CN111914454A - Performance-based slope earthquake vulnerability assessment method - Google Patents
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Abstract
The invention relates to a performance-based slope earthquake vulnerability assessment method, which comprises the following steps: firstly, aiming at the deformation and damage characteristics of the side slope under the earthquake load, selecting earthquake permanent displacement as an earthquake resistance evaluation index, and making a regulation on vulnerable states of different performance levels; then, respectively quantitatively representing the uncertainty of earthquake motion and rock-soil body parameters in the slope dynamic stochastic system by adopting a stochastic earthquake motion model and a stochastic field theory, and analyzing the probability density evolution characteristic of the slope earthquake permanent displacement based on the probability density evolution theory; and calculating the conditional probability of the slope exceeding different performance levels under the seismic loads with different strengths, and constructing seismic vulnerability assessment curves of different vulnerability states. Compared with the prior art, the method has high calculation efficiency, can analyze the probability levels of the slope in different performance states, and provides a more comprehensive, systematic and reliable vulnerability assessment result.
Description
Technical Field
The invention relates to the technical field of earthquake geological disaster risk assessment, in particular to a performance-based slope earthquake vulnerability assessment method.
Background
The earthquake stability analysis of the slope engineering has great significance for preventing and controlling the slope earthquake geological disaster. In the field of slope engineering, most of the existing earthquake-resistant design and evaluation are based on a pseudo-static analysis method based on a limit balance theory, and the influence of uncertainty factors on the earthquake-resistant performance of the slope is not considered.
The earthquake vulnerability analysis is one of probability analysis methods, can represent the influence of uncertainty on the earthquake resistance of the system, gives out the conditional probability that the system exceeds different damage states under the earthquake action of different intensities, is the most core part in the framework of a seismic engineering method based on performance, and is widely applied to earthquake disaster prediction, earthquake risk evaluation, earthquake restoration scheme optimization and decision making. However, the traditional earthquake vulnerability analysis methods have two types, firstly, the fitting of an empirical model is carried out based on survey data or test data after earthquake disaster, but a large amount of survey data after earthquake is difficult to obtain; and secondly, a large amount of numerical calculation is carried out based on methods such as incremental dynamic analysis, a cloud graph method, Monte Carlo random simulation and the like, and a seismic vulnerability analysis curve of the system is fitted by assuming a probability distribution form in combination with moment estimation or maximum likelihood estimation, so that the method has the defects of low calculation efficiency, undetermined rationality of the assumed distribution form and the like. In addition, in the field of analysis of earthquake vulnerability related to the side slope, the vulnerability of engineering structures such as structures and roads is mostly concentrated on analyzing the vulnerability of the side slope under the influence of geological disasters, and the vulnerability of the side slope under the action of the earthquake is not considered, so that a reasonable and objective evaluation result cannot be given.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a performance-based slope earthquake vulnerability assessment method.
The purpose of the invention can be realized by the following technical scheme:
a performance-based slope earthquake vulnerability assessment method comprises the following steps:
s1, selecting earthquake permanent displacement as a slope earthquake resistance evaluation index, and defining different earthquake resistance level requirements and corresponding vulnerable state evaluation indexes of the slope;
establishing a side slope earthquake power time-course analysis model of the actual side slope engineering;
establishing a rock-soil body parameter random field model representing the spatial variability of the slope rock-soil body parameters;
generating a series of random earthquake motion acceleration sample time courses meeting specific site conditions based on a random earthquake motion model according to the site conditions of the slope engineering;
s2, coupling the generated series of random earthquake dynamic acceleration sample time ranges and rock-soil body parameter random field models to the established slope earthquake dynamic time range analysis model, and obtaining a series of slope earthquake permanent displacements by adopting a dynamic time range analysis method;
s3, constructing a generalized probability density evolution equation of the slope earthquake permanent displacement, substituting the series of slope earthquake permanent displacements into the equation, and solving to obtain the probability density evolution characteristic of the slope earthquake permanent displacement;
s4, based on the probability density evolution characteristics of the permanent displacement of the side slope earthquake, combining the side slope displacement evaluation criterion, calculating the conditional failure probability of the side slope exceeding different earthquake resistance performance level requirements under the action of different earthquake intensities, and constructing a side slope earthquake vulnerability analysis curve.
