A method for determining equivalent parameters of a circular ground wall wall equivalent model

Abstract

The application discloses a kind of equivalent parameter determination methods of circular ground connected wall wall equivalent model, it is related to large-span suspension bridge anchorage foundation pit design technical field, this method includes: according to original structure size parameter and material parameter, determine original wall displacement function;According to equivalent structure size parameter, determine equivalent wall displacement function;According to original wall displacement function and equivalent wall displacement function, establish transcendental equation group;Solve the transcendental equation group, obtain equivalent material elastic modulus and equivalent Poisson's ratio.The precision of numerical calculation result is low after the convergence of numerical model is improved in the prior art of circular ground connected wall wall equivalent model, or the convergence of numerical model is insufficient after the precision of numerical calculation result is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of anchorage foundation pit design technology for long-span suspension bridges, specifically to a method for determining the equivalent parameters of an equivalent model of a circular diaphragm wall. Background Technology

[0002] In long-span suspension bridge structures, gravity anchorage foundations are one of the most important structural components for balancing loads through the main cables. Circular diaphragm walls, as deep foundation pit support structures for gravity anchorages, are increasingly widely used. With the construction of a series of mega-projects such as the Lingdingyang Bridge, Yueyang Dongting Lake Bridge, and Yanji Yangtze River Bridge, the engineering community has gained a more extensive understanding and application of ∞-shaped diaphragm wall support structures with stepped inner linings.

[0003] In the existing technology, theoretical calculations for multi-step diaphragm walls often use support springs distributed along the depth as an equivalent; in numerical analysis, shell elements are often used to simulate diaphragm walls or the stepped lining is equivalent to a lining of the same thickness. The above methods have the problem that after the equivalent model of the diaphragm wall improves the convergence of the numerical model, the accuracy of the numerical calculation results is low, or after ensuring the accuracy of the numerical calculation results, the convergence of the numerical model is insufficient. Summary of the Invention

[0004] In view of the deficiencies in the existing technology, the purpose of this invention is to provide a method for determining the equivalent parameters of an equivalent model of a circular diaphragm wall. This method can solve the problems in the existing technology where the accuracy of numerical calculation results is low after improving the convergence of the numerical model, or the convergence of the numerical model is insufficient after ensuring the accuracy of the numerical calculation results.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This solution provides a method for determining the equivalent parameters of an equivalent model of a circular diaphragm wall, including the following steps:

[0007] Determine the original wall displacement function based on the original structural dimensions and material parameters;

[0008] Determine the equivalent wall displacement function based on the equivalent structural dimensions;

[0009] Based on the original wall displacement function and the equivalent wall displacement function, a system of transcendental equations is established;

[0010] Solving the transcendental equations yields the equivalent material elastic modulus and equivalent Poisson's ratio.

[0011] In some alternative schemes, the wall displacement function is established based on plate and shell theory, including:

[0012] Where w(x) is the wall displacement, x is the depth of the diaphragm wall, a is the radius of the wall neutral surface, and γ s Let E be the equivalent unit weight of the soil inside and outside the lining structure, h be the total wall thickness, H be the total height of the diaphragm wall, and β be a trigonometric function variable. μ is the Poisson's ratio of the material.

[0013] In some alternative schemes, the original wall displacement function includes:

[0014] Where w0(x) is the original wall displacement, x is the depth of the diaphragm wall, a0 is the radius of the original wall neutral surface, and γ s Let E0 be the equivalent unit weight of the soil inside and outside the lining structure, h0 be the original material elastic modulus, H be the original total wall thickness, H be the total height of the diaphragm wall, and β0 be the original trigonometric function variable. μ0 is the Poisson's ratio of the original material.

[0015] In some alternative embodiments, the equivalent wall displacement function includes:

[0016]

[0017] Where w1(x) is the equivalent wall displacement, x is the depth of the diaphragm wall, a1 is the radius of the neutral surface of the equivalent wall, and γ s Let E1 be the equivalent unit weight of the soil inside and outside the lining structure, h1 be the equivalent material elastic modulus, H be the equivalent total wall thickness, H be the total height of the diaphragm wall, and β1 be the equivalent trigonometric function variable. μ1 is the equivalent material Poisson's ratio.

[0018] In some alternative schemes, the equivalent wall displacement function equates the original total wall thickness to the total wall thickness of the layer with the largest total thickness of the diaphragm wall and the inner lining.

