A method for calculating the surrounding rock pressure at the portal of a shallow-buried, unbalanced-pressure tunnel

Abstract

The present application provides a method for calculating the surrounding rock pressure at the portal of a shallow-buried biased tunnel in a bedding layer, which relates to the technical field of tunnel design. The method includes: constructing a surrounding rock pressure model of a shallow-buried biased tunnel in a bedding layer; decomposing the outer block and the inner block into multiple stratum blocks by layer based on the stratum interface of the bedding rock mass; determining the first side resistance resultant of the outer block and the second side resistance resultant of the inner block in layers; determining the target gravity of the rock column directly above the tunnel based on the weight of the block at the top of the tunnel, and determining the first vertical surrounding rock pressure and the first horizontal surrounding rock pressure on the outside of the tunnel, and the second vertical surrounding rock pressure and the second horizontal surrounding rock pressure on the inside of the tunnel based on the target gravity, the first side resistance resultant, and the second side resistance resultant. This method can improve the calculation accuracy of the surrounding rock pressure of a bedding biased tunnel in a complex stratum by solving the side resistance resultant of the stratum blocks layer by layer.

Description

Technical Field

[0001] The present application relates to the technical field of tunnel design, and in particular to a method for calculating the surrounding rock pressure at the portal of a shallow-buried, biased-pressure tunnel in a layer. Background Art

[0002] Tunnel construction in mountainous areas often requires traversing complex bedding rock geological sections. Bedding rock forms parallel bedding structures due to sedimentation or tectonic action, and the rock mass exhibits significant anisotropy in strength and deformation properties. When tunneling in shallow, biased terrain, the rock mass at the portal section is prone to asymmetric slippage along weak bedding planes, inducing major engineering accidents such as lining cracking, support failure, and even portal collapse. Many railway and highway tunnel projects at home and abroad, such as a tunnel on the Chengdu-Kunming Railway, the Fengjiaba Tunnel on the Chongqing-Huaihua Railway, and some mountainside tunnels on the Shanghai-Kunming Expressway, have encountered large surrounding rock deformations caused by biased bedding during construction, severely restricting project progress and threatening operational safety.

[0003] Traditional rock mass pressure theory is primarily based on the assumption of homogeneous isotropy. Classical calculation methods, such as the Protzsprung theory and the Terzaghi formula, while somewhat applicable in shallow tunnels buried in a single stratum, struggle to accurately characterize the heterogeneous stress transfer mechanism and progressive failure characteristics along the bedding plane in the bedding rock mass. In recent years, while scholars have revealed the regulatory effect of the bedding inclination on the eccentric load through physical model experiments and simulated the progressive failure process of layered surrounding rock using numerical methods such as discrete element methods and finite difference methods, these studies have primarily focused on describing phenomena and verifying mechanisms, failing to construct analytical models that can quantify the shear effects at the interface of multiple strata.

[0004] The formula for calculating the surrounding rock pressure of shallow, biased tunnels recommended by existing specifications only considers the conditions of a single rock layer and fails to reflect the synergistic effects of the friction characteristics of the fracture surfaces of different rock layers, the shear strength of the interlayer contact surface, and the spatial morphology of the potential slip surface in multi-lithologic strata. Especially when the tunnel passes through complex bedding combinations such as hard upper layers and soft lower layers, or interbedded hard and soft layers, the traditional method can significantly underestimate the horizontal pressure outside the tunnel, resulting in a risky support structure design. Therefore, there is an urgent need to develop a theoretical calculation model that can integrate the characteristics of strata layering, the spatial mechanical equilibrium of sliding blocks, and the biased load transfer mechanism to provide an accurate load input basis for tunnel design under complex geological conditions. Summary of the Invention

[0005] The present application provides a method for calculating the surrounding rock pressure at the portal of a shallow, biased tunnel in a bedding layer. By solving the lateral resistance resultant of the stratum blocks layer by layer, the comprehensive resistance resultant of the slip surface is finally determined, thereby improving the calculation accuracy of the surrounding rock pressure of the bedding biased tunnel in complex strata.

[0006] In a first aspect, the present invention provides a method for calculating the surrounding rock pressure at the portal of a shallow-buried biased tunnel in a bedding layer, comprising: constructing a surrounding rock pressure model of a shallow-buried biased tunnel in a bedding layer; the tunnel is excavated in a bedding rock mass, and the bedding rock mass includes multiple strata; the surrounding rock pressure model includes a tunnel top block, an outer block, and an inner block; wherein the tunnel top block is a rectangular block formed at the top of the tunnel after tunnel excavation, the outer block is a block located on a first side of the tunnel top block, and the inner block is a block located on a second side of the tunnel top block; based on the stratigraphic interface of the bedding rock mass, the outer block and the inner block are decomposed into multiple stratigraphic blocks by layer; the outer block includes a triangular outer block of a first stratum and multiple quadrilateral outer blocks of other strata, and the inner block includes A triangular inner block of a first stratum and multiple quadrilateral inner blocks of other strata; determining the lateral resistance of the triangular outer block and multiple quadrilateral outer blocks in the outer blocks in layers, and determining the first lateral resistance resultant of the outer blocks based on the lateral resistance of each layer of outer blocks; and determining the lateral resistance of the triangular inner block and multiple quadrilateral inner blocks in the inner blocks in layers, and determining the second lateral resistance resultant of the inner blocks based on the lateral resistance of each layer of inner blocks; determining the target gravity of the rock column directly above the tunnel based on the weight of the tunnel top block, and determining the first surrounding rock vertical pressure and the first surrounding rock horizontal pressure outside the tunnel, and the second surrounding rock vertical pressure and the second surrounding rock horizontal pressure inside the tunnel based on the target gravity, the first lateral resistance resultant and the second lateral resistance resultant.

