CN103440530A - Method for predicting ion diffusion coefficients of damaged cement based composite materials - Google Patents

Abstract

The invention discloses a method for predicting ion diffusion coefficients of damaged cement based composite materials. According to the method, regarding the microcosmic structure of damaged cement based composite materials which are discretized into a series of cube three-dimensional space lattices with equal size, each pair of adjacent cube three-dimensional space lattices are used as a lattice diffusion unit, wherein ion diffusion ability exists between each pair of adjacent cube three-dimensional space lattices, all the lattice diffusion units combine together to form a three-dimensional lattice ion transmission network, and each lattice is used as a diffusion node. Damage cracks are processed as hole phases, an ion diffusion matrix equation is established by using diffusion matrix equations between every two adjacent diffusion nodes in the three-dimensional lattice ion transmission network and combining ion concentration boundary conditions, solution is carried out on the ion diffusion matrix equation to obtain ion concentration distribution under a steady state, and finally the ion diffusion coefficients of the damaged cement based composite materials is obtained. The method for predicting the ion diffusion coefficients of damaged cement based composite materials can accurately predict ion diffusion ability change rules of the damaged cement based composite materials under the influences of freeze thawing, loading, air shrinkage and other conditions.

Description

A kind of ionic diffusion coefficient Forecasting Methodology of damaging cement-base composite material

Technical field

The present invention relates to a kind of ionic diffusion coefficient Forecasting Methodology of damaging cement-base composite material, belong to the cement-base composite material field.

Background technology

The transmission performance of cement-base composite material is the key factor that is related to civil engineering material permanance and service life.Be subject to the factor impacts such as external load, freeze thawing circulation, dry contraction when material after, material internal produces defect or existing defect yardstick increases and quantity increases, show as the generation of microfracture and the variation of development or porosity, make the transmission performances such as diffusion, infiltration, electromigration of material increase, thereby cause the permanance of material to reduce and the military service lost of life.Therefore, the Accurate Prediction that damage cement-base composite material transmission performance changes is most important.

Can obtain the transmission performance Changing Pattern with the damage cement-base composite material in crack by quick chlorion migration test, permeability test, carbonization test or diffusion test etc., but these test findings often are limited by test condition and research technique, the test findings dispersion is large.The forecast model of cement-base composite material transmission performance is mostly for harmless cement-base composite material, experience model, analytic model and numerical model are arranged, and less towards the research of the damage cement-base composite material transmission performance forecast model with crack, rarely seen analytic model based on the Micromechanics homogenization method.This analytic model calculates easy, but basic assumption is too idealized, is difficult to realize to consider that the transmission performance of cement-base composite material under single factor such as freeze thawing, load and drying shrinkage or multifactor coupling changes.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiency of existing damage cement-base composite material transmission performance forecasting techniques, the Evolution Microstructure of the damage cement-base composite material based on microfracture, a kind of ionic diffusion coefficient Forecasting Methodology of damaging cement-base composite material is provided, can realizes the accurate fast prediction of all kinds of damage cement-base composite material Ionic diffusions energy.

The present invention is specifically by the following technical solutions:

A kind of ionic diffusion coefficient Forecasting Methodology of damaging cement-base composite material comprises the following steps:

Step 1, for by the discrete damage cement-base composite material microcosmic/microscopical structure that turns to a series of equal-sized square three-dimensional space grids, there is each other the adjacent square three-dimensional space grid of ion diffusivity as a lattice diffusion unit using often a pair of, all lattice diffusion units form a three-dimensional lattice ion transfer network together, and each square three-dimensional space grid wherein is as a diffusion node of this three-dimensional lattice ion transfer network; In described three-dimensional lattice ion transfer network, the diffusion matrix equation between any two adjacent diffusion node i, j is:

$-\frac{D_{\mathrm{ij}}A}{l}\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]\left[\begin{array}{c}{c}_i\\ c_j\end{array}\right]=\left[\begin{array}{c}{q}_{\mathrm{ij}}\\ q_{\mathrm{ji}}\end{array}\right]$

Wherein, A means the area of one of them face of square three-dimensional space grid; L means the length of side on a limit of square three-dimensional space grid; c _iand c _jthe ion concentration that means respectively diffusion node i, j; q _ij, q _jimean respectively to flow to j and flow to the ion-flow rate density of i from diffusion node j from diffusion node i; D _ijmean the ionic diffusion coefficient between diffusion node i, j, determine according to the following formula:

In formula, D _iand D _jthe ionic diffusion coefficient that means respectively the phase of diffusion node i and diffusion node j; The ionic diffusion coefficient that wherein damages Xiang Yu hole, crack phase is identical;

Step 2, from described three-dimensional lattice ion transfer network, choose a cube zone, and the ion concentration boundary condition of setting this cube zone is as follows: the inflow face and the effluent face that are respectively ion with two opposed surfaces in this cube zone, remaining surface does not have ion to exchange with the external world, and the three-dimensional lattice ion transfer network diffusion node of setting on inflow face and effluent face has respectively constant ion concentration c _tand c ₀, c _tc ₀;

