CN102660933A - Cracking warning method for concrete dam - Google Patents

Cracking warning method for concrete dam Download PDF

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Publication number
CN102660933A
CN102660933A CN2012101514179A CN201210151417A CN102660933A CN 102660933 A CN102660933 A CN 102660933A CN 2012101514179 A CN2012101514179 A CN 2012101514179A CN 201210151417 A CN201210151417 A CN 201210151417A CN 102660933 A CN102660933 A CN 102660933A
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crack
fracture aperture
concrete dam
sample
instability
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顾冲时
苏怀智
景继
郑东健
包腾飞
欧斌
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Hohai University HHU
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Hohai University HHU
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Abstract

The invention discloses a cracking warning method for a concrete dam. The method comprises the following steps of: decomposing a crack opening measured value sequence by using a discrete wavelet method, and extracting the secular distortion of a crack; analyzing the secular distortion of a crack opening of the concrete dam, judging whether the crack has excessive instability abnormality or not, and determining an instability moment; extracting annual crack opening measured data generated after the last instability propagation for analysis, and selecting a crack opening measured value sequence obtained during unfavorable load combination to form a sample space; and determining a probability density function of sample distribution by using a maximum entropy principle according to a selected crack opening sample, and fitting a critical opening of the crack according to set instability probability as a warning value of the crack opening. The secular distortion of the crack is extracted, the method is simple and practical, other parameters are not required to be measured, and a completely new technology is provided for regulating and controlling a part of loads in a concrete running process, avoiding the crack instability caused by the unfavorable load combination and ensuring the safe running of the dam.

