CN112329349B - Slope reliability assessment method - Google Patents
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Abstract
The invention discloses a slope reliability evaluation method which comprises the process of constructing a kriging agent model containing a two-parameter correlation function. The evaluation method can obtain evaluation results with high precision, high accuracy and good stability under the condition of a small amount of deterministic slope stability analysis, and the evaluation process is simple and flexible.
Description
Technical Field
The invention relates to the technical field of slope engineering evaluation.
Background
Because uncertainty exists widely and objectively in geotechnical engineering, the method for analyzing the stability of the deterministic slope, which is commonly used in engineering, such as a finite element method and a limit balance method, has certain limitations by using the safety coefficient to measure the safety state of the slope. Therefore, in recent years, the slope reliability has been increasingly emphasized in engineering as an important index for evaluating the slope stability and uncertainty. However, the reliability analysis method generally has a larger calculation amount, a longer calculation time and a larger calculation resource occupation than the conventional method. Particularly, when the Monte Carlo simulation method is adopted, the problem of low calculation efficiency becomes more prominent. Therefore, how to accurately and efficiently calculate the slope reliability has very important theoretical significance and engineering value.
In view of the above computational efficiency problem, the proxy model is widely proposed and applied to slope reliability assessment. The kriging method is widely used among various proxy models due to its ability to accurately predict unknown point results and to evaluate uncertainty of the predicted results. Generally, the method mainly uses a theoretical correlation function to model the observation data correlation structure. However, the correlation function has an important influence on the prediction result, so how to select a proper correlation function is important in the kriging method. However, in the existing method, a function model is generally randomly selected from different single-parameter theoretical correlation functions based on experience, such as a single exponential type, a square exponential type and the like, so that model uncertainty is increased for the implementation process of the kriging method, further deviation is generated between a prediction result and an actual situation, and accurate evaluation of reliability is finally influenced.
Disclosure of Invention
The invention aims to provide a slope reliability assessment method capable of adaptively selecting a correlation function, which has the advantages of good reliability assessment stability, high precision, flexibility and accuracy.
The invention firstly provides the following technical scheme:
a slope reliability assessment method comprises the step of constructing a kriging proxy model containing a two-parameter correlation function.
According to some preferred embodiments of the invention, the two-parameter correlation function is set as:
where ρ represents the correlation between sample points; d represents the distance between sample points; v represents a smoothing coefficient, and the value range of v is more than 0 and less than or equal to infinity; θ represents a correlation coefficient; Γ (·) represents a gamma function; k v (. Cndot.) represents a second modified Bessel function of order v.
In this embodiment, the two-parameter correlation function is a two-parameter correlation function in a one-dimensional state.
According to some preferred embodiments of the invention, the two-parameter correlation function is set as:
where m represents the input data dimension, and θ and v represent the correlation coefficient and the smoothing coefficient in the form of multidimensional vectors, respectively.
In this embodiment, the two-parameter correlation function is a two-parameter correlation function in a multidimensional state.
According to some preferred embodiments of the present invention, the evaluation method further comprises obtaining a two-parameter optimum value of the kriging proxy model by a genetic algorithm.
According to some preferred embodiments of the present invention, the optimization objective function of the kriging proxy model is set as follows:
wherein σ 2 Representing variance and R a correlation matrix.
According to some preferred embodiments of the invention, the correlation matrix is arranged as follows:
wherein x is 1 To x m Representing the input variable, p (x) i ，x j ) Representing the correlation between variables.
According to some preferred embodiments of the invention, the random error term z (x) of the kriging proxy model is set as follows:
wherein E (z (x)) represents expectation; var (z (x)) represents variance; cov (z (x) i )，z(x j ) ) represents the variable x i And x j The covariance between.
According to some preferred embodiments of the present invention, the evaluation method further includes establishing a parameter-determined kriging proxy model based on the two-parameter optimal value, and substituting a monte carlo sample into the parameter-determined kriging proxy model to perform slope stability monte carlo simulation calculation.
According to some preferred embodiments of the present invention, based on the slope stability safety factor obtained by the monte carlo simulation, the following slope failure probability P is obtained f ：
Wherein, FS i Representing the safety factor obtained by simulation; i (·) represents an indication function, I (·) =1 when the safety factor is less than 1, and I (·) =0 when the safety factor is equal to or greater than 1.
According to some preferred embodiments of the invention, the method of evaluating comprises:
s1, establishing a stability analysis model for a slope project to be evaluated;
s2, obtaining an initial training sample;
s3, establishing a kriging proxy model containing double parameters based on the training sample;
s4, obtaining a safety coefficient after simulation through Monte Carlo simulation based on the kriging agent model determined by the parameters;
and S5, obtaining the failure probability of the side slope based on the simulated safety coefficient.
