CN111931281A - Method for searching critical failure path of gravity dam-foundation structure system - Google Patents

Method for searching critical failure path of gravity dam-foundation structure system Download PDF

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CN111931281A
CN111931281A CN202010969098.7A CN202010969098A CN111931281A CN 111931281 A CN111931281 A CN 111931281A CN 202010969098 A CN202010969098 A CN 202010969098A CN 111931281 A CN111931281 A CN 111931281A
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path
unit
failure path
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CN111931281B (en
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裴亮
陈建康
李泽发
李艳玲
吴震宇
张瀚
陈辰
周靖人
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Sichuan University
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Abstract

The invention discloses a method for searching a critical failure path of a gravity dam-foundation structural system, which comprises the steps of constructing a finite element model of the gravity dam-foundation structural system and acquiring unit identification information; loading by adopting a load incremental method to obtain a primary failure unit set and dividing the primary failure unit set into failure paths; constructing a failure path directed graph, and calculating a path weight based on nonlinear energy dissipation; optimizing by adopting a Dijkstra algorithm to find a key path; sequentially applying multi-step incremental loads to the structural system to be wholly failed, and searching a key path according to each step of failure path; and obtaining a final key failure path of the gravity dam-foundation structure system. The scheme provides a path key degree calculation method based on energy dissipation, considers the connection relation of each failure unit in the structure progressive destruction process and the evolution of the failure path under dynamic overload, deletes redundant units with small influence on failure probability, and improves the analysis efficiency of the reliability of a structure system.

Description

Method for searching critical failure path of gravity dam-foundation structure system
Technical Field
The invention relates to the technical field of dam reliability analysis, in particular to a method for searching a critical failure path of a gravity dam-foundation structural system.
Background
The concrete gravity dam is a dam type commonly used for a river blocking dam of a water conservancy and hydropower engineering, plays multiple functions of flood control, power generation and the like, and once the dam fails, not only the engineering is lost, but also more serious downstream disasters are always accompanied, so that the property loss of the downstream and hidden dangers to the life safety of residents living in the downstream are caused, and the safe operation is the primary problem of the dam.
At present, the method for determining the failure path of the gravity dam-foundation structure system is as follows: selecting a typical dam section as a research object, establishing a dam body and foundation finite element grid, gradually loading the dam body and the foundation finite element grid on the upstream surface of the dam body to a dam-foundation structure system to fail according to a certain load increment by adopting a load increment method, directly determining according to the communication condition of failure units in the dam body and the foundation and engineering experience, if a formed plastic yield area is a failure path, considering the area as the failure path, and determining whether the dam is safely operated or not on the basis.
In fact, although the conventional plastic yield criterion based on stress state can be used for judging whether the component fails or not, when the stress state of the failed component is adjusted, the yield function value may show non-uniqueness, so that the criticality of the failed component cannot be evaluated based on the plastic yield; for a large complex structure, the influence degree of a plurality of components/units in each failure path on the whole failure probability of the structure is different, the stability of a dam system is controlled by key components on the failure paths, and the accuracy of dam reliability analysis can be influenced by redundant failure components in the failure paths.
Therefore, how to eliminate the influence of the redundant failure component on the critical failure path during the searching of the critical failure path is an urgent problem to be solved in the reliability analysis of the dam.
Disclosure of Invention
Aiming at the defects in the prior art, the method for searching the critical failure path of the gravity dam-foundation structural system solves the problem that the searching accuracy of the critical failure path is reduced by a redundant failure component in a dam.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
a method for searching a critical failure path of a gravity dam-foundation structural system is provided, which comprises the following steps:
s1, constructing a finite element model of the gravity dam-foundation structure according to the physical parameters of the gravity dam-foundation structure and the concrete material parameters of the dam body, wherein the discretized finite element model consists of a plurality of units;
s2, applying load to the finite element model by adopting a load increment method until a failure unit appears, recording all failure units to form a total failure unit set, and then generating at least one failure path according to the failure units;
s3, determining a starting point set, an intermediate set and an end point set of the non-traversed failure path according to the failure damage process, and forming a single directed graph by adopting any starting point in the starting point set, the intermediate set and the end point set;
s4, calculating the space distance between the centroids of any two failure units in each directed graph, and calculating the nonnegative weight value between the two failure units when the space distance is smaller than the influence distance to obtain the weighted directed graph;
s5, searching the shortest path of each weighted directed graph of the same failure path by adopting a Dijkstra algorithm, and selecting the minimum weight of all the shortest paths corresponding to the same failure path as the key failure path;
s6, judging whether a failure path does not obtain a key failure path, if yes, returning to the step S3, otherwise, entering the step S7;
s7, judging whether the current load is larger than the ultimate bearing capacity of the gravity dam-foundation system, if so, entering the step S8, otherwise, returning to the step S2;
and S8, merging all the searched critical failure paths together to serve as the final critical failure path of the gravity dam after each failure unit occurs.
