A method for constructing a universal potential instability surface model for tunnel face failure

Abstract

The present invention provides a method for constructing a universal potential instability surface model for tunnel face failure. The construction method comprises: constructing a geometric model of the instability surface, which includes a shear slip zone, a columnar collapse zone, and an arched roof fall zone. The shear slip zone is a spatial curved surface formed by the shear slip contour line rotating and changing around the center point; establishing a coordinate system with the center point as the origin of the coordinate axis. xyz Axis coordinate system is used; the shear slip zone, columnar collapse zone, and arched roof fall zone are discretized, and the coordinate information of the discrete points on the outer contours of the shear slip zone, columnar collapse zone, and arched roof fall zone is obtained; based on the coordinate information of the discrete points on the outer contours of the shear slip zone, columnar collapse zone, and arched roof fall zone, a model of the potential instability surface of the tunnel face failure is constructed. The instability surface model constructed by the present invention not only conforms to the actual spatial morphological characteristics but also reflects the irregular characteristics of the external appearance, and can be used to effectively predict the potential instability area of ​​the tunnel face failure.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and in particular relates to a method for constructing a universal potential instability surface model for tunnel face failure. Background Art

[0002] Tunnel face failure is a common engineering accident during tunnel construction. Reliable prediction of potential instability areas of tunnel face failure has the following functions: (1) Based on the prediction results, engineering personnel can predict high-risk instability areas in advance and take corresponding preventive measures to reduce the risk of face failure and ensure the safety of construction personnel; (2) Based on the prediction results, measures can be taken in advance to avoid or reduce losses such as equipment damage, project delays, and additional repair and reinforcement costs caused by face instability, thereby improving construction efficiency and reducing construction costs; (3) Based on the prediction results, it can help to consider the risk of tunnel face failure in the design stage, and then, according to different geological conditions, optimize the support design and construction plan in advance, and take targeted support measures to ensure the stability and effectiveness of the support system during tunnel construction.

[0003] Existing models of potential instability surfaces for tunnel face failure primarily use logarithmic spirals and truncated cones, and wedges and cylinders as potential instability surfaces. While these two methods are widely used in engineering, they also have significant shortcomings. For example, the logarithmic spiral and truncated cone methods struggle to account for potential instability in rectangular tunnel faces, while the wedge and cylinder methods struggle to account for faces with shapes other than rectangles. Furthermore, both methods impose certain restrictions on the potential instability shape, failing to meet the complex spatial morphological characteristics of potential instability surfaces required in actual engineering projects. Summary of the Invention

[0004] The purpose of the present invention is to provide a new method for constructing a universal potential instability surface model of tunnel face failure in view of the fact that existing models are difficult to cope with the complex and changeable characteristics of the potential instability surfaces of tunnel faces of different shapes in complex strata. The construction method divides the potential instability area of ​​tunnel face failure into three parts, and adopts a non-limiting form to construct the potential instability surface of tunnel face failure, so that it conforms to the actual spatial morphological characteristics and can reflect the irregular characteristics of the appearance. Furthermore, discrete technology is applied to construct a universal potential instability surface of tunnel face failure using discrete points, so that the generation of the potential instability area of ​​tunnel face failure becomes simple and easy, thereby providing a strong scientific basis for the reinforcement of the potential instability area of ​​tunnel face failure in actual engineering.

[0005] The present invention provides a method for constructing a universal potential instability surface model for tunnel face destruction, the construction method comprising: step S10, constructing a geometric model of the instability surface based on the spatial characteristics of the potential instability area of ​​the tunnel face destruction and a set shape parameter group, the geometric model of the instability surface comprising a shear slip zone, a columnar collapse zone located above the shear slip zone, and an arched roof fall zone located above the columnar collapse zone, the shear slip zone being a spatial curved surface formed by the shear slip contour line rotating and changing around a center point, the shear slip contour line at the bottom end of the shear slip zone being identical to the tunnel face contour line in size and shape, the plane where the top shear slip contour line of the shear slip zone is located being a horizontal plane, the cross-sectional shape of the columnar collapse zone and the cross-sectional shape of the bottom surface of the arched roof fall zone being identical to the shape of the top shear slip contour line of the shear slip zone; step S20, establishing a coordinate system with the center point as the origin of the coordinate axis. x.y.z Axis coordinate system, where x The axis direction is the longitudinal direction of the tunnel. y The axis direction is the tunnel transverse direction. z The axis direction is determined according to the left-hand rule; Step S30, the shear slip zone, columnar collapse zone and arched roof fall zone are discretized respectively, and based on the x.y.z The axis coordinate system and the dimension data of the bottom shear slip contour line are used to obtain the coordinate information of multiple first discrete points on the outer contour of the shear slip zone, the coordinate information of multiple second discrete points on the outer contour of the columnar collapse zone, the coordinate information of multiple third discrete points on the outer contour of the arch roof fall zone, and the coordinate information of the vertices of the arch roof fall zone; step S40, based on the coordinate information of the multiple first discrete points, the coordinate information of the multiple second discrete points, the coordinate information of the vertices of the arch roof fall zone, and the coordinate information of the multiple third discrete points, construct a potential instability surface model of the tunnel face destruction.

[0006] In a specific embodiment, the shear slip zone is recorded as A B D C ,in A 、 B 、 C and D are the four boundary points of the cross section of the shear slip zone, AC is the upper boundary control line close to the center point, BD is the lower boundary control line away from the center point, and the shear slip contour line of the shear slip zone is a closed curve. AB is the center axis of the bottom shear slip contour line, CD The center axis of the top shear slip contour line is AB The straight line and the CD The intersection of the straight lines.

[0007] In a specific embodiment, the set shape parameter group includes shear slip zone shape parameters, columnar collapse zone shape parameters and arch roof fall zone shape parameters, wherein the shear slip zone shape parameters include r 0. k 1. k 2. l 0. l 1. l 2. l 3. l 4 and g , r 0 is the initial diameter of the upper boundary control line, k 1 is the shape parameter of the upper boundary control line, k 2 is the shape parameter of the lower boundary control line, l 0. l 1. l 2. l 3. l 4 and g are dimensionless parameters for controlling the shape of shear slip contours, among which, l 0=1 and l 1=1–( l 2+ l 3+ l 4), r The value range of 0 is 0m~10m, k 1. k 2. l 2. l 3 and l The value range of 4 is -1~1. g The value range is 0~1; the shape parameter of the columnar collapse area is the height parameter of the columnar collapse area h 1. The shape parameter of the arched roof fall area is the height parameter of the arched roof fall area. h 2, h 1 and h The value range of 2 is 0m~10m.

[0008] In a specific embodiment, the shear slip region is discretized and based on the x.y.z The step of obtaining the coordinate information of a plurality of first discrete points on the outer contour of the shear slip zone comprises: obtaining a set first set of discrete parameters, the first set of discrete parameters including: m and n 0; Taking the center point as the origin of polar coordinates, construct the n 0+1 cross sections, the n 0+1 cross sections discretize the shear slip zone into n0 blocks, where the boundary control line polar angle is AB and CD The angle between each cross section and the shear slip zone is taken as the shear slip contour line, the midpoint of the center line segment of each shear slip contour line is obtained, and the midpoint of the center line segment of the shear slip contour line is used as the discrete center point. Based on the equal division of the center angle, the shear slip contour line on each cross section is discretized into 2 m points, and get ( n 0+1)×2 m The center line segment of the shear slip contour line is a line segment connecting the intersection of the shear slip contour line and the upper boundary control line and the intersection of the shear slip contour line and the lower boundary control line; x.y.z The axis coordinate system is a coordinate axis, and based on the dimension data of the bottom shear slip contour line, the coordinate information of each first discrete point is obtained according to the first calculation method.

[0009] In a specific embodiment, i Shear slip contours on a cross section i Previous j The first discrete point is recorded as point S ij ,in, i and j is an integer, 0≦ i ≦ n 0 and 0≦ j ≦2 m –1, the point S ij for( n 0+1)×2 m Any one of the first discrete points; obtaining the point according to the first calculation method S ij The steps of obtaining the coordinate information of the x.y.z The axis coordinate system is the coordinate axis, and the intersection of the bottom shear slip contour line and the upper boundary control line of the shear slip zone is extracted. A The intersection of the lower boundary control line B Coordinate information of the point A and point B The coordinate information of the solution point A and point B midpoint K 0 coordinate information, the bottom shear slip contour line is i =0 cross section and the intersection of the shear slip zone; based on the point A and point B , get the coordinate information of i The intersection of the shear slip contour line and the upper boundary control line on the cross sectionI i The intersection of the lower boundary control line J i Coordinate information of the point I i and point J i The coordinate information of the solution point I i and point J i midpoint K i Coordinate information of the two points; based on the distance formula of the two points and the point I i and point J i Coordinate information of the calculated point I i and point J i The distance between the points I i The shear slip contour line is at the pole diameter, and the point I i The shear slip contour line is at the point I i and point J i Extract the bottom shear slip contour line j discrete points S 0j Coordinate information of the two points is calculated based on the distance formula between the two points. A and point K 0 distance and point S 0j and point K 0 distance, and calculate the point S 0j Corresponding to the polar diameter ratio, the point S 0j The corresponding polar diameter ratio is point S 0j and point K 0 distance from the point A and point K 0; Apply the cubic polynomial and the sum of the higher-order error remainders to construct the top shear slip contour line of the shear slip zone. j The polar diameter ratio corresponding to the discrete points x nj and polar angle r j The functional relationship of the pole diameter ratio is calculated based on the constructed functional relationship. x nj , wherein the top shear slip contour line isi = n The intersection line of the cross section of 0 and the shear slip zone: Based on the bottom shear slip contour line j discrete points S 0j The diameter ratio of the top shear slip contour line j The diameter ratio of the discrete points and the i The boundary control line polar angle corresponding to the cross section is calculated at point S ij Corresponding pole diameter ratio x ij ; Point-based I i The shear slip contour line polar radius and point S ij Corresponding pole diameter ratio x ij , calculation point S ij The shear slip contour line at the polar radius; based on the point K i Coordinate information, point S ij The shear slip contour line polar radius and point S ij Corresponding polar angle, get point S ij coordinate information.