According to some preferred embodiments of the present invention, the stability analysis model in step S1 is constructed based on a slope geometric model, a rock-soil constitutive model, a potential sliding surface setting and a shear strength requirement;
according to some preferred embodiments of the present invention, the step S2 comprises:
s21, generating N based on soil body parameter statistical indexes 1 Grouping shear strength samples obeying a specified random distribution;
s22, introducing the shear strength samples into the stability analysis model to obtain a safety coefficient corresponding to each group of shear strength;
and S23, combining each group of shear strength and the corresponding safety coefficient into the training sample.
According to some preferred embodiments of the present invention, the step S4 includes:
s41, generating N based on soil parameter statistical indexes 2 A set of monte carlo samples;
s42, inputting the Monte Carlo sample into the Crigy agent model determined by the parameters for Monte Carlo(iv) TerCarlo simulation analysis to obtain N 2 The secondary safety factor.
The invention has the following beneficial effects:
in the evaluation method, the used model uses a double-parameter correlation function, and the smooth coefficient is adjusted to represent different single-parameter correlation functions in a Matern family, so that the correlation structure can be adaptively adjusted in a Krigin method, and optimal fitting parameters are selected to construct the proxy model.
Compared with a single-parameter correlation function Kriging model, the evaluation method provided by the invention can be used for synchronously optimizing the smooth coefficient and the correlation coefficient through a genetic algorithm based on a small amount of deterministic slope stability analysis results, so that a self-adaptive evaluation model is obtained. The method can improve the evaluation accuracy, and has the advantages of innovative conception and good actual engineering value.
The method can effectively improve the calculation precision of the failure probability, the slope failure probability error obtained by evaluation is smaller than that of the traditional method, and meanwhile, the method is simple in steps and stable in result.
Drawings
Fig. 1 is a schematic diagram of slope stability evaluation in example 1.
Detailed Description
The present invention is described in detail below with reference to the following embodiments and the attached drawings, but it should be understood that the embodiments and the attached drawings are only used for the illustrative description of the present invention and do not limit the protection scope of the present invention in any way. All reasonable variations and combinations included within the spirit of the invention are within the scope of the invention.
Slope reliability assessment is performed by the following procedure:
s1, establishing a stability analysis model for the slope engineering to be evaluated.
The stability analysis model is constructed based on a slope geometric model, a rock-soil constitutive model, a potential sliding surface setting and a shear strength requirement.
The stability analysis model can be analyzed by methods such as a simplified Bishou method and the like.
And S2, obtaining an initial training sample.
It may further comprise:
s21, generating N based on soil body parameter statistical indexes 1 Groups were subjected to a specified random distribution of shear strength samples.
In the specific implementation, samples which do not accord with the physical and mechanical significance, such as a negative value of the soil shear strength index, are avoided.
S22, introducing the samples generated in the step S21 into the stability analysis model obtained in the step S1, and obtaining a safety factor corresponding to each group of shear strength.
And S23, combining each group of shear strength and the corresponding safety coefficient into the training sample.
And S3, establishing a kriging proxy model containing double parameters based on the training sample.
The two parameters include a smoothing coefficient and a correlation coefficient, which are related structural parameters of the kriging proxy model.
Further, the correlation function of the kriging proxy model selects a two-parameter correlation function (WM).
Wherein:
the one-dimensional WM is set as follows:
where ρ represents the correlation between sample points; d represents the distance between sample points; nu represents a smoothing coefficient, and the value range of nu is more than 0 and less than or equal to v and more than or equal to infinity; θ represents a correlation coefficient; Γ (·) represents a gamma function; k ν (. Cndot.) represents a second class of modified Bessel function of order v.
The multidimensional WM settings were as follows:
wherein m represents the input data dimension, and θ and ν represent the correlation coefficient and the smoothing coefficient in the form of multidimensional vector, respectively.
S32, obtaining the optimal value of the related structure parameter through a genetic algorithm.
Setting an optimization objective function ψ of the kriging proxy model as follows:
wherein σ 2 Representing variance, R represents a correlation matrix, which may be further set as follows:
wherein x is 1 To x m Representing an input variable, p (x) i ，x j ) Representing the correlation between variables.
Setting a Gaussian process random error term z (x) in the Krigin proxy model, wherein the Gaussian process random error term z (x) meets the following conditions:
wherein E (z (x)) represents desired; var (z (x)) represents the variance; cov (z (x) i )，z(x j ) ) represents x i And x j The covariance between.
And searching the minimum value of the optimization objective function through a genetic algorithm according to the random error term, and further determining the optimal related structure parameters.
