CN112883335A - Real-time slope stability assessment method combining pore water pressure - Google Patents
Real-time slope stability assessment method combining pore water pressure Download PDFInfo
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Abstract
The invention discloses a real-time slope stability evaluation method combining pore water pressure, which comprises the following steps: obtaining the coordinates of the monitored points and the grid coordinates of the unmonitored points; acquiring monitoring data of the pore water pressure at the measuring point according to the monitoring point coordinates; judging a trend structure of the pore water pressure distributed in space according to the monitoring data; judging the autocorrelation structure of the spatial distribution of the pore water pressure according to the monitoring data and the trend structure; according to the autocorrelation structure and the trend structure, carrying out interpolation prediction on the area without the monitoring point to obtain a pore water pressure distribution field; inputting the pore water pressure distribution field into a slope stability analysis model; and calculating the real-time slope safety coefficient by using the slope stability analysis model to generate a real-time early warning signal. This patent has combined the uncertainty that pore water pressure distributes in the space, regards real-time side slope factor of safety as the early warning and judges the index, and the accuracy is good, and the suitability is strong.
Description
Technical Field
The invention relates to the technical field of slope monitoring, in particular to a real-time slope stability evaluation method combining pore water pressure.
Background
Rainfall is the most common factor inducing landslide hazards. In the rainfall process, rainwater infiltrates into the soil body to cause the increase of the pore water pressure of the soil body, the strength of the soil body is reduced, and therefore landslide disasters are caused. This is an important reason why most of shallow landslides occur. In the field of slope monitoring, although the prior art attempts to use pore water pressure as a monitoring indicator. However, the following problems are faced in the analysis of the slope safety pre-alarm by using the monitoring data of the pore water pressure: (1) the early warning threshold value based on the pore water pressure is difficult to be clear; (2) the spatial distribution of the pore water pressure has great randomness, and the pore water pressure of the monitoring point is likely not to reflect the safety state of the slope. For this reason, monitoring of pore water pressure is not commonly used in engineering practice.
Disclosure of Invention
The invention solves the technical problem of providing a real-time slope stability assessment method which not only can combine uncertainty of pore water pressure spatial distribution, but also can combine pore water pressure and slope safety coefficient for early warning judgment.
The invention provides a real-time slope stability evaluation method combined with pore water pressure, which comprises the following steps:
obtaining the coordinates of the monitored points and the grid coordinates of the unmonitored points;
acquiring monitoring data of the pore water pressure at the measuring point according to the monitoring point coordinates;
judging a trend structure of the pore water pressure distributed in space according to the monitoring data;
judging the autocorrelation structure of the spatial distribution of the pore water pressure according to the monitoring data and the trend structure;
according to the autocorrelation structure and the trend structure, carrying out interpolation on the area without the monitored point to obtain a pore water pressure distribution field;
inputting the pore water pressure distribution field into a slope stability analysis model;
and calculating the real-time slope safety coefficient by using the slope stability analysis model to generate a real-time early warning signal.
In one example, the method of "determining a trend structure of pore water pressure distribution spatially based on the monitoring data" is a regression analysis method, and the order of regression equation is determined by the following steps:
determining a smaller order i, wherein i is a natural number;
decision P based on order iFAnd ScvValue if PF>0.05, performing order reduction treatment, otherwise increasing the order to i +1, wherein ScvIs a cross-validation index;
if the order is raised to i +1, comparing the S after the step is raisedcvValue if ScvIs raised and its PFWhen the value reaches the preset value, the step is continuously increased until Scv(i+1)＜Scv(i) Or PF>Up to 0.05.
In one example, the method of "determining an autocorrelation structure of pore water pressure spatially distributed according to the monitoring data and the trend structure" includes:
and judging the autocorrelation structure of the pore water pressure distribution on the space by adopting a maximum likelihood estimation method and combining a Materrn equation.
