A seabed wave velocity structure non-stationary random field simulation method and system

Abstract

The application discloses a seabed wave velocity structure non-stationary random field simulation method and system, and belongs to the field related to marine engineering. The method comprises the following steps: S1, obtaining drilling data, and obtaining seabed soil shear wave velocity based on the drilling data; S2, fitting the relationship between the shear wave velocity and the depth, and calculating the mean value and the standard deviation of the shear wave velocity at different depths based on the fitting parameters; S3, using the mean value and the standard deviation of the shear wave velocity to respectively carry out V s -structure unconditional random field and conditional random field simulation, to obtain a simulation result; S4, based on the simulation result, analyzing the seismic liquefaction to obtain an analysis result. The method can significantly reduce the standard deviation of the seabed random V s -structure simulation result.

Description

Technical Field

[0001] This invention belongs to the technical field of marine engineering sites, specifically relating to a method and system for simulating non-stationary random fields of seabed wave velocity structure. Background Technology

[0002] my country's sea areas are mostly historically prone to strong earthquakes, and the design ground motion parameters for seismic analysis of marine engineering projects need to be based on the shear wave velocity V of the marine soil. s The basic data were determined through seismic response analysis of marine engineering sites. Due to the high difficulty and cost of offshore operations, this data is used to reveal the seabed's seismic response. s - Drilling holes in the structure is very limited. Only the V at the drill location... s The cross-section can be accurately revealed, and the V at other locations s - The structure must be inferred based on the results revealed at the borehole location.

[0003] Currently, deterministic methods are mostly used to establish site shear wave velocity prediction models. Commonly used deterministic methods can be broadly divided into two categories: the first category involves using borehole data combined with interpolation methods to obtain the V values ​​at locations where no boreholes are located. s -The deterministic distribution of the structure means that this type of method cannot provide V between boreholes. s -The structure has many possible distributions; another approach is to use regression analysis to establish a regression equation between soil shear wave velocity and depth h. This approach is only applicable to one-dimensional site models and cannot consider the variability of shear wave velocity in different two-dimensional spatial orientations.

[0004] Therefore, when conducting seismic response analysis of submarine sites, seabed V must be considered. s - Numerous possible structural distributions are considered to meet the safety and accuracy requirements of marine engineering construction and decision-making within a certain risk range; reasonable simulation of seabed randomness V s -Structure is an important prerequisite for the effective prediction of the seismic effects and uncertainties of the seabed site. Summary of the Invention

[0005] The main objective of this invention is to establish a stationary random field using a wave velocity structure to obtain seabed random V s - The series distribution of the structure significantly reduces the random V on the seabed. s - A simulation method for the standard deviation of structural simulation results and its application in liquefaction probability determination, to solve the problem of seabed V s - To address the issue of the accuracy of structural and liquefaction potential predictions, this study aims to provide reasonable shear wave velocity reference values ​​for seismic response analysis and liquefaction probability determination at marine engineering sites.

[0006] To achieve the above objectives, the present invention provides the following solution: a method for simulating non-stationary random fields of seabed wave velocity structure, comprising the following steps:

[0007] S1. Obtain borehole data and obtain the shear wave velocity of the seabed soil based on the borehole data;

[0008] S2. Fit the relationship between the shear wave velocity and depth, and calculate the mean and standard deviation of the shear wave velocity at different depths based on the fitting parameters;

[0009] S3. Using the mean and standard deviation of the shear wave velocity, simulate the unconditional random field and conditional random field of the Vs-structure respectively, and obtain the simulation results;

[0010] S4. Based on the simulation results, the seismic liquefaction is analyzed to obtain the analysis results.

[0011] More preferably, the method for calculating the average shear wave velocity at different depths includes:

[0012] E[V s (h)]=p ++ V s++ +p +- V s+- +p -+ V s-+ +p -- V s-- ,

[0013] In the formula, E[V s [(h)] represents the mean shear wave velocity at depth h; p ++ p -- p +- p -+ The weight function;

[0014] in,

[0015] p ++ =p -- =1+ρ / 4, p +- =p -+ =1-ρ / 4,

[0016] In the formula, ρ represents the correlation coefficient of the fitted parameters;

[0017] V s±± The calculation formula is:

[0018]

[0019] In the formula, σ[a] and σ[b] represent the mean of the fitted parameters, and σ[a] and σ[b] represent the standard deviation of the fitted parameters.

[0020] More preferably, the method for calculating the standard deviation of shear wave velocity at different depths includes:

[0021]

[0022] In the formula, σ[V s [(h)] represents the standard deviation of the shear wave velocity at depth h, E[V s 2 ] represents the second moment of the shear wave velocity, E[V s [(h)] represents the mean shear wave velocity at depth h.

