Method for calculating safe distance of tunnel containing underlying spherical karst cave

Abstract

The invention discloses a safe distance calculation method for a tunnel containing an underlying spherical karst cave, and relates to the technical field of tunnel construction. Compared with a previous distance theoretical derivation method, the problem that an analysis model established by the theoretical derivation method has a certain difference with a real working condition is solved. And the calculation precision of a safe distance calculation formula is influenced. Actual working conditions are comprehensively considered, quantitative calculation of the safe distance is achieved through rigorous theoretical derivation, a scientific and accurate basis is provided for design and construction of the tunnel containing the underlying spherical karst cave, engineering risks caused by the influence of the karst cave are effectively avoided, the reliability and practicability of engineering design are improved, and the safety and rationality of tunnel construction are ensured; the theoretical result can practically guide engineering practice, and the engineering quality and safety are guaranteed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel construction, and particularly relates to a tunnel safety distance calculation method containing underlying spherical karst cave. BACKGROUND

[0002] With the steady progress of urbanization construction, traffic congestion problems are increasingly prominent, and increasing the development of underground space becomes an effective method to alleviate traffic pressure, which promotes the vigorous development of urban subway construction in China. Due to the improvement of construction speed and the expansion of construction area of urban subway construction, the widely distributed concealed karst region is also included in the engineering construction range. When the karst tunnel is constructed, the smaller the allowable distance between the existing structure and the karst cave, the more free the tunnel trend selection is when the line is selected, but the too small spacing is easy to cause the tunnel to be unstable and damaged, and the risk of karst cave collapse is greatly increased. Therefore, how to reasonably determine the distance between the tunnel and the karst cave becomes a problem to be solved in karst tunnel construction, and the safety distance also becomes a common karst tunnel safety evaluation index.

[0003] For the determination of the safety distance of the karst tunnel, many domestic and foreign experts and scholars have analyzed and studied from different angles, focusing on two aspects of theoretical derivation and data fitting. Theoretical derivation: the strength theory and the catastrophe theory focus on the rock stratum between the tunnel and the karst cave, simplify the rock stratum instability as the deformation of the beam and the plate, or regard the internal damage of the rock stratum as the energy accumulation and damage process of the beam and the plate under the action of external force, so as to obtain the safety distance of the tunnel excavation containing different directions, sizes and shapes of karst caves. At the same time, the limit analysis method is also applied to the calculation of the safety distance of the karst tunnel. The basic idea of data fitting is to obtain the real working condition data by means of orthogonal test, uniform test design, and numerical simulation by means of ANSYS, FLAC3D and other numerical software, or by means of scale model test, and finally to carry out multiple regression fitting. The calculation formula fitted by statistical analysis of the data fitting method can also be used as a reference basis for the site construction.

[0004] In summary, the related research of domestic and foreign scholars has achieved fruitful results. Compared with the theoretical derivation method, the conclusion formed by the theoretical derivation method is recognized by most scholars. However, the analysis model established by the theoretical derivation method has certain difference with the real working condition, which further affects the calculation accuracy of the safety distance calculation formula. Therefore, the present application proposes a tunnel safety distance calculation method containing underlying spherical karst cave to solve the above problems. SUMMARY

[0005] The purpose of the present application is to propose a tunnel safety distance calculation method containing underlying spherical karst cave to solve the problems proposed in the background art:

[0006] The analysis model established by the theoretical derivation method has certain difference from the real working condition, and further influences the calculation precision of the safety distance calculation formula.

[0007] In order to achieve the above object, the application adopts the following technical scheme:

[0008] A tunnel safety distance calculation method containing underlying spherical caverns comprises the following steps:

[0009] Step one, according to the combined action of the self-weight of the rock-soil body, the excavation and support of the tunnel and the formation and filling of the underlying cavern, a plane axisymmetric calculation model for the stability analysis of the surrounding rock of the tunnel containing underlying caverns is constructed;

[0010] Step two, the plane rectangular coordinate system and the polar coordinate system are selected, the Laplace displacement method is introduced, and the plane axisymmetric calculation model is solved to obtain a complete solution of the stress distribution of the surrounding rock through theoretical analysis;

[0011] Step three, the complete solution, the failure mode of ground subsidence and the Mohr-Coulomb strength theory are combined to derive a mathematical expression for the safety distance calculation of the tunnel containing underlying caverns;

[0012] Step four, the rock-soil layer density, the Poisson's ratio of the rock-soil body, the overlying stratum thickness, the radius of the spherical cavern, the radial stress of the tunnel lining and the radial stress data of the cavern filling measured in the actual project are substituted into the mathematical expression for calculation to obtain the safety distance of the tunnel containing underlying spherical caverns.

