Seismic liquefaction assessment method based on conditional random field simulation

Abstract

The invention relates to a seismic liquefaction assessment method based on conditional random field simulation, which comprises the following steps: firstly, obtaining a logarithmic normal distribution random field of a target area under a corresponding SPT-N value, then resampling through a Bootstrap method, constructing a weighted prior probability density function of the target area in combination with a likelihood function, and finally calculating the seismic liquefaction of the target area according to a Bayesian theory. A Markov chain Monte Carlo sampling method is combined, through posterior probability density distribution, an optimal horizontal direction correlation distance is determined, a covariance matrix is constructed to generate a conditional random field, and then through multiple times of simulation, the conditional random field is converged; and finally, aiming at the target area, through calculation of a cyclic stress ratio and a cyclic resistance ratio, constructing a liquefaction probability distribution diagram corresponding to the target area. According to the method, a conditional random field simulation method is inferred and improved by combining Bootstrap and Bayesian theories, the precision and reliability of geological parameter simulation are remarkably improved, and reliable data support is provided for seismic liquefaction assessment of deep and uneven site engineering.

Description

Technical Field

[0001] This invention relates to a seismic liquefaction assessment method based on conditional random field simulation, belonging to the fields of geological engineering and earthquake engineering technology. Background Technology

[0002] In the fields of geological engineering and earthquake engineering, accurately assessing the risk of soil liquefaction induced by earthquakes is crucial for ensuring the safety of infrastructure in deep, heterogeneous sites. Traditional geological parameter simulation methods are usually based on assumptions such as homogeneity, isotropy, continuity, linear elasticity, and small strain. However, geological materials in actual sites typically exhibit significant spatial variability, which may stem from a variety of factors, including sedimentary conditions, loading history, the presence of cracks and bedding, hydrogeological conditions, and human activities.

[0003] To more realistically reflect the spatial variability of geological parameters, researchers have developed random field simulation methods. Unconditional random field simulation does not consider the constraints of field borehole data and generates the spatial distribution of geological parameters based solely on assumed correlation distances and statistical parameters. Conditional random field simulation can use field borehole data to constrain simulation results, thereby improving simulation accuracy. However, existing conditional random field simulation methods have limitations such as low computational efficiency and the inability to synchronously update correlation distances and parameter values.

[0004] In seismic liquefaction assessment, traditional liquefaction discrimination methods are mainly based on one-dimensional or isotropic random field models. These models cannot fully describe the significant variability of geological parameters in the depth and horizontal directions, resulting in high uncertainty in the liquefaction assessment results. In addition, existing methods often fail to fully utilize the spatial constraint information of borehole data, affecting the accuracy of liquefaction assessment. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a seismic liquefaction assessment method based on conditional random field simulation, which can improve the accuracy of geological parameter simulation and the reliability of seismic liquefaction assessment.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The present invention designs a seismic liquefaction assessment method based on conditional random field simulation, comprising the following steps:

[0007] Step A. For the target area, based on the horizontal correlation distance, the vertical correlation distance, and the mean and standard deviation of the SPT-N values ​​corresponding to each observation point in the target area, the log-normal random field under the SPT-N values ​​of the target area is obtained through the autocorrelation coefficient analysis between each pair of observation points and combined with Cholesky decomposition. Then proceed to Step B.

[0008] Step B. Resample using the Bootstrap method, combine the likelihood function of the correlation observation matrix X and the horizontal correlation distance in the log-normal random field under the SPT-N value, construct the weighted prior probability density function of the target region under the SPT-N value, and then determine the optimal horizontal correlation distance based on Bayesian theory and Markov chain Monte Carlo sampling method through the posterior probability density distribution, and then proceed to step C;

[0009] Step C. Based on the log-normal random field and the optimal horizontal correlation distance, construct the covariance matrix and generate a conditional random field. Then, through multiple simulations, converge the conditional random field and proceed to step D.

[0010] Step D. Based on the convergent conditional random field, for the target region, construct the liquefaction probability distribution map corresponding to the target region by calculating the cyclic stress ratio and cyclic resistance ratio.

[0011] As a preferred technical solution of the present invention: Step A is performed as follows: Steps A1 to A4 are performed to obtain a log-normal random field under the SPT-N value corresponding to the target region;

[0012] Step A1. Based on the preset initial correlation distances in each horizontal direction and the preset correlation distances in the vertical direction, determine the horizontal correlation distances by analyzing the autocorrelation coefficients between pairs of observation points in the target area and by calculating and comparing the likelihood function. Then proceed to step A2.

[0013] Step A2. For the autocorrelation matrix R formed by the autocorrelation coefficients between pairwise observation points in the target region under the horizontal and vertical correlation distances, according to R = L·L T Perform Cholesky decomposition to obtain the lower triangular matrix L, and then proceed to step A3;

[0014] Step A3. Based on the grid division of the target region that corresponds to the location of each observation point and each grid, generate an independent standard normal distribution random matrix U that conforms to the grid division of the target region, and obtain the standard Gaussian random field lnH by lnH=LU, and then proceed to step A4.

[0015] Step A4. Based on the mean and standard deviation of the SPT-N values ​​corresponding to each observation point in the target area, obtain the corresponding log-normal random field H for the standard Gaussian random field lnH, that is, the log-normal random field H under the SPT-N values ​​corresponding to the target area.

[0016] As a preferred technical solution of the present invention: In step A1, based on the preset initial correlation distances in each horizontal direction, the following steps A1-1 to A1-3 are performed to obtain the likelihood function values ​​corresponding to the initial correlation distances in the horizontal direction, and the initial correlation distance in the horizontal direction corresponding to the largest likelihood function value is selected as the horizontal correlation distance.