The invention has the beneficial effects that: the method is based on a load increment method for primarily searching a failure path of a gravity dam-foundation structure system, and in view of the fact that the existing plastic yield criterion cannot be used for evaluating the criticality of a failure component, a method for representing the criticality of a unit and a corresponding path weight by a nonlinear energy dissipation value in the unit failure process is provided, the problem of searching the critical path is converted into the problem of searching the shortest path of a directed graph, and the final critical path of the gravity dam-foundation structure system is successfully searched in consideration of the dynamic loading process of the load increment method.
According to the scheme, the connection relation of each failure unit in the structure progressive destruction process is considered through the influence distance and the proposed weight calculation formula, the dynamic evolution of the failure path under the condition of gradual load increment overload is considered, the redundant units in the failure path are deleted, the searched final key path is more fit with the engineering practice, the number of functional functions needing to be constructed for reliability analysis is greatly reduced on the basis, the overall analysis efficiency is greatly improved, and the finally obtained key failure path is more accurate.
Analyzing the reliability of the dam under construction and already running based on the obtained key failure path so as to optimize and adjust the construction scheme of the dam and the physical and mechanical parameters of the dam body in the construction period and ensure the safety and stability of the dam in the running period after the construction is finished; corresponding to the dam in the operation period, maintainers can focus on the range of the key failure path conveniently, and a dam reinforcing or maintaining scheme is made in time, so that more reliable guidance is provided for the safety management of the dam in the construction period and the operation period.
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FIG. 1 is a flow chart of a method for searching a critical failure path of a gravity dam-foundation structural system.
Fig. 2 is a cross-sectional view of a gravity dam-foundation in an embodiment.
FIG. 3 is a diagram of a finite element model of a gravity dam-foundation structure system in an embodiment.
FIG. 4 is a diagram of a gravity dam-foundation primary failure unit distribution in an embodiment
FIG. 5 is a diagram of a weighted directed graph in an embodiment;
FIG. 6 is a diagram of the result of weighted directed graph optimization in a specific example;
FIG. 7 is a graph of a gravity dam-foundation ultimate failure unit distribution in an embodiment;
FIG. 8 is a diagram of the ultimate critical failure path of the gravity dam-foundation structural system in an embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Referring to fig. 1, fig. 1 shows a flow chart of a method for searching for a critical failure path of a gravity dam-foundation structure architecture; as shown in fig. 1, the method S includes steps S1 to S8.
In step S1, a finite element model of the gravity dam-foundation structure is constructed according to the physical parameters of the gravity dam-foundation structure and the concrete material parameters of the dam body, the discretized finite element model is composed of a plurality of units, and the grid size of the unit is preferably 1.0-2.5m。
A plurality of unitsDAnd unit centroid coordinatesLIs represented as follows:
Figure 260479DEST_PATH_IMAGE001
wherein the content of the first and second substances,Nis the total number of units; (x 1、y 1、z 1) Is the coordinates of the first cell; (x N 、y N 、z N ) Is as followsNCoordinates of the individual cells.
In step S2, applying a load to the finite element model by using a load incremental method, recording all failure units to form a total failure unit set when a failure unit occurs, and then generating at least one failure path according to the failure unit;
when a load increment method is adopted to apply a load to the finite element model, the load is increased progressively according to a preset increment each time; when a load is initially applied, a failure unit generally cannot appear in the finite element model, when the failure unit generally appears, a plurality of load steps generally appear, and once the failure unit appears, the failure unit exists in each subsequent load step. If it is applied tomStep loadH m The rear finite element model begins to generate failure units to obtain a total failure unit set
Figure 505516DEST_PATH_IMAGE002
WhereinrTo be applied tomStep loadH m And then, the total number of the failure units of the finite element model.
