A tunnel surrounding rock over-break and under-break analysis method based on 3D laser scanning point cloud

Abstract

The present invention discloses a tunnel surrounding rock over-excavation and under-excavation analysis method based on three-dimensional laser scanning point cloud, including: obtaining tunnel point cloud, obtaining actual tunnel excavation contour point cloud and converting it into a general point cloud format, establishing a tunnel surrounding rock over-excavation and under-excavation analysis coordinate system; constructing a tunnel design contour point cloud in the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system; calculating the local normal vectors of all calculated points in the tunnel design contour point cloud; adjusting the direction of the local normal vectors of all calculated points and making them point to the free surface of the tunnel; determining the over-excavation and under-excavation state based on the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud; calculating the over-excavation and under-excavation volume based on spatial region segmentation and rectangular microelement column method. The present invention takes the local geometric features of the tunnel point cloud as the starting point, and realizes the rapid and accurate calculation of the over-excavation and under-excavation state of the tunnel surrounding rock in three-dimensional space and the over-excavation and under-excavation volume by calculating the normal difference between the actual tunnel surrounding rock excavation contour point cloud and the tunnel design contour point cloud.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel surrounding rock over-break and under-break analysis, and in particular relates to a tunnel surrounding rock over-break and under-break analysis method based on three-dimensional laser scanning point cloud. Background Art

[0002] Over-excavation and under-excavation are inevitable in the construction of drilling and blasting tunnels, which have a great impact on the stress state of the tunnel structure, construction quality and project cost. Commonly used tunnel profile detection methods, such as total station method and section instrument method, can only obtain the over-excavation and under-excavation characteristics within the section, and their efficiency is low. 3D laser scanning technology has the advantages of fast scanning speed, high scanning accuracy and little influence from the scanning environment. It can quickly obtain a large number of 3D coordinates and their attributes of the actual excavation surface of the tunnel, that is, point cloud, which makes it possible to quickly judge the over-excavation and under-excavation of the surrounding rock of drilling and blasting tunnels.

[0003] For circular cross-section tunnels, the circular cross-section fitting radius method is usually used, that is, the tunnel is divided into several equal-thickness point clouds along the longitudinal direction, and each equal-thickness point cloud is projected onto the XOZ plane. Then, the cross section is divided into several segments along the tunnel circumference, and the circular equation is used to fit each segment to obtain the fitting radius of the corresponding segment. The area of ​​each segment is calculated by the fan area method in combination with the tunnel design cross-section radius, thereby obtaining the over-excavation and under-excavation area of ​​the cross section, and then the over-excavation and under-excavation volume is indirectly obtained by multiplying the over-excavation and under-excavation areas of multiple cross sections by the longitudinal segment thickness. However, this method is only applicable to circular cross-section tunnels. The cross-section segments are divided equally, and the segment points are not necessarily the over-excavation and under-excavation demarcation points. Therefore, only the over-excavation or under-excavation area of ​​the segment can be calculated. The over-excavation and under-excavation volume calculated by multiplying the cross-section area by the segment thickness does not consider the three-dimensional distribution characteristics of over-excavation and under-excavation. In addition, the circular cross-section fitting radius method is only applicable to situations where the actual excavation profile of the tunnel is not much different from the design profile.

[0004] The spatial surface model comparison method is to establish the actual tunnel excavation surface model from the actual tunnel excavation contour point cloud, and compare it with the over-and-underbreak solid model composed of the tunnel design excavation surface model, thereby calculating the over-and-underbreak. However, this method involves the establishment of two surface models and one solid model. For the problem of massive point clouds, errors are prone to occur in reconstructing the surface mesh and the solid model. This method can only obtain the total volume of over-and-underbreak, but cannot obtain the distribution of over-and-underbreak.

[0005] In addition, the above method cannot independently calculate the volume of independent over-break and under-break areas and the distribution of over-break and under-break, and does not consider the problem of local missing of tunnel point cloud. Summary of the invention

[0006] The purpose of an embodiment of the present invention is to provide a method for analyzing over-excavation and under-excavation of tunnel surrounding rock based on three-dimensional laser scanning point cloud. The method takes the local geometric characteristics of the tunnel point cloud as the starting point, and calculates the normal difference between the actual contour point cloud of the tunnel surrounding rock excavation and the tunnel design contour point cloud. It realizes the three-dimensional spatial over-excavation and under-excavation state identification of the tunnel surrounding rock and the rapid and accurate calculation of the over-excavation and under-excavation amount, so as to solve the problems existing in the prior art.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is a tunnel surrounding rock over-break and under-break analysis method based on three-dimensional laser scanning point cloud, comprising the following steps:

[0008] Step S1, using a ground 3D laser scanning system to obtain a tunnel point cloud, pre-processing the tunnel point cloud to obtain a tunnel actual excavation contour point cloud, and converting the tunnel actual excavation contour point cloud from a dedicated format to a general point cloud format, and then establishing a tunnel over-excavation and under-excavation analysis coordinate system and converting it to a tunnel surrounding rock over-excavation and under-excavation analysis coordinate system;

[0009] Step S2, constructing a tunnel design contour point cloud in a tunnel surrounding rock over-break and under-break analysis coordinate system according to the tunnel point cloud spacing and the design section size;

[0010] Step S3, calculating the local normal vectors of all calculation points in the tunnel design contour point cloud;

[0011] Step S4, adjusting the directions of the local normal vectors of all calculation points of the tunnel design contour so that the local normal vectors all point to the free surface of the tunnel;

[0012] Step S5: determining the over-excavation or under-excavation state based on the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud.

[0013] Furthermore, the preprocessing in step S1 includes uniformly downsampling the tunnel point cloud obtained by scanning and performing denoising on the tunnel point cloud.

[0014] Furthermore, the XOZ plane of the tunnel overbreak and underbreak analysis coordinate system in step S1 represents the tunnel cross section, and the Y coordinate represents the position of the tunnel cross section.

