A method for constructing a universal elliptical disk DFN model based on multi-window trace information

Abstract

The present invention relates to the field of rock mass discrete fracture networks, and aims to provide a method for constructing a universal elliptical disk DFN model based on multi-measurement window trace information. The method comprises: obtaining trace information on a rock mass outcrop or a tunnel face; calculating the geometric parameters of the elliptical disk fractures to construct a universal elliptical disk three-dimensional discrete fracture network model for quantitative characterization of the rock mass. The present invention derives the geometric parameters of the elliptical disk based on an optimization algorithm of multi-measurement window trace information, and further uses it to construct a three-dimensional universal elliptical disk discrete fracture network. The three-dimensional universal elliptical disk discrete fracture network obtained by the present invention has a significantly better characterization effect on the actual rock mass than the existing non-universal elliptical disk model and disk model.

Description

Technical Field

[0001] The invention relates to the field of rock mass discrete fracture networks, and in particular to a method for constructing a universal elliptical disk three-dimensional discrete fracture network (DFN) model based on multi-measurement window trace information. Background Art

[0002] The complexity of rock mass is mainly manifested in discontinuity, heterogeneity and anisotropy, and the main reason for these properties of rock mass is the presence of a large number of structural planes in the rock mass. How to accurately and finely quantitatively describe and characterize the geometric characteristics of structural planes, that is, to build a rock mass structural model, is a key scientific issue in the quantitative analysis of rock mass engineering. Currently, it is recognized that the most effective means to quantitatively characterize and characterize the geometric characteristics of rock mass structural planes is to construct a three-dimensional discrete fracture network (DFN). The goal of three-dimensional DFN simulation is to derive the three-dimensional geometric information (density, size and orientation, etc.) of the complete structural plane based on a small amount of outcrop geometric information.

[0003] The first step in constructing a three-dimensional discrete fracture network is to assume that the fracture surface has a certain shape. Due to mathematical convenience, the disk model has become the most widely used model. However, the shape of the actual rock mass structural surface is complex and diverse. For example, some scholars have found that the structural surface is more likely to be an ellipse than a circle through the study of fully exposed structural surfaces; other related studies have shown that most structural surfaces that are not affected by adjacent geological structures such as stratum boundaries are ellipses (very few are approximately circular), and structural surfaces affected by adjacent geological structures such as stratum boundaries are often rectangular or quasi-rectangular. In fact, for structural surfaces of various shapes such as rectangles, rhombuses, parallelograms, and irregular polygons, the equivalent representation effect of elliptical disks is significantly better than that of disks, and the elliptical disk model has a wider applicability than the disk model. Therefore, a general elliptical disk model was proposed, and the geometric parameters of the elliptical disk were regarded as variables, including the center point, size (ratio of the major axis to the minor axis), and orientation (occurrence and rotation angle).

[0004] There are two types of cracks exposed on rock outcrops: trace type and structural surface type. Trace type is the most common way of crack exposure. The most commonly used method is to derive the three-dimensional geometric information of the structural surface based on the trace information of the rock outcrop. However, when the trace information is used to derive the size and orientation parameters of the elliptical disk model, there is often a problem of assuming the ratio of the short and long axes and the rotation angle of the elliptical disk as fixed values, resulting in the DFN model finally obtained not being able to well characterize the cracks in the rock mass. If this problem cannot be solved, it will directly affect the application of the elliptical disk model in the construction of rock mass structural models and the quantitative analysis of rock mass engineering.

[0005] Therefore, in order to promote the use of the general elliptical disk model, proposing a new discrete fracture network model of an elliptical disk suitable for general use is an urgent problem to be solved in this technical field. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and provide a method for constructing a universal elliptical disk DFN model based on multi-measurement window trace information.

[0007] To solve the technical problem, the solution of the present invention is:

[0008] A method for constructing a universal elliptical disk DFN model based on multi-measurement window trace information is provided, comprising the following steps:

[0009] (1) Obtaining trace information on rock outcrops or tunnel faces

[0010] Photogrammetry is used to obtain trace information on rock outcrops or tunnel faces, and the mean and standard deviation of trace lengths on three measurement windows are further estimated.