[0010] In a specific embodiment, the columnar collapse area is discretized and based on the x.y.z The step of obtaining coordinate information of a plurality of second discrete points on the outer contour of the columnar collapse area through the axis coordinate system includes: obtaining a set second set of discrete parameters, wherein the second set of discrete parameters includes m and n 1. Along the height direction of the columnar collapse area, use multiple horizontal planes set at equal intervals to cut the columnar collapse area into n 1 block segment; obtain multiple collapse area contour lines obtained by cutting the columnar collapse area on each horizontal plane, and each collapse area contour line has the same size and shape as the shear slip contour line at the top of the shear slip area; obtain the midpoint of the center line segment of each collapse area contour line, and use the midpoint of the center line segment of the collapse area contour line as the discrete center point, and discretize each collapse area contour line into 2 equal parts based on the center angle. m Points, get n 1×2 m The second discrete point, wherein the center line segment of the landslide area contour line is the line segment connecting the landslide area contour line at xyz The line segments of the left and right boundary points on the plane; x.y.z The axis coordinate system is the coordinate axis, based on the top shear slip contour line 2m The coordinate information of the first discrete point and the discrete parameters n 1 and the height parameter of the columnar landslide area, and obtain the coordinate information of each second discrete point according to the second calculation method.

[0011] In a specific embodiment, the contour line of the landslide area k Previous j The second discrete point, denoted as point T kj ,in, k and j is an integer, and 1≦ k ≦ n 1, 0≦ j ≦2 m –1, the point T kj for n 1×2 m any one of the second discrete points; obtaining the point according to the second calculation method T kj The coordinate information of the point includes: T kj in x The coordinates on the axis and y The coordinates on the axis are all the same as the top shear slip contour line. j The first discrete point is x The coordinates on the axis and y The coordinates on the axis are the same; the point T kj exist z Coordinates on the axis = ( k / n 1) × h 1, among which, h 1 is the height parameter of the columnar landslide area.

[0012] In a specific embodiment, the arched roof fall area is discretized, and based on the x.y.z The step of obtaining the coordinate information of a plurality of third discrete points on the outer contour of the arched roof fall area and the coordinate information of the vertex of the arched roof fall area by the axis coordinate system includes: obtaining a set third group of discrete parameters, the third group of discrete parameters including m and n 2; n 2 on the contour line of a landslide area m The second discrete point is used as the bottom contour line of the arched roof fall area. m Plane construction points, and based on the 2 m Plane construction points and roof fall area vertices, construct 2 mvertical planes, each vertical plane is perpendicular to the bottom surface of the arched roof fall area and passes through the top of the roof fall area and a plane construction point at the same time. Different vertical planes pass through different plane construction points. n 1. The contour line of the collapse area is the same as the bottom contour line of the arch roof fall area; obtain the intersection line of each vertical plane and the arch roof fall area, and obtain 2 m Rotation curves, each of which is a parabola, with the vertex at the top of the roof fall area and the opening direction downward; each rotation curve is discretized into n 2 points, we get ( n 2+1)×2 m A third discrete point, the discrete points of the arched roof fall area include the top of the roof fall area and ( n 2+1)×2 m The third discrete point; based on the n 1. On the contour line of the landslide area 2 m The coordinate information of the second discrete point, discrete parameters n 2 and the height parameters of the arched roof fall area h 2. Obtain the coordinate information of the vertex of the roof fall area and each third discrete point.

[0013] In a specific embodiment, the n 1. On the contour line of the landslide area 2 m The coordinate information of the second discrete point, discrete parameters n 2 and the height parameters of the arched roof fall area h 2. The step of obtaining the coordinate information of the vertex of the roof fall area and each third discrete point includes: n 1 landslide area outline line xyz The coordinate information of the left and right boundary points on the plane is used to calculate the n The midpoint between the left and right boundary points of a landslide area contour line R Coordinates of; based on the midpoint R The coordinates of the columnar collapse area and the height parameters h 2 , calculate the vertex of the roof fall area G The coordinate information of the vertex of the roof fall area G exist x The coordinates on the axis and y The coordinates on the axis are respectively the same as the midpoint R exist x The coordinates on the axis and y The coordinates on the axis are the same, and the vertex of the roof fall area G exist z The coordinates on the axis are the midpoints R exist z The coordinates on the axis and h2; based on n 1. On the contour line of the landslide area 2 m The coordinate information of the second discrete point, the midpoint R Coordinates and discrete parameters n 2 and the height parameters of the columnar collapse area h 2 , obtain the coordinates of each third discrete point according to the third calculation method.

[0014] In a specific embodiment, the rotation curve of the arched roof fall area j Previous t Points, denoted as points P tj ,in, t and j is a positive integer, 1≦ t ≦ n 2–1 and 0≦ j ≦2 m –1, the point P tj for( n 2+1)×2 m Any third discrete point among the third discrete points; obtaining the point according to the third calculation method P tj The calculation formula of the coordinate information is:

[0015] ;

[0016] In the above formula, 、 and Points P tj exist x 、 y and z Coordinates on the axis; x R 、 y R and z R midpoints R exist x 、 y and z Coordinates on the axis; and Columnar collapse area n 1. On the contour line of the landslide area j discrete points exist x and y The coordinates on the axis, n 2 is a discrete parameter, h 2 is the height parameter of the arched roof fall area.

[0017] The beneficial effects of the present invention include at least:

[0018] 1. When constructing a universal potential instability surface model for tunnel face failure, the present invention first constructs a geometric model of the instability surface based on a set shape parameter group, wherein the geometric model includes a shear slip zone, a columnar collapse zone, and an arched roof fall zone, wherein the shear slip zone is a spatial curved surface formed by the shear slip contour line rotating and changing around a center point, the shear slip contour line at the bottom of the shear slip zone is the same as the tunnel face contour line in size and shape, the plane where the top shear slip contour line of the shear slip zone is located is a horizontal plane, the cross-sectional shape of the columnar collapse zone and the cross-sectional shape of the bottom surface of the arched roof fall zone are the same as the shape of the top shear slip contour line of the shear slip zone; then, the shear slip zone, the columnar collapse zone, and the arched roof fall zone are discretized respectively, and the external shapes of the shear slip zone, the columnar collapse zone, and the arched roof fall zone are obtained. The coordinate information of each discrete point on the contour is obtained; finally, according to the coordinate information of the discrete points on the outer contour of the shear slip zone, the columnar collapse zone and the arched roof fall zone, a potential instability surface model of the tunnel face is constructed; the instability surface model constructed by the construction method of the present invention conforms to the actual spatial morphological characteristics and can reflect the irregular characteristics of the appearance, which solves the technical problem that the existing model is difficult to cope with the complex and changeable characteristics of the potential instability surface of the tunnel face of different shapes in complex strata. At the same time, Example 1 of the present invention also proves that the instability surface model corresponding to the optimal shape parameter group obtained by fitting the set shape parameter group has a fitting degree of 0.9966, so that it can be used to effectively predict the potential instability area of ​​the tunnel face, and provide a strong scientific basis for the reinforcement of the potential instability area of ​​the tunnel face in actual engineering.

[0019] 2. The construction method provided by the present invention has the advantages of wide applicability, high efficiency, strong reliability and low cost. It can independently and intelligently construct the potential instability surface of tunnel face damage in a discrete manner, and can effectively predict the potential instability area of ​​tunnel face damage under non-limited shapes. At the same time, it can realize the universal generation of potential instability areas of tunnel face damage that match different face shapes.