Step 3, utilize in described cube zone the diffusion matrix equation between adjacent diffusion node and ion concentration boundary condition in twos, the ion diffusion matrix equation that builds described cube zone is as follows:

$\left[\begin{array}{ccccccc}{k}_{11}& k_{12}& ...& k_{1i}& k_{1j}& ...& k_{1N}\\ k_{21}& k_{22}& ...& k_{2i}& k_{2j}& ...& k_{2N}\\ ...& ...& ...& ...& ...& ...& ...\\ k_{i1}& {\mathrm{<figure-callout\; id="2"\; label="k\; i"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">k</figure-callout>}}_i& ...& k_{\mathrm{ii}}& k_{\mathrm{ij}}& ...& k_{\mathrm{iN}}\\ k_{j1}& {\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">k</figure-callout>}}_j& ...& k_{\mathrm{ji}}& k_{\mathrm{jj}}& ...& k_{\mathrm{jN}}\\ ...& ...& ...& ...& ...& ...& ...\\ k_{N1}& {\mathrm{<figure-callout\; id="2"\; label="k\; N"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">k</figure-callout>}}_N& ...& k_{\mathrm{Ni}}& k_{\mathrm{Nj}}& ...& k_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{c}_1\\ {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\\ ...\\ c_i\\ c_j\\ ...\\ c_N\end{array}\right]=\left[\begin{array}{c}{\mathrm{\&Sigma;}}_{m=1,...N}{q}_{1m}\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{2m}\\ ...\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{im}}\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{jm}}\\ ...\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{Nm}}\end{array}\right],$

Wherein, $k_{\mathrm{ij}}=\frac{D_{\mathrm{ij}}A}{l},$ $k_{\mathrm{ii}}=-\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{D_{\mathrm{im}}A}{l},$ $k_{\mathrm{ji}}=\frac{D_{\mathrm{ij}}A}{l},$ $k_{\mathrm{jj}}=-\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{D_{\mathrm{jm}}A}{l},$ D _ij, D _im, D _jmbe respectively between i in described cube zone and j diffusion node, the ionic diffusion coefficient between i and m diffusion node, between j and m diffusion node, the area that A is one of them face of square three-dimensional space grid, the length of side on the limit that l is the square three-dimensional space grid, N is diffusion node sum in described cube zone, c _i, c _jmean in described cube zone i and the ion concentration of j diffusion node in N diffusion node, q _im, q _jmmean respectively in described cube zone to flow to m diffusion node and to flow to the ion-flow rate density of m diffusion node from j diffusion node from i diffusion node;

Step 4, the ion diffusion matrix equation in described cube zone is solved, obtained the ion concentration distribution that the ion diffusion reaches the described cube zone under stable state;

Step 5, according to the resulting ion concentration distribution of step 4, calculate the ionic diffusion coefficient D of cement-base composite material:

$D=\frac{Q}{A^{*}}\frac{L^{*}}{c_t-{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA00003665614900033.png,HDA00003665614900041.png"\; state="\{\{state\}\}">c</figure-callout>}}_0},$

In formula, A ^*for the cross-sectional area of described cube zone along inflow face to the effluent face direction; L ^*for the distance between inflow face and effluent face; c _tand c ₀be respectively the inflow face of setting in step 2 and the ion concentration of effluent face; Q means that ion diffusion reaches under stable state by the ion-flow rate of described effluent face, obtains according to following formula:

$Q=\underset{x\&Element;P_o}{\overset{X}{\mathrm{\&Sigma;}}}\underset{y}{\overset{Y}{\mathrm{\&Sigma;}}}{q}_{\mathrm{yx}}A,$

Wherein, x means to be positioned at effluent face P ₀on arbitrary diffusion node, X is for being positioned at effluent face P ₀on the diffusion node sum, y mean to be arranged in described cube zone and can be positioned at effluent face P ₀on diffusion node x jointly form any one diffusion node of lattice diffusion unit, Y for be arranged in described cube zone and can be positioned at effluent face P ₀on diffusion node x jointly form the diffusion node sum of lattice diffusion unit, q _yxexpression flows to the ion-flow rate density of diffusion node x, the area that A is one of them face of square three-dimensional space grid from diffusion node y.

Describedly by the discrete damage cement-base composite material microcosmic/microscopical structure that turns to a series of equal-sized square three-dimensional space grids, can be obtained by damage cement-base composite material sample is carried out to CT scan; Also can carry out in accordance with the following methods discretize by microcosmic/carefully the see continuous structure to the damage cement-base composite material obtains: will damage the microcosmic of cement-base composite material/carefully see continuous structure to be divided into a series of equal-sized square three-dimensional space grids; The phase that at first will wherein comprise each square three-dimensional space grid of damage crack phase is defined as damaging the crack phase; Then to remaining each square three-dimensional space grid, add up the phase at its central point and place, 8 summits, and using the phase of the highest phase of frequency of occurrence as this square three-dimensional space grid, the phase identical if any two phase frequency of occurrences, that the phase that wherein diffusivity is higher of take is this square three-dimensional space grid.

