A cofferdam seepage field calculation method and a calculation system

Abstract

The present application relates to the technical field of underground hydraulic engineering, and discloses a kind of cofferdam seepage field calculation method and calculation system, comprising: based on target cofferdam and the soil body around target cofferdam, construct the three-dimensional seepage analytic model of target cofferdam, and three-dimensional seepage analytic model is divided into four regions;Based on three-dimensional seepage analytic model, the seepage balance equation of four regions is respectively constructed, and the explicit expression of water head distribution of four regions is calculated in combination with the boundary condition of four regions;The continuity condition of four regions is obtained respectively, and the non-homogeneous equation set of four regions is constructed based on the continuity condition of four regions;The non-homogeneous equation set of four regions is solved, the calculation result of water head distribution explicit expression is obtained by bringing the solution result into water head distribution explicit expression, and the calculation result is used as the calculation result of target cofferdam seepage field;The present application solves the problem of low calculation accuracy of the existing cofferdam seepage field calculation method.

Description

Technical Field

[0001] This invention relates to the field of underground hydraulic engineering technology, and in particular to a method and system for calculating the seepage field of a cofferdam. Background Technology

[0002] In recent years, a large number of deep-water projects have emerged in the construction of major projects such as high-rise buildings, underground space development, cross-sea tunnels, and cross-sea bridges in coastal or riverside areas of China. Cofferdams, as a temporary retaining structure, are widely used in the foundation construction of bridge engineering, hydraulic structures, and water supply and drainage engineering structures. Their function is to prevent water from entering the construction site so that drainage, excavation, and construction of foundation engineering facilities can be carried out within the foundation pit enclosed by the cofferdam.

[0003] Studying the seepage and stability of the sealing layer of cofferdams and their foundations to prevent cofferdam instability and seepage damage to the foundation is an important aspect of cofferdam design. Currently, hydrostatic pressure is used to determine the instability of the sealing layer, which introduces a certain error in the actual pressure exerted on the sealing layer. This affects the calculation of seepage flow and seepage pressure on the sealing layer, resulting in low accuracy of seepage field calculations. Therefore, existing methods for calculating the seepage field of cofferdams suffer from low accuracy. Summary of the Invention

[0004] This invention provides a method and system for calculating the seepage field of a cofferdam, in order to solve the problem of low calculation accuracy in existing methods for calculating the seepage field of a cofferdam.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, the present invention provides a method for calculating the seepage field of a cofferdam, comprising: A three-dimensional seepage analysis model of the target cofferdam and the surrounding soil is constructed, and the three-dimensional seepage analysis model is divided into four regions.

[0007] Based on the three-dimensional seepage analytical model, seepage equilibrium equations for four regions were constructed, and explicit expressions for head distribution in the four regions were calculated in combination with the boundary conditions of the four regions.

[0008] Obtain the continuity conditions for each of the four regions, and construct non-homogeneous equation systems for each of the four regions based on the continuity conditions.

[0009] The non-homogeneous equations for the four regions are solved, and the results are substituted into the explicit expression of head distribution to obtain the calculation result of the explicit expression of head distribution. This calculation result is then used as the calculation result of the seepage field of the target cofferdam.

[0010] Secondly, embodiments of this application provide a calculation system for the seepage field of a cofferdam, including a processor and a memory.

[0011] Memory is used to store computer programs.

[0012] When a processor executes a program stored in memory, it implements any of the steps described in the first aspect above.

[0013] Beneficial effects: The method for calculating the seepage field of a cofferdam provided by this invention divides the seepage field around the cofferdam into four regions. The separation of variables method is used to obtain the series solution of the head distribution in cylindrical coordinates for each of the four regions. Combining the continuity condition between regions, and utilizing the orthogonality of Bessel functions, an analytical solution for the steady-state seepage field of a circular cofferdam considering the bottom sealing effect is obtained. Comparison with calculation results from numerical software verifies that this simplified solution has good computational accuracy.