In one embodiment of the invention, a method of generating at least one failure path comprises:
s31, selecting any failure unit in the total failure unit set as a failure path, and calculating the space distance between the centroid of any failure unit in the total failure unit set and the centroid of the failure unit in the failure patha。
Suppose to remembermFailure unit under step
Figure 550832DEST_PATH_IMAGE003
As a failure path
Figure 227932DEST_PATH_IMAGE004
Then the total failure unit is concentrated into any failure unit
Figure 573463DEST_PATH_IMAGE005
Centroid ofAnd a failure path
Figure 723822DEST_PATH_IMAGE004
The spatial distance of the centroids of (a) is:
Figure 272746DEST_PATH_IMAGE006
wherein the content of the first and second substances,
Figure 737225DEST_PATH_IMAGE007
、
Figure 937262DEST_PATH_IMAGE008
and
Figure 461784DEST_PATH_IMAGE009
is a failure unit
Figure 294742DEST_PATH_IMAGE003
The centroid coordinates of (a);
Figure 562913DEST_PATH_IMAGE010
、
Figure 351877DEST_PATH_IMAGE011
and
Figure 63612DEST_PATH_IMAGE012
is a failure unit
Figure 633134DEST_PATH_IMAGE005
The centroid coordinates of (a).
S32, judging the space distanceaWhether the space distance is smaller than or equal to the influence distance or not is judged, if so, a failure unit corresponding to the space distance is added into a failure path, and if not, the step S33 is executed; in this embodiment, the preferred influence distance is the average size of the failed cells.
S33, adding space distanceaThe corresponding failure unit is a failure path;
suppose inmStep loadH m After that, 10 failure units appeared, whichIn
Figure 439416DEST_PATH_IMAGE013
And
Figure 99199DEST_PATH_IMAGE014
and
Figure 965523DEST_PATH_IMAGE003
spatial distance ofaGreater than the influence distance, will
Figure 22341DEST_PATH_IMAGE013
And
Figure 383046DEST_PATH_IMAGE014
as a single failure path, i.e. failure path
Figure 412182DEST_PATH_IMAGE015
Failure path
Figure 449408DEST_PATH_IMAGE016
Adding the remaining failure units of the total failure unit set into the failure path
Figure 931205DEST_PATH_IMAGE004
In (1).
S34, selecting the new failure path which is not traversed, and calculating the space distance between the centroid of the failure unit in the new failure path and the centroid of any failure unit in the total failure unit setb；
S35, judging the space distancebWhether the influence distance is less than or equal to the influence distance or not, if so, adding the corresponding failure unit into the current newly added failure path, otherwise, entering the step S36;
if the operation is performed through S34 and S35, the total failure units are concentrated
Figure 892339DEST_PATH_IMAGE017
、
Figure 775982DEST_PATH_IMAGE018
、
Figure 984109DEST_PATH_IMAGE019
And
Figure 703934DEST_PATH_IMAGE020
and failure path
Figure 452448DEST_PATH_IMAGE015
Spatial distance ofbLess than or equal to the influence distance, then
Figure 456176DEST_PATH_IMAGE017
、
Figure 851516DEST_PATH_IMAGE018
、
Figure 42326DEST_PATH_IMAGE019
And
Figure 797792DEST_PATH_IMAGE020
new to failure path
Figure 937918DEST_PATH_IMAGE021
In (1).
And S36, judging whether all the newly added failure paths have been executed in the steps S34 and S35, if so, outputting all the failure paths, and otherwise, returning to the step S34.
In step S3, the start point set, the intermediate set, and the end point set of the non-traversed failure path are determined according to the failure destruction history, and a single directed graph is formed using any one of the start point set, the intermediate set, and the end point set.
Assuming arbitrary failure paths
Figure 753427DEST_PATH_IMAGE022
Fail unit contained in
Figure 697112DEST_PATH_IMAGE023
Can be divided into starting point sets
Figure 990690DEST_PATH_IMAGE024
Middle set
Figure 442445DEST_PATH_IMAGE025
And endpoint set
Figure 960014DEST_PATH_IMAGE026
The starting point set, the middle set and the end point set form a plurality of directed graphs, wherein each failure unit is equivalent to a node of the directed graph; assuming that a failure path adopts 2 starting point failure units determined according to failure damage history, the failure path has 2 directed graphs.