[0015] Furthermore, the conversion formula of the coordinate system in step S1 is:

[0016]

[0017] In the formula, θ z is the rotation angle around the Z axis of the tunnel overbreak and underbreak analysis coordinate system, t x ,t y ,t z They represent the translation along the X, Y, and Z axes of the tunnel overbreak and underbreak analysis coordinate system, respectively. s ,ys 、z s They represent the coordinate components of the X, Y, and Z directions of the point cloud obtained by the 3D laser scanner; g ,y g 、z g They respectively represent the coordinate components of the point cloud in the X, Y, and Z directions in the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system.

[0018] Furthermore, the step S2 is specifically as follows:

[0019] The tunnel design cross-section point cloud is generated according to the tunnel point cloud spacing and the design section size. Then, the equally spaced cross-section point clouds are generated according to the tunnel point cloud spacing along the Y-axis direction of the overbreak and underbreak analysis coordinate system, and finally the tunnel design contour point cloud is established.

[0020] Furthermore, the step S3 is specifically as follows:

[0021] First, with the calculation point of the tunnel design contour point cloud as the center and a radius of D / 2, the rNN algorithm is used to search for the point set S consisting of all points in the neighborhood of the calculation point. i Then, the principal component analysis method is used to calculate the point set S i The covariance matrix R of the corresponding sample feature matrix is ​​obtained, and the eigenvalues ​​and eigenvectors of the matrix R are calculated. According to the results of principal component analysis, the direction corresponding to the minimum eigenvalue is the normal vector N of the plane corresponding to the calculation point.

[0022] Furthermore, the step S4 is specifically as follows:

[0023] Taking the center of the tunnel section as the symmetry plane, all the calculation points in the tunnel section are divided into two areas, left and right; for the area on the right side of the center line, when the angle between the local normal vector N of the calculation point of the tunnel design contour point cloud and the positive direction of the X-axis is an obtuse angle, the direction of the local normal vector N is positive, otherwise the direction of the normal vector N should be adjusted to its negative direction; for the area on the left side of the center line of the tunnel section, when the angle between the local normal vector N of the calculation point of the tunnel design contour and the positive direction of the X-axis is an acute angle, the local normal vector is positive, otherwise the direction of the normal vector N should be adjusted to its negative direction.

[0024] Furthermore, the step S5 is specifically as follows:

[0025] The local normal vector N of point i of the tunnel design contour point cloud is used as the axis, L and d are respectively used to define a cylinder with length and diameter, and the point cloud subsets of the tunnel design contour point cloud and the actual tunnel excavation contour point cloud within the cylinder are searched respectively, which are recorded as M(i) and N(i);

[0026] Then, the point cloud subsets M(i) and N(i) are projected along the local normal vector direction of the calculation point i, and the average projection centers m(i) and n(i) of the tunnel design contour point cloud subset M(i) and the actual excavation contour point cloud subset N(i) corresponding to point i are calculated respectively. Finally, the algebraic distance l(i) from m(i) to n(i) is calculated as the over-excavation and under-excavation value corresponding to point i of the tunnel design contour point cloud. The over-excavation and under-excavation state of the position corresponding to point i can be judged according to the sign of l(i). When l(i) is positive, the position corresponding to point i is under-excavated, otherwise, it is over-excavated.

[0027] Furthermore, the method further includes: step S6, mapping the over-break and under-break conditions of the tunnel surrounding rock in the three-dimensional space coordinate system to a two-dimensional plane, and assigning different colors to the over-break and under-break conditions, thereby achieving intuitive and rapid identification of the over-break and under-break conditions of the tunnel surrounding rock;

[0028] The specific method of mapping the over-excavation and under-excavation of the tunnel surrounding rock in the three-dimensional space coordinate system to the two-dimensional plane is:

[0029] The tunnel contour point cloud is divided into the top arch area, the left side wall area and the right side wall area; for the cloud computing points of the left and right side wall areas, the Z coordinate component of the corresponding point cloud in the spatial coordinate system is mapped to the component X′ of the two-dimensional plane coordinate system, and the Y coordinate component of the corresponding point cloud in the spatial coordinate system is mapped to the component Y′ of the two-dimensional plane, so as to obtain the over-under-break status of the left and right side wall point clouds corresponding to the plane coordinate system; for the cloud computing points of the top arch area, according to the central coordinates of the tunnel cross section and the tunnel radius, the angle θ between the ray formed by the center of the cross section and the calculation point and the positive direction of the X-axis and the corresponding arc length s are calculated, the arc length s is mapped to the component X′ of the two-dimensional plane, and the Y coordinate component of the calculation point in the spatial coordinate system is mapped to the component Y′ of the two-dimensional plane, so as to obtain the over-under-break status of the point cloud of the top arch area corresponding to the plane coordinate system.

[0030] Furthermore, the method further includes: step S7, calculating the overbreak or underbreak volume corresponding to each overbreak or underbreak area of ​​the tunnel surrounding rock, specifically:

[0031] For each independent overbreak or underbreak area, the rectangular microelement method based on the calculus idea is used to divide the area into multiple microelement columns according to the points in the tunnel design contour point cloud. The overbreak or underbreak volume is obtained by calculating the sum of the volumes of all microelement columns in the independent overbreak or underbreak area; where the volume dV of each microelement column is i The calculation formula is:

[0032] dV i =Δx i ×Δy i × i

[0033] In the formula, Δx i represents the point cloud spacing along the tunnel design section profile, Δy i represents the point cloud spacing along the tunnel extension direction, l i Represents the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud corresponding to point i.