[0023] More preferably, S3 includes:

[0024] S31. Perform V-methods on the mean and standard deviation of the shear wave velocity. s -Structural unconditional random field simulation, obtaining unconditional random field simulation results;

[0025] S32. Correct the unconditional random simulation results using the actual shear wave velocity at the borehole location to obtain V. s -Conditional random field of structure, and obtain the simulation results.

[0026] More preferably, V s - Representation methods for structured unconditional random fields include:

[0027]

[0028] In the formula, H Vs (x,y) denotes an unconditional random field at coordinates (x,y); E[lnV s (h)] and σ[lnV s [(h)] represent lnV at depth h, respectively. s Mean and standard deviation of (h), lnH Vs (x, y) represents a standard Gaussian random field after taking the logarithm of the soil shear wave velocity.

[0029] More preferably, the simulation results include:

[0030] V s，cn =[V s，BH V s，Pcn ],

[0031] In the formula, V s，cn V represents s -Structural conditions in random fields with shear wave velocity structures, V s，BH V represents the actual shear wave velocity at the borehole location. s，Pcn This represents the simulated shear wave velocity in a conditional random field at locations other than boreholes.

[0032] More preferably, the method for obtaining the analysis results includes: when the safety factor is ≤1, the soil will liquefy; otherwise, liquefaction will not occur.

[0033] The method for calculating the safety factor includes:

[0034]

[0035] In the formula, This indicates the cyclic resistance ratio of soil layers under earthquake loading. Indicates magnitude M w =7.5, effective overburden pressure σ′ v =100kPa is the cruising stress ratio of the reference soil layer, F s This represents the safety factor.

[0036] The present invention also provides a simulation system for non-stationary random fields of seabed wave velocity structure, comprising: an acquisition unit, a fitting unit, a simulation unit, and an analysis unit;

[0037] The acquisition unit is used to acquire borehole data and obtain the shear wave velocity of the seabed soil based on the borehole data.

[0038] The fitting unit is used to fit the relationship between the shear wave velocity and the depth, and to calculate the mean and standard deviation of the shear wave velocity at different depths based on the fitting parameters.

[0039] The simulation unit is used to simulate unconditional random fields and conditional random fields of Vs-structure using the mean and standard deviation of the shear wave velocity, respectively, and obtain simulation results.

[0040] The analysis unit is used to analyze earthquake liquefaction based on the simulation results and obtain analysis results.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] The method of this invention can significantly reduce seabed random V s - The standard deviation of the structural simulation results. A series of possible V values ​​for the study area obtained using stochastic simulation. s - The structure was used to assess the soil liquefaction probability, and it was found that neglecting V s - Spatial variability of the structure underestimates the soil liquefaction potential; by comparing the simulation results with the measured soil V at the reserved, unsimulated borehole locations... s The measured values ​​and liquefaction results were compared to verify the effectiveness of the method of the present invention for treating seabed V. s - Improve the accuracy of structural and liquefaction potential predictions; and provide reasonable shear wave velocity reference values ​​for seismic response analysis and liquefaction probability determination of marine engineering sites. Attached Figure Description

[0043] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a schematic diagram of the process for simulating the non-stationary random field of seabed wave velocity structure according to an embodiment of the present invention;

[0045] Figure 2 This is a possible stratigraphic distribution map of the study area in an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram illustrating the process of establishing a power function model and using the point estimation method to describe the spatial variability of soil parameters in an embodiment of the present invention.

[0047] Figure 4 This is a schematic diagram showing the distribution of fitting parameters for various soil shear wave velocities in an embodiment of the present invention;

[0048] Figure 5 This is a schematic diagram showing the relationship between the standard deviations of various soil types obtained by the point estimation method in this embodiment of the invention and the standard deviations of Monte Carlo simulation.

[0049] Figure 6 For the embodiments of the present invention, random V is used without considering the constraints of the measured shear wave velocity profile in the borehole. s - A schematic diagram of the standard deviation of the structural simulation results;

[0050] Figure 7 For embodiments of the present invention, random V considering borehole measured shear wave velocity profile constraints s - A schematic diagram of the standard deviation of the structural simulation results;

[0051] Figure 8 This is a schematic diagram of the liquefaction discrimination process according to an embodiment of the present invention;

[0052] Figure 9 This is a schematic diagram comparing the soil liquefaction discrimination results at a burial depth of 0-20m in the study area with and without considering the structural variability of shear wave velocity in an embodiment of the present invention.

