CN104615826A - Device and method for analyzing reliability of complex geotechnical project - Google Patents
Device and method for analyzing reliability of complex geotechnical project Download PDFInfo
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Abstract
The invention relates to a device and method for analyzing the reliability of a complex geotechnical project. The device comprises a center point switching module, a sampling point generating module, a sampling point rotating module, a finite element analyzing module, a reliability calculating module and a flow controlling module. The method includes the following steps: center point switching, sampling point generating, sampling point rotating, finite element analyzing, reliability calculating and flow controlling. Compared with the prior art, an improved response surface method solves the problems that an original response method is sensitive to step length values, the step length needs to be continuously and manually adjusted in the iterative process, and minus sampling points exist due to the excessively-large step length values, and a theoretical basis is provided for achieving automatic coupling calculation of reliability analysis and deterministic analysis in the complex geotechnical project; by means of the device and method, the workloads of reliability calculation of the complex geotechnical project can be reduced, and automatic coupling calculation of the reliability and the determinacy of the complex geotechnical project can be achieved.
Description
Technical field
The present invention relates to Geotechnical Engineering field, especially relate to a kind of complicated Engineering Reliability Analysis apparatus and method.
Background technology
In order to consider the impact of various uncertainty on Geotechnical Engineering, Reliability Theory has been widely used in all kinds of Geotechnical Engineering.Reliability analysis of geotechnical engineering relates to the coupling of geotechnical model and reliability calculating.For the geotechnical engineering problems of complexity, the mechanism of its stress deformation is quite complicated, must analyze by business software.But current existing Geotechnical Engineering software all can only carry out deterministic parsing, cannot carry out reliability analysis.How Analysis of Complex Geotechnical Engineering fiduciary level is a technical bottleneck in current risk analysis for rock and soil engineering field.If directly use Monte Carlo method to calculate fiduciary level after obtaining Geotechnical Engineering limit state equation implicit solution, calculated amount is huge, time cost is too high, solves so usually use response phase method Implicit Limit State Equation reliability issues to be converted to display limit state equation reliability issues.Response phase method can reduce numerical simulation number of times and clear concept, and thus in reliability analysis of geotechnical engineering, response phase method is widely used.
Response phase method only has higher precision within the scope of interpolation point; Outside interpolation point scope, its precision cannot ensure.Key calculates the accurate location obtaining design points.For this reason, process of iteration can be adopted to upgrade response surface, make the response surface built have degree of precision around design point, thus obtain the accurate location of design points.When adopting process of iteration to calculate, need the response using each novel sampling location of Finite element arithmetic after each Renewal Design point, FEM (finite element) calculation amount is large and loaded down with trivial details.Each time from reliability calculating again to FEM (finite element) calculation owing to not being automatically carry out, easily there is artificial numerical fault.Propose herein to utilize the exchanges data between computational science software Matlab and existing business finite element software to realize the automatic calculating of iteration response phase method to solve the problem.When carrying out response phase method iterative computation, the appearance not allowing negative in rock-soil engineering parameters when carrying out deterministic parsing, due to be all often adopt manual method carry out iterative computation, so sampling step length can be adjusted timely when often walking iteration thus ensure do not have negative in sampling spot, but the automatic calculating computer wanting to realize fiduciary level the often step of intelligence cannot adjust step-length in time, therefore this method proposes a kind of new response surface sampling method, ensures that sampling spots all in iterative process is all positive number.
Summary of the invention
Object of the present invention be exactly in order to overcome above-mentioned prior art exist defect and a kind of complicated Engineering Reliability Analysis apparatus and method are provided.