[0034] The beneficial effects of the present invention are:

[0035] The present invention constructs a tunnel design contour point cloud of the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system, calculates its local normal vector from the local geometric features of the tunnel design contour point cloud and adjusts its direction so that it all points to the tunnel free surface, and establishes a calculation method for the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud based on the tunnel design contour point cloud and the local normal vector and the actual excavation contour point cloud, thereby realizing the identification of the tunnel surrounding rock over-excavation and under-excavation state. In order to facilitate the identification of the tunnel surrounding rock over-excavation and under-excavation state, a method for mapping the tunnel surrounding rock three-dimensional over-excavation and under-excavation state to a two-dimensional plane is proposed. The over-excavation and under-excavation volume of the tunnel surrounding rock is calculated by spatial region segmentation and the rectangular microelement column method based on the calculus idea, so as to realize the accurate calculation of the tunnel surrounding rock over-excavation and under-excavation volume and its distribution. This method breaks through the limitation of the existing analysis method that the actual excavation contour surface model needs to be constructed to calculate the tunnel surrounding rock over-excavation and under-excavation volume, and can obtain the spatial distribution characteristics of the tunnel surrounding rock over-excavation and under-excavation, and is easy to implement programming, with high calculation efficiency and calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0037] Figure 1 It is a flow chart of a tunnel surrounding rock over-excavation and under-excavation analysis method according to an embodiment of the present invention.

[0038] Figure 2 It is a schematic diagram of tunnel profile normal vector calculation according to an embodiment of the present invention.

[0039] Figure 3 It is a schematic diagram of determining over-excavation or under-excavation of surrounding rock of a tunnel according to an embodiment of the present invention.

[0040] Figure 4 It is a schematic diagram of identifying over-excavation and under-excavation of tunnel surrounding rock according to an embodiment of the present invention.

[0041] Figure 5 It is a schematic diagram of the calculation of the over-excavation and under-excavation volume of the tunnel surrounding rock according to an embodiment of the present invention.

[0042] Figure 6 It is a tunnel scanning point cloud contour map of an embodiment of the present invention.

[0043] Figure 7 It is a point cloud diagram of the actual excavation contour of the tunnel according to an embodiment of the present invention.

[0044] Figure 8 This is a point cloud diagram of the tunnel design contour according to an embodiment of the present invention.

[0045] Fig. 9 1 is a diagram showing the identification result of the over-excavation and under-excavation distribution state of the surrounding rock of a tunnel according to an embodiment of the present invention; wherein (a) is a three-dimensional view and (b) is a schematic diagram of the plane mapping result.

[0046] Fig.10 1 is the over-excavation volume and under-excavation volume of the tunnel surrounding rock and its distribution diagram according to an embodiment of the present invention; wherein (a) is the over-excavation volume of the tunnel surrounding rock and its distribution diagram, and (b) is the under-excavation volume of the tunnel surrounding rock and its distribution diagram. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] like Figure 1 As shown, the present invention provides a method for analyzing over-excavation and under-excavation of tunnel surrounding rock based on three-dimensional laser scanning point cloud. The method constructs an equidistant point cloud through the tunnel design contour, and calculates its local normal vector based on the local geometric characteristics of the tunnel design contour. Then, the calculation method of the normal difference between the actual tunnel excavation contour point cloud and the tunnel design contour point cloud is established to realize the calculation of the normal difference between the tunnel point clouds, thereby distinguishing the over-excavation and under-excavation state of the tunnel surrounding rock. Finally, the over-excavation and under-excavation amount of the tunnel surrounding rock and its distribution characteristics are calculated based on the spatial region segmentation and the rectangular microelement column method based on the calculus idea. The method is easy to program, and its calculation accuracy and efficiency are greatly improved, which can meet the needs of rapid detection and analysis of the over-excavation and under-excavation state of the tunnel surrounding rock by drilling and blasting method. Specifically, it includes the following steps:

[0049] 1. Use the ground 3D laser scanning system to obtain the actual point cloud of the tunnel and convert it from a dedicated format to a general point cloud format. Since the number of 3D coordinate points in the tunnel scanning point cloud is usually in the tens of millions or even hundreds of millions, before further application, the original point cloud of the tunnel should be uniformly downsampled by a third-party point cloud analysis software to reduce its density, so as to obtain a point cloud that meets the accuracy of tunnel surrounding rock over-excavation and under-excavation analysis, so as to improve the calculation and analysis efficiency of tunnel surrounding rock over-excavation and under-excavation.

[0050] 2. Establish a coordinate system for tunnel over-break and under-break analysis so that the Y axis of the coordinate system is consistent with the extension direction of the tunnel, the positive direction of the Z axis is vertically upward, and it conforms to the right-hand coordinate system. The XOZ plane represents the tunnel cross section, and the Y coordinate represents the position of the tunnel cross section.

[0051] 3. The tunnel point cloud obtained by the 3D laser scanning system is a massive 3D coordinate system with the scanner center as the origin. In order to facilitate the over-break and under-break analysis of the tunnel surrounding rock, it is necessary to convert it from the coordinate system with the scanner center as the origin to the tunnel surrounding rock over-break and under-break analysis coordinate system according to formula (1).

[0052]

[0053] Where θ z is the rotation angle around the Z axis of the tunnel overbreak and underbreak analysis coordinate system, t x ,t y ,t z They represent the translation along the X, Y, and Z axes of the tunnel overbreak and underbreak analysis coordinate system, respectively. s ,y s 、z s They represent the coordinate components of the X, Y, and Z directions of the point cloud obtained by the 3D laser scanner; g ,y g 、z g They respectively represent the coordinate components of the point cloud in the X, Y, and Z directions in the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system.

[0054] 4. The over-excavation and under-excavation analysis of a tunnel is based on the point cloud of the actual tunnel excavation contour. The tunnel point cloud obtained by the ground 3D scanning system inevitably contains point clouds of other objects besides the actual tunnel excavation contour. Therefore, before conducting the over-excavation and under-excavation analysis of the tunnel surrounding rock, the tunnel point cloud should be denoised to obtain the point cloud of the actual tunnel excavation contour.

