Rectangular tunnel grouting soil disturbance calculation method and system considering terrain effect

Abstract

The invention relates to the field of tunnel engineering, in particular to a rectangular tunnel grouting soil disturbance calculation method and system considering the terrain effect. The method comprises the following steps: determining a conformal mapping function; utilizing the conformal mapping function to establish a physical plane analytic function and construct a calculation model of stress and displacement of soil around the shallow-buried rectangular tunnel; establishing a boundary condition control equation by using the physical plane analytic function; obtaining an image plane analytic function by using the physical plane analytic function; and according to the image plane analytic function and the boundary condition control equation, obtaining a stress field and a displacement field of a soil body around the shallow-buried rectangular tunnel so as to evaluate the influence of the grouting effect on soil body disturbance. According to the method, the solving method of the conformal mapping function coefficient is improved, the solving difficulty of the conformal mapping function coefficient is reduced, the coefficient accuracy is improved, meanwhile, the boundary condition control equation is solved by adopting the series expansion method, the solving process of the analytic function is simplified, and the calculation efficiency is greatly improved.

Description

Technical Field

[0001] The invention relates to the field of tunnel engineering, and in particular to a method and system for calculating soil disturbance caused by grouting in a rectangular tunnel taking terrain effects into consideration. Background Art

[0002] In recent years, urban tunnel construction has developed rapidly, the number has increased significantly, and a variety of non-circular cross-section tunnel designs have emerged. Among them, rectangular tunnels have been widely used in urban planning due to their high cross-section utilization and strong practicality.

[0003] In the existing technology, grouting reinforcement technology is usually used to improve the strength and stability of the soil to ensure the safe construction and long-term operation of the tunnel. However, there are still some shortcomings. First, the grouting operation will cause a certain degree of disturbance to the surrounding soil, thereby changing the stress field and displacement field of the soil; second, the design and construction of the tunnel generally assumes that the surface is horizontal, and does not consider the changes in boundary conditions and stress fields caused by terrain effects; third, most of the research focuses on traditional circular tunnels or deep tunnels, while there is a lack of research on grouting soil disturbance in shallow rectangular tunnels considering terrain effects.

[0004] At present, there is not much research on the soil disturbance caused by grouting of shallow rectangular tunnels. There is no specific calculation method for the soil disturbance caused by grouting of shallow rectangular tunnels considering the terrain effect, which can be used to accurately predict the stress field and displacement field of the surrounding soil caused by grouting reinforcement of shallow rectangular tunnels under different terrain conditions, and provide a scientific basis for the design and safe construction of rectangular tunnel projects. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a method and system for calculating soil disturbance during grouting in a rectangular tunnel taking terrain effects into consideration.

[0006] In the first aspect, the present invention provides a method for calculating the disturbance of soil during grouting in a rectangular tunnel taking into account the terrain effect, comprising the following steps: determining a conformal mapping function; using the conformal mapping function to establish a physical plane analytical function and construct a calculation model for the stress and displacement of soil around a shallow rectangular tunnel; using the physical plane analytical function to establish a boundary condition control equation; using the physical plane analytical function to obtain an image plane analytical function; and obtaining the stress field and displacement field of the soil around the shallow rectangular tunnel based on the image plane analytical function and the boundary condition control equation. The present invention has the following effects: first, by determining the conformal mapping function, a mapping relationship between the physical plane and the image plane is constructed, which provides a solid theoretical basis for subsequent calculations; second, by using the conformal mapping function, a physical plane analytical function is established, and based on the analytical function, a calculation model for the stress and displacement of the soil around the shallow rectangular tunnel is established and a boundary condition control equation is constructed, which realizes an accurate description of the disturbance of the soil around the tunnel during the pressure grouting process; third, by using the physical plane analytical function to obtain the image plane analytical function, and combining the boundary condition control equation, the stress field and displacement field of the soil around the shallow rectangular tunnel are successfully solved, which provides strong technical support for the safety assessment and design of the rectangular tunnel project.