Preferably, the microcosmic of described damage cement-base composite material/carefully see continuous structure to obtain in accordance with the following methods: at first by the micromechanism generation model of Simulated Water slurry body: HYMOSTRUC3D, μ ic, and the microscopical structure generation model of simulation concrete: a kind of model among SPACE, HADES obtains the microcosmic of harmless cement-base composite material/carefully see continuous structure; Then simulate the damage crack under test condition in the microcosmic of described harmless cement-base composite material/carefully see continuous structure.

Preferably, for the micromechanism of damage cement slurry, described phase comprises: not hydrated cement phase, hole phase, outside hydrated product phase, inner hydrated product phase, damage crack phase, and wherein the ionic diffusion coefficient of hydrated cement phase is not 0; For the microscopical structure of damage concrete or damage mortar, described phase comprises: the phase of gathering materials, interfacial transition zone phase, cement matrix phase, damage crack phase, the ionic diffusion coefficient of the phase of wherein gathering materials is 0.

Compared to existing technology, the present invention has following beneficial effect:

On the basis of the virtual microcosmic/microscopical structure of damage cement-base composite material that the present invention can obtain at modelings such as HYMOSTRUC3D, μ ic, SPACE, HADES, direct construction damage cement-base composite material ion diffusion model, compare with setting up empirical model, can save a large amount of time and economic input; The present invention also is applicable to by damage cement-base composite material sample being carried out to the microcosmic/microscopical structure of the cement-base composite material that CT scan obtains, applied range.

The accompanying drawing explanation

Fig. 1 is the harmless cement slurry microcosmic continuous structure by the water cement ratio 0.4 of HYMOSTRUC3D model generation, degree of hydration 0.93;

The harmless cement slurry microcosmic continuous structure that Fig. 2 (a)～Fig. 2 (d) is respectively Fig. 1 at different x under the uniaxial tension conditioning, the crack produced in cement slurry;

Fig. 3 (a), Fig. 3 (b), Fig. 3 (c) are respectively freezing temperature for-5 ℃ ,-10 ℃ ,-20 ℃ the time, the crack produced in the cement slurry microcosmic continuous structure of the water cement ratio 0.4 of HYMOSTRUC3D model generation, degree of hydration 0.69;

Fig. 4 (a) determines principle schematic for crack phase grid, and Fig. 4 (b), Fig. 4 (c) are respectively the principle two-dimensional representation that 9 point control methods are carried out the continuous micromechanism discretize of cement slurry, and the two-dimensional representation after discretize;

Fig. 5 is the schematic diagram of choosing the cube zone and applying boundary condition;

Fig. 6 is the change curve of chloride diffusion coefficient under the different stretch strained condition of damage cement slurry;

Fig. 7 is the change curve of chloride diffusion coefficient under the freezing condition of difference of damage cement slurry.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is elaborated:

The ionic diffusion coefficient Forecasting Methodology of damage cement-base composite material of the present invention specifically comprises the following steps:

The three-dimensional lattice ion transfer network of step 1, structure damage cement-base composite material, specific as follows:

Step 1-1, obtain the microcosmic of harmless cement-base composite material/carefully see continuous structure;

The microcosmic of harmless cement-base composite material/carefully see continuous structure can utilize various existing microcosmic/carefully see model to obtain, for example the micromechanism generation model of Simulated Water slurry body: HYMOSTRUC3D, μ ic, and the microscopical structure generation model of simulation concrete: SPACE, HADES etc.Fig. 1 has shown by the HYMOSTRUC3D model (referring to document [van Breugel K.Simulation of hydration and formation of structure in hardening cement-based materials, PhD thesis, Delft University of Technology, Delft, 1991.] and document [Ye G.Experimental study and numerical simulation of the development of the microstructure and permeability of cementitious materials, PhD thesis, Delft University of Technology, Delft, 2003.]) water cement ratio 0.4 that obtains, the continuous micromechanism of the cement slurry of degree of hydration 0.93.