In one example, the Materrn equation is as follows:
in the formula, hijIs the space distance between any two pore water pressure measuring points, v is a smooth parameter ranging from 0 to infinity, r is a range parameter, r (v) is a gamma equation, KvBessel formula class II, which is order v, R (h)ij) The self-correlation equation of the space distance of a plurality of pore water pressure measuring points is shown, and i and j are natural numbers.
In one example, the maximum likelihood estimation method satisfies the following equation:
wherein W is ═ XTV-1X,Q＝I-XW-1XTV-1X is a matrix containing trend structure and coordinate information of measured points, V is a covariance matrix of original spatial data, I is a unit matrix, θ is a vector, θ contains (V, r, s), n is the number of observation points, p is the number of elements in θ, and p is 3TX)-1XT) And z is the pore water pressure value of the observation point.
In one example, the method of interpolation prediction includes kriging interpolation prediction.
In one example, the step of inputting the pore water pressure distribution field into a slope stability analysis model further comprises:
slope stability analysis model established by slope stability analysis software
In one example, the method of "inputting the pore water pressure distribution field into a slope stability analysis model" includes:
and inputting the pore water pressure distribution field into a slope stability analysis model by utilizing the secondary development function of the slope stability analysis software.
The invention has the following beneficial effects: the monitoring method comprises the following steps: obtaining the coordinates of the monitored points and the grid coordinates of the unmonitored points; acquiring monitoring data of pore water pressure at the measuring point according to the monitoring point coordinates; judging a trend structure of the pore water pressure distributed in space according to the monitoring data; judging self-correlation structures of the pore water pressure distributed in space according to the monitoring data and the trend structure; according to the autocorrelation structure and the trend structure, interpolation prediction is carried out on the area without the monitored point to obtain a pore water pressure distribution field; inputting the pore water pressure distribution field into a slope stability analysis model; and calculating the real-time slope safety coefficient by using the slope stability analysis model to generate a real-time early warning signal. That is, the present invention is bound to the spatial distribution of pore water pressure with great uncertainty, thereby establishing a pore water pressure distribution field. And inputting the distribution field of the pore water pressure into a slope stability analysis model for modeling and slope stability calculation, thereby carrying out real-time stability evaluation on the slope. According to the invention, the problem that the autocorrelation characteristics of the spatial distribution of the pore water pressure are difficult to be clear is solved by judging the autocorrelation structure of the spatial distribution of the pore water pressure. By combining the slope stability analysis model and the pore water pressure field, the early warning judgment standard is converted into the slope safety coefficient with more engineering use experience and physical significance. Therefore, the method has good accuracy and strong applicability.
Drawings
FIG. 1 is a flow chart of the method for real-time slope stability assessment in combination with pore water pressure according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples. It should be noted that, if not conflicting, the embodiments of the present invention and the features of the embodiments may be combined with each other within the scope of protection of the present invention.
Referring to fig. 1, the present invention provides a real-time slope stability assessment method combining pore water pressure, including the following steps:
s1, obtaining the coordinates of the monitoring points and the grid coordinates of the unmonitored points;
the method for acquiring the coordinates of the monitored points and the grid coordinates of the unmonitored points can be acquired by means of site survey, a map, a coordinate measuring device, a sensor with a position detection function and the like, and the acquisition mode is not particularly limited herein.
S2, acquiring monitoring data of the pore water pressure at the measuring point according to the monitoring point coordinates;
the pore water pressure gauge can be arranged at a monitoring point of the side slope, and monitoring data of the pore water pressure of the monitoring point is obtained through the pore water pressure gauge.
S3, determining a trend structure of pore water pressure distribution in space according to the monitoring data;
linear regression was performed according to the least squares method, and the regression parameters of the data were obtained by the following formula:
wherein X is a matrix containing a trend structure and coordinate information of the measuring points, V is a covariance matrix of the monitoring points, and z is a pore water pressure value of the monitoring points. The order of the regression equation is usually assumed in the traditional regression analysis, and the required order of the regression equation is determined by adopting a PF value obtained by subtracting the Wald statistic from the F distribution. It is generally considered that when PF >0.05 of the regression equation, there is an overfitting phenomenon in the regression equation, and the higher-order regression equation should be subjected to order reduction. In addition, the accuracy of the regression equation is verified by adopting a leave-one-cross method.