[0017] Step A1-1. Based on the initial relevant distance δ' in the horizontal direction h Preset vertical distance δ v The coordinates of each observation point in the target area are calculated using the following formula:

[0018]

[0019] The autocorrelation coefficients between each pair of observation points in the target region are obtained, and the autocorrelation matrix R is constructed. Then, ln|R| and R are calculated. -1 , where R c,d This represents the autocorrelation coefficient between observation point c and observation point d in the target region, (x c ,y c (x) represents the position coordinates of observation point c in the target region. d ,y d ) represents the position coordinates of the observation point d in the target area, exp[·] represents the exponential function, and then proceed to step A1-2;

[0020] Step A1-2. Based on the position coordinates of each observation point in the target area and their corresponding SPT-N values, the trend function matrix F under the trend function is constructed, and the observation matrix X is composed of the corresponding SPT-N values ​​of each observation point in the target area, according to the following formula:

[0021]

[0022] Obtaining the trend coefficient And further according to Obtaining variance Among them, F T E represents the transpose of the trend function matrix F. T Let E be the transpose, and n be the number of observation points in the target region. Then proceed to steps A1-3.

[0023] Step A1-3. Use the following formula:

[0024]

[0025] Obtain the likelihood function value L p .

[0026] As a preferred technical solution of the present invention: step A4 includes the following steps A4-1 to A4-2;

[0027] Step A4-1. Based on the mean μ of the SPT-N values ​​corresponding to each observation point in the target area. s With standard deviation σ s According to the following formula:

[0028]

[0029] Obtain σ lnH μ lnH Then proceed to step A4-2;

[0030] Step A4-2. Based on each element lnH in the standard Gaussian random field lnH i According to the following formula:

[0031] H uni =exp(μ lnH +σ lnH lnH i );

[0032] Obtain each element H uni This leads to the formation of a log-normal random field H, which is the log-normal random field H of the target region under the SPT-N value.

[0033] As a preferred embodiment of the present invention: step B is performed as follows: steps B1 to B7;

[0034] Step B1. Use the Bootstrap method to resample the preset initial correlation distances in each horizontal direction to generate a preset number of sample groups, each containing a preset number of initial correlation distances in the horizontal direction, and then proceed to step B2;

[0035] Step B2. Based on the observation matrix X formed by the SPT-N values ​​corresponding to each observation point in the target area, for each sample group, based on the likelihood function of the correlation observation matrix X and the horizontal correlation distance, obtain the likelihood function value corresponding to each initial horizontal correlation distance in the sample group, and select the initial horizontal correlation distance corresponding to the largest likelihood function value as the optimal horizontal correlation distance of the sample group, and then proceed to step B3.

[0036] Step B3. Based on the sample group interval variables constructed by the lowest and highest initial horizontal correlation distances in each sample group, the maximum likelihood estimation theory is used to convert the sample group interval variables into random variable probability distributions and construct the probability density function f(Ⅰ). At the same time, based on the probability distribution followed by the preset horizontal correlation distance, combined with the observation matrix X, the probability density function f(Ⅱ) of the corresponding prior distribution is constructed, and then proceed to step B4.

[0037] Step B4. Calculate the sum of likelihood values ​​A of the optimal level correlation distance for each sample group with respect to the probability density function f(Ⅰ), and simultaneously calculate the sum of likelihood values ​​B of the optimal level correlation distance for each sample group with respect to the probability density function f(Ⅱ), then apply the following formula:

[0038]

[0039] Obtain the coefficients w1 and w2, and then construct the weighted prior probability density function f = w1f(Ⅰ) + w2f(Ⅱ), which is the weighted prior probability density function f of the SPT-N value corresponding to the target region, and then proceed to step B5;

[0040] Step B5. Based on Bayesian theory, construct the posterior probability density distribution according to the likelihood function of the correlation observation matrix X and the horizontal correlation distance, and the weighted prior probability density function f under the SPT-N value corresponding to the target region; and based on the observation matrix X, construct the covariance matrix of the correlation horizontal correlation distance through the two-dimensional exponential autocorrelation function, and construct the likelihood function based on the observation matrix X following a normal distribution, and then proceed to step B6.

[0041] Step B6. Perform Markov chain Monte Carlo sampling. First, based on the posterior probability density distribution, iteratively and randomly sample candidate correlation distances in each horizontal direction. Then, sequentially process the covariance matrix, likelihood function, and weighted prior probability density function f to obtain the reception probability corresponding to each candidate correlation distance in each horizontal direction. Retain the candidate correlation distances in the horizontal direction that meet the reception probability threshold. Finally, for the Markov chain formed by the candidate correlation distances in each horizontal direction in the retained order, remove the candidate correlation distances in each horizontal direction with a preset proportion before the order, update the Markov chain, and then proceed to step B7.

[0042] Step B7. Extract the candidate horizontal correlation distance that appears most frequently in the Markov chain, which is the optimal horizontal correlation distance.

[0043] As a preferred technical solution of the present invention: step C is performed as follows: steps C1 to C3;

[0044] Step C1. Based on the log-normal random field, using the observation matrix X regarding the SPT-N value, the optimal mean μ' of the SPT-N value corresponding to the target region under the log-normal random field is inversely calculated through maximum likelihood estimation. s With the optimal standard deviation σ' s Then proceed to step C2;

[0045] Step C2. Based on the optimal horizontal distance Vertical relative distance δ v Optimal standard deviation σ' s And based on the grid division of the target region that corresponds to the location of each observation point and each grid within it, the coordinates of each observation point and the coordinates of each non-observation point grid are used to construct the covariance matrix R between observation points. BH,BH And the covariance matrix R between observation points and non-observation point grids. P,BH Then proceed to step C3;

[0046] Step C3. Based on the optimal mean μ' s With the optimal standard deviation σ' s and the covariance matrix R between observation points BH,BH And the covariance matrix R between observation points and non-observation point grids. P,BH Constructing a Conditional Random Field B cn Then, simulations are performed for a preset number of iterations to verify the convergence of the results and ensure that the standard deviation coefficient of variation is less than 1%, with convergence condition being a random field.

