CN110110394A - A kind of spatial random field analogy method of Parameters for Rockfill Dams - Google Patents
A kind of spatial random field analogy method of Parameters for Rockfill Dams Download PDFInfo
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Abstract
The invention discloses a kind of spatial random field analogy methods of Parameters for Rockfill Dams, are specifically implemented according to the following steps: step 1 is established rock-fill dams finite element model and is divided to it；Step 2 carries out random field simulation to the rock-fill dams finite element model in step 1, obtains the simulation distribution figure of rock-fill dams finite element model of the present invention；Secondary development to the subprogram of finite element software, the analogue value for calculate using secondary development subroutine call finite element software the random field that step 2 obtains, so that the cloud charts for obtaining rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress verify rock-fill dams finite element model.Analogy method of the invention discloses the Spatial Variability analogy method of rock-fill dams rockfill materials E-B Parameters of constitutive model, and the exploitation of non-intrusion type has been carried out in conjunction with existing business finite element software, so that method proposed by the present invention is combined the spatial random field of research rock-fill dams model well with finite element software.
Description
Technical field
The invention belongs to analogy method fields, and in particular to a kind of spatial random field simulation side of Parameters for Rockfill Dams
Method.
Background technique
Because of the advantages that section is small, adaptable, easy construction, water conservancy diversion are simplified and highly-safe, rock-fill dams become high at present
The preferred dam type in the big library in dam.However, on the one hand, the rockfill materials in rock-fill dams are a kind of extremely complex engineering material, material
Expect that parameter, physico mechanical characteristic randomness is strong, variability is big.Meanwhile because rock-fill dams material partition is more and figure is larger etc.
Reason causes Parameters for Rockfill Dams inevitably to there is spatial diversity.On the other hand, since test measurement error, numerical value calculate reason
By and the limitation of constitutive model can not simulate the stress condition etc. of material in Practical Project completely, and by measurement error institute band
The statistical uncertainty etc. come has a significant impact to the precision of calculated result.Therefore, big model is assumed in conventional finite element calculating
The dam material parameter enclosed is that parameter value that is unique, determining obviously can not reflect engineering reality, and calculated value is caused to deposit with measured value
In biggish error.Moreover, business finite element software cannot achieve STOCHASTIC FINITE ELEMENT calculating, random field simulation and general quotient at present
The interface frame of industry finite element software is incomplete.
Summary of the invention
The object of the present invention is to provide a kind of spatial random field analogy methods of Parameters for Rockfill Dams, can reduce existing
Method calculates the error that stockpile material parameter generates.
The technical scheme adopted by the invention is that a kind of spatial random field analogy method of Parameters for Rockfill Dams, according to
Following steps specific implementation:
Step 1 establishes rock-fill dams finite element model using finite element software, carries out grid to rock-fill dams finite element model and draws
Point；
M material parameter carries out the rock-fill dams finite element model in step 1 random in step 2, selection E-B constitutive model
Field simulation, M=1,2 ..., 9, obtain the simulation distribution figure of rock-fill dams finite element model spatial random field.
The features of the present invention also characterized in that
Step 1 is embodied according to the following steps:
Step 1.1 establishes rock-fill dams finite element model using finite element software, is from upstream to rock-fill dams finite element model
Downstream successively subregion: upstream head weight 1B, the oblique bedding 1A in upstream, concrete slab, bed course area 2A, transition region 3A, main rockfill area 1:
3BI, main rockfill area 2:3BII, secondary rockfill area 3C；
Step 1.2, to each subregion of the rock-fill dams finite element model in step 1.1 using eight node hexahedral elements into
Row FEM meshing obtains several units.