[0019] In some alternative schemes, establishing a system of transcendental equations based on the original wall displacement function and the equivalent wall displacement function includes:

[0020] By selecting two different depths at the observation locations of the diaphragm wall, and substituting the original wall displacement function and the equivalent wall displacement function, a system of transcendental equations is obtained: Where x1 is the first depth of investigation and x2 is the second depth of investigation.

[0021] In some alternative solutions, before determining the original wall displacement function based on the original structural dimensions and material parameters, it is also necessary to determine whether the increase in the thickness of the diaphragm wall and the lining thickness is less than one-tenth of the diameter of the circular cross section.

[0022] In some alternative solutions, after solving the transcendental equations to obtain the equivalent material elastic modulus and equivalent Poisson's ratio, the solution further includes: verifying the equivalent material elastic modulus and equivalent Poisson's ratio.

[0023] In some alternative solutions, the verification of the equivalent material elastic modulus and equivalent Poisson's ratio includes:

[0024] Calculate the equivalent density of each lining layer;

[0025] Based on the original parameters and equivalent density of the diaphragm wall, establish the original parameter finite element model and the equivalent parameter finite element model.

[0026] Calculate and derive the displacement and stress results at the same locations in the original parameter finite element model and the equivalent parameter finite element model, respectively;

[0027] Based on the displacement and stress results of the original parameter finite element model and the equivalent parameter finite element model, the equivalent parameters of the diaphragm wall are checked.

[0028] In some alternative solutions, the equivalent density of each lining layer is determined by the formula: calculate;

[0029] Where ρ0 is the original density, h0 is the original total wall thickness, ρ1 is the equivalent density, and h1 is the equivalent total wall thickness.

[0030] Compared with existing technologies, the advantages of this invention are as follows: This solution determines the original wall displacement function based on the original structural dimension parameters and material parameters; determines the equivalent wall displacement function based on the equivalent structural dimension parameters; establishes a transcendental equation system based on the original wall displacement function and the equivalent wall displacement function; and solves the transcendental equation system to obtain the equivalent material elastic modulus and equivalent Poisson's ratio. This solves the problem in existing technologies where, after improving the convergence of the numerical model using the equivalent model of the diaphragm wall, the accuracy of the numerical calculation results is low, or after ensuring the accuracy of the numerical calculation results, the convergence of the numerical model is insufficient. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram illustrating the steps of determining the equivalent parameters of the equivalent model of the circular diaphragm wall in an embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram of the displacement function parameters in an embodiment of the present invention;

[0034] Figure 3 This is a schematic diagram of the diaphragm wall structure in an example of an embodiment of the present invention;

[0035] Figure 4 This is a schematic diagram of the original parameter finite element model in an example of an embodiment of the present invention;

[0036] Figure 5 This is a schematic diagram of the equivalent parameter finite element model in an example of an embodiment of the present invention;

[0037] Figure 6 This is a schematic diagram comparing the horizontal displacement and Tresca equivalent stress of typical survey lines of the original parameter model and the equivalent parameter model in the fourth excavation step in an example of an embodiment of the present invention.

[0038] Figure 7 This is a schematic diagram comparing the horizontal displacement and Tresca equivalent stress of typical survey lines of the original parameter model and the equivalent parameter model in the seventh excavation step in an embodiment of the present invention.

[0039] Figure 8 This is a schematic diagram comparing the horizontal displacement and Tresca equivalent stress of typical survey lines of the original parameter model and the equivalent parameter model in the tenth excavation step in an embodiment of the present invention.

[0040] Figure 9 This is a schematic diagram comparing the horizontal displacement and Tresca equivalent stress of typical survey lines in the thirteenth excavation step of the original parameter model and the equivalent parameter model in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0042] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0043] like Figure 1 As shown, the present invention provides a method for determining the equivalent parameters of an equivalent model of a circular diaphragm wall, comprising the following steps:

[0044] S1: Determine the original wall displacement function based on the original structural dimensions and material parameters.

[0045] S2: Determine the equivalent wall displacement function based on the equivalent structural dimension parameters.

[0046] S3: Establish a system of transcendental equations based on the original wall displacement function and the equivalent wall displacement function.

[0047] S4: Solve the transcendental equations to obtain the equivalent material elastic modulus and equivalent Poisson's ratio.