[0007] Optionally, determining the conformal mapping function includes: based on conformal mapping theory, determining a coefficient conformal mapping function for mapping a semi-infinite domain containing a rectangular hole on a physical plane to an annular domain on an image plane, wherein the coefficient conformal mapping function is as follows: , in, are coordinates on the physical plane, is the conformal mapping function, are the coordinates on the image plane, represents the slope terrain parameters, are the coefficients of the conformal mapping function, is a constant, is an imaginary unit, ; According to the conformal mapping function of the undetermined coefficients, the least square method and the dichotomy method are used to obtain the accurate conformal mapping function coefficients; the conformal mapping function coefficients are substituted into the conformal mapping function of the undetermined coefficients to obtain the conformal mapping function with determined coefficients. Based on the conformal mapping theory, the present invention constructs a conformal mapping function of undetermined coefficients, aiming to accurately map the semi-infinite domain containing rectangular holes to the annular domain of the image plane, which is of great significance for analyzing complex physical phenomena such as electromagnetic field distribution and fluid dynamics. In order to solve the conformal mapping function of the undetermined coefficients, the strategy of combining the least square method and the dichotomy method is adopted. Through the joint application of these two methods, the coefficients of the conformal mapping function can be accurately solved. Finally, the coefficients obtained by the solution are substituted into the original conformal mapping function of the undetermined coefficients, that is, a conformal mapping function with determined coefficients is obtained. This function not only has a high degree of accuracy and reliability, but also provides a powerful tool for subsequent numerical analysis and physical phenomenon research, and is of great significance for promoting scientific research and technological applications in related fields.

[0008] Optionally, the method of obtaining accurate conformal mapping function coefficients by using least squares and bisection according to the conformal mapping function of the undetermined coefficients includes: obtaining the first approximate calculation result of the overdetermined linear system equation by using least squares according to the conformal mapping function of the undetermined coefficients; correcting the first approximate calculation result to obtain a corrected result; and obtaining accurate conformal mapping function coefficients by using bisection according to the corrected result. The present invention uses least squares and bisection to solve accurate conformal mapping function coefficients according to the conformal mapping undetermined function, and achieves the following effects: first, the accurate solution of the inner boundary of the image plane ring is achieved by bisection, so that the obtained conformal mapping function can meet the accuracy requirements; second, the first approximate calculation of the overdetermined linear system equation by using least squares is beneficial to obtain the preliminary estimate of the conformal mapping function coefficients by minimizing the mapping error; third, more accurate conformal mapping function coefficients are obtained by iteration and optimization, thereby ensuring the accuracy and reliability of the mapping function.

[0009] Optionally, the use of the conformal mapping function to establish a physical plane analytical function and construct a calculation model for soil stress and displacement around a shallow rectangular tunnel includes: using a conformal mapping function with determined coefficients to establish an analytical function on a semi-infinite domain in a physical plane; constructing a calculation model for soil stress around a shallow rectangular tunnel according to the analytical function; and constructing a calculation model for soil displacement around a shallow rectangular tunnel according to the analytical function. The present invention has the following effects: first, using a conformal mapping function with determined coefficients to accurately construct an analytical function on a semi-infinite domain in a physical plane, providing a solid mathematical foundation for subsequent stress and displacement calculations, and ensuring the accuracy and reliability of the calculation model; second, based on the established analytical function, a calculation model for soil stress and displacement around a shallow rectangular tunnel is constructed, which is used to predict the stress and displacement of the surrounding soil during pressure grouting, and provides an important basis for the safety and stability assessment of rectangular tunnel projects.

[0010] Optionally, the calculation model of soil stress around the shallow rectangular tunnel satisfies the following expression: , , in, is the normal stress in the transverse direction of the soil around the tunnel, is the normal stress in the longitudinal direction of the soil around the tunnel, is the shear stress of the soil around the tunnel, For analytical functions The first derivative of For analytical functions The second-order derivative of For analytical functions The first derivative of is an imaginary unit, for The conjugate complex number of; the calculation model of soil displacement around the shallow rectangular tunnel satisfies the following expression: , in, is the displacement of the soil around the tunnel in the horizontal direction, is the displacement of the soil around the tunnel in the longitudinal direction, is the soil shear modulus, is the Poisson's ratio correlation coefficient, is an imaginary unit, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of The present invention provides a specific expression for the soil stress and displacement calculation model around a shallow rectangular tunnel, and achieves the following effects: first, it helps to clearly understand the structure and working principle of the model, so as to more accurately apply the model for prediction and analysis; second, it greatly enhances the operability of the model, which is conducive to quickly and accurately solving the stress and displacement of the soil around the tunnel; third, it provides a clear basis for the verification and improvement of the model.

[0011] Optionally, the boundary condition control equation satisfies the following expression: , , in, for The complex conjugate of Indicates the physical plane The set of points, represents the set of points on the boundary of the rectangular tunnel opening, is the horizontal stress component obtained by path integration of the traction force on the surface boundary, is the horizontal stress component obtained by path integration of the traction force on the tunnel boundary, is the vertical stress component obtained by path integration of the traction force on the surface boundary, is the vertical stress component obtained by path integration of the traction force on the tunnel boundary, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of The present invention achieves the following effects through boundary condition control equations: first, it provides accurate boundary conditions for the calculation of soil stress and displacement around shallow rectangular tunnels, ensuring the accuracy and reliability of the calculation results; second, by clarifying the boundary conditions, it more accurately simulates the influence of tunnel grouting operations on the surrounding soil disturbance, thereby obtaining stress and displacement distributions that are more in line with the actual situation; third, it is conducive to quickly solving the stress field and displacement field of the surrounding soil caused by the grouting disturbance of the rectangular tunnel, thereby improving the calculation efficiency.