[0007] According to one embodiment of the present application, the step of determining the lateral resistance of the triangular outer block includes: determining the force condition of the triangular outer block; establishing the force balance equation and the moment balance equation of the triangular outer block based on the force condition of the triangular outer block, and determining the resultant lateral resistance of the triangular outer block acting on the first slip surface of the multi-layer formation.

[0008] According to one embodiment of the present application, for any of the quadrilateral outer blocks, the step of determining the lateral resistance of the quadrilateral outer block includes: determining the force condition of the quadrilateral outer block; establishing the force balance equation and the moment balance equation of the quadrilateral outer block based on the force condition of the quadrilateral outer block, and determining the resultant lateral resistance of the quadrilateral outer block acting on the corresponding layer slip surface of the multi-layer strata.

[0009] According to one embodiment of the present application, the step of determining the lateral resistance of the triangular inner block includes: determining the force condition of the triangular inner block, establishing the force balance equation and the torque balance equation of the triangular inner block based on the force condition of the triangular inner block, and determining the resultant lateral resistance of the triangular inner block acting on the first slip surface of the multi-layer stratum.

[0010] According to one embodiment of the present application, for any of the inner blocks of the quadrilateral, the step of determining the lateral resistance of the inner block of the quadrilateral includes: determining the force condition of the inner block of the quadrilateral; establishing the force balance equation and the moment balance equation of the inner block of the quadrilateral based on the force condition of the inner block of the quadrilateral, and determining the resultant lateral resistance of the inner block of the quadrilateral acting on the slip surface of the corresponding layer of the multi-layer strata.

[0011] According to one embodiment of the present application, the target gravity of the rock pillar directly above the tunnel is determined based on the weight of the tunnel top block, and the first surrounding rock vertical pressure and the first surrounding rock horizontal pressure outside the tunnel, and the second surrounding rock vertical pressure and the second surrounding rock horizontal pressure inside the tunnel are determined based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force, respectively, including: determining the target gravity of the rock pillar directly above the tunnel based on the weight of the tunnel top block; determining the first surrounding rock vertical pressure and the second surrounding rock vertical pressure based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force; determining the first side pressure coefficient outside the tunnel and the second side pressure coefficient inside the tunnel based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force, and determining the first surrounding rock horizontal pressure and the second surrounding rock horizontal pressure based on the first side pressure coefficient and the second side pressure coefficient.

[0012] According to one embodiment of the present application, the calculation formulas for the first surrounding rock vertical pressure and the second surrounding rock vertical pressure are:

[0013]

[0014] in, is the target gravity, is the gravity of the rectangular block formed on the top of the tunnel, is the resistance force on the first side, is the friction angle of the potential slip surface of the first stratum, is the resultant resistance force on the second side, is the first surrounding rock vertical pressure, is the net width of the tunnel excavation, is the weight of the uppermost rock mass at the top of the tunnel, is the slope angle of the stratum interface, is the second surrounding rock vertical pressure.

[0015] According to one embodiment of the present application, the calculation formulas for the first side pressure coefficient and the second side pressure coefficient are:

[0016]

[0017]

[0018] in, is the first side pressure coefficient, is the resultant lateral resistance of the first layer of stratum outside the tunnel, is the friction angle of the potential slip surface of the first stratum, is the potential slip surface length of the first layer of stratum outside the tunnel, is the total number of strata, For the The weight of the rock mass of the stratum, For the The thickness of the stratum rock mass on the outside, is the second side pressure coefficient, is the resultant lateral resistance of the first layer of ground inside the tunnel, The length of the potential slip surface of the first layer of strata inside the tunnel, For the The thickness of the stratigraphic rock mass on the inner side.

[0019] Compared with the existing technology, the beneficial effects of this application are: by constructing a surrounding rock pressure analysis model under multi-layer stratum conditions, deconstructing the outer and inner sliding blocks of the tunnel according to the stratum layer, solving the lateral resistance force of the stratum blocks layer by layer, and finally determining the comprehensive resistance force of the sliding surface. This application realizes the refined calculation of the surrounding rock pressure of the layer-beam biased tunnel in complex strata, and can simultaneously output the theoretical values ​​of the vertical and horizontal pressures inside and outside the tunnel, breaking through the limitations of the traditional homogeneous stratum model, and can significantly improve the calculation accuracy of the multi-layer rock bias load, thereby providing a more reliable theoretical basis for tunnel design. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of the steps of the method for calculating the surrounding rock pressure at the portal of a shallow-buried, biased-pressure tunnel in the bedding provided in an embodiment of the present application.