[0047] As a preferred technical solution of the present invention: in step C3, the covariance matrix R between observation points is based on... BH,BH Perform Cholesky decomposition, and follow steps C3-1 to C3-4 to construct the conditional random field N. cn ;

[0048] Step C3-1. Perform a Gaussian space transformation on the observation matrix X for the SPT-N values ​​to obtain the corresponding G. BH and based on For the covariance matrix R between observation points BH,BH Performing Cholesky decomposition yields the lower triangular matrix L. BH Then proceed to step C3-2;

[0049] Step C3-2. According to the formula: The intermediate quantity α is solved by forward substitution, and then according to the formula. The intermediate quantity β is solved by backward substitution, and then the formula is applied: μ P|BH =R P,BH ·β, solve to obtain μ P|BH Then proceed to step C3-3;

[0050] Step C3-3. According to the formula: Get R P|BH and based on Performing Cholesky decomposition yields the lower triangular matrix L. P Then follow the formula: GP cn =μ P|BH +L P ·Z, obtain G Pcn , where Z represents an independent standard normal random vector, and then proceed to step C3-4; where I represents the identity matrix;

[0051] Step C3-4. According to the formula: N Pcn =exp(μ' s +σ' s ·G Pcn ), obtain N Pcn Then press N cn =[X,N Pcn ], obtain the conditional random field N cn .

[0052] As a preferred technical solution of the present invention: step D includes the following steps D1 to D4;

[0053] Step D1. For the target area, apply formula (N1) 60 =C N ·C E ·C R ·C B ·C S ·N cn The result is (N1) calculated. 60 ,and Perform fine-grain content correction to obtain Δ(N1). 60 Then press (N1). 60CS =(N1) 60 +Δ(N1) 60 Calculate the corrected standard penetration number (N1). 60CS Then proceed to step D2; where N cn Let C represent a convergent conditional random field. N Indicates the preset overburden stress correction, C E ·C R ·C B ·C S FC represents the percentage of fine soil particles of a predetermined particle size in the borehole at the observation point; C E C represents the preset energy ratio correction factor. R C represents the preset drill pipe length correction factor. B C represents the preset borehole diameter correction factor.S Indicates the preset piercing type correction factor;

[0054] Step D2. Use the following formula:

[0055]

[0056] Calculate the shear stress reduction factor γ d And according to the formula: MSF = 6.9exp(-M w / 4)-0.058, calculate the magnitude conversion factor MSF, and use the following formula:

[0057]

[0058] Calculated overburden pressure correction factor K σ Then proceed to step D3; where M w σ' represents the absolute intensity of the earthquake in the target area, z represents the layer depth of the target area, and σ' represents the depth of the target area. v P represents the effective overburden stress at a preset depth in the soil within the target area. a Indicates the reference value for atmospheric pressure; C σ This indicates the preset soil compressibility correction factor;

[0059] Step D3. For the target area, use the following formula:

[0060]

[0061] The cyclic stress ratio (CSR) is calculated using the following formula:

[0062]

[0063] Calculate the cyclic resistance ratio (CRR), then proceed to step D4; where a max The peak horizontal ground acceleration is represented by g at a location within the target area, where g represents gravitational acceleration and σ represents the acceleration due to gravity. v This indicates the total overburden stress at a preset depth in the soil layer within the target area;

[0064] Step D4. For the target area, apply the formula... Calculate the safety factor F S And define when F S ≤1 indicates soil liquefaction, and is calculated according to the formula: Calculate the soil liquefaction probability P L This means obtaining the soil liquefaction probability corresponding to each location in the target area, thus constructing a liquefaction probability distribution map corresponding to the target area; where N represents the number of times a single location in the target area is counted, and count() represents the counting function.

[0065] The seismic liquefaction assessment method based on conditional random field simulation described in this invention, compared with existing technologies, has the following technical advantages:

[0066] This invention designs a seismic liquefaction assessment method based on conditional random field simulation. First, it obtains a log-normal random field with SPT-N values ​​corresponding to the target area. Then, it resamples using the Bootstrap method and combines it with the likelihood function to construct a weighted prior probability density function for the target area. Next, based on Bayesian theory and the Markov chain Monte Carlo sampling method, it determines the optimal horizontal correlation distance through the posterior probability density distribution, constructing a covariance matrix to generate the conditional random field. This is followed by multiple simulations to converge the conditional random field. Finally, for the target area, it constructs a liquefaction probability distribution map corresponding to the target area by calculating the cyclic stress ratio and cyclic resistance ratio. This invention, by combining Bootstrap and Bayesian theory, infers and improves the conditional random field simulation method, significantly enhancing the accuracy and reliability of geological parameter simulation and providing reliable data support for seismic liquefaction assessment in deep, heterogeneous sites. Attached Figure Description

[0067] Figure 1 The overall flowchart of the earthquake liquefaction assessment method based on conditional random field simulation is designed for this invention;

[0068] Figure 2 This is a schematic diagram illustrating the geological parameter principle of the random field simulation of the present invention;

[0069] Figure 3 This invention relates to the soil layer distribution and SPT-N value distribution in the study area.