Wherein the cross-validation index is obtained by the following formula:
in the formula (I), the compound is shown in the specification,
the residual value vector of the monitoring data is equal to the observed quantity of the pore water pressure of each point minus the corresponding trend structure value, and n is the total number of the monitoring points. Generally considered as cross-validation index ScvThe larger the regression function, the better the fit. That is, the present embodiment is implemented by means of regression analysis by determining the trend structure of the pore water pressure distribution in space.
Specifically, the trend structure of the pore water pressure distribution in space is judged by adopting a regression analysis method, and the order of the regression equation is determined by the following steps:
determining a smaller order i, wherein i is a natural number;
in the case where the decision is based on the order iPFAnd ScvValue if PF>0.05, performing order reduction treatment, otherwise increasing the order to i +1, ScvIs a cross-validation index;
if the order is raised to i +1, comparing the S after the step is raisedcvValue if ScvIs raised and its PFWhen the value reaches the preset value, the step is continuously increased until Scv(i+1)＜Scv(i) Or PF>Up to 0.05.
By the method, the order of the regression equation is not required to be assumed, and the self-adaption of the obtained trend structural equation can be more strongly combined with the distribution characteristics of the pore water pressure in the space.
S4, judging an autocorrelation structure of the spatial distribution of the pore water pressure according to the monitoring data and the trend structure;
in this embodiment, a maximum likelihood estimation method is used in combination with a matern equation to perform data autocorrelation determination on the distribution of the pore water pressure in the space, that is, a matern clustering method is used to estimate parameters of the matern clustering by a maximum likelihood estimation method. Wherein the Materrn equation is as follows:
in the formula, hijIs the space distance between any two pore water pressure measuring points, v is a smooth parameter ranging from 0 to infinity, r is a range parameter, gamma equation is shown as gamma, KvBessel formula class II, R (h), of order vij) An autocorrelation equation of spatial distance for several pore water pressure measurement points, R (h)ij) Used as a parameter for the interpolation prediction in the next step S5, i and j are both natural numbers.
The Materrn equation is governed by v and r, which is a spatial data autocorrelation equation with a flexible form. The autocorrelation distance of the data can be generally considered as R (h)ij) H is equal to 0.05sijThe value is obtained.
In one embodiment, the maximum likelihood estimation method satisfies the following equation:
wherein W is ═ XTV-1X,Q＝I-XW-1XTV-1X is a matrix containing trend structure and coordinate information of measured points, V is a covariance matrix of original space data, I is a unit matrix, θ is a vector, θ contains (V, r, s), n is the number of observed points, p is the number of elements in θ, and p is 3TX)-1XT) And z are displacement values of the observation points, and L (theta | y) is used as a parameter for estimating clustering in the Matern equation.
The method well avoids the traditional moment method-based judgment mode, so that the form of a self-correlation equation needs to be assumed. For the spatial distribution characteristics of pore water pressure, the uncertainty of the spatial distribution form is large, and the form of the autocorrelation equation is difficult to fix. By adopting the self-adaptive Matern equation and combining the maximum likelihood estimation, the autocorrelation structure of the pore water pressure in the spatial distribution can be determined under the condition of not assuming the form of the autocorrelation equation.
S5, carrying out interpolation on the unmonitored point area according to the autocorrelation structure and the trend structure to obtain a pore water pressure distribution field;
the interpolation prediction may be a prediction method such as a kriging interpolation prediction, and in this embodiment, the interpolation prediction is a kriging interpolation prediction. The pore water pressure of an unmeasured point in the space can be assumed as a space random variable, and the prediction and calculation of the pore water pressure of an unmeasured area adopt a linear unbiased interpolation estimation method, wherein the equation is as follows:
zkr,j＝μk(x0)+(z-μk0)Tβ(j)；
in the above formula, l is a vector having all values of 1. Beta is a(j)Is an interpolation weighting factor that contains all pairs of monitored points to unknown points,
lambda is the lagrange multiplier and,
is one n × neIs based on n observation points and neAnd (4) a non-measured point. Mu.sk0And the trend structure value of the observation point. Mu.sk(x0) About a spatial coordinate point x0The trend structure of (1) is obtained from the formula. Wherein, the formula of the covariance equation is as follows:
where Δ x, Δ y, Δ z are the intervals between any two points on the x, y, z axes, respectively, and R () is obtained from the matern equation of step S4.
