Method for predicting overburden pressure evolution on deep tunnel

Abstract

The application discloses a deep tunnel overburden soil pressure evolution prediction method, and the method comprises the following steps: for a deep underground space engineering, determining overburden soil above the tunnel to be treated; obtaining the geometric and physical basic parameters of the overburden soil, wherein the geometric and physical basic parameters comprise a tunnel diameter, a total height of the overburden soil layer, a soil bulk density and an internal friction angle; vertically dividing the overburden soil into an upper undisturbed zone, a middle soil arch zone and a lower loosened zone, and determining the undisturbed zone height of the upper undisturbed zone, the bearing arch thickness of the middle soil arch zone and the loosened zone height of the lower loosened zone, so as to establish a zoned theoretical analysis model of the overburden soil of the tunnel; and according to the geometric and physical basic parameters, the average soil pressure acting on the upper part of the tunnel is predicted through the zoned theoretical analysis model. The application constructs a model reflecting the distribution and evolution law of the soil pressure, and ensures the safe and efficient development of the deep underground space.

Description

Technical Field

[0001] This invention relates to the field of underground safety technology, and in particular to a method, system, and computer-readable storage medium for predicting the evolution of overburden pressure in deep tunnels. Background Technology

[0002] With shallow underground space becoming increasingly scarce, the development and utilization of deep underground space has become an important direction for urban development and resource utilization. Compared with shallow soil, deep underground structures bear higher ground stress, and their mechanical behavior is more complex. During the excavation of deep tunnels, the overlying soil experiences an arching effect due to uneven settlement. The arching effect controls the transmission path and magnitude of the surrounding rock load to the support structure, and its evolution directly determines the stress state of the tunnel support structure.

[0003] However, existing earth pressure theories based on tunnel models are mostly established for shallow underground structures, making it difficult to accurately reflect the true mechanical response of soil in deep underground spaces. In deep tunnels, the shear dilatation characteristics of soil are significantly weakened, and the load transfer mechanism becomes more complex. Traditional theoretical models fail to fully consider this difference and cannot accurately describe the changes in earth pressure caused by the redistribution of soil loads during deep tunnel excavation. This leads to significant deviations in the prediction of tunnel surrounding rock pressure, making it difficult to ensure the safe and efficient construction of deep underground space projects such as deep tunnels.

[0004] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0005] The main objective of this invention is to provide a method, system, terminal, and computer-readable storage medium for predicting the evolution of overburden pressure in deep tunnels. This invention aims to address the problem that existing technologies lack theoretical models that accurately reflect the distribution and evolution of overburden pressure in deep tunnels, making it difficult to accurately predict changes in overburden pressure and ensuring the safe and efficient development of deep underground spaces.

[0006] To achieve the above objectives, the present invention provides a method for predicting the evolution of overburden pressure in deep tunnels, the method comprising the following steps: For deep underground space engineering, identify the overburden soil above the tunnel that needs to be treated; Obtain the basic geometric and physical parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight, and internal friction angle; The overlying soil is vertically divided into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone. The height of the undisturbed zone in the upper part, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower part are determined to establish a zoning theoretical analysis model for the tunnel overlying soil. Among them, the central soil arch area forms a parabolic bearing arch under the action of the overlying soil pressure, and the failure mode of the lower loosening area is parabolic. Based on the aforementioned geometric and physical parameters, the average earth pressure acting above the tunnel is predicted using the zoning theory analysis model.

[0007] Optionally, in the deep tunnel overburden pressure evolution prediction method, the zoning theoretical analysis model satisfies the following assumptions: The overlying soil to be treated is a homogeneous and isotropic medium, and the overlying soil to be treated satisfies the Mohr-Coulomb yield criterion. The parabolic bearing arch and the soil in the lower loosened zone are both in a state of limit equilibrium. The height of the lower loosened zone and the arch thickness of the parabolic bearing arch dynamically evolve with the increase of tunnel stratum loss.

[0008] Optionally, the method for predicting the evolution of overburden pressure in deep tunnels, wherein predicting the average earth pressure acting above the tunnel based on the geometric and physical fundamental parameters and the zoning theory analysis model specifically includes: Based on the total height of the overlying soil layer, the height of the loosened zone, and the thickness of the bearing arch, the height of the undisturbed zone of the upper undisturbed zone is obtained. Based on the height of the undisturbed zone, the unit weight of the soil, the internal friction angle, and the tunnel diameter, the first average earth pressure acting above the middle soil arch zone is obtained. Based on the structural arch theory, the second average earth pressure acting on the top of the lower loosened zone is obtained according to the first average earth pressure and the arch thickness of the parabolic bearing arch. Boundary conditions are established based on the failure mode of the lower loosened area. According to the boundary conditions, the height of the loosened area and the tunnel diameter, the angle between any point on the parabolic slip surface of the lower loosened area and the vertical direction is obtained. Based on the stress equilibrium condition, the normal stress and shear stress acting on the parabolic slip surface are obtained from the internal friction angle and the included angle. Based on the limit equilibrium theory, using the second average earth pressure as the boundary condition, and combining the normal stress and the shear stress, the average earth pressure acting on the tunnel is obtained.

[0009] Optionally, the deep tunnel overburden pressure evolution prediction method, wherein the step of obtaining the undisturbed zone height of the upper undisturbed zone based on the total height of the overburden layer, the height of the loosened zone, and the thickness of the bearing arch, and obtaining the first average earth pressure acting above the middle soil arch zone based on the undisturbed zone height, the soil unit weight, the internal friction angle, and the tunnel diameter, specifically includes: The height of the undisturbed zone is obtained by subtracting the height of the loosened zone and the thickness of the bearing arch from the total height of the overlying soil layer; Based on the moment-free condition that the pressure line of the parabolic bearing arch coincides with the arch axis, the first expression of the parabolic bearing arch is determined, and the arch height of the parabolic bearing arch is calculated according to the internal friction angle using the boundary condition of the slope of the first expression at the arch foot. Based on the soil unit weight, the height of the undisturbed zone, the arch height, and the tunnel diameter, the non-uniformly distributed vertical stress acting at any point above the central soil arch area is integrated along the horizontal projection range of the arch and divided by the tunnel diameter to obtain the first average earth pressure acting above the central soil arch area. ; in, This represents the first average earth pressure. This indicates the diameter of the tunnel. This indicates the unit weight of the soil. This indicates the height of the undisturbed region. Represents any variable in the horizontal direction. Represents the differential unit in the vertical direction. This indicates the height of the arch.

[0010] Optionally, the deep tunnel overburden pressure evolution prediction method, wherein the second average earth pressure acting on the top of the lower loosened zone is obtained based on the structural arch theory, according to the first average earth pressure and the arch thickness of the parabolic bearing arch, specifically includes: Using the arch thickness of the parabolic bearing arch as a geometric parameter, the differential element of the parabolic bearing arch is obtained from the central soil arch region; Based on the assumption in the structural arch theory that the internal moment of the parabolic bearing arch differential unit at any position is zero, a moment balance condition at the arch crown is established, and the horizontal thrust at the arch foot is obtained according to the moment balance condition. Using the first average earth pressure as the input pressure, and combining it with the boundary conditions of the vertical stress at the top of the lower loosened zone, the vertical equilibrium equation of the parabolic bearing arch differential element is established. The vertical equilibrium equation is solved using the finite difference method to obtain the vertical stress acting on the upper boundary of the lower loosened zone. This vertical stress is then integrated along the tunnel diameter and averaged to obtain the second average earth pressure acting on the top of the lower loosened zone. ; in, This represents the second average earth pressure. This indicates the vertical stress. Represents the differential unit in the horizontal direction. In the finite difference method, the first... s +1 vertical coordinates at depth nodes.