[0014] Furthermore, by quickly solving the simplified solution, the head at any point in the seepage field of the circular cofferdam can be obtained. The influence of design parameters such as the cofferdam radius and the insertion depth of the retaining structure on the seepage field can be analyzed quickly and conveniently, providing an accurate basis for the construction and protection of cofferdam projects. It can also calculate the seepage water pressure borne by the sealing layer with relatively accurate results, and make preliminary optimization designs for the thickness of the sealing layer. This is also of significant engineering importance for ensuring the safe construction of the cofferdam. Attached Figure Description

[0015] Figure 1 A flowchart illustrating the calculation method for the seepage field of a cofferdam according to a preferred embodiment of the present invention; Figure 2 This is a schematic diagram of a three-dimensional seepage model of a cofferdam according to a preferred embodiment of the present invention; Figure 3 This is a comparison and verification diagram of the analytical solution and numerical solution of the seepage field in a preferred embodiment of the present invention; Figure 4 The graph shows a comparison of the flow calculation results of the preferred embodiment of the present invention with other methods. Figure 5 This is a diagram showing the seepage water pressure distribution under different sealing layer thicknesses according to a preferred embodiment of the present invention. Figure 6 This is an evaluation diagram of the thickness optimization of the sealing layer in a preferred embodiment of the present invention. Detailed Implementation

[0016] The technical solution of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "connected" or "linked" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up," "down," "left," "right," etc., are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship also changes accordingly.

[0018] It should be understood that the method for calculating the seepage field of a cofferdam according to this application can be applied to cofferdam construction, such as in the foundation construction of bridge engineering, hydraulic structures, water supply and drainage engineering structures, etc. This is only an example and is not intended to limit the application. Example 1: Please see Figure 1-6 This application provides a method for calculating the seepage field of a cofferdam, including: A three-dimensional seepage analysis model of the target cofferdam and the surrounding soil is constructed, and the three-dimensional seepage analysis model is divided into four regions.

[0019] Based on the three-dimensional seepage analytical model, seepage equilibrium equations were constructed for four regions, and explicit expressions of head distribution in the four regions were calculated by combining the boundary conditions of the four regions.

[0020] Obtain the continuity conditions for each of the four regions, and construct non-homogeneous equation systems for each of the four regions based on the continuity conditions.

[0021] The non-homogeneous equations for the four regions are solved, and the results are substituted into the explicit expression of head distribution to obtain the calculation result of the explicit expression of head distribution. This calculation result is then used as the calculation result of the seepage field of the target cofferdam.

[0022] In the above embodiment, the seepage field around the cofferdam is divided into four regions. The separation of variables method is used to obtain the series solution of the head distribution in cylindrical coordinates for each of the four regions. Combining the continuity condition between regions, and utilizing the orthogonality of Bessel functions, the analytical solution of the steady-state seepage field of the circular cofferdam considering the bottom sealing effect is obtained. By comparing the results with those calculated by numerical software, it is verified that the simplified solution has good computational accuracy.

[0023] In this embodiment, the "surrounding" soil around the target cofferdam refers to the cylindrical soil selected with the center of the bottom of the cofferdam as the center of the cylinder's bottom surface. The size of the cylinder can be adjusted according to actual needs.

[0024] Optionally, a three-dimensional seepage analytical model of the target cofferdam is constructed based on the target cofferdam and the surrounding soil, including: A cylindrical soil mass surrounding the cofferdam is selected, and the soil mass is combined with the water mass above it. An axisymmetric three-dimensional seepage analytical model is established with the center of the cofferdam as the Z-axis and the top surface of the impermeable layer at the bottom of the cofferdam as the r-axis.

[0025] Optionally, the three-dimensional seepage analytical model can be divided into four regions, including: The three-dimensional seepage analytical model is divided into four regions: the inner sealing layer of the cofferdam retaining structure is designated as region 1, the soil layer around the cofferdam retaining structure is designated as region 2, the soil layer at the bottom of the cofferdam retaining structure and the top of the impermeable boundary is designated as region 3, and the soil layer inside the cofferdam retaining structure and below the sealing layer is designated as region 4.