[0012] Optionally, the pressure boundary condition of the boundary condition control equation satisfies the following expression: , , in, is the uniform internal pressure in the tunnel bore, Indicates the physical plane The set of points, represents the set of points on the boundary of the rectangular tunnel opening, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of The present invention provides the pressure boundary conditions of the boundary condition control equation, which has the following effects: first, it provides clear pressure boundary conditions for the calculation of soil stress and displacement around shallow rectangular tunnels, ensuring the accuracy and reliability of the calculation results; second, by accurately describing the pressure distribution of the soil around the tunnel, it is conducive to more realistic simulation of the disturbance effect of the tunnel grouting process on the surrounding soil; third, it promotes the research and development in the field of tunnel engineering, and provides a more scientific theoretical basis and technical support for engineering design and construction.

[0013] Optionally, the use of the physical plane analytical function to obtain the image plane analytical function includes: using the physical plane analytical function to convert the object-image plane; and obtaining the image plane analytical function according to the result of the conversion. The present invention converts the object plane analytical function into the image plane analytical function, and achieves the following effects: first, the object-image plane is converted through the physical plane analytical function, and the mapping from the physical plane to the image plane is realized, which provides a powerful tool for analyzing the dynamic behavior of complex systems; second, the image plane analytical function obtained according to the conversion result provides an important basis for the control and design of the system; third, the accuracy and efficiency of soil displacement and stress analysis are improved, and an effective solution is provided for system optimization, fault diagnosis and other problems in engineering practice.

[0014] Optionally, the obtaining of the soil stress field and displacement field around the shallow rectangular tunnel according to the image plane analytical function and the boundary condition control equation comprises: substituting the image plane analytical function into the boundary condition control equation to solve the image plane analytical function; substituting the result of the solution into the soil stress and displacement calculation model around the shallow rectangular tunnel to obtain the soil stress field and displacement field around the shallow rectangular tunnel. The present invention obtains the soil stress field and displacement field around the shallow rectangular tunnel according to the image plane analytical function and the boundary condition control equation, and has the following effects: first, by substituting the image plane analytical function into the boundary condition control equation for solution, an accurate description of the soil stress field and displacement field around the tunnel during the grouting process under complex terrain conditions is achieved, and the accuracy and reliability of the calculation results are improved; second, the calculation model is simplified, making the solution process more efficient and improving the calculation efficiency; third, it is conducive to being applicable to engineering problems with different terrain conditions and different rectangular tunnel sizes, and provides strong support for the research and development in the field of tunnel engineering.

[0015] In the second aspect, the present invention provides a rectangular tunnel grouting soil disturbance calculation system taking into account terrain effects, the system comprising an input device, a processor, an output device and a memory, the input device, the processor, the output device and the memory being interconnected, wherein the memory is used to store a computer program, the computer program comprising program instructions, the processor being configured to call the program instructions, and the system using the method for calculating the soil disturbance of a rectangular tunnel grouting taking into account terrain effects. The present invention provides a rectangular tunnel grouting soil disturbance calculation system considering terrain effects, which has high integration and the following effects: first, by introducing a conformal mapping function, a mapping relationship between a physical plane and an image plane is accurately constructed, which provides a solid theoretical basis for calculating the stress and displacement of the soil around the tunnel, and fully considers the terrain effect; second, based on the conformal mapping function, a physical plane analytical function and a calculation model for the stress and displacement of the soil around a shallow rectangular tunnel are established, and a pressure boundary condition control equation is further constructed, which accurately describes the disturbance of the soil during the tunnel grouting process, and provides strong support for the safety assessment of the rectangular tunnel project; third, advanced computing technology and algorithms are integrated to efficiently and accurately solve the stress field and displacement field of the soil around the tunnel, which provides a scientific basis for the design and construction of the rectangular tunnel project and helps to improve the overall quality and safety of the tunnel project.