[0053] Figure 10 This is a schematic diagram illustrating the accuracy of soil liquefaction discrimination results at 0-20m burial depth at the corresponding locations obtained by simulation after reserving each measured borehole in sequence according to an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0056] Example 1

[0057] like Figure 1 As shown, this embodiment provides a method for simulating non-stationary random fields of seabed wave velocity structure, including the following steps:

[0058] S1. Obtain borehole data and conduct indoor tests based on the borehole data to obtain the shear wave velocity of the seabed soil.

[0059] In this embodiment, the distribution of measured shear wave velocity of seabed soil with depth is obtained by combining borehole data and the embedded Markov chain model method. Using the embedded Markov chain, a possible stratigraphic distribution map of the study area is obtained, such as... Figure 2 As shown.

[0060] S2. Fit the relationship between shear wave velocity and depth, and calculate the mean and standard deviation of shear wave velocity at different depths based on the fitted relationship.

[0061] like Figure 3 As shown, the mean and standard deviation of the shear wave velocity as a function of depth are calculated using the point estimation method, and described by a fitting function. In this embodiment, a power function is used as an example:

[0062] V s (h)=ah b ,

[0063] In the formula, a and b represent the fitting parameters.

[0064] For the same type of soil, the above formula is used to fit the relationship between shear wave velocity and depth for each borehole, and the mean values ​​of parameters a and b are calculated. And standard deviations σ[a] and σ[b].

[0065] The coefficients of determination obtained by fitting the relationship between shear wave velocity and depth using the power function model are all above 0.90, indicating that the power function model can accurately describe its nonlinear relationship. Figure 4(a) and (b) show the distribution of fitting parameters a and b for shear wave velocities of various soil types. According to the Kolmogorov-Smirnov test, at a significance level of 0.05, the distributions of a and b values ​​for various soil types conform to a normal distribution.

[0066] Subsequently, Monte Carlo simulations were used to verify the accuracy of the mean and standard deviation of soil shear wave velocities given by the point estimation method. For example... Figure 5 As shown, Monte Carlo simulation was used to randomly sample parameters a and b. The sampled values ​​were then substituted into the above formula to predict the shear wave velocity values ​​of various soil types at any depth. The predicted shear wave velocity values ​​at different depths were statistically analyzed to obtain the standard deviation of the shear wave velocity at different depths. The figure shows that the difference between the two is small, indicating that the results calculated by the surface point estimation method are reasonable.

[0067] Specifically, the average shear wave velocity of soil at different depths can be calculated using the following formula:

[0068] E[V s (h)]=p ++ V s++ +p +- V s+- +p -+ V s-+ +p -- V s-- ,

[0069] In the formula, E[V s [(h)] represents the mean shear wave velocity at depth h; p ++ p -- p +- p -+ The weight function;

[0070] in,

[0071] p ++ =p -- =1+ρ / 4, p +- =p -+ =1-ρ / 4,

[0072] In the formula, ρ represents the correlation coefficient of the fitted parameters;

[0073] in,

[0074]

[0075] In the formula, COV(a, b) is the covariance of parameters a and b, and V[a] and V[b] are the variances of parameters a and b.

[0076] Among them, V s±± The calculation formula is:

[0077]

[0078] Methods for calculating the standard deviation of shear wave velocity at different depths include:

[0079]

[0080] In the formula, σ[V s [(h)] represents the standard deviation of the shear wave velocity at depth h, E[V s 2 The second moment, representing the shear wave velocity, is calculated as follows:

[0081]

[0082] S3. Using the mean and standard deviation of the obtained shear wave velocity, respectively, V s - Simulation of structured unconditional random fields and conditional random fields, and obtain simulation results;

[0083] Specifically, S3 includes:

[0084] S31. Perform V-test on the mean and standard deviation of the shear wave velocity. s -Structural unconditional random field simulation yields simulation results.

[0085] V s - Representation methods for structured unconditional random fields include:

[0086]

[0087] In the formula, H Vs (x,y) denotes an unconditional random field at coordinates (x,y); E[lnV s (h)] and σ[lnV s [(h)] represent lnV at depth h, respectively. s Mean and standard deviation of (h), lnH Vs (x, y) represents a standard Gaussian random field after taking the logarithm of the soil shear wave velocity.

[0088] in,

[0089] E[lnV s (h)]=lnE[V s (h)]-0.5σ 2 ln[V s (h)],

[0090]

[0091]

[0092] In the formula, S represents the independent standard random sample matrix, and L represents the expression for lnH. Vs The lower triangular matrix obtained by performing Cholliski decomposition on the spatial matrix R of (x,y) is LL. T =R; elements R in matrix R c,d Indicates position (x) c ,y c ) and (x d ,y d lnH at ) Vs Correlation between (x, y); R c,d The two-dimensional exponential autocorrelation function can be used for calculation:

[0093]

[0094] In the formula, δ 水平 and δ 竖向 Soil V s The horizontal and vertical correlation distance of the value.

