CN107393005B - Three-dimensional rock and stone system modeling method - Google Patents

Abstract

The invention discloses a three-dimensional rock mass system modeling method, which comprises the following steps: A. inputting a triangle for representing the boundary of the rock engineering model, determining geometric parameters of a random structural plane, and establishing a topological access relation among triangular faces, edges and points; B. calculating the intersecting lines of all surfaces in the space; C. adopting a recursive algorithm to perform coplanar identification of line segments; D. calculating the intersection points of all line segments in the space; E. identifying closed loops on all faces in space; F. analyzing the inclusion relationship between the closed loops; G. updating the topological access relation of the surfaces, edges and points in the space; H. deleting isolated polygonal faces in the space and generating double faces of non-isolated polygonal faces; J. all three-dimensional rock masses in the space are identified through geometric topological analysis, and the inclusion relationship between the masses is analyzed. The full-space identification of the three-dimensional complex block system is realized through the geometric topological correlation analysis of points, lines, surfaces and bodies of the rock structural surface network, the operation is simple and convenient, and the analysis precision is high.

Description

Three-dimensional rock and stone system modeling method

Technical Field

The invention belongs to the technical field of geotechnical engineering such as water conservancy, traffic, mines and the like, and particularly relates to a three-dimensional rock mass system modeling method which is particularly suitable for stability analysis of rock mass systems of slopes and underground engineering.

Background

After the engineering rock mass is subjected to complex geological action, geological structural surfaces (faults, joints and cracks) with different scales and properties exist in the engineering rock mass, and the deterministic or random structural surfaces are combined with each other to cut the rock mass into rock blocks with different forms, sizes and components. The blocks are easy to induce the instability phenomena of collapse, sliding and the like under the action of environment and engineering, the social development and the safety of people are seriously damaged, and the prevention and treatment work of the blocks becomes a great demand for guaranteeing the national safety and the social economic development.

The block theory is a powerful weapon to solve this problem, and this method was first proposed in the 70's of the 20 th century; in 1985, international famous mathematicians, petrolites, druggery doctor and professor r.e. goodman established a full-space red-flat projection method by adopting a geometric topological theory aiming at the problem of stability of Rock mass blocks cut by cracks, jointly compiled 'Block theory and applications to Rock Engineering', and marked the formal formation of a Block theory system; in 1988, Liu jin Hua and Lu ancest honing have translated and published the book of application of the block theory in engineering rock mass stability analysis, and opened the door for researching the block theory in China. In order to deeply research, apply and popularize the block theory, the Yangtze river water conservancy committee, Yangtze river department academy and the water conservancy and hydropower planning and design institute respectively hold three stages of block theory training classes in 11 months, 8 months and 5 months in 1986, 2017; meanwhile, the block theory is widely applied to stability analysis of major rock mass engineering such as domestic and foreign slopes, caverns and the like.

Engineering applications have found that since the shape and size of a joint fissure are not considered by the key block theory, it is assumed to be an infinitely large discontinuity, resulting in that it can only perform stability analysis on relatively simple convex blocks and cannot quantitatively determine the number, scale and location of rock blocks. In contrast, the patent number 200910220460.4 (invention name: engineering rock three-dimensional space structure modeling and block identification method) firstly collects the engineering rock structure and rock crack data in the construction process, then divides the rock model into a limited number of grids, then sequentially adds the collected structural planes, cuts the existing small blocks, finally removes the grids, and combines the small blocks, thereby identifying all blocks cut by the structural planes; the patent application number is 201210253744.5 (title of the invention: three-dimensional modeling method of complex block), regarding the non-convex block as the combination of a series of convex blocks, dividing the space by the adjacent empty surface of the concave combination, finding the sub-convex block for each sub-area, and finally combining the series of sub-convex blocks into the final complex block. Although the existing methods realize three-dimensional block system modeling of complex rock masses, a small/sub-block combination method is adopted for the complex blocks.

Disclosure of Invention

in order to solve the defects of the prior art, the invention aims to provide a three-dimensional rock mass system modeling method, which realizes the full-space identification of a three-dimensional complex block system by analyzing the geometric topology correlation of points, lines, surfaces and bodies of a rock mass structural surface network, has complete theory, simple and convenient operation and high analysis precision, and provides a geological and mechanical model for key block analysis and discrete block system dynamics calculation.