[0016] Compared with the prior art, the beneficial effects of the present invention include: based on the theory of complex functions, a method for calculating the disturbance of grouting soil in a shallow rectangular tunnel taking into account the terrain effect is derived, the solution method of the coefficients of the conformal mapping function is improved, the difficulty of solving it is reduced, and the accuracy of the coefficients is improved, and at the same time, the method of series expansion is used to solve the boundary condition control equation, which simplifies the solution process of the analytical function and greatly improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a method for calculating soil disturbance of rectangular tunnel grouting considering terrain effect according to an embodiment of the present invention; Figure 2 is a schematic diagram of conformal mapping according to an embodiment of the present invention; Figure 3 A schematic diagram of a rectangular tunnel pressure boundary model according to an embodiment of the present invention; Figure 4 It is a schematic diagram of the structure of a rectangular tunnel grouting soil disturbance calculation system considering terrain effects according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not need to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

[0019] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

[0020] See also Figure 1 The embodiment of the present invention provides a method for calculating soil disturbance of rectangular tunnel grouting considering terrain effect, the method comprising the following steps: S1. Determine a conformal mapping function.

[0021] Among them, S1 includes the following steps: S11. Based on the conformal mapping theory, determine the conformal mapping function of the unknown coefficients.

[0022] See also Figure 2 In one embodiment, based on the conformal mapping theory, a conformal mapping function of the undetermined coefficients is determined to map the semi-infinite domain containing the rectangular hole on the physical plane to the annular domain on the image plane. The conformal mapping function of the undetermined coefficients is as follows: , in, are coordinates on the physical plane, is the conformal mapping function, are the coordinates on the image plane, represents the slope terrain parameters, are the coefficients of the conformal mapping function, is a constant, is an imaginary unit, ; is the slope terrain parameter, satisfying the following relationship: , in, is the distance from the center of the tunnel to the ground surface, is the inclination angle of the slope. Figure 2 middle, , , , , , , , , represents the spatial coordinates, is the polar coordinate, represents the physical plane coordinates, represents the image plane coordinates, Represents the physical plane area, represents the image plane area, Is an imaginary unit.

[0023] S12. According to the undetermined coefficient conformal mapping function, the least square method and the bisection method are used to solve the conformal mapping function coefficients and obtain the solution result.

[0024] Wherein, S12 further comprises the following steps: S121. According to the conformal mapping function of the undetermined coefficients, using the least squares method, obtain the first approximate calculation result of the overdetermined linear system equation.

[0025] In one embodiment, first, the rectangular hole boundary is divided into segment, obtained on the physical plane The rectangular coordinates of the sampling points.

[0026] Furthermore, the same operation is performed on the inner boundary of the ring domain on the image plane to obtain The coordinates of the sampling points. Since the radius of the inner boundary of the image plane ring is unknown, an initial value is set for it first. ,make . The binary search method is then used to iteratively solve it to make it close to the exact value.

[0027] Furthermore, according to the obtained two sets of coordinates, they are numbered correspondingly in the order of counterclockwise sampling.

[0028] In another embodiment, a first approximate calculation is performed based on the result corresponding to the coordinates, and the approximate calculation follows the following formula: Equations An overdetermined linear system equation synthesized by an unknown array satisfies the following expression: , in, represents the set of complex variables in the image plane, represents the coefficient matrix composed of the coefficients of the conformal mapping function, Represents the coordinate set of sampling points on the physical plane orifice boundary.

[0029] in addition, Satisfies the following relationship: , in, represents the inner boundary of the image plane ring The coordinates of the sampling points, is the number of circular rings in the image plane; Satisfies the following expression: , in, is the distance from the center of the tunnel to the ground surface, is the inclination angle of the slope, represents the transpose operation of the matrix, For the The inner boundary radius of the image plane ring; Satisfies the following expression: , in, Represents the physical plane orifice boundary The coordinates of the sampling points, Represents the transpose operation of a matrix.

[0030] Furthermore, based on the least squares method, the overdetermined linear system equations are rearranged, and the rearranged expression is as follows: , Furthermore, according to the rearranged expression, a coefficient matrix of the first iteration is obtained. The coordinate mapping of the coefficient matrix is ​​not accurate enough and needs to be corrected to improve the accuracy.

[0031] S122. Correct the first approximate calculation result to obtain a corrected result.

[0032] In one embodiment, the conformal mapping function coefficient matrix obtained after iteration is substituted into the conformal mapping function to obtain a new set of physical plane coordinate points. , because the coefficient matrix obtained in the first iteration is not accurate enough, the coordinate point set obtained in the first iteration is Therefore, in this embodiment, the perimeter correction method is used to correct the reference point, and the correction process is as follows: The width of the tunnel boundary is defined as , Gao Wei , tunnel boundary perimeter The calculation formula is as follows: , The perimeter of the figure around the reference point For approximate calculation, the calculation formula is as follows: , in, Represents the physical plane orifice boundary The coordinates of the sampling points, is the number of overdetermined linear system equations, .

[0033] Calculate the path length of the reference point on the enclosed graphic curve , the calculation formula is as follows: , in, is the number of reference points.