[0055] 5. Construct the tunnel design contour point cloud in the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system according to the tunnel point cloud spacing and the design section size. First, generate the tunnel design cross-section point cloud according to the tunnel point cloud spacing and the design section size. Then, generate equally spaced cross-section point clouds along the Y-axis direction of the over-excavation and under-excavation analysis coordinate system according to the tunnel point cloud spacing. Finally, establish the tunnel design contour point cloud.

[0056] 6. When conducting over-excavation and under-excavation analysis of tunnel surrounding rock, the tunnel design contour point cloud is used as a calculation reference, and the over-excavation and under-excavation status of the tunnel surrounding rock is determined by calculating the normal difference between the tunnel design contour point cloud and the actual contour point cloud in the direction perpendicular to the tunnel design contour surface. To this end, it is necessary to first calculate the normal direction of the tunnel design contour surface. In this application, the local normal vector direction of the tunnel design contour point cloud is used as the direction perpendicular to the tunnel design contour surface. The calculation steps of the local normal vector of the tunnel design contour point cloud include: first, with the calculation point of the tunnel design contour point cloud as the center and a radius of D / 2, the rNN (radius Nearest Neighbors) algorithm is used to search for a point set S consisting of all points in the neighborhood of the calculation point. i Then, the principal component analysis method is used to calculate the point set S i The covariance matrix R of the corresponding sample feature matrix is ​​calculated, and the eigenvalues ​​and eigenvectors of the matrix R are calculated. According to the results of principal component analysis, the direction corresponding to the minimum eigenvalue is the normal vector N of the plane corresponding to point i. i .

[0057] Through the above steps, the local normal vector N( Figure 2 ).

[0058] Here, the rNN algorithm refers to the radius Nearest Neighbors search algorithm, which is similar to the kNN search algorithm, but rNN requires a specified search neighborhood radius D / 2. Then, for each point, the search algorithm finds all points in the point cloud whose distance to the point is less than or equal to the specified radius.

[0059] 7. In order to facilitate the determination and analysis of the over-excavation and under-excavation status of the tunnel surrounding rock, the local normal vector direction of the tunnel design contour point cloud is pointed to the tunnel free surface, and a determination method for the local normal vector direction of the tunnel point cloud with the tunnel centerline as the reference is established. This method takes the center of the tunnel section as the symmetry plane and divides all the calculation points in the tunnel section into two areas: left and right ( Figure 2 ). For the area to the right of the center line ( Figure 2 ), when the angle between the local normal vector N of the tunnel design contour calculation point and the positive direction of the X-axis is an obtuse angle, the direction of the local normal vector N is positive, otherwise the direction of the normal vector N should be adjusted to its negative direction; for the area to the left of the centerline of the tunnel section ( Figure 2 When the angle between the local normal vector N of the calculated point of the tunnel design contour and the positive direction of the X-axis is acute, the local normal vector is positive. Otherwise, the direction of the normal vector N should be adjusted to its negative direction. This method is used to adjust the directions of the local normal vectors of all calculated points of the tunnel design contour so that they all point to the free surface of the tunnel.

[0060] 8. For the judgment of tunnel surrounding rock over-excavation and under-excavation, the current method mainly uses the distance from the actual tunnel contour point to the tunnel center line to judge the over-excavation and under-excavation state. This method calculates the section where the actual tunnel contour point is located, and then calculates the distance d1 from the point in the cross section to the center of the tunnel section, and calculates the distance d2 from the center of the tunnel section to the tunnel design section contour along this direction. By comparing the relative sizes of d1 and d2, the over-excavation and under-excavation state of the tunnel surrounding rock is judged. When d1>d2, there is over-excavation at this position, otherwise it is under-excavation. However, this method can only judge whether the tunnel has over-excavation or under-excavation, but cannot reflect the actual over-excavation and under-excavation amount of the tunnel.

[0061] In response to this deficiency, the present application proposes a method for determining the over-excavation and under-excavation status based on the normal difference between tunnel point clouds. The calculation steps of the method include: first, taking the local normal vector N of point i of the tunnel design contour point cloud as the axis, L and d are respectively defined as a cylinder with length and diameter, and searching for the point cloud subsets of the tunnel design contour point cloud and the actual excavation contour point cloud within the cylinder, which are denoted as M(i) and N(i), respectively; then, projecting the point cloud subsets M(i) and N(i) along the local normal vector direction of the calculation point i, and calculating the average projection centers m(i) and n(i) of the tunnel design contour point cloud subset M(i) and the actual excavation contour point cloud subset N(i) corresponding to point i, respectively; finally, calculating the algebraic distance l(i) from m(i) to n(i), which is the over-excavation and under-excavation value corresponding to point i of the tunnel design contour point cloud ( Figure 3 ). According to the sign of l(i), the over-excavation and under-excavation state of the position corresponding to point i can be judged. When l(i) is positive, the position corresponding to point i is under-excavation, otherwise, it is over-excavation. Through the above steps, the over-excavation and under-excavation value corresponding to each calculation point of the tunnel design contour point cloud can be calculated, thereby realizing the identification of the over-excavation and under-excavation state of the tunnel surrounding rock.

[0062] The method proposed in the present invention does not require the pre-construction of the actual tunnel excavation contour surface, but calculates the normal difference by directly comparing the tunnel design contour point cloud with the actual excavation contour point cloud, thereby judging the over- and under-excavation status of the tunnel surrounding rock. The calculated algebraic distance can truly reflect the over- and under-excavation values ​​at the corresponding positions, and can provide a basis for the calculation of the over- and under-excavation amounts of the tunnel surrounding rock.