[0070] Figure 4 This is the soil layer modeling result of the present invention;

[0071] Figure 5 This is a graph showing the relationship between the variability of the SPT-N simulation results and the number of simulations in this invention;

[0072] Figure 6 A comparison of the simulation results of unconditional and conditional random fields SPT-N in this invention;

[0073] Figure 7 This is a comparison diagram of the spatial distribution characteristics of the standard deviation of the present invention;

[0074] Figure 8 The results of SPT-N simulation liquefaction discrimination in this invention are as follows;

[0075] Figure 9 This is a diagram illustrating the predicted accuracy of the retained boreholes according to the present invention. Detailed Implementation

[0076] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0077] This invention designs a seismic liquefaction assessment method based on conditional random field simulation, such as... Figure 1 As shown, the design involves the following steps:

[0078] Step A. For the target area, based on the horizontal correlation distance, the vertical correlation distance, and the mean and standard deviation of the SPT-N values ​​corresponding to each observation point in the target area, the log-normal random field under the SPT-N values ​​of the target area is obtained through autocorrelation coefficient analysis between pairs of observation points and Cholesky decomposition. Then, proceed to Step B.

[0079] In practical applications, the above design step A is specifically executed as follows: steps A1 to A4.

[0080] Step A1. Based on preset initial correlation distances in each horizontal direction, such as 30, 60, 90, 120 or 150 meters, and a preset vertical correlation distance, such as 3 meters, perform steps A1-1 to A1-3 as follows: through autocorrelation coefficient analysis between pairs of observation points in the target area, and likelihood function calculation and comparison, obtain the likelihood function value corresponding to the initial correlation distance in the horizontal direction, and select the initial correlation distance in the horizontal direction corresponding to the largest likelihood function value as the horizontal correlation distance, and then proceed to step A2.

[0081] Step A1-1. Based on the initial relevant distance δ' in the horizontal direction h Preset vertical distance δ v The coordinates of each observation point in the target area are calculated using the following formula:

[0082]

[0083] The autocorrelation coefficients between each pair of observation points in the target region are obtained, and the autocorrelation matrix R is constructed. Then, ln|R| and R are calculated. -1 , where R c,d This represents the autocorrelation coefficient between observation point c and observation point d in the target region, (x c ,y c (x) represents the position coordinates of observation point c in the target region. d ,y d ) represents the position coordinates of the observation point d in the target area, exp[·] represents the exponential function, and then proceed to step A1-2.

[0084] Step A1-2. Based on the position coordinates of each observation point in the target area and their corresponding SPT-N values, the trend function matrix F under the trend function is constructed, and the observation matrix X is composed of the corresponding SPT-N values ​​of each observation point in the target area, according to the following formula:

[0085]

[0086] Obtaining the trend coefficient And further according to Obtaining variance Among them, F T E represents the transpose of the trend function matrix F. T Let E be the transpose of E, and n be the number of observation points in the target region. Then proceed to steps A1-3.

[0087] Step A1-3. Use the following formula:

[0088]

[0089] Obtain the likelihood function value L p .

[0090] Step A2. For the autocorrelation matrix R formed by the autocorrelation coefficients between pairwise observation points in the target region under the horizontal and vertical correlation distances, according to R = L·L T Perform Cholesky decomposition to obtain the lower triangular matrix L, and then proceed to step A3.

[0091] Step A3. Based on the grid division of the target region that corresponds to the location of each observation point and each grid, generate an independent standard normal distribution random matrix U that conforms to the grid division of the target region, and obtain the standard Gaussian random field lnH by lnH = LU, and then proceed to step A4.

[0092] Step A4. Based on the mean and standard deviation of the SPT-N values ​​corresponding to each observation point in the target area, for the standard Gaussian random field lnH, perform the following steps A4-1 to A4-2 to obtain the corresponding log-normal random field H, that is, the log-normal random field H under the SPT-N values ​​corresponding to the target area.

[0093] Step A4-1. Based on the mean μ of the SPT-N values ​​corresponding to each observation point in the target area. s With standard deviation σ s According to the following formula:

[0094]

[0095]

[0096] Obtain σlnH μ lnH Then proceed to step A4-2.

[0097] Step A4-2. Based on each element lnH in the standard Gaussian random field lnH i According to the following formula:

[0098] H uni =exp(μ lnH +σ lnH lnH i );

[0099] Obtain each element H uni This leads to the formation of a log-normal random field H, which is the log-normal random field H of the target region under the SPT-N value.

[0100] Step B. Resample using the Bootstrap method, and combine the likelihood function of the correlation observation matrix X and the horizontal correlation distance in the log-normal random field under the SPT-N value to construct the weighted prior probability density function of the target region under the SPT-N value. Then, based on Bayesian theory and the Markov chain Monte Carlo sampling method, determine the optimal horizontal correlation distance through the posterior probability density distribution, and then proceed to Step C.

[0101] In practical applications, step B above is specifically designed to be executed as follows: steps B1 to B7.

[0102] Step B1. Use the Bootstrap method to resample the preset initial correlation distances in each horizontal direction to generate a preset number of sample groups, each containing a preset number of initial correlation distances in the horizontal direction, and then proceed to step B2.

[0103] Step B2. Based on the observation matrix X formed by the SPT-N values ​​corresponding to each observation point in the target area, for each sample group, based on the likelihood function of the correlation observation matrix X and the horizontal correlation distance, obtain the likelihood function value corresponding to each initial horizontal correlation distance in the sample group, and select the initial horizontal correlation distance corresponding to the largest likelihood function value as the optimal horizontal correlation distance of the sample group, and then proceed to step B3.

[0104] Step B3. Based on the sample group interval variables constructed from the lowest and highest initial correlation distances in the horizontal direction in each sample group, the maximum likelihood estimation theory is used to convert the sample group interval variables into random variable probability distributions and construct the probability density function f(Ⅰ). At the same time, based on the probability distribution followed by the preset horizontal correlation distance, combined with the observation matrix X, the probability density function f(Ⅱ) of the corresponding prior distribution is constructed, and then proceed to step B4.