[0011] Optionally, the deep tunnel overburden pressure evolution prediction method, wherein establishing boundary conditions based on the failure morphology of the lower loosened zone, and obtaining the angle between any point on the parabolic slip surface of the lower loosened zone and the vertical direction according to the boundary conditions, the height of the loosened zone, and the tunnel diameter, specifically includes: Based on the parabolic nature of the failure morphology of the lower loosened area, the slip surface of the lower loosened area is expressed as a parabolic shape. The angle between the bottom of the parabolic sliding surface and the bottom of the vertical direction is obtained based on the height of the loosened area and the diameter of the tunnel. Based on the boundary conditions established by the parabolic slip surface, these boundary conditions are substituted into the parabolic shape expression, and combined with the bottom included angle, the second expression of the parabolic slip surface is determined: ; in, y This represents the second expression. This represents the angle between the bottom of the parabolic sliding surface and the bottom in the vertical direction; Differentiating the second expression of the parabolic slip surface determines the angle between any point on the parabolic slip surface and the vertical direction. : ; in, This represents any point on the parabolic sliding surface of the lower loosening zone.

[0012] Optionally, the method for predicting the evolution of overburden pressure in deep tunnels, wherein obtaining the normal stress and shear stress acting on the parabolic slip surface based on the internal friction angle and the included angle according to the stress balance condition, specifically includes: The Rankine passive lateral earth pressure coefficient is determined based on the internal friction angle. Based on the stress equilibrium condition, and considering the stress equilibrium of the parabolic bearing arch differential element at the parabolic slip surface, combined with the included angle and the Rankine passive lateral earth pressure coefficient, the normal stress and the shear stress are obtained: ; ; in, This represents the normal stress. This represents the shear stress. This represents the Rankine passive lateral earth pressure coefficient. Indicates the minimum principal stress. This represents the angle between the direction of the major principal stress and the vertical direction. The value taken at a specific location.

[0013] Optionally, the method for predicting the evolution of overburden pressure in deep tunnels, wherein the step of obtaining the average earth pressure acting on the tunnel based on the limit equilibrium theory, using the second average earth pressure as the boundary condition, and combining the normal stress and the shear stress, specifically includes: Using the second average earth pressure as the boundary condition, the parabolic bearing arch differential element is obtained from any depth of the lower loosening zone. Under the assumption that the minor principal stress at any point on the parabolic bearing arch differential element changes linearly along the principal stress trajectory, the resultant force of the minor principal stress at the upper boundary and the resultant force of the minor principal stress at the lower boundary acting on the parabolic bearing arch differential element are solved respectively. Calculate the vertical force acting on the two sliding surfaces based on the normal stress and the shear stress on the two sliding surfaces; Based on the resultant force of the minor principal stresses at the upper boundary, the resultant force of the minor principal stresses at the lower boundary, and the vertical forces on the sliding surfaces on both sides, the vertical force equilibrium equation of the parabolic bearing arch differential element is established. The vertical force equilibrium equations are solved using the finite difference method to obtain the minor principal stresses acting above the tunnel. Based on the geometric relationship of the Mohr stress circle, the vertical stress in the lower loosening zone is obtained according to the minor principal stress acting above the tunnel. The average earth pressure acting on the tunnel is obtained by integrating the vertical stress along the tunnel diameter and taking the average. ; in, This represents the average earth pressure acting on the tunnel. This indicates the vertical stress within the lower loosened area. Indicates slip surface M The minor principal stress at the point, Represents the minor principal stress and slip surface at any point M The height difference of the minor principal stress at the location, The differential element represents the angle of deflection of the major principal stress direction.

[0014] Furthermore, to achieve the above objectives, the present invention also provides a deep tunnel overburden pressure evolution prediction system, wherein the deep tunnel overburden pressure evolution prediction system includes: The processing object confirmation module is used to identify the overburden soil above the tunnel to be processed for deep underground space engineering. The basic parameter acquisition module is used to acquire the geometric and physical basic parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight, and internal friction angle. The analysis model construction module is used to vertically divide the overlying soil into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone, and to determine the height of the undisturbed zone in the upper undisturbed zone, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower loosened zone, so as to establish a zonal theoretical analysis model of the tunnel overlying soil; wherein, the middle soil arch zone forms a parabolic bearing arch under the action of overlying soil pressure, and the failure mode of the lower loosened zone is parabolic; The pressure prediction module is used to predict the average earth pressure acting above the tunnel based on the geometric and physical basic parameters and the partition theory analysis model.

[0015] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a deep tunnel overburden pressure evolution prediction program, and the deep tunnel overburden pressure evolution prediction program, when executed by a processor, implements the steps of the deep tunnel overburden pressure evolution prediction method as described above.

[0016] In this invention, for deep underground space engineering, the overburden soil to be treated above the tunnel is determined; the basic geometric and physical parameters of the overburden soil are obtained, including: tunnel diameter, total height of the overburden layer, soil unit weight, and internal friction angle; the overburden soil is vertically divided into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone, and the height of the undisturbed zone in the upper undisturbed zone, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower loosened zone are determined to establish a zonal theoretical analysis model for the tunnel overburden soil; wherein, the middle soil arch zone forms a parabolic bearing arch under the action of overburden soil pressure, and the failure mode of the lower loosened zone is parabolic; based on the basic geometric and physical parameters, the average earth pressure acting above the tunnel is predicted through the zonal theoretical analysis model. This invention constructs a model reflecting the distribution and evolution of earth pressure, ensuring the safe and efficient development of deep underground spaces. Attached Figure Description

[0017] Figure 1 This is a flowchart of a preferred embodiment of the deep tunnel overburden pressure evolution prediction method of the present invention; Figure 2 This is a diagram of the architecture of the zoning theory analysis model in the deep tunnel overburden pressure evolution prediction method of this invention; Figure 3 This is a force analysis diagram of the parabolic bearing arch in the deep tunnel overburden pressure evolution prediction method of this invention; Figure 4This is a diagram illustrating the variation of the shear zone inclination angle with the increase of tunnel stratum loss in the deep tunnel overburden pressure evolution prediction method of this invention. Figure 5 This is a geometric relationship diagram of the Mohr stress circle in the deep tunnel overburden pressure evolution prediction method of the present invention; Figure 6 This is a force analysis diagram of the parabolic bearing arch differential element in the deep tunnel overburden pressure evolution prediction method of the present invention; Figure 7 This is a graph showing the relationship between soil pressure and discrete quantities in the deep tunnel overburden soil pressure evolution prediction method of this invention; Figure 8 This is a comparison chart of theoretical values ​​and numerical simulation results in the deep tunnel overburden pressure evolution prediction method of this invention; Figure 9 This is a graph showing the variation of the bearing arch thickness with the increase of tunnel stratum loss in the deep tunnel overburden pressure evolution prediction method of this invention. Figure 10 This is a graph showing the relationship between the soil arch ratio and tunnel displacement calculated by different theoretical methods when the total soil height is 30m in the deep tunnel overburden pressure evolution prediction method of this invention. Figure 11 This is a graph showing the relationship between the soil arch ratio and tunnel displacement calculated by different theoretical methods when the total soil height is 90m in the deep tunnel overburden pressure evolution prediction method of this invention. Figure 12 This is a structural diagram of a preferred embodiment of the deep tunnel overburden pressure evolution prediction system of the present invention; Figure 13 This is a structural diagram of a preferred embodiment of the terminal of the present invention. Detailed Implementation

[0018] This application provides a method, system, and terminal for predicting the evolution of overburden pressure in deep tunnels. To make the objectives, technical solutions, and effects of this application clearer and more explicit, the following detailed description is provided with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining this application and are not intended to limit this application.