Step 1-2, in the microcosmic of harmless cement-base composite material/carefully see continuous structure, simulate the damage crack under test condition;

Simulation damage crack can adopt three-dimensional lattice fracture Analysis, Finite Element Methods etc. are (referring to document [Qian Z.Multiscale modeling of fracture process in cementitious materials, PhD thesis, Delft University of Technology, Delft, 2012.], document [Liu L., Ye G., Schlangen E., Chen, H.S., Qian Z.W., Sun W., van Breugel K.Modeling of the internal damage of saturated cement paste due to ice crystallization pressure during freezing.Cement and Concrete Composites, 33 (5) (2011) 562-571] and document [Snozzi L., Caballero A., Molinari J.F.Influence of the meso-structure in dynamic fracture simulation of concrete under tensile loading.Cem Concr Res41 (11) (2011) 1130-1142.]), the present invention preferably adopts three-dimensional lattice fracture Analysis.According to three-dimensional lattice fracture Analysis, at first will can't harm cement-base composite material microcosmic/carefully seeing continuous structure changes the three-dimensional lattice force structure be comprised of a series of lattice unit with mechanical property into, then apply certain acting force or displacement on this three-dimensional lattice force structure, such as the stretching displacement under the ice force under freezing environment or uniaxial tension condition, calculate afterwards the stress distribution of this three-dimensional lattice force structure inside under applied acting force or displacement, while in a series of lattice unit with mechanical property, having the suffered drawing stress in lattice unit to be greater than the pulling strengrth of this lattice unit, this lattice unit fracture, thereby produce a columniform damage crack.The harmless cement slurry microcosmic continuous structure that Fig. 2 (a)～Fig. 2 (d) is respectively Fig. 1 at different x under the uniaxial tension conditioning, the crack produced in cement slurry, x is followed successively by 0.5d to uniaxial tension displacement d _pek, 1.0d _pek, 4.5d _pek, 8.7d _pek, d _pekmean the displacement at peak load place.Fig. 3 (a), Fig. 3 (b), Fig. 3 (c) are respectively the freezing temperature of simulation for-5 ℃ ,-10 ℃ ,-20 ℃ the time, the crack produced in the cement slurry microcosmic continuous structure of the water cement ratio 0.4 of HYMOSTRUC3D model generation, degree of hydration 0.69.

Step 1-3, to the damage cement-base composite material microcosmic/carefully seeing continuous structure carries out discretize;

When carrying out discretize, should determine the ion diffusion property of damage crack phase, think in the present invention that damage Xiang Yu hole, crack has identical ion diffusion property mutually, therefore the damage crack directly can be attributed to the hole phase mutually, perhaps separately as a phase identical with the ionic diffusion coefficient of hole phase, adopt the latter's processing mode in this embodiment: for the micromechanism of damage cement slurry, described phase comprises: hydrated cement phase not, the hole phase, outside hydrated product phase, inner hydrated product phase, damage crack phase, wherein the ionic diffusion coefficient of hydrated cement phase is not 0, for the microscopical structure of damage concrete or damage mortar, described phase comprises: the phase of gathering materials, interfacial transition zone phase, cement matrix phase, damage crack phase, the ionic diffusion coefficient of the phase of wherein gathering materials is 0.

The present invention adopt 9 point control methods in conjunction with crack phase precedence method to the damage cement-base composite material microcosmic/carefully seeing continuous structure carries out discretize, specific as follows: will damage the microcosmic of cement-base composite material/carefully see continuous structure to be divided into a series of equal-sized square three-dimensional space grids; The phase that at first will wherein comprise each square three-dimensional space grid of damage crack phase is defined as damaging the crack phase; Then to remaining each square three-dimensional space grid, add up the phase at its central point and place, 8 summits, and using the phase of the highest phase of frequency of occurrence as this square three-dimensional space grid, the phase identical if any two phase frequency of occurrences, that the phase that wherein diffusivity is higher of take is this square three-dimensional space grid.While carrying out discretize, at first as shown in Figure 4 (a), all phases that include the square three-dimensional space grid of damage crack phase (being that crack is passed) are defined as damaging the crack phase; Then to remaining square three-dimensional space grid, utilize 9 point control methods to carry out discretize.(it is two-dimensional representation to Fig. 4 (b), a two dimensional cross-section that has only shown the three-dimensional microcosmic structure) shown that 9 point control methods carry out the principle of cement slurry micromechanism discretize, as shown in the figure, for any one hydrated cement particle, therefrom the outer solid phase of mind-set is respectively not hydrated cement particle, inner hydrated product and outside hydrated product, and being filled between solid phase particles is pore mutually.Each square three-dimensional space grid may comprise more than one phase, the present invention carrys out the phase of unique definite square three-dimensional space grid according to square three-dimensional space grid central point and place, 8 summits phase, the highest phase of the frequency of occurrence of usining is as the phase of this square three-dimensional space grid, for two kinds of situations that the phase frequency of occurrence is identical of accidental appearance, using two kinds of phases as this square three-dimensional space grid that phase intermediate ion coefficient of diffusion is higher; For example wherein the phase of 4 points is the hole phase, and the phase of other 4 points is inner hydrated product phase, and with ionic diffusion coefficient, higher hole is as the criterion mutually.The structure of the continuous micromechanism of Fig. 4 (b) after 9 point control methods are carried out the discretize processing as shown in Figure 4 (c).