[0013] Preferably, in step one, when the cavern is of asymmetric shape, the equivalent radius method is used to convert it into a spherical model, and a shape correction coefficient is introduced to adjust the cavern radius in the mathematical expression.

[0014] Preferably, in step two, the plane rectangular coordinate system and the polar coordinate system are combined, the Laplace displacement method is introduced to analyze the combined action of the tunnel excavation and the cavern filling on the surrounding rock, and an analytical solution containing the radial stress, the hoop stress and the shear stress is obtained.

[0015] Preferably, in step three, based on the shear failure mode of ground subsidence, the Mohr-Coulomb strength theory is combined to derive the limit equilibrium equation, and the imaginary solution and the negative solution in the limit equilibrium equation are screened out, and the positive real solution is retained as the effective safety distance.

[0016] Preferably, in step four, the parameters in the mathematical expression are dynamically corrected by real-time monitoring of the cavern filling stress, the surrounding rock strain and the underground water level data, the safety distance calculation result is iteratively updated, and a warning threshold is established.

[0017] Compared with the prior art, the tunnel safety distance calculation method containing underlying spherical karst cave has the following beneficial effects:

[0018] The tunnel safety distance calculation method containing underlying spherical karst cave comprehensively considers the self weight of the rock-soil body, the tunnel excavation support effect and the filling state of the karst cave, constructs a plane axisymmetric model, solves the stress distribution of the surrounding rock by using the theory of elasticity, deduces the mathematical expression of the safety distance by combining the ground collapse failure mode and the Mohr-Coulomb strength theory, and is verified by engineering examples. BRIEF DESCRIPTION OF DRAWINGS

[0019] Fig. 1 The method flowchart mentioned in embodiment 1 of the present application is provided.

[0020] Fig. 2 The method logic diagram mentioned in embodiment 1 of the present application is provided. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0022] The tunnel safety distance calculation method containing underlying spherical karst cave comprehensively considers the self weight of the rock-soil body, the tunnel excavation support effect and the filling state of the karst cave, constructs a plane axisymmetric model, solves the stress distribution of the surrounding rock by using the theory of elasticity, deduces the mathematical expression of the safety distance by combining the ground collapse failure mode and the Mohr-Coulomb strength theory, and is verified by engineering examples.

[0023] Embodiment 1

[0024] Please refer to Figs. 1-2 The tunnel safety distance calculation method containing underlying spherical karst cave provided by the present application comprises the following steps.

[0025] Step one, according to the self-weight of rock-soil mass, the excavation and support of tunnel and the formation and filling of underlying karst cave, the common action of the analysis model is constructed to construct the plane axisymmetric calculation model of the stability analysis of the surrounding rock of the tunnel containing underlying karst cave;

[0026] The construction of the plane axisymmetric calculation model is as follows:

[0027] The shape of the karst cave is obtained by three-dimensional scanning data. When the karst cave is asymmetric, it is converted into a spherical model by the equivalent radius method, and a shape correction coefficient η is introduced to correct the radius of the karst cave. The corrected radius of the karst cave is obtained, wherein the radius of the karst cave is determined by geological radar or drilling data; η can be determined according to the ellipsoidal degree of the karst cave or the actual three-dimensional scanning data. This step converts the asymmetric karst cave into a spherical model by the equivalent radius method and the shape correction coefficient, solving the adaptation problem of the actual complex karst cave shape and the theoretical calculation model (spherical). On the one hand, the geometric characteristics (such as ellipsoidal degree) of the karst cave are obtained by geological radar, drilling data and three-dimensional scanning technology to ensure that the corrected radius can truly reflect the actual size effect of the asymmetric karst cave; on the other hand, the equivalent radius is adjusted by the shape correction coefficient to make up for the simplification error of the spherical model for the asymmetric shape, so that the safety distance calculation method based on the spherical karst cave can be applied to the various shapes of the karst cave in actual engineering, effectively improving the applicability of the calculation model to complex working conditions and the reliability of the safety distance calculation result, and providing a reasonable theoretical basis for tunnel design and construction under the condition of asymmetric karst cave.

