CN110083879B - Concrete internal temperature and humidity field distribution calculation method based on grid structure - Google Patents
Concrete internal temperature and humidity field distribution calculation method based on grid structure Download PDFInfo
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Abstract
The invention discloses a method for calculating distribution of temperature and humidity fields in concrete based on a grid structure, which comprises the following steps: performing pretreatment work, dispersing continuous concrete media into a Lattice structure with space rod units connected with each other, and giving corresponding parameters to the rod units; finite element analysis and solution, establishing a concrete damp-heat coupling control equation, setting initial conditions and boundary conditions, converting the control equation into an equation set with the node temperature and humidity as unknown quantities by using a Galerkin method, dispersing the equation set in a time domain by using a finite difference method, and performing iterative solution on the equation set; and performing post-processing work, and analyzing data obtained by processing the heat and mass transfer model simulation to obtain a temperature and humidity distribution rule in the concrete. The invention takes the one-dimensional rod unit in the Lattice structure as the medium for heat and mass transfer, simplifies the three-dimensional heat and mass transfer problem into the local one-dimensional heat and mass transfer problem, and greatly reduces the calculation amount.
Description
Technical Field
The invention belongs to the field of concrete temperature and humidity field numerical analysis, and particularly relates to establishment of a concrete mass and heat transfer model and calculation of temperature and humidity fields in different environments.
Background
Concrete is widely applied to various building structures as a building material with the widest application range at present, such as: highways, bridges, hydraulic structures, airport runways, military engineering, etc. Under normal conditions, a concrete structure with good durability can be obtained by adopting a correct construction and maintenance method, and the service life can reach more than one hundred years. However, concrete has a volume change from the start of casting, and cracks caused by volume instability affect the durability of concrete, and thus, the research on the durability of concrete has been focused.
Without external force, the main causes of deformation of the concrete structure are: plastic shrinkage, drying shrinkage, self-shrinkage (internal drying), temperature shrinkage, carbonization shrinkage, creep, and the like. The volume deformation caused by various reasons causes stresses inside the concrete, which are more non-uniform when the concrete is subjected to internal or external constraints, and cracks occur when the local stresses exceed the tensile strength of the material itself. When the concrete is in a temperature-changing environment, the concrete is greatly influenced by temperature stress. Repeated changes in ambient temperature will affect the temperature field distribution in the concrete structure, causing a change in temperature stress, which will cause microcracks in the concrete if it exceeds the maximum load that the concrete can bear. In addition, the change of the environmental humidity is also an important factor for generating surface cracks of the concrete. When the humidity of the surrounding environment is lower than that of the surface of the concrete, the moisture contained in the concrete is dissipated to the external environment, so that a drying shrinkage effect is generated, and drying shrinkage cracks can be caused. Under the action of external force, the micro defects are subjected to distributed growth and polymerization to form a macroscopic main crack, and the subjective crack continuously expands to cause the final damage of the concrete. The temperature and humidity changes are the most important factors influencing the deformation of concrete materials in the early cement hydration process after concrete pouring and in the service operation period of a concrete structure. Temperature and humidity in concrete often influence each other, temperature gradient can accelerate the diffusion of vapor, and moisture can also take away part of heat in the structure in the process of moisture transmission to influence temperature distribution, and the coupling effect of the two should be considered when discussing the problem. Many scholars monitor the temperature and humidity distribution of concrete through experimental means, but experimental conditions are often limited, and the temperature and humidity distribution conditions of only a few measuring points can be obtained, so that the study on the temperature and humidity distribution in the concrete through simulation means has important significance.