In step S4, calculating a spatial distance between centroids of any two failure units in each directed graph, and when the spatial distance is smaller than the influence distance, calculating a non-negative weight value between the two failure units to obtain a weighted directed graph;
in one embodiment of the present invention, when the criticality of each failure unit of the gravity dam-foundation system is represented by a nonlinear energy dissipation value, a calculation formula for calculating a nonnegative weight value between two failure units is as follows:
Figure 390996DEST_PATH_IMAGE027
，
Figure 973418DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 806245DEST_PATH_IMAGE029
and
Figure 494715DEST_PATH_IMAGE030
are respectively the firstmSecondary applied loadH m Time of day, failure path
Figure 163725DEST_PATH_IMAGE031
Any two failed units in a directed graph;
Figure 799105DEST_PATH_IMAGE032
as a failure path
Figure 220859DEST_PATH_IMAGE031
Failing unit in corresponding one directed graph
Figure 96543DEST_PATH_IMAGE029
And
Figure 236537DEST_PATH_IMAGE030
a non-negative weight value therebetween;
Figure 941188DEST_PATH_IMAGE033
and
Figure 217448DEST_PATH_IMAGE034
are respectively failure units
Figure 467295DEST_PATH_IMAGE029
And
Figure 891323DEST_PATH_IMAGE030
under loadH m (ii) a non-linear energy dissipation density under influence;
Figure 134086DEST_PATH_IMAGE035
as a failure path
Figure 15585DEST_PATH_IMAGE031
The maximum value of the nonlinear energy dissipation density of each failure unit in the corresponding one of the directed graphs;V i is a failure unit
Figure 685601DEST_PATH_IMAGE029
The volume of (a);
Figure 596925DEST_PATH_IMAGE036
is a failure unit
Figure 128532DEST_PATH_IMAGE029
Under load ofH m The nonlinear dissipation of energy under action.
Wherein, renNon-linear dissipated energy of latent failure unitE P The calculation formula of (2) is as follows:
Figure 379385DEST_PATH_IMAGE037
wherein the content of the first and second substances,
Figure 220302DEST_PATH_IMAGE038
and
Figure 822184DEST_PATH_IMAGE039
stress tensor and plastic strain tensor of the dam body or dam foundation material corresponding to the failure unit are respectively set;Vis the volume of the failed cell.
In step S5, a Dijkstra algorithm is used to find the shortest path of each weighted directed graph of the same failure path, and the minimum weight of all shortest paths corresponding to the same failure path is selected as the critical failure path.
Assuming that two starting points are determined for the same failure path, the same failure path corresponds to 2 weighted directed graphs, the failure path has two shortest paths, and when the critical failure path of the failure path is determined, one of the two shortest paths with the smallest weight is selected as the finally determined critical failure path.
In order to facilitate understanding of the shortest path selection process, the following description, in an exemplary form, is provided by combining with Dijkstra algorithm to describe a method for acquiring a critical failure path:
if failure path
Figure 954220DEST_PATH_IMAGE040
Two of any failure unit
Figure 325158DEST_PATH_IMAGE041
And
Figure 71397DEST_PATH_IMAGE042
in abutting relationship, i.e. from
Figure 645729DEST_PATH_IMAGE041
Can directly reach
Figure 830723DEST_PATH_IMAGE042
Is marked as
Figure 56168DEST_PATH_IMAGE043
Corresponding path weights
Figure 989620DEST_PATH_IMAGE044
Calculating by adopting a calculation formula of a non-negative weight value, and if the calculation formula does not exist
Figure 300515DEST_PATH_IMAGE045
Let the weight value
Figure 226883DEST_PATH_IMAGE046
(ii) a The initial time order search starting point set only contains the vertex
Figure 306835DEST_PATH_IMAGE047
I.e. by
Figure 473505DEST_PATH_IMAGE048
Node set to be searched
Figure 271697DEST_PATH_IMAGE049
Is composed of
Figure 736176DEST_PATH_IMAGE050
(ii) a From
Figure 421366DEST_PATH_IMAGE049
Selecting a vertex with the smallest path weight value to be added
Figure 211468DEST_PATH_IMAGE051
Update
Figure 293693DEST_PATH_IMAGE049
、
Figure 312596DEST_PATH_IMAGE051
And
Figure 101561DEST_PATH_IMAGE049
in each node pair
Figure 62563DEST_PATH_IMAGE051
The weight of (2); go through
Figure 117238DEST_PATH_IMAGE049
Until all nodes join the set
Figure 189099DEST_PATH_IMAGE051
(ii) a Selecting the path with the minimum weight as
Figure 98149DEST_PATH_IMAGE047
Shortest path under starting point
Figure 964474DEST_PATH_IMAGE052
；
Traverse failure path
Figure 975287DEST_PATH_IMAGE040
Set of starting points in (1)
Figure 381997DEST_PATH_IMAGE053
Until finding the shortest failure path under each starting point
Figure 411133DEST_PATH_IMAGE054
Comparing failure paths
Figure 933513DEST_PATH_IMAGE040
Path weights of all corresponding shortest failure paths, if path
Figure 680889DEST_PATH_IMAGE055
The smallest weight value is then
Figure 891290DEST_PATH_IMAGE055
As a failure path
Figure 349884DEST_PATH_IMAGE040
The following critical failure path.