And S6, inputting the pore water pressure distribution field into a slope stability analysis model.
In this embodiment, the "inputting the pore water pressure distribution field into the slope stability analysis model" includes: and establishing a slope stability analysis model by using slope stability analysis software, and inputting the pore water pressure distribution field into the slope stability analysis model by using a secondary development function of the slope stability analysis software.
The Slope stability analysis software is Slope stability analysis software (such as Slope/W, Flac, Abaqus and the like) based on a static balance method, a limit analysis method, a strength reduction method and the like. The secondary development function refers to a secondary development interface of the software. For example, the Slope/W and Abaqus can save and export the created models via files (e.g., Slope/W export ". xml" file, Abaqus export ". inp" file, etc.). The pore water pressure field can be input into the slope stability model by processing the file. And Flac has a secondary development language (Fish) which can realize the combination and operation of pore water pressure field and slope stability analysis models. It should be appreciated that there are many ways to couple pore water pressure distribution fields to slope stability analysis models, and are not limited herein.
The secondary development function of slope stability analysis software is combined with the pore water pressure distribution field and the slope stability analysis model, so that a user does not need to write a complex slope stability calculation program by himself, and the applicability of the method is improved.
And S7, calculating a real-time slope safety coefficient by using the slope stability analysis model, and generating a real-time pre-alarm signal.
And (4) according to the slope stability analysis model of the pore water pressure field in the step S6, performing slope stability analysis calculation. The slope stability analysis and calculation is realized by a calculation program carried by the slope stability analysis software. The computing program may be called by an application program, and the application program may be implemented in a variety of computing languages (e.g., JAVA and Python), and the implementation manner is not limited herein.
And the real-time slope safety coefficient is sent to a monitoring and early warning platform, so that the early warning platform carries out early warning judgment according to the real-time slope safety coefficient. The pre-warning decision threshold may be user defined. Preferably, the early warning judgment threshold value is usually set to be that the real-time safety coefficient of the side slope is smaller than 1.2.
In summary, the monitoring method of the present invention includes the following steps: obtaining the coordinates of the monitored points and the grid coordinates of the unmonitored points; acquiring monitoring data of the pore water pressure at the measuring point according to the monitoring point coordinates; judging a trend structure of the pore water pressure distributed in space according to the monitoring data; judging the autocorrelation structure of the spatial distribution of the pore water pressure according to the monitoring data and the trend structure; according to the autocorrelation structure and the trend structure, carrying out interpolation prediction on the area without the monitoring point to obtain a pore water pressure distribution field; inputting the pore water pressure distribution field into a slope stability analysis model; and calculating the real-time slope safety coefficient by using the slope stability analysis model to generate a real-time early warning signal. That is, the present invention incorporates a large uncertainty in the spatial distribution of pore water pressure, thereby establishing a pore water pressure distribution field. And inputting the distribution field of pore water pressure into a slope stability analysis model for modeling and slope stability calculation, thereby carrying out real-time stability evaluation on the slope. According to the method, the problem that the autocorrelation characteristics of the spatial distribution of the pore water pressure are difficult to define is solved through judging the autocorrelation structure of the spatial distribution of the pore water pressure. By combining the slope stability analysis model and the pore water pressure field, the early warning judgment standard is converted into the slope safety coefficient with more engineering use experience and physical significance. Therefore, the method has good accuracy and strong applicability.