[0095] S32. Correct the unconditional random simulation results using the actual shear wave velocity at the borehole location to obtain V. s -Conditional random fields with a structure were constructed, and simulation results were obtained.

[0096] In this embodiment, the simulation result is V s -Soil shear wave velocity structure in a conditional random field, i.e.:

[0097] V s，cn =[V s，BH V s，Pcn ],

[0098] In the formula, V s，cn V represents s -Structural conditions in random fields with shear wave velocity structures, V s，BH V represents the actual shear wave velocity at the borehole location. s，Pcn This represents the simulated shear wave velocity in a conditional random field at locations other than boreholes.

[0099] Among them, V s,Pcn =V s,Pu +[C P,BH [C] BH,BH ] -1 (V s,BH -V s,BHu ),

[0100] In the formula, V s，Pu and V s，BHu Let V represent the values ​​at non-drilling locations and drilling locations, respectively, obtained from unconditional random field simulations. s Value; [C P，BH[] represents the V value after local averaging between the non-drilled and drilled areas. s The covariance matrix between values; [C BH，BH [] indicates the V value after local averaging at the borehole location. s The covariance matrix between values.

[0101] Figure 6 , Figure 7 These are random V values ​​that ignore the constraints of measured shear wave velocity profiles in boreholes. s- A schematic diagram of the standard deviation of the structural simulation results, and a random V considering the constraints of the borehole measured shear wave velocity profile. s- A schematic diagram of the standard deviation of structural simulation results; using, for example Figure 2 The stratigraphic distribution shown was subjected to 3000 random V tests. s- Structural simulations show that the standard deviation of the shear wave velocity is 0 at the borehole location; outside the borehole location, the standard deviation of the shear wave velocity varies with depth. Figure 6 , 7 It can be seen that when the constraint of the measured shear wave velocity profile at the borehole is ignored, the V in a certain region at a distance from the borehole location... s- The standard deviation of the structural simulation results increased significantly, while for areas more than 2000 meters around the borehole, the standard deviation was significantly higher. Figure 7 In comparison, the standard deviation hardly increases anymore.

[0102] To verify the random V in the study area s - To ensure the accuracy of the structural simulation, one borehole is reserved for each simulation and randomly simulated along with the other six boreholes. The difference between the simulated and measured shear wave velocity values ​​at the reserved borehole is compared. The V0 value at the reserved borehole is then calculated. s - The error in the structural simulation results can be calculated using the following formula:

[0103]

[0104] In the formula, P E (u α ) is a grid u α China V s The representation error of the value; g j (u α ) is the value in the j-th simulation at grid u α V generated randomly in s Value; g(u) α ) is a grid u α China V s The measured value; calculate the V at the corresponding position obtained by simulation after each reserved borehole. s The prediction error of the value is distributed between 0-12%, indicating that the random V value obtained in the study area using the method of this embodiment is within acceptable limits. s - The structural simulation results have good accuracy.

[0105] S4. Based on the simulation results, the seismic liquefaction is analyzed, and the analysis results are obtained.

[0106] like Figure 8 The diagram shows a flowchart of a soil liquefaction assessment method based on shear wave velocity. Specifically, soil liquefaction potential is represented by a safety factor. The method for obtaining the analysis results includes: when the safety factor ≤ 1, the soil will liquefy; otherwise, liquefaction will not occur. The calculation method for the safety factor includes:

[0107]

[0108] In the formula, This indicates the cyclic resistance ratio of soil layers under earthquake loading. Indicates magnitude M w =7.5, effective overburden pressure σ′ v =100kPa is the cruising stress ratio of the reference soil layer, F s This represents the safety factor.

[0109] Then any grid u α The probability P of soil liquefaction L (u α It can be calculated using the following formula:

[0110]

[0111] With magnitude M w =7.5, with effective overburden pressure = 100 kPa as the cruise stress ratio of the reference soil layer. It can be represented as:

[0112]

[0113] In the formula, σ v a represents the total overburden stress at depth h. max The peak horizontal acceleration is represented by g, and the acceleration due to gravity is r. d K represents the shear stress flexural factor of the soil layer, MSF represents the magnitude calibration factor; σ This represents the effective overburden pressure correction factor.

