CN111931379A - Rockfall size and recurrence period prediction method thereof - Google Patents
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Abstract
The invention relates to a rockfall size and a resurgence period prediction method thereof, which comprises the following steps: acquiring the occurrence frequency n of a rockfall event and the rockfall volume v of an observation field within the observation time length t; obtaining a rockfall volume threshold vt(ii) a Correcting the observation time length t according to the occurrence times n of the rock falling events to obtain a calculation time length t; constructing a rockfall event occurrence frequency probability model and a rockfall size probability model; constructing annual maximum value v of falling rock size according to falling rock event occurrence frequency probability model and falling rock size probability modelmA probabilistic model of (2); obtaining annual maximum value v of rockfall sizemA preset probability value of the probability model of (1); according to preset probability value and annual maximum value v of rockfall sizemIs obtained by a probabilistic modelAnd predicting the maximum falling rock size and the recurrence period of the field to be measured according to the maximum falling rock size and the recurrence period model thereof. The method can predict the maximum size of future falling rocks of a certain field and the reappearance period of the falling rocks.
Description
Technical Field
The invention relates to the technical field of rockfall size prediction, in particular to a rockfall size and a rockfall recurrence period prediction method.
Background
With the advance of the western strategy, the network of highway and railway traffic is continuously perfected. In recent years, a large number of bridges and tunnels are built for both western mountain traffic construction and planning. Dangerous rockfall is the most common natural disaster in mountainous areas in China, and the rockfall disaster is extremely large in destructiveness and unpredictability, so that the rockfall is one of the most important limiting factors for the great development of western traffic construction in China. For example, in the Bao line built in the 50 s of the 20 th century, 26 tunnels with open cut holes more than 40m are grown in the Bao chicken-Mianyang period due to the threat of cave mouth collapse and rockfall disasters. According to statistics, in 1971 to 1992, rockfall 214 occurs 238 times in the north section of the adult railway, and the running is interrupted for 910 hours and 16 minutes.
For the design of the rockfall protection structure of the traffic road, the determination of the size (corresponding to the volume or weight of the rockfall) and the recurrence period of the rockfall is a precondition for determining the rockfall load. Because the occurrence of the rockfall event has larger uncertainty, the spatio-temporal characteristics of the rockfall disaster can be researched by utilizing a probability statistics method according to historical observation data by referring to natural disasters such as earthquake, flood and the like so as to evaluate the intensity (destructive power) and frequency (recurrence period) of the rockfall disaster, but at present, a prediction method system of the intensity-recurrence period is not established for disasters such as earthquake, flood and the like.
Disclosure of Invention
The invention aims to provide a rockfall size and a rockfall recurrence period prediction method, which can predict the maximum future rockfall size and the rockfall recurrence period of a certain site.
In order to achieve the purpose, the invention provides the following scheme:
a rockfall size and its recurrence period prediction method includes:
acquiring the occurrence frequency n of a rockfall event and the rockfall volume v of an observation field within the observation time length t;
obtaining a rockfall volume threshold vt；
Correcting the observation time length t according to the occurrence times n of the rock falling events to obtain a calculation time length t;
constructing a rockfall event occurrence frequency probability model and a rockfall size probability model;
constructing a annual maximum value v of the falling rock size according to the falling rock event occurrence frequency probability model and the falling rock size probability modelmA probabilistic model of (2);
obtaining the annual maximum value v of the size of the falling rocksmA preset probability value of the probability model of (1);
according to the preset probability value and the annual maximum value v of the size of the falling rocksmThe probability model of (2) obtains the maximum rockfall size and the model of the recurrence period thereof,
and predicting the maximum falling rock size and the recurrence period of the field to be tested according to the maximum falling rock size and the recurrence period model thereof.
Optionally, predicting the maximum rockfall size and the recurrence period of the site to be tested according to the maximum rockfall size and the recurrence period model thereof, including:
acquiring the actual observation time length t of the field to be measured1And during said actual observation time period t1Number of occurrences of falling rocks n1And rockfall volume v1；
According to the occurrence frequency n of the rock falling event1For the actual observation time length t1Correcting to obtain the actual calculation time length t1；
According to the probability model of the occurrence times of the rock falling events and the occurrence times n of the rock falling events1And the actual calculation time length t1Calculating annual incidence rate lambda of rockfall events1；
According to the rockfall volume v1Rockfall volume threshold vtAnd obtaining a scale parameter sigma by a rockfall size probability model1Shape parameter of1And a position parameter mu1；
According to the annual incidence rate of the rockfall events lambda1Scale parameter σ1Shape parameter of1Position parameter mu1And obtaining the maximum rockfall size and the recurrence period of the site to be measured by the maximum rockfall size and the recurrence period model.