[0034] Calculate the proportion of the path passed by the reference point to the total perimeter. The calculation formula is as follows: , Determine the path length corresponding to the corrected reference point on the rectangular boundary , the calculation formula is as follows: , According to the corrected path length of the reference point, the rectangular coordinates of the reference point on the physical plane are determined as follows: , , , , , in, is the rectangular coordinate of the rectangular tunnel boundary on the physical plane and perpendicular to the ground surface, , is the rectangular coordinate of the rectangular tunnel boundary on the physical plane and parallel to the ground surface, is an imaginary unit, is the slope inclination angle, for The coordinates after coordinate rotation, , for and The coordinates formed by superimposing the components of is the number of reference points, is the tunnel half width, The tunnel is half height. is the distance from the tunnel center to the ground surface.

[0035] S123. According to the correction result, use the dichotomy method to obtain accurate conformal mapping function coefficients.

[0036] In one embodiment, according to the above correction process, the reference point coordinates are corrected again and again, that is, the conformal mapping function coefficients are corrected. When the corrected coefficients reach the convergence criterion, the correction is stopped to obtain accurate conformal mapping function coefficients. The convergence criterion is set as:

[0037] in, for . Due to the assumed initial value It is not true and needs to be corrected by combining the dichotomy.

[0038] Specifically, set , , obtained by the above calculation method The total perimeter of the mapped graph at convergence , by distinguishing and The size of The true value of: when hour, , use the binary method to reduce it to make it approach the true value, let , = ;when hour, , use the binary method to increase it so that it approaches the true value, let , = , according to this step, gradually reduce The value range of , using the updated , repeat the above operation for iterative calculation until the accuracy requirement is met, and set the convergence criterion as: , when the convergence criterion is met, is the true value.

[0039] In another embodiment, the solved coefficients of the precise conformal mapping function are substituted into the coefficient-to-be-determined conformal mapping function to obtain a precise conformal mapping function with determined coefficients.

[0040] The implementation effects of this embodiment are as follows: First, it can accurately map one area to another area according to a predetermined coefficient, keeping the angle unchanged and the local shape similarity; second, complex or irregular areas can be converted into simpler or more regular shapes, thereby simplifying subsequent mathematical analysis or calculations; third, it can improve the visualization of data, making the relationship and distribution characteristics between data points more obvious, which is helpful for data analysis and decision making.

[0041] S2. Construct a computational model for soil stress and displacement around a shallow rectangular tunnel.

[0042] Among them, S2 includes the following steps: S21. Using the conformal mapping function with determined coefficients, establish an analytical function on a semi-infinite domain in the physical plane.

[0043] In one embodiment, the precise conformal mapping function determined in step S1 is used to establish an analytical function without a specific expression on a semi-infinite domain in the physical plane.

[0044] Specifically, the analytical function is and .

[0045] S22. Based on the analytical function, a calculation model for soil stress around a shallow rectangular tunnel is constructed.

[0046] In one embodiment, a calculation model of soil stress around a shallow rectangular tunnel is constructed according to the analytical function mentioned in step S21.

[0047] Specifically, the calculation model of soil stress around the shallow rectangular tunnel satisfies the following expression: , , in, is the normal stress in the transverse direction of the soil around the tunnel, is the normal stress in the longitudinal direction of the soil around the tunnel, is the shear stress of the soil around the tunnel, For analytical functions The first derivative of For analytical functions The second-order derivative of For analytical functions The first derivative of is an imaginary unit, for The complex conjugate of .

[0048] Furthermore, the above expressions are separated into virtual and real parts to obtain the specific expressions of stress components: , , , S23. Based on the analytical function, a calculation model for soil displacement around a shallow rectangular tunnel is constructed.

[0049] In one embodiment, a calculation model for soil displacement around a shallow rectangular tunnel is constructed according to the analytical function mentioned in step S21.

[0050] Specifically, the calculation model of soil displacement around the shallow rectangular tunnel satisfies the following expression: , in, is the displacement of the soil around the tunnel in the horizontal direction, is the displacement of the soil around the tunnel in the longitudinal direction, is the soil shear modulus, is the Poisson's ratio correlation coefficient, is an imaginary unit, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of are coordinates on the physical plane.

[0051] Furthermore, the above expressions are separated into real and imaginary forms to obtain the specific expression of the displacement component: , , S3. Using the physical plane analytical function, establish boundary condition control equations.

[0052] In one embodiment, based on the theory of complex functions, the boundary condition control equation is established using the physical plane analytical function. Since the surface load and the influence of soil deadweight are not considered in the physical plane, the surface boundary adopts a zero stress boundary; a uniform internal pressure is given in the tunnel opening. To consider the grouting pressure of the tunnel, the pressure boundary is used for control.