[0105] Step B4. Calculate the sum of likelihood values ​​A of the optimal level correlation distance for each sample group with respect to the probability density function f(Ⅰ), and simultaneously calculate the sum of likelihood values ​​B of the optimal level correlation distance for each sample group with respect to the probability density function f(Ⅱ), then apply the following formula:

[0106]

[0107] Obtain the coefficients w1 and w2, and then construct the weighted prior probability density function f = w1f(Ⅰ) + w2f(Ⅱ), which is the weighted prior probability density function f of the SPT-N value corresponding to the target region, and then proceed to step B5.

[0108] Step B5. Based on Bayesian theory, construct the posterior probability density distribution according to the likelihood function of the correlation observation matrix X and the horizontal correlation distance, and the weighted prior probability density function f under the SPT-N value corresponding to the target region; and based on the observation matrix X, construct the covariance matrix of the correlation horizontal correlation distance through the two-dimensional exponential autocorrelation function, and construct the likelihood function based on the observation matrix X following a normal distribution, and then proceed to step B6.

[0109] Step B6. Perform Markov chain Monte Carlo sampling. First, based on the posterior probability density distribution, iteratively and randomly sample candidate correlation distances in each horizontal direction. Then, sequentially process the covariance matrix, likelihood function, and weighted prior probability density function f to obtain the reception probability corresponding to each candidate correlation distance in each horizontal direction. Retain the candidate correlation distances in the horizontal direction that meet the reception probability threshold. Finally, for the Markov chain formed by the candidate correlation distances in each horizontal direction in the retained order, remove the candidate correlation distances in each horizontal direction with a preset proportion before the order, update the Markov chain, and then proceed to step B7.

[0110] Step B7. Extract the candidate horizontal correlation distance that appears most frequently in the Markov chain, which is the optimal horizontal correlation distance.

[0111] Step C. Perform steps C1 to C3 as follows: construct the covariance matrix based on the log-normal random field and the optimal horizontal correlation distance, and generate a conditional random field. Then, through multiple simulations, converge the conditional random field and proceed to step D.

[0112] Step C1. Based on the log-normal random field, using the observation matrix X regarding the SPT-N value, the optimal mean μ' of the SPT-N value corresponding to the target region under the log-normal random field is inversely calculated through maximum likelihood estimation. s With the optimal standard deviation σ' s Then proceed to step C2.

[0113] Step C2. Based on the optimal horizontal distance Vertical relative distance δv Optimal standard deviation σ' s And based on the grid division of the target region that corresponds to the location of each observation point and each grid within it, the coordinates of each observation point and the coordinates of each non-observation point grid are used to construct the covariance matrix R between observation points. BH,BH And the covariance matrix R between observation points and non-observation point grids. P,BH Then proceed to step C3.

[0114] Step C3. Based on the optimal mean μ' s With the optimal standard deviation σ' s and the covariance matrix R between observation points BH,BH And the covariance matrix R between observation points and non-observation point grids. P,BH Perform steps C3-1 to C3-4 to construct the conditional random field N. cn Then, simulations are performed for a preset number of iterations (such as 3000 times) to verify the convergence of the results and ensure that the standard deviation coefficient of variation is less than 1%, and the convergence condition is a random field.

[0115] Step C3-1. Perform a Gaussian space transformation on the observation matrix X for the SPT-N values ​​to obtain the corresponding G. BH and based on For the covariance matrix R between observation points BH,BH Performing Cholesky decomposition yields the lower triangular matrix L. BH Then proceed to step C3-2.

[0116] Step C3-2. According to the formula: The intermediate quantity α is solved by forward substitution, and then according to the formula. The intermediate quantity β is solved by backward substitution, and then the formula is applied: μ P|BH =R P,BH ·β, solve to obtain μ P|BH Then proceed to step C3-3.

[0117] Step C3-3. According to the formula: Get R P|BH and based on Performing Cholesky decomposition yields the lower triangular matrix L. P Then, according to the formula: G Pcn =μ P|BH +L P ·Z, obtain G Pcn , where Z represents an independent standard normal random vector, and then proceed to step C3-4; where I represents the identity matrix.

[0118] Step C3-4. According to the formula: N Pcn =exp(μ's +σ' s ·G Pcn ), obtain N Pcn Then press N cn =[X,N Pcn ], obtain the conditional random field N cn .

[0119] Step D. Based on the convergent conditional random field, for the target region, perform the following steps D1 to D4 to construct the liquefaction probability distribution map corresponding to the target region by calculating the cyclic stress ratio and cyclic resistance ratio.

[0120] Step D1. For the target area, apply formula (N1) 60 =C N ·C E ·C R ·C B ·C S ·N cn The result is (N1) calculated. 60 ,and Perform fine-grain content correction to obtain Δ(N1). 60 Then press (N1). 60CS =(N1) 60 +Δ(N1) 60 Calculate the corrected standard penetration number (N1). 60CS Then proceed to step D2; where N cn Let C represent a convergent conditional random field. N Indicates the preset overburden stress correction, C E ·C R ·C B ·C S FC represents the percentage of fine soil particles of a predetermined size in the borehole at the observation point. In practical applications, it is typically expressed as 5% ≤ FC ≤ 35%. E C represents the preset energy ratio correction factor. R C represents the preset drill pipe length correction factor. B C represents the preset borehole diameter correction factor. S This indicates the preset piercing type correction factor.

[0121] Step D2. Use the following formula:

[0122]

[0123] Calculate the shear stress reduction factor γ d And according to the formula: MSF = 6.9exp(-M w / 4)-0.058, calculate the magnitude conversion factor MSF, and use the following formula:

[0124]

[0125] Calculated overburden pressure correction factor K σ Then proceed to step D3; where M w σ' represents the absolute intensity of the earthquake in the target area, z represents the layer depth of the target area, and σ' represents the depth of the target area. v P represents the effective overburden stress at a preset depth in the soil within the target area. a Indicates the reference value for atmospheric pressure; C σ This represents the preset soil compressibility correction factor.