[0019] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0020] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0021] The preferred embodiment of the present invention describes a method for predicting the evolution of overburden pressure in deep tunnels, such as... Figure 1 The method for predicting the evolution of overburden pressure in deep tunnels includes the following steps: Step S10: For deep underground space engineering, determine the overburden soil to be treated above the tunnel.

[0022] In this embodiment, for deep underground space engineering, the overburden soil above the tunnel to be treated is first determined. This overburden soil is the range of soil and rock mass that needs to be analyzed for earth pressure change. Vertically, it extends from the top of the tunnel to the ground surface or the upper boundary specified in the design, and horizontally it covers at least the area corresponding to the tunnel diameter. This provides a clear analysis object and geometric boundary for the subsequent establishment of a zonal theoretical analysis model and calculation of average earth pressure.

[0023] Step S20: Obtain the basic geometric and physical parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight, and internal friction angle.

[0024] Specifically, the geometric and physical parameters of the overlying soil to be processed are obtained, including the tunnel diameter. B Total height of overlying soil layer C Soil bulk density γ and internal friction angle φ Tunnel diameter B The horizontal span of the underground structure's roof slab or tunnel slab, and the total height of the overlying soil layer. C This is the vertical distance from the tunnel top surface to the ground surface or the design upper boundary. These two geometric parameters together define the computational domain of the soil being analyzed, where the tunnel diameter... B The horizontal integration interval is determined, and the total height of the overlying soil layer is determined. C Height of the loosened area h loo and the thickness of the arch h pro Together, they determined the extent of the upper undisturbed zone.

[0025] Soil unit weight γ Angle of friction with soil φ These are key parameters describing the physical and mechanical properties of the overlying soil. Among them, the soil unit weight... γ The internal friction angle φ reflects the magnitude of the soil's self-weight load and directly determines the initial geostress field and the subsequent vertical stress distribution in each zone. The internal friction angle φ characterizes the shear strength of the soil under the limit equilibrium state. The soil weight and internal friction angle are obtained through laboratory tests according to the relevant geotechnical test procedures (National Standard GB / T 50123). For example, the soil weight can be calculated by weighing and drying the undisturbed soil sample using the ring cutter method. The internal friction angle can be determined by direct shear test or triaxial compression test and obtained by drawing the Mohr-Coulomb strength envelope.

[0026] Step S30: Vertically divide the overlying soil into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone, and determine the height of the undisturbed zone in the upper undisturbed zone, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower loosened zone, in order to establish a zoning theoretical analysis model for the tunnel overlying soil.

[0027] Understandably, based on numerical simulation and experimental results, this invention establishes a zoning theoretical analysis model for the tunnel overburden, vertically dividing the tunnel overburden into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone. In the undisturbed zone, the soil stress is close to its own weight stress. The middle soil arch zone forms a parabolic bearing arch under the pressure of the overburden, and the failure mode of the lower loosened zone is parabolic.

[0028] Specifically, the central soil arch zone forms a load-bearing arch under the action of overlying soil pressure, which is responsible for transferring the upper load to the arch foot. When the tunnel displacement is small, the soil arch zone is in a state of limit equilibrium. At this time, the soil arch zone is a potential failure surface and is not yet completely stable. Local failure is likely to occur in the stress concentration area, and part of the load of the soil arch zone needs to be borne by the lower loose zone.

[0029] The loosened zone, as the main area of ​​failure, develops in a parabolic pattern. Due to the large displacement and plastic state in this area, the soil inside the loosened zone will experience uneven settlement under the constraint of the frictional resistance of the shear surfaces on both sides, which will cause a significant deflection of the principal stress direction, resulting in a substantial reduction in the earth pressure acting on the tunnel.

[0030] The theoretical analysis model established in this invention, such as Figure 2 As shown in (a), the model illustrates the development of different regions of the overburden soil of the tunnel with displacement. Under different displacements, the model consists of an undisturbed zone, a parabolic bearing arch zone, and a loosened zone. Furthermore, as the tunnel displacement increases, the loosened zone and the soil arch zone gradually increase, while the undisturbed zone gradually decreases. Figure 2 (b) in the model presents the load transfer mechanism above the tunnel. In this model, the self-weight load of the soil in the undisturbed upper zone is borne by the parabolic bearing arch and transferred to the arch feet on both sides. At the same time, due to uneven settlement in the loosened zone, the direction of the principal stress rotates significantly, and the trajectory of the major principal stress is assumed to be a circular arch.

[0031] Furthermore, based on the aforementioned zoning theory analysis model, this embodiment makes the following assumptions: the overburden to be treated is a homogeneous and isotropic medium; the overburden to be treated satisfies the Mohr-Coulomb yield criterion; the parabolic bearing arch and the soil in the lower loosened zone are both in a state of limit equilibrium; the height of the lower loosened zone and the arch thickness of the parabolic bearing arch dynamically evolve with the increase of tunnel stratum loss. These assumptions are to provide a theoretical description of the stress-deformation behavior of the overburden to be treated, and these three assumptions together constitute the physical basis of the zoning theory analysis model of this calculation method.

[0032] Step S40: Based on the aforementioned geometric and physical fundamental parameters, the average earth pressure acting above the tunnel is predicted using the partitioning theory analysis model.

[0033] Based on the total height of the overlying soil layer, the height of the loosened zone, and the thickness of the bearing arch, the height of the undisturbed zone of the upper undisturbed zone is obtained. Based on the height of the undisturbed zone, the unit weight of the soil, the internal friction angle, and the tunnel diameter, the first average earth pressure acting above the middle soil arch zone is obtained.

[0034] Specifically, the height of the loosened zone and the thickness of the bearing arch are subtracted from the total height of the overlying soil layer to obtain the height of the undisturbed zone of the upper undisturbed zone; Based on the moment-free condition that the pressure line of the parabolic bearing arch coincides with the arch axis, the first expression of the parabolic bearing arch is determined, and the arch height of the parabolic bearing arch is calculated according to the internal friction angle using the boundary condition of the slope of the first expression at the arch foot. Based on the soil unit weight, the height of the undisturbed zone, the arch height, and the tunnel diameter, the non-uniformly distributed vertical stress acting at any point above the central soil arch area is integrated along the horizontal projection range of the arch and divided by the tunnel diameter to obtain the first average earth pressure acting above the central soil arch area. ; in, This represents the first average earth pressure. This indicates the diameter of the tunnel. This indicates the unit weight of the soil. This indicates the height of the undisturbed region. Represents any variable in the horizontal direction. Represents the differential unit in the vertical direction. This indicates the height of the arch.

[0035] Understandably, the load transfer path in the parabolic bearing arch region is similar to that of a structural arch, making the quantification of earth pressure in this region using a physical structural arch approach quite applicable. This effectively simplifies the calculation while ensuring the accuracy of the results. This paper assumes that the soil arch region is a concentric parabolic bearing arch, such as... Figure 3 As shown, the load-bearing arch satisfies the no-bending-moment condition of a physical structural arch, that is, its pressure line coincides with the arch axis. From this, the first expression for the load-bearing arch line of the earth arch in the form of a quadratic parabola can be derived: (1) in, This represents the first expression, i.e., the ordinate of the parabolic arch. Indicates the height of the arch. B This indicates the diameter of the tunnel. It represents any variable in the horizontal direction.