[0053] Specifically, the general expression of the boundary condition control equation is as follows: , , in, for The complex conjugate of Indicates the physical plane The set of points, represents the set of points on the boundary of the rectangular tunnel opening, is the horizontal stress component obtained by path integration of the traction force on the surface boundary, is the horizontal stress component obtained by path integration of the traction force on the tunnel boundary, is the vertical stress component obtained by path integration of the traction force on the surface boundary, is the vertical stress component obtained by path integration of the traction force on the tunnel boundary, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of are coordinates on the physical plane. and It also satisfies the following relationship: , in, and is the traction force on the tunnel surface, is the arc length of the cavity boundary.

[0054] Furthermore, a uniform internal pressure is set in the tunnel opening. The grouting pressure of the tunnel is considered based on the stress boundary, such as Figure 3 As shown, the width of the rectangular tunnel boundary is , Gao Wei , the pressure control boundary condition is given: , , in, is the uniform internal pressure in the tunnel bore, Indicates the physical plane The set of points, represents the set of points on the boundary of the rectangular tunnel opening, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of are coordinates on the physical plane.

[0055] S4. Using the physical plane analytical function, obtain the image plane analytical function.

[0056] Wherein, S4 includes the following steps: S41. Using the physical plane analytical function, perform the transformation of the object-image plane.

[0057] In one embodiment, the analytical function without a specific expression on the physical plane is and The transformation is an analytical function with a specific expression on the imaging plane and , the relationship conversion formula is as follows: , , According to the theory of complex functions, the specific expressions are as follows: , , in, and are the coefficients of the analytical function to be determined.

[0058] S42. Obtain an image plane analytical function according to the result of the conversion.

[0059] In one embodiment, the chain rule is used to differentiate the transformed analytical function: , , , Furthermore, the derivative results are substituted into the boundary condition control equations and the calculation equations of the stress and displacement of the soil around the tunnel, and a series of differential transformations are performed on them. The substitution results include the precise calculation equations of the stress and displacement of the soil around the tunnel and the precise control equations of the boundary conditions.

[0060] The precise calculation equations for the stress and displacement of the soil around the tunnel are as follows: , , , , , The precise control equation of the boundary condition is as follows: , , in, Represents the outer boundary of the annular domain in the image plane, corresponding to the surface stress boundary of the physical plane, represents the inner boundary of the annular domain in the image plane, corresponding to the tunnel orifice pressure boundary condition in the physical plane. The coordinate expression of the point on the image plane is: ,make ,but .

[0061] S5. According to the image plane analytical function and the boundary condition control equation, the displacement field and stress field of the soil around the shallow rectangular tunnel are obtained.

[0062] Wherein, S5 includes the following steps: S51. Substitute the image plane analytical function into the boundary condition control equation to solve the image plane analytical function.

[0063] In one embodiment, an analytical function with a specific expression form is substituted into the boundary condition equation for solution. A series solution method is used, which performs series expansion on non-series terms and analytical functions to solve the two non-series terms coexisting in the equation, which are and .

[0064] Specifically, based on the conformal mapping function and the polar coordinate expression of the points on the image plane, the non-series terms in the boundary equation are After expansion, the expression is as follows: , It should be noted that The expanded expression is too complex to be converted into a series form, so it is expanded in series using the Fourier series to obtain the following series form expression: Surface zero stress boundary: , Tunnel orifice pressure boundary: , Further, Perform Fourier series expansion and obtain the following expression: , , in, , , are Fourier series coefficients.

[0065] Furthermore, the analytical function in the boundary condition equation is expanded in series: , , Furthermore, the analytical function The series expansion and complex terms of Substitute the series expansion of into the zero stress boundary condition equation: , Furthermore, the equation is combined and simplified: , Further, let the coefficients of the series terms be zero, and we get a set of and The relational expression is: , Furthermore, the series expansion of the analytical function and and Substituting the series expansion of into the tunnel opening pressure boundary equation, we get: , Furthermore, the above equations are combined and simplified to obtain: , Furthermore, by setting the coefficients of the series terms on both sides of the above equation equal, we can obtain and Another set of relational expressions: , Further, using and We get two sets of relational expressions: , , Furthermore, using the two sets of relational expressions, the coefficients of the analytical function are solved and , and thus obtain accurate and .

[0066] S52. Substitute the solution result into the soil stress and displacement calculation model around the shallow rectangular tunnel to obtain the soil displacement field and stress field around the shallow rectangular tunnel.

[0067] In one embodiment, the accurate and Substituting the calculation equations of tunnel soil stress and displacement into the equations, the displacement field and stress field of the surrounding soil caused by grouting reinforcement of a shallow rectangular tunnel considering the terrain effect are obtained.

