Slope digital twinning construction method and system based on patch algorithm

Abstract

The invention discloses a slope digital twinning construction method based on a patch algorithm. The method comprises the following steps: obtaining probability distribution of key parameters of a rock-soil body; establishing a slope finite element model, and extracting integral point coordinates; generating a parameter unconditional random field; determining an influence range according to coordinates of known points or known measuring lines and real parameter values in an actual physical field, and generating a parameter condition random field obeying standard normal distribution on integral point coordinates by using a patch algorithm; converting into a parameter conditional random field obeying real distribution; calculating to obtain a slope target output response result; known points or known measuring lines are added, so that the conditional random field is closer to a real site, and a reliable slope stability analysis result is obtained. According to the method, the parameter space variability is considered, the patch algorithm is adopted to construct the parameter conditional random field to reflect the real geological condition of the side slope, the method is suitable for the large-scale and sparse sampling site investigation condition of geotechnical engineering, side slope digital twinning is achieved, and a reliable side slope stability evaluation result is obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of slope uncertainty analysis and stability evaluation, and specifically relates to a slope digital twin construction method and system based on a patch algorithm. Background Art

[0002] With the expansion of the construction scale of infrastructure projects such as water conservancy and hydropower, high-speed railways, highways, and urban rail transit in my country, a large number of engineering slopes have emerged. Affected by natural factors and human activities, landslides and other disasters caused by slope instability are numerous, widely distributed, and difficult to prevent. The stability evaluation and safety control of slopes have become the focus of geotechnical engineering research.

[0003] As a new technology that solves the problem of two-way mapping, dynamic interaction, and real-time connection between virtual space and real entities, digital twins have attracted widespread attention from all walks of life. In order to promote the application of digital twin technology in slope engineering, it is of great practical significance to use available site survey data such as on-site and indoor test data to accurately and realistically reconstruct geological conditions and establish a reliable slope calculation model to lay a solid foundation for subsequent design and construction.

[0004] Natural rock and soil have spatial variability due to the effects of deposition, post-deposition, weathering, transportation, and different load histories, indicating that the material properties at different locations in space are different but have certain statistical correlations. For slope engineering, the inherent spatial variability of rock and soil will affect the failure mode of the slope to a certain extent, which is one of the main sources of slope uncertainty. However, most related studies generate unconditional random fields based on prior information to characterize the spatial variability of rock and soil parameters, without making full use of available field and indoor test data and other site survey data, which leads to large differences between model calculation results and field measured data.

[0005] In addition, although the conditional random fields developed in recent years can use survey data to update the probability distribution and statistical characteristics of spatially variable rock and soil parameters, the existing conditional random field generation methods have cumbersome calculation processes and are difficult to adapt to the large-scale and sparsely sampled site survey characteristics commonly seen in slope engineering. Therefore, they are difficult to promote and apply in actual engineering projects. Summary of the invention

[0006] The purpose of the present invention is to address the above-mentioned deficiencies in the prior art and provide a method and system for constructing a digital twin of a slope based on a patch algorithm, which is used to consider the spatial variability of rock and soil bodies, and adopt the patch algorithm to use the available actual survey data to construct a parameter conditional random field to reflect the real geological conditions of the slope, thereby realizing a digital twin. The digital twin is suitable for large-scale and sparsely sampled site surveys in geotechnical engineering, and provides technical support for subsequent slope stability evaluation.

[0007] The present invention provides a slope digital twin construction method based on a patch algorithm, comprising the following steps: Step 1: Determine one or more key parameters of the rock and soil mass whose spatial variability needs to be considered, and obtain the probability distribution of the parameters and their statistical characteristics; Step 2: Determine the dimensions and scale of the slope site to be simulated, establish a finite element model of the slope, set loads and boundary conditions, divide the finite element grid, and extract the coordinates of the integration points; Step 3: Based on random field theory, generate an unconditional random field of parameters that obeys the standard normal distribution at the coordinates of the integration points; Step 4: Obtain the coordinates of multiple known points or known survey lines and the real parameter values ​​in the actual physical field through geological survey, determine the influence range of the known points or known survey lines, and generate a parameter conditional random field that obeys the standard normal distribution on the integral point coordinates using the patch algorithm based on the unconditional random field obtained in step 3; Step 5: According to the statistical characteristic values ​​of the parameters, the parameter conditional random field that obeys the standard normal distribution is transformed into the parameter conditional random field that obeys the true distribution; Step 6: Based on the conditional random field generated values ​​of the parameters at the material integration points, a finite element analysis is performed on the slope stability problem to calculate the corresponding slope target output response results; Step 7: Add known points or known survey lines and repeat steps 4 to 6 to reduce the uncertainty of parameters, making the conditional random field closer to the real site and making the slope stability analysis results more reliable.

[0008] Furthermore, the step 1 specifically includes the following sub-steps: Step 1.1: From the parameters of cohesion, internal friction angle, permeability and elastic modulus of the rock mass, select and determine the key parameters of the rock mass with spatial variability X = [X1, X2, ...X k ], where X1, X2, ...X k are all random variables, k is the number of variables; Step 1.2, determining the probability distribution type of the key parameters of the rock and soil mass, wherein the probability distribution type includes normal distribution or lognormal distribution; Step 1.3: Statistical analysis is performed on the data obtained through actual survey to obtain statistical characteristics of key parameters of the rock and soil mass, wherein the statistical characteristics include mean, coefficient of variation, autocorrelation function and autocorrelation distance.