In order to achieve the purpose, the invention adopts the following technical measures:

A three-dimensional rock mass system modeling method comprises the following steps:

Step 1: inputting a triangle for representing the boundary of the rock engineering model, determining geometric parameters of a random structural plane, numbering all triangular planes, edges and points in the space, and establishing a topological access relationship between the triangular planes, the edges and the points; and calculating the normal vector of the surface of each triangle and the local coordinate transformation matrix.

Step 2: and taking any two triangles, judging the intersection condition of the two triangles, and recording the intersection point coordinates and the numbers of the intersected triangles if the intersected line segments exist.

And step 3: and (3) performing coplanar identification on all triangle edges and intersected line segments in the space by adopting a recursive algorithm in computer science to obtain the number of the composition point and the belonging surface of all line segments (any two line segments are not superposed).

And 4, step 4: and taking any two line segments in the space to analyze the intersection condition, and recording the serial number and the corresponding segmentation proportion of each intersection line segment passing through the intersection point if the intersection point exists.

and 5: and (3) aiming at each surface in the space, obtaining all closed loops through loop search of line segments and intersection points on the surface, and recording the surface number of each loop and the composition line segment (represented by the intersection point number).

Step 6: and analyzing the inclusion relationship among all the loops, and correcting the line segments forming the loops for those containing other loops.

and 7: and regarding each loop as a polygonal surface, and updating the topological access relation among the surfaces, edges and points in the space, namely the line segment number of each polygonal surface, the number of the polygonal surface to which each line segment belongs, the numbers of two points of each line segment and the three-dimensional coordinates of each point.

And 8: deleting all isolated polygonal faces in the space; for each reserved polygon surface, generating a double-cell polygon surface (the normal vector of which is opposite to that of the original polygon surface) of the polygon surface, namely storing the line segments of the original polygon surface in a reverse order; and updating the topological access relation of the face, the edge and the point again.

And step 9: performing geometric topological analysis on all polygonal surfaces in the space, identifying all rock blocks, and judging the inclusion relationship of any two rock blocks; thereby obtaining all rock blocks in the space, forming a topological structure accessed by polygonal surface numbers, line segment numbers, vertex numbers and three-dimensional coordinates, and simultaneously obtaining the inclusion relationship among the rock blocks.

Through the technical measures, the analysis of the intersection line of the surface and the intersection point of the line and the line is realized by utilizing the three-dimensional computational geometry and the topological theory, the problems of the geometric correlation of the line-line coplanarity, the surface-surface inclusion and the body-body inclusion are solved, and the topological structure for accessing the rock block by the multi-side surface number, the line segment number, the vertex number and the three-dimensional coordinate is established.

Compared with the prior art, the invention has the following advantages and effects:

By analyzing the geometric topology of points, lines, surfaces and bodies of the rock structural surface network, a three-dimensional convex block body and concave block body full-space unified identification method is established, the defect that the complex block bodies are identified by small/sub block body combination in the prior art is overcome, and the method has the advantages of complete theory, simplicity and convenience in operation, high analysis precision and the like.

The applicant realizes the modeling method on a computer by using a C language programming program so as to verify the effectiveness and the practicability of the method provided by the invention. FIG. 1 shows two examples of three-dimensional rock mass systems identified by the present modeling method, the number of blocks identified in the slope project of FIG. 1(a) being 142, and the total volume being 650000m³The maximum value and the minimum value of the volume of the block are 540799.912 m and 0.049m respectively³(ii) a The total number of blocks identified in the tunnel project of fig. 1(b) was 2401, and the total volume was 768000m³468 pieces in the tunnel and 66697.383m in volume³(ii) a Therefore, the modeling method can provide an effective numerical model for the stability analysis of the rock and rock mass system of the slope and underground engineering.

drawings

FIG. 1 is a schematic diagram of an example three-dimensional rock mass system identified using the present modeling method.

Wherein: figure a three-dimensional rock object system example for slope engineering

Drawing b three-dimensional rock object system example for tunnel engineering

FIG. 2 is a flowchart of the identification of coplanar line segments in space based on a recursive algorithm.

Fig. 3 is a flow chart of polygon surface identification based on loop search.

Fig. 4 is a schematic diagram of analysis of a polygonal surface containing relationship.