[0114] Where r at depth h d It can be calculated using the following formula:

[0115] r d =exp[α(h)+β(h)M] w ],

[0116] In the formula, α(h) and β(h) are depth-related parameters, as detailed below:

[0117]

[0118] When the magnitude is not equal to 7.5, it needs to be determined using MSF:

[0119] MSF = 6.9exp(-M w / 4)-0.058;

[0120] Effective overburden pressure correction factor K σ The following formula can be used for calculation:

[0121] K σ =1-C σ ln(σ′ v / P a ),

[0122] In the formula, P a Indicates standard atmospheric pressure;

[0123] in,

[0124] In the formula, (N1) 60cs The parameters related to the fine particle content and the modified standard penetration test blow count of the clean sand can be obtained through iterative calculation.

[0125] Cyclic resistance ratio of soil layers under earthquake loading for:

[0126]

[0127] In the formula, V s1 The actual measured value of the shear wave velocity at the site is calculated according to the following formula:

[0128]

[0129] To facilitate soil liquefaction assessment, the V values ​​obtained from each simulation will be... s Multiply the value by 0.91 to correspond to the on-site V. s After the value is determined, liquefaction is judged.

[0130] The above methods were used to determine the liquefaction of silt, silt, sandy silt and fine sand at a burial depth of 0-20 meters in the study area. Figure 9 (a) gives the following Figure 10 The V given in s -The deterministic result of soil liquefaction assessment after multiplying the structure by 0.91 to correspond to the on-site shear wave velocity value; Figure 9 (b) then gives the consideration of the study area V s -Probability distribution of soil liquefaction due to structural variability; Figure 9 (a) Some areas that were determined to be non-liquefiable are in Figure 9(b) has a higher liquefaction potential; therefore, site V is not considered. s - Spatial variability of the structure may underestimate the liquefaction potential of the site soil, thus increasing the risk.

[0131] To verify the accuracy of the soil liquefaction discrimination results in the study area in this embodiment, one measured borehole was reserved and not included in the random simulation each time, while the remaining 6 boreholes were simulated. The V values ​​within each grid at the reserved borehole location were then calculated. s The simulated value is multiplied by 0.91 to convert it to the field V value. s The value is then used for liquefaction determination, and the result is compared with the V value at that grid location. s Measured value (needs to be converted to on-site V) s The liquefaction results obtained from the values ​​are compared. The accuracy of the soil liquefaction discrimination results at each measured borehole can be calculated using the following formula:

[0132]

[0133] L A (u α ) is the grid u α The accuracy of the liquefaction discrimination result; IndexStra(u α ) j It is the indicator function for the j-th simulation, when u α The liquefaction discrimination result at that location is based on the measured V. s The value is 1 if the liquefaction judgment result is consistent with the value, otherwise it is 0. Figure 10 The prediction accuracy of soil liquefaction discrimination results at corresponding locations obtained by simulation after sequentially reserving each measured borehole is given. The prediction accuracy ranges from 88% to 100%, indicating that the random V-type soil liquefaction in the study area of ​​this embodiment is within a certain range. s The soil liquefaction discrimination results obtained from the structural simulation results have good accuracy.

[0134] Example 2

[0135] The present invention also provides a simulation system for non-stationary random fields of seabed wave velocity structure, comprising: an acquisition unit, a fitting unit, a simulation unit, and an analysis unit;

[0136] The acquisition unit is used to acquire borehole data and obtain the shear wave velocity of the seabed soil based on the borehole data;

[0137] Specifically, the process of acquiring the unit includes:

[0138] In this embodiment, the distribution of measured shear wave velocity of seabed soil with depth is obtained by combining borehole data and the embedded Markov chain model method. Using the embedded Markov chain, a possible stratigraphic distribution map of the study area is obtained, such as... Figure 2 As shown.

[0139] The fitting unit is used to fit the relationship between shear wave velocity and depth, and calculate the mean and standard deviation of shear wave velocity at different depths based on the fitting parameters.

[0140] The specific working process of the fitting unit includes:

[0141] like Figure 3 As shown, the mean and standard deviation of the shear wave velocity as a function of depth are calculated using the point estimation method, and described by a fitting function. In this embodiment, a power function is used as an example:

[0142] V s (h)=ah b ,

[0143] In the formula, a and b represent the fitting parameters.

[0144] For the same type of soil, the above formula is used to fit the relationship between shear wave velocity and depth for each borehole, and the mean values ​​of parameters a and b are calculated. And standard deviations σ[a] and σ[b].

[0145] The coefficients of determination obtained by fitting the relationship between shear wave velocity and depth using the power function model are all above 0.90, indicating that the power function model can accurately describe its nonlinear relationship. Figure 4 (a) and (b) show the distribution of fitting parameters a and b for shear wave velocities of various soil types. According to the Kolmogorov-Smirnov test, at a significance level of 0.05, the distributions of a and b values ​​for various soil types conform to a normal distribution.