[0028] In this embodiment, the existing axisymmetric model can also be extended to a three-dimensional asymmetric model by introducing the karst cave shape coefficient (such as ellipsoidal degree, irregular index) as a new parameter; the existing axisymmetric model can be extended to a three-dimensional asymmetric model, which can significantly improve the accuracy and applicability of the safety distance calculation of the tunnel containing underlying spherical karst cave. The axisymmetric model is based on the simplification assumption and only considers the idealized concentric circular structure, which cannot accurately capture the irregular shape (such as ellipsoidal shape, multiple hole interaction) of the karst cave in actual geology and the influence of the anisotropy of rock-soil mass on the stability of surrounding rock. Through three-dimensional asymmetric modeling, the geometric characteristics (such as major axis, minor axis, inclination angle) of the karst cave in different directions in space and the local stress concentration effect can be quantified, and combined with numerical simulation technology (such as finite element analysis), the complex mechanical interaction between the tunnel and the karst cave can be more truly reflected, especially the asymmetric stress transmission and potential shear failure path of the karst cave edge. In addition, the three-dimensional model can analyze the stress superposition effect when multiple karst caves coexist, optimize the critical threshold of safety distance, and thus reduce the engineering risk caused by model simplification, providing a more scientific and reliable theoretical basis for the design of tunnels in complex karst strata.

[0029] According to the concentric circular structure of the corrected tunnel and karst cave, the three-dimensional effect is ignored, and the problem is simplified into a plane strain axisymmetric model; the boundary conditions are preset:

[0030] Tunnel inner wall is subjected to tunnel lining radial stress p i ; wherein, tunnel lining radial stress p i is calculated by supporting structure design parameters (such as concrete strength, supporting thickness).

[0031] Cave boundary is subjected to cave filling radial stress p l ; cave filling radial stress p l is estimated according to filling material properties (such as clay, concrete) and compactness, and is taken as 0 if not filled.

[0032] Far-field stratum horizontal stress p1=k0γ(H1+2r1+H2+r2+y); wherein, k0 is lateral pressure coefficient, which is calculated according to Poisson's ratio μ, such as Poisson's ratio is the ratio of lateral strain to axial strain of rock-soil mass, and the lateral strain and axial strain of rock-soil mass are determined by triaxial compression test; γ is the self-weight of rock-soil mass, which is determined by indoor soil test, for example, the container weight test is carried out on undisturbed soil sample; H1 is the thickness of overlying soil layer, which is measured by geological profile; r1 is the tunnel radius, which is determined by geological radar or drilling data; H2 is the thickness of soil layer between tunnel and cave, which is measured by geological profile; r2 is the modified cave radius; y is the additional stress correction term.

[0033] The above steps build a plane axisymmetric calculation model by comprehensively considering the self-weight of rock-soil mass, the effects of tunnel excavation and support, and the formation and filling state of underlying cave, and clearly define the key parameters such as the thickness of overlying soil layer of tunnel, the thickness of soil layer between tunnel and cave, the radii of tunnel and cave, the radial stress of lining and cave filling, and the horizontal stress of stratum, which provides geometric relationship and mechanical boundary conditions for solving the stress distribution of surrounding rock and deducing the mathematical expression of safety distance in the subsequent steps, is the key link of converting actual engineering problems into theoretical analysis model, and ensures that the calculation model can truly reflect the mechanical properties of tunnel and cave interaction, and lays a foundation for quantitative calculation of safety distance.

[0034] Step two, select the plane rectangular coordinate system and polar coordinate system, introduce the Laplace displacement method, and obtain the complete solution of stress distribution of surrounding rock by theoretical analysis on the plane axisymmetric calculation model;

[0035] The complete solution of stress distribution of surrounding rock includes radial stress σ r , hoop stress σ θ and shear stress τ rθ , which are as follows:

[0036]

[0037] wherein, is a comprehensive coefficient, used to combine the horizontal stress characteristics of the rock-soil mass, as a parameter in the surrounding rock stress distribution formula, simplifying the formula structure, providing a basis for subsequent stability analysis of the tunnel and underlying karst cave, derivation of safety distance, and other aspects, and is an important parameter reflecting the influence of the inherent properties of the rock-soil mass on the mechanical behavior in the quantitative analysis process;

[0038]

[0039] B is a basic stress term, used to reflect the combined effect of the self-weight of the rock-soil mass, support and filling stress, and dominate the overall distribution of the stress field;

[0040]

[0041] C is a second harmonic term, used to describe the stress fluctuation on both sides of the symmetry axis, and embody the interaction between the tunnel and the underlying karst cave;

[0042]

[0043]

[0044] D and F are high-order harmonic terms, used to correct local stress concentration (such as the edge of the karst cave) and improve the accuracy of the model;

[0045] The above steps are theoretically analyzed by introducing the plane rectangular coordinate system, polar coordinate system and Laplace displacement method to the plane axisymmetric model constructed in step one, and the complete solution of the surrounding rock stress distribution (including the radial stress, tangential stress and shear stress formulas) that can comprehensively reflect the combined action of the underlying karst cave and the tunnel excavation and support is solved, the mathematical relationship between the stress distribution and the rock-soil mass parameters (specific gravity, Poisson's ratio), geometric dimensions (tunnel and karst cave radius, interlayer thickness) and support conditions (lining and karst cave filling stress) is clarified, which provides core mechanical parameters and theoretical basis for deriving the mathematical expression of the safety distance in step three in combination with the ground collapse failure mode and Mohr-Coulomb strength theory, ensuring that the safety distance calculation can accurately reflect the actual stress state and stability conditions of the surrounding rock, and is a key theoretical link from model construction to formula derivation.