The Lattice model introduces a simple unit constitutive relation, and macroscopic complex damage phenomena can be reflected by interaction among rod units, so that the Lattice model is often used for simulating the damage process of concrete. If the temperature and humidity distribution of concrete is simulated by using a Lattice structure, the three-dimensional heat and mass transfer problem can be converted into simple one-dimensional transmission, the influence of aggregate distribution in the concrete on the temperature and humidity distribution is also considered for a structure with a small size, and the temperature and humidity distribution data obtained by simulation can be directly used for simulating the cracking of the concrete structure under the action of temperature and humidity stress. Therefore, a heat and mass transfer model based on a Lattice structure is invented and used for simulating the temperature and humidity distribution of concrete in different environments.
Disclosure of Invention
Based on the problems of the existing concrete and the limitations of the traditional experimental means, the invention aims to provide a modeling and analyzing method capable of effectively calculating the distribution of the temperature and humidity field in the concrete.
A method for calculating the distribution of temperature and humidity fields in concrete based on a grid structure comprises the following steps:
(1) Dispersing continuous concrete media into a Lattice structure with space rod units connected with each other, and endowing the rod units with corresponding performance parameters;
(2) Finite element analysis and solution, establishing a concrete damp-heat coupling control equation, setting initial conditions and boundary conditions, converting the control equation into an equation set with node temperature and humidity as unknown quantities by using a Galerkin method, dispersing the equation set in a time domain by using a finite difference method, and performing iterative solution on the equation set;
(3) And analyzing according to the result of the iterative solution of the equation set to obtain the distribution rule of the temperature field and the humidity field in the concrete.
Further, the step (1) specifically comprises:
(11) Firstly, dividing a concrete microscopic structure chart obtained by simulation or experiment into a plurality of square grids with the same size and the same side length of s, generating a small square with the side length of a in each grid, and finally randomly generating a node in the small square, wherein each node represents one phase in a concrete structure, and s/a is defined as the randomness of Lattice and is used for representing the non-uniformity of materials;
(12) Constructing a Delaunay triangular grid in a Lattice structure of Lattice by using Delaunay triangulation, and connecting three nodes which are nearest to each other by using beams or rods so as to obtain the Lattice structure of Lattice;
(13) And overlapping the generated Lattice structure with the microscopic structure diagram of the concrete, and endowing the rod units with corresponding performance parameters.
Further, the rod unit of the Lattice grid structure includes: the two nodes are all located in the rod units in the mortar phase, the two nodes are all located in the rod units in the coarse aggregate phase, the two nodes are respectively located in the rod units in the mortar phase and the coarse aggregate phase, and different rod units are respectively endowed with different performance parameters.
Further, the step (2) specifically comprises:
(21) Establishing a control equation of concrete damp-heat coupling:
wherein H is the moisture content of the concrete; d m To account for the wet diffusion coefficient of Knudsen diffusion; rho is the density of the concrete; c ρ The specific heat capacity of the concrete; lambda is the heat conductivity coefficient of the concrete; t is the temperature; r is a phase change factor; h is lv Is the latent heat of vaporization; delta is the thermal gradient coefficient.
(22) Setting initial conditions and boundary conditions according to an external environment;
(23) The weak form of the hygrothermal coupling control equation is found using the Galerkin method:
wherein N is i As a shape function of node i
Substituting the boundary conditions to obtain a balance matrix equation of each rod unit, assembling a unit rigidity matrix and a node flux, and obtaining an equation set taking the temperature and the humidity of the node 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]The coefficient matrices, both of which are rod element dependent, { f1} and { f2} are driving force vectors.
(24) Discretizing the equation set in the time domain by using a finite difference method:
([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}
where Δ t is the selected iteration time step.
And substituting the given initial condition to iteratively solve the matrix equation system in matlab.
Further, the step (3) comprises:
analyzing according to the result of the iterative solution of the equation set to obtain the temperature field distribution and the humidity field distribution of the concrete at a certain moment;
and obtaining the change conditions of the temperature and the humidity of the nodes at different positions along with the time according to the result of the iterative solution of the equation set.