[0009] Furthermore, the dimension of the slope site in step 2 can be two-dimensional or three-dimensional. Taking two-dimensional as an example, the horizontal axis direction is the X-axis direction, the vertical axis direction is the Y-axis direction, the X-axis direction is perpendicular to the Y-axis direction, and the extracted integral point coordinates are D n×2 It is expressed as:

[0010] In the formula, n is the number of integral points, x i , y i Respectively i The horizontal and vertical coordinates of the coordinate points, 1≤ i ≤ n .

[0011] Furthermore, step 3 discretizes the continuous parameter random field into a finite number of random variables at the integral point based on the random field theory, and can adopt the covariance matrix decomposition method, the spectral decomposition method, the Karhunen-Loève (KL) expansion method, etc. Taking the covariance matrix decomposition method as an example, step 3 specifically includes the following steps: Step 3.1: For each random variable, based on the autocorrelation function and the autocorrelation distance in the horizontal and vertical directions determined in step 1 l X , l Y ,generate n dimensional independent random sample A 1×n , which follows a standard normal distribution with a mean of 0 and a variance of 1; Step 3.2: Use the autocorrelation function to calculate the correlation coefficient matrix between the integral point coordinates ρ n×n :

[0012] In the formula, ρ i,j For the i and j Correlation coefficient of parameters at coordinate points, 1≤ i ≤ n , 1≤ j ≤ n ; Step 3.3: For the correlation coefficient matrix ρ n×n Perform Cholesky decomposition:

[0013] Get the upper triangular matrix E n×n , using the matrix E n×n Pair Matrix A 1×n Perform a linear transformation:

[0014] Obtain a parameterized unconditional random field that obeys a standard normal distribution B 1×n .

[0015] Furthermore, in step 4, the site investigation data is a known point or a known survey line. The site investigation data obtained by means of drilling sampling or cross-plate shear test is regarded as a known point; the site investigation data obtained by means of static penetration test or standard penetration test is regarded as a known survey line; The real parameter values ​​of known points and known measurement lines in the actual physical field are z , according to the parameter mean determined in step 1 μ X and coefficient of variation COV X , the true parameter value z Transformed into known values ​​that follow a standard normal distribution Z : ; Where ln represents the natural logarithm function.

[0016] Furthermore, step 4 uses a patch algorithm to generate a parameter conditional random field that obeys a standard normal distribution on the integral point coordinates. When the site survey data is a known point, step 4 specifically includes the following sub-steps: Step 4.1: Get the coordinates of known points P i = ( x i , y i ), 1≤ i ≤ m , m is the number of known points; Step 4.2: Determine the influence range of the known point. In the two-dimensional coordinate system, the influence range is an ellipse with the known point as the center. The lengths of the major and minor axes are equal to the autocorrelation distances in the horizontal and vertical directions, respectively. l X , l Y , l X ≥ l Y ; Step 4.3, traverse each integral point, when its coordinates are outside the influence range of the known point, the parameter value of the conditional random field C is the generated value of the unconditional random field in step 3; when its coordinates are equal to the known point coordinates, the parameter value of the conditional random field C Equal to the known value; when its coordinates are within the influence range of one or more known points, the patch algorithm is used to calculate the parameter value within the influence range of the known points. The steps are as follows: Step 4.3.1, the interpolation point b is located at v Within the influence range of known points, 1≤ v ≤ m , for each known point a i , 1≤ i ≤ v , take the known point as the endpoint, draw a ray through the known point and the point to be interpolated, and intersect the boundary of the influence range of the known point at the mapping point c i , the mapping point, the point to be interpolated and the known point are collinear, and the distances between the point to be interpolated and the known point and the mapping point are calculated as p i , q i , 1≤ i ≤ v ; Step 4.3.2: For each known point a i , based on the known value Z i and the generated value of the unconditional random field at the mapping point coordinates B i To interpolate: ; Step 4.3.3: Interpolate the results of each known point R i Linear addition obtains the parameter value of the conditional random field at the interpolation point b C : ; In the formula v Indicates the number of known points within the influence range of the interpolation point b.

[0017] Furthermore, in step 4, a parameter conditional random field obeying a standard normal distribution is generated on the integral point coordinates. When the site survey data is a known survey line, step 4 specifically includes the following sub-steps: Step 4.1: Get the horizontal coordinates of the known survey line x i , 1≤ i ≤ t , t The number of known survey lines and the depth direction coordinates of the known survey lines y , y 1≤ y ≤ y 2, y 1. y 2 are the coordinates of the lower and upper endpoints of the known survey line, and the depth of the survey line b = y2- y 1. All points within the survey line depth are known; Step 4.2: Determine the influence range of the known survey line. In the two-dimensional coordinate system, within the depth range of the survey line, the influence range is a rectangle, the length of the rectangle is the depth of the survey line, and the width of the rectangle is equal to the horizontal autocorrelation distance. l X twice; outside the depth range of the survey line, the influence range is a semi-ellipse, the center point is the two end points of the known survey line, and the length of the major semi-axis and the minor semi-axis is equal to the autocorrelation distance in the horizontal and vertical coordinate directions respectively. l X , l Y ; Step 4.3, traverse each integral point, when its coordinates are outside the influence range of the known survey line, the parameter value of the conditional random field C is the generated value of the unconditional random field in step 3; when its coordinates are on a known survey line, the parameter value of the conditional random field is C Equal to the known value on the known survey line; when its coordinates are within the influence range of one or more known survey lines, the patch algorithm is used to calculate the parameter value within the influence range of the known survey lines. The steps are as follows: Step 4.3.1, the interpolation point b is located at Known survey lines s i In the scope of influence, , when the depth coordinate of the interpolation point y 3 Within the depth range of the survey line, that is y 1≤ y 3≤ y 2. Draw a straight line through the interpolation point, perpendicular to the known survey line, and intersect the known survey line at the known point a i , intersecting the boundary of the influence range of the known survey line at the mapping point c i , calculate the distances between the interpolation point and the known survey line and mapping point respectively p i , q i , ; When the depth coordinates of the interpolation point y 3 Outside the depth range of the survey line, that is y 3≤ y 1 or y 3≥ y 2. For each known survey line, from the known survey line endpoint ss i Draw a ray through the interpolation point and intersect the boundary of the known survey line influence range at the mapping point c i , the mapping point, the point to be interpolated, and the known endpoint of the survey line are collinear; the distances between the point to be interpolated and the known endpoint of the survey line and the mapping point are calculated as follows: pi , q i , ; Step 4.3.2: For each known survey line s i , , based on the known value Z i and the generated value of the unconditional random field at the mapping point coordinates B i To interpolate: ; Step 4.3.3: Interpolate the interpolation results of each known survey line R i Linear addition obtains the parameter value of the conditional random field at the point to be interpolated C : ; In the formula Indicates the number of known survey lines within the influence range of the interpolation point b.