In step S6, it is determined whether there is a failure path without obtaining a critical failure path, if yes, the process returns to step S3, otherwise, the process proceeds to step S7;
when inmStep loading stepH m When the key failure paths of all the failure paths under action are found, the first step ismStep loading stepH m The set of critical failure paths under action may be represented as
Figure 558011DEST_PATH_IMAGE056
。
In step S7, it is determined whether the current load is greater than the ultimate bearing capacity of the gravity dam-foundation system, if so, the process proceeds to step S8, otherwise, the process returns to step S2;
in step S8, all the searched critical failure paths are merged together as the final critical failure path of the gravity dam after each occurrence of a failure unit.
When applying the load increment method, step-by-step loading, assume from the secondmStep (b) to generate a fail unitnStep loading stepH n Under the action, the gravity dam-foundation system reaches the ultimate bearing capacity, so that the system fails; searching to obtain the key failure path of the gravity dam-foundation system under each load step
Figure 527104DEST_PATH_IMAGE057
(ii) a Ultimate critical failure path
Figure 478880DEST_PATH_IMAGE058
Load taking stepH m ToH n Union of sets of lower critical failure paths, i.e.
Figure 30078DEST_PATH_IMAGE059
。
And when the gravity dam-foundation structure is a Drucker-Prager model, judging whether the unit fails by adopting a Drucker-Prager plastic yield criterion.
The following describes the searching process of the critical failure path in the present solution with reference to specific examples:
the section of a typical dam section of a concrete gravity dam is shown in fig. 2, the height of the dam is 143m, the width of the top of the dam is 14m, the width of the bottom of the dam is 123m, and the slope rate of the upstream dam surface is 1: the slope rate of the downstream dam slope of the 0.3 slope-folding section is 1:0.75, and the rock foundation comprises a deep structure surface. And judging the failure of the dam and the foundation unit by adopting a Drucker-Prager failure criterion, in the example, the unit centroid coordinate is two-dimensional, namely the coordinate in the Z direction is zero, the Z direction coordinate of the unit centroid is not given in the following operation, and the value in the Z direction in the formula is equivalent to zero when the space distance of the centroid is calculated.