S33, establishing a Krigin agent model determined by the parameters based on the optimal values of the related structure parameters.
And S4, obtaining a safety coefficient calculated by the proxy model through Monte Carlo simulation based on the kriging proxy model determined by the parameters.
It may further comprise:
s41 generating N based on soil parameter statistical indexes 2 A set of monte carlo samples;
s42, mixing the MonteInputting the Carlo sample into the Critical agent model determined by the parameters, and performing Monte Carlo simulation analysis to obtain N 2 The secondary safety factor.
The process requires replacing the slope stability analysis with a kriging proxy model for monte carlo simulation analysis.
And S5, calculating the obtained safety coefficient based on the agent model to obtain the slope failure probability.
Wherein the probability of slope failure P f Can be expressed as follows:
wherein, FS i Representing the simulated safety factor; i (·) denotes an indication function, I (·) =1 when a safety factor is less than 1, and I (·) =0 when the safety factor is equal to or greater than 1.
Example 1
As shown in the attached figure 1, the reliability of a three-layer soil slope is evaluated by the evaluation method of the invention.
The three-layer soil weight of the three-layer soil slope is 19.5kN/m 3 And the shear strength of the soil on the 1 st layer is a constant, the cohesive force is 0, the internal friction angle is 38 degrees, and the cohesive force and the internal friction angle of the soil on the 2 nd and 3 rd layers are random variables obeying normal distribution. In order to avoid that the samples lose physical significance due to the negative value generated by the normal distribution, the samples within three times of standard deviation of the mean value of the random variable are taken as effective samples. The average values of cohesive force of the 2 nd layer soil and the 3 rd layer soil are 5.3kPa and 7.2kPa respectively, and the coefficient of variation is 0.3. The mean values of the internal friction angles of the 2 nd and 3 rd layers of soil are 23 degrees and 20 degrees respectively, and the coefficient of variation is 0.2.
The soil parameters are averaged and a simplified Bishou method is used for deterministic slope stability analysis to obtain a sliding surface with the minimum safety coefficient, namely the sliding surface is called a critical sliding surface, as shown in the mark of figure 1.
On this basis, the following reliability evaluations were performed:
step 1: modeling the slope engineering to be evaluated, establishing a model comprising a slope geometric model, potential slip surface parameters, a geotechnical constitutive model and shear strength parameters, and selecting a simplified Bischopper method to calculate the safety coefficient. The stability analysis is based on the principle of ultimate balance, the sliding soil body is regarded as a rigid body rotating around the circle center, the soil body is divided into a plurality of strip-shaped units through a strip division method, and the sliding moment and the anti-sliding moment of the soil body are respectively calculated. The safety factor FS of the obtained whole slope is shown as the following formula:
wherein M is R Is the total anti-skid moment of all soil strips, M A Is the total slip moment of all the soil strips. In the model of the embodiment, slope stability analysis is performed on a deterministic slope model formed based on the mean value of the shear strength of the soil body, and the safety coefficient of the slope is 1.382.
Step 2: and generating 60 groups of samples which are subjected to random distribution based on the soil parameter statistical indexes. In the embodiment, the cohesive force and the internal friction angle of the soil bodies on the 2 nd and 3 rd layers are random variables, and a 4 × 60 random sample matrix conforming to normal distribution is generated based on the soil body shear strength statistical index. For example, the expression [5.26,29.31,9.11,14.35] is a set of random samples, wherein the first term and the second term are respectively the cohesive force and the internal friction angle of the second layer of soil body, and the third term and the fourth term are respectively the cohesive force and the internal friction angle of the third layer of soil body. Importing the safety coefficient corresponding to each group of samples into deterministic slope stability calculation to be used as a training sample for a Krigin model;
and step 3: based on a training sample, searching and optimizing related structures and parameters including related coefficients and smooth coefficients by using the WM model and the genetic algorithm in the specific implementation mode, and establishing a Krigin agent model. Based on experience and trial calculation results, initial population parameters in the genetic algorithm are set to be 50, the maximum propagation algebra is set to be 100, the generation ditches are set to be 0.99, the cross probability is set to be 0.7, and the mutation probability is set to be 0.01. Searching the minimum value of the optimization objective function and the corresponding correlation coefficient and smooth coefficient thereof to form an optimal solution through a genetic algorithm based on global optimization, thereby establishing a kriging agent model based on double parameters.
And 4, step 4: generating 1 x 10 based on soil parameter statistical index 5 The set of Monte Carlo samples is 4 × (1 × 10) in this embodiment 5 ) And (4) matrix. Inputting each group of Monte Carlo samples as input data into the proxy model, and calculating the safety factor to obtain 1 × 10 5 A safety factor;
and 5: and taking the safety coefficient less than 1 as a failure sample, counting to obtain 1310 the number of the failure samples, and obtaining 1.31 percent of failure probability of the slope.