[0126] Step D3. For the target area, use the following formula:

[0127]

[0128] The cyclic stress ratio (CSR) is calculated using the following formula:

[0129]

[0130] Calculate the cyclic resistance ratio (CRR), then proceed to step D4; where a max The peak horizontal ground acceleration is represented by g at a location within the target area, where g represents gravitational acceleration and σ represents the acceleration due to gravity. v This indicates the total overburden stress at a preset depth in the soil layer at a location within the target area.

[0131] Step D4. For the target area, apply the formula... Calculate the safety factor F S And define when F S ≤1 indicates soil liquefaction, and is calculated according to the formula: Calculate the soil liquefaction probability P L This means obtaining the soil liquefaction probability corresponding to each location in the target area, forming a liquefaction probability distribution map of the target area, which is used to assess the liquefaction risk of the target area; where N represents the number of times a single location in the target area is counted, and count() represents the counting function.

[0132] The above-mentioned seismic liquefaction assessment method based on conditional random field simulation is applied in practice, such as... Figure 2 As shown, a random field model was used to simulate the strata and SPT-N values ​​at a deep, heterogeneous site along the Yangtze River. Each borehole had an initial diameter of 130 mm, a final diameter of 110 mm, and a depth of 30 m.

[0133] The initial stage of this invention involves determining the grid size, such as Figure 3As shown, a total of 27 boreholes (labeled J1 to J27) are located on the profile to facilitate two-dimensional simulation. The selection of boreholes depends on the scope of the engineering exploration. To optimize the utilization of the borehole profile, especially those located at the boundaries, lateral extensions of 160 meters and 100 meters were added to the outermost boreholes. Therefore, the resulting simulated site includes a lateral span of 5 kilometers and a depth of 30 meters. The stratigraphic information obtained from the boreholes is crucial for determining the stratigraphy of the study site, a step essential for the simulation of SPT-N random fields. Therefore, all 27 boreholes are projected onto a common profile to facilitate the simulation of stratigraphic arrangement using an embedded Markov chain model. Figure 4 This shows that the random stratigraphic distribution generated by the model represents the actual subsurface conditions.

[0134] Next, the design method described in this patent application will be followed, wherein when performing step C3 in step C, a conditional random field N will be constructed. cn ,like Figure 5 The relationship between the SPT-N stochastic simulation results in the study area and the number of simulations N is shown to verify the convergence of the results and ensure that the coefficient of variation of the standard deviation is less than 1%, which is a convergence conditional random field.

[0135] like Figure 6 The results of simulated SPT-N random fields under unconstrained conditions and conditional SPT-N random field simulations of the same borehole are shown respectively. Figure 7 The spatial distribution characteristics of the standard deviations of the SPT-N value predictions obtained using the traditional Hoffman Conditional Random Field (CRF) method and the improved simulation algorithm proposed in this study are shown. Comparative analysis shows that, compared with the traditional method, the method designed in this invention significantly reduces the prediction uncertainty of the simulation results by optimizing the spatial autocorrelation structure modeling mechanism.

[0136] Then continue with step D and subsequent steps until the liquefaction probability distribution map corresponding to the target area is obtained.

[0137] Continuing with the above embodiments, as follows: Figure 8 The results of SPT-N (Solution-Proof-of-Conditional Random Field) simulations for liquefaction are shown, such as... Figure 9 The accuracy of liquefaction assessments for 10 retained borehole locations is shown. Specifically, all accuracies are above 85%, with most predictions exceeding 95%. These data demonstrate that the reliability information obtained by the design method of this invention can be valuable for assessing the safety of real-world meshes.

[0138] This invention designs a seismic liquefaction assessment method based on conditional random field simulation. First, it obtains a log-normal random field with SPT-N values ​​corresponding to the target area. Then, it resamples using the Bootstrap method and combines it with the likelihood function to construct a weighted prior probability density function for the target area. Next, based on Bayesian theory and the Markov chain Monte Carlo sampling method, it determines the optimal horizontal correlation distance through the posterior probability density distribution, constructing a covariance matrix to generate the conditional random field. This is followed by multiple simulations to converge the conditional random field. Finally, for the target area, it constructs a liquefaction probability distribution map corresponding to the target area by calculating the cyclic stress ratio and cyclic resistance ratio. This invention, by combining Bootstrap and Bayesian theory, infers and improves the conditional random field simulation method, significantly enhancing the accuracy and reliability of geological parameter simulation and providing reliable data support for seismic liquefaction assessment in deep, heterogeneous sites.

[0139] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A seismic liquefaction assessment method based on conditional random field simulation, characterized in that, Includes the following steps: Step A. For the target area, based on the horizontal correlation distance, the vertical correlation distance, and the mean and standard deviation of the SPT-N values ​​corresponding to each observation point in the target area, the log-normal random field under the SPT-N values ​​of the target area is obtained through the autocorrelation coefficient analysis between each pair of observation points and combined with Cholesky decomposition. Then proceed to Step B. Step B. Resample using the Bootstrap method, combine the likelihood function of the correlation observation matrix X and the horizontal correlation distance in the log-normal random field under the SPT-N value, construct the weighted prior probability density function of the target region under the SPT-N value, and then determine the optimal horizontal correlation distance based on Bayesian theory and Markov chain Monte Carlo sampling method through the posterior probability density distribution, and then proceed to step C; Step C. Based on the log-normal random field and the optimal horizontal correlation distance, construct the covariance matrix and generate a conditional random field. Then, through multiple simulations, converge the conditional random field and proceed to step D. Step D. Based on the convergent conditional random field, for the target region, construct the liquefaction probability distribution map corresponding to the target region by calculating the cyclic stress ratio and cyclic resistance ratio.