The parameters of the dam body concrete material are as follows: modulus of elasticityE d Density of 35GPaρ d =2500kg/m3Poisson ratioμ d =0.2, coefficient of frictionf d =1.35, cohesionc d The parameters of the bedrock material are as follows: modulus of elasticityE f Density of 18GPaρ f =2700kg/m3Poisson ratioμ f =0.22, coefficient of frictionf f =1.3, cohesionc f The material parameters of the structural surface are as follows: modulus of elasticityE r Density of =1GPaρ r =2000kg/m3Poisson ratioμ r =0.3, coefficient of frictionf r =0.6, cohesionc r =0.15MPa。
As shown in fig. 1, the method for searching the critical failure path of the gravity dam-foundation structure system includes the following steps:
1. the finite element model of the constructed gravity dam-foundation structure system is shown in figure 3, which comprises 5775 corresponding element number sequencesDAnd unit centroid coordinatesLRespectively expressed as:D=[1，2，…5775]coordinates of unit centroid
Figure DEST_PATH_IMAGE061A
Comprises the following steps:
Figure 284473DEST_PATH_IMAGE062
2. loading step by adopting a load increment method, and increasing the water head at each step on the upstream surface
Figure 475283DEST_PATH_IMAGE063
And next, a failure unit appears at the 16 th dam body heel part, as shown in figure 4. Failure unit set
Figure 981482DEST_PATH_IMAGE064
Plastic energy dissipation assembly
Figure 636454DEST_PATH_IMAGE065
. At the moment, only the dam heel has failure units, and the failure paths are divided into
Figure 451963DEST_PATH_IMAGE066
；
3. According to the failure damage course, the failure path in step 2
Figure 146381DEST_PATH_IMAGE067
Can be divided into starting point sets
Figure 174380DEST_PATH_IMAGE068
Middle set
Figure 887121DEST_PATH_IMAGE069
And endpoint set
Figure 421001DEST_PATH_IMAGE070
The starting point set, the middle set and the end point set can form a plurality of directed graphs, wherein each failure unit is a node of the directed graph;
4. for the start points 78, 112 and 79 in step 3, it is possible to separately combine the intermediate set and the end point set
Figure 851983DEST_PATH_IMAGE071
、
Figure 683672DEST_PATH_IMAGE072
Composing a single directed graph, i.e. a failure path
Figure 250920DEST_PATH_IMAGE067
3 directed graphs can be obtained; judging the adjacent relation of nodes of the directed graph, and calculating the non-negative weight of the path between the nodes, wherein the directed graph corresponding to the starting point 78 forms the weighted directed graph as shown in FIG. 5;
5. applying Dijkstra algorithm to the weighted directed graph in step 4 to find the critical path, and since the critical failure path with the starting point of 79 has the largest weight, the critical failure path with the starting point of 79 is omitted in this description, and the critical failure paths of the starting point 78 and the starting point 112 are respectively the critical failure path with the starting point of 79
Figure 158964DEST_PATH_IMAGE073
，
Figure 873979DEST_PATH_IMAGE074
The critical failure path corresponding to the starting point 78 is shown in FIG. 6. If the searched path is optimal when the starting point is 112, the failure path
Figure 243781DEST_PATH_IMAGE067
The critical path of
Figure 681847DEST_PATH_IMAGE075
。
6. Repeating the step 3-5 to obtain a loading stepH 16Key path of failure path of gravity dam-foundation system under action
Figure 10060DEST_PATH_IMAGE076
(ii) a (the objective here is to find the critical failure path within each failure path at a single load step, since the load stepH 16Under the action, only 1 failure path exists, so that the key failure path also only has 1:
Figure 946792DEST_PATH_IMAGE077
。
7. and repeating the steps 2-6, and continuously and gradually overloading by applying a load increment method, wherein in the process, failure units at the dam heel continue to evolve, and meanwhile failure units begin to appear at the upstream slope bending part of the dam body, the upstream side of the dam head, the dam toe part and the deep foundation structure surface.
Until the gravity dam-foundation system reaches the ultimate bearing capacity at the 37 th load step, the structural system fails, and at the moment, each failure path is respectively
Figure 402175DEST_PATH_IMAGE078
，
Figure 944015DEST_PATH_IMAGE079
As shown in fig. 7.
The method provided by the scheme is adopted to further search each failure path, and the key path corresponding to each failure path obtained by searching is respectively
Figure 177550DEST_PATH_IMAGE080
、
Figure 804840DEST_PATH_IMAGE081
、
Figure 532756DEST_PATH_IMAGE082
、
Figure 991419DEST_PATH_IMAGE083
And
Figure 395856DEST_PATH_IMAGE084
. Key failure path of gravity dam-foundation system under each load step
Figure DEST_PATH_IMAGE085
。
8. In the loading stepH 16ToH 37Under dynamic loading, the final key failure path of the gravity dam-foundation structural system is
Figure DEST_PATH_IMAGE086
Such asAs shown in fig. 8.
The implementation case shows that by applying the method for searching the critical failure path of the gravity dam-foundation structural system, the searched critical failure path accords with the actual engineering, the redundant unit with small influence on failure probability is deleted, the failure path is greatly simplified, the internal weak part of the searched gravity dam-foundation structural system is more definite, the analysis on the structural reliability of the gravity dam-foundation structural system can be more accurate and quicker, and more reliable guidance is provided for the operation safety of the engineering.