[0021] Figure 2 Schematic diagram of pressure calculation for the surrounding rock pressure model provided in the embodiment of this application.

[0022] Figure 3 A schematic diagram of the forces acting on the outer block provided in an embodiment of the present application.

[0023] Figure 4A schematic diagram of the forces acting on the triangular outer block provided in an embodiment of the present application.

[0024] Figure 5 This is a schematic diagram of the forces acting on points F and A on the potential slip surface AF provided in an embodiment of the present application.

[0025] Figure 6 A schematic diagram of the forces acting on the quadrilateral outer block of the second layer of stratum outside the tunnel provided in an embodiment of the present application.

[0026] Figure 7 This is a schematic diagram of the forces acting on points F and G on the potential slip surface FG provided in an embodiment of the present application.

[0027] Figure 8 A schematic diagram of the forces acting on the inner block provided in an embodiment of the present application.

[0028] Figure 9 A schematic diagram of the forces acting on the inner triangular block provided in an embodiment of the present application.

[0029] Figure 10 Schematic diagram of surrounding rock pressure in a shallow biased tunnel in a single stratum provided in an embodiment of the present application. DETAILED DESCRIPTION

[0030] The present application is further described in detail below in conjunction with test examples and specific implementation methods. However, this should not be understood as limiting the scope of the above-mentioned subject matter of the present application to the following embodiments. All technologies implemented based on the content of the present application fall within the scope of protection of the present application.

[0031] Unless otherwise specified, in the description of the specific embodiments of this application, the terms indicating the orientation or position relationship such as "up", "down", "left", "right", "center", "inside", "outside", and "side" are based on the expression of the orientation or position relationship shown in the accompanying drawings, or the orientation or position relationship in which the product / device / apparatus is placed when it is usually used. These terms of orientation or position relationship are only for the convenience of describing the scheme of this application or simplifying the description in the specific embodiments to facilitate the technicians to quickly understand the scheme, and do not indicate or imply that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific position relationship, and therefore should not be understood as limiting this application.

[0032] In the description of the embodiments of this application, the technical terms "first," "second," etc., merely distinguish one entity or operation from another and are not to be understood as indicating or implying relative importance or implicitly specifying the quantity, specific order, or primary-secondary relationship of the indicated technical features. In the description of the embodiments of this application, "plurality" means two or more, unless otherwise specifically defined.

[0033] References herein to "embodiments" mean that a particular feature, structure, or characteristic described in connection with the embodiments may be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0034] Please see Figure 1 , Figure 1 Schematic diagram of the steps of the method for calculating the surrounding rock pressure at the entrance of a shallow-buried and biased tunnel provided in an embodiment of the present application. The steps of the method for calculating the surrounding rock pressure at the entrance of a shallow-buried and biased tunnel may include:

[0035] S1. Construct a surrounding rock pressure model for a shallow-buried, unbalanced tunnel in the bedding layer.

[0036] In the embodiments of the present application, the tunnel is excavated in bedding rock mass, which includes multiple strata. Bedding rock mass refers to a combination of rock layers with a distinct layered structure formed by geological tectonic action. The rock formations of the bedding rock mass, such as strike, dip, and inclination, are highly consistent with or nearly parallel to the surface slope or the artificial excavation surface.

[0037] For example, the surrounding rock pressure model includes the tunnel top block, outer block and inner block; see Figure 2 , Figure 2 A schematic diagram of pressure calculation of the surrounding rock pressure model provided in the embodiment of the present application, wherein the tunnel is covered with Layers of different lithologies, the interfaces of each layer are parallel to each other and have an angle with the horizontal direction of The top block AA'I'I of the tunnel is the block formed on the top of the tunnel after the tunnel is excavated, and the outer block ABCDEI is the block located on the first side of the top block of the tunnel, that is, Figure 2 The blocks on the left side of the middle, the inner blocks A'B'C'D'E'I' are the blocks on the second side of the tunnel top block, that is, Figure 2 The block on the middle right.

[0038] S2. Based on the stratigraphic interface of the bedding rock mass, the outer block and the inner block are decomposed into multiple stratigraphic blocks by layer.

[0039] For example, the net width of the excavation in the stratum is In a tunnel, the top block AA'I'I of the tunnel sinks, driving the polygonal blocks ABCDEI and A'B'C'D'E'I' on both sides to slide along the irregular fracture surfaces ABCDE and A'B'C'D'E', respectively, via potential slip surfaces AI and A'I'. Therefore, based on the stratigraphic interface, the outer block can be decomposed into a triangular outer block of the first stratum and multiple quadrilateral outer blocks of other strata, and the inner block can be decomposed into a triangular inner block of the first stratum and multiple quadrilateral inner blocks of other strata.

[0040] S3. Determine the lateral resistance of the triangular outer blocks and multiple quadrilateral outer blocks in the outer blocks in a layered manner, and determine the first lateral resistance resultant of the outer blocks based on the lateral resistance of each layer of outer blocks; and determine the lateral resistance of the triangular inner blocks and multiple quadrilateral inner blocks in the inner blocks in a layered manner, and determine the second lateral resistance resultant of the inner blocks based on the lateral resistance of each layer of inner blocks.