Wherein: a is a schematic diagram of two polygon faces separated

b is a schematic diagram of two polygonal surfaces adjacent to each other

c is a schematic diagram of the case that two polygonal surfaces contain

FIG. 5 is an example of a topological relationship of representing a spatial plane, line and point.

Fig. 6 is a flow chart of three-dimensional rock mass recognition based on geometric topological analysis.

Detailed Description

The invention will be described in detail below with reference to the drawings, it being noted that the described embodiments are only intended to facilitate the understanding of the invention and do not limit it in any way.

The technical conception of the invention is as follows: and obtaining the geometric parameters of a deterministic structural plane and a random structural plane through field geological survey and mathematical statistical analysis, and identifying all rock blocks through geometric topological analysis of a structural plane network.

Example 1:

A three-dimensional rock mass system modeling method comprises the following steps:

1. Inputting a triangle for representing the boundary of the rock engineering model, determining the geometric parameters of the random structural plane, and establishing the topological access relation of each plane in the space.

Taking triangle ABC as an example, it is composed of sides AB, BC, CA, where side AB takes point A and point B as end points, side BC takes point B and point C as end points, side CA takes point C and point A as end points, and point A, B, C is composed of three-dimensional coordinates (x)_i，y_i，z_i) Wherein i is A, B, C. For triangle ABC.

2. The intersection of all the surfaces in space is calculated.

taking any two triangles in the space, setting the triangles as a triangle ABC (the surface number is 1) and a triangle DEF (the surface number is 2), and if the two triangles have an intersecting line segment GH; storing the intersecting line segment GH, recording the three-dimensional coordinates of the end point G, H of the line segment GH, and the two triangle numbers (1 and 2) forming the intersection

3. Based on a recursive algorithm, the coplanar identification of line segments in the space is completed, and the implementation flow is shown in fig. 2.

The specific implementation steps are as follows:

Step 1: the intersection of all triangle sides and all faces in space, including the end points of these segments and their face numbers, are entered and marked as valid segments.

Step 2: coplanar recognition is started, and a judgment parameter k is set to 0.

And step 3: and (4) selecting any two effective line segments in the space, and entering the step 8 if the traversal is finished. Let two line segments be P respectively₀P₃、P₁P₂In which the end point P of the line section_iThe three-dimensional coordinate of (i ═ 0,1,2,3) is (x)_i，y_i，z_i)。

And 4, step 4: and (4) judging whether the two line segments are collinear, and if not, entering the step 3.

and 5: calculating the intersection point P of the two line segments_tPartition P₀P₃The calculation formula is as follows:

If x₂≠x₁；

If y₂≠y₁；

If z is₂≠z₁。

Wherein, t₀Is P₀P_tAnd P₀P₃The vector ratio of (a); t is t₃Is P_tP₃and P₀P₃The vector ratio of (2).

step 6: if the two line segments do not coincide, i.e. t₀t is less than or equal to 0₃0 or less, or t₀T is not less than 1₃And (4) entering the step (3) when the temperature is more than or equal to 1.

And 7: according to P₀P₃、P₁P₂Judging and correcting the original line segment P₀P₃、P₁P₂and adding a new effective line segment by using an end point in the space and storing the number of the corresponding surface, and modifying the judgment parameter k to be 1.

and 8: and after the coplane identification is finished, outputting the number of the composition end points and the belonged surface of all the updated effective line segments.

4. The intersection of all line segments in space is calculated. Let any two line segments in the selected space be P respectively₀P₃(line segment No. 1) and P₁P₂(line segment No. 2) wherein a line segment end point P_iThe three-dimensional coordinate of (i ═ 0,1,2,3) is (x)_i，y_i，z_i). If λ ≠ 0, and satisfies 0 ≦ t₁t is not less than 1 and not more than 0₂1 or less, then the intersection point P_tThe coordinates can be calculated as follows, and if not, no intersection point exists.

x_t＝x₀+(x₃-x₀)t₁y_t＝y₀+(y₃-y₀)t₁z_t＝z₀+(z₃-z₀)t₁

Or x_t＝x₁+(x₂-x₁)t₂y_t＝y₁+(y₂-y₁)t₂z_t＝z₁+(z₂-z₁)t₂

Wherein:Is P₀P_tAnd P₀P₃The vector ratio of (a);Is P_tP₃and P₀P₃the vector ratio of (a); lambda, lambda₁、 λ₂Is the calculation of the process parameters and,If there is an intersection point P_trecording through P_tthe intersection line segment numbers 1 and 2, and the corresponding division ratio t₁And t₂。

5. A closed loop is identified on all faces in space. As can be seen from fig. 3, a method for identifying a closed loop on all sides in a space includes the following steps:

Step 1: selecting a plane f in space_i(i ═ 1,2, ·, N), if all faces are traversed, go to step 8 (end of all closed-loop searches in space).

