Method for rapidly determining plastic zone range of rectangular section roadway and application of method

Abstract

The invention belongs to the field of coal mine roadway tunneling stress analysis, and particularly relates to a method for rapidly determining the plastic zone range of a rectangular section roadway and application of the method. Based on plastic mechanics and roadway surrounding rock plastic loosening circle theories, calculating a lateral wall plastic circle according to mechanical parameters of the coal seam; calculating a roof plastic ring according to the mechanical parameters of the roof rock stratum; calculating a bottom plate plastic ring according to the mechanical parameters of the bottom plate rock stratum; and making an arc or a semi-elliptic arc based on vertexes at two ends of the top plate, the side wall and the bottom plate of the rectangular roadway and the deepest position point of the corresponding plastic ring to obtain a corresponding plastic region. According to the method, on the basis of an existing classical circular section roadway plastic zone calculation method, the distribution shape of the rectangular section plastic zone is considered, the mechanical property difference of the coal and rock mass around the roadway is also considered, and the method has great significance in guiding rectangular section supporting.

Description

Technical Field

[0001] The invention belongs to the field of stress analysis of coal mine tunnel excavation, and in particular relates to a method for quickly determining the plastic zone range of a rectangular cross-section tunnel and an application thereof. Background Art

[0002] After the coal mine tunnel is excavated, the coal and rock mass around the tunnel will produce plastic failure, forming a loose zone of tunnel surrounding rock. The loose zone of tunnel surrounding rock is generally aimed at circular cross-section tunnels. After the circular cross-section tunnel is excavated, a plastic failure zone will be formed around the circular cross-section tunnel, which is concentric with the circular cross-section tunnel but has a larger diameter than the circular cross-section tunnel. For tunnels with other cross-sectional shapes such as rectangles, the existing technologies such as CN107133381A, a method for determining the length of anchor rods for tunnel support, and CN108629122A, a method for determining the length of anchor rod support for mining tunnels based on the arching effect of guiding surrounding rock, mostly first make a circumscribed circle of the rectangular cross-section tunnel, and then make the rectangular cross-section tunnel equivalent to its circumscribed circular cross-section tunnel, and calculate the plastic zone of the rectangular cross-section tunnel based on the circumscribed circular cross-section tunnel, but the error of this approximate method is very large, especially at the four corners of the rectangular tunnel.

[0003] Through numerical simulation and other theoretical calculation methods, it can be concluded that the plastic zone range of the rectangular cross-section roadway is smaller than the plastic zone range calculated by its circumscribed circle. The maximum range of the plastic zone on both sides of the roadway is slightly different, and the maximum range of the plastic zone on the top and bottom sides of the roadway is slightly different. It is completely different at the four corners, and there is almost no plastic zone at the four corners of the rectangular section.

[0004] In addition, when calculating the plastic zone of various existing cross-sectional shapes of tunnels, the coal rock mass around the tunnel is simplified into a rock mass with the same mechanical properties. However, most of the current tunnels are constructed in coal seams, and the roof and floor plates are rock layers. The mechanical properties of coal seams and rock layers are quite different. Therefore, the plastic zone of the tunnel calculated in this simplified form has a large error compared with the actual one.

[0005] Therefore, if we can integrate the existing classic circular section roadway plastic zone calculation method, and consider the distribution shape of the rectangular section plastic zone and the differences in the mechanical properties of the coal and rock mass around the roadway, and study a method to quickly determine the range of the rectangular section plastic zone, it will be of great significance for obtaining the range of the rectangular section plastic zone and guiding the support of the rectangular section roadway. Summary of the invention

[0006] In view of the above technical problems, the present invention proposes a method for quickly determining the range of the plastic zone of a rectangular cross-section roadway, which is particularly suitable for the case where the lateral pressure coefficient is close to 1 and the aspect ratio of the rectangular cross-section is close to 1, and comprises the following steps:

[0007] S1: The rectangular tunnel is constructed in the coal seam, the upper part of the rectangular tunnel is the roof rock layer, the lower part is the floor rock layer, and the circumscribed circle of the rectangular tunnel is used;