2. The seismic liquefaction assessment method based on conditional random field simulation according to claim 1, characterized in that: In step A, the following steps A1 to A4 are performed to obtain a log-normal random field under the SPT-N value corresponding to the target region; Step A1. Based on the preset initial correlation distances in each horizontal direction and the preset correlation distances in the vertical direction, determine the horizontal correlation distances by analyzing the autocorrelation coefficients between pairs of observation points in the target area and by calculating and comparing the likelihood function. Then proceed to step A2. Step A2. For the autocorrelation matrix R formed by the autocorrelation coefficients between pairwise observation points in the target region under the horizontal and vertical correlation distances, according to R = L·L T Perform Cholesky decomposition to obtain the lower triangular matrix L, and then proceed to step A3; Step A3. Based on the grid division of the target region that corresponds to the location of each observation point and each grid, generate an independent standard normal distribution random matrix U that conforms to the grid division of the target region, and obtain the standard Gaussian random field lnH by lnH=LU, and then proceed to step A4. Step A4. Based on the mean and standard deviation of the SPT-N values ​​corresponding to each observation point in the target area, obtain the corresponding log-normal random field H for the standard Gaussian random field lnH, that is, the log-normal random field H under the SPT-N values ​​corresponding to the target area.

3. The seismic liquefaction assessment method based on conditional random field simulation according to claim 2, characterized in that: In step A1, based on the preset initial correlation distances in each horizontal direction, the following steps A1-1 to A1-3 are performed to obtain the likelihood function values ​​corresponding to the initial correlation distances in the horizontal direction, and the initial correlation distance in the horizontal direction corresponding to the largest likelihood function value is selected as the horizontal correlation distance. Step A1-1. Based on the initial relevant distance δ' in the horizontal direction h Preset vertical distance δ v The coordinates of each observation point in the target area are calculated using the following formula: The autocorrelation coefficients between each pair of observation points in the target region are obtained, and the autocorrelation matrix R is constructed. Then, ln|R| and R are calculated. -1 , where R c,d This represents the autocorrelation coefficient between observation point c and observation point d in the target region, (x c ,y c (x) represents the position coordinates of observation point c in the target region. d ,y d ) represents the position coordinates of the observation point d in the target area, exp[·] represents the exponential function, and then proceed to step A1-2; Step A1-2. Based on the position coordinates of each observation point in the target area and their corresponding SPT-N values, the trend function matrix F under the trend function is constructed, and the observation matrix X is composed of the corresponding SPT-N values ​​of each observation point in the target area, according to the following formula: Obtaining the trend coefficient And further according to Obtaining variance Among them, F T E represents the transpose of the trend function matrix F. T Let E be the transpose, and n represent the number of observation points in the target region. Then proceed to step A1-3; Step A1-3. Use the following formula: Obtain the likelihood function value L p .

4. The seismic liquefaction assessment method based on conditional random field simulation according to claim 2, characterized in that: Step A4 includes the following steps A4-1 to A4-2; Step A4-1. Based on the mean μ of the SPT-N values ​​corresponding to each observation point in the target area. s With standard deviation σ s According to the following formula: Obtain σ lnH μ lnH Then proceed to step A4-2; Step A4-2. Based on each element lnH in the standard Gaussian random field lnH i According to the following formula: H uni =exp(μ lnH +σ lnH lnH i ) Obtain each element H uni This leads to the formation of a log-normal random field H, which is the log-normal random field H of the target region under the SPT-N value.

5. The seismic liquefaction assessment method based on conditional random field simulation according to claim 1, characterized in that: Step B is performed as follows: Steps B1 to B7; Step B1. Use the Bootstrap method to resample the preset initial correlation distances in each horizontal direction to generate a preset number of sample groups, each containing a preset number of initial correlation distances in the horizontal direction, and then proceed to step B2; Step B2. Based on the observation matrix X formed by the SPT-N values ​​corresponding to each observation point in the target area, for each sample group, based on the likelihood function of the correlation observation matrix X and the horizontal correlation distance, obtain the likelihood function value corresponding to each initial horizontal correlation distance in the sample group, and select the initial horizontal correlation distance corresponding to the largest likelihood function value as the optimal horizontal correlation distance of the sample group, and then proceed to step B3. Step B3. Based on the sample group interval variables constructed by the lowest and highest initial horizontal correlation distances in each sample group, the maximum likelihood estimation theory is used to convert the sample group interval variables into random variable probability distributions and construct the probability density function f(Ⅰ). At the same time, based on the probability distribution followed by the preset horizontal correlation distance, combined with the observation matrix X, the probability density function f(Ⅱ) of the corresponding prior distribution is constructed, and then proceed to step B4. Step B4. Calculate the sum of likelihood values ​​A of the optimal level correlation distance for each sample group with respect to the probability density function f(Ⅰ), and simultaneously calculate the sum of likelihood values ​​B of the optimal level correlation distance for each sample group with respect to the probability density function f(Ⅱ), then apply the following formula: Obtain the coefficients w1 and w2, and then construct the weighted prior probability density function f = w1f(Ⅰ) + w2f(Ⅱ), which is the weighted prior probability density function f of the SPT-N value corresponding to the target region, and then proceed to step B5; Step B5. Based on Bayesian theory, construct the posterior probability density distribution according to the likelihood function of the correlation observation matrix X and the horizontal correlation distance, and the weighted prior probability density function f under the SPT-N value corresponding to the target region; and based on the observation matrix X, construct the covariance matrix of the correlation horizontal correlation distance through the two-dimensional exponential autocorrelation function, and construct the likelihood function based on the observation matrix X following a normal distribution, and then proceed to step B6. Step B6. Perform Markov chain Monte Carlo sampling. First, based on the posterior probability density distribution, iteratively and randomly sample candidate correlation distances in each horizontal direction. Then, sequentially process the covariance matrix, likelihood function, and weighted prior probability density function f to obtain the reception probability corresponding to each candidate correlation distance in each horizontal direction. Retain the candidate correlation distances in the horizontal direction that meet the reception probability threshold. Finally, for the Markov chain formed by the candidate correlation distances in each horizontal direction in the retained order, remove the candidate correlation distances in each horizontal direction with a preset proportion before the order, update the Markov chain, and then proceed to step B7. Step B7. Extract the candidate horizontal correlation distance that appears most frequently in the Markov chain, which is the optimal horizontal correlation distance.