Claims (8)

1. The method for searching the critical failure path of the gravity dam-foundation structure system is characterized by comprising the following steps:
s1, constructing a finite element model of the gravity dam-foundation structure according to the physical parameters of the gravity dam-foundation structure and the concrete material parameters of the dam body, wherein the discretized finite element model consists of a plurality of units;
s2, applying load to the finite element model by adopting a load increment method until a failure unit appears, recording all failure units to form a total failure unit set, and then generating at least one failure path according to the failure units;
s3, determining a starting point set, an intermediate set and an end point set of the non-traversed failure path according to the failure damage process, and forming a single directed graph by adopting any starting point in the starting point set, the intermediate set and the end point set;
s4, calculating the space distance between the centroids of any two failure units in each directed graph, and calculating the nonnegative weight value between the two failure units when the space distance is smaller than the influence distance to obtain the weighted directed graph;
s5, searching the shortest path of each weighted directed graph of the same failure path by adopting a Dijkstra algorithm, and selecting the minimum weight of all the shortest paths corresponding to the same failure path as the key failure path;
s6, judging whether a failure path exists and a key failure path is not searched yet, if yes, returning to the step S3, otherwise, entering the step S7;
s7, judging whether the current load is larger than the ultimate bearing capacity of the gravity dam-foundation system, if so, entering the step S8, otherwise, returning to the step S2;
and S8, merging all the searched critical failure paths together to serve as the final critical failure path of the gravity dam after each failure unit occurs.
2. The method of claim 1, wherein the method of generating at least one failure path comprises:
s31, selecting any failure unit in the total failure unit set as a failure path, and calculating the space distance between the centroid of any failure unit in the total failure unit set and the centroid of the failure unit in the failure patha；
S32, judging the space distanceaWhether the space distance is smaller than or equal to the influence distance or not is judged, if so, a failure unit corresponding to the space distance is added into a failure path, and if not, the step S33 is executed;
s33, adding space distanceaThe corresponding failure unit is a failure path;
s34, selecting the new failure path which is not traversed, and calculating the space distance between the centroid of the failure unit in the new failure path and the centroid of any failure unit in the total failure unit setb；
S35, judging the space distancebWhether the influence distance is less than or equal to the influence distance or not, if so, adding the corresponding failure unit into the current newly added failure path, otherwise, entering the step S36;
and S36, judging whether all the newly added failure paths have been executed in the steps S34 and S35, if so, outputting all the failure paths, and otherwise, returning to the step S34.
3. The method for searching the critical failure path of the gravity dam-foundation structure system as claimed in claim 1, wherein when the criticality of each failure unit of the gravity dam-foundation system is represented by the nonlinear energy dissipation value, the calculation formula for calculating the non-negative weight value between two failure units is as follows:
Figure DEST_PATH_IMAGE001
，
Figure DEST_PATH_IMAGE002
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE003
and
Figure DEST_PATH_IMAGE004
are respectively the firstmSecondary applied loadH m Time of day, failure path
Figure DEST_PATH_IMAGE005
Any two failed units in a directed graph;
Figure DEST_PATH_IMAGE006
as a failure path
Figure 311794DEST_PATH_IMAGE005
Failing unit in corresponding one directed graph
Figure 25673DEST_PATH_IMAGE003
And
Figure 274251DEST_PATH_IMAGE004
a non-negative weight value therebetween;
Figure DEST_PATH_IMAGE007
and
Figure DEST_PATH_IMAGE008
are respectively failure units
Figure 325253DEST_PATH_IMAGE003
And
Figure 608467DEST_PATH_IMAGE004
under loadH m (ii) a non-linear energy dissipation density under influence;
Figure DEST_PATH_IMAGE009
as a failure path
Figure 758825DEST_PATH_IMAGE005
The maximum value of the nonlinear energy dissipation density of each failure unit in the corresponding one of the directed graphs;V i is a failure unit
Figure 642771DEST_PATH_IMAGE003
The volume of (a);
Figure DEST_PATH_IMAGE010
is a failure unit
Figure 903988DEST_PATH_IMAGE003
Under load ofH m The nonlinear dissipation of energy under action.