[0011] (2) Calculation of geometric parameters of elliptical disk cracks

[0012] According to formulas (10), (11), (14)-(16), the parameters k2, γ are calculated using Matlab software. m , μ k , σ k ;

[0013]

[0014]

[0015] Where: α i , β i , γ i , k i are the inclination, tilt, rotation angle and ratio of the minor and major axes of the elliptical disk crack i, where i = 1, 2, 3…, N, and 0 ≤ α i ≤2π,0≤β i ≤π, -π / 2≤γ i ≤π / 2, 0<k i ≤1, N is (α i , β i , γ i , k i ) is the number of random cracks generated within its corresponding range; μ k , σ k is the mean and standard deviation of the ratio of the short axis to the long axis; k1 is the concentration parameter of the Fisher distribution, α m is the average tendency, β m is the average inclination angle; κ2 is the concentration parameter of von-Mises distribution, γ m is the average rotation angle, I0(κ2) is the modified Bessel function; αsj , β sj is the inclination and dip angle of the measuring window j; ω(α i , β i , γ i , α sj , β sj ) represents the angle between the trace generated by the intersection of the elliptical disk crack i and the measuring window j and the major axis of the elliptical disk; for convenience, we use and Respectively replace the above two complex Monte Carlo integration formulas;

[0016]

[0017]

[0018]

[0019] Where: μ l1 , σ l1 is the mean and standard deviation of the trace length obtained in measurement window 1; μ l2 , σ l2 is the mean and standard deviation of the trace length obtained in measurement window 2; μ l3 , σ l3 is the mean and standard deviation of the trace length obtained in measurement window 3; and It is the measurement window 1 and 's code; and It is for measuring window 2 and 's code; and It is the measurement window 3 and Code: E mn (p) represents the pth optimization function constructed by the trace information of the mth and nth measurement windows;

[0020] Then use formula (17) to determine the best estimate, and then use formula (18) to determine μ a and σ a :

[0021] E sum =E 12(1) +E 12(2) +E 13(1) +E 13(2) +E 23(1) +E 23(2) (17)

[0022]

[0023] Where: E sum is the sum of all optimization function solutions; μ a is the mean length of the major axis of the cracks in the elliptical disk, σ a is the standard deviation of the length of the major axis of the elliptical disk crack; E(k) is the first moment of the ratio of the minor axis to the major axis of the elliptical disk;

[0024] (3) Constructing a three-dimensional discrete fracture network model of a general elliptical disk

[0025] The parameters k2 and γ calculated using step (2) are m , μ k , σ k , μ a and σ a , a three-dimensional general elliptical disk discrete fracture network model is generated by Monte Carlo simulation method for quantitative characterization of rock mass.

[0026] As a preferred embodiment of the present invention, in step (1), the estimation methods of the mean and standard deviation of trace lengths include a circular window method and a rectangular window method.

[0027] Description of the invention principle:

[0028] In the simulation of discrete fracture networks in rock mass, the disk model has become the most widely used model due to its single parameter. Based on stereology, scholars have established a relationship between the trace and the disk diameter, which can be applied to the derivation of model size parameters. However, the fracture surfaces of rock mass in nature are not all equidimensional. For long fractures, the disk model is not very suitable. In recent years, the elliptical disk model has also been developed to a certain extent. In comparison, the elliptical disk model has more parameters. Therefore, in the process of deriving geometric parameters from trace information, for the sake of simplicity, scholars set the ratio of the short axis to the long axis and the rotation angle of the long axis of the ellipse to fixed values, so it is called a non-universal elliptical disk model. However, such a model can only be applied to some fractures but not all. Therefore, a universal elliptical disk model was proposed, which regards the center point, size (ratio of the long axis to the short axis) and orientation (occurrence and rotation angle) as variables.

[0029] Therefore, the present invention proposes a method for deriving geometric parameters of a universal elliptical disk model. Deriving crack geometric information based on trace information is one of the most commonly used methods. In order to derive the geometric parameters of the elliptical disk, the calculation formulas for the mean and standard deviation of the trace length of the universal elliptical disk model are firstly forward derived based on the principle of stereology. According to the formula, a method for reversely deriving parameters is proposed on the premise of assuming the distribution form of size and orientation parameters in advance. This method combines Monte Carlo simulation integration, constructs an optimization function using the trace information of multiple measurement windows, and transforms the derivation of parameters into solving the problem of solving the minimum value of the function.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. The present invention derives the geometric parameters of the elliptical disk based on the optimization algorithm of multi-measurement window trace information, and further uses it to construct a three-dimensional universal elliptical disk discrete fracture network.