6. The seismic liquefaction assessment method based on conditional random field simulation according to claim 1, characterized in that: Step C is performed as follows: Steps C1 to C3; Step C1. Based on the log-normal random field, using the observation matrix X regarding the SPT-N value, the optimal mean μ' of the SPT-N value corresponding to the target region under the log-normal random field is inversely calculated through maximum likelihood estimation. s With the optimal standard deviation σ' s Then proceed to step C2; Step C2. Based on the optimal horizontal distance Vertical relative distance δ v Optimal standard deviation v' s And based on the grid division of the target region that corresponds to the location of each observation point and each grid within it, the coordinates of each observation point and the coordinates of each non-observation point grid are used to construct the covariance matrix R between observation points. BH,BH And the covariance matrix R between observation points and non-observation point grids. P,BH Then proceed to step C3; Step C3. Based on the optimal mean μ' s With the optimal standard deviation σ' s and the covariance matrix R between observation points BH,BH And the covariance matrix R between observation points and non-observation point grids. P,BH Construct a conditional random field N cn Then, simulations are performed for a preset number of iterations to verify the convergence of the results and ensure that the standard deviation coefficient of variation is less than 1%, with convergence condition being a random field.

7. The seismic liquefaction assessment method based on conditional random field simulation according to claim 6, characterized in that: In step C3, the covariance matrix R between observation points is used as a basis. BH,BH Perform Cholesky decomposition, and follow steps C3-1 to C3-4 to construct the conditional random field N. cn ; Step C3-1. Perform a Gaussian space transformation on the observation matrix X for the SPT-N values ​​to obtain the corresponding G. BH and based on For the covariance matrix R between observation points BH,BH Performing Cholesky decomposition yields the lower triangular matrix L. BH Then proceed to step C3-2; Step C3-2. According to the formula: The intermediate quantity α is solved by forward substitution, and then according to the formula. The intermediate quantity β is solved by backward substitution, and then the formula is applied: μ P|BH =R P,BH ·β, solve to obtain μ P|BH Then proceed to step C3-3; Step C3-3. According to the formula: Get R P|BH and based on Performing Cholesky decomposition yields the lower triangular matrix L. P Then, according to the formula: G Pcn =μ P|BH +L P ·Z, obtain G Pcn , where Z represents an independent standard normal random vector, and then proceed to step C3-4; where I represents the identity matrix; Step C3-4. According to the formula: N Pcn =exp(μ' s +σ' s ·G Pcn ), obtain N Pcn Then press N cn =[X,N Pcn ], obtain the conditional random field N cn .

8. The seismic liquefaction assessment method based on conditional random field simulation according to claim 1, characterized in that: Step D includes the following steps D1 to D4; Step D1. For the target area, apply formula (N1) 60 =C N ·C E ·C R ·C B ·C S ·N cn The result is (N1) calculated. 60 ,and Perform fine-grain content correction to obtain Δ(N1). 60 Then press (N1). 60CS =(N1) 60 +Δ(M1) 60 Calculate the corrected standard penetration number (N1). 60CS Then proceed to step D2; where N cn Let C represent a convergent conditional random field. N Indicates the preset overburden stress correction, C E ·C R ·C B ·C S FC represents the percentage of fine soil particles of a predetermined particle size in the borehole at the observation point; C E C represents the preset energy ratio correction factor. R C represents the preset drill pipe length correction factor. B C represents the preset borehole diameter correction factor. S Indicates the preset piercing type correction factor; Step D2. Use the following formula: γ d =exp[α(z)+β(z)M w ] Calculate the shear stress reduction factor γ d And according to the formula: MSF = 6.9exp(-M w / 4)-0.058, calculate the magnitude conversion factor MSF, and use the following formula: K σ J1-C σ ln(σ' v / P a ) Calculated overburden pressure correction factor K σ Then proceed to step D3; where M w σ' represents the absolute intensity of the earthquake in the target area, z represents the layer depth of the target area, and σ' represents the depth of the target area. v P represents the effective overburden stress at a preset depth in the soil within the target area. a Indicates the reference value for atmospheric pressure; C σ This indicates the preset soil compressibility correction factor; Step D3. For the target area, use the following formula: The cyclic stress ratio (CSR) is calculated using the following formula: Calculate the cyclic resistance ratio CRR, then proceed to step D4; where a max The peak horizontal ground acceleration is represented by g at a location within the target area, where g represents gravitational acceleration and σ represents the acceleration due to gravity. v This indicates the total overburden stress at a preset depth in the soil layer within the target area; Step D4. For the target area, apply the formula... Calculate the safety factor F S And define when F S ≤1 indicates soil liquefaction, and is calculated according to the formula: Calculate the soil liquefaction probability P L This means obtaining the soil liquefaction probability corresponding to each location in the target area, thus forming a liquefaction probability distribution map of the target area; where N represents the number of times a single location in the target area is counted, and count() represents the counting function.

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