[0048] In this embodiment, based on the moment theory of cylindrical shells in plate and shell theory, and comprehensively applying the displacement calculation theory of a cylindrical thin shell with a fixed lower end and the numerical solution method of nonlinear equations, a method for calculating the equivalent stiffness parameters of a circular diaphragm wall and its inner lining structure as a whole is proposed. This method can improve the convergence of the numerical model and ensure the accuracy of the numerical calculation results by changing the material stiffness. This solves the problem in the prior art where the accuracy of the numerical calculation results is low after improving the convergence of the numerical model using the equivalent model of the circular diaphragm wall, or the convergence of the numerical model is insufficient after ensuring the accuracy of the numerical calculation results.

[0049] In some optional embodiments, the wall displacement function is established based on plate and shell theory, including:

[0050] like Figure 2 As shown, w(x) is the wall displacement, x is the depth of the diaphragm wall, a is the radius of the wall neutral surface, and γ is the radius of the wall neutral surface. s Let E be the equivalent unit weight of the soil inside and outside the lining structure, h be the total wall thickness, H be the total height of the diaphragm wall, and β be a trigonometric function variable. μ is the Poisson's ratio of the material.

[0051] In this embodiment, different cross sections of each step of the cylindrical structure are selected as the analysis objects. Without considering the influence of the weight of the diaphragm wall itself, the displacement calculation function of the diaphragm wall is established based on the plate and shell theory.

[0052] In some optional embodiments, the original wall displacement function includes:

[0053] Where w0(x) is the original wall displacement, x is the depth of the diaphragm wall, a0 is the radius of the original wall neutral surface, and γ s Let E0 be the equivalent unit weight of the soil inside and outside the lining structure, h0 be the original material elastic modulus, H be the original total wall thickness, H be the total height of the diaphragm wall, and β0 be the original trigonometric function variable. μ0 is the Poisson's ratio of the original material.

[0054] In this embodiment, different depths of the diaphragm wall are selected, and the original displacement function of the diaphragm wall is calculated based on the cross-sectional parameters at the selected depths.

[0055] In some optional embodiments, the equivalent wall displacement function includes:

[0056] Where w1(x) is the equivalent wall displacement, x is the depth of the diaphragm wall, a1 is the radius of the neutral surface of the equivalent wall, and γ s Let E1 be the equivalent unit weight of the soil inside and outside the lining structure, h1 be the equivalent material elastic modulus, H be the equivalent total wall thickness, H be the total height of the diaphragm wall, and β1 be the equivalent trigonometric function variable. μ1 is the equivalent material Poisson's ratio.

[0057] In some optional embodiments, the equivalent wall displacement function equates the original total wall thickness to the total wall thickness of the diaphragm wall and the layer with the largest total thickness of the lining.

[0058] In some optional embodiments, establishing a system of transcendental equations based on the original wall displacement function and the equivalent wall displacement function includes:

[0059] By selecting two different depths at the observation locations of the diaphragm wall, and substituting the original wall displacement function and the equivalent wall displacement function, a system of transcendental equations is obtained: Where x1 is the first depth of investigation and x2 is the second depth of investigation.

[0060] In this embodiment, for each inner lining step, two different investigation positions of the diaphragm wall are selected and substituted into the original wall displacement function and the equivalent wall displacement function to obtain a set of transcendental equations with the equivalent material elastic modulus and the equivalent Poisson's ratio as unknowns.

[0061] In some optional embodiments, before determining the original wall displacement function based on the original structural dimensions and material parameters, the method further includes: determining whether the increase in the thickness of the diaphragm wall and the thickness of the lining are both less than one-tenth of the diameter of the circular cross-section.

[0062] In this embodiment, if the increase in both the thickness of the diaphragm wall and the thickness of the lining are less than one-tenth of the diameter of the circular cross-section, the diaphragm wall structure can be analyzed as a thin-walled cylinder, and subsequent steps can be performed. Otherwise, the equivalent parameter determination method of the local diaphragm wall equivalent model is not applicable to this diaphragm wall.

[0063] In some optional embodiments, after solving the transcendental equations to obtain the equivalent material elastic modulus and equivalent Poisson's ratio, the method further includes: verifying the equivalent material elastic modulus and equivalent Poisson's ratio.

[0064] In this embodiment, the applicability of the equivalent parameters determined by this method can be verified by checking the equivalent material elastic modulus and equivalent Poisson's ratio.

[0065] In some optional embodiments, the verification of the equivalent material elastic modulus and equivalent Poisson's ratio includes:

[0066] Calculate the equivalent density of each lining layer;

[0067] Based on the original parameters and equivalent density of the diaphragm wall, establish the original parameter finite element model and the equivalent parameter finite element model.