Step 2 is embodied according to the following steps:
Step 2.1, each unit in step 1 bed course area 2A is numbered: Ai, i=1,2 ..., N, N are that unit is total
Number；
Step 2.2, the center point coordinate value matrix of each unit in step 2.1 is calculated:
Wherein, i=1,2 ..., N, xij(j=1,2 ..., 8) be i-th of unit, j-th of node abscissa value, yij
(j=1,2 ..., 8) is the ordinate value of i-th of unit, j-th of node；xiFor the central point abscissa value of i-th of unit, yi
For the central point ordinate value of i-th of unit；
Step 2.3 is sampled M material parameter of each unit of bed course area 2A using LHS method, constructs bed course area
The independent standard normal random sample matrix of 2A:
Wherein i=1,2 ... n, ξiFor the matrix that i-th is sampled, SljJ-th of material parameter of first of unit
Sampling results；
Step 2.4: the equivalent interaction matrix R of M material parameter in selecting step 2.3M×M:
To above-mentioned matrix RM×MCholesky decomposition is carried out, lower triangular matrix L is obtained1(M×M):
By lower triangular matrix L obtained above1Transposition is carried out to obtain
Step 2.5: the relative value between each unit central point transverse and longitudinal coordinate obtained using step 2.2 calculates Gaussian certainly
Correlation function:
Wherein, τx, τyRelative value respectively between each unit central point transverse and longitudinal coordinate of step 2.2 calculating, τx=| xi-
xj|, τy=| yi-yj|, δhFor horizontal fluctuation range, δvFor vertical fluctuation range；
The auto-correlation function matrix ρ of N number of unit in bed course area 2A is calculated by above-mentioned Gaussian auto-correlation functionN×N:
Wherein, pijFor the related coefficient between i-th of unit and j-th of unit；
To above-mentioned matrix ρN×NCholesky is carried out to decompose to obtain lower triangular matrix L2(N×N):
Step 2.6: the right side independent standard normal random sample matrix ξ in step 2.3 is multiplied into lower three angular moment that step 2.5 obtains
Battle array L2, then premultiplication step 2.4 obtainsFinally obtain relevant criterion Gaussian random field sample
Wherein, i=1,2 ... n,For L1Transposition.
Step 2.7: the relevant criterion Gaussian random field sample that step 2.6 is obtainedFetching number obtains bed course area
The related lognormal random field matrix H of 2Ai(x, y):
Wherein, For the random field parameters of each unit
Mean value,For the coefficient of variation of the random field parameters of each unit；
Step 2.8, step 2.1~step 2.7 is repeated in other subregions of rock-fill dams finite element model, and then obtained
The related lognormal random field matrix H of each subregioni(x, y), by the related lognormal random field H of each subregioni(x,y)
The analogue value be assigned to corresponding unit in subregion, obtain the spatial random field H (x, y) of rock-fill dams finite element model of the present inventionN×n
Simulation distribution figure.
Gaussian auto-correlation function can also be index type auto-correlation function, second-order auto-regressive type auto-correlation in step 2.5
Any one of function, index longitudinal cosine type auto-correlation function, triangular form auto-correlation function.
The analogue value for the random field that step 2.8 obtains is counted using the secondary development software of finite element software subprogram
It calculates, the cloud charts of rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress is obtained, to obtained rock-fill dams
The cloud charts of the dam body settlement of finite element model random field, horizontal displacement and each principal stress are verified, verifying it is specific
Step are as follows:
Step a, the material parameter for each unit for being obtained step 2 using the secondary development software of finite element software subprogram
The original material parameter of each unit in random field analogue value replacement step 2；
Step b, using the secondary development software transfer finite element software of finite element software subprogram, by step a with
The airport analogue value substitutes into FEM calculation, obtains rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress
Cloud charts；
Step c, by point of obtained rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress of step b
Cloth cloud atlas and its data and the dam body data of actual measurement compare, and are verified result.
The secondary development of finite element software subprogram is implemented including step in detail below in step 3:
The initial value of 9 material parameters of rock-fill dams E-B constitutive model is arranged in step I；
Step II, according to unit number, by each unit material parameter random field analogue value replacement step obtained in step 2
9 raw material parameters in 1；
Step III, elastic modulus E is calculatedtWith bulk modulus Bt, judge load perhaps unload using load or unloading
Elasticity modulus forms tangent modulus matrix, ultimately forms strain-stress relation matrix；
Step IV, define load and apply step: preceding 30 step is staged-filling step, and the 30th~34 step is to apply water ballast(ing) by stages
Step；
Step V, dam body later period rheology is calculated using the Bo Gesi model of rock-fill dams；
Step VI, customized output item: horizontal displacement, Vertical Settlement, maximum principal stress, minimum principal stress, stress is set
Level and panel axial direction and inclined slope aspect stress；
Step VII, secondary development program is loaded under DOS environment and model data file calls directly finite element software
Marc is calculated, and is repeated step I~step V and is iterated calculating；
Step VIII, the destination file calculated step VII is handled, and obtains the cloud atlas of the response quautities such as ess-strain.