[0046] Step three, combining the complete solution, the failure mode of ground collapse and the Mohr-Coulomb strength theory, the mathematical expression of the safety distance calculation for the underlying karst cave tunnel is derived;

[0047] The radial stress σ r , the hoop stress σ θ and the shear stress τ rθ of the surrounding rock obtained in step two are used to extract the normal stress σ nand shear stress τ; for example, the normal stress and shear stress are calculated at the most dangerous cross section (usually the horizontal or vertical symmetry plane) between the cave and the tunnel, with θ = 0° or θ = 90°; wherein c is the cohesion; φ is the internal friction angle; according to the Mohr-Coulomb criterion, the failure condition is τ ≥ τ f = c + σ n tan φ; the actual shear stress is compared with the critical shear stress τ

[0048]

[0049] a, b, d, e and f represent and the corresponding coefficients, H2 is H2, is a constant term; by solving the above mathematical expression by numerical method (such as Newton iteration method), four solutions of the safety distance H2 are obtained:

[0050]

[0051] In the formula:

[0052]

[0053] or (take the longer one) ;

[0054] (if u is 0, then v is also 0) ;

[0055]

[0056] wherein P is a discriminant parameter; D is a discriminant; u and v are open cubic variables; ω is a cubic unit root; m, S and T are root construction parameters, and k is an index parameter of ω; i is an imaginary number.

[0057] The imaginary solutions x1, x2 and the negative solution x4 are discarded, and the positive real solution x3 is retained as the effective safety distance.

[0058] The above step combines the complete solution of the surrounding rock stress distribution obtained in step two with the ground collapse failure mode and the Mohr-Coulomb strength theory, and establishes a safety distance mathematical expression taking the thickness of the soil layer between the tunnel and the karst cave as an unknown quantity through the coupling analysis of the mechanical equilibrium condition and the strength criterion. This step directly associates the stress state of the surrounding rock with the material failure condition by introducing the strength parameters such as the cohesion and the internal friction angle of the rock-soil mass, and clearly defines the mechanical criterion for the safety distance calculation, thereby providing a specific calculation formula that can be substituted with the measured parameters for the engineering application in step four. At the same time, by solving the quartic equation and selecting the positive real number solution with reasonable physical meaning, the calculation result is ensured to meet the stability requirements of the engineering practice, which is a key link for converting the theoretical stress analysis into a quantitative index of the safety distance, and lays the foundation for the core mathematical model and the discrimination basis of the safety distance calculation.

[0059] Step four, substitute the measured rock-soil layer specific weight, Poisson's ratio of the rock-soil mass, overburden thickness, radius of the spherical karst cave, tunnel lining radial stress, and karst cave filling radial stress data into the mathematical expression for calculation to obtain the safety distance of the tunnel containing underlying spherical karst caves.

[0060] Taking the actual implementation of an engineering project as an example, according to the project's corresponding preliminary exploration report, the thick limestone is the main component of the site's lithology. At the same time, geophysical prospecting techniques such as borehole ground penetrating radar have found the existence of spherical karst caves, which is consistent with the research background of this paper. Based on the relevant parameters provided by the survey report and the interpretation results of the two-dimensional ground penetrating radar images obtained from the field geological radar detection, the physical and mechanical parameters of the study area are determined as shown in Table 1:

[0061] Table 1 Physical and mechanical parameters of the study area

[0062]

[0063] Since p l = 0, substitute the parameters into the quartic equation of the second case to solve H2. The obtained solution is:

[0064] x1= -12.0631 - 9.3340i; x2= -12.0631 + 9.3340i;

[0065] x3= 6.2578; x4= -5.7317;

[0066] Discard the imaginary solutions x1 and x2, and the negative solution x4, and retain the positive real solution x3, which is:

[0067] σ M = 0; σ N = 1843.15;

[0068] The check calculation shows that σ N > σ M>0, the calculation is valid. In this case, the minimum safety distance H2 = 6.2578 m, and the distance between the tunnel and the cave during excavation should not be less than this value. According to Table 1, the actual design distance between the tunnel and the cave (8.4 m) is greater than the calculated safety distance (6.2578 m), and the tunnel design is safe.