[0041] S4. Determine the target gravity of the rock column directly above the tunnel based on the weight of the block at the top of the tunnel, and determine the first vertical pressure and the first horizontal pressure of the surrounding rock outside the tunnel, and the second vertical pressure and the second horizontal pressure of the surrounding rock inside the tunnel based on the target gravity, the resultant force of the first side resistance, and the resultant force of the second side resistance, respectively.

[0042] For example, the following describes the step S3 of determining the lateral resistance of each block in layers. Figure 3 , Figure 3 The force diagram of the outer block provided in the embodiment of the present application. The deadweight of the layers 1 to n in the polygonal block ABCDEI is respectively recorded as ( ); The irregular fracture surface ABCDE is acted upon by the resultant supporting force. ( ) are the resultant forces acting on strata 1 to n, and the angle between the direction of the force and the normal of the fracture surface ( ) are the calculated friction angles on the fracture surface from stratum 1 to stratum n; the potential slip surface AI is acted upon by the resultant lateral resistance force, ( ) are the resultant lateral resistance forces acting on strata 1 to n, and the angle between the direction of the force and the normal of the potential slip surface is ( ) are the friction angles on the potential slip surface from stratum 1 to stratum n, and the friction angle on the potential slip surface is obtained by subtracting the friction angle calculated on the fracture surface.

[0043] The calculation model for surrounding rock pressure of shallow unbiased tunnels takes into account homogeneous strata conditions, and the resultant lateral resistance force on its potential slip surface is derived from the force balance equation. However, in the calculation model for surrounding rock pressure of shallow unbiased tunnels under bedding conditions, the fracture surface and potential slip surface of each stratum have unknown resultant support force and resultant lateral resistance force, respectively. This makes the force on the polygonal block more complex, and the resultant lateral resistance force cannot be solved solely by the force balance equation. It is necessary to introduce the moment balance equation and increase the number of equations to solve the resultant lateral resistance force.

[0044] For the triangular outer block, the step of determining the lateral resistance of the triangular outer block may include:

[0045] Determine the stress condition of the triangular outer block.

[0046] Based on the stress condition of the triangular outer block, a force balance equation and a moment balance equation of the triangular outer block are established to determine the resultant lateral resistance force of the triangular outer block acting on the first slip surface of the multi-layer stratum.

[0047] Please see Figure 4 , Figure 4 This is a force diagram of the triangular outer block provided in the embodiment of the present application. Take the ABF of the triangular block of the first outer stratum for analysis. is the interaction force between strata 1 and 2, and the angle between the force direction and the normal direction of the stratum interface is the friction angle on the interface between strata 1 and 2. Since the strata interface is also a potential slip surface, The value of can also be obtained by calculating the friction angle reduction on the fracture surface. Establish a local coordinate system ( , ), the abscissa is horizontal and passes through Point, the ordinate is vertical and passes through Point. According to the local coordinate system, establish 、 The force balance equations in the direction are

[0048]

[0049]

[0050] in, is the angle between the fracture surface AB and the horizontal direction. Combining the above formulas, we can get the lateral resistance force on the potential slip surface AF The expression is:

[0051]

[0052] Fracture surface The resultant force on the support The action point is the moment center, and the moment balance equation is established as:

[0053]

[0054] In the formula 、 and Force 、 and Resultant force of the action point and the support force The distance between the action points. Substituting Equation (4) into Equation (3), we can obtain the resultant lateral resistance force on the potential slip surface AF. The expression is:

[0055]

[0056] in, is the resultant lateral resistance The resultant force from the point of action to the support The vertical distance, is the formation interface force The resultant force from the point of action to the support The vertical distance from the point of action.

[0057] The deadweight of the triangular outer block ABF is:

[0058]

[0059] Where, is the weight of the first stratum rock mass; is the length of the potential slip surface AF.

[0060] The following describes how to solve the distance between the point of action of each force and the point of action of the resultant force of the support force. Figure 5 , Figure 5 This is a schematic diagram of the forces acting on points F and A on the potential slip surface AF provided in the embodiment of the present application. Point F is simultaneously subjected to the horizontal self-weight stress and the vertical friction force. The vertical friction force is equal to the horizontal self-weight stress multiplied by the potential slip surface friction coefficient. ,thus The lateral resistance at point ,in, is the lateral pressure coefficient of the first formation; Indicates the The weight of the rock mass of the stratum; Representative The thickness of the stratum. Similarly, the lateral resistance at point A is The lateral resistance on the potential slip surface AF is the height of the potential slip surface AF. It is distributed in a trapezoidal shape, and the center of gravity height of the trapezoid is the resultant resistance force on the upper side of the potential slip surface AF. Height of the action point, resultant lateral resistance The horizontal coordinate of the action point can be determined by the geometric relationship of the triangular block ABF, so the lateral resistance force is The action point is in the local coordinate system ( , ) in the coordinates are ( , ).