[0020] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A flowchart of the steps of a method for constructing a universal potential instability surface model for tunnel face failure provided by one embodiment of the present invention;

[0022] Figure 2 A schematic diagram of the geometric model of the instability surface provided by the present invention;

[0023] Figure 3 Schematic diagram of the tunnel face shape and the cross-sectional shape of the potential instability zone of the tunnel face provided by the present invention;

[0024] Figure 4 A schematic diagram of the spatial surface of the shear slip zone provided by the present invention;

[0025] Figure 5 A discrete schematic diagram of the shear slip zone provided by the present invention;

[0026] Figure 6 A discrete schematic diagram of a columnar collapse area provided by the present invention;

[0027] Figure 7 This is a discrete schematic diagram of the arched roof fall area provided by the present invention.

[0028] Description of Reference Numerals

[0029] DETAILED DESCRIPTION

[0030] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0031] See also Figure 1 The present invention provides a method for constructing a universal potential instability surface model for tunnel face failure, the method comprising:

[0032] Step S10: Based on the spatial characteristics of the potential unstable area of ​​the tunnel face damage and the set shape parameter group, a geometric model of the unstable surface is constructed, wherein the geometric model of the unstable surface includes a shear slip zone, a columnar collapse zone located above the shear slip zone, and an arched roof fall zone located above the columnar collapse zone. The shear slip zone is a spatial curved surface formed by the shear slip contour line rotating and changing around the center point. The shear slip contour line at the bottom of the shear slip zone is the same as the tunnel face contour line in size and shape. The plane where the top shear slip contour line of the shear slip zone is located is a horizontal plane. The cross-sectional shape of the columnar collapse zone and the cross-sectional shape of the bottom surface of the arched roof fall zone are both the same as the shape of the top shear slip contour line of the shear slip zone.

[0033] In the present invention, the shear slip zone is the area in front of the tunnel face where shear failure may occur, the columnar collapse zone is the area above the shear slip zone where collapse may occur, and the arched roof fall zone is the arched stable area above the columnar collapse zone formed due to stress redistribution.

[0034] In the present invention, the set shape parameter group includes shear slip zone shape parameters, columnar collapse zone shape parameters and arched roof fall zone shape parameters.r 0. k 1. k 2. l 0. l 1. l 2. l 3. l 4 and g , r 0 is the initial diameter of the upper boundary control line, k 1 is the shape parameter of the upper boundary control line, k 2 is the shape parameter of the lower boundary control line, l 0. l 1. l 2. l 3. l 4 and g are dimensionless parameters for controlling the shape of shear slip contours, among which, l 0=1 and l 1=1–( l 2+ l 3+ l 4), r The value range of 0 is 0m~10m, k 1. k 2. l 2. l 3 and l The value range of 4 is -1~1. g The value range is 0~1; the shape parameter of the columnar collapse area is the height parameter of the columnar collapse area h 1. The shape parameter of the arched roof fall area is the height parameter of the arched roof fall area. h 2, h 1 and h The value range of 2 is 0m~10m.

[0035] In the present invention, the morphology of the shear slip zone, columnar collapse zone, and arched roof fall zone is affected by the shape of the tunnel face, and the cross-section of each zone maintains a similar shape to the face and has the same symmetry as the tunnel face. For the shear slip zone, it is a spatial surface formed by the shear slip contour line rotating and changing around the center point. The formation of this surface is constrained by the upper and lower boundary control lines, and the upper and lower boundary control lines can be approximated as a general logarithmic spiral. In addition, at the bottom of the shear slip zone, the bottom shear slip contour line is a known face contour line. At the top of the shear slip zone, the top shear slip contour line is an unknown closed curve on the horizontal plane. The corresponding curve function can be established using a polynomial equation. At other parts of the shear slip zone, the shear slip contour line will be solved using a linear interpolation method based on the bottom and top shear slip contour lines. For the columnar collapse zone, it is a spatial surface obtained by extending the top shear slip contour line of the shear slip zone upward to a certain height in the vertical direction. For the arched roof fall area, it is an arched surface formed by the rotation and change of a parabola around the vertical central axis, wherein the vertex of the parabola is the vertex of the arched roof fall area, the height of the parabola is the height of the arched roof fall area, and the trajectory of the endpoints of the rotating parabola is the horizontal bottom surface contour line of the roof fall area, which is also the contour line of the landslide area.

[0036] Please refer to Figure 2 Under deep burial conditions, the general potential instability surface of the tunnel face 2 of the tunnel 1 usually does not extend to the ground surface 3 and exhibits certain spatial morphological characteristics. Based on these spatial morphological characteristics, the constructed instability surface geometric model is divided into three parts, namely the shear slip zone 4, the columnar collapse zone 5, and the arched roof fall zone 6. Figure 2 in A B D C represents the shear slip zone, Figure 2 in CDFE Indicates columnar landslide area, Figure 2 in EFG Indicates the arched roof fall area. It should be noted that A 、 B 、 C 、 D 、 E 、 F and G It can be understood as the boundary point of the cross section of each area.

[0037] In the present invention, the shear slip zone A B D C The area in front of the tunnel face where shear failure may occur. Its cross-sectional shape is constrained by the shape of the tunnel face, and its size is controlled by the upper boundary control line 7 (the boundary control line close to the center point) and the lower boundary control line 8 (the boundary control line far from the center point). AC is the upper boundary control line 7, BD It is the lower boundary control line 8; columnar landslide area CDFEThe area above the shear slip zone where collapse may occur has the same cross-sectional shape as the top shear slip contour line 9 of the shear slip zone and extends vertically to a certain height. h 1. Arched roof fall area EGF It is an arched stable area located above the columnar collapse area and formed due to stress redistribution. Its bottom shape is the same as the cross-sectional shape of the columnar collapse area, and its size is related to the height of the roof collapse area. h 2.

[0038] See Figure 2 It is known that the top shear slip contour line of the shear slip zone and the bottom contour line (bottom cross section) of the columnar collapse zone are the same contour line, the top contour line (top cross section) of the columnar collapse zone and the bottom contour line (bottom cross section) of the arch cap zone are the same contour line, and the bottom contour line of the columnar collapse zone and the top contour line of the columnar collapse zone have the same size and shape. In this way, the cross-sectional shape of the columnar collapse zone, the cross-sectional shape of the bottom of the arched roof collapse zone and the top shear slip contour line shape of the shear slip zone are all the same. This setting facilitates the calculation of subsequent discrete point coordinates.

[0039] Please refer to Figure 3 Tunnel faces can have various shapes, including circular, rectangular, horseshoe, and Tansan circular, all of which are bilaterally symmetrical about their central axes. Due to tunnel excavation, the stress constraints at the tunnel face are released, becoming a free interface, thus creating conditions for the collapse of the rock mass in front of the tunnel face. At the same time, the collapse of the rock mass in front of the tunnel face also causes face failure, and different shapes of tunnel faces will affect the morphology of the potential instability area of ​​the face failure. For a circular tunnel face, the cross-section 11 of its shear slip zone can be circular or elliptical or irregular shapes derived from a circular shape; for a rectangular tunnel face, the cross-section 11 of its shear slip zone can be rectangular or irregular shapes derived from a rectangular shape; for a horseshoe-shaped tunnel face, the cross-section of its shear slip zone can be horseshoe-shaped or irregular shapes derived from a horseshoe shape; for a Tansan circular tunnel face, the cross-section of its shear slip zone can be Tansan circular or irregular shapes derived from a Tansan circular shape. Furthermore, the cross-section of the shear slip zone is similar in shape to the tunnel face. If the tunnel face is spatially symmetrical, the cross-section of the shear slip zone is also spatially symmetrical. Furthermore, the shape of the shear slip zone's cross-section also influences the shape of the columnar collapse zone and arched roof fall zone above it.

[0040] Please refer to Figure 4 , shear slip zone A B D C It can be seen as a spatial curved surface formed by the shear slip contour line 12 rotating and changing around the center point, wherein the shear slip contour line 12 is a closed curve. ABis the center axis of the bottom shear slip contour line, CD is the center axis of the top shear slip contour line. At the bottom of the shear slip zone, the shear slip contour line is located at AB The cross section of the connecting line is consistent with the size and shape of the tunnel face contour line. CD The cross section of the connecting line is horizontal. At any part of the shear slip zone, the shear slip contour line is located at the point O On the cross section of the corresponding ray, point O is the center of rotation, and point O For the sake of AB The straight line and the CD The intersection of the straight lines. As the shear slip contour line rotates around the center point, on the one hand, the shear slip contour lines at different locations vary in shape and size, making the shear slip zone appear non-specific. On the other hand, influenced by the shear slip mechanism, the shear slip contour lines at different locations have certain connections in shape and size, and can be considered to be related to the shear slip contour lines at the bottom and top of the shear slip zone.

[0041] Furthermore, when the shear slip contour line rotates around the center point, it is controlled by two boundary lines, namely the upper boundary control line AC and the Lower Boundary Control Line BD According to actual engineering experience, the upper boundary control line AC and the Lower Boundary Control Line BD It can be approximated as a general logarithmic spiral, where the point A and point B Represent the upper and lower intersection points of the tunnel face center axis and the face contour line, respectively. C and point D Located on the same level.