[0032] 2. The three-dimensional universal elliptical disk discrete fracture network obtained by the present invention has a significantly better characterization effect on the actual rock mass than the existing non-universal elliptical disk model and disk model. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of forward derivation and reverse parameter derivation of the general elliptical disk model;

[0034] Figure 2 This is a schematic diagram of the intersection of the elliptical disk crack and the measuring window;

[0035] Figure 3 It is the trace length probability distribution histogram of actual rock fractures and three characterization models in the same measurement window. DETAILED DESCRIPTION

[0036] The present invention is further described in detail below in conjunction with the accompanying drawings. The following specific implementation steps can enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any form.

[0037] Part I: Derivation of the calculation formula

[0038] As mentioned above, based on the cognition of the relationship between the universal elliptical disk model and the trace information, the present invention proposes a parameter acquisition method based on forward derivation and reverse derivation, thereby transforming the derivation of parameters into solving the problem of minimum function. The whole process is described as follows:

[0039] 1. Forward derivation of the calculation formula for the mean and standard deviation of the crack trace length of a universal elliptical disk

[0040] like Figure 1 As shown in Figure 1, in the process of constructing a universal elliptical disk DFN model, the actual problem to be solved is to deduce the geometric parameters of the elliptical disk crack from the trace information. In order to solve this problem, the relationship between the geometric parameters of the elliptical disk crack and the trace length needs to be positively established first.

[0041] like Figure 2 The figure shows the trace generated by the intersection of the elliptical disk crack and the measuring window. The trace length l is related to the elliptical disk major axis length a, the ratio of the minor axis to the major axis k, the occurrence (inclination α, inclination β) and the rotation angle γ, as well as the measuring window parameters (inclination α s , inclination angle β s). Assuming that the ratio of the major axis to the minor axis, the occurrence and the rotation angle all obey a specific probability distribution, the probability density functions are g(a), g(k), f(α, β) and f(γ), respectively, and the probability distributions of all parameters are independent of each other. Therefore, based on the principle of stereology, it is deduced that the elliptical disk crack is located in a certain measurement window (inclination α s , inclination angle β s )The mean value of the trace length μ l and standard deviation σ l The calculation formula is:

[0042]

[0043]

[0044] Where: μ a and σ a are the mean and standard deviation of a; E(k) is the first moment of the ratio of the minor axis to the major axis; τ and η are the codes for two complex quadruple integrals respectively; E(k), τ and η can be further expressed as follows:

[0045]

[0046]

[0047]

[0048] Among them, ω(α, β, γ, α s , β s ) represents the angle between the trace generated by the intersection of the elliptical disk and the measuring window and the major axis of the elliptical disk. The specific expression is:

[0049]

[0050] 2. Reverse derivation of the geometric parameters of the general elliptical disk crack based on the trace information

[0051] (1) Distribution form assumption

[0052] According to equation (1-5), the mean and standard deviation of the trace length are related to the specific distribution form of the geometric parameters of the elliptical disk crack, and only μ l and σ l It is not enough to derive the distribution form of all parameters, so firstly, we make assumptions about the distribution forms of the major axis, the ratio of the minor axis to the major axis, the occurrence and the rotation angle. Assuming that the major axis obeys the negative exponential distribution, the ratio of the minor axis to the major axis obeys the normal distribution, the occurrence obeys the Fisher distribution, and the rotation angle obeys the von Mises distribution, then equation (3-5) can be further expressed as

[0053]

[0054]

[0055]

[0056] In the formula, μ k , σ k is the mean and standard deviation of the ratio of the short axis to the long axis; k1 is the concentration parameter of the Fisher distribution, α m is the average tendency, β m is the average inclination angle; κ2 is the concentration parameter of von-Mises distribution, γ m is the average rotation angle; I0(κ2) is the modified Bessel function; where κ1, α m , β m can be known in advance from the angle information of the trace. Based on the above assumptions, the parameters to be estimated include μ a , σ a , κ2, γ m , μ k , σ k .

[0057] (2) Monte Carlo simulation integration

[0058] Equations (8) and (9) are very complex quadruple integrals, and it is difficult to obtain their analytical solutions. Therefore, Monte Carlo integration is used to approximate the solutions. According to the Monte Carlo simulation integration principle, the approximate solution values ​​of τ and η are and It can be expressed as

[0059]

[0060]

[0061] Where: α i , β i , γ i , k i are the inclination, tilt, rotation angle and ratio of the minor and major axes of the elliptical disk crack i, where i = 1, 2, 3…, N, and 0 ≤ α i ≤2π,0≤β i ≤π, -π / 2≤γ i ≤π / 2, 0<k i ≤1, N is (α i , β i , γ i , k i ) is the number of random cracks generated within its corresponding range; ω(α i , β i , γ i , α sj , β sj) represents the angle between the trace generated by the intersection of the elliptical disk crack j and the measuring window j and the major axis of the elliptical disk.