Preferably, the slope vibration force time-course analysis model is based on finite elements or finite difference.
Preferably, the rock-soil body parameter random field model is established by adopting a KL decomposition method.
Preferably, the KL decomposition method has the formula:
wherein, mukAnd σkRespectively representing the mean value and the standard deviation of the rock-soil body parameters;representing standard normal random variables which are independent of each other;representing external spatial coordinates; (x, y) represent the random field model coordinates of the two-dimensional structural system Ω; lambda [ alpha ]iAndrespectively representing the characteristic value and the characteristic function of the rock-soil body autocorrelation function; n represents the number of terms of the expansion order number,and representing a rock-soil body parameter two-dimensional random field.
Preferably, the process of generating the series of random seismic oscillation acceleration sample time courses meeting the specific site conditions adopts a spectral representation method, which specifically comprises the following steps:
wherein,representing an evolved power spectral density function of non-stationary random seismic oscillations; { Xk,Yk} (k ═ 1,2,3 … N) denotes orthonormal random variables; Δ ω represents a frequency interval;representing the seismic motion random process, k representing the number of terms and N representing the total number of terms.
Preferably, the generalized probability density evolution equation of the permanent displacement of the slope earthquake specifically comprises:
the initial condition of this equation is ρYθ(y,θ,t0)=ρYθ(θ,t)(y-y0) The boundary condition is rhoyθ(y,θ,t0)|y→±∞0, where ρYθ(y, theta, t) represents the joint probability density function of y (t) and theta, represents the Dirac function, and y (t) and theta are respectively shownShowing the time course of displacement and variables characterizing randomness,time derivative, y, representing the time course of the displacement0Denotes the initial value of the displacement, t0Indicating the initial time.
Preferably, the S1 includes: firstly, a high-dimensional probability space formed by representing rock-soil body parameters and seismic motion uncertain random variables is subdivided, representative sample points are selected, and then a rock-soil body parameter random field model and a series of random seismic motion acceleration sample time courses are established.
Preferably, in the step S1, according to the survey data of the established slope engineering, the probability statistical characteristics of the rock-soil body parameters are analyzed, and a rock-soil body parameter random field model representing the spatial variability of the slope rock-soil body parameters is established by combining a random field theory.
Preferably, in S3, a finite difference algorithm is used to solve to obtain the probability density evolution characteristic of the permanent displacement of the slope earthquake.
Preferably, the representative sample site is selected from vibration and soil parameters.
Compared with the prior art, the invention has the following advantages:
1. the method is high in calculation efficiency, can analyze the probability levels of different performance states of the side slope, provides a more comprehensive, systematic and reliable vulnerability assessment result, and has certain guiding significance for evaluating the risk of the earthquake geological disaster of the side slope, designing the earthquake resistance of the side slope, optimizing the performance and the like.
2. The conventional slope earthquake stability analysis takes the safety coefficient as an evaluation index, and different damage states and earthquake resistance of the slope under earthquake load cannot be represented; the method is based on the dynamic destruction characteristics of the side slope, adopts the earthquake permanent displacement as the evaluation index of the side slope, and defines the evaluation criteria of different vulnerable states.
3. In the existing earthquake vulnerability method, the randomness of earthquake motion is generally represented by selecting a certain number of earthquake sample time courses, but the selected earthquake motion time courses cannot meet specific engineering field conditions, and the number is small, so that the uncertainty of the earthquake motion cannot be well represented; the method is based on a random earthquake motion model, and a series of random earthquake motion samples are generated based on an engineering field to represent the uncertainty of earthquake motion.
4. The existing earthquake vulnerability analysis method generally ignores the spatial variability of rock-soil body parameters; based on a random field theory, a series of random field models are generated by adopting a KL decomposition method to quantitatively represent the spatial variability of the parameters of the slope rock-soil body.