The beneficial effects of the present invention are: existing method can not consider the variability of stockpile material parameter spatially, make
It obtains FEM calculation strain value and is often below measured value, the present invention develops rock non-intrusion type STOCHASTIC FINITE ELEMENT side
Method carries out random process and FEM calculation independently, can be applied in different case histories, in different finite elements
Interface routine only need to be modified in software, is more advantageous to the popularization and use of Stochastic Finite Element Method, and calculate accurate
Have great importance with the ess-strain problem for holding concrete face rockfill dam, effectively reduces the strain of FEM calculation
The error of value and measured value.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the spatial random field analogy method of Parameters for Rockfill Dams of the present invention；
Fig. 2 is the flow chart of Investigation of FEM Software Further-development of the present invention；
Fig. 3 is the section size figure of rock finite element model of the present invention；
Fig. 4 is rock finite element model FEM meshing figure of the present invention；
Fig. 5 is the random field simulation drawing of rock E-B Parameters of constitutive model K of the present invention；
Fig. 6 is rock E-B Parameters of constitutive model of the present inventionRandom field simulation drawing；
Fig. 7 is rock E-B Parameters of constitutive model K of the present inventionbRandom field simulation drawing；
Fig. 8 is the rock settlement-contour map that the mentioned method of invention calculates；
Fig. 9 is a kind of spatial random field analogy method of Parameters for Rockfill Dams of the present invention and the comparison diagram of conventional method.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
As shown in Figure 1, be a kind of flow chart of the spatial random field analogy method of Parameters for Rockfill Dams of the present invention, according to
Following steps specific implementation:
Step 1 establishes rock-fill dams finite element model using finite element software, carries out grid to rock-fill dams finite element model and draws
Point:
Step 1.1: establishing rock-fill dams finite element model using finite element software, rock-fill dams finite element model is from upstream to
Downstream successively subregion: upstream head weight (1B), the oblique bedding in upstream (1A), concrete slab, bed course area (2A), transition region (3A), main
Rockfill area 1 (3BI), main rockfill area 2 (3BII), secondary rockfill area (3C).
Step 1.2: to each subregion of the rock-fill dams finite element model in step 1.1 using eight node hexahedral elements into
Row FEM meshing obtains several units.
Step 2, M material parameter in E-B constitutive model is chosen to carry out at random the rock-fill dams finite element model in step 1
Field simulation, M=1,2 ..., 9, obtain the simulation distribution figure of rock-fill dams finite element model spatial random field, specific random field simulation
Process are as follows:
Step 2.1, to each unit is numbered in bed course area 2A subregion in step 1: Ai(i=1,2 ..., N, N are single
First sum)；
Step 2.2, the center point coordinate value matrix of each unit in step 2.1 is calculated:
Wherein, i=1,2 ..., N, xij(j=1,2 ..., 8) be i-th of unit, j-th of node abscissa value, yij
(j=1,2 ..., 8) be i-th of unit, j-th of node ordinate value, xiFor the central point abscissa value of i-th of unit, yi
For the central point ordinate value of i-th of unit.
Step 2.3 is sampled M material parameter of each unit of bed course area 2A using LHS method, constructs bed course area
The independent standard normal random sample matrix of 2A:
Wherein i=1,2 ... n, ξiFor the matrix that i-th is sampled, SljFor j-th of material parameter of first of unit
LHS sampling results.
Step 2.4: the equivalent cross correlation matrix number R of M material parameter in selecting step 2.3M×M:
To above-mentioned matrix RM×MCholesky decomposition is carried out, lower triangular matrix L is obtained1(M×M):
By lower triangular matrix L obtained above1Transposition is carried out to obtain
Step 2.5: the relative value between each unit central point transverse and longitudinal coordinate obtained using step 2.2 calculates Gaussian certainly
Correlation function:
Wherein, τx, τyRelative value respectively between each unit central point transverse and longitudinal coordinate of step 2.2 calculating, τx=| xi-
xj|, τy=| yi-yj|, δhFor horizontal fluctuation range, need to be determined according to geology statistical result；δvFor vertical fluctuation range, basis is needed
Geological statistics result determines.