Step 2: extracting for recognition of the face f_iOf closed loop, including the plane f_iAll the valid line segments, all the intersections, and the line segment numbers passing through each intersection, and the corresponding division ratios.

And step 3: deletion surface f_iAnd regarding all the line segments which cannot form a closed loop and intersection point information, regarding all the remaining line segments as vectors, copying a line segment vector which is opposite to each line segment vector in direction and has the same coordinates as two control end points, and setting all the line segment vectors as unmarked. Such as line segment vectorswherein the line segment end point P_iThe three-dimensional coordinate of (i ═ 1,2) is (x)_i，y_i，z_i) Its unit direction vector is:

wherein the content of the first and second substances,Is thatThe unit direction vector of (1);

Then the vector of the line segment with its opposite direction, the same coordinates of the two control end points, isits unit direction vector is:

Wherein the content of the first and second substances,Is thatThe unit direction vector of (1);

And 4, step 4: a new closed loop L is started_jselecting any unmarked line segment vector, and entering the 7 th step (surface f) if all line segment vectors are marked_iAnd after all the closed loops are searched, outputting and recording the number of the surface where each loop is located and forming line segments). Marking the line segment vector and recording the line segment vector into a closed loop L_jAnd as a search closed loop L_jThe starting edge of the next edge of (2).

And 5: for the selected line segment vector, set asHaving a unit vector ofAccording to its termination point P₂finding all unlabeled neighboring line segment vectorscorresponding unit vector isCalculate the adjacent segment andThe calculation formula is as follows:

if it is not

if it is not

Wherein, theta_iIs composed ofThe direction angle of the line segment adjacent to the direction angle;Is a face f_iA unit normal vector of (d); and pi is the circumferential ratio.

Take theta_max＝max(θ₁,θ₂,…,θ_n) Taking the corresponding line segment vector asThe nearest neighbor line segment vector.

Step 6: markingAnd record it as L_jThe edge of (1); if the end point of the nearest line segment vector is equal to L_jthe starting end points of the first edges of L are the same, then L_jafter the search is finished, the step 4 is entered, otherwise, the nearest line segment vector is used as the search L_jThe starting edge of the next edge of (2) proceeds to step 5 above.

And 7: face f_iAfter all closed loops are searched, the number of the surface where each loop is located and the line segments (represented by intersection point numbers) are output and recorded. The process proceeds to step 1 to start the recognition of the next surface.

And 8: all closed loop searches in space end.

6. containment relationship analysis between closed loops (polygons) in space. Fig. 4 is a schematic diagram of analysis of the inclusion relationship of polygonal surfaces, and the specific operation steps are as follows:

Step 1: regarding each closed loop as a polygonal surface, the centroid coordinate (x) of each closed loop is calculated₀，y₀，z₀) Radius r of circumscribed circle₀Coordinate (x) of any point on the polygon edge₁，y₁，z₁) Coordinate (x) of any point inside the polygon₂， y₂，z₂)。

Step 2: selecting two coplanar closed loops (polygons) L_iAnd L_jIf all closed loops (polygons) are traversed, then step 6 is entered.

And step 3: judgment of L_iAnd L_jWhether or not they are separated. If they are separated (satisfying the following equation), the process proceeds to step 2 as shown in fig. 4 (a).

Wherein, the centroid coordinate (x)_0i，y_0i，z_0i)、(x_0j，y_0j，z_0j) Are each L_iAnd L_jThree-dimensional coordinates of (a); r is_0i、r_0jAre each L_iAnd L_jRadius of the circumscribed circle of (a).

And 4, step 4: judgment of L_iAnd L_jWhether or not they are adjacent, i.e. polygons L_iPoint (x) of_1i，y_1i，z_1i) In the polygon L_jOn the edge of or in the polygon L_jPoint (x) of_1j，y_1j，z_1j) In the polygon L_iThe edge of (a); if so, as shown in FIG. 4(b), proceed to step 2.