Optionally, using formulas
And correcting the observation time length t, wherein t is the calculation time length, t is the observation time length, and n is the occurrence frequency of the rockfall event.
Optionally, the probability model of the occurrence times of the rockfall event is a poisson distribution model.
Optionally, the rockfall size probability model is a generalized pareto distribution model.
Optionally, the probability model of the occurrence times of the rock falling event is
n is 0,1,2, wherein λ is a constant, λ>0, lambda is the mean value of the Poisson distribution and the variance of the Poisson distribution, n is the occurrence number of the rock fall event, and t is the calculation time length.
Optionally, the falling rock size probability model is
v is more than or equal to mu, 1+ (v-mu)/sigma is more than 0, wherein mu belongs to R as a position parameter, sigma is more than 0 as a scale parameter, belongs to R as a shape parameter, R represents the whole real number, and v is the rockfall volume.
Optionally, the annual maximum rockfall size vmIs a probabilistic model of
Wherein, P (v)mV) is less than or equal to the annual maximum value v of the size of falling rocksmMathematical expression of probability of falling rock volume v or less, F (v) being annual maximum value of falling rock size vmMethod for representing distribution function, e is base of natural logarithm, λ is constant, λ>0, lambda is the mean value of the Poisson distribution and the variance of the Poisson distribution, belongs to R as a shape parameter, v is the rockfall volume, mu belongs to R as a position parameter, and sigma is more than 0 as a scale parameter.
Optionally, the maximum rockfall size and its recurrence period model are
Wherein T is the rockfall recovery period, λ is a constant, λ>0, λ is both the mean and variance of the Poisson distribution, ∈ R is the shape parameter, vpFor the maximum rockfall size in T year, mu belongs to R as a position parameter, and sigma >0 is a scale parameter.
Optionally, the maximum likelihood method is adopted to carry out the scale parameter sigma1Is estimated and the shape parameter is calculated1Is estimated.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the occurrence characteristics of the rockfall disasters, the occurrence frequency of the rockfall events is considered according to the conditions that Poisson distribution is obeyed and rockfall size is obeyed generalized pareto distribution, a threshold value is introduced to avoid the influence of relatively small-sized rockfall on the rationality of a prediction result, based on an extreme value theory, a Poisson-generalized pareto composite extreme value model for evaluating the rockfall size and the recurrence period of the rockfall is established, the historical record of the rockfall events in a research site is taken as a sample database, and the maximum size and the recurrence period of the rockfall in the future of the site can be predicted by utilizing the extreme value model, so that an effective way is provided for rockfall disaster risk assessment, rockfall load determination and protection structure reliability design of a site in a hard mountain area.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method for predicting the size of falling rocks and their recurrence period according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a rockfall size and a rockfall recurrence period prediction method, which can predict the maximum future rockfall size and the rockfall recurrence period of a certain site.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The invention discloses a rockfall size and recurrence period prediction method, the whole implementation flow is shown in figure 1, and the method is summarized as follows:
1. generation of rockfall event record database
The rockfall events of the analyzed field are observed and recorded, and a rockfall event record database is formed by combining historical event collection and sorting, wherein the rockfall event record database comprises the occurrence times n of the rockfall events, the size (volume) v of the rockfall events, and the time length t (which can also be called as observation time length or recording time length) of the whole observation and recording period, namely the time window length from the occurrence time of the first rockfall event to the end of the observation period.
2. Rockfall volume threshold vtSetting of (2)
Since the falling rocks are impacted and broken into a plurality of falling rocks during the falling process, the actual observation records are often recorded not at the first time but after being broken, and the recorded falling rocks are smaller in size than the actual falling rocks. Based on this, by introducing a rockfall volume threshold vtWhen in subsequent analysis and calculation, only the falling rock volume v is statistically analyzed to be more than or equal to vtThereby reducing the influence of the falling rock data with smaller size on the analysis result.
3. Determination of the calculation time length t
Since rockfall recordings tend to start recording with a significant rockfall event, the window time between the last unrecorded rockfall event is often ignored. Therefore, to reduce the impact of the open window time on the analysis, a half of the regression period of the rockfall event is added on the basis of the recording time length t.
Thus, the calculation formula for obtaining the calculation time length t is as follows:
(1) wherein t is the recording time length, and n is the occurrence frequency of the rock falling event.