[0061] To simplify the calculation, it is assumed that the support force The distance between the point of action and the horizontal axis is equal to the resultant lateral resistance force The point of action and The distance between points, according to the geometric relationship, the resultant force of the support The point of action is in the local coordinate system ( , ) in the coordinates are ( , ). According to the resultant support force The point of action and the resultant lateral resistance The coordinates of the point of action can be obtained The expression is as follows:

[0062]

[0063] Determine triangular blocks based on geometric relationships Each vertex is in the local coordinate system ( , ) in the coordinates of A( , )、B ( , ) and F ( , ). Determine the center of gravity of the triangular block ABF and combine the support force The coordinates of the action point can be used to obtain the resultant force of the triangular block ABF to the support force Vertical distance The expression is:

[0064]

[0065] The load on the stratum interface BF is evenly distributed along the interface. The point of action of the force on the stratum interface BF is located at the midpoint of the line segment. Combined with the support force, the resultant force The coordinates of the action point can be obtained The expression is as follows:

[0066]

[0067] Substituting Equations (6)-(9) into Equation (5) we can solve the resultant lateral resistance force on the potential slip surface AF: size.

[0068] For any of the quadrilateral outer blocks, the step of determining the lateral resistance of the quadrilateral outer block comprises:

[0069] Determine the stress condition of the outer blocks of the quadrilateral.

[0070] Based on the stress condition of the outer block of the quadrilateral, a force balance equation and a moment balance equation of the outer block of the quadrilateral are established to determine the resultant lateral resistance force of the outer block of the quadrilateral acting on the slip surface of the corresponding layer of the multi-layer formation.

[0071] For example, see Figure 6 , Figure 6 A schematic diagram of the forces acting on the quadrilateral outer block of the second layer of stratum outside the tunnel provided in an embodiment of the present application.

[0072] In the picture is the interaction force between strata 2 and 3, and the angle between the direction of the force and the normal direction of the stratum interface is the friction angle on the interface between strata 2 and 3. Since the strata interface is also a potential slip surface, The value of can also be obtained by calculating the friction angle reduction on the fracture surface. Establish a local coordinate system ( , ), the horizontal axis is the horizontal direction, the vertical axis is the vertical direction, and the coordinate origin is Point. According to the local coordinate system, establish 、 The force balance equations in the directions are:

[0073]

[0074]

[0075] In the formula is the angle between the fracture surface BC and the horizontal direction. Combining equations (10) and (11) yields the resultant lateral resistance on the potential slip surface FG: for:

[0076]

[0077] The resultant force of the support force on the fracture surface BC The action point is the moment center, and the moment balance equation is established as:

[0078]

[0079] In the formula 、 、 and Force 、 、 and Resultant force of the action point and the support force The distance between the action points. Substituting Equation (13) into Equation (12), we can obtain the resultant lateral resistance force on the potential slip surface FG. The expression:

[0080] (14)

[0081] The interaction force between stratum 1 and stratum 2 in the above formula is It can be obtained according to formula (4).

[0082] The self-weight of the quadrilateral block BCGF is:

[0083]

[0084] Where: is the weight of the second stratum rock mass; is the length of the potential slip surface FG.

[0085] The following describes how to solve the distance between the point of action of each force and the point of action of the resultant force of the support force. Figure 7 , Figure 7 This is a schematic diagram of the forces acting on points F and G on the potential slip surface FG provided in the embodiment of the present application. Point G is simultaneously subjected to the horizontal self-weight stress and the vertical friction force. The vertical friction force is equal to the horizontal self-weight stress multiplied by the potential slip surface friction coefficient. , thus The lateral resistance at point ,in is the lateral pressure coefficient of the second layer. Similarly, The lateral resistance at point Potential slip surface The lateral resistance along the potential slip surface Height It is distributed in a trapezoidal shape, and the center of gravity of the trapezoid is the potential slip surface. Upper resistance force The height of the action point, combined with the quadrilateral block The geometric relationship of the side resistance is determined The action point is in the local coordinate system ( , ) in the coordinates are ( , ). To simplify the calculation, it is assumed that the resultant support force The distance between the point of action and the horizontal axis is equal to the resultant lateral resistance force The point of action and The distance between points, according to the geometric relationship, the resultant force of the support The point of action is in the local coordinate system ( , ) in the coordinates are ( , ). According to the resultant support force The point of action and the resultant lateral resistance The coordinates of the point of action can be obtained The expression is as follows:

[0086]

[0087] Determine quadrilateral blocks based on geometric relationships Each vertex is in the local coordinate system ( , ) is the coordinates in ( , ), ( , ), ( , )and ( , ). Determine the quadrilateral block The center of gravity, combined with the supporting force The coordinates of the action point can be obtained The expression is:

[0088]

[0089] Stratigraphic interface The upper load is evenly distributed along the interface, and the stratum interface The point of action of the upper force is at the midpoint of the line segment, combined with the supporting force The coordinates of the action point can be obtained The expression is:

[0090]

[0091] Similarly, the stratum interface The upper load is evenly distributed along the interface, and the stratum interface The point of action of the upper force is at the midpoint of the line segment, combined with the supporting force The coordinates of the action point can be obtained The expression is:

[0092]

[0093] Substituting Equations (15)-(19) into Equation (14) can solve the potential slip surface The resultant lateral drag force size.

[0094] Based on the same idea as that of finding the lateral resistance of the quadrilateral outer block of the second layer of stratum outside the tunnel, the lateral resistance of the outer third to the third layer can be determined in sequence. The stress condition of the outer blocks of the quadrilateral of each stratum can be further determined to determine the corresponding lateral resistance of the outer blocks of the quadrilateral. ( ).

