A method for calculating lateral deformation of ground-connected walls using third-order shear deformation plate theory

Abstract

The invention discloses a method for calculating the lateral deformation of a ground-connected wall using a third-order shear deformation plate theory, comprising the following steps: combining actual working conditions to obtain parameters of a calculation object, the parameters including geometric and physical mechanical parameters of a soil layer, a ground-connected wall and a support system; determining a deformation function of the underground continuous wall according to the third-order shear deformation plate theory; determining a coefficient matrix according to the Ritz method, the minimum potential energy principle and the earth pressure theory; obtaining a matrix equation according to the minimum potential energy principle; bringing the coefficient matrix into the matrix equation to solve the lateral deformation function of the underground continuous wall; the invention has the advantages of high precision of the calculation result and fast calculation speed, and providing optimized design guidance for the internal support arrangement mode, excavation step, ground-connected wall thickness and insertion ratio in actual construction.

Description

Technical Field

[0001] The invention relates to the technical field of lateral deformation simulation calculation of foundation pit retaining structure, and in particular to a method for calculating lateral deformation of ground-connected wall using third-order shear deformation plate theory. Background Art

[0002] With the development of urban underground space, underground continuous wall support with internal support has been widely used in the field of foundation pit engineering. In my country, underground pipelines are intricate and the excavation of deep foundation pits will inevitably have an adverse impact on the surrounding environment. If the stability of the foundation pit is not properly handled, it will cause major engineering accidents. Therefore, from the perspective of limiting foundation pit deformation and construction safety, it is of great significance to study how to accurately calculate and predict the lateral deformation of the foundation pit. In addition, the parameters that affect the lateral deformation of the underground continuous wall, such as the arrangement of internal supports, the thickness of the ground-connected wall and the depth of burial, need to be reasonably designed, which also requires the accuracy of the calculation and prediction of the lateral deformation of the retaining structure.

[0003] The existing methods for obtaining the deformation of underground continuous walls mainly include field monitoring or the finite element method. However, field monitoring can only obtain the deformation of part of the wall and cannot grasp the overall deformation characteristics of the underground continuous wall. Although the finite element method can obtain the overall deformation of the wall more accurately, its calculation is relatively complicated and the parameter setting is highly empirical, which has limited guidance for actual engineering design.

[0004] Compared with the elastic thin plate theory, the third-order shear deformation theory can more accurately consider the influence of the thickness of the underground continuous wall on the lateral deformation of the wall, so its calculation results are highly reliable. Summary of the invention

[0005] In view of the defects of the prior art, the present invention provides a method for calculating the lateral deformation of the ground-connected wall using the third-order shear deformation plate theory, which can more accurately obtain the overall deformation of the wall while ensuring a fast calculation speed, thereby further providing optimization design guidance for the internal support arrangement, ground-connected wall thickness and insertion ratio in actual construction.

[0006] In order to achieve the above invention object, the technical solution adopted by the present invention is as follows:

[0007] A method for calculating the lateral deformation of a ground-connected wall using a third-order shear deformation plate theory comprises the following steps:

[0008] The first step is to obtain the parameters of the calculation object based on the actual working conditions, including the geometric and physical mechanical parameters of the soil layer, ground-connected wall, and support system;

[0009] The second step is to determine the deformation function of the underground continuous wall according to the third-order shear deformation plate theory;

[0010] The third step is to determine the coefficient matrix according to the pb-2 Ritz method, the minimum potential energy principle and the earth pressure theory; the matrix equation is obtained according to the minimum potential energy principle;

[0011] The fourth step is to substitute the coefficient matrix into the matrix equation to solve the lateral deformation function of the underground continuous wall;

[0012] Step 5: Compare the solution value with the measured value to verify whether the parameter value and calculation are correct; if not, return to step 2; if correct, proceed to step 6;

[0013] Step 6: Modify the thickness of the underground continuous wall, the arrangement of the internal supports and the depth of the buried soil for parameter analysis;

[0014] Step 7. After completing the above steps and confirming that they are correct, the deformation results of the underground continuous wall can be predicted before construction.

[0015] Furthermore, in the first step, the parameters of the calculation object are obtained in combination with the actual working conditions. The parameters include the geometric and physical mechanical parameters of the soil layer, ground-connected wall, and support system. The active earth pressure is calculated using the earth pressure theory, and the passive earth pressure is calculated using the linear elastic "m" method. The internal support is simulated by elastic rods.