[0062] (3) Constructing an optimization function for parameter estimation

[0063] According to the number of unknowns of the parameters to be estimated, at least three different measurement windows are required to obtain the mean and standard deviation of the trace length. From formulas (1) and (2), we can see that the difference in the mean and standard deviation of the traces of different measurement windows mainly lies in the difference in τ and η. Therefore, by using the trace information of the three measurement windows and performing pairwise comparison, we can first simplify the common parameter μ. a and σ a

[0064]

[0065]

[0066] In the formula, μ l1 , σ l1 , τ1 and η1 are the trace information of measurement window 1, μ l2 , σ l2 , τ2 and η2 are the trace information of measurement window 2, μ l3 , σ l3 , τ3 and η3 are the trace information of measurement window 3.

[0067] Combined with the Monte Carlo simulation integral formula, we can further obtain

[0068]

[0069]

[0070] In the formula and is the Monte Carlo integral expression of τ1, η1, τ2, η2, τ3 and η3. The optimization function is constructed using equations (14) and (15), and the solution of the parameters is transformed into the problem of solving the minimum value of the maximum function. The optimization function is constructed as follows

[0071]

[0072] In the formula, E mn (p) represents the pth optimization function constructed by the trace information of the mth and nth measurement windows; each optimization function represents each objective function, and the multi-objective function is used to estimate the parameters κ2, γ m , μ k , σ k It is worth noting that there may be multiple sets of solutions when solving by optimization, so the optimal value needs to be determined according to formula (16)

[0073] E sum =E12(1) +E 12(2) +E 13(1) +E 13(2) +E 23(1) +E 23(2) (17)

[0074] When the estimation result makes E sum When is the minimum value, it is the best estimation result. Based on the estimated parameters, E(k), and Further, according to the assumption that the major axis follows a negative exponential distribution, μ a and σ a It can be determined by the trace information of any measuring window. The following is to obtain μ according to the trace information of measuring window 1. a and σ a

[0075]

[0076] Part II: Construction method of general elliptical disk DFN model

[0077] Based on the above derivation and calculation process, the present invention innovatively proposes a method for constructing a universal elliptical disk DFN model based on multi-measurement window trace information, including the following steps:

[0078] 1. Obtain trace information on rock outcrops or tunnel faces

[0079] Photogrammetry is used to obtain trace information on rock outcrops or tunnel faces, and the mean and standard deviation of trace lengths on three measurement windows are further estimated.

[0080] Among them, the estimation methods of the mean and standard deviation of trace length include: circular window method and rectangular window method.

[0081] 2. Calculate the geometric parameters of the elliptical disk crack

[0082] According to formulas (10), (11), (14)-(16), the parameters κ2, γ are calculated using Matlab software. m , μ k , σ k ;

[0083] Then use formula (17) to determine the best estimate, and then use formula (18) to determine μ a and σ a :

[0084] The contents of each formula and the calculation process are as described above and will not be repeated here.

[0085] 3. Construct a three-dimensional discrete fracture network model of a general elliptical disk

[0086] The parameters κ2 and γ calculated using step (2) are m , μ k , σ k , μ a and σ a , a three-dimensional general elliptical disk discrete fracture network model is generated by Monte Carlo simulation method for quantitative characterization of rock mass.

[0087] Part III: Verification of Validity

[0088] In order to verify the effectiveness of the method of the present invention, the trace information obtained by actual measurement of a rock outcrop is taken as an example to further illustrate the application of the derivation of geometric parameters of the general elliptical disk model and the superiority of characterizing rock mass fractures.

[0089] 1. For the rock outcrop, trace information on three different measurement windows is obtained and displayed in Table 1.

[0090] Table 1 The occurrence of the three measurement windows and their corresponding trace length means and standard deviations

[0091]

[0092] 2. The actual rock mass is characterized by using the universal elliptical disk model of the present invention, the non-universal elliptical disk model described in Zhang et al. (2002), and the circular disk model described in Baecher et al. (1977). Before the characterization, the geometric parameters of the model need to be derived.