[0063] 9. According to step 8, the over-excavation or under-excavation state of the tunnel surrounding rock is obtained, that is, the over-excavation or under-excavation state corresponding to the tunnel design contour point cloud, which corresponds to the distribution of the tunnel surrounding rock in the three-dimensional space coordinate system. In order to facilitate analysis and application, the over-excavation and under-excavation state of the tunnel surrounding rock in the three-dimensional space coordinate system needs to be mapped to a two-dimensional plane.

[0064] To this end, the tunnel contour point cloud is divided into three regions, namely the top arch area, the left and right side wall areas ( Figure 3), for the left and right side wall areas, the Z coordinate component of the corresponding point cloud in the spatial coordinate system is mapped to the component X′ of the two-dimensional plane coordinate system, and the Y coordinate component in the spatial coordinate system is mapped to the component Y′ of the two-dimensional plane, then the over-excavation and under-excavation states of the left and right side wall point clouds corresponding to the plane coordinate system can be obtained; for the calculation points in the top arch area, according to the center coordinates of the tunnel cross section and the tunnel radius, the angle θ between the ray formed by the center of the cross section and the calculation point and the positive direction of the X-axis and the corresponding arc length s are calculated, and the arc length s is mapped to the component X′ of the two-dimensional plane, and the Y coordinate component of the calculation point in the spatial coordinate system is mapped to the component Y′ of the two-dimensional plane, then the over-excavation and under-excavation states of the top arch area point cloud corresponding to the plane coordinate system can be obtained. At this point, the over-excavation and under-excavation states of the tunnel surrounding rock in the three-dimensional spatial coordinate system can be mapped to the two-dimensional plane. By assigning different colors to the over-excavation and under-excavation states, the intuitive and rapid identification of the over-excavation and under-excavation states of the tunnel surrounding rock can be achieved ( Figure 4 ).

[0065] 10. When analyzing the over-excavation and under-excavation of tunnel surrounding rock, in addition to paying attention to its over-excavation and under-excavation status, more attention should be paid to the over-excavation and under-excavation volume of tunnel surrounding rock, that is, it is necessary to calculate the over-excavation or under-excavation volume corresponding to each over-excavation and under-excavation area of ​​tunnel surrounding rock. Since the over-excavation and under-excavation volume of tunnel surrounding rock in the tunnel side wall and top arch area is more concerned during the tunnel excavation stage, the calculation of the over-excavation and under-excavation volume of tunnel surrounding rock in the bottom plate area is not considered for the time being. At present, the calculation of the over-excavation and under-excavation volume of tunnel surrounding rock is mainly to construct the actual excavation contour surface model of the tunnel through the actual excavation contour point cloud of the tunnel, and to obtain the over-excavation and under-excavation volume of the tunnel surrounding rock by three-dimensional superposition analysis with the tunnel design contour surface model. This method can only calculate the total over-excavation and under-excavation volume of the tunnel surrounding rock, but cannot obtain the over-excavation and under-excavation volume of each independent area of ​​the tunnel surrounding rock and its distribution characteristics. In addition, this method also needs to construct a surface model corresponding to the actual excavation contour point cloud of the tunnel, which is difficult for the actual excavation contour point cloud of the surrounding rock of a deep buried complex tunnel, and when the tunnel length is large, the requirements for the calculation configuration are higher.

[0066] According to the calculations in the above steps, the over-break and under-break distances between the tunnel design contour point cloud and the actual excavation contour point cloud and the corresponding over-break and under-break states are obtained. The corresponding over-break and under-break distances can reflect the over-break and under-break values ​​of the tunnel surrounding rock in three-dimensional space.

[0067] In order to calculate the over-excavation and under-excavation of each independent area of ​​the tunnel surrounding rock, firstly, the tunnel design contour point cloud is divided into two point cloud subsets, over-excavation and under-excavation, according to the over-excavation and under-excavation status of the tunnel surrounding rock. Then, according to the number of independent over-excavation areas of the tunnel surrounding rock, the spatial segmentation method based on hierarchical analysis is used to divide it into independent spatial areas. The independent spatial areas of the tunnel surrounding rock under-excavation point cloud are obtained in the same way.

[0068] For each independent over-excavation or under-excavation area, the over-excavation or under-excavation volume of the corresponding area is calculated by the rectangular column micro-element method based on the calculus idea, that is, the points in the tunnel design contour point cloud are divided into multiple micro-element columns, and the sum of the volumes of all micro-element columns in the independent over-excavation or under-excavation area is the over-excavation or under-excavation volume. For the volume dV of each micro-element column i Calculate according to formula 2 ( Figure 5 ). In this way, the volume of over-break or under-break areas corresponding to different over-break or under-break areas of the tunnel surrounding rock is calculated, and finally the over-break or under-break volume distribution of the tunnel surrounding rock is obtained.

[0069] dV i =Δx i ×Δy i × i (2)

[0070] Where Δx i represents the point cloud spacing along the tunnel design section profile, Δy i represents the point cloud spacing along the tunnel extension direction, l i Represents the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud corresponding to point i.

[0071] Example

[0072] 1. Determine the tunnel section for over-excavation and under-excavation analysis of the surrounding rock according to the actual tunnel excavation progress and design requirements, and use the ground 3D laser scanning system to obtain the actual tunnel excavation contour point cloud ( Figure 6 ), and the processing software of the ground 3D laser scanning system converts the acquired special format into a universal point cloud format. The original point cloud of the tunnel is uniformly sampled downward using a third-party universal point cloud software. Under the condition of ensuring the accuracy of the tunnel surrounding rock over-break and under-break analysis, the density of the tunnel scanning point cloud is reduced to improve the efficiency of tunnel over-break and under-break calculation and analysis. The selected tunnel point cloud interval in this example is 0.05m, and the length of the tunnel surrounding rock over-break and under-break segment is 10m.