[0008] S2: Based on the theory of plastic mechanics and the plastic loosening zone of tunnel surrounding rock, the side wall plastic zone of the rectangular tunnel is calculated with the mechanical parameters of the coal seam; the roof plastic zone of the rectangular tunnel is calculated with the mechanical parameters of the roof rock layer; the bottom plate plastic zone of the rectangular tunnel is calculated with the mechanical parameters of the bottom plate rock layer;

[0009] S3: Based on the top and bottom points of the side wall of the rectangular tunnel and the deepest point of the side wall plastic zone, an arc is drawn to obtain the side wall plastic zone;

[0010] The plastic zone of the roof is obtained by making an arc based on the end point of the roof of the rectangular tunnel and the deepest point of the plastic circle of the roof;

[0011] The bottom plate plastic zone is obtained by making an arc based on the end points of the rectangular tunnel bottom plate and the deepest point of the bottom plate plastic circle.

[0012] Preferably, in step S2, the calculation formula based on plastic mechanics and the theory of plastic loosening zone of tunnel surrounding rock is:

[0013]

[0014] Where R is the radius of the loosening zone in the plastic zone, r0 is the radius of the circumscribed circle, p is the formation stress, and C is the formation cohesion. is the internal friction angle of the formation.

[0015] Preferably, in step S3, or, based on the top and bottom points of the side wall of the rectangular tunnel and the deepest position point of the side wall plastic zone, a semi-elliptical arc is made to obtain the side wall plastic zone;

[0016] A semi-elliptical arc is made based on the end points of the rectangular tunnel roof and the deepest point of the roof plastic circle to obtain the roof plastic zone;

[0017] The bottom plate plastic zone is obtained by making a semi-elliptical arc based on the end points of the rectangular tunnel bottom plate and the deepest point of the bottom plate plastic circle.

[0018] After the plastic zone of the rectangular tunnel is determined by the method described above, the present invention further proposes a rectangular tunnel support method, comprising the following steps:

[0019] Step 1: Construction of closed steel beams

[0020] Several groups of closed steel beams are constructed at set intervals along the axial direction of the rectangular tunnel, among which the side support beams adopt a U-shaped cross-section structure with openings facing inwards, and the top plate support beams and bottom plate support beams adopt a convex cross-section structure with openings facing inwards, and the top plate support beams and bottom plate support beams are located between the side support beams on both sides;

[0021] Step 2: Construction anchor

[0022] Top corner anchors are constructed at the two top corners of the rectangular tunnel; bottom corner anchors are constructed at the two bottom corners of the rectangular tunnel; a number of plastic zone anchors are vertically constructed on the top plate of the rectangular tunnel, and a number of plastic zone anchors are vertically constructed on the two side walls of the rectangular tunnel respectively; the plastic zone anchors are divided into a threaded drilling section and a grouting section along their length direction, and the length of the grouting section of the anchors in different plastic zones is the same as the depth of the plastic zone at their location.

[0023] Preferably, each side of the side support beams is completely adjacent to the tunnel wall, and only the protruding sides of the top plate support beams and the bottom plate support beams are adjacent to the tunnel wall.

[0024] Preferably, the top angle anchor rod passes through the side support beam and the top plate support beam, and the construction angle of the top angle anchor rod is 45°.

[0025] Preferably, the bottom angle anchor rod passes through the side support beam and the bottom plate support beam, and the construction angle of the bottom angle anchor rod is 45°.

[0026] Preferably, the length of the threaded drilling sections of all plastic zone anchors is the same.

[0027] Preferably, the plastic zone around it is reinforced by grouting through the grouting section.

[0028] Preferably, the plastic zone anchor also includes a fixed section, on which a gasket and a nut are sequentially sleeved, the grouting section of the plastic zone anchor adopts a hollow structure with holes, the fixed section of the plastic zone anchor adopts a hollow structure without holes, and a grouting plug is arranged on the outermost part.

[0029] Beneficial technical effects: 1. The method for determining the plastic zone of the present invention is based on the existing classic circular section roadway plastic zone calculation method. It not only takes into account the distribution shape of the rectangular section plastic zone, but also takes into account the differences in mechanical properties of the coal and rock mass around the roadway, which is of great significance for guiding rectangular section support.