[0146] Subsequently, Monte Carlo simulations were used to verify the accuracy of the mean and standard deviation of soil shear wave velocities given by the point estimation method. For example... Figure 5 As shown, Monte Carlo simulation was used to randomly sample parameters a and b. The sampled values ​​were then substituted into the above formula to predict the shear wave velocity values ​​of various soil types at any depth. The predicted shear wave velocity values ​​at different depths were statistically analyzed to obtain the standard deviation of the shear wave velocity at different depths. The figure shows that the difference between the two is small, indicating that the results calculated by the surface point estimation method are reasonable.

[0147] Specifically, the average shear wave velocity of soil at different depths can be calculated using the following formula:

[0148] E[V s (h)]=p ++ V s++ +p +- V s+- +p -+ V s-+ +p -- V s-- ,

[0149] In the formula, E[V s [(h)] represents the mean shear wave velocity at depth h; p ++ p -- p +- p -+ The weight function;

[0150] in,

[0151] p ++ =p -- =1+ρ / 4, p +- =p -+ =1-ρ / 4,

[0152] In the formula, ρ represents the correlation coefficient of the fitted parameters;

[0153] in,

[0154]

[0155] In the formula, COV(a, b) is the covariance of parameters a and b, and V[a] and V[b] are the variances of parameters a and b.

[0156] Among them, V s±± The calculation formula is:

[0157]

[0158] Methods for calculating the standard deviation of shear wave velocity at different depths include:

[0159]

[0160] In the formula, σ[V s [(h)] represents the standard deviation of the shear wave velocity at depth h, E[V s 2 The second moment, representing the shear wave velocity, is calculated as follows:

[0161]

[0162] The simulation unit is used to perform V-wave analysis using the mean and standard deviation of the shear wave velocity. s- Simulations of structural unconditional random fields and conditional random fields were performed, and simulation results were obtained.

[0163] The working process of the simulation unit includes:

[0164] V-shaped curves were used to analyze the mean and standard deviation of the shear wave velocity. s -Structural unconditional random field simulation yields simulation results.

[0165] V s- Representation methods for structured unconditional random fields include:

[0166]

[0167] In the formula, H Vs (x,y) denotes an unconditional random field at coordinates (x,y); E[lnV s (h)] and σ[lnV s [(h)] represent lnV at depth h, respectively. s Mean and standard deviation of (h), lnH Vs (x, y) represents a standard Gaussian random field after taking the logarithm of the soil shear wave velocity.

[0168] in,

[0169] E[lnV s (h)]=lnE[V s (h)]-0.5σ 2 ln[V s (h)],

[0170]

[0171]

[0172] In the formula, S represents the independent standard random sample matrix, and L represents the expression for lnH. Vs The lower triangular matrix obtained by performing Cholliski decomposition on the spatial matrix R of (x,y) is LL. T =R; elements R in matrix R c,d Indicates position (x) c ,y c ) and (x d ,y d lnH at ) Vs Correlation between (x, y); R c,d The two-dimensional exponential autocorrelation function can be used for calculation:

[0173]

[0174] In the formula, δ 水平 and δ 竖向 Soil V s The horizontal and vertical correlation distance of the value.

[0175] The unconditional stochastic simulation results were corrected using the actual shear wave velocity at the borehole location to obtain V. s -Conditional random fields with a structure were constructed, and simulation results were obtained.

[0176] In this embodiment, the simulation result is V s-Soil shear wave velocity structure in a conditional random field, i.e.:

[0177] V s，cn =[V s，BH V s，Pcn ],

[0178] In the formula, V s，cn V represents s -Structural conditions in random fields with shear wave velocity structures, V s，BH V represents the actual shear wave velocity at the borehole location. s，Pcn This represents the simulated shear wave velocity in a conditional random field at locations other than boreholes.

[0179] Among them, V s,Pcn =V s,Pu +[C P,BH [C] BH,BH ] -1 (V s,BH -V s,BHu ),

[0180] In the formula, V s，Pu and V s，BHu Let V represent the values ​​at non-drilling locations and drilling locations, respectively, obtained from unconditional random field simulations. s Value; [C P，BH [] represents the V value after local averaging between the non-drilled and drilled areas. s The covariance matrix between values; [C BH，BH [] indicates the V value after local averaging at the borehole location. s The covariance matrix between values.