Compared with the prior art, the analysis object is divided into the Lattice, and the one-dimensional rod units in the Lattice are taken as the heat and mass transfer channels, so that the three-dimensional heat and mass transfer problem is simplified into the one-dimensional heat and mass transfer, the calculated amount is greatly reduced, and the temperature and humidity distribution data obtained by simulation can be directly used for simulating the cracking of the concrete structure under the action of temperature and humidity stress.
Drawings
FIG. 1 is a flow chart of a concrete heat and mass transfer model modeling method.
FIG. 2 is a schematic representation of the Hundt test.
FIG. 3 is a schematic diagram of a concrete Lattice model.
FIG. 4 is a schematic diagram of the temperature change obtained by concrete heat and mass transfer model simulation.
FIG. 5 is a schematic diagram of humidity change obtained by concrete heat and mass transfer model simulation.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
the method is characterized in that a Hundt diffusion test is simulated by using a heat and mass transfer model, as shown in FIG. 2, the Hundt diffusion test is a schematic diagram of the Hundt test, the size of a concrete test piece is 2.4m multiplied by 0.4m, the side surface (without an end surface) of the test piece is processed into a heat insulation and moisture insulation state to ensure one-dimensional diffusion of the test piece, one end of the test piece is sealed and placed in an environment with the temperature of 80 ℃, the other end of the test piece is not sealed and placed in an environment with the ambient temperature of Ta =20 ℃ and the relative humidity of RH =45%, the temperature of different positions of the concrete test piece is measured after the test piece is molded, and the humidity distribution and deformation test is continuously carried out on the concrete test piece after the 28d standard curing.
As shown in fig. 1, a method for calculating distribution of temperature and humidity fields in concrete based on a grid structure includes the steps:
(1) Executing preprocessing work:
(1) dividing a concrete sample with the size of 2.4m multiplied by 0.4m into a plurality of square grids with the same size and the side length of 40mm, selecting 0.5 for the random degree, generating a small square with the side length of 20mm in each grid, and finally randomly generating a node in the small square.
(2) The Delaunay triangulation is used to construct the Delaunay triangulation in the Lattice structure, and the three nodes closest to each other are connected by beams or rods, so as to obtain the Lattice structure shown in fig. 3.
(3) Since the test piece is large in size, it is considered as a homogeneous material, and the performance parameters of the rod unit are shown in table 1:
(2) Finite element analysis and solving:
(1) considering the interaction between the temperature and the humidity inside the concrete, the mutual influence between the possible heat source and the wet-heat coupling parameters, a control equation of the wet-heat coupling of the concrete is established:
wherein H is the moisture content of the concrete; d m To account for the wet diffusion coefficient of Knudsen diffusion; rho is the density of the concrete; c ρ The specific heat capacity of the concrete; lambda is the heat conductivity coefficient of the concrete; t is the temperature; r is a phase change factor; h is lv Is the latent heat of vaporization; delta is the thermal gradient coefficient.
(2) Setting initial conditions and boundary conditions according to the external environment, wherein the initial conditions are as follows: ta =20 ℃, RH =10.5%, the specimen end face 1 boundary conditions were set to Ti =80 ℃, the end face 2 boundary conditions were set to Ta =20 ℃, RH =45%.
(3) The weak form of the hygrothermal coupling control equation is found using the Galerkin method:
where Ni is the shape function of node i.
Substituting the boundary conditions to obtain a balance matrix equation of each rod unit, assembling a unit rigidity matrix and a node flux, and obtaining an equation set taking the temperature and the humidity of the node 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]The coefficient matrices, both of which are rod element dependent, { f1} and { f2} are driving force vectors.
(4) Discretizing the equation system in the time domain by using a finite difference method:
([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}
where Δ t is the time step selected for iteration, which in this example is 0.5.
And substituting the given initial condition to iteratively solve the matrix equation system in matlab.
(3) And (3) post-treatment work:
the distribution rule of the temperature field and the humidity field in the concrete is obtained according to the result of the iterative solution of the equation set, and the distribution rule comprises the temperature distribution in the concrete in different ages and the humidity distribution condition in the concrete at 550d, which are obtained through data processing, and the comparison of the measured data in the test is shown in fig. 4 and 5.