[0042] In the present invention, the point O As the center point, the upper boundary control line AC and the Lower Boundary Control Line BD The polar coordinate functions of are shown in formula (1) and formula (2), respectively, where:

[0043] (1).

[0044] (2).

[0045] In formulas (1) and (2), r 1 is the upper boundary control line diameter, r 2 is the lower boundary control line diameter; r 01 and r 02are the initial polar diameters of the upper and lower boundary control lines, respectively; i The polar angle of the upper or lower boundary control line; k 1 and k 2 are the shape parameters of the upper and lower boundary control lines respectively.

[0046] Please combine Figure 4 , the upper boundary control line diameter r 1 refers to the upper boundary control line AC Any point on I To the polar coordinate origin O The distance between the lower boundary and the control line r 2 refers to the lower boundary control line BD Any point on J To the polar coordinate origin O distance; r 01 Corresponding to the upper boundary control line A Point to polar coordinate origin O distance, r 02 Corresponding to the lower boundary control line B Point to polar coordinate origin O distance; r 02 and r 01 The difference is AB The length of the connecting line, which represents the tunnel excavation height h 0, if r 01 = r 0, then r 02 = r 0+ h 0; i for OI or O.J. and OB The angle between the connecting lines, with the counterclockwise direction being positive.

[0047] In the present invention, k 1 can be understood as a parameter used to control the curvature of the upper boundary control line. k 2 can be understood as a parameter used to control the curvature of the lower boundary control line.

[0048] Step S20: Establish a coordinate system with the center point as the origin of the coordinate axis. x.y.z Axis coordinate system, where x The axis direction is the longitudinal direction of the tunnel. y The axis direction is the tunnel transverse direction. z The axis directions are determined according to the left-hand rule.

[0049] In the present invention, the center point and the polar coordinate originO same.

[0050] Please refer to Figure 5 , Figure 5 The number 16 is the longitudinal direction of the tunnel, i.e. the extension direction of the tunnel.

[0051] Step S30: Discretize the shear slip zone, columnar collapse zone and arched roof fall zone respectively, and x.y.z The axis coordinate system and the dimension data of the bottom shear slip contour line are used to obtain the coordinate information of multiple first discrete points on the outer contour of the shear slip area, the coordinate information of multiple second discrete points on the outer contour of the columnar collapse area, the coordinate information of multiple third discrete points on the outer contour of the arched roof fall area, and the coordinate information of the vertex of the arched roof fall area.

[0052] In an optional embodiment, the shear slip zone is discretized and based on the x.y.z The step of obtaining the coordinate information of a plurality of first discrete points on the outer contour of the shear slip zone using the axis coordinate system and the dimension data of the bottom shear slip contour line comprises:

[0053] Step 3.1-1, obtain the first set of discrete parameters, the first set of discrete parameters includes m and n 0.

[0054] In the present invention, the first set of discrete parameters is used to determine the number of discrete points in the shear slip zone. It can be understood that the more discrete points there are, the higher the accuracy of the constructed model will be, but correspondingly, the amount of calculation will also be greater, which will be determined by those skilled in the art based on the size and experience of the shear slip zone.

[0055] Step 3.1-2: Take the center point as the polar coordinate origin, use the boundary control line polar angle equal division method, and construct the boundary control line polar angle equal division method. n 0+1 cross sections, the n 0+1 cross sections discretize the shear slip zone into n 0 blocks, where the boundary control line polar angle is AB and CD The angle between them.

[0056] Please refer to Figure 5 , when the boundary control line polar angle is divided into n When the number of equal divisions is 0, the number of equal divisions from the center point can be obtained. O Departure n 0+1 rays, i The intersection points of ray 13 and the upper and lower boundary control lines are points I i and point Ji , I i J i The midpoint of the connecting line is the point K i .when i = 0, the 0th ray is the bottom ray 14, and point I i and point J i will be replaced by dots respectively A and point B .when i = n 0 o'clock, n 0 rays are the top rays 15, and point I i and point J i will be replaced by dots respectively C and point D Taking these rays as the reference, we can expand them along the horizontal space to form a series of planes, which cut the shear slip zone and construct n 0+1 cross sections, and discretize the shear slip zone into n 0 blocks. For the bottom cross section (i.e. i = 0), which corresponds to AB The cross section, i.e. the tunnel face, for the top cross section (i.e. i = n 0), which corresponds to CD The cross section is horizontal. i There are 17 cross sections, and the corresponding boundary control line polar angle is i i ,and i i = i n × ( i / n 0), where i n for point C The upper boundary control line polar angle or point D The polar angle of the lower boundary control line.

[0057] Step 3.1-3: Take the intersection of each cross section and the shear slip zone as the shear slip contour line, obtain the midpoint of the center line segment of each shear slip contour line, and use the midpoint of the center line segment of the shear slip contour line as the discrete center point. Based on the center angle equal division method, the shear slip contour line on each cross section is discretized into 2 m points, and get ( n 0+1)×2 mThe center line segment of the shear slip contour line is a line segment connecting the intersection point of the shear slip contour line with the upper boundary control line and the intersection point of the shear slip contour line with the lower boundary control line.

[0058] Please refer to Figure 5 , in the shear slip zone, i The shear slip contour line 18 on the cross section is set as the shear slip contour line i Since the cross section of the shear slip zone is similar to the tunnel face in shape, and the tunnel face is symmetrical, the shear slip contour line i It is also a symmetrical curve, and the central axis is I i J i In the i In the cross section, the point K i As the center point, the shear slip contour line is divided into equal parts by the center angle. i Discretize and then cut the slip contour i Discretized into 2 m points, and from point I i Starting from counterclockwise direction, the numbers are 0 to 2 m –1. Thus, the shear slip zone will be discretized into ( n 0+1)×2 m points.

[0059] Steps 3.1-4, as described x.y.z The axis coordinate system is a coordinate axis, and based on the dimension data of the bottom shear slip contour line, the coordinate information of each first discrete point is obtained according to the first calculation method.

[0060] For the i Shear slip contours on a cross section i (0≦ i ≦ n 0) Previous j (0≦ j ≦2 m –1) discrete points, let it be point S ij .point K i and point S ij Lines and Dots K i and point I i The angle between the connecting lines is the point S ij Corresponding polar angle r j, this angle is counterclockwise, and r j = 2π × j / 2 m .when j = 0, shear slip contour i Upper discrete point S ij will be replaced by a dot I i ,when j = m When the shear slip contour line i Upper discrete point S ij will be replaced by a dot J i .

[0061] From the calculation formula of polar angle, we can see that polar angle is only related to m and j Each shear slip contour is discretized into 2 m points, so that the first point on each shear slip contour line j The polar angles corresponding to the discrete points are the same. For ease of understanding, let’s take an example to illustrate that the polar angles of the bottom shear sliding contour line are the same. j The polar angle corresponding to the discrete point, the top shear sliding contour line j The polar angle corresponding to the discrete point, the first shear slip contour line j The polar angles corresponding to the discrete points are the same.

[0062] Said point S ij The steps for obtaining the coordinate information of include:

[0063] Step (1), with the x.y.z The axis coordinate system is the coordinate axis, and the intersection of the bottom shear slip contour line and the upper boundary control line of the shear slip zone is extracted. A The intersection of the lower boundary control line B Coordinate information of the point A and point B The coordinate information of the solution point A and point B midpoint K 0 coordinate information, the bottom shear slip contour line is i =0 and the intersection of the shear slip zone.

[0064] In the present invention, the size and shape of the tunnel face contour are known, and the size and shape of the bottom shear slip contour are consistent with the size and shape of the tunnel face contour. In this way, the position information of each point on the bottom shear slip contour is known.S 0j (0≦ j ≦2 m –1) In x 、 y and z Coordinates on the axis coordinates 、 and This is known information.

[0065] Step (2), based on point A and point B , get the coordinate information of i The intersection of the shear slip contour line and the upper boundary control line on the cross section I i The intersection of the lower boundary control line J i Coordinate information of the point I i and point J i The coordinate information of the solution point I i and point J i midpoint K i coordinate information.

[0066] In the present invention, the intersection I i The calculation formula is shown in formula (3), the intersection point J i The calculation formula is shown in formula (4).

[0067] Wherein, formula (3) is:

[0068] (3).

[0069] Formula (4) is:

[0070] (4).

[0071] point I i and point J i midpoint K i The calculation formula of the coordinate information is shown in formula (5), where formula (5) is:

[0072] (5).

[0073] In formula (3) to formula (5), 、 and Points I i exist x 、 y and z Coordinates on the axis; 、 and Points J i exist x 、 y and z The coordinates on the axis, r 0 is the initial diameter of the upper boundary control line, h 0 is the tunnel excavation height, k 1 is the shape parameter of the upper boundary control line, k 2 is the shape parameter of the lower boundary control line, i i For the i The polar angle of the boundary control line corresponding to each cross section.