The auto-correlation function matrix ρ of N number of unit in bed course area 2A is calculated by above-mentioned Gaussian auto-correlation functionN×N:
Wherein, pijFor the related coefficient between i-th of unit and j-th of unit；
To above-mentioned matrix ρN×NCholesky is carried out to decompose to obtain lower triangular matrix L2(N×N):
Above-mentioned Gaussian auto-correlation function can also be index type auto-correlation function, second-order auto-regressive type auto-correlation function,
Any one of index longitudinal cosine type auto-correlation function, triangular form auto-correlation function.
Step 2.6: the right side independent standard normal random sample matrix ξ in step 2.3 is multiplied into lower three angular moment that step 2.5 obtains
Battle array L2, then premultiplication step 2.4 obtainsFinally obtain relevant criterion Gaussian random field sample
Wherein, i=1,2 ... n,For L1Transposition.
Step 2.7: the relevant criterion Gaussian random field sample that step 2.6 is obtainedFetching number obtains bed course area
The related lognormal random field matrix H of 2Ai(x, y):
Wherein, For the random field parameters of each unit
Mean value,For the coefficient of variation of the random field parameters of each unit.
Step 2.8, step 2.1~step 2.7 is repeated in other subregions of rock-fill dams finite element model, and then obtained
The related lognormal random field matrix H of each subregioni(x, y), by the related lognormal random field matrix H of each subregioni
The analogue value of (x, y) is assigned to corresponding unit in subregion, obtain rock-fill dams finite element model of the present invention random field H (x,
y)N×nDistribution map.
The secondary development software that the analogue value for the random field that step 2.8 obtains brings finite element software subprogram into is counted
It calculates, obtains the cloud charts of the dam body settlement of rock-fill dams finite element model of the present invention, horizontal displacement and each principal stress, to obtaining
The dam body settlement of rock-fill dams finite element model random field, horizontal displacement and each principal stress cloud charts verified, test
The specific steps of card are as follows:
Step a: the material of each unit obtained in step 2 is joined using the secondary development program of finite element software subprogram
The original material parameter of each unit in number random field analogue value replacement step 2.
Step b: calling directly finite element software using the secondary development program of finite element software subprogram, will be in step a
The random field analogue value substitute into FEM calculation, obtain rock-fill dams finite element model dam body settlement, horizontal displacement and each master and answer
The cloud charts of power.
Step c, by point of obtained rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress of step b
Cloth cloud atlas and its data and the dam body data of actual measurement compare, and are verified result.
As shown in Fig. 2, being the flow chart of the secondary development program of finite element software subprogram of the present invention, finite element software
The secondary development of program is calculated by setting initial parameter module, parameter assignment module, calculating step definition module, E-B constitutive model
Module, rheological model computing module, customized output module and finite element iterative computing module composition, calculate in step definition procedure
Consider the influence of by-stage impoundment, staged-filling and dam body later period rheology.
Secondary development program based on finite element software, including step is developed in detail below:
The initial value of step I, 9 material parameters of setting rock-fill dams E-B constitutive model；
Step II, according to unit number, by each unit material parameter random field analogue value replacement step obtained in step 2
9 original material parameters in 2；
Step III calculates elastic modulus EtWith bulk modulus Bt, judge load perhaps unload using load or unloading
Elasticity modulus forms tangent modulus matrix, ultimately forms strain-stress relation matrix；
Step IV defines load application step: preceding 30 step is staged-filling step, and the 30th~34 step is to apply water ballast(ing) by stages
Step；
Step V calculates dam body later period rheology using the Bo Gesi model of rock-fill dams；
Step VI, the customized output item of setting: horizontal displacement, Vertical Settlement, maximum principal stress, minimum principal stress, stress
Level and panel axial direction and inclined slope aspect stress；
Step VII loads secondary development program (.F file) and model data file (.dat file) directly under DOS environment
It connects and finite element software Marc is called to be calculated, without opening or modifying finite element software, with realization " non-intrusion type " calculating, weight
Multiple step I~step V is iterated calculating；
Step VIII, the destination file (.t16 file) calculated step VII are handled, and obtain the response quautities such as ess-strain
Cloud atlas.