[0030] 2. The method for quickly determining the scope of the plastic zone of a rectangular cross-section tunnel of the present invention can quickly and accurately determine the scope of the plastic zone of a rectangular tunnel constructed in a coal seam. The method for determining the plastic zone of the side wall has a large overlap with the plastic zone range determined by numerical simulation. The plastic zone range of the roof and the plastic zone range of the bottom plate determined on the basis of considering the rock properties of the roof and bottom plates also have a large overlap with the plastic zone range determined by numerical simulation. In particular, the plastic zones determined at the four corners by this determination method of the present invention are consistent with actual engineering, which is of great significance for guiding the support of rectangular tunnels.

[0031] 3. The closed steel beam of the present invention cleverly utilizes the location relationship of the overlap structure to better resist the large deformation of the side wall; the support method of the present invention only uses relatively short anchor rods without long anchor cables, which can greatly increase the construction speed and reduce the construction cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A schematic diagram of determining the deepest position of the plastic zone of a rectangular cross-section roadway according to the present invention;

[0033] Figure 2 A schematic diagram for determining the plastic zone range of a rectangular cross-section roadway according to the present invention (based on circular arcs);

[0034] Figure 3 A schematic diagram for determining the plastic zone range of a rectangular cross-section roadway in the present invention (based on an elliptical arc);

[0035] Figure 4 The overall schematic diagram of the steel beam support of a rectangular-section roadway of the present invention (taking an arc as an example);

[0036] Figure 5 This is the first schematic diagram of the steel beam support of a rectangular cross-section roadway according to the present invention (taking an arc as an example);

[0037] Figure 6 This is the second schematic diagram of the steel beam support of a rectangular cross-section roadway according to the present invention (taking an arc as an example);

[0038] Figure 7 The third schematic diagram of the steel beam support of a rectangular cross-section roadway of the present invention (taking an arc as an example);

[0039] Figure 8 This is the fourth schematic diagram of the steel beam support of a rectangular cross-section roadway according to the present invention (taking an arc as an example);

[0040] Fig. 9 The schematic diagram of the steel beam and anchor support of the rectangular cross-section roadway of the present invention (taking the arc as an example);

[0041] Fig.10 It is a schematic diagram of the structure of the plastic zone support anchor rod of the present invention;

[0042] In the figure, roof rock layer 1, coal seam 2, bottom rock layer 3, rectangular tunnel 4, circumscribed circle 51, bottom plate plastic circle 52, roof plate plastic circle 53, side wall plastic circle 54, side wall plastic zone 61, roof plate plastic zone 62, bottom plate plastic zone 63, side wall support beam 71, roof plate support beam 72, bottom plate support beam 73, top angle anchor rod 81, bottom angle anchor rod 82, plastic zone anchor rod 83, threaded drilling section 91, grouting section 92, pad 93, nut 94, and grouting plug 95. DETAILED DESCRIPTION

[0043] The present invention will be further described below in conjunction with the accompanying drawings.

[0044] The present invention proposes a method for quickly determining the range of the plastic zone of a rectangular cross-section roadway, which is particularly suitable for the case where the lateral pressure coefficient is close to 1 and the aspect ratio of the rectangular cross-section is close to 1 (the close here includes the case where the ratio is equal). The method for determining the plastic zone of the present invention is based on the existing classical circular cross-section roadway plastic zone calculation method, which not only considers the distribution shape of the rectangular cross-section plastic zone, but also considers the difference in mechanical properties of the coal and rock mass around the roadway, which is of great significance for guiding the rectangular cross-section support.

[0045] The method for quickly determining the plastic zone range of a rectangular cross-section roadway specifically comprises the following steps:

[0046] S1: Figure 1 As shown, the rectangular tunnel 4 is constructed in the coal seam 2, the upper part of the rectangular tunnel 4 is the roof rock layer 1, and the lower part is the floor rock layer 3, which is the minimum circumscribed circle 51 of the rectangular tunnel 4;

[0047] S2: Based on the theory of plastic mechanics and the plastic loosening zone of tunnel surrounding rock, the side wall plastic zone 54 of the rectangular tunnel 4 is calculated with the mechanical parameters of the coal seam 2; the roof plastic zone 53 of the rectangular tunnel 4 is calculated with the mechanical parameters of the roof rock layer 1; and the bottom plate plastic zone 52 of the rectangular tunnel 4 is calculated with the mechanical parameters of the bottom rock layer 3;