Object of the present invention can be achieved through the following technical solutions:
A kind of complicated Engineering Reliability Analysis device, is characterized in that, comprises central point modular converter, sampling spot generation module, sampling spot revolution module, finite element analysis module, reliability calculating module and process control module;
Described central point modular converter, for being converted to standard normal space stochastic variable central point { y by the central point of the stochastic variable of input in luv space
1, y
2..., y
n, wherein 1≤i≤n, y
ifor the value of described stochastic variable central point in the i-th dimension;
Described sampling spot generation module, according to the stochastic variable central point { y that central point modular converter or process control module input
1, y
2..., y
ncalculate 2n+1 sampling spot in standard normal space, complete the response surface sampling in standard normal space;
Described sampling spot revolution module, for converting back in its luv space by the sampling spot of the 2n+1 in standard normal space;
Described finite element analysis module, sets up the numerical model of finite element or finite element Difference Calculation, and according to the value of the described 2n+1 converting back luv space sampling spot calculating limit state equation;
Described reliability calculating module, the value according to 2n+1 sampling spot in described standard normal space and described limit state equation sets up response surface in standard normal space, and obtains fiduciary level and design points by design point method;
Described process control module, for after each acquisition fiduciary level result, this fiduciary level result and a front fiduciary level result are done difference, when the absolute value of done difference is greater than the threshold value of setting, then this design points is re-entered sampling spot generation module as central point; Otherwise then with this fiduciary level be final fiduciary level result export.
2n+1 sampling spot in the standard normal space that described sampling spot generation module generates is respectively stochastic variable central point { y
1, y
2..., y
n, and { y
1± k, y
2..., y
n, { y
1, y
2± k ..., y
n..., { y
1, y
2..., y
n± k}; Wherein, 1≤i≤n, y
ifor the value of stochastic variable central point in the i-th dimension.
When described luv space is lognormality space, the transformational relation in lognormality space and standard normal space is: x=exp (λ+ξ y), wherein:
Wherein, x is the value of variable in lognormality space, y be variable transitions to the value in standard normal space, ξ is the standard deviation in positive state space, δ
xfor the standard deviation in lognormality space, λ is the average in positive state space; μ
xfor the average in lognormality space.
The threshold value of described setting is 0.01.
The revolution of described central point modular converter, sampling spot generation module, sampling spot module, reliability calculating module and process control module are realized by MATLAB, described finite element analysis module is realized by FLAC3D, and MATLAB and FLAC3D carries out data communication by text.
A kind of complicated Engineering Reliability Analysis method, is characterized in that, comprise the following steps:
(1) central point of the stochastic variable of input in luv space is converted to standard normal space stochastic variable central point { y
1, y
2..., y
n, wherein 1≤i≤n, y
ifor the value of described stochastic variable central point in the i-th dimension;
(2) according to the stochastic variable central point { y that step (1) or step (6) input
1, y
2..., y
ncalculate 2n+1 sampling spot in standard normal space, complete the response surface sampling in standard normal space;
(3) sampling spot of the 2n+1 in standard normal space is converted back in its luv space;
(4) numerical model of finite element or finite element Difference Calculation is set up, and according to the value of the described 2n+1 converting back luv space sampling spot calculating limit state equation;
(5) in standard normal space, set up response surface according to the value of 2n+1 sampling spot in described standard normal space and described limit state equation, and obtain fiduciary level and design points by design point method;
(6), after obtaining fiduciary level result, this fiduciary level result and a front fiduciary level result are done difference, when the absolute value of done difference is greater than the threshold value of setting, then this design points is re-entered sampling spot generation module as central point; Otherwise then with this fiduciary level be final fiduciary level result export.
2n+1 sampling spot in the standard normal space that described step (2) generates is respectively stochastic variable central point { y
1, y
2..., y
n, and { y
1± k, y
2..., y
n, { y
1, y
2± k ..., y
n..., { y
1, y
2..., y
n± k}; Wherein, 1≤i≤n, y
ifor the value of stochastic variable central point in the i-th dimension.
When described luv space is lognormality space, the transformational relation in lognormality space and standard normal space is: x=exp (λ+ξ y), wherein:
Wherein, x is the value of variable in lognormality space, y be variable transitions to the value in standard normal space, ξ is the standard deviation in positive state space, δ
xfor the standard deviation in lognormality space, λ is the average in positive state space; μ
xfor the average in lognormality space.
The threshold value of described setting is 0.01.
Described step (1), step (2), step (3), step (5), step (6) are realized by MATLAB, described step (4) is realized by FLAC3D, and MATLAB and FLAC3D carries out data communication by text.