4. The method for searching the critical failure path of the gravity dam-foundation structural system as claimed in claim 3, wherein the nonlinear dissipation energy of any failure unit adopts plastic dissipation energy,E P the calculation formula of (2) is as follows:
Figure DEST_PATH_IMAGE011
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE012
and
Figure DEST_PATH_IMAGE013
stress tensor and plastic strain tensor of the dam body or dam foundation material corresponding to the failure unit are respectively set;Vis the volume of the failed cell.
5. The method of claim 1, wherein Drucker-Prager plastic yield criterion is used to determine if a unit fails when a Drucker-Prager constitutive model is used for the gravity dam-foundation structure.
6. The method of claim 1, wherein the impact distance is an average size of failed units.
7. The method of claim 1, wherein the loading is incrementally increased by a predetermined increment each time the finite element model is loaded by the load increment method.
8. The method for searching for the critical failure path of the gravity dam-foundation structural system as claimed in any one of claims 1 to 7, wherein the grid size of the cells in step S1 is 1.0-2.5m。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112446142A (en) * 2020-11-16 2021-03-05 贵州翰凯斯智能技术有限公司 Method for designing chassis structure for additive manufacturing of arc fuse

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102055664A (en) * 2009-11-10 2011-05-11 武汉大学 Fast alternative route distribution method based on overlay network environment
CN106294967A (en) * 2016-08-02 2017-01-04 浙江大学 A kind of cement-based material probability of fatigue failure considering Loading frequency and the method for building up of repeated strain probabilistic model
JP2017025491A (en) * 2015-07-16 2017-02-02 大成建設株式会社 Construction method of water passage, and jacking machine
CN106638538A (en) * 2016-12-29 2017-05-10 西安理工大学 Discrimination method for foundation bearing capacity safety
CN107563046A (en) * 2017-08-30 2018-01-09 国家电网公司 Failure risk rate computational methods and device based on dam invalidation functions function model
CN109117540A (en) * 2018-08-02 2019-01-01 三峡大学 A kind of probability statistical analysis method solving dam concrete mechanics parameter inverting nonuniqueness
CN110119585A (en) * 2019-05-20 2019-08-13 华电福新周宁抽水蓄能有限公司 The analysis method and device that transformation temperature load influences Compacted Concrete Gravity Dam Section

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102055664A (en) * 2009-11-10 2011-05-11 武汉大学 Fast alternative route distribution method based on overlay network environment
JP2017025491A (en) * 2015-07-16 2017-02-02 大成建設株式会社 Construction method of water passage, and jacking machine
CN106294967A (en) * 2016-08-02 2017-01-04 浙江大学 A kind of cement-based material probability of fatigue failure considering Loading frequency and the method for building up of repeated strain probabilistic model
CN106638538A (en) * 2016-12-29 2017-05-10 西安理工大学 Discrimination method for foundation bearing capacity safety
CN107563046A (en) * 2017-08-30 2018-01-09 国家电网公司 Failure risk rate computational methods and device based on dam invalidation functions function model
CN109117540A (en) * 2018-08-02 2019-01-01 三峡大学 A kind of probability statistical analysis method solving dam concrete mechanics parameter inverting nonuniqueness
CN110119585A (en) * 2019-05-20 2019-08-13 华电福新周宁抽水蓄能有限公司 The analysis method and device that transformation temperature load influences Compacted Concrete Gravity Dam Section

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
XIANG LU 等: "Research and Application of a Seismic Damage Classification Method of Concrete Gravity Dams Using Displacement in the Crest", 《APPLIED SCIENCES》 *
YANTAO ZHU 等: "Using the DEMATEL‐VIKOR Method in Dam Failure Path Identification", 《INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH》 *
徐强 等: "非平稳地震动过程中混凝土重力坝受拉失效路径可靠度分析", 《工程力学》 *
王超: "重力坝系统动力性态的随机数学分析", 《中国博士学位论文全文数据库 工程科技Ⅱ辑》 *
范书立 等: "基于能量耗散碾压混凝土重力坝地震损伤分析", 《振动与冲击》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112446142A (en) * 2020-11-16 2021-03-05 贵州翰凯斯智能技术有限公司 Method for designing chassis structure for additive manufacturing of arc fuse
CN112446142B (en) * 2020-11-16 2023-02-28 贵州翰凯斯智能技术有限公司 Method for designing chassis structure for additive manufacturing of arc fuse

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