[0018] Furthermore, in step 4, according to the stationary characteristics of the random field, the probability density function of the random variable at each point in the unconditional random field is the same and obeys the standard normal distribution, that is, the mean μ = 0, variance σ 2 = 1; According to the properties of normal distribution, the interpolation points within the influence range of the known points also obey the normal distribution, and their mean and variance They are: ; ; From the above formula, we can see that any interpolation point within the influence range of the known point in the conditional random field also obeys the standard normal distribution; Similarly, any interpolation point within the influence range of the known measurement line in the conditional random field also obeys the standard normal distribution; Therefore, the mean and variance of the conditional random field generated by the patch algorithm are stationary.

[0019] Furthermore, the patch algorithm used in step 4 limits the influence range of known points, and can regard the survey data with small sampling intervals as continuous known survey lines rather than discrete points for direct interpolation. Compared with other conditional random field generation methods, the patch algorithm is simple and efficient, and is more suitable for large-scale and sparsely sampled site surveys commonly seen in geotechnical engineering. It can provide an effective tool for the field of geotechnical engineering to characterize the spatial variability of rock and soil parameters using field or indoor test data.

[0020] Furthermore, step 5 is based on the parameter mean determined in step 1 μ X and coefficient of variation COV X , the parameter conditional random field that obeys the standard normal distribution C Transformed into a parameter conditional random field that obeys the true distribution C z :

[0021] Furthermore, although the patch algorithm is based on the fact that the parameters obey the standard normal distribution, since the standard normal distribution can be transformed into any non-standard normal distribution through a simple linear transformation, and the normal distribution can be extended to simulate correlated non-normal random fields through the Nataf transformation, this method is also applicable to the case where the parameters obey other common distributions.

[0022] Furthermore, the target output response of the slope in step 6 may be a slope stability safety factor, a slope deformation displacement, etc., which is determined according to actual engineering requirements; Furthermore, in step 7, known points or known survey lines are added and steps 4 to 6 are repeated to reduce the uncertainty of parameters, making the conditional random field closer to the real site and the stability analysis results of the slope more reliable, which emphasizes the necessity of comprehensive investigation of important slope projects.

[0023] Another object of the present invention is to provide a slope digital twin construction system based on a patch algorithm, comprising: A data acquisition module is used to determine one or more key parameters of the rock and soil mass that need to take into account spatial variability, and obtain the probability distribution of the parameters and their statistical characteristics; The model building module is used to determine the dimensions and scale of the slope site to be simulated, establish the slope finite element model, set the load and boundary conditions, divide the finite element mesh, and extract the coordinates of the integration points; The unconditional random field construction module that obeys the standard normal distribution is used to generate parameter unconditional random fields that obey the standard normal distribution at the integration point coordinates; The conditional random field construction module that obeys the standard normal distribution is used to generate a parameter conditional random field that obeys the standard normal distribution on the integral point coordinates using the patch algorithm based on the coordinates of the known points or known survey lines obtained from actual surveys and the real parameter values ​​in the actual physical field; A conditional random field construction module that obeys the true distribution is used to transform the parameter conditional random field that obeys the standard normal distribution into the parameter conditional random field that obeys the true distribution according to the statistical characteristic values ​​of the parameters; The response prediction module is used to generate values ​​based on the conditional random field of parameters at the material integration points, perform finite element analysis on the slope stability problem, and calculate the corresponding slope target output response results; The optimization module is used to increase known points, reduce parameter uncertainty, make the conditional random field closer to the real site, and make the slope stability analysis results more reliable.

[0024] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) The slope digital twin construction method based on the patch algorithm provided by the present invention is based on engineering digital twin technology and random field theory, combines the finite element modeling method with the patch algorithm, and uses the available site survey data to generate a conditional random field that reflects the spatial variability of rock and soil parameters and satisfies known correlations. A numerical model that can reflect the real soil properties and a slope digital twin model are constructed, which lays a solid foundation for subsequent design and construction and promotes the development of digital twins in the field of geotechnical engineering.