[0074] Step (3), based on the distance formula between two points and point I i and point J i Coordinate information of the calculated point I i and point J i The distance between the points I i The shear slip contour line is at the pole diameter, and the point I i The shear slip contour line is at the point I i and point J i half the distance between them.

[0075] Point I i The calculation formula of the shear slip contour line polar diameter at is shown in formula (6), where formula (6) is:

[0076] (6) .

[0077] Step (4), extract the bottom shear slip contour line j discrete points S 0j Coordinate information of the two points is calculated based on the distance formula between the two points. A and point K 0 distance and point S 0j and point K 0 distance, and calculate the pointS 0j Corresponding to the polar diameter ratio, the point S 0j The corresponding polar diameter ratio is point S 0j and point K 0 distance from the point A and point K The distance ratio is 0.

[0078] In the present invention, the A and point K The distance of 0 can be understood as a point A The shear slip contour line is at the extreme point S 0j and point K 0 distance can be understood as a point S 0j The polar diameter of the shear slip contour line.

[0079] Step (5): Apply the sum of the cubic polynomial and the higher-order error remainder to construct the top shear slip contour line of the shear slip zone. j The polar diameter ratio corresponding to the discrete points x nj and polar angle r j The functional relationship of the pole diameter ratio is calculated based on the constructed functional relationship. x nj , wherein the top shear slip contour line is i = n The intersection line of the cross section at 0 and the shear slip zone.

[0080] Among them, point S ij Corresponding pole diameter ratio x nj and polar angle r j The functional relationship of is shown in formula (7), where formula (7) is:

[0081] (7).

[0082] In formula (7), substitute r j = 2π × j / 2 m , then we can get formula (8) as follows:

[0083] (8).

[0084] In formula (7) and formula (8), l 0. l 1. l 2. l 3. l 4 and g Both are dimensionless parameters that control the shape of the shear slip curve.

[0085] Step (6), based on the bottom shear slip contour line j discrete points S 0j The diameter ratio of the top shear slip contour line j The diameter ratio of the discrete points and the i The boundary control line polar angle corresponding to the cross section is calculated at point S ij Corresponding pole diameter ratio x ij .

[0086] like Figure 5 As shown, the shear slip contour lines at different locations have certain connections in shape and size, and can be considered to be related to the bottom shear slip contour line and the top shear slip contour line of the shear slip zone. Therefore, the shear slip contour line i Previous j The first discrete point's diameter ratio x ij The first j The first discrete point's diameter ratio x 0j and the top shear slip contour line j The first discrete point's diameter ratio x nj and let this correlation be a linear function of the polar angle of the boundary control line corresponding to the cross section of the shear slip zone.

[0087] In the present invention, the S ij Corresponding pole diameter ratio x ij The corresponding calculation formula is shown in formula (9), where formula (9) is:

[0088] (9).

[0089] In formula (9), i i For the i The boundary control line polar angle corresponding to the cross section is i n for point C The upper boundary control line polar angle or point D The polar angle of the lower boundary control line.

[0090] In the present invention, in is 90 degrees.

[0091] It is understood that in the present invention, i All discrete points on the shear slip contour line on the cross section have the same boundary control line polar angle. i The polar angle of the boundary control line corresponding to each cross section.

[0092] Step (7), based on the points calculated in step (3) I i The shear slip contour line polar radius at and the point calculated in step (6) S ij Corresponding pole diameter ratio x ij , calculation point S ij The polar diameter of the shear slip contour line at .

[0093] In the present invention, the S ij The shear slip contour line at for point I i The shear slip contour line at with dot S ij Corresponding pole diameter ratio x ij The product of is calculated as shown in formula (10), where formula (10) is:

[0094] (10).

[0095] Step (8), based on point K i Coordinate information, point S ij The shear slip contour line polar radius and point S ij Corresponding polar angle, get point S ij coordinate information.

[0096] point S ij The calculation formula of the coordinate information is shown in formula (11), where formula (11) is:

[0097] (11).

[0098] In formula (11), 、 and Points Sij exist x 、 y and z The coordinates on the axis, 、 and Points K i exist x 、 y and z The coordinates on the axis, for point S ij The shear slip contour line polar diameter at r j for point S ij The corresponding polar angle, i i For the i cross sections (points S ij ) corresponds to the boundary control line polar angle.

[0099] In the present invention, r j for K i S ij and K i I i The angle between the points K i and point S ij Lines and points K i and I i The counterclockwise angle of the line connecting .

[0100] In an optional embodiment, the columnar collapse area is discretized and based on the x.y.z The step of obtaining coordinate information of a plurality of second discrete points on the outer contour of the columnar collapse area using the axis coordinate system includes:

[0101] Step 3.2-1, obtain the second set of discrete parameters, the second set of discrete parameters includes m and n 1.

[0102] In the present invention, the second set of discrete parameters is used to determine the number of discrete points in the columnar collapse area. It can be understood that the more discrete points there are, the higher the accuracy of the constructed model will be, but correspondingly, the amount of calculation will also be greater. Those skilled in the art will determine this based on the size and experience of the columnar collapse area.

[0103] Step 3.2-2: Cut the columnar collapse area into sections along the height direction of the columnar collapse area using multiple horizontal planes set at equal intervals. n 1 block segment.

[0104] See also Figure 6 , columnar landslide area CDFE The top shear slip zone shear slip contour line extends vertically upwards to a height of h 1. The same discrete method is used to construct the columnar collapse area, and then the horizontal plane is used to cut the columnar collapse area into equal intervals in its height direction. n 1 block segment, and number these horizontal planes from bottom to top, respectively 0, 1, 2, ..., k 、…、 n 1, Figure 6 The 19 in the number represents the horizontal plane. k .

[0105] Step 3.2-3: obtain multiple collapse area contour lines obtained by cutting the columnar collapse area on each horizontal plane, and each collapse area contour line has the same size and shape as the shear slip contour line at the top of the shear slip area.

[0106] In the present invention, the contour line of the landslide area can be understood as the intersection line of the horizontal plane used for cutting and the columnar landslide area.

[0107] In the present invention, since the cross-section of the columnar landslide area and the cross-section of the top of the shear slip zone are the same in shape and size, and the cross-section of the top of the shear slip zone is the shear slip contour line at the top of the shear slip zone, each of the landslide area contour lines and the shear slip contour line at the top of the shear slip zone are the same in shape and size, when the landslide area contour line is discretized, the same method as the discrete shear slip contour line can be used for discretization.

[0108] In the present invention, the horizontal plane k The contour line of the landslide area obtained by cutting the cylindrical landslide area space surface is named the landslide area contour line k。

[0109] Step 3.2-4, obtain the midpoint of the center line segment of each landslide area contour line, and use the midpoint of the center line segment of the landslide area contour line as the discrete center point, and divide each landslide area contour line into 2 equal parts based on the center angle. m Points, get n 1×2 m The second discrete point, wherein the center line segment of the landslide area contour line is the line segment connecting the landslide area contour line at xyz The line segments of the left and right boundary points on the plane.

[0110] Please refer to Figure 6 , specifically: for the contour line of the landslide area k , which is in xyz The left and right boundary points on the plane are points M k and point N k , M k N k The connecting line is the center segment, M k N k The midpoint of the connecting line is the point Q k ,and M k N k The straight line where the connection line is located is the contour line of the landslide area k The central axis. k = 0, point M k and point N k will be replaced by dots respectively C and point D ,when k = n 1 o'clock M k and point N k will be replaced by dots respectively E and point F .

[0111] In the present invention, due to the contour line of the landslide area k The size and shape of the top shear slip contour are exactly the same, so the landslide contour can be discretized in the same way as the shear slip contour. k To this end, Q k As the center point, the contour line of the landslide area is divided into equal parts based on the center angle. k Discrete to 2 m points, and from point M i Starting from counterclockwise direction, the numbers are 0 to 2 m –1. Thus, the columnar collapse area will be discretized into n 1×2 m points.

[0112] Steps 3.2-5, as described above x.y.z The axis coordinate system is the coordinate axis, based on the top shear slip contour line 2 m The coordinate information of the first discrete point and the discrete parametersn 1 and the height parameter of the columnar landslide area, and obtain the coordinate information of each second discrete point according to the second calculation method.

[0113] In an optional embodiment, the landslide area contour line k Previous j The second discrete point, denoted as point T kj ,in, k and j is an integer, and 1≦ k ≦ n 1, 0≦ j ≦2 m –1, the point T kj for n 1×2 m Any second discrete point among the second discrete points.

[0114] Obtain the point according to the second calculation method T kj The coordinate information of the point includes: T kj in x The coordinates on the axis and y The coordinates on the axis are all the same as the top shear slip contour line. j The first discrete point is x The coordinates on the axis and y The coordinates on the axis are the same; the point T kj exist z Coordinates on the axis = ( k / n 1) × h 1, among which, h 1 is the height parameter of the columnar landslide area.

[0115] Specifically, the point T kj The calculation formula of the coordinate information is shown in (12), where formula (12) is:

[0116] (12).