The safety early warning method for geotechnical structures provided by the invention is described in detail, a specific example is applied in the method to explain the principle and the implementation mode of the invention, and the description of the example is only used for helping to understand the method and the core idea of the invention. Meanwhile, for a person skilled in the art, according to the idea of the present invention, the embodiments and the application range may be changed. In summary, the present disclosure is only an embodiment of the present disclosure, and not intended to limit the scope of the present disclosure, and all equivalent structures or equivalent flow transformations made by using the present disclosure and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present disclosure, and should not be construed as limiting the present disclosure.
Claims (8)
1. A real-time slope stability assessment method combined with pore water pressure is characterized by comprising the following steps:
obtaining the coordinates of the monitored points and the grid coordinates of the unmonitored points;
acquiring monitoring data of the pore water pressure at the measuring point according to the monitoring point coordinates;
judging a trend structure of the pore water pressure distributed in space according to the monitoring data;
judging the autocorrelation structure of the spatial distribution of the pore water pressure according to the monitoring data and the trend structure;
according to the autocorrelation structure and the trend structure, carrying out interpolation prediction on the area without the monitored point to obtain a pore water pressure distribution field;
inputting the pore water pressure distribution field into a slope stability analysis model;
and calculating the real-time slope safety coefficient by using the slope stability analysis model to generate a real-time early warning signal.
2. The method for real-time slope stability assessment in combination with pore water pressure as claimed in claim 1, wherein the method of "determining the trend structure of the spatial distribution of pore water pressure according to the monitored data" is a regression analysis method, and the order of the regression equation is determined by the following steps:
determining a smaller order i, wherein i is a natural number;
decision P based on order iFAnd ScvValue if PF>0.05, reducing the order, otherwise increasing the order to i +1, wherein ScvIs a cross-validation index;
if the order is raised to i +1, comparing the S after the step is raisedcvValue if ScvIs raised and its PFWhen the value reaches the preset value, continuing the step-up until Scv(i+1)＜Scv(i) Or PF>Up to 0.05.
3. The method for real-time slope stability assessment in combination with pore water pressure according to claim 1, wherein the method of "determining the autocorrelation structure of pore water pressure distribution spatially according to the monitoring data and the trend structure" comprises:
and judging the autocorrelation structure of the pore water pressure distribution on the space by adopting a maximum likelihood estimation method and combining a Materrn equation.
4. The method for real-time slope stability assessment in combination with pore water pressure according to claim 3 or wherein the Materrn equation is as follows:
in the formula, hijIs the space distance between any two pore water pressure measuring points, v is a smooth parameter ranging from 0 to infinity, r is a range parameter, gamma equation is shown as gamma, KvBessel formula of the second kind, R (h), of order vij) The self-correlation equation of the space distance of a plurality of pore water pressure measuring points is shown, wherein i and j are natural numbers.
5. The method for real-time slope stability assessment in combination with pore water pressure as claimed in claim 3, wherein the maximum likelihood estimation method satisfies the following formula:
wherein W is ═ XTV-1X，Q＝I-XW-1XTV-1X is a matrix containing a trend structure and coordinate information of measuring points, V is a covariance matrix of original space data, I is a unit matrix, theta is a vector, theta contains (V, r and s), n is the number of observation points, p is the number of elements in theta, and p is 3TX)-1XT) And z is the pore water pressure value of the observation point.
6. The method for real-time slope stability assessment in combination with pore water pressure according to claim 1, wherein the method of interpolation prediction comprises kriging interpolation prediction.
7. The method for real-time slope stability assessment in combination with pore water pressure as claimed in claim 1, further comprising before the step of inputting the pore water pressure distribution field into a slope stability analysis model:
and establishing a slope stability analysis model by using slope stability analysis software.
8. The method for real-time slope stability assessment in combination with pore water pressure according to claim 7 or the above, wherein the method of inputting the pore water pressure distribution field into the slope stability analysis model comprises:
and inputting the pore water pressure distribution field into a slope stability analysis model by utilizing the secondary development function of the slope stability analysis software.
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