The above examples of the present invention are merely examples for clearly illustrating the present invention and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (4)
1. A method for calculating distribution of temperature and humidity fields in concrete based on a grid structure is characterized by comprising the following steps:
(1) Dispersing continuous concrete media into a Lattice structure of space rod units connected with each other, and endowing the rod units with corresponding performance parameters;
(2) Finite element analysis and solution, establishing a concrete damp-heat coupling control equation, setting initial conditions and boundary conditions, converting the control equation into an equation set with the node temperature and humidity as unknown quantities by using a Galerkin method, dispersing the equation set in a time domain by using a finite difference method, and performing iterative solution on the equation set; the method specifically comprises the following steps:
(21) Establishing a control equation of concrete damp-heat coupling:
wherein H is the moisture content of the concrete; d m To account for the wet diffusion coefficient of Knudsen diffusion; rho is the density of the concrete; c ρ The specific heat capacity of the concrete; lambda is the heat conductivity coefficient of the concrete; t is the temperature; r is a phase change factor; h is lv Is the latent heat of vaporization; delta is the thermal gradient coefficient;
(22) Setting initial conditions and boundary conditions according to an external environment;
(23) The weak form of the hygrothermal coupling control equation is found using the Galerkin method:
wherein Ni is a shape function of the node i;
substituting the boundary conditions to obtain a balance matrix equation of each rod unit, assembling a unit rigidity matrix and a node flux, and obtaining an equation set taking the temperature and the humidity of the node 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]A matrix of coefficients, both of which are rod element dependent, { f1} and { f2} are driving force vectors;
(24) Discretizing the equation set in the time domain by using a finite difference method:
([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}
wherein, Δ t is a time step selected by iteration, and the value of θ represents different difference methods;
substituting the given initial condition to carry out iterative solution on the matrix equation set in the matlab;
(3) And analyzing according to the result of the iterative solution of the equation set to obtain the distribution rule of the temperature field and the humidity field in the concrete.
2. The method for calculating the distribution of the temperature and humidity field in the concrete based on the grid structure according to claim 1, wherein the step (1) specifically comprises the following steps:
(11) Firstly, dividing a concrete microscopic structure chart obtained by simulation or experiment into a plurality of square grids with the same size and the same side length of s, generating a small square with the side length of a in each grid, and finally randomly generating a node in the small square, wherein each node represents one phase in a concrete structure, and s/a is defined as the randomness of Lattice and is used for representing the non-uniformity of materials;
(12) Constructing a Delaunay triangular grid in a Lattice structure of Lattice by using Delaunay triangulation, and connecting three nodes which are nearest to each other by using beams or rods so as to obtain the Lattice structure of Lattice;
(13) And overlapping the generated Lattice structure with the microscopic structure diagram of the concrete, and endowing the rod units with corresponding performance parameters.
3. The method for calculating the distribution of the temperature and humidity field in the concrete based on the grid structure as claimed in claim 2, wherein the rod units of the Lattice grid structure comprise: the two nodes are all located in the rod units in the mortar phase, the two nodes are all located in the rod units in the coarse aggregate phase, the two nodes are respectively located in the rod units in the mortar phase and the coarse aggregate phase, and different rod units are respectively endowed with different performance parameters.
4. The method for calculating the distribution of the humiture field inside the concrete based on the grid structure as claimed in claim 1, wherein the step (3) comprises:
analyzing according to the result of the iterative solution of the equation set to obtain the temperature field distribution and the humidity field distribution of the concrete at a certain moment;
and obtaining the change conditions of the temperature and the humidity of the nodes at different positions along with the time according to the result of the iterative solution of the equation set.
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| CN114324832B (en) * | 2021-11-24 | 2022-09-02 | 河海大学 | Concrete hydration-temperature-humidity and pressure stress multi-field coupling model construction method |
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