[0068] Calculate and derive the displacement and stress results at the same locations in the original parameter finite element model and the equivalent parameter finite element model, respectively;

[0069] Based on the displacement and stress results of the original parameter finite element model and the equivalent parameter finite element model, the equivalent parameters of the diaphragm wall are checked.

[0070] In some optional embodiments, the equivalent density of each liner layer is determined by the formula: calculate;

[0071] Where ρ0 is the original density, h0 is the original total wall thickness, ρ1 is the equivalent density, and h1 is the equivalent total wall thickness.

[0072] The following is a specific example to facilitate understanding of the present invention.

[0073] like Figure 3 As shown in the schematic diagram, this is the diaphragm wall deep foundation pit support structure of an ∞-shaped anchorage for a cross-river bridge. The cap beam is 2.8m thick and 3.0m deep; the diaphragm wall is 1.2m thick and 48.0m deep; the inner lining structure is divided into 4 layers: the first layer is 1.5m thick with a 0.75m thick central partition wall; the second layer is 2.0m thick with a 1.0m thick central partition wall; the third layer is 2.5m thick with a 1.25m thick central partition wall; and the fourth layer is 3.0m thick with a 1.5m thick central partition wall. The radius of the neutral surface of the ∞-shaped diaphragm wall is 36.9m. Except for the cap beam, the inner lining is installed every 9m along the depth direction of the diaphragm wall, with the diaphragm wall embedded in the rock at a depth of 9m. The material is C30 concrete. The geological parameters are shown in Table 1.

[0074] Table 1

[0075]

[0076]

[0077] In this example, the soil layers are numbered from top to bottom. Assuming that x is in the i-th soil layer, the equivalent unit weight of the soil at depth x is defined as the weighted average unit weight of the soil layers above depth x, that is: The equivalent soil weight values ​​at different depths can be obtained from this. The geometric and strength parameters of the diaphragm wall at different lining layers are shown in Table 2.

[0078] Table 2

[0079]

[0080]

[0081] From Table 2 and the original displacement calculation function The original displacement at each x point can be calculated.

[0082] The cross-sections of the first to third layers of the lining are equivalent to the geometric parameters of the standard fourth layer lining cross-section, i.e., h1 = 4.2, a1 = 35.4.

[0083] Taking the third lining layer as an example, the parameters of the third lining layer are substituted into the equivalent displacement calculation function. A system of transcendental equations is formed simultaneously with the original displacement function described above. Numerical calculations yielded E3 = 26.8 GPa and μ3 = 0.207.

[0084] The equivalent density of the wall can be calculated by the following formula:

[0085]

[0086] Similarly, we can obtain the equivalent E1, E2, μ1, μ2, ρ1, ρ2, and thus obtain the wall equivalent parameters of the inner lining of the first to third layers and the diaphragm wall as a whole, as shown in Table 3.

[0087] Table 3

[0088]

[0089]

[0090] To verify the accuracy of the obtained equivalent stiffness parameters of the diaphragm wall, a finite element model with original parameters and a finite element model with equivalent parameters were established as follows: Figure 4 and Figure 5 As shown, except for the cross-sectional dimensions and material parameters within each lining height range, all other parameters of the two finite element models are kept consistent. The original parameters of the diaphragm wall in the finite element model are taken from the actual parameters, and the equivalent parameters of the diaphragm wall in the finite element model are taken from Table 3. The data of each soil layer parameter are shown in Table 1. The penalty function method is used for the contact between the diaphragm wall and the outer soil.

[0091] Since this ∞-shaped diaphragm wall support structure is centrally symmetrical, a 1 / 4 model can be taken as the research object. This anchorage foundation pit is excavated in 13 steps, with each step excavating 3m. Therefore, the calculation results of the 4th, 7th, 10th and 13th excavation steps can be compared.

[0092] Extract the horizontal displacement and Tresca equivalent stress values ​​at corresponding depths from three typical survey lines, such as... Figures 6 to 9 As shown, the comparison reveals that when the foundation pit excavation is shallow, the differences in horizontal displacement and Tresca equivalent stress values ​​at different depths for each survey line in the finite element model before and after the equivalence model are small. As the excavation depth increases, the differences in horizontal displacement and Tresca equivalent stress values ​​at different depths of the diaphragm wall gradually increase. However, the response values ​​of the finite element model after the equivalence model are all greater than those before the equivalence model, indicating a conservative design that is beneficial to structural safety. Furthermore, the number of elements in the finite element model before and after the equivalence model are 182,311 and 104,806 respectively, a 43% reduction compared to the original model, significantly reducing the computational load. Simultaneously, since the equivalent model does not exhibit abrupt shape changes at the lining steps, it avoids the existence of local stresses to a certain extent, greatly improving the convergence of the computational model and reducing the workload.