And 5: judgment of L_iAnd L_jIf the polygon L contains_iPoint (x) of_2i，y_2i，z_2i) In the polygon L_jInner, then L_jComprises L_i(ii) a If the polygon L_jPoint (x) of_2j，y_2j，z_2j) In the polygon L_iInternal, then L_iComprises L_j. As shown in FIG. 4(c), L_iComprises L_j。

Step 6: for those loops that contain other loops, the line segments that make up it are modified. For example, FIG. 4(c) includes L_jL of_iits initial loop is recorded as ABCDEF, and loop L is recorded_j(GHMN) reverse order is stored in loop L_ithen L is_iThe corrected loop of (a) is recorded as ABCDEF-NMHG.

7. Only the information of the edges and points related to the closed loops in the space is reserved, each closed loop is regarded as a polygonal surface, and the topological access relation among the surfaces, the edges and the points in the space is updated, namely the line segment number of each polygonal surface, the polygonal surface number to which each line segment belongs, the two point numbers of each line segment and the three-dimensional coordinates of each point. Taking FIG. 5 as an example, a polygonal CDEF consists of sides CD, DE, EF, FC; edge EF belongs to plane CDEF, plane EFGH, and plane EFM at the same time, and the control end point is E, F.

8. And finding isolated polygonal faces in the space by using a recursive method, wherein the judgment criterion is that the line segments only belonging to the surface exist in the line segments forming the surface, and deleting the isolated polygonal faces. As shown in fig. 5, firstly, the edge EM in the face EFM only belongs to the face, so the face EFM is an isolated face and needs to be deleted; then the opposite CFMN, whose sides FM, MN, MC all belong only to that face, the lone face CFMN is deleted.

For each non-isolated polygon, generating a double-cell polygon (the normal vector of which is opposite to that of the original polygon), namely storing the line segments of the original polygon in a reverse order. Still taking fig. 5 as an example, the opposite CDEF has a double polygonal surface, which is FEDC. Due to the introduction of the double-polygonal surface, each surface and each line segment in the space have two directions, for example, two direction surfaces with the surface CDEF and the surface FEDC being normal directions different, and two direction edges with the edge EF and the variable FE being direction vectors different. And updating the topological access relation of the direction surface, the direction edge and the point.

9. Geometric topological analysis is performed on all polygonal surfaces in the space, and as shown in fig. 6, the three-dimensional rock block body identification process includes the following specific operation steps:

Step 1: and (4) preparing analysis data. And extracting all direction surfaces, direction edges and point data in the space, and setting each direction surface and each direction edge as unmarked.

Step 2: starting a new three-dimensional rock mass B_ifinding an unmarked direction plane in the space, and if all the direction planes are marked, entering step 6. Record the orientation as a three-dimensional rock mass B_iAnd as search make up a three-dimensional rock mass B_iThe starting surface of the direction plane.

And step 3: the selected start surface is defined as f₀Selecting composition plane f₀If all the direction edges are marked, the following step 4 is carried out; let the unit direction vector of the direction side beMarking the direction edge, and selecting all direction surfaces f which are not marked and comprise the line segment where the direction edge is positioned in the line segments_j(j ═ 1,2, ·, n), calculate the orientation plane f₀And f_jBetween themAngle, the calculation formula is as follows:

If it is not

If it is not

Wherein alpha is_jIs a direction plane f₀And f_jThe included angle between them;are respectively a face f₀、f_jA unit normal vector of (d); and pi is the circumferential rate.

Take alpha_max＝max(α₁,α₂,…,α_n) The corresponding direction surface is taken as the direction sideThe nearest neighboring direction face.

And 4, step 4: marking the selected start surface f₀To f for₀Each of the nearest neighboring directional planes corresponding to each of the directional edges if the plane is not a three-dimensional rock mass B_iAdding the flour of (1).

And 5: from three-dimensional rock masses B_iFinding an unmarked surface, if all the direction surfaces are marked, finishing the identification of the three-dimensional block body i, and entering the step 2; forming a three-dimensional rock block B by taking the direction plane as a search_iThe starting surface of the direction surface of (2) is entered into the step (3);

step 6: and (4) finishing the identification of all the three-dimensional blocks, and recording all the direction surface numbers forming each block.