[0093] For the general elliptical disk model, the trace information in Table 1 is substituted into formulas (14) and (15), and the right side of the equation can be solved. The left side of the equation can be solved by formulas (10) and (11). Among them, based on a large number of numerical simulation results, considering the calculation accuracy and time, the number of simulations N is selected as 300,000 times. Therefore, according to formulas (14) and (15), the optimization function (16) can be constructed, and the parameters κ2, γ can be estimated by Matlab software. m , μ k , σ k , and determine the best estimation result according to formula (17), and then determine μ according to formula (18) a and σ a For the non-universal elliptical disk model and the circular disk model, their geometric parameters can also be derived based on the trace information. Through the derived geometric parameters of the three models, a discrete fracture network representing the actual rock mass can be further generated.

[0094] 3. In order to further compare the characterization effects of the three models, the trace information of the actual rock mass fracture network and the three model fracture networks in the same measurement window (inclination 180°, dip angle 30°) was obtained respectively, and the trace information was statistically analyzed and displayed in Figure 3 By comparing the trace information, it can be found that the total number of traces, mean trace length, standard deviation and probability distribution histogram of the universal elliptical disk model are closest to the actual rock mass, while the non-universal elliptical disk model and the disk model are quite different from the actual rock mass. In addition, by comparing their distribution forms using the KS test, only the trace length distribution form of the universal elliptical disk model is consistent with the actual rock mass. This shows that the method of deriving the geometric parameters of the universal elliptical disk based on trace information is effective, and the universal elliptical disk model is significantly better than the existing non-universal elliptical disk model and disk model in representing the actual rock mass.

[0095] It should be noted that the actual scope of the present invention includes not only the specific embodiments disclosed above, but also all equivalent solutions that implement or perform the present invention under the claims.

Claims

1. A method for constructing a general elliptical disk DFN model based on multi-measurement window trace information, characterized in that: The following steps are involved: (1) Obtaining trace information on rock outcrops or tunnel faces Photogrammetry is used to obtain trace information on rock outcrops or tunnel faces, and the mean and standard deviation of trace lengths on three measurement windows are further estimated. (2) Calculation of geometric parameters of elliptical disk cracks According to formulas (10), (11), (14)-(16), the parameters k2, γ are calculated using Matlab software. m , μ k , σ k ; Where: α i , β i , γ i , k i are the inclination, tilt, rotation angle and ratio of the minor and major axes of the elliptical disk crack i, where i = 1, 2, 3…, N, and 0 ≤ α i ≤2π,0≤β i ≤π, -π / 2≤γ i ≤π / 2, 0<k i ≤1, N is (α i , β i , γ i , k i ) is the number of random cracks generated within its corresponding range; μ k , σ k is the mean and standard deviation of the ratio of the short axis to the long axis; κ1 is the concentration parameter of the Fisher distribution, α m is the average tendency, β m is the average inclination angle; κ2 is the concentration parameter of von-Mises distribution, γ m is the average rotation angle, I0(κ2) is the modified Bessel function; a sj , β sj is the inclination and dip angle of the measuring window j; ω(α i , β i , γ i , α sj , β sj ) represents the angle between the trace generated by the intersection of the elliptical disk crack i and the measuring window j and the major axis of the elliptical disk; for convenience, we use and Respectively replace the above two complex Monte Carlo integration formulas; Where: μ l1 , σ l1 is the mean and standard deviation of the trace length obtained in measurement window 1; μ l2 , σ l2 is the mean and standard deviation of the trace length obtained in measurement window 2; μ l3 , σ l3 is the mean and standard deviation of the trace length obtained in measurement window 3; and It is the measurement window 1 and 's code; and It is for measuring window 2 and 's code; and It is the measurement window 3 and Code: E mn (p) represents the pth optimization function constructed by the trace information of the mth and nth measurement windows; Then use formula (17) to determine the best estimate, and then use formula (18) to determine μ a and σ a : AND sum =And 12(1) +E 12(2) +E 13(1) +E 13(2) +E 23(1) +E 23(2) (17) Where: E sum is the sum of all optimization function solutions; μ a is the mean length of the major axis of the cracks in the elliptical disk, σ a is the standard deviation of the length of the major axis of the elliptical disk crack; E(k) is the first moment of the ratio of the minor axis to the major axis of the elliptical disk; (3) Constructing a three-dimensional discrete fracture network model of a general elliptical disk The parameters k2 and γ calculated using step (2) are m , μ k , σ k , μ a and σ a , a three-dimensional general elliptical disk discrete fracture network model is generated according to the Monte Carlo simulation method for quantitative characterization of rock mass.

2. The method according to claim 1, characterized in that: In the step (1), the estimation methods of the mean and standard deviation of the trace length include a circular window method and a rectangular window method.

Images