5. In the prior art, the construction of vulnerability analysis curves is obtained based on a specific probability distribution hypothesis; the probability of the slope exceeding different vulnerability states under the earthquake load with different strengths is directly solved based on the probability density evolution theory, and the earthquake vulnerability analysis curves of the slope in different vulnerability states are directly constructed.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a finite element power time course analysis model of a slope in an embodiment;
FIG. 3 is a schematic diagram of two typical slope cohesive force and internal friction angle random field models, wherein (a) and (b) are schematic diagrams of the cohesive force and the friction angle of the random field model 1, respectively, and (c) and (d) are schematic diagrams of the cohesive force and the friction angle of the random field model 2, respectively;
FIG. 4 (a), (b), (c), and (d) are schematic diagrams of 4 typical random seismic acceleration time-course samples of a specific field in the example, respectively;
FIG. 5 is a graph of the cumulative distribution function of the permanent displacement of the slope earthquake under the earthquake load of 0.3g in the embodiment;
FIG. 6 is an earthquake vulnerability analysis curve of the lower slope influenced by the composite random factors in the embodiment.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, the application provides a performance-based slope earthquake vulnerability assessment method, which includes the following 3 major links: selecting a slope earthquake vulnerability state evaluation index and an evaluation criterion, quantitatively representing the randomness and the influence of a slope dynamic system, and constructing a slope earthquake vulnerability analysis curve. The method comprises the steps of firstly, aiming at the deformation and damage characteristics of a side slope under earthquake load, selecting earthquake permanent displacement as an earthquake resistance evaluation index, and making provisions for vulnerable states of different performance levels; then, respectively quantitatively representing the uncertainty of earthquake motion and rock-soil body parameters in the slope dynamic stochastic system by adopting a stochastic earthquake motion model and a stochastic field theory, and analyzing the probability density evolution characteristic of the slope earthquake permanent displacement based on the probability density evolution theory; and calculating the conditional probability of the slope exceeding different performance levels under the seismic loads with different strengths, and constructing seismic vulnerability assessment curves of different vulnerability states. The method specifically comprises the following steps:
s1, selecting earthquake permanent displacement as a slope earthquake resistance evaluation index, and defining different earthquake resistance level requirements and corresponding vulnerable state evaluation indexes of the slope;
establishing a side slope earthquake dynamic time-course analysis model of the actual side slope engineering according to the geometric conditions, the boundary conditions and the like of the actual side slope engineering;
analyzing probability statistical characteristics of rock-soil body parameters of the set side slope engineering according to survey data of the side slope engineering, and establishing a rock-soil body parameter random field model representing the spatial variability of the side slope rock-soil body parameters by combining a random field theory;
generating a series of random earthquake motion acceleration sample time courses meeting specific site conditions based on a random earthquake motion model according to the site conditions of slope engineering, and selecting parameters such as earthquake motion peak values and the like as earthquake motion intensity measurement indexes in a vulnerability curve;
s2, coupling the generated series of random earthquake dynamic acceleration sample time ranges and rock-soil body parameter random field models to the established slope earthquake dynamic time range analysis model, and obtaining a series of slope earthquake permanent displacements by adopting a dynamic time range analysis method;
s3, constructing a generalized probability density evolution equation of the permanent displacement of the slope earthquake based on a probability density evolution theory, substituting the series of permanent displacement of the slope earthquake into the equation, and solving by adopting a finite difference algorithm to obtain the probability density evolution characteristic of the permanent displacement of the slope earthquake;
s4, based on the probability density evolution characteristics of the permanent displacement of the side slope earthquake, combining the side slope displacement evaluation criterion, calculating the conditional failure probability of the side slope exceeding different earthquake resistance performance level requirements under the action of different earthquake intensities, and constructing a side slope earthquake vulnerability analysis curve.
In S1, a high-dimensional probability space formed by characterizing rock-soil body parameters and seismic motion uncertain random variables is firstly split, representative sample points are selected, and then a rock-soil body parameter random field model and a series of random seismic motion acceleration sample time courses are established.