Compared with prior art, the present invention has the following advantages:
1. it may be the problem of negative that the response phase method based on spatial mappings using the present invention to propose solves response surface sampling spot when realizing reliability calculating, the response phase method of solving over is responsive to step-length, and need the problem of constantly adjustment step-length, provide theoretical foundation for the automatic coupling realizing reliability analysis and deterministic parsing in complicated Geotechnical Engineering calculates.
2. for complexity Geotechnical Engineering each deterministic parsing all need to expend the huge time, consider that each iteration of response phase method all needs to carry out deterministic parsing to multiple sampling spot, then record deterministic parsing result and carry out reliability analysis again, therefore the workload of the reliability calculating needs of complicated Geotechnical Engineering is huge.Device of the present invention can greatly reduce the workload of complicated Geotechnical Engineering reliability calculating.
3. huge to the data volume that reliability analysis is wherein involved again from reliability analysis to deterministic parsing, be very easy to when manually carrying out occur error in data and loss of data, use the fiduciary level of device calculation of complex Geotechnical Engineering of the present invention can avoid error in data and loss.
4., by setting up the data communication between two conventional business softwares (such as Matlab and FLAC), device of the present invention can be realized easily; In Matlab, set up reliability analysis model, set up Geotechnical Engineering finite difference simulator in FLAC, both be coupled, achieve the automatic calculating of complicated Geotechnical Engineering, the reliability analysis for complicated Geotechnical Engineering provides means easily and efficiently; Except FLAC, the present invention is equally applicable to other ground deterministic parsing softwares such as ABAQUS, concerning Practical Project, have practical value widely.
Accompanying drawing explanation
Fig. 1 is the graph of a relation of each module in device of the present invention;
Fig. 2 is the cross-sectional view of composite foundation arrangenent diagram;
Fig. 3 is the vertical view of composite foundation arrangenent diagram;
Fig. 4 is compound foundation with deep mixing pile displacement-load curve.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.
Embodiment 1
As shown in Figure 1, the complicated Engineering Reliability Analysis device of one of the present invention is turned round module 103, finite element analysis module 104, reliability calculating module 105 and process control module 106 formed by central point modular converter 101, sampling spot generation module 102, sampling spot, and wherein central point modular converter 101, sampling spot generation module 102, sampling spot turn round the functional realiey that module 103, reliability calculating module 105 and process control module 106 all can be carried by numerical evaluation software Matlab; Finite element analysis module 104 then can carry out finite element analysis computation by finite-difference program FLAC3D; Owing to needing the exchanges data of carrying out sampling spot and Limiting Equations value between Matlab and FLAC3D, therefore the communication between two programs is realized by the mode of text in the present embodiment, namely Matlab by the sampling spot that calculates stored in TXT text document, FLAC3D reads text document and obtains sampling spot, and after calculating completes, Limiting Equations value is write back text document, calculate design points and fiduciary level for Matlab.Specific works principle is as follows:
(1) central point of stochastic variable is transformed in standard normal space by Matlab;
(2) Matlab generates 2n+1 sampling spot according to the central point in standard normal space;
(3) 2n+1 sampling spot rotates back in its luv space by Matlab, and stored in after TXT file, it is notified that FLAC3D starts working;
(4) FLAC3D obtains sampling spot and carries out FEM (finite element) calculation according to the numerical model preset and obtains limit state equation value from TXT file, and is write back TXT file;
(5) Matlab obtains limit state equation value from TXT file, in conjunction with before the sampling spot that generates, calculate fiduciary level and design points;
(6) fiduciary level of adjacent twice contrasts by Matlab, determines whether carrying out next iteration according to whether both gaps are enough little.
Embodiment 2
Deep-mixed pile is adopted to reinforce the reliability analysis plant and principle introducing the present invention's proposition for certain soft soil foundation below.The deep-mixed pile layout investigated and clay distribution are as shown in Figures 2 and 3.Foundation soil is divided into two-layer, and 0 to-12.1 meters is clay seam, and-12.1 to-17.6 is farinose argillic horizon.Deep-mixed pile stake footpath is 0.9 meter, and pile spacing is 1.6 meters, and stake is long is 14 meters.The load that ground bears is 85kPa.