In the present invention, describedly by the discrete damage cement-base composite material microcosmic/microscopical structure that turns to a series of equal-sized square three-dimensional space grids, also can be obtained by damage cement-base composite material sample is carried out to CT scan: at first according to concrete experiment needs, produce the damage crack by modes such as freeze thawing, load or drying shrinkage in the cement-base composite material sample, obtain damage cement-base composite material sample; Then utilize the damage cement-base composite material microcosmic/microscopical structure after the CT scan method obtains discretize.

Step 1-4, will be every a pair ofly there is each other the adjacent square three-dimensional space grid of ion diffusivity as a lattice diffusion unit, all lattice diffusion units form a three-dimensional lattice ion transfer network together, and each square three-dimensional space grid wherein is as a diffusion node of this three-dimensional lattice ion transfer network;

In above-mentioned model, the diffusion coefficient D of each lattice diffusion unit _ijthe coefficient of diffusion that depends on the phase of two diffusion node (i and j) that form this lattice diffusion unit, suppose to meet the diffusion coefficient D between two diffusion node that the equal-volume parallel model forms the lattice diffusion unit _ijcomputing formula is as the formula (1):

$D_{\mathrm{ij}}=\frac{2}{1/D_i+1/D_j}---\left(1\right)$

In formula, D _iand D _jthe ionic diffusion coefficient of the diffusion node i of the lattice of expression formation respectively diffusion unit and the phase of diffusion node j.For any two diffusion node that do not form the lattice diffusion unit in three-dimensional lattice ion transfer network, the coefficient of diffusion defined between them is 0.The ionic diffusion coefficient D between any two diffusion node i, j in three-dimensional lattice ion transfer network _ijas follows:

In formula, D _iand D _jthe ionic diffusion coefficient that means respectively the phase of diffusion node i and diffusion node j.

Suppose that the ion diffusion of material between any two diffusion node i, j all meets the Fick First Law, have,

$q_{\mathrm{ij}}=-D_{\mathrm{ij}}\frac{{\mathrm{dc}}_{\mathrm{ij}}}{\mathrm{dx}}---\left(2\right)$

Q wherein _ijexpression flows to the ion-flow rate density of diffusion node j from diffusion node i; c _iand c _jthe ion concentration that means respectively two diffusion node i and j place,

for ion concentration gradient.

The diffusion matrix equation that can obtain arbitrarily between two adjacent diffusion node i, j according to formula (2) is:

$-\frac{D_{\mathrm{ij}}A}{l}\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]\left[\begin{array}{c}{c}_i\\ c_j\end{array}\right]=\left[\begin{array}{c}{q}_{\mathrm{ij}}\\ q_{\mathrm{ji}}\end{array}\right]---\left(3\right)$

Wherein, A means the area of one of them face of square three-dimensional space grid; L means the length of side on a limit of square three-dimensional space grid; c _iand c _jthe ion concentration that means respectively diffusion node i, j; q _ij, q _jimean respectively to flow to j and flow to the ion-flow rate density of i from diffusion node j from diffusion node i; D _ijmean the ionic diffusion coefficient between diffusion node i, j.

Step 2, as shown in Figure 5, choose a cube zone from described three-dimensional lattice ion transfer network, and the ion concentration boundary condition of setting this cube zone is as follows: the inflow face and the effluent face that are respectively ion with two opposed surfaces in this cube zone, remaining surface does not have ion to exchange with the external world, and the three-dimensional lattice ion transfer network diffusion node of setting on inflow face and effluent face has respectively constant ion concentration c _tand c ₀, c _tc ₀.

Step 3, utilize in described cube zone the diffusion matrix equation between adjacent diffusion node and ion concentration boundary condition in twos, build the ion diffusion matrix equation in described cube zone;

According to the matrix equation of formula (3), each diffusion node has 1 degree of freedom, if the total number of diffusion node of the three-dimensional lattice ion transfer network comprised in selected cube zone is N, total degree of freedom is N.Diffusion matrix system of equations between each adjacent diffusion node in the cube zone is combined into to the ion diffusion matrix equation in the cube zone shown in formula (4):

$\left[\begin{array}{ccccccc}{k}_{11}& k_{12}& ...& k_{1i}& k_{1j}& ...& k_{1N}\\ k_{21}& k_{22}& ...& k_{2i}& k_{2j}& ...& k_{2N}\\ ...& ...& ...& ...& ...& ...& ...\\ k_{i1}& {\mathrm{<figure-callout\; id="2"\; label="k\; i"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">k</figure-callout>}}_i& ...& k_{\mathrm{ii}}& k_{\mathrm{ij}}& ...& k_{\mathrm{iN}}\\ k_{j1}& {\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">k</figure-callout>}}_j& ...& k_{\mathrm{ji}}& k_{\mathrm{jj}}& ...& k_{\mathrm{jN}}\\ ...& ...& ...& ...& ...& ...& ...\\ k_{N1}& {\mathrm{<figure-callout\; id="2"\; label="k\; N"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">k</figure-callout>}}_N& ...& k_{\mathrm{Ni}}& k_{\mathrm{Nj}}& ...& k_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{c}_1\\ {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00003665614900012.png,HDA00003665614900033.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\\ ...\\ c_i\\ c_j\\ ...\\ c_N\end{array}\right]=\left[\begin{array}{c}{\mathrm{\&Sigma;}}_{m=1,...N}{q}_{1m}\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{2m}\\ ...\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{im}}\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{jm}}\\ ...\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{Nm}}\end{array}\right]---\left(4\right)$