The slope vibration force time course analysis model can be based on finite elements and can also be based on finite difference. The rock-soil body parameters of the model comprise weight, internal friction angle, cohesive force, shear modulus, damping ratio and the like, and part of main influence parameters can be generally determined to meet the specific probability distribution model according to parameter analysis.
A rock-soil body parameter random field model is established by adopting a KL decomposition method, and the concrete formula is as follows:
wherein, mukAnd σkRespectively representing the mean value and the standard deviation of the rock-soil body parameters;representing standard normal random variables which are independent of each other;representing external spatial coordinates; (x, y) represent the random field model coordinates of the two-dimensional structural system Ω; lambda [ alpha ]iAndrespectively representing the characteristic value and the characteristic function of the rock-soil body autocorrelation function; n represents the number of terms representing the expansion order number,and representing a rock-soil body parameter two-dimensional random field.
The process of generating the series of random earthquake motion acceleration sample time courses meeting the specific site conditions adopts a spectral representation method, which specifically comprises the following steps:
wherein,representing an evolved power spectral density function of non-stationary random seismic oscillations; { Xk,Yk} (k ═ 1,2,3 … N) denotes orthonormal random variables; Δ ω represents a frequency interval;representing the earthquake motion random process, k representing the number of terms and N representing the total number of terms.
The generalized probability density evolution equation of the permanent displacement of the slope earthquake is specifically as follows:
the initial condition of this equation is ρYθ(y,θ,t0)=ρYθ(θ,t)(y-y0) The boundary condition is rhoyθ(y,θ,t0)|y→±∞0, where ρYθ(y, theta, t) represents the joint probability density function of y (t) and theta, representing the Dirac function, y (t) and theta represent the displacement time course and the variable characterizing randomness, respectively,when indicating a displacementTime derivative of the course, y0Denotes the initial value of the displacement, t0Indicating the initial time.
Examples
The embodiment is a typical soil slope, the slope height is 10 meters, and the slope is 1: 1. The method provided by the invention is adopted to evaluate the earthquake vulnerability.
1) Considering the limitation that the earthquake safety coefficient cannot represent different damage characteristics of the slope when evaluating the earthquake resistance of the slope, the slope earthquake resistance evaluation criterion based on the earthquake permanent displacement shown in the table 1 can be adopted as the slope displacement evaluation criterion by referring to relevant documents and specification requirements.
TABLE 1 evaluation criterion for earthquake-resistant performance of slope based on earthquake permanent displacement
Performance level | State of destruction | Displacement criterion (Rice) |
|
Slight damage | 0.01 |
Level 2 | Moderate destruction | 0.05 |
Level 3 | Severe damage | 0.15 |
2) A side slope earthquake dynamic time-course analysis model is established according to the geometric form, boundary conditions and the like of a side slope, and as shown in figure 2, the slope height of the model is 10 meters, and the slope is 1: 1. In order to facilitate the assignment of a subsequent rock-soil body parameter random field model, the unit meshes of the slope model are divided, in the implementation case, the slope is divided into 1210 finite units by utilizing 1281 nodes, wherein the 1210 finite units comprise 1190 quadrilateral units with the size of 0.5m and 20 triangular units positioned in a slope transition area of an empty surface.
3) Determining basic random variables and probability distribution forms thereof in the randomness of earthquake motion and rock-soil body parameters in a slope random power system, subdividing a high-dimensional probability space consisting of the basic random variables by adopting a tangent ball point selection strategy, and selecting representative sample points of the earthquake motion and the soil body parameters.
4) Considering that the strength parameters cohesion and friction angle have the greatest effect on slope stability, the two parameters are modeled as random fields, which obey a lognormal distribution. The correlation between cohesion and internal friction angle is considered and characterized by a mutual coefficient. Due to the anisotropic characteristics of rock-soil mass, different autocorrelation distances are adopted in the horizontal direction and the numerical direction, and specific random field parameters are shown in table 2. Other parameters are regarded as fixed values, and the gravity of the soil body is set to be 20kN/m3The poisson ratio is 0.334 and the damping ratio is 0.05. A KL decomposition method based on a random field theory is adopted, a random field model of the side slope cohesive force and the friction angle is established according to the following formula for representing the space variability of soil body parameters, and the specific formula is as follows:
the method adopts an exponential correlation function, and the specific form is as follows:
wherein lxAnd lyRespectively, the relative distances in the horizontal and vertical directions. Combining the method and226 pairs of representative sample points of the rock-soil body parameters in the step 2) can respectively generate 226 spatial random field models of cohesive force and friction angle, and two typical random field distribution models of cohesive force and friction angle are shown in fig. 3.