4. Probability statistical model of rock fall event occurrence times
Assuming that observed rock fall events are independent of each other and the occurrence of the rock fall event is a small probability event, a Poisson distribution (Poisson distribution) can be used to describe the probability of the occurrence number n of the rock fall event, that is, the value of the random variable n may be 0,1,2, …, and the probability that n takes a certain value is:
(2) in the formula, λ is a constant, λ >0, which is both the mean value and the variance of the poisson distribution, and can be estimated by using a maximum likelihood method:
(3) in the formula, λ1Is the estimated value of λ, representing the physical meaning of the annual incidence of rockfall events, in units: the next time/year; n is the occurrence number of rock fall events in units: secondly; t is the calculated time length, see formula (1), in units: and (5) year.
5. Probability statistical model of falling rock size
The size of the falling rocks can be described by their volume v, considered to obey a Generalized Pareto Distribution (GPD), and the distribution function of the random variable v is:
(4) in the formula, mu belongs to R as a position parameter, sigma is more than 0 as a scale parameter, belongs to R as a shape parameter, R represents the whole real number, and the parameter sigma sum can be calculated according to sample dataEstimating by maximum likelihood method, and taking the rockfall volume threshold v set in the above 2 as the position parameter mutI.e. mu-vt。
6. Probability statistical model of annual maximum value of rockfall size
From the foregoing 4 and 5, it can be seen that the occurrence number n of falling rock events follows poisson distribution, the falling rock size (volume) v follows generalized pareto distribution, and n and v are independent of each other, so that the annual maximum value v of the falling rock sizem(maximum of all falling rock events observed in one year) probability statistic feature description can be carried out by using Poisson-generalized pareto composite extreme value model, and distribution function of probability statistic feature is
(5) In the formula, P (v)mV) is less than or equal to v) is the annual maximum value v of the size (volume) of falling rocksmMathematical expression of probability of v or less, F (v) being the annual maximum value v of the size (volume) of falling rocksmMethod of representing distribution function, P (v)mV) is equivalent to F (v) and is a common expression method in probability and mathematical statistics; e is the base number of the natural logarithm; the other parameters are as before.
The above equation (5) establishes a relationship between the annual incidence of rockfall events λ and the rockfall volume v.
7. Maximum rockfall size and its recurrence period prediction
In practical applications, let equation (5) equal a given probability value p (0< p <1), resulting in
(6) In the formula, vpCalled "meet once in T year" maximum rockfall size, in units: m is3(ii) a T is the falling rock reappearance period, unit: and (5) year.
Substituting formula (5) for formula (6) to obtain the maximum falling rock size vp-the relation of the recurrence period T:
in practical applications, the preparation for predicting the size of a site rockfall and its recurrence period according to equation (7) includes:
step 1: substituting the calculated lambda of the formula (3) into the formula (7);
step 2: estimating the parameter sigma sum in the formula (7) according to the maximum likelihood method according to the sample data in the above 1 and 2;
and step 3: for the position parameter μ, the falling rock volume threshold v set in the above 2 is takentI.e. mu-vt；
Thus, the predicted maximum falling rock size v can be obtained according to equation (7)pAnd the corresponding recurrence period T.
The invention also discloses the following technical effects:
according to the invention, by combining the occurrence characteristics of rockfall disasters, Poisson distribution is obeyed according to the occurrence frequency of rockfall events, generalized pareto distribution is obeyed to rockfall size (represented by the volume of rockfall blocks), a rockfall volume threshold is introduced to solve the influence of relatively small rockfall size on the rationality of a prediction result, a Poisson-generalized pareto composite extreme value model is established, the maximum rockfall size of a researched area and the corresponding recurrence period can be predicted according to rockfall event historical record data, and an effective way is provided for building rockfall disaster risk assessment and protection structure reliability design in a hard mountain area.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A rockfall size and its recurrence period prediction method is characterized by comprising:
acquiring the occurrence frequency n of a rockfall event and the rockfall volume v of an observation field within the observation time length t;
obtaining a rockfall volume threshold vt；
Correcting the observation time length t according to the occurrence times n of the rock falling events to obtain a calculation time length t;
constructing a rockfall event occurrence frequency probability model and a rockfall size probability model;
constructing a annual maximum value v of the falling rock size according to the falling rock event occurrence frequency probability model and the falling rock size probability modelmA probabilistic model of (2);
obtaining the annual maximum value v of the size of the falling rocksmA preset probability value of the probability model of (1);
according to the preset probability value and the annual maximum value v of the size of the falling rocksmObtaining the maximum rockfall size and a model of the maximum rockfall size in the reappearance period by using the probability model;
and predicting the maximum falling rock size and the recurrence period of the field to be tested according to the maximum falling rock size and the recurrence period model thereof.