And 7: calculating the volume of each block by adopting a simplex integral method, and deleting the rock blocks with negative block volumes;

And 8: analysing containment relationships between any two rock masses, e.g. B₁and B₂if B is₂In which there is a vertex at B₁Internally, then B is considered₁comprising B₂(ii) a And recording the inclusion relationship of each block with other blocks.

by the technical measures, the problem of coplanar identification of all line segments in space is solved by using a recursive algorithm in computer science, closed loop search in any polygonal surface is realized, and the judgment of the relation of separation, adjacency and inclusion between the polygonal surfaces is completed, so that a three-dimensional convex block and concave block full-space unified identification method is established, and a topological structure for accessing the rock block by using a polygonal surface number, a line segment number, a vertex number and a three-dimensional coordinate is formed. The modeling method has the advantages of complete theory, simplicity and convenience in operation and high analysis precision, and can provide an effective numerical model for the stability analysis of the rock and stone body system.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention should be covered within the scope of the present invention.

Claims (1)

1. A three-dimensional rock mass system modeling method comprises the following steps:

A. Inputting triangles representing geometrical parameters of rock mass engineering model boundaries, deterministic structural planes and random structural planes, numbering all triangular faces, edges and points in space, and establishing topological access relations among the triangular faces, the edges and the points; calculating a normal vector and a local coordinate transformation matrix of the surface of each triangle;

B. Taking any two triangles, judging the intersection of the two triangles, and recording the coordinates of the intersection points and the numbers of the intersected triangles if the intersected line segments exist;

C. Carrying out collinear identification and overlapping processing on sides and intersected line segments of a triangle in space by adopting a recursive algorithm in computer science to obtain effective line segments after overlapping processing, and recording the composition end points and the numbers of the surfaces of the line segments;

D. Taking any two effective line segments in the space, and recording the serial number and the corresponding segmentation proportion of each intersection line segment passing through an intersection point if the intersection point exists;

E. Aiming at each surface in the space, obtaining a closed loop through loop search of line segments and intersection points on the surface, recording the surface number of each loop and forming the line segments;

F. Analyzing the inclusion relationship among the loops, and correcting line segments forming the loops aiming at the loops containing other loops;

G. Regarding each loop as a polygonal surface, updating the topological access relation of surfaces, edges and points in the space, namely the line segment number of each polygonal surface, the number of the polygonal surface to which each line segment belongs, the numbers of two points of each line segment and the three-dimensional coordinates of each point;

H. Delete all isolated polygon faces in space: generating a double-cell polygon surface of each reserved polygon surface, storing line segments of the original polygon surface in a reverse order, and updating the topological access relation of the surface, the edge and the point again;

J. Performing geometric topological analysis on polygonal surfaces in the space, identifying rock blocks, and judging the inclusion relationship of any two rock blocks; obtaining rock blocks in a space, forming a topological structure accessed by polygonal surface numbers, line segment numbers, vertex numbers and three-dimensional coordinates, and simultaneously obtaining the inclusion relationship among the rock blocks;

The step (C) is based on a recursive algorithm to finish the collinear identification and overlapping processing of the line segments in the space, and comprises the following steps:

Step 1: inputting the intersection lines of the sides, the faces and the faces of all triangles in the space, including the end points of the line segments and the numbers of the faces to which the line segments belong, and marking the line segments as effective line segments;

step 2: starting collinear identification and overlapping processing, and setting a judgment parameter k to be 0;

and step 3: selecting any two effective line segments in the space, and entering step 8 if traversal is finished, and setting the two line segments as P₀P₃、P₁P₂In which the end point P of the line section_iThe three-dimensional coordinate of (i ═ 0,1,2,3) is x_i，y_i，z_i；

And 4, step 4: judging whether the two line segments are collinear, if not, entering the step 3;

And 5: calculating the intersection segmentation P of two line segments₀P₃The ratio of (a) to (b) is calculated as follows:If x₂≠x₁；

if y₂≠y₁；

If z is₂≠z₁；

Wherein: t is t₀Is P₀P_tAnd P₀P₃The vector ratio of (a); t is t₃Is P_t P₃And P₀P₃The vector ratio of (a); p_tIs the intersection of the two line segments;

Step 6: if the two line segments do not coincide, i.e. t₀t is less than or equal to 0₃0 or less, or t₀T is not less than 1₃If the value is more than or equal to 1, entering the step 3;