Table 2 case slope model random field parameters
5) According to the side slope engineering site condition of the embodiment, based on a random earthquake motion model, a series of earthquake acceleration time courses meeting the specific site condition are generated by adopting a spectral representation method, and the formula is as follows:
combining the method with 226 representative sample points of seismic motion in step 2), 226 edge slope engineering field random seismic motion acceleration time courses can be generated, and fig. 4 is a schematic diagram of 4 typical acceleration time courses. And selecting the seismic oscillation peak value as a seismic oscillation intensity measuring index in the vulnerability curve, and carrying out amplitude modulation on a set of generated random seismic oscillation acceleration sample time courses to obtain a plurality of sets of seismic acceleration sample time courses with different acceleration peak values.
6) And coupling the generated series of random earthquake dynamic acceleration sample time courses and rock-soil body parameter random field models to the established slope earthquake dynamic time course analysis model, performing series deterministic dynamic time course analysis by adopting a dynamic time course analysis method, and deriving a series slope earthquake permanent displacement calculation result.
7) Based on the probability density evolution theory, a generalized probability density evolution equation of the permanent displacement of the slope earthquake is constructed as follows:
its initial condition is ρYθ(y,θ,t0)=ρYθ(θ,t)(y-y0) (ii) a The boundary condition is ρyθ(y,θ,t0)|y→±∞0. In the formula, ρYθ(y, θ, t) represents the joint probability density function of y (t) and θ; is a Dirac function. And substituting the series of deterministic slope earthquake permanent displacement calculation results into the equation, and solving by adopting a finite difference algorithm to obtain the probability density evolution characteristics of the slope earthquake permanent displacement and the cumulative distribution function of the extreme value thereof. Fig. 5 is a cumulative distribution function of the slope earthquake permanent displacement considering the seismic oscillation and soil parameter coupling uncertainty under the action of 226 random seismic waves with a peak value of 0.3g, and in the curve, the failure probability of the slope exceeding different earthquake resistance performance levels under the action of 0.3g earthquake in the embodiment can be obtained by combining the earthquake permanent displacement evaluation criteria of different damages in the step 1).
8) And (3) obtaining the failure probability of the embodiment exceeding different failure states under the action of different seismic intensities (0-0.8 g) by amplitude modulation of the 226 fields generated in the step 5) and repeating the step 6) and the step 7).
9) And (3) constructing a slope seismic vulnerability analysis curve shown in the figure 6 by taking the abscissa as an input seismic peak value and the ordinate as the probability of the slope exceeding different damage states and combining the calculation result of the step 8), wherein the slope seismic vulnerability analysis curve comprises three vulnerability states of slight damage, medium damage and serious damage.
The embodiment shows that by adopting the method, the influence of the composite randomness of the earthquake motion and rock-soil body parameters on the earthquake resistance of the side slope can be considered, the dynamic failure probability of the side slope and earthquake vulnerability curves of different vulnerability states are obtained, and the risk of the side slope geological disaster is reasonably evaluated.