Description

A kind of concrete dam cracking method for early warning
Technical field
The present invention relates to a kind of concrete dam cracking method for early warning.
Background technology
For concrete dam, the crack is that ubiquity, and nearly all concrete dam is the cracking of various degrees all.The crack is very big to the harmfulness of concrete dam, is one of main reflection of the aging pathology of structure.The crack whether stablize the safe condition that is related to total, be an important indicator judging structural stability.Research through to concrete dam crack INSTABILITY CRITERION can be predicted the ability of dam bearing load; Analyze the stability of concrete dam crack under unfavorable load action; Thereby can in the concrete dam running, control fractional load; Make the crack unstability to avoid unfavorable load combination occurring, guarantee the safe operation of concrete dam when taking into account project benefit.In the research of concrete dam crack INSTABILITY CRITERION; Method comparatively commonly used at present is to judge according to Theory of Fracture Mechanics whether the crack unstable propagation can take place; But in actual application, then be difficult to realize; Subcritical extension length like the cracking length in crack and seam end all is difficult to measure real-time and accurately, confirms that all there is certain difficulty etc. in the fragmentation parameters such as stress intensity factor, seam end opening displacement in crack.
Summary of the invention
Goal of the invention: the objective of the invention is to deficiency, provide a kind of simple, only need to analyze the real-time monitoring materials in concrete dam crack, need not to measure the concrete dam cracking method for early warning of other parameter to prior art.
Technical scheme: fracture aperture measured value sequence can be regarded the data signal of being made up of the signal component of different frequency as; Wherein receive the part of factor affecting such as water level, temperature to have obvious periodic property Changing Pattern; The part that influenced by enchancement factor and observation error constitutes the vibration of signal high frequency, and it then is low-frequency variation that the timeliness in crack changes.Concrete dam cracking method for early warning of the present invention may further comprise the steps:
(1) with the discrete wavelet method fracture aperture measured value sequence is decomposed; Removal receives the high-frequency part of water level, variations in temperature and enchancement factor and error effect; Remaining low frequency part is just being represented the development trend of crack measured value sequence, is the secular distortion in crack.With wavelet transform the measured data of fracture aperture is analyzed, the wavelet basis function formula table is shown:
Figure 2012101514179100002DEST_PATH_IMAGE001
，j=0,1,2,…,?k∈Z （1）
Wavelet transform to measured signal is:
（2）
(2) timeliness of concrete dam fracture aperture is analyzed, whether the characteristic that changes according to the fracture aperture timeliness is analyzed the crack and is committed a fault and surely change different, and definite unstability moment of taking place.The secular distortion that the concrete dam crack becomes in time, can represent with the first order nonlinear differential equation:
Figure 508751DEST_PATH_IMAGE004
（3）
In the formula;
Figure 2012101514179100002DEST_PATH_IMAGE005
is the secular distortion in crack;
Figure 288488DEST_PATH_IMAGE006
is the crack secular distortion to the derivative of time, and
Figure 2012101514179100002DEST_PATH_IMAGE007
is parameter.
Figure 621380DEST_PATH_IMAGE005
and
Figure 435752DEST_PATH_IMAGE006
characterize the fracture system at any one time state of motion.With
Figure 462931DEST_PATH_IMAGE005
is transverse axis;
Figure 661831DEST_PATH_IMAGE006
is the longitudinal axis; With the numerical value of timeliness
Figure 330710DEST_PATH_IMAGE005
and rate of change
Figure 261757DEST_PATH_IMAGE006
thereof as a point on the plane; Make the change procedure line of
Figure 16086DEST_PATH_IMAGE008
, can show the development law of fracture aperture thus intuitively.If it is different that the crack takes place to change, then its secular distortion generally non-linearly increases by changing reposefully to change into suddenly fast.The typical timeliness that the crack possibly changeed different changes as shown in Figure 1, and the graph of its timeliness and timeliness rate of change
Figure 753098DEST_PATH_IMAGE008
is as shown in Figure 2.
Among Fig. 2 t A Constantly, the Changing Pattern of crack timeliness changes, Graph on this time be carved with
Figure 2012101514179100002DEST_PATH_IMAGE009
, flex point appears. t A The secular distortion in crack is constantly become by slow increase and increases sharply, and this is exactly that moment of changeing different takes place in the crack constantly, and the timeliness that corresponding point constantly is the crack in the secular distortion of crack is changeed dissimilarity.
The crack timeliness is changeed the dissimilarity judgment criterion:
（4）
In the formula;
Figure 2012101514179100002DEST_PATH_IMAGE011
is the timeliness in crack;
Figure 823319DEST_PATH_IMAGE012
is the first derivative of timeliness, and
Figure 2012101514179100002DEST_PATH_IMAGE013
is the second dervative of timeliness.
Timeliness when the crack K θ When satisfying criterion listed in the formula (4), constantly t A Be that the crack is to take place the different moment of commentaries on classics, the point on the corresponding secular distortion curve is timeliness changes dissimilarity.