Use E
s, c
s,
represent the elastic modulus of clay, cohesion and angle of internal friction respectively, use E
p, c
p,
represent deep-mixed pile modulus, cohesion and angle of internal friction respectively.In the present embodiment soil layer and deep-mixed pile parameter as shown in table 1.The sedimentation of mechanical characteristic to composite foundation of weak soil and reinforcing pile body has material impact.By E
s, c
s,
e
p, c
p,
be modeled to stochastic variable, its distribution and statistical value as shown in table 2.
Table 1 soil layer mechanics parameter value
The distribution of table 2 stochastic variable and statistical value
For considering pile soil common action mechanism as far as possible truly, adopt FLAC3D to solve the allowable bearing of composite foundation, therefore limit state equation is not explicit.Implicit Limit State Equation reliability issues can be converted to display limit state equation reliability issues and solve by response phase method.The following quadratic polynomial not containing cross term is specifically adopted to carry out matching limit state equation:
In formula: a, b
i, d
i(i=1,2 ..., n) be undetermined coefficient, amount to 2n+1 undetermined coefficient.Generally speaking, response surface only has higher precision within the scope of interpolation point; Outside interpolation point scope, its precision cannot ensure.For design point method, key calculates the accurate location obtaining design points.For this reason, the present invention can be adopted to carry out iterative computation response surface is upgraded, make the response surface built have degree of precision around design point, thus obtain the accurate location of design points.Specifically as follows:
The equal obeys logarithm normal distribution of (a) stochastic variable as shown in Table 2 corresponding to the present embodiment, the new method utilizing the present invention to propose obtains 2n+1 sampling spot, be specially: be specially: the conversion formula utilizing lognormality space and positive state space, by the average point X={x in original lognormal space
1, x
2, x
3, wherein x
1, x
2, x
3represent E respectively
s, E
p, c
paverage point in lognormality space, utilizes formula x=exp (λ+ξ y), wherein
wherein, x is the value of variable in lognormality space, y be variable transitions to the value in standard normal space, ξ is the standard deviation in positive state space, δ
xfor the standard deviation in lognormality space, λ is the average in positive state space; μ
xfor the average in lognormality space.Be converted to standard normal space: { y
1, y
2, y
3.Step-length gets 2 in the present embodiment, therefore gets following 7 points in standard normal space: { y
1, y
2, y
3, { y
1± 2, y
2, y
3, { y
1, y
2± 2, y
3, { y
1, y
2, y
3± 2}, more secondary 7 points are converted to lognormality space, as the input parameter of deterministic parsing according to the conversion formula of lognormality space and positive state space.Write in a TXT text by sampling spot in the luv space obtained in Matlab, FLAC3D reads in these sampling spots, calculates the allowable bearing of composite foundation at these some places, then result is write in TXT text.
B the value of above-mentioned 2n+1 point and allowable bearing is taken back by (), set up 2n+1 ultimate limit state fit equation, 2n+1 undetermined coefficient thus in solution formula, obtain the response surface in normed space in normed space.
C (), based on the quadratic polynomial obtained in step (b), Matlab solves composite foundation Low confidence limit and design points.
Centered by d design points that () obtains in step (c), regenerate 2n+1 sampling spot by step (a), calculate the allowable bearing of composite foundation at this 2n+1 some place.Return step (b).Repeat above step until the absolute value of difference of RELIABILITY INDEX that adjacent two steps obtain is less than or equal to 0.01.
Get a pile spacing in order to save model computing time edge perpendicular to paper direction, xsect gets half.The displacement of numerical model right boundary horizontal direction is 0; Model edge is 0 perpendicular to the both sides horizontal shift of paper direction; The level of model bottom node and the displacement of vertical aspect are 0.Deep-mixed pile adopts solid model to simulate.In order to simplify numerical model, circular deep-mixed pile adopts the square stake of equivalent area to replace.Circular deep-mixed pile diameter is 0.9 meter, is equivalent to the square stake that the length of side is 0.8 meter.