2. The method of claim 1, wherein predicting the maximum rockfall size and the recurrence period thereof in the site to be tested according to the maximum rockfall size and the recurrence period thereof model comprises:
acquiring the actual observation time length t of the field to be measured1And during said actual observation time period t1Number of occurrences of falling rocks n1And rockfall volume v1；
According to the occurrence frequency n of the rock falling event1For the actual observation time length t1Correcting to obtain the actual calculation time length t1；
According to the probability model of the occurrence times of the rock falling events and the occurrence times of the rock falling eventsNumber n1And the actual calculation time length t1Calculating annual incidence rate lambda of rockfall events1；
According to the rockfall volume v1Rockfall volume threshold vtAnd obtaining a scale parameter sigma by a rockfall size probability model1Shape parameter of1And a position parameter mu1；
According to the annual incidence rate of the rockfall events lambda1Scale parameter σ1Shape parameter of1Position parameter mu1And obtaining the maximum falling rock size and the recurrence period of the measured field by the maximum falling rock size and the recurrence period model.
3. A rockfall size and its recurrence period prediction method according to claim 1, wherein a formula is adopted
And correcting the observation time length t, wherein t is the calculation time length, t is the observation time length, and n is the occurrence frequency of the rockfall event.
4. The method of claim 1, wherein the probability model of the occurrence times of rockfall events is a poisson distribution model.
5. The method of claim 1, wherein the rockfall size probability model is a generalized pareto distribution model.
6. A rockfall size and its recurrence period prediction method according to claim 1 or 4, wherein the probability model of the number of occurrence times of rockfall events is
Wherein λ is a constant, λ>0, lambda is the mean value and the variance of the Poisson distribution, n is the occurrence number of the falling stone event, and t isThe length of time is calculated.
7. A rockfall size and its recurrence period prediction method according to claim 1 or 5, wherein the rockfall size probability model is
Wherein, mu belongs to R as a position parameter, sigma is more than 0 as a scale parameter, belongs to R as a shape parameter, R represents the whole real number, and v is the rockfall volume.
8. A rockfall size and its recurrence period prediction method according to claim 1, wherein the annual maximum rockfall size value vmIs a probabilistic model of
Wherein, P (v)mV) is less than or equal to the annual maximum value v of the size of falling rocksmMathematical expression of probability of falling rock volume v or less, F (v) being annual maximum value of falling rock size vmMethod for representing distribution function, e is base of natural logarithm, λ is constant, λ>0, lambda is the mean value of the Poisson distribution and the variance of the Poisson distribution, belongs to R as a shape parameter, v is the rockfall volume, mu belongs to R as a position parameter, and sigma is more than 0 as a scale parameter.
9. The method of claim 1, wherein the maximum rockfall size and its recurrence period model is
Wherein T is the rockfall recovery period, λ is a constant, λ>0, λ is both the mean and variance of the Poisson distribution, ∈ R is the shape parameter, vpThe maximum rockfall size is 'T year one time', mu belongs to R as a position parameter, and sigma is greater than 0 as a scale parameter.
10. The method of claim 2, wherein the size of falling rocks and the period of their recurrence are predicted by the methodIs characterized in that a maximum likelihood method is adopted to carry out a scale parameter sigma1Is estimated and the shape parameter is calculated1Is estimated.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102121999A (en) * | 2009-12-29 | 2011-07-13 | 韩国地质资源硏究院 | Contactless falling rock detection method using photo sensors |
| CN107247858A (en) * | 2017-08-10 | 2017-10-13 | 西南交通大学 | There is backfill arch open cut tunnel structure probability Reliability design method under rock-fall impact |
| CN110222369A (en) * | 2019-05-05 | 2019-09-10 | 西南交通大学 | A kind of impact force of falling stone calculation method for considering backfill cushioning layer material and strengthening |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102121999A (en) * | 2009-12-29 | 2011-07-13 | 韩国地质资源硏究院 | Contactless falling rock detection method using photo sensors |
| CN107247858A (en) * | 2017-08-10 | 2017-10-13 | 西南交通大学 | There is backfill arch open cut tunnel structure probability Reliability design method under rock-fall impact |
| CN110222369A (en) * | 2019-05-05 | 2019-09-10 | 西南交通大学 | A kind of impact force of falling stone calculation method for considering backfill cushioning layer material and strengthening |
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| Title |
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| VALERIO DE BIAGI等: "Estimation of the return period of rockfall blocks according to their size", 《NATURAL HAZARDS AND EARTH SYSTEM SCIENCES》 * |
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