[0048] Among them, the calculation formula based on plastic mechanics and the theory of plastic loosening zone of tunnel surrounding rock is:

[0049]

[0050] Where R is the radius of the loosening zone in the plastic zone, r0 is the radius of the circumscribed circle, p is the formation stress, and C is the formation cohesion. is the internal friction angle of the formation;

[0051] S3: Figure 2 As shown, based on the right side vertex E (H), bottom point F (G) of the rectangular tunnel 4 and the deepest position point A of the side side plastic circle 54, an arc is made (three-point circle method), and the arc area EFA (HGA) is the side side plastic area 61;

[0052] Based on the end point HE of the rectangular tunnel roof and the deepest point B of the roof plastic circle 53, an arc is made (three-point circle method), and the arc area HEB is the roof plastic area 62;

[0053] Based on the end point GF of the rectangular tunnel floor and the deepest point C of the floor plastic circle 52, an arc is made (three-point circle method), and the arc area GFC is the floor plastic area 63;

[0054] or

[0055] like Figure 3As shown, a semi-elliptical arc is made based on the right side vertex E (H), the bottom point F (G) and the deepest position point A of the side plastic circle 54 of the rectangular tunnel 4 (the axis and the end points are made into an elliptical method), and the semi-elliptical arc area EFA (HGA) is the side plastic area 61;

[0056] A semi-elliptical arc is made based on the end point HE of the rectangular tunnel roof and the deepest position point B of the roof plastic circle 53 (the axis and the end point are used to make an ellipse method), and the semi-elliptical arc area HEB is the roof plastic area 62;

[0057] A semi-elliptical arc is made based on the end point GF of the bottom plate of the rectangular tunnel and the deepest position point C of the bottom plate plastic circle 52 (the axis and end points are made into an elliptical method), and the semi-elliptical arc area GFC is the bottom plate plastic area 63;

[0058] The side wall plastic zone 61, the top plate plastic zone 62, and the bottom plate plastic zone 63 are rectangular section plastic zones.

[0059] The method for quickly determining the scope of the plastic zone of a rectangular cross-section tunnel of the present invention can quickly and accurately determine the scope of the plastic zone of a rectangular tunnel constructed in a coal seam. The method for determining the plastic zone of the side wall has a large overlap with the plastic zone scope determined by actual engineering (or using numerical simulation). The plastic zone scope of the roof and the plastic zone scope of the bottom plate determined on the basis of considering the lithology of the roof and bottom plates also have a large overlap with the plastic zone scope determined by actual engineering (or using numerical simulation); in particular, the plastic zones determined at the four corners by this determination method of the present invention are consistent with the actual engineering, which is of great significance for guiding the support of rectangular tunnels.

[0060] The method for quickly determining the range of the plastic zone of a rectangular cross-section roadway according to the present invention is of great significance for guiding the support of rectangular roadways. After the plastic zone of the rectangular roadway 4 is determined by using the method for quickly determining the range of the plastic zone of a rectangular cross-section roadway according to the present invention, the support method comprises the following steps:

[0061] Step 1: Construction of closed steel beams

[0062] like Figure 4-Figure 5As shown, along the axial direction of the rectangular tunnel 4, a plurality of groups of closed steel beams are constructed at set intervals, such as 1-2m, and the closed steel beams include side support beams 71, roof support beams 72 and bottom support beams 73; since the mechanical properties of the coal seam 2 are generally weaker than those of the roof rock layer 1 and the bottom rock layer 3, the range of the side wall plastic zone 61 is larger than that of the roof plastic zone 62 and the bottom plastic zone 63, that is, the side wall is more likely to deform and the deformation is large, and the displacement into the rectangular tunnel 4 is large, so the side wall should be relatively strengthened. Support, for this, the closed steel beam of the present invention cleverly utilizes the lap structure positional relationship to better resist the large deformation of the side wall. Specifically, the side wall support beam 71 adopts a U-shaped cross-section structure with an opening inward, and the top plate support beam 72 and the bottom plate support beam 73 adopt a convex cross-section structure with an opening inward, and the top plate support beam 72 and the bottom plate support beam 73 are located between the side wall support beams 71 on both sides, and each side of the side wall support beam 71 is completely adjacent to the tunnel wall, and only the protruding sides of the top plate support beam 72 and the bottom plate support beam 73 are adjacent to the tunnel wall;