[0117] Where, 、 and Points T kj exist x 、 y and z The coordinates on the axis, n 1 is a discrete parameter, h 1 is the height parameter of the columnar landslide area.

[0118] like Figure 7 As shown, the arched roof fall area EGF Can be seen as a curve GE The arched surface is formed by rotating and changing around the vertical central axis, where the point E For curve GE The end point of the point, when rotating around the vertical center axis, is the horizontal bottom contour line of the roof fall area, and it is also the EF The contour line of the landslide area. For the vertical center axis, it is GR Connect lines, dots G is the vertex of the arched roof fall area, point R for EF In addition, GR The length of the connecting line is the arched roof fall area EGF Height h 2. According to actual engineering experience, the curve GE It is approximately a parabola, and the vertex of this parabola is the point G And the opening direction is downward. Therefore, based on point G and point E The coordinates of the curve can be determined GE At the same time, although the arched roof fall area is formed by the curve rotation method, and the rotation curve will change during the rotation, the rotation curve is still a parabola during the rotation process, and the vertex of the curve is also a point. G .

[0119] In an optional embodiment, the arched roof fall area is discretized and based on the x.y.z The step of obtaining the coordinate information of a plurality of third discrete points on the outer contour of the arched roof fall area and the coordinate information of the vertex of the arched roof fall area in the axis coordinate system includes:

[0120] Step 3.3-1, obtain the set third set of discrete parameters, the third set of discrete parameters includes m and n 2.

[0121] In the present invention, the third set of discrete parameters is used to determine the number of discrete points in the arched roof caving area. It can be understood that the more discrete points there are, the higher the accuracy of the constructed model will be, but correspondingly, the amount of calculation will also be greater. Those skilled in the art will determine this based on the size and experience of the arched roof caving area.

[0122] Step 3.3-2, n 2 on the contour line of a landslide area m The second discrete point is used as the bottom contour line of the arched roof fall area. m Plane construction points, and based on the 2 mPlane construction points and roof fall area vertices, construct 2 m vertical planes, each vertical plane is perpendicular to the bottom surface of the arched roof fall area and passes through the top of the roof fall area and a plane construction point at the same time. Different vertical planes pass through different plane construction points. n A contour line of a landslide area is the same contour line as the bottom contour line of the arched roof collapse area.

[0123] Step 3.3-3, obtain the intersection line of each vertical plane and the arched roof fall area, and obtain 2 m There are rotation curves, each of which is a parabola, with its vertex being the vertex of the roof fall area and its opening direction being downward.

[0124] Step 3.3-4: Use the projection length on the horizontal plane to equally divide each rotation curve into n 2 points, we get ( n 2+1)×2 m A third discrete point, the discrete points of the arched roof fall area include the top of the roof fall area and ( n 2+1)×2 m A third discrete point.

[0125] Please refer to Figure 7 , Figure 7 This is a discrete schematic diagram of the arched roof fall area of ​​the present invention. Figure 7 The 20 in the figure represents the contour line of the landslide area. k , Figure 7 21 is the horizontal bottom contour line of the arch roof collapse area / the horizontal bottom contour line of the columnar collapse area n 1 contour line of the landslide area, Figure 7 22 in the figure is the rotation curve j .

[0126] In an optional embodiment, step 3.3-4 further includes a step of obtaining the projection length of each rotation curve on the horizontal plane.

[0127] Specifically: point R As the coordinate origin, point R and discrete points on the horizontal bottom contour line of the arched roof fall area j The length direction of the line is l Axis direction and vertical direction h Axis direction, establish lh Axis local coordinate system, then, we can get lh Rotation curve in axis coordinate system j The equation is:

[0128] .

[0129] In the above formula, l jFor the rotation curve j Length of projection on the horizontal plane; l is the length coordinate axis, h is the height coordinate axis, h 2 is the height parameter of the arched roof fall area.

[0130] Step 3.3-5, based on n 1. On the contour line of the landslide area 2 m The coordinate information of the second discrete point, discrete parameters n 2 and the height parameters of the arched roof fall area h 2. Obtain the coordinate information of the vertex of the roof fall area and each third discrete point.

[0131] The steps 3.3-5 include:

[0132] Step (1), based on n 1 landslide area outline line xyz The coordinate information of the left and right boundary points on the plane is used to calculate the n The midpoint between the left and right boundary points of a landslide area contour line R 's coordinates.

[0133] The left boundary point is , the right boundary point is ,midpoint R The coordinates are calculated as follows:

[0134] .

[0135] in, 、 and Left boundary point exist x 、 y and z The coordinates on the axis, 、 and Right boundary point exist x 、 y and z Coordinates on the axis.

[0136] See also Figure 7 ,point E and point F Corresponding to the discrete points of the columnar collapse area and discrete points ,point R for EF The midpoint of the connecting line.

[0137] Step (2), based on the midpointR The coordinates of the columnar collapse area and the height parameters h 2. Calculate the vertex of the roof fall area G The coordinate information of the vertex of the roof fall area G exist x The coordinates on the axis and y The coordinates on the axis are respectively the same as the midpoint R exist x The coordinates on the axis and y The coordinates on the axis are the same, and the vertex of the roof fall area G exist z The coordinates on the axis are the midpoints R exist z The coordinates on the axis and h The sum of 2.

[0138] The calculation formula for the coordinate information of the vertex of the roof fall area is:

[0139] .

[0140] in, x G 、 y G and z G Points G exist x 、 y and z The coordinates on the axis, x R 、 y R and z R Points R exist x 、 y and z The coordinates on the axis, h 2 is the height parameter of the arched roof fall area.

[0141] Step (3), based on n 1. On the contour line of the landslide area 2 m The coordinate information of the second discrete point, the midpoint R Coordinates and discrete parameters n 2 and the height parameters of the columnar collapse area h 2. Obtain the coordinates of each third discrete point according to the third calculation method.

[0142] In an optional embodiment, the arc-shaped roof fall area rotation curve j Previous t Points, denoted as points P tj ,in, t andj is a positive integer, 1≦ t ≦ n 2–1 and 0≦ j ≦2 m –1, the point P tj for( n 2+1)×2 m Any third discrete point among the third discrete points.

[0143] Said point P tj The calculation formula of the coordinate information is:

[0144] .

[0145] In the above formula, 、 and Points P tj exist x 、 y and z Coordinates on the axis; x R 、 y R and z R Points R exist x 、 y and z Coordinates on the axis; and Columnar collapse area n 1. On the contour line of the landslide area j discrete points exist x and y The coordinates on the axis, n 2 is a discrete parameter, h 2 is the height parameter of the arched roof fall area.

[0146] In the present invention, due to the bottom contour line of the arched roof fall area and the contour line of the columnar collapse area n 1 is coincident, that is, when calculating the coordinate information of the vertex of the roof fall area and the third discrete point, R Point coordinates and discrete points The coordinates of are known.

[0147] Step S40: constructing a potential instability surface model of the tunnel face failure based on the coordinate information of the plurality of first discrete points, the coordinate information of the plurality of second discrete points, the coordinate information of the apex of the arched roof fall area, and the coordinate information of the plurality of third discrete points.

[0148] It can be understood that the instability surface model constructed using the construction method provided in steps S10 to S40 of the present invention has a corresponding relationship with the set shape parameter group. When the set shape parameter group is changed, the structure of the constructed instability surface model will also change accordingly. In this way, when multiple instability surface models are constructed using the construction method provided by the present invention, there will be an instability surface model that has a high similarity with the tunnel face failure area, which can be used to effectively predict the potential instability area of ​​tunnel face failure, and is feasible.

[0149] In an optional embodiment, the construction method further includes:

[0150] Based on a plurality of different setting parameter groups, steps S10 to S40 are repeated to obtain a plurality of instability surface models corresponding to each setting parameter group.

[0151] The volume of each instability surface model is compared with the volume of the tunnel face failure area to obtain the optimal setting parameter group, and the instability surface model corresponding to the optimal setting parameter group is used as the theoretical model of the potential instability surface of the tunnel face failure, wherein the absolute value of the difference between the volume of the instability surface model corresponding to the optimal setting parameter group and the volume of the tunnel face failure area is the smallest.

[0152] In the present invention, the volume of the damaged area of ​​the tunnel face is obtained based on a numerical model of tunnel excavation.

[0153] In another optional embodiment, the construction method further includes:

[0154] Step (a): obtaining the current set parameter group, repeating steps S10 to S40, obtaining the current instability surface model corresponding to the current set parameter group, and obtaining the volume of the current instability surface model.

[0155] Step (b): comparing the volume of the current instability surface model with the volume of the tunnel face failure area to obtain a comparison result.

[0156] Step (c), when the comparison result shows that the absolute value of the difference between the volume of the current instability surface model and the volume of the tunnel face failure area is less than the target difference, the current instability surface model is used as the theoretical model of the potential instability surface of the tunnel face failure; when the comparison result shows that the absolute value of the difference between the volume of the current instability surface model and the volume of the tunnel face failure area is less than the target difference, a new setting parameter group is reset as the current setting parameter group, and steps (a) and (b) are repeated.