[0181] Figure 6 , Figure 7 These are random V values ​​that ignore the constraints of measured shear wave velocity profiles in boreholes. s- A schematic diagram of the standard deviation of the structural simulation results, and a random V considering the constraints of the borehole measured shear wave velocity profile. s- A schematic diagram of the standard deviation of structural simulation results; using, for example Figure 2 The stratigraphic distribution shown was subjected to 3000 random V tests. s- Structural simulations show that the standard deviation of the shear wave velocity is 0 at the borehole location; outside the borehole location, the standard deviation of the shear wave velocity varies with depth. Figure 6 , 7 It can be seen that when the constraint of the measured shear wave velocity profile at the borehole is ignored, the V in a certain region at a distance from the borehole location... s- The standard deviation of the structural simulation results increased significantly, while for areas more than 2000 meters around the borehole, the standard deviation was significantly higher. Figure 7 In comparison, the standard deviation hardly increases anymore.

[0182] To verify the random V in the study areas - To ensure the accuracy of the structural simulation, one borehole is reserved for each simulation and randomly simulated along with the other six boreholes. The difference between the simulated and measured shear wave velocity values ​​at the reserved borehole is compared. The V0 value at the reserved borehole is then calculated. s - The error in the structural simulation results can be calculated using the following formula:

[0183]

[0184] In the formula, P E (u α ) is a grid u α China V s The representation error of the value; g j (u α ) is the value in the j-th simulation at grid u α V generated randomly in s Value; g(u) α ) is a grid u α China V s The measured value; calculate the V at the corresponding position obtained by simulation after each reserved borehole. s The prediction error of the value is distributed between 0-12%, indicating that the random V value obtained in the study area using the method of this embodiment is within acceptable limits. s - The structural simulation results have good accuracy.

[0185] The analysis unit is used to analyze seismic liquefaction based on simulation results and obtain analysis results.

[0186] Specifically, soil liquefaction potential is expressed using a safety factor. The analysis unit obtains the analysis results using the following methods: when the safety factor is ≤1, the soil will liquefy; otherwise, liquefaction will not occur. The calculation method for the safety factor includes:

[0187]

[0188] In the formula, This indicates the cyclic resistance ratio of soil layers under earthquake loading. Indicates magnitude M w =7.5, effective overburden pressure σ′ v =100kPa is the cruising stress ratio of the reference soil layer, F s This represents the safety factor.

[0189] Then any grid u α The probability P of soil liquefaction L (u α It can be calculated using the following formula:

[0190]

[0191] With magnitude Mw =7.5, with effective overburden pressure = 100 kPa as the cruise stress ratio of the reference soil layer. It can be represented as:

[0192]

[0193] In the formula, σ v a represents the total overburden stress at depth h. max The peak horizontal acceleration is represented by g, and the acceleration due to gravity is r. d K represents the shear stress flexural factor of the soil layer, MSF represents the magnitude calibration factor; σ This represents the effective overburden pressure correction factor.

[0194] Where r at depth h d It can be calculated using the following formula:

[0195] r d =exp[α(h)+β(h)M] w ],

[0196] In the formula, α(h) and β(h) are depth-related parameters, as detailed below:

[0197]

[0198] When the magnitude is not equal to 7.5, it needs to be determined using MSF:

[0199] MSF = 6.9exp(-M w / 4)-0.058;

[0200] Effective overburden pressure correction factor K σ The following formula can be used for calculation:

[0201] K σ =1-C σ ln(σ′ v / P a ),

[0202] In the formula, P a Indicates standard atmospheric pressure;

[0203] in,

[0204] In the formula, (N1) 60cs The parameters related to the fine particle content and the modified standard penetration test blow count of the clean sand can be obtained through iterative calculation.

[0205] Cyclic resistance ratio of soil layers under earthquake loading for:

[0206]

[0207] In the formula, V s1 The actual measured value of the shear wave velocity at the site is calculated according to the following formula:

[0208]

[0209] To facilitate soil liquefaction assessment, the V values ​​obtained from each simulation will be... s Multiply the value by 0.91 to correspond to the on-site V. s After the value is determined, liquefaction is judged.