[0073] 2. Establish a coordinate system for over-excavation and under-excavation analysis of tunnel surrounding rock, make the positive direction of the Y axis of the coordinate system consistent with the extension direction of the tunnel, keep the positive direction of the Z axis vertically upward, and comply with the right-hand coordinate system rule. Then the XOZ plane can represent the tunnel cross section, and the Y coordinate can represent the tunnel mileage.

[0074] 3. Perform coordinate transformation on the actual excavation point cloud of the tunnel surrounding rock so that its extension direction is consistent with the positive direction of the Y-axis of the tunnel surrounding rock excavation over-excavation and under-excavation analysis coordinate system.

[0075] 4. Since the tunnel point cloud obtained by the ground 3D laser scanning system inevitably contains point clouds of other objects besides the tunnel outline, the point clouds of these corresponding objects should be deleted before further analysis. Considering that the main object of the tunnel point cloud involved in this example is the tunnel excavation outline point cloud, the non-outline points of the tunnel can be deleted manually. To this end, the third-party general point cloud processing software Cloud Compare is used to delete the non-outline points of the tunnel point cloud to obtain the actual tunnel excavation outline point cloud ( Figure 7 ).

[0076] 5. Construct the tunnel design contour point cloud of the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system according to the tunnel point cloud spacing and the tunnel design excavation contour cross-sectional dimensions. In this example, the tunnel length is 10m, the average point cloud interval is 0.05m, the tunnel cross-sectional form is a semi-circular arch tunnel, the design excavation contour radius is 2.7m, and the side wall height is 2.7m. First, establish the tunnel design contour cross-sectional point cloud according to the tunnel point cloud spacing and the tunnel design excavation contour cross-sectional dimensions. Then, generate several equally spaced cross-sectional point clouds along the Y-axis of the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system according to the tunnel point cloud spacing of 0.05m. Finally, generate the tunnel design contour point cloud as shown in the figure below. Figure 8 shown.

[0077] 6. In order to calculate the local normal vector N of the tunnel design contour point cloud, for a certain point i in the point cloud, first, with point i as the center and the normal scale D = 0.03m as the diameter, the rNN search algorithm is used to calculate the point cloud subset S belonging to the neighborhood of the point i Then, the principal component analysis method is used to calculate the point set S i The covariance matrix R of the sample feature matrix is ​​obtained, and the eigenvalues ​​and eigenvectors of the matrix R are calculated. According to the results of principal component analysis, the direction corresponding to the minimum eigenvalue is the normal vector N of the plane corresponding to the point. i The local normal vector N of each point of the tunnel design contour point cloud is calculated according to the above method.

[0078] 7. In order to compare the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud, the direction of the local normal vector N of the point cloud should be unified. To this end, the direction of the local normal vector N of the tunnel design contour point cloud is adjusted to point to the free surface of the tunnel. First, the YOZ plane passing through the origin in the over-excavation and under-excavation coordinate system is taken as the symmetry plane and divided into two left and right regions. For the left region, when the local normal vector N of point i is i When the angle with the positive direction of the X-axis is acute, the local normal vector N i When the direction is positive and the angle is obtuse, the local normal vector N i The direction is negative, and its direction should be adjusted, that is, by multiplying the local normal vector of the point by -1; for the calculation point located on the symmetry plane, the angle is a right angle, and the local normal vector N of the point should be calculated again.i The angle with the positive Z axis. When the angle is 180 degrees, the local normal vector N i is positive, otherwise, its local normal vector N should be adjusted i For the right area, when the local normal vector N of the calculation point is i When the angle with the positive direction of the X-axis is an obtuse angle, the direction of the local normal vector is positive. Otherwise, the local normal vector N i The direction of is negative, and its direction should be adjusted, that is, by multiplying the local normal vector of the point by -1. The local normal vector N of the contour point cloud designed through the above tunnel i The direction of the local normal vector N is adjusted so that it is perpendicular to the tunnel surface and points to the free side of the tunnel.

[0079] The purpose of adjusting the local direction of the point cloud here is to make the directions of the local normal vectors point to the inner surface of the tunnel, so as to facilitate the distinction between over-excavation and under-excavation.

[0080] When the directions of the local normal vectors all point to the inner surface of the tunnel and the algebraic distance of the normal difference between the point clouds is positive, it corresponds to under-excavation, and when the algebraic distance is negative, it corresponds to over-excavation.

[0081] 8. Through steps 6 and 7, the local normal vector of the tunnel design contour point cloud is obtained, and its direction is pointed to the free surface of the tunnel. On this basis, the over-excavation and under-excavation of the tunnel surrounding rock and the visualization of the spatial distribution state are carried out, and the length L of the projection cylinder is selected as 1.0m and the diameter d of the projection cylinder is selected as 0.3m. First, the local normal vector N of point i of the tunnel design contour point cloud is i The axis is L and d are the length and diameter of the cylinder, respectively. The point cloud subsets of the tunnel design contour point cloud and the actual excavation contour point cloud within the cylinder are calculated, respectively, and recorded as M(i) and N(i). Then, the point cloud subsets M(i) and N(i) are respectively calculated along the local normal vector N of the calculation point i. i The projection is performed in the direction, and the average projection centers m(i) and n(i) of the tunnel design contour point cloud subset M(i) and the tunnel excavation contour point cloud subset N(i) corresponding to point i are calculated respectively. Finally, the algebraic distance l(i) from m(i) to n(i) is calculated, which is the over-excavation value corresponding to point i in the tunnel design contour point cloud. The over-excavation state of the position corresponding to point i can be judged according to the sign of l(i). When l(i) is positive, the position corresponding to point i is calculated to be under-excavated, otherwise, it is over-excavated. Through the above steps, the over-excavation distribution corresponding to the tunnel design contour point cloud can be calculated ( Fig. 9 (a)).

[0082] The over-break and under-break calculation method of the present invention is to obtain the over-break and under-break values ​​of corresponding points by comparing the actual tunnel excavation contour with the tunnel design contour point cloud, and then calculate the over-break and under-break volume. Therefore, it can also be understood as the normal difference between the actual tunnel contour point cloud and the tunnel design contour point cloud.

