lattice grids, and regards the one-dimensional rod elements in the Lattice grids as channels for heat and mass transfer, thereby simplifying the three-dimensional heat and mass transfer problems into one-dimensional Heat and mass transfer greatly reduces the amount of calculation, and the simulated temperature and humidity distribution data can be directly used to simulate the cracking of concrete structures under the action of temperature and humidity stress.

Description of drawings

Figure 1 is a flow chart of the modeling method of concrete heat and mass transfer model.

Figure 2 is a schematic diagram of the Hundt test.

Figure 3 is a schematic diagram of the concrete Lattice model.

Figure 4 is a schematic diagram of the temperature change obtained from the simulation of the concrete heat and mass transfer model.

Fig. 5 is a schematic diagram of the humidity change obtained from the simulation of the concrete heat and mass transfer model.

Detailed ways

The present invention will be further described below in conjunction with accompanying drawing:

We use the heat and mass transfer model to simulate the Hundt diffusion test. Figure 2 is a schematic diagram of the Hundt test. The concrete specimen size is 2.4m×0.4m×0.4m, and the side surface (excluding the end surface) of the specimen is treated Become a heat-insulating and moisture-insulating state to ensure its one-dimensional diffusion. One end of the test piece is sealed and placed in a temperature environment of 80°C, and the other end is not sealed and placed in an environment with an ambient temperature of Ta=20°C and a relative humidity of RH=45%. After forming, the temperature of different positions of the concrete specimens was measured, and the humidity distribution and deformation tests of the concrete specimens after 28d standard curing were continued.

As shown in Figure 1, a method for calculating the temperature and humidity field distribution inside concrete based on grid structure includes steps:

(1) Perform pre-processing work:

① Divide a concrete specimen with a size of 2.4m×0.4m×0.4m into several square grids with the same size and a side length of 40mm, and select a randomness of 0.5 to generate a small square with a side length of 20mm in each grid , and finally randomly generate a node in the small square.

②Use Delaunay triangulation to construct the Delaunay triangular grid in the Lattice grid structure, and connect the three nearest nodes with beams or rods to obtain the Lattice grid structure shown in Figure 3.

③ Due to the large size of the specimen, it is regarded as a homogeneous material, and the performance parameters of the rod element are shown in Table 1:

(2) Finite element analysis and solution:

①Considering the interaction between temperature and humidity inside concrete, possible heat sources, and the interaction between moisture-heat coupling parameters, the control equation for concrete moisture-heat coupling is established:

Among them, H is the moisture content of concrete; D _m is the moisture diffusion coefficient considering Knudsen diffusion; ρ is the density of concrete; C _ρ is the specific heat capacity of concrete; λ is the thermal conductivity of concrete; T is temperature; r is phase change factor; h _lv is the latent heat of evaporation; δ is the thermal gradient coefficient.

②Set the initial conditions and boundary conditions according to the external environment. The initial conditions are set as: Ta=20°C, RH=10.5%, the boundary conditions of the end face 1 of the specimen are set as Ti=80°C, and the boundary conditions of the end face 2 are set as Ta=20°C. RH = 45%.

③Using the Galerkin method to obtain the weak form of the moisture-heat coupling governing equation:

Among them, Ni is the shape function of node i.

Substituting the boundary conditions to obtain the balance matrix equation of each bar element, assembling the element stiffness matrix and node flux, and obtaining a system of equations with node temperature and humidity as unknown quantities:

和

是温度和湿度对时间的导数向量，[C]、[K]、[P]、[M]、[L]、[N]均为杆单元相关的系数矩阵，{f1}和{f2}是驱动力向量。where {T} and {H} are temperature and humidity vectors,

and

is the derivative vector of temperature and humidity with respect to time, [C], [K], [P], [M], [L], [N] are coefficient matrices related to rod elements, {f1} and {f2} are driving force vector.

④ Use the finite difference method to discretize the equations in the time domain:

([C]+0.5Δt[K]){T} ⁿ⁺¹ ＝([C]-0.5Δt[K]){T} ⁿ +[P]({u} ⁿ⁺¹ -{u} ⁿ ) +0.5Δt{f1}

([M]+0.5Δt[L]){H} ⁿ⁺¹ ＝([M]-0.5Δt[L]){H} ⁿ -0.5Δt[N]({T} ⁿ⁺¹ +{T} ⁿ )+0.5Δt{f2}

Among them, Δt is the time step selected for iteration, which is 0.5 in this example.