[0036] Furthermore, based on the Mohr-Coulomb failure criterion, under the limit equilibrium condition, it can be known that the angle between the maximum principal stress and the horizontal direction is 45° + 10°. φ / 2. Based on the above conclusions, the model in this invention adopts the same assumptions, assuming that the axis of the earth arch forms a 45° angle with the horizontal direction at the arch foot. φ An angle of / 2. Therefore, when x = B / At time 2, the angle of inclination between the arch axis and the horizontal direction is The slope at the arch foot is Substituting these values ​​into formula (1), the arch height can be obtained: (2) Therefore, the non-uniformly distributed vertical stress acting at any x point above the soil arch area It can be represented as: (3) in, The height of the undisturbed upper undisturbed zone is obtained by subtracting the height of the loosened zone and the thickness of the bearing arch from the total height of the overlying soil layer.

[0037] Integrate formula (3) along the horizontal projection interval of the arch and divide by the tunnel diameter. B The first average earth pressure (load) acting above the central earth arch area can be obtained: (4) Furthermore, based on the structural arch theory, the second average earth pressure acting on the top of the lower loosened zone is obtained according to the first average earth pressure and the arch thickness of the parabolic bearing arch.

[0038] Specifically, using the arch thickness of the parabolic bearing arch as a geometric parameter, the differential unit of the parabolic bearing arch is obtained from the central soil arch region; Based on the assumption in the structural arch theory that the internal moment of the parabolic bearing arch differential unit at any position is zero, a moment balance condition at the arch crown is established, and the horizontal thrust at the arch foot is obtained according to the moment balance condition. Using the first average earth pressure as the input pressure, and combining it with the boundary conditions of the vertical stress at the top of the lower loosened zone, the vertical equilibrium equation of the parabolic bearing arch differential element is established. The vertical equilibrium equation is solved using the finite difference method to obtain the vertical stress acting on the upper boundary of the lower loosened zone. This vertical stress is then integrated along the tunnel diameter and averaged to obtain the second average earth pressure acting on the top of the lower loosened zone. ; in, This represents the second average earth pressure. This indicates the vertical stress. Represents the differential unit in the horizontal direction. In the finite difference method, the first... s+ Vertical coordinates at a depth node.

[0039] like Figure 3 As shown, in this embodiment, an arbitrary parabolic bearing arch differential element is taken for the soil arch region, and the load is applied at any position on the upper boundary of the differential element. x The non-uniformly distributed vertical stress at a certain point can be expressed as: (5) in, The vertical stress at the crown of the arch acts on the arbitrary upper boundary of the arch-shaped differential element. x The difference between the vertical stress at point A and the vertical stress at point B is _____. .

[0040] For formula (5) along the tunnel diameter B Integrating, we can obtain the average vertical stress acting on the upper boundary of the differential element: (6) Similarly, the average vertical stress acting on the lower boundary of the differential element Represented as: (7) The specificity of the parabolic differential unit is: (8) in, This indicates the specific weight of the parabolic differential unit. This indicates the length of the arch supported by the parabola. Represents the differential unit in the vertical direction. This indicates the height of the arch.

[0041] The parabolic bearing arch length is obtained by integrating formula (1) along the tunnel diameter: (9) Assuming the internal moment at any point in the arch is zero, and establishing the moment equilibrium condition at the arch crown, then the horizontal thrust at the arch corners... dF h It can be calculated using the following formula: (10) In addition, the horizontal thrust at the arch foot can be represented by the vertical stress and lateral pressure coefficient at the lower boundary of the differential element: (11) Combining formulas (10) and (11), for Figure 3 The vertical equilibrium equations for the differential unit shown can be established as follows: (12) Because there is information about formula (12) z Since the function cannot be given a general solution expression, formula (12) can be solved using the finite difference method: (13) Combining formulas (12) and (13), and simplifying, we can obtain the vertical stress acting on the upper boundary of the loosened zone as: ; (14) Substitute formula (14) into formula (5) along the tunnel diameter B Perform the integration and divide by the length of the integration interval. B The second average earth pressure acting on the top of the loosened zone can be obtained: . (15) Furthermore, boundary conditions are established based on the failure mode of the lower loosened area. Based on the boundary conditions, the height of the loosened area, and the diameter of the tunnel, the angle between any point on the parabolic slip surface of the lower loosened area and the vertical direction is obtained.

[0043] Specifically, based on the parabolic nature of the failure morphology of the lower loosening zone, the slip surface of the lower loosening zone is set as a parabolic expression; The angle between the bottom of the parabolic sliding surface and the bottom of the vertical direction is obtained based on the height of the loosened area and the diameter of the tunnel. Based on the boundary conditions established by the parabolic slip surface, these boundary conditions are substituted into the parabolic shape expression, and combined with the bottom included angle, the second expression of the parabolic slip surface is determined: ; in, This represents the second expression. This represents the angle between the bottom of the parabolic sliding surface and the bottom in the vertical direction; Differentiating the second expression of the parabolic slip surface determines the angle between any point on the parabolic slip surface and the vertical direction. : ; in, This represents any point on the parabolic sliding surface of the lower loosening zone.

[0044] It is understandable that in the deep underground space environment where deep tunnels are located, as tunnel displacement increases, the failure mode mainly exhibits a parabolic shape, and the height of the parabola changes with the increase of tunnel displacement. Therefore, this embodiment assumes that the shear zone of the loosened area is parabolic, and the general expression of the parabola is: (16) according to Figure 3 The parabolic slip surface shown is given the following boundary conditions: x=B / 2 , ; x=0 , ; x=0 , z=0 Substituting the boundary conditions into formula (16), the second expression for the parabolic slip surface is obtained as follows: y (17) in, This represents the angle between the bottom of the parabolic slip surface and the bottom of the vertical direction, which varies with the vertical displacement distance of the tunnel.

[0045] The height of the loosened area can be obtained according to formula (17). h loo for: (18) In this formula, αThe angle between the bottom of the slip surface and the vertical direction is the angle between the slip surface and the vertical direction. This parameter can be determined by inversion from the experimental results and is used to describe the geometric characteristics of the slip surface.

[0046] like Figure 4 As shown, by varying the dip angle of the sliding surface under different burial depth conditions... α Vertical displacement of the soil above the tunnel δ (After dimensionless conversion) δ / B To perform nonlinear regression analysis, its functional expression is established as follows: ; in, δ This refers to the vertical displacement of the soil above the tunnel. B The diameter of the tunnel. δ / B It is a dimensionless displacement ratio used to describe the degree of ground loss caused by tunnel excavation; a and b These are the fitting parameters determined through nonlinear regression analysis. a The value range is 87.798~89.286. b The value range is 0.11 to 0.16.

[0047] any point on the parabola xi , zi The angle between point ) and the vertical direction The slope that can be passed through this point Sure: (19) Considering the parabolic slip surface about z Axisymmetric, only need to be taken during analysis x ∈[ 0,B / 2]. Substituting formula (19) into formula (17), we can obtain the included angle at any position. for: (20) Furthermore, based on the stress equilibrium condition, the normal stress and shear stress acting on the parabolic slip surface are obtained from the internal friction angle and the included angle.