[0025] (2) The present invention uses a patch algorithm to limit the influence range of known points. The survey data with a small sampling interval can be regarded as continuous known survey lines instead of discrete points for direct interpolation. Compared with the traditional conditional random field generation method, the patch algorithm is simple and efficient, and is more suitable for large-scale and sparsely sampled site surveys commonly seen in geotechnical engineering. It can provide an effective tool for the field of geotechnical engineering to characterize the spatial variability of rock and soil parameters using field or indoor test data.

[0026] (3) After establishing a conditional random field that is consistent with the actual site of the slope, the present invention further analyzes and calculates the slope stability problem to obtain more reliable slope stability analysis results, effectively improving the accuracy of slope stability evaluation.

[0027] (4) The present invention constructs a digital twin system for slopes, which can accurately and realistically reconstruct geological conditions. As the number of exploration points increases, the constructed conditional random field infinitely approaches the real site, highlighting the necessity of comprehensive surveys of important slope projects, providing a feasible method for the effective use of site survey data, and providing guidance for the design and risk prevention and control of important slope projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 This is a flow chart of the slope digital twin construction method described in the present invention.

[0029] Figure 2Schematic diagram of the slope finite element model of a preferred embodiment of the present invention.

[0030] Figure 3 Schematic diagram of an unconditional random field according to a preferred embodiment of the present invention.

[0031] Figure 4 A schematic diagram of a real site of a preferred embodiment of the present invention.

[0032] Figure 5 It is a schematic diagram of interpolation based on known points by a patch algorithm in a preferred embodiment of the present invention.

[0033] Figure 6 FIG. 1 is a schematic diagram of a conditional random field based on a known point according to a preferred embodiment of the present invention.

[0034] Figure 7 It is a schematic diagram of interpolation based on known survey lines by a patch algorithm in a preferred embodiment of the present invention.

[0035] Figure 8 Schematic diagram of actual parameter values ​​of known survey lines according to a preferred embodiment of the present invention.

[0036] Fig. 9 FIG. 4 is a schematic diagram of a conditional random field based on a known measurement line according to a preferred embodiment of the present invention.

[0037] Fig.10 Schematic diagram of a conditional random field based on three known points according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0039] Slope digital twin construction method based on patch algorithm, such as Figure 1 shown.

[0040] In one embodiment of the present invention, in the construction of a certain slope digital twin system, the slope digital twin construction method based on the patch algorithm provided by the present invention is adopted, and the specific implementation steps are as follows: Step 1: Determine one or more key parameters of the rock and soil mass whose spatial variability needs to be considered, and obtain the probability distribution of the parameters and their statistical characteristics. c Spatial variability of cohesion c It follows a log-normal distribution with a mean μ c = 10 kPa, coefficient of variation COV c = 0.3, using a square exponential correlation function ρ Describe the variability of a random field:

[0041] Where: τ X and τ Y Respectively represent the relative distance between two points in the horizontal and vertical directions. l X = 20 m and l Y = 2 m represents the autocorrelation distance in the horizontal and vertical directions respectively.

[0042] Step 2: In the embodiment, a slope model is established by using finite element software ABAQUS, such as Figure 2 As shown in the figure, the slope height is 10 m, the foundation depth is 5 m, the slope angle is 45°, and the soil weight is γ = 0.3. CPE4 units are used for meshing, with 1443 units, 5772 integration points, and the coordinates of the integration points are extracted. Assuming that the stability of the soil slope belongs to a plane strain problem, the boundary conditions are set as fixed constraints at the bottom of the model, normal constraints on both sides, and the normal displacement is 0, which means that sliding is allowed along the sliding surface, and the three upper surfaces are free boundaries. The soil material is described based on the ideal elastic-plastic constitutive model and the Moore-Coulomb yield criterion, and the strength reduction method is used to analyze the stability of the slope.

[0043] Step 3: Based on random field theory, the covariance matrix decomposition method is used to generate an unconditional random field of parameters that obey the standard normal distribution at the integration point coordinates, such as Figure 3 As shown, the specific steps include: Step 3.1, Generate n dimensional independent random sample A 1×n , n = 5772, which follows a standard normal distribution with a mean of 0 and a variance of 1; Step 3.2: Use the autocorrelation function to calculate the correlation coefficient matrix between the integral point coordinates ρ n×n :

[0044] In the formula, ρ i,j For the i and j Correlation coefficient of parameters at coordinate points, 1≤ i ≤ n , 1≤ j ≤ n ; Step 3.3: Correlation coefficient matrix ρ n×nPerform Cholesky decomposition:

[0045] Get the upper triangular matrix E n×n , using the matrix E n×n Pair Matrix A 1×n Perform a linear transformation:

[0046] Obtain a parameterized unconditional random field that obeys a standard normal distribution B 1×n ,like Figure 3 shown.