(3) because the crack excessive ess-strain of seam end can cause fracture propagation, and seam end ess-strain when big corresponding fracture aperture also bigger.Therefore, got in the data series the annual fracture aperture field data since the last unstable propagation and analyze, the fracture aperture sequence of observations when selecting unfavorable load combination forms sample space.
In dam safety monitoring, for the development of monitoring the crack develops situation, arrange that at location of cracks joint meter measures the aperture in crack usually, the common arrangement form of joint meter is as shown in Figure 3.
The crack tip opening displacement CTODThe fracture aperture that records with joint meter δBetween have a following relations of fact: when unstable propagation takes place in the crack, CTODReach its threshold CTOD c , meanwhile, corresponding fracture aperture δAlso should reach a threshold δ c From statistical angle, unstable propagation takes place in the crack is a small probability event, can confirm with little probability method δ c In field data, the fracture aperture when selecting unfavorable load to make up δ i , then δ i Be stochastic variable, can obtain an increment number by the observational data sequence and do Sample space:
Figure 2012101514179100002DEST_PATH_IMAGE015
（5）
(4) according to selected fracture aperture sample, confirm the probability density function of sample distribution with principle of maximum entropy, draft the critical angle in crack according to the unstability probability of setting, as the warning value of fracture aperture.
For random variable of continuous type, its comentropy is:
Figure 679597DEST_PATH_IMAGE016
（6）
In the formula;
Figure 2012101514179100002DEST_PATH_IMAGE017
is the distribution density function of random variable of continuous type
Figure 967095DEST_PATH_IMAGE018
;
Figure 2012101514179100002DEST_PATH_IMAGE019
is the integration space, and is comentropy.
Comentropy has characterized the size of information content, can be used as the probabilistic tolerance of fracture aperture sample distribution.Can find out from the definition of comentropy; If the probability of known stochastic variable; Just can calculate its entropy; Exist corresponding relation between entropy
Figure 712514DEST_PATH_IMAGE020
probability distribution, therefore can confirm probability distribution through entropy
Figure 210492DEST_PATH_IMAGE020
.According to principle of maximum entropy, when inquiring into the probability distribution of stochastic variable according to partial information, the maximum probability distribution of necessary selective entropy, the entropy maximum just means that artificial supposition is minimum, the result of acquisition tallies with the actual situation most, and is the most objective.
According to principle of maximum entropy; The desirable entropy that makes is issued to the estimation of peaked probability as the fracture aperture probability distribution in the condition of known sample data message, that is:
max
Figure 2012101514179100002DEST_PATH_IMAGE021
?（7）
Constraints:
（8）
Figure 2012101514179100002DEST_PATH_IMAGE023
（9）
In the formula, RBe the integration space; μ i ( I=1,2 ..., N) be iThe rank moment of the orign can obtain by calculating sample; NExponent number for used square.
This is the optimization problem of a belt restraining, can adopt method of Lagrange multipliers to find the solution, and sets up following Lagrangian:
Figure 752965DEST_PATH_IMAGE024
（10）
Make
Figure 2012101514179100002DEST_PATH_IMAGE025
, can solve probability density function and be:
（11）
Can know by formula (11), confirmed Lagrangian coefficient ( λ 0 , λ 1 , , λ N ), just can draw the probability density function of fracture aperture sample distribution, for try to achieve Lagrangian coefficient ( λ 0 , λ 1 , , λ N ), can formula (11) substitution formula (8) be obtained:
Figure 2012101514179100002DEST_PATH_IMAGE027
（12）
Can get after the arrangement:
Figure 923364DEST_PATH_IMAGE028
（13）
Again formula (11) and formula (13) substitution formula (9) can be got through arrangement:
Figure 2012101514179100002DEST_PATH_IMAGE029
（14）
In the following formula r i Be residual error, represented one group ( λ 1 , , λ N ) under f( x) depart from the degree of constraints, have in ideal conditions r i =0.Residual error obviously is more little good more, therefore, for confirm Lagrangian coefficient ( λ 1 , , λ N ), can select to make residual sum of squares (RSS) to reach one group of minimum Lagrange coefficient, just find the solution
Figure 361298DEST_PATH_IMAGE030
Thereby solve ( λ 1 , , λ N ), and then can draw the probability density function of fracture aperture sample distribution.Suppose the unstability probability α c =0.01, obtain the critical crack aperture according to the above maximum entropy density function that calculates.
Find the solution above formula with numerical integration method, need to confirm integrating range, for comparatively common normal distribution situation, if [ A, b] be taken as [ μ 1 -3 σ, μ 1 + 3 σ] ( μ 1 Be average, σBe standard deviation), the error that then approximate processing caused is less than 0.27%.The distribution of considering stochastic variable in the reality possibly be a skewness, can the scope of integral domain further be enlarged, for example get [ μ 1 -5 σ, μ 1 + 5 σ].Moment of the orign can adopt preceding 4 rank moment of the origns to calculate in above calculating; Just get
Figure 2012101514179100002DEST_PATH_IMAGE031
; This is because the characteristic of concrete dam fracture aperture sample can be described with its preceding 4 rank moment of the origns basically: 1 rank square is an average, has portrayed the value center of sample; 2 rank squares have been portrayed the dispersion degree of the relative average of sample value; 3 rank squares have been portrayed the symmetry of sample value; 4 rank squares have been portrayed concentrating and degree of scatter of sample value.