[0063] like Figure 6 As shown, the present invention also illustrates the arrangement of closed steel beams when the mechanical properties of the roof rock layer 1 and the bottom rock layer 3 are weaker than those of the coal seam 2;

[0064] like Figure 7 As shown, the present invention also illustrates the arrangement of the closed steel beam when the mechanical properties of the roof rock layer 1 are stronger than those of the coal layer 2, and the mechanical properties of the bottom rock layer 3 are weaker than those of the coal layer 2;

[0065] like Figure 8 As shown, the present invention also illustrates the arrangement of the closed steel beam when the mechanical properties of the roof rock layer 1 are weaker than those of the coal layer 2, and the mechanical properties of the bottom rock layer 3 are stronger than those of the coal layer 2;

[0066] Step 2: Construction anchor

[0067] like Figure 9-10 As shown, corner anchor rods 81 are constructed at two corners of the rectangular tunnel, and the corner anchor rods 81 pass through the side support beams 71 and the top plate support beams 72. The construction angle of the corner anchor rods 81 is about 45°. This angle setting can fully consider the problem of large deformation of the side wall and improve the anchoring force by utilizing the feature of high strength of the top plate. The corner anchor rods 81 can adopt existing full-length anchoring anchor rods or prestressed anchor rods.

[0068] Bottom corner anchors 82 are constructed at two bottom corners of the rectangular tunnel. The bottom corner anchors 82 pass through the side support beams 71 and the bottom plate support beams 73. The construction angle of the bottom corner anchors 82 is about 45°. This angle setting allows it to fully consider the problem of large deformation of the side walls and to improve the anchoring force by utilizing the high strength of the bottom plate. The bottom corner anchors 82 can use existing full-length anchoring anchors or prestressed anchors.

[0069] Three plastic zone anchor rods 83 are constructed at equal intervals and perpendicular to the top plate of the rectangular tunnel 4, and three plastic zone anchor rods 83 are constructed at equal intervals and perpendicular to the two side walls of the rectangular tunnel 4; the plastic zone anchor rods 83 are divided into a threaded drilling section 91 and a grouting section 92 along their length direction, and the threaded drilling sections 91 of all plastic zone anchor rods 83 are the same length, and the lengths of the grouting sections 92 of different plastic zone anchor rods 83 are the same as the depth of the plastic zone at which they are located, and the grouting section 92 is used for grouting reinforcement of the plastic zone around them.

[0070] Further, such as Fig.10 As shown, the plastic zone anchor 83 is composed of a threaded drilling section 91, a grouting section 92 and a fixed section in sequence along the length direction. The threaded drilling section 91 enables the plastic zone anchor 83 to be directly drilled into the stratum without drilling a hole before installing the anchor, and the effect of the thread can increase the anchoring performance. The length of the grouting section 92 of the plastic zone anchor 83 is the same as the depth of the plastic zone at its location. The grouting section 92 is used to grout and reinforce the plastic zone around it, thereby increasing the strength of the plastic zone and the anchoring force. A pad 93 and a nut 94 are sequentially sleeved on the fixed section for fixing the plastic zone anchor 83. The grouting section 92 of the plastic zone anchor 83 adopts a hollow structure with holes, and the fixed section of the plastic zone anchor 83 adopts a hollow structure without holes, and a grouting plug 95 is arranged on the outermost part.

[0071] The above support method is an illustration based on the plastic zone range determined by making a circular arc. The support method is the same for the plastic zone range determined by making an elliptical arc. The above support method only uses relatively short anchor rods without long anchor cables, which can greatly increase construction speed and reduce construction costs.

[0072] The present invention is not limited to the above-mentioned optimal implementation mode. Anyone can derive other various forms of methods under the inspiration of the present invention. Any technical solution that is the same or similar to that of the present application falls within the protection scope of the present invention.