Wherein, $k_{\mathrm{ij}}=\frac{D_{\mathrm{ij}}A}{l},$ $k_{\mathrm{ii}}=-\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{D_{\mathrm{im}}A}{l},$ $k_{\mathrm{ji}}=\frac{D_{\mathrm{ij}}A}{l},$ $k_{\mathrm{jj}}=-\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{D_{\mathrm{jm}}A}{l},$ D _ij, D _im, D _jmionic diffusion coefficient between j and m diffusion node respectively in described cube zone between i and j diffusion node, between i and m diffusion node,, the area that A is one of them face of square three-dimensional space grid, the length of side on the limit that l is the square three-dimensional space grid, N is diffusion node sum in described cube zone, c _i, c _jmean in described cube zone i and the ion concentration of j diffusion node in N diffusion node, q _im, q _jmmean respectively in described cube zone to flow to m diffusion node and to flow to the ion-flow rate density of m diffusion node from j diffusion node from i diffusion node.

Step 4, the ion diffusion matrix equation in above-mentioned cube zone is solved, obtained the ion concentration distribution that the ion diffusion reaches the described cube zone under stable state;

Solving of ion diffusion matrix equation can adopt existing various algorithm, Newton method for example, method of finite difference etc., the present invention preferably adopts method of conjugate gradient, the method obtains the ion concentration distribution of stable state diffusion micromechanism inside by iteration progressively, more detailed content about method of conjugate gradient can be referring to document [Shewchuk J.R.An Introduction to the Conjugate gradient Method without the Agonizing Pain[M] .11/4Edition, Pittsburgh:Carnegie Mellon University, 1994.], repeat no more herein.

Step 5, damage cement-base composite material ionic diffusion coefficient calculate:

Ion increases in time and increases gradually by the flow of cement-base composite material effluent face, and is tending towards steady state value.When the flow Q of effluent face reaches steady state value, the diffusion of material reaches stable state, and the ionic diffusion coefficient D of cement-base composite material can calculate by following formula:

$D=\frac{Q}{A^{*}}\frac{L^{*}}{c_t-c_0}---\left(5\right)$

In formula, A ^*for the cross-sectional area of described cube zone along inflow face to the effluent face direction, unit is m ²; L ^*for the distance between inflow face and effluent face, unit is m; c _tand c ₀be respectively the inflow face of setting in step 2 and the ion concentration of effluent face, unit is molm ^-3; Q means that ion diffusion reaches under stable state by the ion-flow rate of described effluent face, and unit is mols ^-1, according to following formula, obtain:

$Q=\underset{x\&Element;P_o}{\overset{X}{\mathrm{\&Sigma;}}}\underset{y}{\overset{Y}{\mathrm{\&Sigma;}}}{q}_{\mathrm{yx}}A,$

Wherein, x means to be positioned at effluent face P ₀on arbitrary diffusion node, X is for being positioned at effluent face P ₀on the diffusion node sum, y mean to be arranged in described cube zone and can be positioned at effluent face P ₀on diffusion node x jointly form any one diffusion node of lattice diffusion unit, Y for be arranged in described cube zone and can be positioned at effluent face P ₀on diffusion node x jointly form the diffusion node sum of lattice diffusion unit, q _yxexpression flows to the ion-flow rate density of diffusion node x, the area that A is one of them face of square three-dimensional space grid from diffusion node y.

Step 6, the ionic diffusion coefficient that difference damage is produced to the damage cement-base composite material under environment are predicted respectively; Thereby can obtain the Ionic diffusion energy Changing Pattern of the lower damage cement-base composite materials of different condition impact such as freeze thawing, load or drying shrinkage.

The present invention considers the diffusion in transmission performance, the micromechanism of the damage cement-base composite material based on microfracture, a kind of ionic diffusion coefficient Forecasting Methodology of damaging cement-base composite material has been proposed, the Ionic diffusion energy Changing Pattern of the lower damage of the condition impact cement-base composite materials such as application the method can the Accurate Prediction freeze thawing, load or drying shrinkage, have great importance for the service life prediction of civil engineering material.

In order to verify effect of the present invention, use respectively under the external load action of the inventive method and under frost action cement slurry chlorion diffusion change and to be predicted.

The cement slurry micromechanism of using under external load function is by the water cement ratio 0.4 of HYMOSTRUC3D model generation, the continuous micromechanism of cement slurry (referring to Fig. 1) of degree of hydration 0.93, then simulate under the different stretch displacement condition, the cylindrical microfracture produced in the hydrated cement slurry (referring to Fig. 2 (a)～Fig. 2 (d)), then dope chloride diffusion coefficient according to the inventive method.