[0095] For outer blocks, see Figure 8 , Figure 8 The force diagram of the inner block provided in the embodiment of the present application. The deadweight of the layers 1 to n in the polygonal block A'B'C'D'E'I' is recorded as ( ); The irregular fracture surface A'B'C'D'E' is subjected to the combined force of the supporting forces. ( ) are the resultant supporting forces acting on strata 1 to strata n, and the angle between the direction of the force acting on the fracture surface from strata 1 to strata n and the normal of the fracture surface is still ( ); potential slip surface The upper side is subjected to the combined force of lateral resistance. ( ) are the resultant lateral resistance forces acting on strata 1 to n, and the angle between the direction of the force and the normal to the potential slip surface is still ( The analysis method here is the same as the analysis method for the outer side in the above description, so it will not be repeated here.

[0096] For the triangular inner block, the step of determining the lateral resistance of the triangular inner block includes:

[0097] Determine the stress condition of the inner block of the triangle.

[0098] Based on the stress condition of the triangular inner block, the force balance equation and the moment balance equation of the triangular inner block are established to determine the resultant lateral resistance force of the triangular inner block acting on the first slip surface of the multi-layer stratum.

[0099] Please see Figure 9 , Figure 9 A schematic diagram of the forces acting on the inner triangular block provided in an embodiment of the present application.

[0100] In the picture is the interaction force between stratum 1 and stratum 2, and the angle between the direction of the force and the normal direction of the stratum interface is still Based on the same analysis process as the triangular outer block, we can obtain:

[0101]

[0102] The self-weight of the inner triangular block A'B'F' is:

[0103]

[0104] in, is the length of the potential slip surface A'F'.

[0105]

[0106]

[0107]

[0108] Substituting Equations (21)-(24) into Equation (20) yields the resultant lateral resistance on the potential slip surface A'F': size.

[0109] For any of the quadrilateral inner blocks, the step of determining the lateral resistance of the quadrilateral inner block comprises:

[0110] Determining the stress condition of the inner block of the quadrilateral;

[0111] Based on the stress conditions of the inner block of the quadrilateral, a force balance equation and a moment balance equation of the inner block of the quadrilateral are established to determine the resultant lateral resistance force of the inner block of the quadrilateral acting on the slip surface of the corresponding layer of the multi-layer stratum.

[0112] For example, is the interaction force between strata 2 and 3, and the angle between the force direction and the normal direction of the stratum interface is still Based on the same analysis process as the outer blocks of the quadrilateral, we can obtain:

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] Substituting Equations (38)-(42) into Equation (25) can determine the potential slip surface The resultant lateral drag force size.

[0120] Based on the same idea as that of finding the lateral resistance of the quadrilateral outer block of the second layer of stratum inside the tunnel, the lateral resistance of the third to the third layers inside the tunnel can be determined in sequence. The stress condition of the inner block of the quadrilateral of each stratum can be used to determine the corresponding lateral resistance of the outer block of the quadrilateral. ( ).

[0121] By way of example, the following describes step S4 for determining the target gravity of the rock column directly above the tunnel based on the weight of the tunnel top block, and determining the first surrounding rock vertical pressure and the first surrounding rock horizontal pressure outside the tunnel, and the second surrounding rock vertical pressure and the second surrounding rock horizontal pressure inside the tunnel based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force.

[0122] Step S4 may specifically include:

[0123] S41. Determine the target gravity of the rock pillar directly above the tunnel based on the weight of the block at the top of the tunnel.

[0124] S42: Determine the first surrounding rock vertical pressure and the second surrounding rock vertical pressure based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force.

[0125] S43. Determine a first side pressure coefficient on the outside of the tunnel and a second side pressure coefficient on the inside of the tunnel based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force, and determine the first surrounding rock horizontal pressure and the second surrounding rock horizontal pressure based on the first side pressure coefficient and the second side pressure coefficient.

[0126] For example, to determine the target gravity of the rock column directly above the tunnel in S41, please continue to refer to Figure 2 The self-weight of the rock mass at the top of the tunnel excavation face is the sum of the self-weights of strata 1 to n at the top of the excavation face, and the expression is:

[0127]

[0128] In the embodiment of the present application, the vertical pressure acting on the lining , equal to the cylinder The gravity minus the lateral resistance of the polygonal blocks on both sides of the column 、 ( ).but The calculation formula can be based on Determined as:

[0129]

[0130] Assuming that the distribution of the bias pressure at the top of the tunnel is consistent with the ground slope, the vertical pressure of the first surrounding rock outside the tunnel is and the second surrounding rock vertical pressure inside The calculation formula is:

[0131]

[0132] in, is the target gravity, is the gravity of the rectangular block formed on the top of the tunnel, is the resistance force on the first side, is the friction angle of the potential slip surface of the first stratum, is the resultant resistance force on the second side, is the first surrounding rock vertical pressure, is the net width of the tunnel excavation, is the weight of the uppermost rock mass at the top of the tunnel, is the slope angle of the stratum interface, is the second surrounding rock vertical pressure.