[0016] Furthermore, in the second step, the deformation function of the underground continuous wall is determined according to the third-order shear deformation plate theory:

[0017]

[0018]

[0019] w(x,y,z)=w0(x,y)

[0020] Where u0(x,y) is the displacement of the mid-surface along the y-axis, v0(x,y) is the displacement of the mid-surface along the x-axis, w0(x,y) is the displacement of the mid-surface along the z-axis, and θ(x,y) is the bending slope along the y-axis. is the curvature slope along the x-axis, c1 is

[0021] Furthermore, in the third step, according to the pb-2 Ritz method, u0(x,y), v0(x,y), w0(x,y), θ(x,y) and The expression is as follows:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] In the formula, φ xi (x,y),φ yi (x,y),φ zi (x,y),ψ xi (x,y) and ψ yi (x, y) are some functions related only to x and y; a i 、b i 、c i ,d i and e i are the unknown parameters that can be solved; m, n, l, o and p are the number of unknown parameters

[0028] Furthermore, in the fourth step, the expression of potential energy is obtained by combining the support conditions and soil layer information of the actual working conditions, as follows:

[0029] E p =UJ

[0030] Where U is the strain energy of the underground continuous wall, which is related to the deformation function established above; J is the work done by the external load, including the work done by the internal support, the work done by the active earth pressure and the work done by the passive earth pressure.

[0031] Furthermore, in the fourth step, according to the principle of minimum potential energy and The following matrix equation is obtained.

[0032]

[0033] Where [K] is the coefficient stiffness matrix for solving five unknown parameters; middle and

[0034] Furthermore, in the fourth step, the matrix equation is used to obtain the unknown parameter c i Then, substitute it into The overall lateral deformation of the underground continuous wall can be obtained.

[0035] Furthermore, the soil pressure work calculation can be combined with different soil pressure theories to improve the accuracy of the calculation results.

[0036] Furthermore, the accuracy of the calculation result is related to the number of unknown parameters m, n, l, o and p. In actual calculations, the accuracy of the calculation can be improved by increasing the number of parameters, but too many parameters may cause a decrease in calculation efficiency. Therefore, an appropriate number of parameters is taken to improve the calculation speed while ensuring the calculation accuracy.

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] Taking into full consideration the characteristics of the third-order shear deformation theory and the deformation and stress of the ground-connected wall, a model that regards the ground-connected wall as a third-order shear deformation plate is proposed, and a method for simulating and calculating the lateral deformation is realized. In this method, the support form, soil pressure calculation, etc. can be conveniently embedded in the calculation model according to different working conditions, and the stress deformation of the entire wall can be calculated by combining the third-order shear deformation plate theory, the Ritz method and the minimum potential energy principle. The calculation results of the present invention are high in accuracy and fast in calculation speed, providing optimization design guidance for the internal support arrangement method, excavation step, ground-connected wall thickness and insertion ratio in actual construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic diagram of a coordinate system according to an embodiment of the present invention; Figure 1 Where h is the thickness of the underground continuous wall, L is the length of the underground continuous wall parallel to the ground, and H is the length of the underground continuous wall perpendicular to the ground;

[0040] Figure 2 A schematic diagram of a calculation process of an embodiment of the present invention;

[0041] Figure 3 A calculation diagram of an embodiment of the present invention;

[0042] Figure 4 A schematic diagram of the overall deformation of the underground continuous wall obtained from the calculation results of an embodiment of the present invention;

[0043] Figure 5 Schematic diagram of comparison between wall deformation results and construction monitoring values ​​according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0045] like Figure 1 As shown in the figure, the coordinate system is established according to the third-order shear deformation plate system establishment method in the figure, where h is the thickness of the underground continuous wall, L is the length of the underground continuous wall in the direction parallel to the ground, and H is the length of the underground continuous wall in the direction perpendicular to the ground;

[0046] like Figure 2As shown, a method for calculating the lateral deformation of a ground-connected wall using a third-order shear deformation plate theory includes the following steps:

[0047] The first step is to obtain the parameters of the calculation object in combination with the actual working conditions, including the geometric and physical mechanical parameters of the soil layer, ground-connected wall, and support system. The active earth pressure is calculated using the earth pressure theory, the passive earth pressure is calculated using the linear elastic "m" method, and the elastic rods are used to simulate the internal support.

[0048] In the second step, the deformation function of the underground continuous wall is determined according to the third-order shear deformation plate theory:

[0049]

[0050]

[0051] w(x,y,z)=w0(x,y)

[0052] Where u0(x,y) is the displacement of the mid-surface along the y-axis, v0(x,y) is the displacement of the mid-surface along the x-axis, w0(x,y) is the displacement of the mid-surface along the z-axis, and θ(x,y) is the bending slope along the y-axis. is the curvature slope along the x-axis, c1 is

[0053] The third step is to set up u0(x,y), v0(x,y), w0(x,y), θ(x,y) and as follows:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] In the formula, φ xi (x,y),φ yi (x,y),φ zi (x,y),ψ xi (x,y) and ψ yi (x, y) are some functions related only to x and y; a i 、b i 、c i ,d i and e i are the unknown parameters required; m, n, l, o and p are the number of unknown parameters

[0060] The fourth step is to combine the actual working conditions and soil layer information to obtain the potential energy expression as follows:

[0061] E p =UJ

[0062] Where U is the strain energy of the underground continuous wall, which is related to the deformation function established above; J is the work done by the external load, including the work done by the internal support, the work done by the active earth pressure and the work done by the passive earth pressure.

[0063] Step 5: According to the principle of minimum potential energy and The following matrix equation can be obtained.