The cement slurry micromechanism of using under frost action is by the water cement ratio 0.4 of HYMOSTRUC3D model generation, the cement slurry of degree of hydration 0.93, then simulate under condition of different temperatures, the cylindrical microfracture produced in the hydrated cement slurry (referring to Fig. 3 (a), Fig. 3 (b), Fig. 3 (c)), then dope chloride diffusion coefficient according to the inventive method.

Damage the chloride diffusion coefficient value of each phase in cement slurry in experiment in Table 1.

Table 1

Under the different stretch strained condition, the chloride diffusion coefficient of damage cement slurry predicts the outcome as shown in Figure 6, and under different freezing conditions, the chloride diffusion coefficient of damage cement slurry predicts the outcome as Fig. 7.

Claims (7)

1. an ionic diffusion coefficient Forecasting Methodology of damaging cement-base composite material, it is characterized in that, comprise the following steps: step 1, for by the discrete damage cement-base composite material microcosmic/microscopical structure that turns to a series of equal-sized square three-dimensional space grids, there is each other the adjacent square three-dimensional space grid of ion diffusivity as a lattice diffusion unit using often a pair of, all lattice diffusion units form a three-dimensional lattice ion transfer network together, each square three-dimensional space grid wherein is as a diffusion node of this three-dimensional lattice ion transfer network, in described three-dimensional lattice ion transfer network, the diffusion matrix equation between any two adjacent diffusion node i, j is:

$-\frac{D_{\mathrm{ij}}A}{l}\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]\left[\begin{array}{c}{c}_i\\ c_j\end{array}\right]=\left[\begin{array}{c}{q}_{\mathrm{ij}}\\ q_{\mathrm{ji}}\end{array}\right]$

Wherein, A means the area of one of them face of square three-dimensional space grid; L means the length of side on a limit of square three-dimensional space grid; c _iand c _jthe ion concentration that means respectively diffusion node i, j; q _ij, q _jimean respectively to flow to j and flow to the ion-flow rate density of i from diffusion node j from diffusion node i; D _ijmean the ionic diffusion coefficient between diffusion node i, j, determine according to the following formula:

In formula, D _iand D _jthe ionic diffusion coefficient that means respectively the phase of diffusion node i and diffusion node j; The ionic diffusion coefficient that wherein damages Xiang Yu hole, crack phase is identical;

Step 2, from described three-dimensional lattice ion transfer network, choose a cube zone, and the ion concentration boundary condition of setting this cube zone is as follows: the inflow face and the effluent face that are respectively ion with two opposed surfaces in this cube zone, remaining surface does not have ion to exchange with the external world, and the three-dimensional lattice ion transfer network diffusion node of setting on inflow face and effluent face has respectively constant ion concentration c _tand c ₀, c _tc ₀;

Step 3, utilize in described cube zone the diffusion matrix equation between adjacent diffusion node and ion concentration boundary condition in twos, the ion diffusion matrix equation that builds described cube zone is as follows:

$\left[\begin{array}{ccccccc}{k}_{11}& k_{12}& ...& k_{1i}& k_{1j}& ...& k_{1N}\\ k_{11}& k_{22}& ...& k_{2i}& k_{2j}& ...& k_{2N}\\ ...& ...& ...& ...& ...& ...& ...\\ k_{i1}& k_{i2}& ...& k_{\mathrm{ii}}& k_{\mathrm{ij}}& ...& k_{\mathrm{iN}}\\ k_{j1}& k_{j2}& ...& k_{\mathrm{ji}}& k_{\mathrm{jj}}& ...& k_{\mathrm{jN}}\\ ...& ...& ...& ...& ...& ...& ...\\ k_{N1}& k_{N2}& ...& k_{\mathrm{Ni}}& k_{\mathrm{Nj}}& ...& k_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{c}_1\\ c_2\\ ...\\ c_i\\ c_j\\ ...\\ c_N\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Sigma;}}_{m=1,...N}{q}_{1m}\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{2m}\\ ...\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{im}}\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{jm}}\\ ...\\ {\mathrm{\&Sigma;}}_{m=1,...N}{q}_{\mathrm{Nm}}\end{array}\right],$

Wherein, $k_{\mathrm{ij}}=\frac{D_{\mathrm{ij}}A}{l},$ $k_{\mathrm{ii}}=-\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{D_{\mathrm{im}}A}{l},$ $k_{\mathrm{ji}}=\frac{D_{\mathrm{ij}}A}{l},$ $k_{\mathrm{jj}}=-\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{D_{\mathrm{jm}}A}{l},$ D _ij, D _im, D _jmbe respectively between i in described cube zone and j diffusion node, the ionic diffusion coefficient between i and m diffusion node, between j and m diffusion node, the area that A is one of them face of square three-dimensional space grid, the length of side on the limit that l is the square three-dimensional space grid, N is diffusion node sum in described cube zone, c _i, c _jmean in described cube zone i and the ion concentration of j diffusion node in N diffusion node, q _im, q _jmmean respectively in described cube zone to flow to m diffusion node and to flow to the ion-flow rate density of m diffusion node from j diffusion node from i diffusion node;