[0083] 9. Step 8 calculates the over-break and under-break state and its distribution of the tunnel surrounding rock in the three-dimensional space coordinate system. For the convenience of analysis, the over-break and under-break state is mapped to the plane. To this end, the tunnel design contour point cloud is divided into three areas, namely the top arch area, the left side wall area and the right side wall area. For the point cloud of the left side wall area, the Z coordinate component in the over-break and under-break analysis coordinate system is mapped to the component X′ of the two-dimensional plane, and the Y coordinate component in the over-break and under-break analysis coordinate system is mapped to the component Y′ of the two-dimensional plane, so that the over-break and under-break state of the left side wall and the right side wall corresponding to the plane coordinate system can be obtained; for the point cloud of the top arch area, according to the center coordinates of the tunnel cross section and the tunnel radius, the angle θ between the ray formed by the cross section center and the calculation point and the positive direction of the X axis and the corresponding arc length s are calculated, and the arc length s is mapped to the component X′ of the two-dimensional plane, and the Y coordinate component of the calculation point in the over-break and under-break analysis coordinate system is mapped to the component Y′ of the two-dimensional plane. At this point, the over-break and under-break states of all points in the over-break and under-break analysis coordinate system can be mapped to a two-dimensional plane. By assigning red and blue to the over-break and under-break states, respectively, the plane mapping result corresponding to the three-dimensional over-break and under-break states of the tunnel surrounding rock can be obtained ( Fig. 9 (b)).

[0084] 10. Through the calculation and analysis of steps 8 and 9, the normal difference value between the tunnel design contour point cloud and the actual excavation contour point cloud in the direction perpendicular to the tunnel design contour surface and the corresponding over-excavation and under-excavation status are obtained. The results can be used to calculate the over-excavation and under-excavation volume of the tunnel surrounding rock and its distribution. During the tunnel excavation stage, more attention is paid to the over-excavation and under-excavation of the surrounding rock in the tunnel side wall and top arch area. Therefore, the over-excavation and under-excavation of the surrounding rock in the tunnel floor area are not considered for the time being. The area with a tunnel floor height of more than 0.5m is selected to calculate the over-excavation and under-excavation volume of the tunnel surrounding rock. According to the calculation results of step 8 ( Fig. 9 ) shows that the number of tunnel surrounding rock over-excavation areas is 1, while the number of tunnel surrounding rock under-excavation areas is 4. According to the number of independent over-excavation and under-excavation areas of the tunnel, the corresponding over-excavation and under-excavation point clouds are divided into point cloud subsets of independent areas using the hierarchical analysis method.

[0085] For each over-excavation or under-excavation area of ​​the tunnel surrounding rock, the over-excavation or under-excavation volume of the corresponding area is calculated using a rectangular microelement column based on the idea of ​​calculus. The volume of the rectangular microelement column is calculated using formula (2), and the sum of the volumes corresponding to all points in the area is the over-excavation or under-excavation volume of the corresponding area. In this way, the volume and distribution of the over-excavation or under-excavation area corresponding to different over-excavation or under-excavation areas of the tunnel surrounding rock can be calculated.

[0086] dV i =Δx i ×Δy i × i Formula (2)

[0087] In the formula, Δx i represents the point cloud spacing along the tunnel design section profile, Δy i represents the point cloud spacing along the tunnel extension direction, l i It represents the distance between the calculated point i in the tunnel design contour point cloud and the actual tunnel excavation contour point cloud along its local normal direction.

[0088] Based on the above calculation method, the tunnel surrounding rock over-excavation distribution and its corresponding volume are obtained as follows: Fig.10 As shown in (a), the distribution of tunnel surrounding rock undercut and its corresponding volume are as follows: Fig.10 (b) As shown in the figure, the overcut volume of the surrounding rock of the tunnel section used for the example calculation is -20.25m 3 , the undercut volume is 5.68m 3 .

[0089] It should be noted that when the calculation method involved in this embodiment is used to calculate the over-excavation volume, when the calculation result is positive, it means that the corresponding part is under-excavation, and when the calculation result is negative, the corresponding part is over-excavation. This method stipulates that when the direction of the corrected local normal vector (specifying the inner surface of the surrounding rock) is positive and the sign of the algebraic distance is positive, the calculation result is positive, which corresponds to under-excavation; when the direction is opposite, the calculation result is negative, which corresponds to over-excavation.