[0047] Step 4: In the embodiment, the method of step 3 is used to generate a typical simulation sample of a random field as a real field, such as Figure 4 As shown. Site survey data comes from the real site, which can be known points or known survey lines. In actual projects, the data obtained by survey methods with larger sampling intervals such as drilling sampling and cross-plate shear test are considered as known points, and the sampling interval is greater than 1m; the data obtained by survey methods with smaller sampling intervals such as static penetration test and standard penetration test are considered as known survey lines, and the sampling interval is about 0.1m. Assuming that the real site obeys the standard normal distribution, in actual projects, the real parameter values ​​of known points and known survey lines in the actual physical field are z , according to the parameter mean determined in step 1 μ c and coefficient of variation COV c , the true parameter value z Transformed into known values ​​that follow a standard normal distribution Z :

[0048] (1) When the site survey data are known points, the patch algorithm is used to generate a parameter conditional random field that obeys the standard normal distribution at the integral point coordinates, such as Figure 5 As shown, the specific steps include: Step 4.1: Get the coordinates of known points P i = ( x i , y i ), 1≤ i ≤ m , m is the number of known points; Step 4.2: Determine the influence range of the known point. In the two-dimensional coordinate system, the influence range is an ellipse with the known point as the center. The lengths of the major and minor axes are equal to the autocorrelation distances in the horizontal and vertical coordinate directions, respectively. l X , l Y , l X ≥ l Y ; Step 4.3, traverse each integral point, when its coordinates are outside the influence range of the known point, the parameter value of the conditional random field C is the generated value of the unconditional random field in step 3; when its coordinates are equal to the known point coordinates, the parameter value of the conditional random field C Equal to the known value; when its coordinates are within the influence range of one or more known points, the patch algorithm is used to calculate the parameter value within the influence range of the known points. The steps are as follows: Step 4.3.1, the interpolation point b is located at v Within the influence range of known points, 1≤ v ≤ m , for each known point a i , 1≤ i ≤ v , take the known point as the endpoint, draw a ray through the known point and the point to be interpolated, and intersect the boundary of the influence range of the known point at the mapping point c i , the mapping point, the point to be interpolated, and the known point are collinear, and the distances between the point to be interpolated and the known point and the mapping point are calculated as p i , q i , 1≤ i ≤ v ,; Step 4.3.2: For each known point a i , based on the known value Z i and the generated value of the unconditional random field at the mapping point coordinates B i To interpolate:

[0049] Step 4.3.3: Interpolate the results of each known point R i Linear addition obtains the parameter value of the conditional random field at the interpolation point b C :

[0050] In the embodiment, taking a known point a as an example, the coordinates P= (5, 7.5), known value Z From Figure 4 The actual venue shown, Z = 9.8 kPa, parameter conditional random field that follows standard normal distribution C like Figure 6 shown.

[0051] (2) When the site survey data is a known survey line, the patch algorithm is used to generate a parameter conditional random field that obeys the standard normal distribution at the integration point coordinates, such as Figure 7 As shown, the specific steps include: Step 4.1: Get the horizontal coordinates of the known survey line x i , 1≤ i ≤ t , t The number of known survey lines and the depth direction coordinates of the known survey lines y , y 1≤ y ≤ y 2, y 1. y 2 are the coordinates of the lower and upper endpoints of the known survey line, and the depth of the survey line b = y 2- y 1. All points within the survey line depth are known; Step 4.2: Determine the influence range of the known survey line. In the two-dimensional coordinate system, within the depth range of the survey line, the influence range is a rectangle with a length of the survey line depth and a width of 2 times the horizontal autocorrelation distance. l X ; Outside the depth range of the survey line, the influence range is a semi-ellipse, the center point of which is the two end points of the known survey line, and the length of the major semi-axis and the minor semi-axis are equal to the autocorrelation distance in the horizontal and vertical coordinate directions respectively l X , l Y ; Step 4.3, traverse each integral point, when its coordinates are outside the influence range of the known survey line, the parameter value of the conditional random field C is the generated value of the unconditional random field in step 3; when its coordinates are on a known survey line, the parameter value of the conditional random field is C Equal to the known value on the known survey line; when its coordinates are within the influence range of one or more known survey lines, the patch algorithm is used to calculate the parameter value within the influence range of the known survey lines. The steps are as follows: Step 4.3.1, the interpolation point b is located at v Known survey lines s i Influence range, 1≤ v ≤ t, when the depth coordinate of the interpolation point y 3 Within the depth range of the survey line, that is y 1≤ y 3≤ y 2. Draw a straight line through the interpolation point, perpendicular to the known survey line, and intersect the known survey line at the known point a i , intersecting the boundary of the known survey line influence range at the mapping point c i , calculate the distances between the interpolation point and the known survey line and mapping point respectively p i , q i , 1≤ i ≤ v ; When the depth coordinates of the interpolation point y 3 Outside the depth range of the survey line, that is y 3≤ y 1 or y 3≥ y 2. For each known survey line, from the known survey line endpoint ss i Draw a ray through the interpolation point and intersect the boundary of the known survey line influence range at the mapping point c i , the mapping point, the point to be interpolated, and the known endpoint of the survey line are collinear. The distances between the point to be interpolated and the known endpoint of the survey line and the mapping point are calculated as follows: p i , q i , 1≤ i ≤ v ; Step 4.3.2: For each known survey line s i , 1≤ i ≤ v , based on the known value Z i and the generated value of the unconditional random field at the mapping point coordinates B i To interpolate:

[0052] Step 4.3.3: Interpolate the interpolation results of each known survey line R i Linear addition obtains the parameter value of the conditional random field at the point to be interpolated C :

[0053] In the embodiment, taking a known survey line s as an example, the horizontal coordinate of the known survey line x = 5 m, the depth direction coordinates of the survey line are known y , y1≤ y ≤ y 2, y 1 = 3 m, y 2= ​​15 m are the coordinates of the lower and upper endpoints of the known survey line, and the depth of the survey line b = y 2- y 1 = 12 m, the depth of all points in the survey line is known, such as Figure 8 As shown, the value comes from Figure 4 The actual site shown is a parameter conditional random field that follows a standard normal distribution C like Fig. 9 shown.