And 7: p₀P₃、P₁P₂judging and correcting the original line segment P when the coincidence exists₀P₃、P₁P₂adding a new effective line segment by using an end point in the space and storing the number of the surface to which the new effective line segment belongs, and modifying a judgment parameter k to be 1;

And 8: finishing the collinear identification and overlapping processing, and outputting the number of the composition end point and the belonging surface of the effective line segment after the overlapping processing;

The method for analyzing the inclusion relationship between the closed loops in the step (F) comprises the following steps:

Step 1: calculating the centroid coordinate x of each closed loop as a polygonal surface₀，y₀，z₀Radius r of circumscribed circle₀Coordinate x of any point on polygon edge₁，y₁，z₁Coordinate x of any point in the polygon₂，y₂，z₂；

Step 2: selecting two coplanar closed loops L_iAnd L_jIf all closed loops are traversed, entering step 6;

And step 3: judgment of L_iAnd L_jIf the phase separation is carried out, entering the step 2;

wherein: centroid coordinate x_0i，y_0i，z_0i、x_0j，y_0j，z_0jare each L_iAnd L_jthree-dimensional coordinates of (a); r is_0i、r_0jare each L_iAnd L_jradius of the circumscribed circle of (a);

And 4, step 4: judgment of L_iAnd L_jAre adjacent, i.e. polygons L_iPoint x of_1i，y_1i，z_1iIn the polygon L_jEdge or polygon L_jpoint x of_1j，y_1j，z_1jin the polygon L_iThe edge; if the two are adjacent, entering the step 2;

And 5: judgment of L_iand L_jIf the polygon L contains_iPoint x of_2i，y_2i，z_2iIn the polygon L_jinternal, then L_jComprises L_i(ii) a If the polygon L_jPoint x of_2j，y_2j，z_2jIn the polygon L_iInternal, then L_iComprises L_j；

Step 6: for the loop containing other loops, correcting the line segment forming the loop, and storing the line segment forming the loop in the reverse order in the loop;

In the step (J), a three-dimensional convex and concave block full-space unified identification and rock block relation analysis method is established through geometric topological analysis of points, lines, surfaces and bodies of a rock structure surface network, and the method comprises the following steps:

Step 1: extracting all direction surfaces, direction edges and point data in the space, and setting each direction surface and each direction edge as unmarked;

Step 2: starting a new three-dimensional rock mass B_iFinding an unmarked direction plane in the space, and entering step 6 if all the direction planes are marked; record the orientation as a three-dimensional rock mass B_ias a search for composing a three-dimensional rock mass B_ithe starting surface of the direction plane of (1);

And step 3: let this selected start face be f₀selecting composition plane f₀If all the direction edges are marked, the step 4 is carried out; let the unit direction vector of the direction side beMarking the direction edge, and selecting all direction surfaces f which are not marked and comprise the line segment where the direction edge is positioned in the line segments_jCalculating the direction plane f₀And f_jThe included angle between them is calculated as follows:

If it is

If it is

wherein: alpha is alpha_jIs a squareTo the face f₀And f_jthe included angle between them;Are respectively a face f₀、f_ja unit normal vector of (d); pi is the circumference ratio;

Take alpha_max＝max(α₁,α₂,…,α_n) The corresponding direction surface is taken as the direction sideThe nearest neighbor direction face of (a);

And 4, step 4: marking the selected start surface f₀to f for₀Each of the nearest neighboring directional planes corresponding to each of the directional edges if the plane is not a three-dimensional rock mass B_iAdding the flour into the dough;

And 5: from three-dimensional rock masses B_iFinding an unmarked surface, if all the direction surfaces are marked, finishing the identification of the three-dimensional block body i, and entering the step 2; forming a three-dimensional rock block B by taking the direction plane as a search_iThe starting surface of the direction surface of (2) enters step (3);

Step 6: after all the three-dimensional rock blocks are identified, recording the serial numbers of all the direction surfaces forming each block;

And 7: calculating the volume of each block by adopting a simplex integral method, and deleting the rock blocks with negative block volumes;

And 8: analyzing the inclusion relationship of any two rock blocks, pair B₁And B₂If B is₂In which there is a vertex at B₁inner, then B₁Comprising B₂(ii) a And recording the inclusion relationship of each block with other blocks.