[0093] Therefore, the diaphragm wall support structure with stepped lining can be simplified using the equivalent stiffness method described above. This greatly reduces the workload of numerical calculations while improving the convergence of numerical calculations, provided that the calculation accuracy and design requirements are met.

[0094] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0095] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0096] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for determining the equivalent parameters of an equivalent model of a circular diaphragm wall, characterized in that, Includes the following steps: Determine the original wall displacement function based on the original structural dimensions and material parameters; Determine the equivalent wall displacement function based on the equivalent structural dimensions; Based on the original wall displacement function and the equivalent wall displacement function, a system of transcendental equations is established; Solving the transcendental equations yields the equivalent material elastic modulus and equivalent Poisson's ratio; The wall displacement function is established based on plate and shell theory, including: ; in, This is for wall displacement. The depth of the diaphragm wall location. Let the radius be the neutral surface radius of the wall. The equivalent unit weight of the soil inside and outside the lining structure. The elastic modulus of the material. This is the total thickness of the wall. The total height of the diaphragm wall. For trigonometric function variables, , Poisson's ratio of the material; The original wall displacement function includes: ; in, This represents the original wall displacement. The depth of the diaphragm wall location. The radius of the original wall neutral surface. The equivalent unit weight of the soil inside and outside the lining structure. The elastic modulus of the original material. This represents the original total wall thickness. The total height of the diaphragm wall. For the original trigonometric function variables, , Poisson's ratio of the original material; The equivalent wall displacement function includes: ; in, This is the equivalent wall displacement. The depth of the diaphragm wall location. The radius of the equivalent wall neutral surface. The equivalent unit weight of the soil inside and outside the lining structure. This is the equivalent material elastic modulus. This is the equivalent total wall thickness. The total height of the diaphragm wall. For equivalent trigonometric function variables, , The equivalent material Poisson's ratio.

2. The method for determining the equivalent parameters of the equivalent model of a circular diaphragm wall as described in claim 1, characterized in that, The equivalent wall displacement function equates the original total wall thickness to the total wall thickness of the layer with the largest total thickness of the diaphragm wall and the inner lining.

3. The method for determining the equivalent parameters of the equivalent model of a circular diaphragm wall as described in claim 1, characterized in that, The establishment of a transcendental equation system based on the original wall displacement function and the equivalent wall displacement function includes: By selecting two different depths at the observation locations of the diaphragm wall, and substituting the original wall displacement function and the equivalent wall displacement function, a system of transcendental equations is obtained: ,in, The first level of investigation. This is the second depth of investigation.

4. The method for determining the equivalent parameters of the equivalent model of a circular diaphragm wall as described in claim 1, characterized in that, Before determining the original wall displacement function based on the original structural dimensions and material parameters, the process also includes: determining whether the increase in the thickness of the diaphragm wall and the lining thickness is less than one-tenth of the diameter of the circular cross section.

5. The method for determining the equivalent parameters of the equivalent model of a circular diaphragm wall as described in claim 1, characterized in that, After solving the transcendental equations to obtain the equivalent material elastic modulus and equivalent Poisson's ratio, the method further includes: verifying the equivalent material elastic modulus and equivalent Poisson's ratio.

6. The method for determining the equivalent parameters of the equivalent model of a circular diaphragm wall as described in claim 5, characterized in that, The verification of the equivalent material elastic modulus and equivalent Poisson's ratio includes: Calculate the equivalent density of each lining layer; Based on the original parameters and equivalent density of the diaphragm wall, establish the original parameter finite element model and the equivalent parameter finite element model; Calculate and derive the displacement and stress results at the same locations in the original parameter finite element model and the equivalent parameter finite element model, respectively; Based on the displacement and stress results of the original parameter finite element model and the equivalent parameter finite element model, the equivalent parameters of the diaphragm wall are checked.

7. The method for determining the equivalent parameters of the equivalent model of a circular diaphragm wall as described in claim 6, characterized in that, The equivalent density of each lining layer is determined by the formula: calculate; in, Original density, This represents the original total wall thickness. For equivalent density, This represents the equivalent total wall thickness.

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