[0068] S53. Substitute it into the soil stress and displacement calculation model around the shallow rectangular tunnel to obtain the displacement value at the infinite point on the ground surface.

[0069] In one embodiment, since the displacement value at infinity on the ground surface is zero, the rigid body displacement can be eliminated by subtracting the displacement value at infinity on the ground surface from the obtained soil displacement field, thereby obtaining the actual soil displacement field.

[0070] In another embodiment, the accuracy of the theoretical calculation is verified using the finite element method.

[0071] Specifically, the corresponding numerical model was established using Abaqus software, and its numerical simulation results were compared and verified with this scheme. The model settings are as follows: the bottom of the slope is 100 m long, the two sides are 40 m and 60 m long, and the angle is 11°; the tunnel width is 3 m, the height is 2 m, the burial depth is 5 m, and the grouting pressure is 0.5 MPa. The material parameters are set to elastic modulus 10 MPa and Poisson's ratio 0.3. Normal constraints in the axial direction keep the bottom free to avoid the influence of rigid body displacement.

[0072] See also Figure 4 , Figure 4 The present invention is a schematic diagram of a rectangular tunnel grouting soil disturbance calculation system considering terrain effects in an embodiment of the present invention. The system includes an input device, a processor, an output device and a memory, wherein the input device, the processor, the output device and the memory are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, the processor is configured to call the program instructions, and the system uses the rectangular tunnel grouting soil disturbance calculation method considering terrain effects.

[0073] In this embodiment, the input device is used to input basic parameters, including but not limited to tunnel width, length, height, burial depth, and grouting pressure, for calculating soil disturbance during grouting in a rectangular tunnel.

[0074] The processor has built-in various mathematical algorithms, including solving the coefficients of the conformal mapping function, solving the stress and displacement of the soil around the tunnel, boundary condition control, differential transformation, bisection, series solution, and least squares algorithm, which are used to obtain the accurate solution of the soil stress and displacement caused by the grouting process of the shallow rectangular tunnel considering the terrain effect.

[0075] The output device uses a display screen to display the calculation results processed by the processor.

[0076] The memory adopts a high-speed solid-state hard disk to store the basic parameters input by the input device and the calculation results processed by the processor. The memory has the characteristics of fast reading and writing speed, large capacity and high reliability, and can meet the needs of large data storage.

[0077] In summary, the present invention provides a method for calculating the disturbance of the rectangular tunnel grouting soil considering the terrain effect. Based on the complex function theory and conformal mapping technology, it can efficiently and easily solve the complex function solution of the stress and displacement of the surrounding soil caused by the grouting reinforcement of the shallow rectangular tunnel considering the terrain effect. First, based on the least squares method and the improved conformal mapping function coefficient solution method of the bisection method, the semi-infinite domain containing rectangular holes under the slope terrain is mapped to the annular domain of the image plane. Secondly, the complex function method is used to represent the analytical functions of stress and displacement and construct the boundary condition equation controlled by the grouting pressure. Finally, the boundary condition control equation is subjected to a series of differential transformations, the stress and displacement functions are solved using the series method, and the complex terms are expanded by Fourier series, and the analytical solution of the stress field and displacement field of the surrounding soil caused by the grouting reinforcement of the shallow rectangular tunnel considering the terrain effect is derived. The correctness of this method has been verified by finite element calculation. The rectangular tunnel grouting soil disturbance calculation system considering terrain effect provided by the present invention accurately constructs the mapping relationship between the physical plane and the image plane by introducing a conformal mapping function, provides a solid theoretical basis for the calculation of soil stress and displacement around the tunnel, and fully considers the terrain effect; based on the conformal mapping function, a calculation model of soil stress and displacement around the shallow rectangular tunnel is established, and the boundary condition control equation is further constructed based on this, which accurately describes the disturbance of the soil during the tunnel grouting process, and provides strong support for the safety assessment of the rectangular tunnel project; it integrates advanced computing technology and algorithms, and efficiently and accurately solves the displacement field and stress field of the surrounding soil caused by grouting reinforcement of the shallow rectangular tunnel considering the terrain effect, which provides a scientific basis for the design and construction of the rectangular tunnel project and helps to improve the overall quality and safety of the tunnel project.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effects, characterized in that: The method comprises the following steps: determining a conformal mapping function; By using the conformal mapping function, a physical plane analytical function is established and a calculation model of soil stress and displacement around a shallow rectangular tunnel is constructed; Using the physical plane analytical function, establishing boundary condition control equations; Using the physical plane analytical function, obtaining an image plane analytical function; According to the image plane analytical function and the boundary condition control equation, the soil stress field and displacement field around the shallow rectangular tunnel are obtained.