Claims (10)
1. A performance-based slope earthquake vulnerability assessment method is characterized by comprising the following steps:
s1, selecting earthquake permanent displacement as a slope earthquake resistance evaluation index, and defining different earthquake resistance level requirements and corresponding vulnerable state evaluation indexes of the slope;
establishing a side slope earthquake power time-course analysis model of the actual side slope engineering;
establishing a rock-soil body parameter random field model representing the spatial variability of the slope rock-soil body parameters;
generating a series of random earthquake motion acceleration sample time courses meeting specific site conditions based on a random earthquake motion model according to the site conditions of the slope engineering;
s2, coupling the generated series of random earthquake dynamic acceleration sample time ranges and rock-soil body parameter random field models to the established slope earthquake dynamic time range analysis model, and obtaining a series of slope earthquake permanent displacements by adopting a dynamic time range analysis method;
s3, constructing a generalized probability density evolution equation of the slope earthquake permanent displacement, substituting the series of slope earthquake permanent displacements into the equation, and solving to obtain the probability density evolution characteristic of the slope earthquake permanent displacement;
s4, based on the probability density evolution characteristics of the permanent displacement of the side slope earthquake, combining the side slope displacement evaluation criterion, calculating the conditional failure probability of the side slope exceeding different earthquake resistance performance level requirements under the action of different earthquake intensities, and constructing a side slope earthquake vulnerability analysis curve.
2. The method of claim 1, wherein the side slope seismic vulnerability assessment method is based on finite elements or finite differences.
3. The performance-based slope earthquake vulnerability assessment method according to claim 1, characterized in that the rock-soil mass parameter random field model is established by using a KL decomposition method.
4. The method according to claim 3, wherein the KL decomposition method is formulated as:
wherein, mukAnd σkRespectively representing the mean value and the standard deviation of the rock-soil body parameters; xik,i(θ) represents standard normal random variables independent of each other; θ represents an external spatial coordinate; (x, y) represent the random field model coordinates of the two-dimensional structural system Ω; lambda [ alpha ]iAndrespectively representing the characteristic value and the characteristic function of the rock-soil body autocorrelation function; n represents the number of terms of the expansion order number,and representing a rock-soil body parameter two-dimensional random field.
5. The performance-based slope seismic vulnerability assessment method according to claim 1, wherein the process of generating the series of random seismic dynamic acceleration sample time courses satisfying specific site conditions adopts a spectral representation method, specifically:
wherein,representing an evolved power spectral density function of non-stationary random seismic oscillations; { Xk,YkN denotes an orthonormal random variable; Δ ω represents a frequency interval;representing the seismic motion random process, k representing the number of terms and N representing the total number of terms.
6. The performance-based slope earthquake vulnerability assessment method according to claim 1, wherein the generalized probability density evolution equation of the slope earthquake permanent displacement is specifically as follows:
the initial condition of this equation is ρYθ(y,θ,t0)=ρYθ(θ,t)(y-y0) The boundary condition is rhoyθ(y,θ,t0)|y→±∞0, where ρYθ(y, theta, t) represents the joint probability density function of y (t) and theta, representing the Dirac function, y (t) and theta represent the displacement time course and the variable characterizing randomness, respectively,time derivative, y, representing the time course of the displacement0Denotes the initial value of the displacement, t0Indicating the initial time.
7. The method for performance-based slope seismic vulnerability assessment according to claim 1, wherein the S1 includes: firstly, a high-dimensional probability space formed by representing rock-soil body parameters and seismic motion uncertain random variables is subdivided, representative sample points are selected, and then a rock-soil body parameter random field model and a series of random seismic motion acceleration sample time courses are established.
8. The method of claim 1, wherein in step S1, according to survey data of a given slope project, probabilistic statistical characteristics of rock-soil body parameters of the slope project are analyzed, and a rock-soil body parameter random field model representing spatial variability of the rock-soil body parameters of the slope is established in combination with a random field theory.
9. The performance-based slope seismic vulnerability assessment method according to claim 1, wherein a finite difference algorithm is adopted in S3 to solve to obtain probability density evolution characteristics of slope seismic permanent displacement.
10. The method of claim 7, wherein the representative sample points selectively vibrate and soil parameters.
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CN112883454A (en) * | 2020-12-29 | 2021-06-01 | 煤炭科学研究总院 | Method and device for rapidly evaluating permanent deformation of unsaturated side slope under earthquake action |
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CN117951921A (en) * | 2024-03-26 | 2024-04-30 | 云南农业大学 | Slope earthquake vulnerability assessment method |
CN117951921B (en) * | 2024-03-26 | 2024-06-04 | 云南农业大学 | Slope earthquake vulnerability assessment method |
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