[0054] (3) The mean and variance of the conditional random field generated by the patch algorithm in step 4 are stationary, as derived as follows: According to the stationary characteristics of the random field, the probability density function of the random variables at each point in the unconditional random field containing known points and known measurement lines is the same and obeys the standard normal distribution, that is, the mean μ = 0, variance σ 2 = 1. According to the properties of normal distribution, the interpolation points within the influence range of known points or known measurement lines also obey normal distribution, and their mean and variance are:

[0055] It can be seen from the above formula that any interpolation point within the influence range of a known point or a known measurement line in the conditional random field also obeys the standard normal distribution. Therefore, the mean and variance of the conditional random field generated by the patch algorithm are stable.

[0056] Step 5: Calculate the mean of the parameters determined in step 1 μ c and coefficient of variation COV c , the parameter conditional random field that obeys the standard normal distribution C Transformed into a parameter conditional random field that obeys the true distribution C z :

[0057] Although the patch algorithm is based on the parameters obeying the standard normal distribution, since the standard normal distribution can be transformed into any non-standard normal distribution through a simple linear transformation, and the normal distribution can be extended to simulate correlated non-normal random fields through the Nataf transformation, this method is also applicable to the case where the parameters obey other common distributions.

[0058] Step 6: Based on the conditional random field generated values ​​of the parameters at the material integration points, a finite element analysis is performed on the slope stability problem to calculate the corresponding slope target output response result. In the embodiment, the slope target output response is the slope stability safety factor F s , based on the unconditional random field generation value, F s = 1.23, based on a conditional random field generated value at a known point, F s = 1.21, based on a conditional random field generated value of a known survey line, F s = 1.17, which is due to the fact that most of the known values ​​are less than the mean value of 10 kPa.

[0059] Step 7: The number of known points increases from one to three, and their coordinates are P 1= (5, 3), P 2= ​​(5, 7.5), P 3= (5,12), known value comes from Figure 4 The real sites shown are Z 1 = 11.3 kPa, Z 2 = 9.8 kPa, Z 3 = 8.2 kPa, the generated parameter conditional random field follows the standard normal distribution C like Fig.10 As shown in the figure, the slope stability safety factor is calculated F s =1.19. The known points increase from one point to three points and then to a known line. The conditional random fields are as follows: Figure 6 , Fig. 9 , Fig.10 As shown in Figure 2, as the known information increases, the uncertainty of the parameters decreases, and the conditional random field becomes closer to Figure 4 For the real site shown, the slope stability analysis results are more reliable.

[0060] The implementation results show that the slope digital twin construction method based on the patch algorithm provided by the present invention can generate a conditional random field that reflects the spatial variability of rock and soil parameters and satisfies the known correlation by using the patch algorithm and available site survey data, and can construct a slope digital twin system that reflects the real geological conditions. The patch algorithm used limits the influence range of known points, and can treat the survey data with a small sampling interval as a continuous known survey line instead of directly interpolating discrete points. Compared with other conditional random field generation methods, the patch algorithm is simple and efficient, and is more suitable for large-scale and sparsely sampled site surveys commonly seen in geotechnical engineering. It can provide an effective tool for the field of geotechnical engineering to characterize the spatial variability of rock and soil parameters using field or indoor test data. With the increase in the number of exploration points, the constructed conditional random field is closer to the real site, and the numerical calculation model provided is more reliable. This emphasizes the necessity of comprehensive survey of important slope projects, provides a feasible method for the effective use of site survey data, provides guidance for the design and risk prevention and control of important slope projects, and promotes the development of digital twins in the field of geotechnical engineering.

[0061] The present invention also provides a slope digital twin construction system based on conditional random fields, comprising: A data acquisition module is used to determine one or more key parameters of the rock and soil mass that need to take into account spatial variability, and obtain the probability distribution of the parameters and their statistical characteristics; The model building module is used to determine the dimensions and scale of the slope site to be simulated, establish the slope finite element model, set the load and boundary conditions, divide the finite element mesh, and extract the coordinates of the integration points; The unconditional random field construction module that obeys the standard normal distribution is used to generate parameter unconditional random fields that obey the standard normal distribution at the integration point coordinates; The conditional random field construction module that obeys the standard normal distribution is used to generate a parameter conditional random field that obeys the standard normal distribution on the integral point coordinates using the patch algorithm based on the coordinates of the known points or known survey lines obtained from actual surveys and the real parameter values ​​in the actual physical field; A conditional random field construction module that obeys the true distribution is used to transform the parameter conditional random field that obeys the standard normal distribution into the parameter conditional random field that obeys the true distribution according to the statistical characteristic values ​​of the parameters; The response prediction module is used to generate values ​​based on the conditional random field of parameters at the material integration points, perform finite element analysis on the slope stability problem, and calculate the corresponding slope target output response results; The optimization module is used to increase known points, reduce parameter uncertainty, make the conditional random field closer to the real site, and make the slope stability analysis results more reliable.