2. A method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effects according to claim 1, characterized in that: Determining the conformal mapping function comprises: Based on the conformal mapping theory, the conformal mapping function of the undetermined coefficients is determined, and the conformal mapping function of the undetermined coefficients is as follows: , in, are coordinates on the physical plane, is the conformal mapping function, are the coordinates on the image plane, is the slope terrain parameter, are the coefficients of the conformal mapping function, is a constant, is an imaginary unit, ; According to the undetermined coefficient conformal mapping function, using the least square method and the bisection method, accurate conformal mapping function coefficients are obtained; Substitute the conformal mapping function coefficients into the undetermined coefficient conformal mapping function to obtain a conformal mapping function with determined coefficients.

3. The method for calculating the disturbance of rectangular tunnel grouting soil considering terrain effect according to claim 2 is characterized in that: The method of obtaining accurate conformal mapping function coefficients by using least square method and bisection method according to the undetermined coefficient conformal mapping function comprises: According to the conformal mapping function of the undetermined coefficients, using the least squares method, a first approximate calculation result of the overdetermined linear system equation is obtained; Correcting the first approximate calculation result to obtain a corrected result; According to the correction result, accurate conformal mapping function coefficients are obtained by using the dichotomy method.

4. The method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effect according to claim 1 is characterized in that: The method of using the conformal mapping function to establish a physical plane analytical function and construct a calculation model of soil stress and displacement around a shallow rectangular tunnel includes: Using the conformal mapping function, an analytical function on a semi-infinite domain of a physical plane is established; According to the analytical function, a calculation model of soil stress around a shallow rectangular tunnel is constructed; According to the analytical function, a calculation model for soil displacement around a shallow rectangular tunnel is constructed.

5. The method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effect according to claim 4 is characterized in that: The calculation model of soil stress around the shallow rectangular tunnel satisfies the following expression: , , in, is the normal stress in the transverse direction of the soil around the tunnel, is the normal stress in the longitudinal direction of the soil around the tunnel, is the shear stress of the soil around the tunnel, For analytical functions The first derivative of For analytical functions The second-order derivative of For analytical functions The first derivative of is an imaginary unit, are coordinates on the physical plane, for The conjugate complex number of; the calculation model of soil displacement around the shallow rectangular tunnel satisfies the following expression: , in, is the displacement of the soil around the tunnel in the horizontal direction, is the displacement of the soil around the tunnel in the longitudinal direction, is the soil shear modulus, is the Poisson's ratio correlation coefficient, is an imaginary unit, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of are coordinates on the physical plane.

6. The method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effect according to claim 1, characterized in that: The boundary condition control equation satisfies the following expression: , , in, for The complex conjugate of Indicates the physical plane The set of points, represents the set of points on the boundary of the rectangular tunnel opening, is the horizontal stress component obtained by path integration of the traction force on the surface boundary, is the horizontal stress component obtained by path integration of the traction force on the tunnel boundary, is the vertical stress component obtained by path integration of the traction force on the surface boundary, is the vertical stress component obtained by path integration of the traction force on the tunnel boundary, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of are coordinates on the physical plane.

7. A rectangular tunnel grouting soil disturbance calculation method considering terrain effect according to claim 6, characterized in that: The pressure boundary condition of the boundary condition control equation satisfies the following expression: , , in, is the uniform internal pressure in the tunnel bore, Indicates the physical plane The set of points, represents the set of points on the boundary of the rectangular tunnel opening, is the analytical function, For analytical functions First Derivative The complex conjugate of For analytical functions The complex conjugate of are coordinates on the physical plane.

8. The method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effect according to claim 1, characterized in that: The obtaining of the image plane analytical function by using the physical plane analytical function comprises: Using the physical plane analytical function, transform the object-image plane; According to the result of the conversion, an image plane analytical function is obtained.

9. The method for calculating soil disturbance during grouting of a rectangular tunnel considering terrain effect according to claim 1, characterized in that: The step of obtaining the soil stress field and displacement field around the shallow rectangular tunnel according to the image plane analytical function and the boundary condition control equation comprises: Substituting the image plane analytical function into the boundary condition control equation to solve the image plane analytical function; The solution result is substituted into the soil stress and displacement calculation model around the shallow rectangular tunnel to obtain the soil stress field and displacement field around the shallow rectangular tunnel.

10. A rectangular tunnel grouting soil disturbance calculation system considering terrain effect, the system using a rectangular tunnel grouting soil disturbance calculation method considering terrain effect according to any one of claims 1 to 9, characterized in that: The system includes an input device, a processor, an output device and a memory, wherein the input device, the processor, the output device and the memory are connected to each other, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions.

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