[0048] Specifically, the Rankine passive lateral earth pressure coefficient is determined based on the internal friction angle; Based on the stress equilibrium condition, and considering the stress equilibrium of the parabolic bearing arch differential element at the parabolic slip surface, combined with the included angle and the Rankine passive lateral earth pressure coefficient, the normal stress and the shear stress are obtained: ; ; in, This represents the normal stress. This represents the shear stress. This represents the Rankine passive lateral earth pressure coefficient. Indicates the minimum principal stress. This represents the angle between the direction of the major principal stress and the vertical direction. The value taken at a specific location.

[0049] Understandably, considering the principal stress deflection caused by tunnel settlement is crucial for determining the overlying soil pressure. In theoretical calculations, existing techniques mainly use equations for trajectories such as catenaries, circular arcs, and parabolas to reflect the influence of soil arching on the lateral pressure coefficient, which neglects the non-uniformity of the principal stresses. Therefore, this embodiment employs the arched differential element method to analyze the impact of principal stress deflection on earth pressure.

[0050] like Figure 5 Based on the geometric relationship of the Mohr's circle in the figure, the vertical stress and horizontal stress can be expressed as follows: (21-1) (21-2) (21-3) in, and These are the maximum and minimum principal stresses, respectively.

[0051] Furthermore, the determination of the Rankine passive lateral earth pressure coefficient based on the internal friction angle can be expressed as: ;(twenty two) Based on the arched differential element defined by the principal stress trajectory, the normal stress and shear stress of the soil element on the slip surface are expressed as follows: and Based on the triangular element at the point M The stress equilibrium condition at the point can be expressed as follows: (23-1) (23-2) Substituting equation (22) into equations (23-1) and (23-2), the normal stress and shear stress are further expressed as: (24-1) (24-2) Furthermore, based on the limit equilibrium theory, using the second average earth pressure as the boundary condition, and combining the normal stress and the shear stress, the average earth pressure acting on the tunnel is obtained.

[0052] Specifically, using the second average earth pressure as the boundary condition, the parabolic bearing arch differential element is obtained from any depth of the lower loosening zone. Under the assumption that the minor principal stress at any point on the parabolic bearing arch differential element changes linearly along the principal stress trajectory, the resultant force of the minor principal stress at the upper boundary and the resultant force of the minor principal stress at the lower boundary acting on the parabolic bearing arch differential element are solved respectively. Calculate the vertical force acting on the two sliding surfaces based on the normal stress and the shear stress on the two sliding surfaces; Based on the resultant force of the minor principal stresses at the upper boundary, the resultant force of the minor principal stresses at the lower boundary, and the vertical forces on the sliding surfaces on both sides, the vertical force equilibrium equation of the parabolic bearing arch differential element is established. The vertical force equilibrium equations are solved using the finite difference method to obtain the minor principal stresses acting above the tunnel. Based on the geometric relationship of the Mohr stress circle, the vertical stress in the lower loosening zone is obtained according to the minor principal stress acting above the tunnel. The average earth pressure acting on the tunnel is obtained by integrating the vertical stress along the tunnel diameter and taking the average. ; in, This represents the average earth pressure acting on the tunnel. This indicates the vertical stress within the lower loosened area. ， Indicates slip surface M The minor principal stress at the point, Represents the minor principal stress and slip surface at any point M The height difference of the minor principal stress at the location, The differential element represents the angle of deflection of the major principal stress direction.

[0053] like Figure 6 As shown, in this embodiment, an arched differential element is taken at any depth of the loosened area for stress analysis, with a thickness of [missing information]. dz Width is The action is applied to the arbitrary boundary of the arched differential element. x The minor principal stress is Acting on the slip surface M The minor principal stress at the location is any point x minor principal stress and M The height difference of the minor principal stress at the location is Assuming minor principal stress It varies linearly with height along the principal stress trajectory, and its expression is: (25) in, , , R MN Let be the radius of the arc segment at the upper boundary of the arched differential unit. Similarly, the radius of the arc segment at the lower boundary can be expressed as: .

[0054] Furthermore, the resultant force of the minor principal stresses acting on the upper boundary of the arched differential element for: (26) Substituting formula (25) into formula (26) and solving, we get: (27) in, .

[0055] Similarly, the action applied to the lower boundary arc R MN’ The combined force It can be represented as: (28) Based on the symmetry of the theoretical model, the vertical forces on the two slip surfaces can be expressed as: (29) Substituting formulas (24-1) and (24-2) into formula (29), we get: (30) in, .

[0056] Furthermore, the specific weight of the arched differential element is approximated as: (31) in, and Let be the arc lengths of the upper and lower boundaries of the arched differential unit, respectively, which can be expressed as: (32) (33) right Figure 5 Vertical force equilibrium analysis of the arched differential element shown yields the following results: (34) Substituting formulas (27), (28), (30), and (31) into formula (34), we get: (35) in, , .

[0057] It is understandable that in formula (35) It is about z Since the function cannot provide a general solution expression, the finite difference method is also used to solve it: (36) By combining equations (35) and (36), the minor principal stresses acting above the tunnel can be obtained. for: ; (37) Substituting formula (37) into formula (25) and combining it with formula (21), we can obtain the average earth pressure acting on the tunnel: (38) Solving formula (38) further yields: (39) in, .

[0058] Furthermore, this invention verifies the performance of the newly established model: when calculating the earth pressure distribution in the soil arching and loosening zones, the presence of nonlinear differential equations makes it difficult to directly obtain the analytical general solution. Therefore, this paper employs the finite difference method for numerical discretization. The finite difference method discretizes the continuous solution domain into finite nodes, using difference approximations to replace differentials, transforming the differential equations into a system of algebraic equations for solution. However, the accuracy of discretization directly affects the accuracy of the calculation results. Therefore, it is necessary to optimize the number of discretized nodes while ensuring computational accuracy, in order to reduce the number of iterations and improve computational efficiency.

[0059] like Figure 7 As shown, earth pressure varies with discrete quantities. n The changes show that as the number of discrete elements increases, the residual earth pressure in the soil arch zone gradually increases, while the earth pressure acting on the tunnel from the loosened zone gradually decreases. Specifically, the soil arch zone... n When the value is less than 10, the earth pressure fluctuates significantly, and the calculation accuracy decreases markedly. n When the value is ≥10, the earth pressure in both regions tends to level off, with the change in earth pressure being less than 1%. Therefore, this embodiment selects... n =30 is used as a discrete number, which ensures both calculation accuracy and reduces the difficulty of calculation.

[0060] like Figure 8 The figure shows a comparison between the newly established theoretical model and the numerical simulation results, where the internal friction angle is 34° and the arch thickness is... h pro according to Figure 9 It has been confirmed that the tunnel diameter is 0.1m. From Figure 8 It can be seen that as the tunnel displacement increases, the soil arch ratio first decreases rapidly, then decreases slowly, and finally tends to stabilize, exhibiting typical three-stage characteristics. The comparison results show that the theoretical value and the numerical simulation results of this method are highly consistent in both numerical magnitude and trend, thus the theoretical model has good reliability.

[0061] like Figure 9 As shown, the normalized bearing arch thickness varies under different burial depths. h pro / B and normalized displacement δ / B The relationship between them. The results show that, h pro / B Follow δ / B The value increases with the increase of [variable name], showing a good linear relationship. Through linear regression analysis, an empirical formula was established: h pro / B = k (δ / B) + m ;in, k and m These are the fitting parameters determined through linear regression analysis. k Take 1.478, m The value range is 1.205 to 1.765.