[0133] The horizontal surrounding rock pressure outside the tunnel is equal to the vertical self-weight stress multiplied by the first side pressure coefficient of the first layer of stratum The horizontal surrounding rock pressure inside the tunnel is equal to the vertical self-weight stress multiplied by the second side pressure coefficient of the first layer of stratum . and The calculation formula is as follows

[0134]

[0135]

[0136] in, is the first side pressure coefficient, is the resultant lateral resistance of the first layer of stratum outside the tunnel, is the friction angle of the potential slip surface of the first stratum, is the potential slip surface length of the first layer of stratum outside the tunnel, is the total number of strata, For the The weight of the rock mass of the stratum, For the The thickness of the stratum rock mass on the outside, is the second side pressure coefficient, is the resultant lateral resistance of the first layer of ground inside the tunnel, The length of the potential slip surface of the first layer of strata inside the tunnel, For the The thickness of the stratigraphic rock mass on the inner side.

[0137] After determining the first side pressure coefficient and the second side pressure coefficient, the outer horizontal surrounding rock pressure and the inner horizontal surrounding rock pressure of the tunnel can be determined. Combined with the first surrounding rock vertical pressure and the second surrounding rock vertical pressure determined in the above steps, the overall tunnel entrance surrounding rock pressure can be determined.

[0138] In the above implementation process, a surrounding rock pressure analysis model under multi-layer stratum conditions is constructed. By deconstructing the outer and inner sliding blocks of the tunnel according to the stratum layer, the lateral resistance of the stratum blocks is solved layer by layer, and the comprehensive resistance of the sliding surface is finally determined. This application realizes the refined calculation of the surrounding rock pressure of the layer-beam biased tunnel in complex strata, and can simultaneously output the theoretical values ​​of the vertical and horizontal pressures inside and outside the tunnel. It breaks through the limitations of the traditional homogeneous stratum model and can significantly improve the calculation accuracy of the multi-layer rock bias load, thereby providing a more reliable theoretical basis for tunnel design.

[0139] The following description is a comparative verification of the method for calculating the surrounding rock pressure at the portal of a shallow-buried, biased-pressure tunnel provided in the embodiment of the present application.

[0140] Please see Figure 10 , Figure 10 The schematic diagram of surrounding rock pressure of a shallow biased tunnel in a single stratum provided in the embodiment of the present application. The schematic diagram of pressure calculation of surrounding rock pressure model ( Figure 2 ) in which the thickness of stratum 2 to stratum n is set to zero, which is a schematic diagram of the surrounding rock pressure of a shallow biased tunnel in a single stratum. Under the condition of a single stratum, the constructed calculation model for the surrounding rock pressure of a shallow biased tunnel in the layer can be degenerated into the calculation model for the surrounding rock pressure of a shallow biased tunnel in the standard method. Among them, the column at the top of the tunnel sinks, and the triangular blocks on both sides slide along the fracture surface through the potential slip surface. The resultant lateral resistance force on both sides of the column is calculated using formula (3) and formula (26) respectively. Since there is no load on the stratum surface (i.e. ), Equation (3) and Equation (26) can be rewritten as:

[0141]

[0142]

[0143] The weight of the triangular block and Substituting equations (6) and (29) into the above equation, we can obtain:

[0144]

[0145]

[0146] Substituting the resultant force of the lateral resistance on both sides of the column and the column self-weight stress into formula (32) we can obtain:

[0147]

[0148] The above formula is the calculation formula for the vertical pressure at the top of the tunnel in the standard method.

[0149] Substituting the resultant lateral resistance force on both sides of the column (Equations (39) and (40)) into Equations (35) and (36), we obtain:

[0150]

[0151]

[0152] The above formula is the lateral pressure coefficient of the outer and inner surrounding rocks of the tunnel in the standard method.

[0153] Under single formation conditions, the calculation model and standard method are:

[0154]

[0155]

[0156] Get the fracture angle of the surrounding rock outside and inside the tunnel and The expression is:

[0157]

[0158]

[0159] Under multi-layer strata conditions, the rupture angles of the strata outside and inside the tunnel and ( ) still uses the above formula, that is:

[0160]

[0161]

[0162] From the above verification process, it can be seen that the tunnel portal surrounding rock pressure calculation method provided in the embodiment of the present application inherits the theoretical basis of the traditional method and shows more refined mechanical adaptability under complex stratum conditions. In terms of degradation verification, when the model is simplified to a single homogeneous stratum (i.e., the number of layers ), the derived formula for the resultant lateral resistance (such as Expression), vertical surrounding rock pressure calculation formula ( ) and horizontal side pressure coefficient ( ) completely degenerates into the classic shallow-buried bias-load tunnel solution in the railway tunnel design code, proving that this method is compatible with traditional theories and has theoretical self-consistency.

[0163] Based on the same application concept, an embodiment of the present application further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the method described in the above description.