Example 2
The evaluation method of example 1 was compared with different conventional kriging methods, wherein the most common correlation functions of the single exponential and the square exponential in slope engineering were analyzed as the comparison model, and the calculation model, the training sample and the monte carlo sample settings were all kept the same as in example 1. The results of the conventional monte carlo simulation reliability calculation were compared as reference results, and the evaluation results are shown in table 1.
Wherein:
the single exponential correlation function is expressed as follows:
ρ＝exp(-θ·|d|)
the square exponential correlation function is expressed as follows:
ρ＝exp(-θ·d 2 )
where ρ represents the correlation between sample points; d represents the distance between sample points; θ represents a correlation coefficient;
TABLE 1 evaluation of the reliability of the different methods
Compared with the calculation result of the correlation function of the square exponential type and the single exponential type commonly used in the traditional kriging method, the method has the advantages that the relative error is effectively reduced, and therefore the calculation accuracy of the kriging proxy model can be effectively improved.
The above examples are merely preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples. All technical schemes belonging to the idea of the invention belong to the protection scope of the invention. It should be noted that modifications and adaptations to those skilled in the art without departing from the principles of the present invention should also be considered as within the scope of the present invention.
Claims (8)
1. A slope reliability assessment method is characterized in that: the evaluation method comprises the steps of constructing a kriging proxy model containing a double-parameter correlation function; in the two-parameter correlation function, a one-dimensional two-parameter correlation function is set as follows:
where ρ represents the correlation between sample points; d represents the distance between sample points; v represents a smoothing coefficient, and the value range of v is more than 0 and less than and equal to infinity; θ represents a correlation coefficient; Γ (·) represents a gamma function; k is ν (. H) represents a second modified Bessel function of order v; the multidimensional two-parameter correlation function is set as:
wherein m represents the input data dimension, and θ and ν represent the correlation coefficient and the smoothing coefficient in the form of multidimensional vector, respectively.
2. The evaluation method according to claim 1, wherein: the evaluation method further comprises the step of obtaining the two-parameter optimal value of the kriging agent model through a genetic algorithm.
3. The evaluation method according to claim 2, wherein: the optimization objective function of the kriging proxy model is set as follows:
wherein σ 2 Representing variance and R a correlation matrix.
4. The evaluation method according to claim 3, wherein: the correlation matrix is set as follows:
wherein x is 1 To x m Representing the input variable, p (x) i ，x j ) Representing the correlation between variables.
5. The evaluation method according to claim 2, wherein: the random error term z (x) of the kriging proxy model is set as follows:
wherein E (z (x)) represents expectation; var (z (x)) represents the variance; cov (z (x) i )，z(x j ) ) represents a variable x i And x j The covariance between them.
6. The evaluation method according to claim 2, wherein: and the evaluation method also comprises the steps of establishing a kriging proxy model determined by the parameters based on the double-parameter optimal value, and substituting the Monte Carlo sample into the kriging proxy model determined by the parameters to carry out slope stability Monte Carlo simulation calculation.
7. The evaluation method according to claim 6, wherein: based on the slope stability safety coefficient obtained by Monte Carlo simulation, the following slope failure probability is obtainedP f ：
Wherein, FS i Representing the safety factor obtained by simulation; i (·) represents an indication function, I (·) =1 when the safety factor is less than 1, and I (·) =0 when the safety factor is equal to or greater than 1.
8. The evaluation method according to claim 1, wherein: the method comprises the following steps:
s1, establishing a stability analysis model for a slope project to be evaluated;
s2, obtaining an initial training sample;
s3, establishing a kriging proxy model containing double parameters based on the training sample;
s4, obtaining a safety coefficient after simulation through Monte Carlo simulation based on the kriging agent model determined by the parameters;
s5, obtaining the failure probability of the side slope based on the simulated safety coefficient;
the stability analysis model in the step S1 is constructed based on a slope geometric model, a rock-soil constitutive model, a potential sliding surface setting and a shear strength requirement;
the step S2 includes:
s21, generating N based on soil body parameter statistical indexes 1 Grouping shear strength samples obeying a specified random distribution;
s22, introducing the shear strength samples into the stability analysis model to obtain a safety coefficient corresponding to each group of shear strength;
s23, combining each group of shear strength and the corresponding safety coefficient to form the training sample;
the step S4 includes:
s41 generating N based on soil parameter statistical indexes 2 A set of monte carlo samples;
s42, inputting the Monte Carlo sample into the kriging agent model determined by the parameters for Monte Carlo simulationAnalyzing to obtain N 2 The secondary safety factor.
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