For obtaining foundation bearing capacity when corresponding to Admissible displacement, adopt FLAC3D medium velocity load mode to obtain the load-displacement curve (Fig. 3) of composite foundation, then obtain by carrying out interpolation to load-displacement curve the bearing capacity (load that in figure, A point is corresponding) corresponding to Admissible displacement place.
Fiduciary level convergence after iteration three step, three times result of calculation is respectively: 3.70,3.17,3.16.Above three results are all use the method for the present invention's proposition automatically to carry out iterative computation to obtain, also use manual method to carry out solving the result obtained to this engineering reliability problem as follows: 3.67,3.17,3.16 simultaneously, can find that the method computational accuracy that the present invention proposes is high.Because the deterministic parsing of this engineering is complicated, each deterministic parsing needs 2 hours, therefore need the deterministic parsing of 42 hours to complete these 3 iterative computation and all need manually to record result after often completing a deterministic parsing and the parameter changing deterministic parsing calculates, so finally consume 3 talentes manually complete this reliability analysis next time.But result has calculated only to need program of opening then to wait for after the new method using the present invention to propose, and for this engineering, reliability calculating just can save the time of 3 days.If need to carry out detailed Parameter analysis for large complicated Geotechnical Engineering, then calculative fiduciary level One's name is legion, be limited by huge calculated amount, often simplify deterministic parsing model, therefore obtain analysis result and have certain error, after the method using the present invention to propose reduces workload, complicated deterministic parsing model can be adopted to calculate RELIABILITY INDEX for large complicated Geotechnical Engineering, obtain reliability analysis result more accurately.
Claims (10)
1. a complicated Engineering Reliability Analysis device, is characterized in that, comprises central point modular converter, sampling spot generation module, sampling spot revolution module, finite element analysis module, reliability calculating module and process control module;
Described central point modular converter, for being converted to standard normal space stochastic variable central point { y by the central point of the stochastic variable of input in luv space
1, y
2..., y
n, wherein 1≤i≤n, y
ifor the value of described stochastic variable central point in the i-th dimension;
Described sampling spot generation module, according to the stochastic variable central point { y that central point modular converter or process control module input
1, y
2..., y
ncalculate 2n+1 sampling spot in standard normal space, complete the response surface sampling in standard normal space;
Described sampling spot revolution module, for converting back in its luv space by the sampling spot of the 2n+1 in standard normal space;
Described finite element analysis module, sets up the numerical model of finite element or finite element Difference Calculation, and according to the value of the described 2n+1 converting back luv space sampling spot calculating limit state equation;
Described reliability calculating module, the value according to 2n+1 sampling spot in described standard normal space and described limit state equation sets up response surface in standard normal space, and obtains fiduciary level and design points by design point method;
Described process control module, for after each acquisition fiduciary level result, this fiduciary level result and a front fiduciary level result are done difference, when the absolute value of done difference is greater than the threshold value of setting, then this design points is re-entered sampling spot generation module as central point; Otherwise then with this fiduciary level be final fiduciary level result export.
2. the complicated Engineering Reliability Analysis device of one according to claim 1, is characterized in that, 2n+1 sampling spot in the standard normal space that described sampling spot generation module generates is respectively stochastic variable central point { y
1, y
2..., y
n, and { y
1± k, y
2..., y
n, { y
1, y
2± k ..., y
n..., { y
1, y
2..., y
n± k}; Wherein, 1≤i≤n, y
ifor the value of stochastic variable central point in the i-th dimension.
3. the complicated Engineering Reliability Analysis device of one according to claim 1 and 2, it is characterized in that, when described luv space is lognormality space, the transformational relation in lognormality space and standard normal space is: x=exp (λ+ξ y), wherein:
Wherein, x is the value of variable in lognormality space, y be variable transitions to the value in standard normal space, ξ is the standard deviation in positive state space, δ
xfor the standard deviation in lognormality space, λ is the average in positive state space; μ
xfor the average in lognormality space.
4., according to the complicated Engineering Reliability Analysis device of the one described in claim 1, it is characterized in that, the threshold value of described setting is 0.01.