Beneficial effect: a kind of concrete dam cracking actual measurement method for early warning that the present invention announces extracts the secular distortion in crack; Simple; Need not to measure other parameter; Be fractional load regulation and control in the concrete running, avoid occurring unfavorable load and make up and make the crack unstability that the safe operation of assurance dam provides a kind of brand-new technology.
Description of drawings
Different typical secular distortion sketch map takes place to change in Fig. 1 crack;
Different time graph takes place to change in Fig. 2 crack;
Fig. 3 joint meter arrangement form;
Fig. 4 fracture aperture actual measurement graph;
The secular distortion graph in Fig. 5 crack;
The graph of Fig. 6 crack timeliness and timeliness rate of change ;
Fig. 7 fracture aperture sample probability density function.
The specific embodiment
Be elaborated in the face of technical scheme of the present invention down, but protection scope of the present invention is not limited to said embodiment.
Embodiment:A kind of concrete dam cracking method for early warning of the present invention is that example is analyzed with certain thick arch dam downstream face 105m elevation crack measuring point from the fracture aperture measured value in 1972 to 2007, and fracture aperture actual measurement graph is as shown in Figure 4.
The fracture aperture measured data is carried out the discrete wavelet analysis, the HFS that its decomposition of elimination obtains, the timeliness that remaining low frequency part changes as fracture aperture, the timeliness change procedure line that extracts is as shown in Figure 5.
The aperture that from actual measurement graph Fig. 4, can find out this crack 1976 to 1978 in the period of with the changes phase that experienced two emergentnesses respectively in 1987; On the secular distortion graph that the discrete wavelet analysis extracts, also reflect the variation of these two emergentnesses significantly, consistent with the actual conditions match.
Secular distortion to extracting is analyzed; The change procedure line of making timeliness and timeliness rate of change
Figure 243301DEST_PATH_IMAGE008
is as shown in Figure 6; As can be seen from the figure; Curve flex point occurs at A point place; The different typical change feature similarity of commentaries on classics takes place in the variation characteristic of curve and crack shown in Figure 2 near the A point, so the A point is the timeliness commentaries on classics dissimilarity in crack.A point time corresponding interval was at 1976 to 1978, and dam has experienced the attack of twice high temperature low water stage and three low temperature low water stage, and the unfavorable load combination that occurs continuously causes the crack that unstable propagation has taken place.Analysis through above shows that in the dam running, a unstability once took place in the crack changes different, and taking place to change the different time is in April, 1977.
Get the measured data after in April, 1977 and calculate the critical crack aperture; Because the crack excessive ess-strain of seam end can cause fracture propagation; And the fracture aperture of stitching correspondence when holding ess-strain big is also bigger; The fracture aperture sample of the maximum value of getting annual fracture aperture in 1978 ~ 2007 observational data sequences during as unfavorable load combination seen table 1.
Table 1 fracture aperture year maximum value statistical form
Sequence number Maximum value (mm) Sequence number Maximum value (mm) Sequence number Maximum value (mm)
1 3.06 11 3.31 21 3.77
2 3.18 12 3.50 22 3.77
3 3.20 13 3.47 23 3.77
4 3.08 14 3.52 24 3.77
5 3.08 15 3.73 25 4.03
6 3.33 16 3.95 26 4.04
7 3.43 17 3.54 27 4.07
8 3.29 18 3.75 28 4.29
9 3.37 19 3.81 29 4.25
10 3.14 20 3.62 30 4.21
The preceding 4 rank moment of the origns that calculate sample are respectively: μ 1 =3.611, μ 2 =13.171, μ 3 =48.518, μ 4 =180.468.The standard deviation of sample is σ=0.3686.Find the solution the distribution probability density function of sample according to principle of maximum entropy, get integrating range for [ μ 1 -5 σ, μ 1 + 5 σ], find the solution with nonlinear least square method, obtain maximum entropy density function and be:
Figure 2012101514179100002DEST_PATH_IMAGE033
The maximum entropy density function distribution map is as shown in Figure 7.
By engineering experience supposition unstability probability α=0.01; Obtaining the critical crack aperture according to the above maximum entropy density function that calculates is 4.33mm; With the warning value of this threshold as fracture aperture, when fracture aperture surpassed this warning value, unstable propagation probably can take place in the crack; Thereby in concrete dam operational management process, should pay close attention to the concrete dam load; Avoid occurring unfavorable load combination and make the crack unstability, prevent that the situation of critical crack opening value from appearring surmounting in concrete dam, produce concrete dam structural safety hidden danger and cause the dam crack unstable failure to occur.
As stated, although represented and explained the present invention that with reference to specific preferred embodiment it shall not be construed as the restriction to the present invention self.Under the spirit and scope of the present invention prerequisite that does not break away from the accompanying claims definition, can make various variations in form with on the details to it.