[0090] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A tunnel surrounding rock over-break and under-break analysis method based on 3D laser scanning point cloud, characterized in that: The following steps are involved: Step S1, using a ground 3D laser scanning system to obtain a tunnel point cloud, pre-processing the tunnel point cloud to obtain a tunnel actual excavation contour point cloud, and converting the tunnel actual excavation contour point cloud from a dedicated format into a general point cloud format, and then establishing a tunnel over-excavation and under-excavation analysis coordinate system and converting it to the tunnel surrounding rock over-excavation and under-excavation analysis coordinate system through a coordinate system conversion formula; The method for establishing the coordinate system for tunnel overbreak and underbreak analysis is as follows: the Y axis of the coordinate system is consistent with the extension direction of the tunnel, the positive direction of the Z axis is vertically upward, and it conforms to the right-hand coordinate system, then the XOZ plane represents the tunnel cross section, and the Y coordinate represents the position of the tunnel cross section; Among them, the conversion formula of the coordinate system is: In the formula, θ z is the rotation angle around the Z axis of the tunnel overbreak and underbreak analysis coordinate system, t x ,t y ,t z They represent the translation along the X, Y, and Z axes of the tunnel overbreak and underbreak analysis coordinate system, respectively. s ,y s 、z s They represent the coordinate components of the X, Y, and Z directions of the point cloud obtained by the 3D laser scanner; g ,y g 、z g They respectively represent the coordinate components of the point cloud in the X, Y and Z directions in the coordinate system of the tunnel surrounding rock over-break and under-break analysis; Step S2, constructing a tunnel design contour point cloud in a tunnel surrounding rock over-break and under-break analysis coordinate system according to the tunnel point cloud spacing and the design section size; Step S3, calculating the local normal vectors of all calculation points in the tunnel design contour point cloud; specifically: First, with the calculation point of the tunnel design contour point cloud as the center and a radius of D / 2, the rNN algorithm is used to search for the point set S consisting of all points in the neighborhood of the calculation point. i Then, the principal component analysis method is used to calculate the point set S i The covariance matrix R of the corresponding sample feature matrix is ​​calculated, and the eigenvalues ​​and eigenvectors of the matrix R are calculated. According to the results of principal component analysis, the direction corresponding to the minimum eigenvalue is the normal vector N of the plane corresponding to the calculation point; Step S4, adjusting the directions of the local normal vectors of all calculation points of the tunnel design contour so that the local normal vectors all point to the free surface of the tunnel; Step S5, determining the over-excavation and under-excavation status based on the normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud; specifically, taking the local normal vector N of point i of the tunnel design contour point cloud as the axis, L and d are respectively used to define a cylinder with length and diameter, and searching for the point cloud subsets of the tunnel design contour point cloud and the tunnel actual excavation contour point cloud within the cylinder, respectively, which are recorded as M(i) and N(i); Then, the point cloud subsets M(i) and N(i) are projected along the local normal vector direction of the calculation point i, and the average projection centers m(i) and n(i) of the tunnel design contour point cloud subset M(i) and the actual excavation contour point cloud subset N(i) corresponding to point i are calculated respectively. Finally, the algebraic distance l(i) from m(i) to n(i) is calculated as the over-excavation value corresponding to point i of the tunnel design contour point cloud. The over-excavation state of the position corresponding to point i can be judged according to the sign of l(i). When l(i) is positive, the position corresponding to point i is under-excavated, otherwise, it is over-excavated. Step S6, mapping the over-break and under-break conditions of the tunnel surrounding rock in the three-dimensional space coordinate system to a two-dimensional plane, and assigning different colors to the over-break and under-break conditions, thereby achieving intuitive and rapid identification of the over-break and under-break conditions of the tunnel surrounding rock; The specific method of mapping the over-excavation and under-excavation of the tunnel surrounding rock in the three-dimensional space coordinate system to the two-dimensional plane is: The tunnel contour point cloud is divided into the top arch area, the left side wall area and the right side wall area; for the cloud computing points of the left and right side wall areas, the Z coordinate component of the corresponding point cloud in the spatial coordinate system is mapped to the component X′ of the two-dimensional plane coordinate system, and the Y coordinate component of the corresponding point cloud in the spatial coordinate system is mapped to the component Y′ of the two-dimensional plane, so as to obtain the over-under-break state of the left and right side wall point cloud corresponding to the plane coordinate system; for the cloud computing points of the top arch area, according to the center coordinates of the tunnel cross section and the tunnel radius, the angle θ between the ray formed by the center of the cross section and the calculation point and the positive direction of the X-axis and the corresponding arc length s are calculated, and the arc length s is mapped to the component X′ of the two-dimensional plane, and the Y coordinate component of the calculation point in the spatial coordinate system is mapped to the component Y′ of the two-dimensional plane, so as to obtain the over-under-break state of the point cloud of the top arch area corresponding to the plane coordinate system; Step S7, calculating the overbreak or underbreak volume corresponding to each overbreak or underbreak area of ​​the tunnel surrounding rock, specifically: For each independent overbreak or underbreak area, the rectangular microelement method based on the calculus idea is used to divide the area into multiple microelement columns according to the points in the tunnel design contour point cloud. The overbreak or underbreak volume is obtained by calculating the sum of the volumes of all microelement columns in the independent overbreak or underbreak area; where the volume dV of each microelement column is i The calculation formula is: dV i =△x i ×△y i ×l i In the formula, Δx i represents the point cloud spacing along the tunnel design section profile, Δy i represents the point cloud spacing along the tunnel extension direction, l i It represents the average normal difference between the tunnel design contour point cloud and the actual excavation contour point cloud corresponding to point i.

2. The method for analyzing over-break and under-break of tunnel surrounding rock based on three-dimensional laser scanning point cloud according to claim 1, characterized in that: The preprocessing in step S1 includes uniformly downsampling the tunnel point cloud obtained by scanning and performing denoising on the tunnel point cloud.

3. The method for analyzing over-break and under-break of tunnel surrounding rock based on three-dimensional laser scanning point cloud according to claim 1, characterized in that: The step S2 is specifically as follows: The tunnel design cross-section point cloud is generated according to the tunnel point cloud spacing and the design section size. Then, the equally spaced cross-section point clouds are generated according to the tunnel point cloud spacing along the Y-axis direction of the overbreak and underbreak analysis coordinate system, and finally the tunnel design contour point cloud is established.

4. The method for analyzing over-break and under-break of tunnel surrounding rock based on three-dimensional laser scanning point cloud according to claim 1, characterized in that: The step S4 is specifically as follows: Taking the center of the tunnel section as the symmetry plane, all the calculation points in the tunnel section are divided into two areas, left and right; for the area on the right side of the center line, when the angle between the local normal vector N of the calculation point of the tunnel design contour point cloud and the positive direction of the X-axis is an obtuse angle, the direction of the local normal vector N is positive, otherwise the direction of the normal vector N should be adjusted to its negative direction; for the area on the left side of the center line of the tunnel section, when the angle between the local normal vector N of the calculation point of the tunnel design contour and the positive direction of the X-axis is an acute angle, the local normal vector is positive, otherwise the direction of the normal vector N should be adjusted to its negative direction.

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