Claims

1. A slope digital twin construction method based on patch algorithm, characterized in that: The following steps are involved: Step 1: determine the key parameters of the rock and soil mass that need to consider spatial variability, and obtain the probability distribution and statistical characteristics of the key parameters of the rock and soil mass; Step 2: Determine the dimensions and scale of the slope site to be simulated, establish a finite element model of the slope, set loads and boundary conditions, divide the finite element grid, and extract the coordinates of the integration points; Step 3: Based on random field theory, generate an unconditional random field of parameters that obeys the standard normal distribution at the coordinates of the integration points; Step 4: Obtain the coordinates of multiple known points or known survey lines and the real parameter values ​​in the actual physical field through geological survey, determine the influence range of the known points or known survey lines, and generate a parameter conditional random field that obeys the standard normal distribution on the integral point coordinates using the patch algorithm based on the unconditional random field obtained in step 3; Step 5: According to the statistical characteristic values ​​of the parameters, the parameter conditional random field that obeys the standard normal distribution is transformed into the parameter conditional random field that obeys the true distribution; Step 6: Based on the conditional random field generated values ​​of the parameters at the material integration points, a finite element analysis is performed on the slope stability problem to calculate the slope target output response result; Step 7: Add known points or known survey lines and repeat steps 4 to 6 to reduce the uncertainty of parameters, make the conditional random field closer to the real site, and obtain reliable slope stability analysis results.

2. The slope digital twin construction method based on patch algorithm according to claim 1 is characterized in that: The step 1 specifically includes the following sub-steps: Step 1.1: From the parameters of cohesion, internal friction angle, permeability and elastic modulus of the rock mass, select and determine the key parameters of the rock mass with spatial variability X = [X1, X2, ...X k ], where X1, X2, ...X k are all random variables, k is the number of variables; Step 1.2, determining the probability distribution type of the key parameters of the rock and soil mass, wherein the probability distribution type includes normal distribution or lognormal distribution; Step 1.3: Statistical analysis is performed on the data obtained through actual survey to obtain statistical characteristics of key parameters of the rock and soil mass, wherein the statistical characteristics include mean, coefficient of variation, autocorrelation function and autocorrelation distance.

3. The slope digital twin construction method based on patch algorithm according to claim 1 or 2 is characterized in that: In step 2, the slope site is two-dimensional or three-dimensional. Taking two-dimensional as an example, the extracted integral point coordinates are D n×2 for: ； In the formula, n is the number of points, x i , y i , i =1,2… n Respectively i The horizontal and vertical coordinates of a coordinate point.

4. The slope digital twin construction method based on patch algorithm according to claim 2 is characterized in that: The step 3 uses the covariance matrix decomposition method, the spectral decomposition method or the Karhunen-Loève expansion method to discretize the continuous parameter random field into a finite number of random variables at the integration points. Taking the covariance matrix decomposition method as an example, the step 3 specifically includes the following sub-steps: Step 3.1: For each random variable, based on the autocorrelation function and the autocorrelation distance in the horizontal and vertical directions determined in step 1 l X , l Y ,generate n dimensional independent random sample A 1×n , which follows a standard normal distribution with a mean of 0 and a variance of 1; Step 3.2: Use the autocorrelation function to calculate the correlation coefficient matrix between the integral point coordinates ρ n×n : ； In the formula, ρ i,j , i =1,2… n , j =1,2… n For the i and j Correlation coefficient of parameters at coordinate points; Step 3.3: For the correlation coefficient matrix ρ n×n Perform Cholesky decomposition: ； Get the upper triangular matrix E n×n , using the matrix E n×n Pair Matrix A 1×n Perform a linear transformation: ； Obtain a parameterized unconditional random field that obeys a standard normal distribution B 1×n .

5. The slope digital twin construction method based on patch algorithm according to claim 4 is characterized in that: In step 4, the site survey data is a known point or a known survey line, and the known point is obtained by means of drilling sampling or cross plate shear test; the known survey line is obtained by means of static penetration test or standard penetration test; The real parameter values ​​of known points and known measurement lines in the actual physical field are z , according to the parameter mean determined in step 1 μ X and coefficient of variation COV X , the true parameter value z Transformed into known values ​​that follow a standard normal distribution Z : ； Where ln represents the natural logarithm function.

6. The slope digital twin construction method based on patch algorithm according to claim 5 is characterized in that: Step 4 uses the patch algorithm to generate a parameter conditional random field that obeys the standard normal distribution on the integral point coordinates. When the site survey data is a known point, step 4 specifically includes the following sub-steps: Step 4.1: Get the coordinates of known points P i = ( x i , y i ), 1≤ i ≤ m , m is the number of known points; Step 4.2: Determine the influence range of the known point. In the two-dimensional coordinate system, the influence range is an ellipse with the center point being the known point. The lengths of the major and minor axes are equal to the autocorrelation distances in the horizontal and vertical directions, respectively. l X , l Y , l X ≥ l Y ; Step 4.3, traverse each integral point, when its coordinates are outside the influence range of the known point, the parameter value of the conditional random field C is the generated value of the unconditional random field in step 3; when its coordinates are equal to the known point coordinates, the parameter value of the conditional random field C Equal to the known value; when its coordinates are within the influence range of one or more known points, the patch algorithm is used to calculate the parameter value within the influence range of the known points. The steps are as follows: Step 4.3.1, the interpolation point b is located at v Within the influence range of known points, 1≤ v ≤ m , for each known point a i , 1≤ i ≤ v , take the known point as the endpoint, draw a ray through the known point and the point to be interpolated, and intersect the boundary of the influence range of the known point at the mapping point c i , the mapping point, the point to be interpolated and the known point are collinear, and the distances between the point to be interpolated and the known point and the mapping point are calculated as p i , q i , 1≤ i ≤ v ; Step 4.3.2: For each known point a i , based on the known value Z i and the generated value of the unconditional random field at the mapping point coordinates B i To interpolate: ； Step 4.3.3: Interpolate the results of each known point R i Linear addition obtains the parameter value of the conditional random field at the interpolation point b C : ； In the formula v Indicates the number of known points within the influence range of the interpolation point b.