Claims

1. A method for quickly determining the plastic zone range of a rectangular cross-section roadway, characterized in that: The following steps are involved: S1: The rectangular tunnel is constructed in the coal seam, the upper part of the rectangular tunnel is the roof rock layer, the lower part is the floor rock layer, and the circumscribed circle of the rectangular tunnel is used; S2: Based on the theory of plastic mechanics and the plastic loosening zone of tunnel surrounding rock, the side wall plastic zone of the rectangular tunnel is calculated with the mechanical parameters of the coal seam; the roof plastic zone of the rectangular tunnel is calculated with the mechanical parameters of the roof rock layer; the bottom plate plastic zone of the rectangular tunnel is calculated with the mechanical parameters of the bottom plate rock layer; S3: Based on the top and bottom points of the side wall of the rectangular tunnel and the deepest point of the side wall plastic zone, an arc is drawn to obtain the side wall plastic zone; The plastic zone of the roof is obtained by making an arc based on the end point of the roof of the rectangular tunnel and the deepest point of the plastic circle of the roof; The bottom plate plastic zone is obtained by making an arc based on the end points of the rectangular tunnel bottom plate and the deepest point of the bottom plate plastic circle.

2. The method for quickly determining the plastic zone range of a rectangular cross-section roadway according to claim 1 is characterized in that: The method is applicable to the case where the lateral pressure coefficient is close to 1 and the aspect ratio of the rectangular section is close to 1.

3. The method for quickly determining the plastic zone range of a rectangular cross-section roadway according to claim 1 is characterized in that: In step S2, the calculation formula based on plastic mechanics and the theory of plastic loosening zone of tunnel surrounding rock is: Where R is the radius of the loosening zone in the plastic zone, r0 is the radius of the circumscribed circle, p is the formation stress, and C is the formation cohesion. is the internal friction angle of the formation.

4. The method for quickly determining the plastic zone range of a rectangular cross-section roadway according to claim 1, characterized in that: In step S3, alternatively, a semi-elliptical arc is drawn based on the top and bottom points of the side wall of the rectangular tunnel and the deepest position point of the side wall plastic zone to obtain the side wall plastic zone; A semi-elliptical arc is made based on the end points of the rectangular tunnel roof and the deepest point of the roof plastic circle to obtain the roof plastic zone; The bottom plate plastic zone is obtained by making a semi-elliptical arc based on the end points of the rectangular tunnel bottom plate and the deepest point of the bottom plate plastic circle.

5. A rectangular tunnel support method, which supports the rectangular tunnel based on the plastic zone range determined by any one of claims 1 to 4, characterized in that: The following steps are involved: Step 1: Construction of closed steel beams Several groups of closed steel beams are constructed at set intervals along the axial direction of the rectangular tunnel, among which the side support beams adopt a U-shaped cross-section structure with openings facing inwards, and the top plate support beams and bottom plate support beams adopt a convex cross-section structure with openings facing inwards, and the top plate support beams and bottom plate support beams are located between the side support beams on both sides; Step 2: Construction anchor Top corner anchors are constructed at the two top corners of the rectangular tunnel; bottom corner anchors are constructed at the two bottom corners of the rectangular tunnel; a number of plastic zone anchors are vertically constructed on the top plate of the rectangular tunnel, and a number of plastic zone anchors are vertically constructed on the two side walls of the rectangular tunnel respectively; the plastic zone anchors are divided into a threaded drilling section and a grouting section along their length direction, and the length of the grouting section of the anchors in different plastic zones is the same as the depth of the plastic zone at their location.

6. The rectangular tunnel support method according to claim 5, characterized in that: Each side of the side support beam is completely adjacent to the tunnel wall, and only the protruding sides of the top plate support beam and the bottom plate support beam are adjacent to the tunnel wall.

7. The rectangular tunnel support method according to claim 5, characterized in that: The top angle anchor rod passes through the side support beam and the top plate support beam, and the construction angle of the top angle anchor rod is 45°.

8. The rectangular tunnel support method according to claim 5, characterized in that: The bottom angle anchor rod passes through the side support beam and the bottom plate support beam, and the construction angle of the bottom angle anchor rod is 45°.

9. The rectangular tunnel support method according to claim 5, characterized in that: The length of the threaded drilling section of all plastic zone anchors is the same.

Images