Step 4, the ion diffusion matrix equation in described cube zone is solved, obtained the ion concentration distribution that the ion diffusion reaches the described cube zone under stable state;

Step 5, according to the resulting ion concentration distribution of step 4, calculate the ionic diffusion coefficient D of cement-base composite material:

$D=\frac{Q}{A^{*}}\frac{L^{*}}{c_t-c_0},$

In formula, A ^*for the cross-sectional area of described cube zone along inflow face to the effluent face direction; L ^*for the distance between inflow face and effluent face; c _tand c ₀be respectively the inflow face of setting in step 2 and the ion concentration of effluent face; Q means that ion diffusion reaches under stable state by the ion-flow rate of described effluent face, obtains according to following formula:

$Q=\underset{x\&Element;P_o}{\overset{X}{\mathrm{\&Sigma;}}}\underset{y}{\overset{Y}{\mathrm{\&Sigma;}}}{q}_{\mathrm{yx}}A,$

Wherein, x means to be positioned at effluent face P ₀on arbitrary diffusion node, X is for being positioned at effluent face P ₀on the diffusion node sum, y mean to be arranged in described cube zone and can be positioned at effluent face P ₀on diffusion node x jointly form any one diffusion node of lattice diffusion unit, Y for be arranged in described cube zone and can be positioned at effluent face P ₀on diffusion node x jointly form the diffusion node sum of lattice diffusion unit, q _yxexpression flows to the ion-flow rate density of diffusion node x, the area that A is one of them face of square three-dimensional space grid from diffusion node y.

2. damage as claimed in claim 1 the ionic diffusion coefficient Forecasting Methodology of cement-base composite material, it is characterized in that, described by the discrete damage cement-base composite material microcosmic/microscopical structure that turns to a series of equal-sized square three-dimensional space grids, carry out in accordance with the following methods discretize by microcosmic/carefully the see continuous structure to the damage cement-base composite material and obtain: will damage the microcosmic of cement-base composite material/carefully see continuous structure to be divided into a series of equal-sized square three-dimensional space grids; The phase that at first will wherein comprise each square three-dimensional space grid of damage crack phase is defined as damaging the crack phase; Then to remaining each square three-dimensional space grid, add up the phase at its central point and place, 8 summits, and using the phase of the highest phase of frequency of occurrence as this square three-dimensional space grid, the phase identical if any two phase frequency of occurrences, that the phase that wherein diffusivity is higher of take is this square three-dimensional space grid.

3. damage as claimed in claim 2 the ionic diffusion coefficient Forecasting Methodology of cement-base composite material, it is characterized in that, the microcosmic of described damage cement-base composite material/carefully see continuous structure to obtain in accordance with the following methods: at first by the micromechanism generation model of Simulated Water slurry body: HYMOSTRUC3D, μ ic, and the microscopical structure generation model of simulation concrete: a kind of model among SPACE, HADES obtains the microcosmic of harmless cement-base composite material/carefully see continuous structure; Then simulate the damage crack under test condition in the microcosmic of described harmless cement-base composite material/carefully see continuous structure.

4. damage as claimed in claim 3 the ionic diffusion coefficient Forecasting Methodology of cement-base composite material, it is characterized in that, use three-dimensional lattice fracture Analysis to simulate the damage crack under test condition in the microcosmic of described harmless cement-base composite material/carefully see continuous structure.

5. damage as claimed in claim 1 the ionic diffusion coefficient Forecasting Methodology of cement-base composite material, it is characterized in that, describedly obtained by damage cement-base composite material sample is carried out to CT scan by the discrete damage cement-base composite material microcosmic/microscopical structure that turns to a series of equal-sized square three-dimensional space grids.

6. damage as claimed in claim 1 the ionic diffusion coefficient Forecasting Methodology of cement-base composite material, it is characterized in that, micromechanism for the damage cement slurry, described phase comprises: not hydrated cement phase, hole phase, outside hydrated product phase, inner hydrated product phase, damage crack phase, and wherein the ionic diffusion coefficient of hydrated cement phase is not 0; For the microscopical structure of damage concrete or damage mortar, described phase comprises: the phase of gathering materials, interfacial transition zone phase, cement matrix phase, damage crack phase, the ionic diffusion coefficient of the phase of wherein gathering materials is 0.

7. damage as claimed in claim 1 the ionic diffusion coefficient Forecasting Methodology of cement-base composite material, it is characterized in that, also comprise:

Step 6, the ionic diffusion coefficient that difference damage is produced to the damage cement-base composite material under environment are predicted respectively.

Images