Substituting the given initial conditions to iteratively solve the matrix equations in matlab.

(3) Post-processing work:

According to the result analysis of the iterative solution to the equations, the distribution law of the temperature and humidity field inside the concrete is obtained, including the temperature distribution inside the concrete of different ages obtained through data processing, and the humidity distribution inside the concrete at 550d, and The comparison of the experimental data is shown in Figure 4 and Figure 5.

The above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (4)

1. a method for calculating the temperature and humidity field distribution inside concrete based on grid structure, is characterized in that, comprises the steps: (1) The continuous concrete medium is discretized into a Lattice grid structure in which spatial rod units are connected to each other, and corresponding performance parameters are assigned to the rod units; (2) Finite element analysis and solution, establishing the governing equation of concrete moisture-heat coupling, setting the initial conditions and boundary conditions, using the Galerkin method to transform the governing equation into a system of equations with node temperature and humidity as unknown quantities, and using the finite difference method to analyze the The equations are discretized in the time domain, and the equations are solved iteratively; specifically include: (21) Establish the governing equation of concrete moisture-heat coupling:

Among them, H is the moisture content of concrete; D _m is the moisture diffusion coefficient considering Knudsen diffusion; ρ is the density of concrete; C _ρ is the specific heat capacity of concrete; λ is the thermal conductivity of concrete; T is temperature; r is phase change factor; h _lv is the latent heat of evaporation; δ is the thermal gradient coefficient; (22) Set initial conditions and boundary conditions according to the external environment; (23) Use the Galerkin method to obtain the weak form of the moisture-heat coupling governing equation:

Among them, Ni is the shape function of node i; Substituting the boundary conditions to obtain the balance matrix equation of each bar element, assembling the element stiffness matrix and node flux, and obtaining a system of equations with node temperature and humidity as unknown quantities:

where {T} and {H} are temperature and humidity vectors,

and

is the derivative vector of temperature and humidity with respect to time, [C], [K], [P], [M], [L], [N] are coefficient matrices related to rod elements, {f1} and {f2} are driving force vector; (24) Use the finite difference method to discretize the system of equations in the time domain: ([C]+θΔt[K]){T} ⁿ⁺¹ ＝([C]-(1-θ)Δt[K]){T} ⁿ +[P]({H} ⁿ⁺¹ -{H } ⁿ )+0.5Δt{f1} ([M]+θΔt[L]){H} ⁿ⁺¹ ＝([M]-(1-θ)Δt[L]){H} ⁿ -0.5Δt[N]({T} ⁿ⁺¹ + {T} ⁿ )+0.5Δt{f2} Among them, Δt is the time step selected for iteration, and the value of θ represents different difference methods; Substituting the given initial conditions to iteratively solve the matrix equations in matlab; (3) Obtain the distribution law of the temperature and humidity field inside the concrete according to the result of iteratively solving the equations. 2. a kind of concrete internal temperature and humidity field distribution calculation method based on grid structure according to claim 1, is characterized in that, step (1) specifically comprises: (11) First, divide the concrete mesoscopic structure diagram obtained by simulation or experiment into several square grids with the same size and side length s, and generate small squares with side length a in each grid, and finally in the small squares Randomly generate a node, each node represents a phase in the concrete structure, s/a is defined as the random degree of Lattice, which is used to represent the heterogeneity of the material; (12) Use Delaunay triangulation to construct the Delaunay triangular grid in the Lattice grid structure, and connect the three nearest nodes with beams or rods to obtain the Lattice grid structure; (13) Overlay the generated Lattice grid structure with the concrete mesoscopic structure diagram, and the rod elements are given corresponding performance parameters. 3. a kind of concrete internal temperature and humidity field distribution calculation method based on grid structure according to claim 2, is characterized in that, the bar element of described Lattice grid structure comprises: two nodes all are positioned at mortar phase The rod unit, the rod unit with both nodes located in the coarse aggregate, and the rod unit with the two nodes located in the mortar phase and the coarse aggregate phase respectively, different performance parameters are assigned to different rod units. 4. a kind of concrete internal temperature and humidity field distribution calculation method based on grid structure according to claim 1, is characterized in that, step (3) comprises: The temperature field distribution and the humidity field distribution of the concrete at a certain moment are obtained according to the result analysis of the iterative solution to the equation group; According to the result of iteratively solving the equations, the temperature and humidity of the nodes at different positions change with time.

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