Claims (2)

1. concrete dam cracking method for early warning is characterized in that may further comprise the steps:
(1) with the discrete wavelet method fracture aperture measured value sequence is decomposed, remove the high-frequency part that receives water level, variations in temperature and enchancement factor and error effect, extracting low frequency part is the secular distortion in crack;
(2) timeliness of concrete dam fracture aperture is analyzed, whether the characteristic that changes according to timeliness is analyzed the crack and is committed a fault and surely change different, and definite unstability moment of taking place;
(3) the annual fracture aperture field data of having got since the last unstable propagation is analyzed, and the fracture aperture sequence of observations when selecting unfavorable load combination forms sample space;
(4) according to selected fracture aperture sample, confirm the probability density function of sample distribution with principle of maximum entropy, draft the critical angle in crack according to the unstability probability of setting, as the warning value of fracture aperture.
2. a kind of concrete dam cracking method for early warning according to claim 1 is characterized in that: the described fracture aperture observation of step (3), the common aperture of measuring the crack at location of cracks layout joint meter.
CN2012101514179A 2012-05-16 2012-05-16 Cracking warning method for concrete dam Pending CN102660933A (en)

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Cited By (4)

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Publication number Priority date Publication date Assignee Title
CN103048056A (en) * 2012-12-18 2013-04-17 东南大学 Determination method of probability density of sunshine temperature difference acquisition sample
CN105200954A (en) * 2015-09-25 2015-12-30 中国电建集团成都勘测设计研究院有限公司 Method for classifying concrete dam cracks
CN108716904A (en) * 2018-04-09 2018-10-30 水利部南京水利水文自动化研究所 Dam deflection acquisition methods based on limited inclinometer measuring point measured value
CN111089544A (en) * 2020-03-19 2020-05-01 浙江交工集团股份有限公司 Tunnel monitoring measurement data analysis method based on maximum entropy method reliability theory

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CN101482406A (en) * 2009-01-20 2009-07-15 长江水利委员会长江勘测规划设计研究院 Built-in joint meter and method for detecting openness of slit

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103048056A (en) * 2012-12-18 2013-04-17 东南大学 Determination method of probability density of sunshine temperature difference acquisition sample
CN103048056B (en) * 2012-12-18 2014-09-10 东南大学 Determination method of probability density of sunshine temperature difference acquisition sample
CN105200954A (en) * 2015-09-25 2015-12-30 中国电建集团成都勘测设计研究院有限公司 Method for classifying concrete dam cracks
CN108716904A (en) * 2018-04-09 2018-10-30 水利部南京水利水文自动化研究所 Dam deflection acquisition methods based on limited inclinometer measuring point measured value
CN108716904B (en) * 2018-04-09 2020-05-05 水利部南京水利水文自动化研究所 Dam body deflection obtaining method based on measuring point measuring value of finite inclinometer
CN111089544A (en) * 2020-03-19 2020-05-01 浙江交工集团股份有限公司 Tunnel monitoring measurement data analysis method based on maximum entropy method reliability theory

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Application publication date: 20120912