[0062] To compare the results of the newly established theoretical model with those of numerical simulations, the peak friction angle and residual friction angle used in the theoretical calculations were derived from material strength parameters determined under different confining pressures. At the maximum arch stage, the arch thickness of the bearing arch... hpro The value range is 0.8 B Up to 1.4 B In the ultimate limit state, the thickness of the load-bearing arch ranges from 1.2. B Up to 1.8 B .from Figure 7 It can be seen that as tunnel displacement increases, the soil arch ratio first decreases rapidly, then decreases slowly, and finally stabilizes, exhibiting a typical three-stage characteristic. Furthermore, in the maximum arch stage, the soil pressure also increases with increasing burial depth. The comparative results show that the theoretical values ​​and numerical simulation results of this method are in high agreement in both numerical magnitude and trend, thus demonstrating the good reliability of the theoretical model.

[0063] like Figure 10 and Figure 11 As shown, graphs depicting the relationship between the soil arch ratio calculated using different theoretical methods and tunnel displacement are presented for soil layer heights of 30m and 90m, respectively. Figure 8 and Figure 9It is known that under deep tunnels, both model tests and numerical simulations exhibit a three-stage evolution characteristic of "rapid decrease—slow decrease—tend to stability". The theoretical model newly developed in this method can reflect this trend well, but the decrease obtained from its calculation results is slightly greater than that of the test and simulation results. In contrast, the calculation methods in the existing technology show a slow increase in theoretical results with increasing tunnel displacement. This trend is consistent with the changes in earth pressure in shallow layers, but it cannot effectively reflect the evolution mechanism of soil arching in the deep underground space environment where deep tunnels are located. In addition, the Terzaghi theory assumes that the height of the soil arch is twice the tunnel diameter (2... B This method can only solve for the soil arch in the limit state, but cannot reveal the gradual development process of the soil arch, resulting in the calculation results remaining unchanged (linear). Therefore, the calculation results of the theoretical model of this method can better reflect the changing trend of the overburden pressure in deep tunnels.

[0064] Furthermore, such as Figure 12 As shown, based on the above-mentioned method for predicting the evolution of overburden pressure in deep tunnels, this invention also provides a system for predicting the evolution of overburden pressure in deep tunnels, wherein the system includes: The processing object confirmation module 51 is used to determine the overburden soil to be processed above the tunnel for deep underground space engineering. The basic parameter acquisition module 52 is used to acquire the geometric and physical basic parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight and internal friction angle; The analysis model construction module 53 is used to vertically divide the overlying soil into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone, and to determine the height of the undisturbed zone in the upper undisturbed zone, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower loosened zone, so as to establish a zonal theoretical analysis model of the tunnel overlying soil; wherein, the middle soil arch zone forms a parabolic bearing arch under the action of overlying soil pressure, and the failure mode of the lower loosened zone is parabolic; The pressure prediction module 54 is used to predict the average earth pressure acting above the tunnel based on the geometric and physical basic parameters and the partition theory analysis model.

[0065] Furthermore, such as Figure 13 As shown, based on the above-mentioned method and system for predicting the evolution of overburden pressure in deep tunnels, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 13 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0066] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the terminal. Further, the memory 20 may include both internal and external storage units of the terminal. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code installed on the terminal. The memory 20 may also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a deep tunnel overburden pressure evolution prediction program 40, which can be executed by the processor 10 to implement the deep tunnel overburden pressure evolution prediction method of this application.

[0067] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the deep tunnel overburden pressure evolution prediction method.

[0068] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The components of the terminal communicate with each other via a system bus.

[0069] In one embodiment, when processor 10 executes the deep tunnel overburden pressure evolution prediction program 40 in memory 20, the following steps are performed: For deep underground space engineering, identify the overburden soil above the tunnel that needs to be treated; Obtain the basic geometric and physical parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight, and internal friction angle; The overlying soil is vertically divided into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone. The height of the undisturbed zone in the upper part, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower part are determined to establish a zoning theoretical analysis model for the tunnel overlying soil. Among them, the central soil arch area forms a parabolic bearing arch under the action of the overlying soil pressure, and the failure mode of the lower loosening area is parabolic. Based on the aforementioned geometric and physical parameters, the average earth pressure acting above the tunnel is predicted using the zoning theory analysis model.

[0070] The partitioning theory analysis model satisfies the following assumptions: The overlying soil to be treated is a homogeneous and isotropic medium, and the overlying soil to be treated satisfies the Mohr-Coulomb yield criterion. The parabolic bearing arch and the soil in the lower loosened zone are both in a state of limit equilibrium. The height of the lower loosened zone and the arch thickness of the parabolic bearing arch dynamically evolve with the increase of tunnel stratum loss.

[0071] Specifically, the prediction of the average earth pressure acting above the tunnel based on the aforementioned geometric and physical fundamental parameters and through the zoning theory analysis model includes: Based on the total height of the overlying soil layer, the height of the loosened zone, and the thickness of the bearing arch, the height of the undisturbed zone of the upper undisturbed zone is obtained. Based on the height of the undisturbed zone, the unit weight of the soil, the internal friction angle, and the tunnel diameter, the first average earth pressure acting above the middle soil arch zone is obtained. Based on the structural arch theory, the second average earth pressure acting on the top of the lower loosened zone is obtained according to the first average earth pressure and the arch thickness of the parabolic bearing arch. Boundary conditions are established based on the failure mode of the lower loosened area. According to the boundary conditions, the height of the loosened area and the tunnel diameter, the angle between any point on the parabolic slip surface of the lower loosened area and the vertical direction is obtained. Based on the stress equilibrium condition, the normal stress and shear stress acting on the parabolic slip surface are obtained from the internal friction angle and the included angle. Based on the limit equilibrium theory, using the second average earth pressure as the boundary condition, and combining the normal stress and the shear stress, the average earth pressure acting on the tunnel is obtained.

[0072] Specifically, the step of obtaining the undisturbed zone height of the upper undisturbed zone based on the total height of the overlying soil layer, the height of the loosened zone, and the thickness of the bearing arch, and obtaining the first average earth pressure acting above the middle soil arch zone based on the undisturbed zone height, the soil unit weight, the internal friction angle, and the tunnel diameter, includes: The height of the undisturbed zone is obtained by subtracting the height of the loosened zone and the thickness of the bearing arch from the total height of the overlying soil layer; Based on the moment-free condition that the pressure line of the parabolic bearing arch coincides with the arch axis, the first expression of the parabolic bearing arch is determined, and the arch height of the parabolic bearing arch is calculated according to the internal friction angle using the boundary condition of the slope of the first expression at the arch foot. Based on the soil unit weight, the height of the undisturbed zone, the arch height, and the tunnel diameter, the non-uniformly distributed vertical stress acting at any point above the central soil arch area is integrated along the horizontal projection range of the arch and divided by the tunnel diameter to obtain the first average earth pressure acting above the central soil arch area. ; in, This represents the first average earth pressure. This indicates the diameter of the tunnel. This indicates the unit weight of the soil. This indicates the height of the undisturbed region. Represents any variable in the horizontal direction. Represents the differential unit in the vertical direction. This indicates the height of the arch.