[0164] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for calculating the surrounding rock pressure at the entrance of a shallow-buried, biased-pressure tunnel, characterized in that: include: Constructing a surrounding rock pressure model for a shallow, biased tunnel in a bedding layer; the tunnel is excavated in a bedding rock mass comprising multiple strata; the surrounding rock pressure model comprises a tunnel top block, an outer block, and an inner block; wherein the tunnel top block is a block formed at the tunnel top after tunnel excavation, the outer block is a block located on a first side of the tunnel top block, and the inner block is a block located on a second side of the tunnel top block; Decomposing the outer block and the inner block into a plurality of stratigraphic blocks by layer based on the stratigraphic interface of the bedding rock mass; the outer block includes a triangular outer block of a first stratigraphic layer and a plurality of quadrilateral outer blocks of other stratigraphic layers, and the inner block includes a triangular inner block of the first stratigraphic layer and a plurality of quadrilateral inner blocks of other stratigraphic layers; Determining the lateral resistances of the triangular outer blocks and the plurality of quadrilateral outer blocks in the outer blocks in layers, and determining a first lateral resistance resultant force of the outer blocks based on the lateral resistances of the outer blocks in each layer; and determining the lateral resistances of the triangular inner blocks and the plurality of quadrilateral inner blocks in the inner blocks in layers, and determining a second lateral resistance resultant force of the inner blocks based on the lateral resistances of the inner blocks in each layer; determining a target gravity of the rock pillar directly above the tunnel based on the weight of the tunnel top block, and determining a first vertical pressure of the surrounding rock and a first horizontal pressure of the surrounding rock outside the tunnel, and a second vertical pressure of the surrounding rock and a second horizontal pressure of the surrounding rock inside the tunnel based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force; The calculation formulas for the first surrounding rock vertical pressure and the second surrounding rock vertical pressure are: in, is the target gravity, is the gravity of the rectangular block formed on the top of the tunnel, is the resistance force on the first side, is the friction angle of the potential slip surface of the first stratum, is the resultant resistance force on the second side, is the first surrounding rock vertical pressure, is the net width of the tunnel excavation, is the weight of the uppermost rock mass at the top of the tunnel, is the slope angle of the stratum interface, is the second surrounding rock vertical pressure.

2. The method according to claim 1, characterized in that The step of determining the lateral resistance of the triangular outer block comprises: Determine the stress condition of the triangle outer block; Based on the stress condition of the triangular outer block, a force balance equation and a moment balance equation of the triangular outer block are established to determine the resultant lateral resistance force of the triangular outer block acting on the first slip surface of the multi-layer stratum.

3. The method according to claim 1, characterized in that For any of the quadrilateral outer blocks, the step of determining the lateral resistance of the quadrilateral outer block comprises: Determining the stress conditions of the outer blocks of the quadrilateral; Based on the stress condition of the outer block of the quadrilateral, a force balance equation and a moment balance equation of the outer block of the quadrilateral are established to determine the resultant lateral resistance force of the outer block of the quadrilateral acting on the slip surface of the corresponding layer of the multi-layer formation.

4. The method according to claim 1, wherein The step of determining the lateral resistance of the triangular inner block comprises: Determine the stress condition of the triangle inner block; Based on the stress condition of the triangular inner block, the force balance equation and the moment balance equation of the triangular inner block are established to determine the resultant lateral resistance force of the triangular inner block acting on the first slip surface of the multi-layer stratum.

5. The method according to claim 4, characterized in that For any of the quadrilateral inner blocks, the step of determining the lateral resistance of the quadrilateral inner block comprises: Determining the stress condition of the inner block of the quadrilateral; Based on the stress conditions of the inner block of the quadrilateral, a force balance equation and a moment balance equation of the inner block of the quadrilateral are established to determine the resultant lateral resistance force of the inner block of the quadrilateral acting on the slip surface of the corresponding layer of the multi-layer stratum.

6. The method according to claim 1, characterized in that The method further comprises: determining a target gravity of the rock pillar directly above the tunnel based on the weight of the tunnel top block, and determining a first vertical pressure of the surrounding rock and a first horizontal pressure of the surrounding rock outside the tunnel, and a second vertical pressure of the surrounding rock and a second horizontal pressure of the surrounding rock inside the tunnel based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force. Determining the target gravity of the rock column directly above the tunnel based on the weight of the block at the top of the tunnel; determining the first surrounding rock vertical pressure and the second surrounding rock vertical pressure based on the target gravity, the first side resistance resultant force, and the second side resistance resultant force; The first side pressure coefficient outside the tunnel and the second side pressure coefficient inside the tunnel are determined based on the target gravity, the first side resistance resultant force and the second side resistance resultant force, and the first surrounding rock horizontal pressure and the second surrounding rock horizontal pressure are determined based on the first side pressure coefficient and the second side pressure coefficient.

7. The method according to claim 6, characterized in that The calculation formulas for the first side pressure coefficient and the second side pressure coefficient are: in, is the first side pressure coefficient, is the resultant lateral resistance of the first layer of stratum outside the tunnel, is the friction angle of the potential slip surface of the first stratum, is the potential slip surface length of the first layer of stratum outside the tunnel, is the total number of strata, For the The weight of the rock mass of the stratum, For the The thickness of the stratum rock mass on the outside, is the second side pressure coefficient, is the resultant lateral resistance of the first layer of ground inside the tunnel, The length of the potential slip surface of the first layer of strata inside the tunnel, For the The thickness of the stratigraphic rock mass on the inner side.

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