[0064]

[0065] Where [K] is the coefficient stiffness matrix for solving five unknown parameters; middle and

[0066] In the embodiment of the present invention, the unknown parameter c is obtained by using a matrix equation. i Then, substitute it into The overall lateral deformation of the underground continuous wall is obtained.

[0067] Since the calculation amount of the embodiment of the present invention is large, involving matrix solving and multiple integrations, it is suitable to use software programming to implement the calculation process, and the interface can make the calculation method a solution software that can directly calculate the underground continuous wall by inputting parameters, so as to facilitate its promotion and use in engineering. Further, using MATLAB programming software, the third-order shear deformation plate theory is combined with engineering practice, and the rationality of the present invention is verified by case analysis.

[0068] Figure 3 The case shown is the foundation pit of Dinggong Road South Station on Metro Line 2 in a typical stratum in Nanchang. The specific working condition of this project is that the station adopts the open-cut method to construct the main structure, and its retaining structure type is underground continuous wall + internal support. The thickness of the underground continuous wall is 800mm, and the concrete wall grade is C35. There are three vertical supports in the standard section of the station foundation pit. The first one adopts 800×1000mm reinforced concrete support, and the support spacing is about 9m; the second and third steel supports are Ф800 (t=16mm), and the horizontal spacing is about 3m. Figure 4 and 5 As shown, the calculation results of the present invention are accurate and can simulate the overall lateral deformation of the underground continuous wall, providing a theoretical basis for the lateral deformation control and parameter optimization of the wall-supported ground-connected wall.

[0069] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and should be understood that the protection scope of the present invention is not limited to such special statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for calculating the lateral deformation of a ground-connected wall using the third-order shear deformation plate theory, characterized in that: The following steps are involved: The first step is to obtain the parameters of the calculation object based on the actual working conditions, including the geometric and physical mechanical parameters of the soil layer, ground-connected wall, and support system; The second step is to determine the deformation function of the underground continuous wall according to the third-order shear deformation plate theory, as follows: w(x,y,z)=w0(x,y) Where u0(x,y) is the displacement of the mid-surface along the y-axis, v0(x,y) is the displacement of the mid-surface along the x-axis, w0(x,y) is the displacement of the mid-surface along the z-axis, and θ(x,y) is the bending slope along the y-axis. is the curvature slope along the x-axis, c1 is The third step is to determine the coefficient matrix according to the pb-2 Ritz method, the minimum potential energy principle and the earth pressure theory; the matrix equation is obtained according to the minimum potential energy principle; The fourth step is to substitute the coefficient matrix into the matrix equation to solve the lateral deformation function of the underground continuous wall; Step 5: Compare the solution value with the measured value to verify whether the parameter value and calculation are correct; if not, return to step 2; if correct, proceed to step 6; Step 6: Modify the thickness of the underground continuous wall, the arrangement of the internal supports and the depth of the buried soil for parameter analysis; Step 7. After completing the above steps and confirming that they are correct, the deformation results of the underground continuous wall can be predicted before construction.

2. The method for calculating lateral deformation of ground-connected walls using third-order shear deformation plate theory according to claim 1 is characterized in that: In the first step, the parameters of the calculation object are obtained in combination with the actual working conditions. The parameters include the geometric and physical mechanical parameters of the soil layer, ground-connected wall, and support system. The active earth pressure is calculated using the earth pressure theory, and the passive earth pressure is calculated using the linear elastic "m" method. The internal support is simulated by elastic rods.

3. The method for calculating lateral deformation of ground-connected walls using third-order shear deformation plate theory according to claim 1 is characterized in that: In the fourth step, the expression of potential energy is obtained by combining the support conditions and soil layer information of the actual working conditions, as follows: HAVE BEEN p =UJ Where U is the strain energy of the underground continuous wall, which is related to the deformation function established above; J is the work done by the external load, including the work done by the internal support, the work done by the active earth pressure and the work done by the passive earth pressure.

4. The method for calculating lateral deformation of ground-connected walls using third-order shear deformation plate theory according to claim 1 is characterized in that: In the fourth step, according to the principle of minimum potential energy and The following matrix equation is obtained; Where [K] is the coefficient stiffness matrix for solving five unknown parameters; middle and 5. The method for calculating lateral deformation of ground-connected wall using third-order shear deformation plate theory according to claim 1 is characterized in that: In the fourth step, the unknown parameter c is obtained by using the matrix equation i Then, substitute it into The overall lateral deformation of the underground continuous wall can be obtained.

6. The method for calculating lateral deformation of ground-connected walls using third-order shear deformation plate theory according to claim 1 is characterized in that: The soil pressure work calculation is combined with different soil pressure theories to improve the accuracy of the calculation results.

7. The method for calculating lateral deformation of ground-connected walls using third-order shear deformation plate theory according to claim 1 is characterized in that: The accuracy of the calculation result is related to the number of unknown parameters m, n, l, o and p. In actual calculation, an appropriate number of parameters is selected to improve the calculation speed while ensuring the calculation accuracy.

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