[0073] Specifically, based on the structural arch theory, the second average earth pressure acting on the top of the lower loosened zone is obtained according to the first average earth pressure and the arch thickness of the parabolic bearing arch, including: Using the arch thickness of the parabolic bearing arch as a geometric parameter, the differential element of the parabolic bearing arch is obtained from the central soil arch region; Based on the assumption in the structural arch theory that the internal moment of the parabolic bearing arch differential unit at any position is zero, a moment balance condition at the arch crown is established, and the horizontal thrust at the arch foot is obtained according to the moment balance condition. Using the first average earth pressure as the input pressure, and combining it with the boundary conditions of the vertical stress at the top of the lower loosened zone, the vertical equilibrium equation of the parabolic bearing arch differential element is established. The vertical equilibrium equation is solved using the finite difference method to obtain the vertical stress acting on the upper boundary of the lower loosened zone. This vertical stress is then integrated along the tunnel diameter and averaged to obtain the second average earth pressure acting on the top of the lower loosened zone. ; in, This represents the second average earth pressure. This indicates the vertical stress. Represents the differential unit in the horizontal direction. In the finite difference method, the first... s +1 vertical coordinates at depth nodes.

[0074] Specifically, the step of establishing boundary conditions based on the failure mode of the lower loosened zone, and obtaining the angle between any point on the parabolic slip surface of the lower loosened zone and the vertical direction according to the boundary conditions, the height of the loosened zone, and the tunnel diameter, includes: Based on the parabolic nature of the failure morphology of the lower loosened area, the slip surface of the lower loosened area is expressed as a parabolic shape. The angle between the bottom of the parabolic sliding surface and the bottom of the vertical direction is obtained based on the height of the loosened area and the diameter of the tunnel. Based on the boundary conditions established by the parabolic slip surface, these boundary conditions are substituted into the parabolic shape expression, and combined with the bottom included angle, the second expression of the parabolic slip surface is determined: ; Where y represents the second expression. This represents the angle between the bottom of the parabolic sliding surface and the bottom in the vertical direction; Differentiating the second expression of the parabolic slip surface determines the angle between any point on the parabolic slip surface and the vertical direction. : ; in, This represents any point on the parabolic sliding surface of the lower loosening zone.

[0075] Specifically, the step of obtaining the normal stress and shear stress acting on the parabolic slip surface based on the stress equilibrium condition, using the internal friction angle and the included angle, includes: The Rankine passive lateral earth pressure coefficient is determined based on the internal friction angle. Based on the stress equilibrium condition, and considering the stress equilibrium of the parabolic bearing arch differential element at the parabolic slip surface, combined with the included angle and the Rankine passive lateral earth pressure coefficient, the normal stress and the shear stress are obtained: ; ; in, This represents the normal stress. This represents the shear stress. This represents the Rankine passive lateral earth pressure coefficient. Indicates the minimum principal stress. This represents the angle between the direction of the major principal stress and the vertical direction. The value taken at a specific location.

[0076] Specifically, the average earth pressure acting on the tunnel, based on the limit equilibrium theory and using the second average earth pressure as the boundary condition, combined with the normal stress and the shear stress, includes the following: Using the second average earth pressure as the boundary condition, the parabolic bearing arch differential element is obtained from any depth of the lower loosening zone. Under the assumption that the minor principal stress at any point on the parabolic bearing arch differential element changes linearly along the principal stress trajectory, the resultant force of the minor principal stress at the upper boundary and the resultant force of the minor principal stress at the lower boundary acting on the parabolic bearing arch differential element are solved respectively. Calculate the vertical force acting on the two sliding surfaces based on the normal stress and the shear stress on the two sliding surfaces; Based on the resultant force of the minor principal stresses at the upper boundary, the resultant force of the minor principal stresses at the lower boundary, and the vertical forces on the sliding surfaces on both sides, the vertical force equilibrium equation of the parabolic bearing arch differential element is established. The vertical force equilibrium equations are solved using the finite difference method to obtain the minor principal stresses acting above the tunnel. Based on the geometric relationship of the Mohr stress circle, the vertical stress in the lower loosening zone is obtained according to the minor principal stress acting above the tunnel. The average earth pressure acting on the tunnel is obtained by integrating the vertical stress along the tunnel diameter and taking the average. ; in, This represents the average earth pressure acting on the tunnel. This indicates the vertical stress within the lower loosened area. Indicates slip surface M The minor principal stress at the point, Represents the minor principal stress and slip surface at any point M The height difference of the minor principal stress at the location, The differential element represents the angle of deflection of the major principal stress direction.

[0077] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a deep tunnel overburden pressure evolution prediction program, and the deep tunnel overburden pressure evolution prediction program, when executed by a processor, implements the steps of the deep tunnel overburden pressure evolution prediction method as described above.

[0078] In summary, this invention provides a method for predicting the evolution of overburden pressure in deep tunnels. The method includes: determining the overburden to be treated above the tunnel for deep underground space engineering; obtaining the basic geometric and physical parameters of the overburden, including the tunnel diameter, total height of the overburden layer, soil unit weight, and internal friction angle; vertically dividing the overburden into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone, and determining the height of the undisturbed zone in the upper undisturbed zone, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower loosened zone, to establish a zonal theoretical analysis model of the tunnel overburden; wherein, the middle soil arch zone forms a parabolic bearing arch under the action of overburden pressure, and the failure mode of the lower loosened zone is parabolic; based on the basic geometric and physical parameters, the average earth pressure acting above the tunnel is predicted through the zonal theoretical analysis model. This invention constructs a model reflecting the distribution and evolution of earth pressure, ensuring the safe and efficient development of deep underground spaces.

[0079] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal that includes that element.

[0080] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0081] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for predicting the evolution of overburden pressure in deep tunnels, characterized in that, The method for predicting the evolution of overburden pressure in deep tunnels includes: For deep underground space engineering, identify the overburden soil above the tunnel that needs to be treated; Obtain the basic geometric and physical parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight, and internal friction angle; The overlying soil is vertically divided into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone. The height of the undisturbed zone in the upper part, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower part are determined to establish a zoning theoretical analysis model for the tunnel overlying soil. Among them, the central soil arch area forms a parabolic bearing arch under the action of the overlying soil pressure, and the failure mode of the lower loosening area is parabolic. Based on the aforementioned geometric and physical parameters, the average earth pressure acting above the tunnel is predicted using the zoning theory analysis model.

2. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 1, characterized in that, The partitioning theory analysis model satisfies the following assumptions: The overlying soil to be treated is a homogeneous and isotropic medium, and the overlying soil to be treated satisfies the Mohr-Coulomb yield criterion. The parabolic bearing arch and the soil in the lower loosened zone are both in a state of limit equilibrium. The height of the lower loosened zone and the arch thickness of the parabolic bearing arch dynamically evolve with the increase of tunnel stratum loss.

3. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 1, characterized in that, The method of predicting the average earth pressure acting above the tunnel based on the aforementioned geometric and physical fundamental parameters and the aforementioned zoning theory analysis model specifically includes: Based on the total height of the overlying soil layer, the height of the loosened zone, and the thickness of the bearing arch, the height of the undisturbed zone of the upper undisturbed zone is obtained. Based on the height of the undisturbed zone, the unit weight of the soil, the internal friction angle, and the tunnel diameter, the first average earth pressure acting above the middle soil arch zone is obtained. Based on the structural arch theory, the second average earth pressure acting on the top of the lower loosened zone is obtained according to the first average earth pressure and the arch thickness of the parabolic bearing arch. Boundary conditions are established based on the failure mode of the lower loosened area. According to the boundary conditions, the height of the loosened area and the tunnel diameter, the angle between any point on the parabolic slip surface of the lower loosened area and the vertical direction is obtained. Based on the stress equilibrium condition, the normal stress and shear stress acting on the parabolic slip surface are obtained from the internal friction angle and the included angle. Based on the limit equilibrium theory, using the second average earth pressure as the boundary condition, and combining the normal stress and the shear stress, the average earth pressure acting on the tunnel is obtained.

4. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 3, characterized in that, The undisturbed zone height of the upper undisturbed zone is obtained based on the total height of the overlying soil layer, the height of the loosened zone, and the thickness of the bearing arch. The first average earth pressure acting above the middle soil arch zone is then obtained based on the undisturbed zone height, the soil unit weight, the internal friction angle, and the tunnel diameter. Specifically, this includes: The height of the undisturbed zone is obtained by subtracting the height of the loosened zone and the thickness of the bearing arch from the total height of the overlying soil layer; Based on the moment-free condition that the pressure line of the parabolic bearing arch coincides with the arch axis, the first expression of the parabolic bearing arch is determined, and the arch height of the parabolic bearing arch is calculated according to the internal friction angle using the boundary condition of the slope of the first expression at the arch foot. Based on the soil unit weight, the height of the undisturbed zone, the arch height, and the tunnel diameter, the non-uniformly distributed vertical stress acting at any point above the central soil arch area is integrated along the horizontal projection range of the arch and divided by the tunnel diameter to obtain the first average earth pressure acting above the central soil arch area. ； in, This represents the first average earth pressure. This indicates the diameter of the tunnel. This indicates the unit weight of the soil. This indicates the height of the undisturbed region. Represents any variable in the horizontal direction. Represents the differential unit in the vertical direction. This indicates the height of the arch.

5. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 4, characterized in that, Based on the structural arch theory, and according to the first average earth pressure and the arch thickness of the parabolic bearing arch, the second average earth pressure acting on the top of the lower loosened zone is obtained, specifically including: Using the arch thickness of the parabolic bearing arch as a geometric parameter, the differential element of the parabolic bearing arch is obtained from the central soil arch region; Based on the assumption in the structural arch theory that the internal moment of the parabolic bearing arch differential unit at any position is zero, a moment balance condition at the arch crown is established, and the horizontal thrust at the arch foot is obtained according to the moment balance condition. Using the first average earth pressure as the input pressure, and combining it with the boundary conditions of the vertical stress at the top of the lower loosened zone, the vertical equilibrium equation of the parabolic bearing arch differential element is established. The vertical equilibrium equation is solved using the finite difference method to obtain the vertical stress acting on the upper boundary of the lower loosened zone. This vertical stress is then integrated along the tunnel diameter and averaged to obtain the second average earth pressure acting on the top of the lower loosened zone. ； in, This represents the second average earth pressure. This indicates the vertical stress. Represents the differential unit in the horizontal direction. In the finite difference method, the first... s+ Vertical coordinates at a depth node.

6. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 5, characterized in that, The boundary conditions are established based on the failure mode of the lower loosened zone. Based on these boundary conditions, the height of the loosened zone, and the tunnel diameter, the angle between any point on the parabolic slip surface of the lower loosened zone and the vertical direction is obtained. Specifically, this includes: Based on the parabolic nature of the failure morphology of the lower loosened area, the slip surface of the lower loosened area is expressed as a parabolic shape. The angle between the bottom of the parabolic sliding surface and the bottom of the vertical direction is obtained based on the height of the loosened area and the diameter of the tunnel. Based on the boundary conditions established by the parabolic slip surface, these boundary conditions are substituted into the parabolic shape expression, and combined with the bottom included angle, the second expression of the parabolic slip surface is determined: ； in, This represents the second expression. This represents the angle between the bottom of the parabolic sliding surface and the bottom in the vertical direction; Differentiating the second expression of the parabolic slip surface determines the angle between any point on the parabolic slip surface and the vertical direction. : ； in, This represents any point on the parabolic sliding surface of the lower loosening zone.

7. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 6, characterized in that, The method of obtaining the normal stress and shear stress acting on the parabolic slip surface based on the stress balance condition, using the internal friction angle and the included angle, specifically includes: The Rankine passive lateral earth pressure coefficient is determined based on the internal friction angle. Based on the stress equilibrium condition, and considering the stress equilibrium of the parabolic bearing arch differential element at the parabolic slip surface, combined with the included angle and the Rankine passive lateral earth pressure coefficient, the normal stress and the shear stress are obtained: ； ； in, This represents the normal stress. This represents the shear stress. This represents the Rankine passive lateral earth pressure coefficient. Indicates the minimum principal stress. This represents the angle between the direction of the major principal stress and the vertical direction. The value taken at a specific location.

8. The method for predicting the evolution of overburden pressure in deep tunnels according to claim 7, characterized in that, Based on the limit equilibrium theory, using the second average earth pressure as the boundary condition, and combining the normal stress and the shear stress, the average earth pressure acting on the tunnel is obtained, specifically including: Using the second average earth pressure as the boundary condition, the parabolic bearing arch differential element is obtained from any depth of the lower loosened zone. Under the assumption that the minor principal stress at any point on the parabolic bearing arch differential element changes linearly along the principal stress trajectory, the resultant force of the minor principal stress at the upper boundary and the resultant force of the minor principal stress at the lower boundary acting on the parabolic bearing arch differential element are solved respectively. Calculate the vertical force acting on the two sliding surfaces based on the normal stress and the shear stress on the two sliding surfaces; Based on the resultant force of the minor principal stresses at the upper boundary, the resultant force of the minor principal stresses at the lower boundary, and the vertical forces on the sliding surfaces on both sides, the vertical force equilibrium equation of the parabolic bearing arch differential element is established. The vertical force equilibrium equations are solved using the finite difference method to obtain the minor principal stresses acting above the tunnel. Based on the geometric relationship of the Mohr stress circle, the vertical stress in the lower loosening zone is obtained according to the minor principal stress acting above the tunnel. The average earth pressure acting on the tunnel is obtained by integrating the vertical stress along the tunnel diameter and taking the average. ； in, This represents the average earth pressure acting on the tunnel. This indicates the vertical stress within the lower loosened area. Indicates slip surface M The minor principal stress at the point, Represents the minor principal stress and slip surface at any point M The height difference of the minor principal stress at the location, The differential element represents the angle of deflection of the major principal stress direction.

9. A system for predicting the evolution of overburden pressure in deep tunnels, characterized in that, The deep tunnel overburden pressure evolution prediction system includes: The processing object confirmation module is used to identify the overburden soil above the tunnel to be processed for deep underground space engineering. The basic parameter acquisition module is used to acquire the geometric and physical basic parameters of the overlying soil, including: tunnel diameter, total height of the overlying soil layer, soil unit weight, and internal friction angle. The analysis model construction module is used to vertically divide the overlying soil into an upper undisturbed zone, a middle soil arch zone, and a lower loosened zone, and to determine the height of the undisturbed zone in the upper undisturbed zone, the thickness of the bearing arch in the middle soil arch zone, and the height of the loosened zone in the lower loosened zone, so as to establish a zonal theoretical analysis model of the tunnel overlying soil; wherein, the middle soil arch zone forms a parabolic bearing arch under the action of overlying soil pressure, and the failure mode of the lower loosened zone is parabolic; The pressure prediction module is used to predict the average earth pressure acting above the tunnel based on the geometric and physical basic parameters and the partition theory analysis model.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a deep tunnel overburden pressure evolution prediction program, which, when executed by a processor, implements the steps of the deep tunnel overburden pressure evolution prediction method as described in any one of claims 1-8.

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