[0026] Optionally, seepage equilibrium equations for the four regions are constructed based on a three-dimensional seepage analytical model, including: Based on a three-dimensional analytical model of seepage, the seepage equilibrium equation is constructed as follows: .

[0027] in, , , , Let these represent the total head functions for regions 1, 2, 3, and 4, respectively. Represents the differential symbol. r , z These represent the two independent variables in the head function.

[0028] Optionally, the boundary conditions for the four regions are as follows: The boundary conditions for region 1 are shown in the following equation: Upper boundary: .

[0029] Outer boundary: .

[0030] The boundary conditions for region 2 are as follows: Upper boundary: .

[0031] Outer boundary: .

[0032] The boundary conditions for region 3 are as follows: Lower boundary: .

[0033] Outer boundary: .

[0034] The boundary conditions for region 4 are as follows: Outer boundary: .

[0035] in, Indicates the water level inside the enclosure structure. This indicates the water level outside the enclosure structure. This represents the distance from the enclosure structure to the outer boundary of the model. Indicates the radius of the cofferdam. This indicates the thickness of the soil layer on the outside of the retaining structure.

[0036] Optionally, the explicit expressions for the head distribution in the four regions can be calculated separately, taking into account the boundary conditions of each region. Substituting the boundary conditions of the four regions into the seepage equilibrium equation, and using the method of separation of variables, the explicit expressions for the head distribution in the four regions are calculated, as shown below: .

[0037] .

[0038] ; .

[0039] Where, in the formula It is a constant term that can be determined by continuous boundary conditions on the region interface; J 0( x ), Y 0( x These are the zeroth-order Bessel functions of the first and second kind, respectively. Represents the separation constant. Represents the separation constant. Represents a sine hyperbolic function. This represents a cosine hyperbolic function.

[0040] Optionally, the continuity conditions for the four regions are as follows: .

[0041] .

[0042] .

[0043] in, Indicates the permeability coefficient of the sealing layer. Indicates the permeability coefficient of soil layer 1. This represents the soil permeability coefficient.

[0044] Optionally, based on the continuity conditions of the four regions, construct four sets of non-homogeneous equations for each region, including: A non-homogeneous system of equations is constructed using the continuity conditions of the four regions, as shown below: .

[0045] .

[0046]

[0047]

[0048] .

[0049] Where 'a' represents the distance from the enclosure structure to the bottom impermeable boundary. The separator represents the separation constant, and d represents the thickness of the sealing layer. This indicates the thickness of the soil layer inside the retaining structure. Represents the first-order Bessel function of the second kind. This represents a first-order Bessel function of the first kind.

[0050] Example 2: Please see Figure 2-6 The specific calculation method for the seepage field of the cofferdam can also be as follows: Step S100: Construct a mathematical analysis model. Select a cylindrical soil mass within a limited area surrounding the cofferdam. Using the center of the circular cofferdam as the Z-axis and the top surface of the impermeable layer at the bottom of the cofferdam as the r-axis, establish an axisymmetric three-dimensional seepage analytical model as follows: Figure 1 The outer boundary of the cofferdam is infinite and can be approximated as impermeable. The retaining structure is also considered impermeable, and its thickness is relatively small compared to the overall width of the model, so its thickness can be ignored. The model is divided into four regions: Region 1 is the sealing layer, Region 2 is the annular soil layer of the outer column of the cofferdam, Region 3 is the columnar soil layer at the bottom of the cofferdam, and Region 4 is the soil layer at the bottom of the sealing layer.

[0051] Step S200: Solve for the expression of the head distribution function. Assuming the soil in the calculation area above the impermeable layer is homogeneous, and the soil seepage is isotropic and conforms to Darcy's law, then the head in each area satisfies the seepage equilibrium equation: .

[0052] In the formula, H1, H2, H3, and H4 represent the total water head of regions 1, 2, 3, and 4, respectively, with the bottom surface of the permeable layer as the reference for water head calculation. The coordinate system is based on the center of the circular cofferdam as the Z-axis and the top surface of the impermeable layer at the bottom of the cofferdam as the r-axis.