A kind of analogy method of the spatial random field based on Parameters for Rockfill Dams of the present invention discloses rock-fill dams heap stone material
Expect the Spatial Variability analogy method of E-B Parameters of constitutive model, the stochastic simulation process and finite element of rock-fill dams finite element model
Independent progress is calculated, can go to be calculated using different finite element softwares, can be applied in different actual engineerings, increase
The big practicability of the present invention in practical applications.Moreover, the present invention carries out secondary development to finite element software, can precisely count
The specific values such as stress, the strain of rock-fill dams finite element model are calculated, the calculated value and reality in rock-fill dams finite element model are reduced
Error between measured value.The present invention combines existing business finite element software to carry out the exploitation of non-intrusion type, makes proposition of the present invention
Method combine well with finite element software, convenient for the promotion and application of Stochastic Finite Element Method proposed by the present invention.
Embodiment
Step 1: certain rock normal pool level 2005.00m, check flood level 2008.00m.Crest elevation
2010.00m, maximum height of dam 139.00m, dam middle part are laid with electromagnetic type sedimentometer survey line ES2；It is from upstream to downstream subregion difference
Are as follows: upstream head weight (1B), the oblique bedding in upstream (1A), concrete slab, bed course area (2A), transition region (3A), main rockfill area 1
(3BI), main rockfill area 2 (3BII), secondary rockfill area (3C), as shown in Figure 3.FEM meshing is carried out to model, such as Fig. 4 institute
Show, is divided into 1430 units, 2946 nodes altogether, wherein 28, the area 2A unit, 32, the area 2B unit, 378, the area 3BI list
Member, 434, the area 3BII unit, 310, the area 3C unit, remaining is ground unit.
Step 2: random field simulation is carried out to the material parameter of each subregion in step 1.
Step 2.1: bed course area (2A), transition region (3A), main rockfill area 1 (3BI), main rockfill area 2 (3BII), secondary rockfill area
The material parameter characteristic value value such as following table of (3C).
Step 2.2: by taking bed course area (2A) as an example, random field simulation uses grid same as FEM calculation, calculates pad
The center point coordinate value matrix of floor area (2A) unit are as follows:
Wherein, first it is classified as unit number, abscissa value is put centered on secondary series, third is classified as central point ordinate value；
Step 2.3: using the LHS methods of sampling to K in each unit,KbThree material parameters are sampled, and building is every
The independent standard normal random sample matrix of a unit, the building number of each unit are 1000 times, and the separate standards of generation are just
State random sample matrix are as follows:
Step 2.4: due to being independent from each other between E-B Parameters of constitutive model, take in step 2.3 between three parameters etc.
Effect cross correlation matrix number is R:
Cholesky decomposition is carried out to above-mentioned matrix R, obtains lower triangular matrix L1:
By lower triangular matrix L obtained above1Transposition is carried out to obtain
Step 2.5: selection Gaussian auto-correlation function obtains 28, bed course area (area 2A) unit auto-correlation coefficient matrix
ρ28×28:
To above-mentioned auto-correlation coefficient matrix ρ28×28Cholesky is carried out to decompose to obtain another lower triangular matrix L2:
Step 2.6: lower three that the independent standard normal random sample matrix ξ premultiplication step 2.5 that step 2.3 obtains is obtained
Angular moment battle array step L2, and obtained in premultiplication step 2.4Finally obtain relevant criterion Gaussian random field sampleThat is:
Wherein,For L1Transposition.
Step 2.7: the random field sample that step 2.6 is obtainedFetching number obtains the related logarithm of each subregion
The random field matrix of normal state:
Similarly, the discrete of stochastic parameter field is carried out to transition region, the area 3BI, the area 3BII and the area 3C respectively, obtains each subregion
Stochastic parameter field matrix discrete value, each discrete value is then assigned to corresponding unit in subregion, is obtained of the invention random
Simulation distribution figure, Fig. 5, Fig. 6 and Fig. 7 be respectively three material parameter K in dam body,KbRandom field pattern, wherein
Abscissa in Fig. 5, Fig. 6 and Fig. 7 is dam width, and ordinate is height of dam, and what each point represented is the random field mould of the unit in figure
Analog values.Since random field unit and FEM calculation use same nested grid, the corresponding random field simulation of a unit
Value.