5. according to the complicated Engineering Reliability Analysis device of the one described in claim 1, it is characterized in that, the revolution of described central point modular converter, sampling spot generation module, sampling spot module, reliability calculating module and process control module are realized by MATLAB, described finite element analysis module is realized by FLAC3D, and MATLAB and FLAC3D carries out data communication by text.
6. a complicated Engineering Reliability Analysis method, is characterized in that, comprise the following steps:
(1) central point of the stochastic variable of input in luv space is converted to standard normal space stochastic variable central point { y
1, y
2..., y
n, wherein 1≤i≤n, y
ifor the value of described stochastic variable central point in the i-th dimension;
(2) according to the stochastic variable central point { y that step (1) or step (6) input
1, y
2..., y
ncalculate 2n+1 sampling spot in standard normal space, complete the response surface sampling in standard normal space;
(3) sampling spot of the 2n+1 in standard normal space is converted back in its luv space;
(4) numerical model of finite element or finite element Difference Calculation is set up, and according to the value of the described 2n+1 converting back luv space sampling spot calculating limit state equation;
(5) in standard normal space, set up response surface according to the value of 2n+1 sampling spot in described standard normal space and described limit state equation, and obtain fiduciary level and design points by design point method;
(6), after obtaining fiduciary level result, this fiduciary level result and a front fiduciary level result are done difference, when the absolute value of done difference is greater than the threshold value of setting, then this design points is re-entered sampling spot generation module as central point; Otherwise then with this fiduciary level be final fiduciary level result export.
7. the complicated Engineering Reliability Analysis method of one according to claim 5, is characterized in that, 2n+1 sampling spot in the standard normal space that described step (2) generates is respectively stochastic variable central point { y
1, y
2..., y
n, and { y
1± k, y
2..., y
n, { y
1, y
2± k ..., y
n..., { y
1, y
2..., y
n± k}; Wherein, 1≤i≤n, y
ifor the value of stochastic variable central point in the i-th dimension.
8. the complicated Engineering Reliability Analysis method of the one according to claim 5 or 6, it is characterized in that, when described luv space is lognormality space, the transformational relation in lognormality space and standard normal space is: x=exp (λ+ξ y), wherein:
Wherein, x is the value of variable in lognormality space, y be variable transitions to the value in standard normal space, ξ is the standard deviation in positive state space, δ
xfor the standard deviation in lognormality space, λ is the average in positive state space; μ
xfor the average in lognormality space.
9., according to the complicated Engineering Reliability Analysis method of one described arbitrarily in claim 5, it is characterized in that, the threshold value of described setting is 0.01.
10. according to the complicated Engineering Reliability Analysis device of the one described in claim 1, it is characterized in that, described step (1), step (2), step (3), step (5), step (6) are realized by MATLAB, described step (4) is realized by FLAC3D, and MATLAB and FLAC3D carries out data communication by text.
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| CN201510053548.7A CN104615826B (en) | 2015-02-02 | A kind of complicated Engineering Reliability Analysis device |
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Family
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| CN105926465A (en) * | 2016-04-15 | 2016-09-07 | 武汉理工大学 | Modeling method for bridge preventive maintenance model under overload operation condition and maintenance method |
| CN108108244A (en) * | 2017-12-15 | 2018-06-01 | 中南大学 | A kind of side slope strength reduction factor multithreads computing method |
| CN111444608A (en) * | 2020-03-24 | 2020-07-24 | 成都理工大学 | Method for determining optimal truncation order in geotechnical engineering reliability analysis |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN105926465A (en) * | 2016-04-15 | 2016-09-07 | 武汉理工大学 | Modeling method for bridge preventive maintenance model under overload operation condition and maintenance method |
| CN108108244A (en) * | 2017-12-15 | 2018-06-01 | 中南大学 | A kind of side slope strength reduction factor multithreads computing method |
| CN111444608A (en) * | 2020-03-24 | 2020-07-24 | 成都理工大学 | Method for determining optimal truncation order in geotechnical engineering reliability analysis |
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