[0157] In the present invention, the target difference can be 0.01m 3 , 0.05m 3 , 0.1m 3, 0.2m 3 etc., which are not limited here and shall be determined based on actual engineering experience.

[0158] Example 1

[0159] The engineering geological parameters of a certain tunnel section show that the tunnel depth is 30 m, the tunnel face is circular, and the diameter is D =10 m, that is, the tunnel excavation height h 0=10 m, the corresponding rock and soil strength parameters are: heavy c =19 kN / m 3 , cohesion c =10 kPa, internal friction angle f =25°, bulk modulus E =120 MPa, shear modulus G =60MPa and Poisson's ratio n =0.33. The surrounding rock quality of this tunnel section is poor, and there is a great risk of instability and damage to the tunnel face. In order to prevent disasters caused by face damage during tunnel excavation, it is necessary to obtain the potential instability area of ​​the tunnel face damage. In order to verify that the method in this article can effectively predict the potential instability area of ​​the tunnel face damage, first, a tunnel excavation numerical model is established, and a numerical analysis of the tunnel face stability is carried out to obtain the potential instability area of ​​the tunnel face damage. Then, the model constructed by the present invention is used to perform optimal fitting on the actual damage area, thereby determining the feasibility and reliability of the model of the present invention. The specific operations are as follows:

[0160] (1) Based on the tunnel engineering geological parameters, a tunnel excavation numerical model was established, and the tunnel face stability analysis was carried out. Then, based on the numerical results of the maximum shear plastic strain, the size of the tunnel face failure area was obtained, and the volume of the tunnel face failure area was 887.94 m 3 At the same time, the location of the damaged area of ​​the tunnel face is obtained, and the discrete point data of the damaged area boundary grid is extracted, and the coordinates of the two-dimensional boundary discrete points corresponding to the damaged area on the longitudinal section of the tunnel are further obtained, that is, the curve is determined. ACEGFDB The coordinates of discrete points.

[0161] It should be noted that the existing technologies are used to establish the tunnel excavation numerical model and obtain the volume of the damaged area of ​​the tunnel face, and the present invention does not make any improvements.

[0162] (2) Determine the shape parameters of the shear slip zone r 0. k 1. k 2. l 0. l 1. l 2. l 3. l 4 and g , propose the height of columnar landslide area h 1 and the height of the arched roof fall area h 2, among which, l 0=1 and l 1=1–( l 2+ l 3+ l 4), r The value range of 0 is 0m~10m, k 1. k 2. l 2. l 3 and l The value range of 4 is -1~1. g The value range is 0~1, h 1 and h The value range of 2 is 0 m~10 m.

[0163] (3) Determine the rotation center point of the shear slip zone O , and point O Established as the origin x.y.z Axis coordinate system, where x The axis direction is the longitudinal direction of the tunnel. y The axis direction is the tunnel transverse direction. z The axis direction is determined by the left-hand rule, so based on the existing survey data, the point A exist x 、 y and z The coordinates on the axis are (0, 0, r 0), point B exist x 、 y and z The coordinates on the axis are (0, 0, r 0+ h 0).

[0164] (4) Determine the discrete information of shear slip zone, columnar collapse zone and arch roof fall zone, that is, m = 50, n 0= 30, n 1=20 and n 2= ​​30.

[0165] (5) Within the parameter value range, any set of parameters r 0. k 1. k 2. l 2. l 3. l 4. g 、 h 1 andh 2. Then, the potential instability surface of tunnel face failure is constructed and implemented using the steps to obtain the potential instability surface of tunnel face failure. Subsequently, it is compared with the results obtained by numerical simulation. With the help of mathematical optimization algorithms, the theoretical model of the potential instability surface of tunnel face failure that is closest to the actual tunnel face failure area and the optimal fitting parameters are determined by comparing and analyzing the differences between the failure areas obtained by numerical simulation and the method in this paper. In this process, the optimal fitting of parameters is implemented in two steps. The first step is to perform the best fitting of the upper and lower boundary control curves of the shear slip zone to obtain r 0. k 1 and k 2, the second step is to perform the best fitting on the potential instability area of ​​the tunnel face after determining the upper and lower boundary control curves of the shear slip zone, and obtain l 2. l 3. l 4. g 、 h 1 and h The best fitting parameters of 2.

[0166] (6) After the best fitting, the discrete point coordinate information of the optimal tunnel face failure potential instability surface and the corresponding shape control parameters are output. The volume of the tunnel face failure potential instability area obtained by the theoretical model is 887.9565 m 3 , the general potential instability surface shape control parameters for tunnel face failure are: r 0=0.6199 m, k 1 = –0.724, k 2 = –0.213, l 0=1.000, l 1=0.468, l 2=0.229, l 3=0.291, l 4=0.012, g =0.745, h 1 = 1.98 m and h 2=5.28 m, the fitting results show the goodness of fit under the optimal fitting parameters R 2 The difference between the numerical result and the fitting result in the volume of the tunnel face failure area is 0.0011m 3 .

[0167] Example 1 verifies that the construction method provided by the present invention can construct a model with substantially the same shape and size as the potential instability area of ​​tunnel face failure after fitting the parameters, verifying the feasibility and reliability of the model of the present invention, which can be used to effectively predict the potential instability area of ​​tunnel face failure.

[0168] The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for constructing a universal potential instability surface model for tunnel face failure, characterized in that: The construction method comprises: Step S10: Based on the spatial characteristics of the potential instability area of ​​the tunnel face damage and the set shape parameter group, a geometric model of the instability surface is constructed, wherein the geometric model of the instability surface includes a shear slip zone, a columnar collapse zone located above the shear slip zone, and an arched roof fall zone located above the columnar collapse zone. The shear slip zone is a spatial curved surface formed by the shear slip contour line rotating and changing around the center point. The shear slip contour line at the bottom of the shear slip zone is the same as the tunnel face contour line in size and shape. The plane where the shear slip contour line at the top of the shear slip zone is located is a horizontal plane. The cross-sectional shape of the columnar collapse zone and the cross-sectional shape of the bottom surface of the arched roof fall zone are both the same as the cross-sectional shape of the columnar collapse zone and the cross-sectional shape of the bottom surface of the arched roof fall zone. The top shear slip contour lines of the shear slip zone have the same shape, wherein the shear slip zone is recorded as ABDC, wherein A, B, C and D are four boundary points of the cross section of the shear slip zone, AC is an upper boundary control line close to the center point, BD is a lower boundary control line far from the center point, the shear slip contour line of the shear slip zone is a closed curve, AB is the central axis of the bottom shear slip contour line, CD is the central axis of the top shear slip contour line, the center point is the intersection of the straight line passing through AB and the straight line passing through CD, the formation of the spatial curved surface is constrained by the upper boundary control line and the lower boundary control line, and the upper boundary control line and the lower boundary control line can be approximated as a general logarithmic spiral; Step S20: establishing an xyz coordinate system with the center point as the origin of the coordinate axes, wherein the x-axis direction is the longitudinal direction of the tunnel, the y-axis direction is the transverse direction of the tunnel, and the z-axis direction is determined according to the left-hand rule; Step S30: Discretize the shear slip zone, the columnar collapse zone, and the arched roof fall zone respectively, and obtain, based on the xyz-axis coordinate system and the dimension data of the bottom shear slip contour line, coordinate information of a plurality of first discrete points on the outer contour of the shear slip zone, coordinate information of a plurality of second discrete points on the outer contour of the columnar collapse zone, coordinate information of a plurality of third discrete points on the outer contour of the arched roof fall zone, and coordinate information of the vertex of the arched roof fall zone; Step S40: constructing a potential instability surface model of the tunnel face failure based on the coordinate information of the plurality of first discrete points, the coordinate information of the plurality of second discrete points, the coordinate information of the apex of the arched roof fall area, and the coordinate information of the plurality of third discrete points.

2. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 1 is characterized in that: The set shape parameter group includes shear slip zone shape parameters, columnar collapse zone shape parameters and arch roof fall zone shape parameters, wherein the shear slip zone shape parameters include r0, k1, k2, λ0, λ1, λ2, λ3, λ4 and ζ, r0 is the initial pole diameter of the upper boundary control line, k1 is the shape parameter of the upper boundary control line, k2 is the shape parameter of the lower boundary control line, λ0, λ1, λ2, λ3, λ4 and ζ are all dimensionless parameters for shear slip contour shape control, wherein λ0=1 and λ1=1–(λ2+λ3+λ4), the value range of r0 is 0m~10m, the value range of k1, k2, λ2, λ3 and λ4 are all –1~1, and the value range of ζ is 0~1; the columnar collapse zone shape parameter is the height parameter h1 of the columnar collapse zone, the arch roof fall zone shape parameter is the height parameter h2 of the arch roof fall zone, The value range of h1 and h2 is 0m~10m.

3. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 2 is characterized in that: The step of discretizing the shear slip zone and obtaining coordinate information of a plurality of first discrete points on the outer contour of the shear slip zone based on the xyz axis coordinate system and the size data of the bottom shear slip contour line comprises: Obtaining a first set of discrete parameters, wherein the first set of discrete parameters includes m and n0; Taking the center point as the polar coordinate origin, n0+1 cross sections are constructed based on the boundary control line polar angle division method, and the n0+1 cross sections discretize the shear slip zone into n0 blocks, wherein the boundary control line polar angle is the angle between AB and CD; The intersection line of each cross section and the shear slip zone is taken as the shear slip contour line, and the midpoint of the center line segment of each shear slip contour line is obtained. The midpoint of the center line segment of the shear slip contour line is used as the discrete center point. Based on the equal division of the center angle, the shear slip contour line on each cross section is discretized into 2m points, and (n0+1)×2m first discrete points are obtained. Among them, the center line segment of the shear slip contour line is the line segment connecting the intersection point of the shear slip contour line with the upper boundary control line and the intersection point of the shear slip contour line with the lower boundary control line; With the xyz axis coordinate system as the coordinate axis, based on the size data of the bottom shear slip contour line, the coordinate information of each first discrete point is obtained according to the first calculation method.

4. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 3 is characterized in that: The jth first discrete point on the shear slip contour line i on the i-th cross section is recorded as point S ij , where i and j are integers, 0≦i≦n0 and 0≦j≦2m–1, the point S ij is any first discrete point among the (n0+1)×2m first discrete points; Obtain the point S according to the first calculation method ij The steps of obtaining coordinate information include: Taking the xyz axis coordinate system as the coordinate axis, extracting the coordinate information of the intersection point A of the bottom shear slip contour line of the shear slip zone with the upper boundary control line and the intersection point B with the lower boundary control line, and solving the coordinate information of the midpoint K0 between points A and B based on the coordinate information of points A and B, wherein the bottom shear slip contour line is the intersection line of the cross section at i=0 and the shear slip zone; Based on the coordinate information of point A and point B, obtain the intersection point I of the shear slip contour line and the upper boundary control line on the i-th cross section i The intersection point J with the lower boundary control line i The coordinate information of point I i and point J i The coordinate information of point I i and point J i The midpoint K i Coordinate information of Based on the two-point distance formula and point I i and point J i Coordinate information of point I i and point J i The distance between them, get point I i The shear slip contour line is at the pole diameter, and the point I i The shear slip contour line is at point I i and point J i half the distance between them; Extract the jth discrete point S on the bottom shear slip contour line 0j The coordinate information of point A and point K0 is calculated based on the two-point distance formula, and the distance between point S 0j The distance from point K0 is calculated and point S is obtained 0j Corresponding to the polar diameter ratio, the point S 0j The corresponding polar diameter ratio is point S 0j The ratio of the distance from point A to point K0 to the distance from point A to point K0; The polar radius ratio ξ corresponding to the jth discrete point on the top shear slip contour line of the shear slip zone is constructed by using the sum of the cubic polynomial and the higher-order error residuals. nj and polar angle ρ j The functional relationship of the polar diameter ratio ξ is calculated based on the constructed functional relationship nj , wherein the top shear slip contour line is the intersection line of the cross section at i=n0 and the shear slip zone: Based on the jth discrete point S on the bottom shear slip contour line 0j The polar diameter ratio of the jth discrete point on the top shear slip contour line and the polar angle of the boundary control line corresponding to the i-th cross section are used to calculate the point S ij Corresponding polar diameter ratio ξ ij ; Based on point I i The shear slip contour line at the pole and point S ij Corresponding polar diameter ratio ξ ij , calculate point S ij The polar diameter of the shear slip contour line at ; Based on point K i Coordinate information of point S ij The shear slip contour line at the pole and point S ij Corresponding polar angle, get point S ij coordinate information.

5. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 3 is characterized in that: The steps of discretizing the columnar collapse area and acquiring coordinate information of a plurality of second discrete points on the outer contour of the columnar collapse area based on the xyz axis coordinate system include: Obtaining a second set of discrete parameters, where the second set of discrete parameters includes m and n1; Along the height direction of the columnar collapse area, the columnar collapse area is cut into n1 blocks by using multiple horizontal planes set at equal intervals; Obtaining multiple collapse area contour lines obtained by cutting the columnar collapse area on each horizontal plane, wherein each collapse area contour line has the same size and shape as the shear slip contour line at the top of the shear slip area; Obtain the midpoint of the center line segment of each landslide area contour line, and use the midpoint of the center line segment of the landslide area contour line as the discrete center point, discretize each landslide area contour line into 2m points based on the central angle equal division method, and obtain n1×2m second discrete points, wherein the center line segment of the landslide area contour line is a line segment connecting the left and right boundary points of the landslide area contour line on the xy plane; With the xyz axis coordinate system as the coordinate axis, based on the coordinate information of the 2m first discrete points on the top shear slip contour line, the discrete parameter n1 and the height parameter of the columnar collapse area, the coordinate information of each second discrete point is obtained according to the second calculation method.

6. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 5 is characterized in that: The jth second discrete point on the contour line k of the landslide area is denoted as point T kj , where k and j are integers, and 1≦k≦n1, 0≦j≦2m–1, the point T kj is any second discrete point among n1×2m second discrete points; Obtain the point T according to the second calculation method kj The coordinate information of point T kj The coordinates on the x-axis and the coordinates on the y-axis are the same as the coordinates on the x-axis and the coordinates on the y-axis of the j-th first discrete point on the top shear slip contour line; point T kj The coordinate on the z-axis = (k / n1) × h1, where h1 is the height parameter of the columnar landslide area.

7. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 5, characterized in that: The steps of discretizing the arched roof fall area and obtaining coordinate information of a plurality of third discrete points on the outer contour of the arched roof fall area and coordinate information of the vertex of the arched roof fall area based on the xyz axis coordinate system include: Obtaining a set third group of discrete parameters, wherein the third group of discrete parameters includes m and n2; 2m second discrete points on the n1th collapse area contour line are used as 2m plane construction points of the bottom contour line of the arched roof fall area, and based on the 2m plane construction points and the vertex of the roof fall area, 2m vertical planes are constructed, each vertical plane is perpendicular to the bottom surface of the arched roof fall area and passes through the vertex of the roof fall area and a plane construction point at the same time, and different vertical planes pass through different plane construction points, wherein the n1th collapse area contour line and the bottom contour line of the arched roof fall area are the same contour line; Obtain the intersection line of each vertical plane and the arched roof fall area to obtain 2m rotation curves. Each rotation curve is a parabola with the vertex at the top of the roof fall area and the opening direction downward. Each rotation curve is discretized into n2 points by equally dividing the projection length on the horizontal plane, obtaining (n2+1)×2m third discrete points. The discrete points of the arched roof fall area include the vertex of the roof fall area and (n2+1)×2m third discrete points. Based on the coordinate information of 2m second discrete points on the n1th collapse area contour line, the discrete parameter n2 and the height parameter h2 of the arched roof fall area, the coordinate information of the roof fall area vertex and each third discrete point is obtained.

8. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 7, characterized in that: The step of obtaining the coordinate information of the vertex of the roof fall area and each third discrete point based on the coordinate information of 2m second discrete points on the n1th collapse area contour line, the discrete parameter n2, and the height parameter h2 of the arched roof fall area includes: Based on the coordinate information of the left and right boundary points of the n1th landslide area contour line on the xy plane, the coordinates of the midpoint R between the left boundary point and the right boundary point of the n1th landslide area contour line are calculated; Based on the coordinates of the midpoint R and the height parameter h2 of the columnar collapse area, the coordinate information of the vertex G of the roof fall area is calculated, wherein the coordinates of the vertex G of the roof fall area on the x-axis and the coordinates of the vertex G on the y-axis are respectively the same as the coordinates of the midpoint R on the x-axis and the coordinates of the vertex G on the y-axis, and the coordinate of the vertex G of the roof fall area on the z-axis is the sum of the coordinates of the midpoint R on the z-axis and h2; Based on the coordinate information of 2m second discrete points on the n1th landslide area contour line, the coordinates of the midpoint R, the discrete parameter n2 and the height parameter h2 of the columnar landslide area, the coordinates of each third discrete point are obtained according to the third calculation method.

9. The method for constructing a universal potential instability surface model for tunnel face failure according to claim 8, characterized in that: The tth point on the rotation curve j of the arched roof fall area is denoted as point P tj , where t and j are positive integers, 1≦t≦n2–1 and 0≦j≦2m–1, the point P tj is any one of the (n2+1)×2m third discrete points; obtain the point P according to the third calculation method tj The calculation formula of the coordinate information is: ； In the above formula, 、 and Point P tj Coordinates on the x, y, and z axes; x R 、y R and z R are the coordinates of the midpoint R on the x, y and z axes respectively; and are the jth discrete points on the n1th landslide contour line of the columnar landslide area The coordinates on the x and y axes, n2 is the discrete parameter, and h2 is the height parameter of the arched roof fall area.

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