Step 3: using the secondary development program of finite element software, the raw material parameter of each unit being replaced with into random field
The parameter value of simulation, Fig. 8 are the rock settlement-contour map calculated using the method for the present invention, and line smoothing is poor,
Fluctuation is stronger, partial closure curve occurs, is more in line with actual conditions, and Fig. 9 is that the method for the present invention and dam body shown in Fig. 2 are surveyed
The dam body settlement comparative result figure that the measured value and conventional method of line calculate, as can be seen from Figure 9: current conventional finite
First method calculated value and measured settlement have obvious gap, and especially in the middle part of dam body and top, measured settlement are obviously big
In calculated value, the fact that this meets the remote hyper-finite element calculated value of rock sedimentation value in practice；The present invention mentions to be had at random
Limit first method calculated value and measured settlement in the middle part of dam body, the middle and upper part goodness of fit it is higher, slightly have in dam body low portion measuring point
Error, but overall fit is good；And calculated value and measured value are relatively, it was demonstrated that NSFEM method is by considering dam material
Randomness and inhomogeneities, calculated value coincide compared with measured value.
Claims (6)
1. a kind of spatial random field analogy method of Parameters for Rockfill Dams, which is characterized in that be embodied according to the following steps:
Step 1 establishes rock-fill dams finite element model using finite element software, carries out grid dividing to rock-fill dams finite element model；
M material parameter carries out random field mould to the rock-fill dams finite element model in step 1 in step 2, selection E-B constitutive model
It is quasi-, M=1,2 ..., 9, obtain the simulation distribution figure of rock-fill dams finite element model spatial random field.
2. a kind of spatial random field analogy method of Parameters for Rockfill Dams according to claim 1, which is characterized in that institute
Step 1 is stated to be embodied according to the following steps:
Step 1.1 establishes rock-fill dams finite element model using finite element software, is from upstream to downstream to rock-fill dams finite element model
Successively subregion: upstream head weight 1B, the oblique bedding 1A in upstream, concrete slab, bed course area 2A, transition region 3A, main rockfill area 1:3BI,
Main rockfill area 2:3BII, secondary rockfill area 3C；
Step 1.2 has each subregion of the rock-fill dams finite element model in step 1.1 using eight node hexahedral elements
First grid dividing is limited, several units are obtained.
3. a kind of spatial random field analogy method of Parameters for Rockfill Dams according to claim 2, which is characterized in that institute
Step 2 is stated to be embodied according to the following steps:
Step 2.1, each unit in step 1 bed course area 2A is numbered: Ai, i=1,2 ..., N, N are unit sum；
Step 2.2, the center point coordinate value matrix of each unit in step 2.1 is calculated:
Wherein, i=1,2 ..., N, xij(j=1,2 ..., 8) be i-th of unit, j-th of node abscissa value, yij(j=1,
2 ..., 8) be i-th of unit, j-th of node ordinate value；xiFor the central point abscissa value of i-th of unit, yiIt is i-th
The central point ordinate value of unit；
Step 2.3 is sampled M material parameter of each unit of bed course area 2A using LHS method, building bed course area 2A's
Independent standard normal random sample matrix:
Wherein i=1,2 ... n, ξiFor the matrix that i-th is sampled, SljThe sampling of j-th of material parameter of first of unit
As a result；
Step 2.4: the equivalent interaction matrix R of M material parameter in selecting step 2.3M×M:
To above-mentioned matrix RM×MCholesky decomposition is carried out, lower triangular matrix L is obtained1(M×M):
By lower triangular matrix L obtained above1Transposition is carried out to obtain
Step 2.5: the relative value between each unit central point transverse and longitudinal coordinate obtained using step 2.2 calculates Gaussian auto-correlation
Function:
Wherein, τx, τyRelative value respectively between each unit central point transverse and longitudinal coordinate of step 2.2 calculating, τx=| xi-xj|,
τy=| yi-yj|, δhFor horizontal fluctuation range, δvFor vertical fluctuation range；
The auto-correlation function matrix ρ of N number of unit in bed course area 2A is calculated by above-mentioned Gaussian auto-correlation functionN×N:
Wherein, pijFor the related coefficient between i-th of unit and j-th of unit；
To above-mentioned matrix ρN×NCholesky is carried out to decompose to obtain lower triangular matrix L2(N×N):
Step 2.6: the right side independent standard normal random sample matrix ξ in step 2.3 is multiplied into the lower triangular matrix L that step 2.5 obtains2,
Premultiplication step 2.4 obtains againFinally obtain relevant criterion Gaussian random field sample
Wherein, i=1,2 ... n,For L1Transposition.