[0069] The above steps are illustrated by an actual project. The physical and mechanical parameters such as the bulk density of the stratum obtained by investigation, the Poisson ratio, the thickness of the overlying stratum, and the radius of the cave are substituted into the mathematical expression to solve and select a reasonable positive real solution as the safety distance (such as H2 = 6.2578 m in the case). After confirming the effectiveness through stress calculation, the actual design distance is compared with the calculated value (in the case, the actual distance 8.4 m is greater than the calculated value 6.2578 m), and the safety of the tunnel design is determined. This process verifies the feasibility and practicality of the calculation method in actual engineering, converts the theoretical formula into engineering practice, and provides a reliable basis for the design and construction of tunnels containing underlying spherical caves, ensuring that theoretical calculations can guide actual engineering and ensure the safety and rationality of tunnel construction.

[0070] Embodiment 2

[0071] The embodiment provides a dynamic tunnel safety distance calculation method applied to embodiment 1, including the following steps:

[0072] On the basis of the model in embodiment 1, the influence of dynamic parameters (such as excavation rate, support timing, and mechanical vibration frequency) in the tunnel construction process on the stability of surrounding rock is analyzed;

[0073] Real-time monitoring technologies such as ground penetrating radar and optical fiber sensors are combined to obtain dynamic change data of surrounding rock stress, cave filling state, and groundwater level during construction;

[0074] Real-time monitoring data are input into the mathematical model to dynamically correct key parameters (such as cave filling stress and stratum horizontal stress) in safety distance calculation;

[0075] Through the combination of numerical simulation software (such as FLAC3D) and theoretical models, safety distance is calculated in real time, and a warning threshold is established. When the monitoring data approach the safety limit, the warning is triggered.

[0076] The above steps can compensate for the shortcomings of traditional static models through dynamic parameters and real-time feedback mechanisms, and improve the adaptability of the model to complex construction environments.

[0077] The above description is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can make equivalent substitutions or changes to the technical solutions and inventive concepts of the present application within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for calculating the safe distance of a tunnel containing an underlying spherical karst cave, characterized in that, Includes the following steps: Step 1: Based on the combined effects of the self-weight of the soil and rock mass, the excavation and support of the tunnel, and the formation and filling of the underlying karst cave, construct a planar axisymmetric calculation model for the stability analysis of the surrounding rock of the tunnel containing the underlying karst cave. Step 2: Select a plane rectangular coordinate system and a polar coordinate system, introduce the Lap displacement method, and solve the plane axisymmetric calculation model through theoretical analysis to obtain a complete solution for the stress distribution of the surrounding rock; Step 3: By combining the complete solution, the failure mode of ground collapse, and the Mohr-Coulomb strength theory, a mathematical expression for calculating the safe distance of tunnels containing underlying karst caves is derived. Step 4: Substitute the measured unit weight of the soil and rock layer, Poisson's ratio of the soil and rock mass, thickness of the overlying stratum, radius of the spherical karst cave, radial stress of the tunnel lining, and radial stress of the karst cave filling data obtained in the actual project into the mathematical expression to calculate the safe distance of the tunnel containing the underlying spherical karst cave.

2. The method for calculating the safe distance of a tunnel containing an underlying spherical karst cave as described in claim 1, characterized in that, In step one, when the cave is asymmetrical, it is converted into a spherical model using the equivalent radius method, and a shape correction coefficient is introduced to adjust the cave radius in the mathematical expression.

3. The method for calculating the safe distance of a tunnel containing an underlying spherical karst cave as described in claim 1, characterized in that, In step two, by combining the plane rectangular coordinate system and the polar coordinate system, the Laplace displacement method is introduced to analyze the combined effect of tunnel excavation and karst cave filling on the surrounding rock, and an analytical solution including radial stress, circumferential stress and shear stress is obtained.

4. The method for calculating the safe distance of a tunnel containing an underlying spherical karst cave as described in claim 1, characterized in that, In step three, based on the shear failure mode of ground collapse and combined with the Mohr-Coulomb strength theory, the limit equilibrium equation is derived, and the imaginary and negative solutions in the limit equilibrium equation are screened, retaining the positive real solutions as the effective safety distance.

5. The method for calculating the safe distance of a tunnel containing an underlying spherical karst cave according to claim 1, characterized in that, In step four, by real-time monitoring of the karst cave filling stress, surrounding rock strain, and groundwater level data, the parameters in the mathematical expression are dynamically corrected, the safe distance calculation results are iteratively updated, and an early warning threshold is established.

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