7. The slope digital twin construction method based on patch algorithm according to claim 5 is characterized in that: In step 4, a parameter conditional random field that obeys a standard normal distribution is generated on the integral point coordinates. When the site survey data is a known survey line, step 4 specifically includes the following sub-steps: Step 4.1: Get the horizontal coordinates of the known survey line x i , 1≤ i ≤ t , t The number of known survey lines and the depth direction coordinates of the known survey lines y , y 1≤ y ≤ y 2, y 1. y 2 are the coordinates of the lower and upper endpoints of the known survey line, and the depth of the survey line b = y 2- y 1. All points within the survey line depth are known; Step 4.2: Determine the influence range of the known survey line. In the two-dimensional coordinate system, within the depth range of the survey line, the influence range is a rectangle, the length of the rectangle is the depth of the survey line, and the width of the rectangle is equal to the horizontal autocorrelation distance. l X twice; outside the depth range of the survey line, the influence range is a semi-ellipse, the center point is the two end points of the known survey line, and the length of the major semi-axis and the minor semi-axis is equal to the autocorrelation distance in the horizontal and vertical coordinate directions respectively. l X , l Y ; Step 4.3, traverse each integral point, when its coordinates are outside the influence range of the known survey line, the parameter value of the conditional random field C is the generated value of the unconditional random field in step 3; when its coordinates are on a known survey line, the parameter value of the conditional random field is C Equal to the known value on the known survey line; when its coordinates are within the influence range of one or more known survey lines, the patch algorithm is used to calculate the parameter value within the influence range of the known survey lines. The steps are as follows: Step 4.3.1, the interpolation point b is located at Known survey lines s i In the scope of influence, , when the depth coordinate of the interpolation point y 3 Within the depth range of the survey line, that is y 1≤ y 3≤ y 2. Draw a straight line through the interpolation point, perpendicular to the known survey line, and intersect the known survey line at the known point a i , intersecting the boundary of the influence range of the known survey line at the mapping point c i , calculate the distances between the interpolation point and the known survey line and mapping point respectively p i , q i , ; When the depth coordinates of the interpolation point y 3 Outside the depth range of the survey line, that is y 3≤ y 1 or y 3≥ y 2. For each known survey line, from the known survey line endpoint ss i Draw a ray through the interpolation point and intersect the boundary of the known survey line influence range at the mapping point c i , the mapping point, the point to be interpolated, and the known endpoint of the survey line are collinear; the distances between the point to be interpolated and the known endpoint of the survey line and the mapping point are calculated as follows: p i , q i , ; Step 4.3.2: For each known survey line s i , , based on the known value Z i and the generated value of the unconditional random field at the mapping point coordinates B i To interpolate: ； Step 4.3.3: Interpolate the interpolation results of each known survey line R i Linear addition obtains the parameter value of the conditional random field at the point to be interpolated C : ； In the formula Indicates the number of known survey lines within the influence range of the interpolation point b.

8. The slope digital twin construction method based on patch algorithm according to claim 6 or 7 is characterized in that: In step 4, according to the stationary characteristics of the random field, the probability density function of the random variable at each point in the unconditional random field is the same and obeys the standard normal distribution, that is, the mean μ = 0, variance σ 2 = 1; According to the properties of normal distribution, the interpolation points within the influence range of the known points also obey the normal distribution, and their mean and variance They are: ； ； From the above formula, we can see that any interpolation point within the influence range of the known point in the conditional random field also obeys the standard normal distribution; Similarly, any interpolation point within the influence range of the known measurement line in the conditional random field also obeys the standard normal distribution; Therefore, the mean and variance of the conditional random field generated by the patch algorithm are stationary.

9. The slope digital twin construction method based on patch algorithm according to claim 8 is characterized in that: Step 5 is based on the parameter mean determined in step 1 μ X and coefficient of variation COV X , the parameter conditional random field that obeys the standard normal distribution C Transformed into a parameter conditional random field that obeys the true distribution C z : Where exp represents the exponential function.

10. The system of the slope digital twin construction method according to claim 1 or 2 or 4 or 5 or 6 or 7 or 9, characterized in that: include: A data acquisition module is used to determine one or more key parameters of the rock and soil mass that need to consider spatial variability, and obtain the probability distribution of the parameters and their statistical characteristics; The model building module is used to determine the dimensions and scale of the slope site to be simulated, establish the slope finite element model, set the load and boundary conditions, divide the finite element mesh, and extract the coordinates of the integration points; The unconditional random field construction module that obeys the standard normal distribution is used to generate parameter unconditional random fields that obey the standard normal distribution at the integration point coordinates; The conditional random field construction module that obeys the standard normal distribution is used to generate a parameter conditional random field that obeys the standard normal distribution on the integral point coordinates using the patch algorithm based on the coordinates of the known points or known survey lines obtained from actual surveys and the real parameter values ​​in the actual physical field; A conditional random field construction module that obeys the true distribution is used to transform the parameter conditional random field that obeys the standard normal distribution into the parameter conditional random field that obeys the true distribution according to the statistical characteristic values ​​of the parameters; The response prediction module is used to generate values ​​based on the conditional random field of parameters at the material integration points, perform finite element analysis on the slope stability problem, and calculate the corresponding slope target output response results; The optimization module is used to increase known points, reduce parameter uncertainty, make the conditional random field closer to the real site, and make the slope stability analysis results more reliable.

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