Step 2.7: the relevant criterion Gaussian random field sample that step 2.6 is obtainedFetching number obtains bed course area 2A's
Related lognormal random field matrix Hi(x, y):
Wherein, For the mean value of the random field parameters of each unit,For the coefficient of variation of the random field parameters of each unit；
Step 2.8, step 2.1~step 2.7 is repeated in other subregions of rock-fill dams finite element model, and then obtained each
The related lognormal random field matrix H of subregioni(x, y), by the related lognormal random field H of each subregioniThe mould of (x, y)
Analog values are assigned to corresponding unit in subregion, obtain the spatial random field H (x, y) of rock-fill dams finite element model of the present inventionN×nMould
Quasi- distribution map.
4. a kind of spatial random field analogy method of Parameters for Rockfill Dams according to claim 3, which is characterized in that institute
Stating Gaussian auto-correlation function in step 2.5 can also be index type auto-correlation function, second-order auto-regressive type auto-correlation function, refers to
Any one of number longitudinal cosine type auto-correlation function, triangular form auto-correlation function.
5. a kind of spatial random field analogy method of Parameters for Rockfill Dams according to claim 3, which is characterized in that will
The analogue value for the random field that the step 2.8 obtains is calculated using the secondary development software of finite element software subprogram, is obtained
To the cloud charts of rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress, verified, verifying it is specific
Step are as follows:
Step a, the material parameter for each unit for being obtained step 2 using the secondary development software of finite element software subprogram is random
The original material parameter of each unit in field analogue value replacement step 2；
Step b, using the secondary development software transfer finite element software of finite element software subprogram, by the random field in step a
The analogue value substitutes into FEM calculation, obtains rock-fill dams finite element model dam body settlement, horizontal displacement and the distribution of each principal stress
Cloud atlas；
Step c, by the distribution clouds of obtained rock-fill dams finite element model dam body settlement, horizontal displacement and each principal stress of step b
Figure and its data and the dam body data of actual measurement compare, and are verified result.
6. a kind of spatial random field analogy method of Parameters for Rockfill Dams according to claim 5, which is characterized in that institute
The secondary development for stating finite element software subprogram in step 3 is implemented including step in detail below:
The initial value of 9 material parameters of rock-fill dams E-B constitutive model is arranged in step I；
Step II will be 9 in each unit material parameter random field analogue value replacement step 2 obtained in step 2 according to unit number
A original material parameter；
Step III, elastic modulus E is calculatedtWith bulk modulus Bt, judge that load perhaps unloads the elasticity using load or unloading
Modulus forms tangent modulus matrix, ultimately forms strain-stress relation matrix；
Step IV, define load and apply step: preceding 30 step is staged-filling step, and the 30th~34 step is to apply water ballast(ing) step by stages；
Step V, dam body later period rheology is calculated using the Bo Gesi model of rock-fill dams；
Step VI, customized output item: horizontal displacement, Vertical Settlement, maximum principal stress, minimum principal stress, stress level is set,
And panel is axial with inclined slope aspect stress；
Step VII, loaded under DOS environment secondary development program and model data file call directly finite element software Marc into
Row calculates, and repeats step I~step V and is iterated calculating；
Step VIII, the destination file calculated step VII is handled, and obtains the cloud atlas of the response quautities such as ess-strain.
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| CN111914321A (en) * | 2020-06-09 | 2020-11-10 | 西安理工大学 | Method for establishing rock-fill concrete three-phase mesoscopic model |
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