[0210] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for simulating non-stationary random fields of seabed wave velocity structure, characterized in that, Includes the following steps: S1. Obtain borehole data and obtain the shear wave velocity of the seabed soil based on the borehole data; S2. Fit the relationship between the shear wave velocity and depth using a power function model, and calculate the mean and standard deviation of the shear wave velocity at different depths based on the fitting parameters. S3. Using the mean and standard deviation of the shear wave velocity respectively, perform... V s - Simulation of structured unconditional random fields and conditional random fields, and obtain simulation results; S4. Based on the simulation results, the seismic liquefaction is analyzed to obtain the analysis results; The power function model is In the formula, , b The methods for calculating the mean shear wave velocity at different depths, representing the fitting parameters, include: ， In the formula, E [ V s ( h )] indicates depth h The mean shear wave velocity at the location; p ++ , p -- , p +- , p -+ The weight function; in, p ++ = p -- =1+ ρ / 4， p +- = p -+ =1- ρ / 4， In the formula, ρ The correlation coefficient represents the fitted parameters; V s ± ± The calculation formula is: ， , This represents the mean of the fitted parameters. σ [ ]、 σ [ b ] represents the standard deviation of the fitted parameters; S3 includes: S31. The mean and standard deviation of the shear wave velocity are analyzed. Vs -Structural unconditional random field simulation, obtaining unconditional random field simulation results; S32. Correct the unconditional random simulation results using the actual shear wave velocity at the borehole location, and obtain... Vs - A conditional random field for the structure, and the simulation results are obtained; Vs - Representation methods for structured unconditional random fields include: ， In the formula, Indicates the coordinates ( x , y An unconditional random field at ( ) location; E [ln V s ( h )]and σ [ln V s [h] respectively represent the depth h ln V s ( h The mean and standard deviation of ), ln H Vs ( x , y ) represents the standard Gaussian random field after taking the logarithm of the soil shear wave velocity.

2. The method for simulating non-stationary random fields of seabed wave velocity structure according to claim 1, characterized in that, Methods for calculating the standard deviation of shear wave velocity at different depths include: ， In the formula, σ [ Vs ( h )] indicates depth h The standard deviation of the shear wave velocity at that location, The second moment representing the shear wave velocity, E [ V s( h )] indicates depth h The average shear wave velocity at that location.

3. The method for simulating non-stationary random fields of seabed wave velocity structure according to claim 1, characterized in that, The simulation results include: V s，cn =[ V s，BH ， V s，Pcn ]， In the formula, V s，cn express V s - Shear wave velocity structure in structural conditional random fields. V s，BH This represents the actual shear wave velocity at the borehole location. V s，Pcn This represents the simulated shear wave velocity in a conditional random field at locations other than boreholes.

4. The method for simulating non-stationary random fields of seabed wave velocity structure according to claim 1, characterized in that, The method for obtaining the analysis results includes: when the safety factor is ≤1, the soil will liquefy; otherwise, liquefaction will not occur. The method for calculating the safety factor includes: ， In the formula, This indicates the cyclic resistance ratio of soil layers under earthquake loading. Indicates magnitude =7.5, effective overburden pressure =100 kPa is the cruising stress ratio of the reference soil layer. This represents the safety factor.

5. A seabed wave velocity structure non-stationary random field simulation system, characterized in that, include: Acquisition unit, fitting unit, simulation unit, and analysis unit; The acquisition unit is used to acquire borehole data and obtain the shear wave velocity of the seabed soil based on the borehole data. The fitting unit is used to fit the relationship between the shear wave velocity and the depth using a power function model, and to calculate the mean and standard deviation of the shear wave velocity at different depths based on the fitting parameters. The simulation unit is used to perform simulations using the mean and standard deviation of the shear wave velocity. V Simulations of s-structured unconditional random fields and conditional random fields were performed, and simulation results were obtained. The analysis unit is used to analyze earthquake liquefaction based on the simulation results and obtain analysis results; The power function model is In the formula, , b The methods for calculating the mean shear wave velocity at different depths, representing the fitting parameters, include: ， In the formula, E [ V s ( h )] indicates depth h The average shear wave velocity at that location; p ++ , p -- , p +- , p -+ The weight function; in, p ++ = p -- =1+ ρ / 4， p +- = p -+ =1- ρ / 4， In the formula, ρ The correlation coefficient represents the fitted parameters; V s ± ± The calculation formula is: ， , This represents the mean of the fitted parameters. σ [ ]、 σ [ b ] represents the standard deviation of the fitted parameters; The working process of the simulation unit includes: The mean and standard deviation of the shear wave velocity were analyzed. Vs -Structural unconditional random field simulation, obtaining unconditional random field simulation results; The unconditional random simulation results were corrected using the actual shear wave velocity at the borehole location to obtain... Vs - A conditional random field for the structure, and the simulation results are obtained; Vs - Representation methods for structured unconditional random fields include: ， In the formula, Indicates the coordinates ( x , y An unconditional random field at ( ) location; E [ln Vs ( h )]and σ [ln Vs [h] respectively represent the depth h ln Vs ( h The mean and standard deviation of ), ln HV s( x , y ) represents the standard Gaussian random field after taking the logarithm of the soil shear wave velocity.

Images