[0053] The boundary conditions for region 1 are as follows: upper boundary ( ), outer boundary ( ), .

[0054] The boundary conditions for region 2 are as follows: upper boundary ( ), outer boundary ( ),when When the value is very large, it can be approximated as .

[0055] The boundary conditions for region 3 are as follows: lower boundary ( ), outer boundary ( ), .

[0056] The boundary conditions for region 4 are as follows: outer boundary ( ), .

[0057] Based on the boundary conditions of each region in the seepage field of the foundation pit, the explicit expression for the head distribution in each region when the number of series terms is 1 can be obtained using the method of separation of variables: .

[0058] .

[0059] .

[0060] .

[0061] Step S300: Determine the unknown coefficients in the head function expression. Continuity conditions exist between different regions, as follows: .

[0062] .

[0063] .

[0064] Construct a system of nonhomogeneous equations using the continuity conditions between the four regions: .

[0065] .

[0066]

[0067]

[0068] By using MATLAB code to solve the system of equations, all undetermined coefficients in the head function obtained in step S200 can be determined.

[0069] Example 3: Based on the above calculation method for the seepage field of cofferdams, a design system for optimizing the thickness of the sealing layer based on this calculation method is proposed, including: Seepage field calculation module. A three-dimensional steady-state seepage model of a circular cofferdam is established. The seepage field around the circular cofferdam is divided into four regions. After solving the seepage equilibrium equations in each region using the method of separation of variables, the series solution of the head distribution in the cylindrical coordinate system can be obtained for each of the four regions. Combining the continuity condition between regions and utilizing the orthogonality of Bessel functions, the analytical solution of the steady-state seepage field of the circular cofferdam considering the bottom sealing effect is obtained.

[0070] Seepage flow calculation module. Based on the definition of seepage flow and combined with the analytical solution of the seepage field, the formula for calculating the seepage flow at the cofferdam excavation face is derived using calculus.

[0071] According to Darcy's law, the seepage flow rate at the excavation face of the cofferdam is: (1) Q represents the water inflow rate. S is the cross-sectional area of ​​the seepage. ; seepage velocity ; The hydraulic gradient is given by H1(r,z), which is the head analysis formula for region 1. The hydraulic gradient at any point on the cofferdam excavation face can be obtained.

[0072] (2) From equation (2), it can be seen that the hydraulic gradient has axisymmetry, that is, the hydraulic gradient at a distance r from the central axis z of the cofferdam is equal everywhere. The total seepage flow at the excavation face can be understood as the superposition of the seepage flows of any number of annular regions centered on the z-axis. The seepage flow per unit annular region can be expressed as: (3) right Integrating from 0 to c yields the total seepage flow at the excavation face.

[0073] (4) Water pressure calculation module. Based on Bernoulli's equation and the analytical solution from module 1, the calculation formula for the seepage water pressure on the sealing layer is derived.

[0074] A module for determining the instability limit of the sealing layer is proposed. Based on the "Technical Standard for Steel Cofferdam Engineering GB / T51295-2018", a formula for determining the instability limit of the sealing layer considering seepage force is presented.

[0075] Subsoil layer thickness evaluation module. Based on the discrimination formula obtained from the subsoil layer instability limit discrimination module, a graph describing the relationship between subsoil layer seepage flow and subsoil layer thickness variation is plotted for subsoil layer thickness evaluation.

[0076] In the seepage flow calculation module, the formula for calculating the seepage flow at the considered circular cofferdam excavation face is as follows: .

[0077] In the water pressure calculation module, the formula for calculating the seepage water pressure on the sealing layer is as follows: .

[0078] In the module for determining the instability limit of the sealing layer, a formula for determining the instability limit of the sealing layer considering the permeability force is proposed.

[0079] .

[0080] This application also provides a calculation system for the seepage field of a cofferdam, including a processor and a memory.

[0081] Memory is used to store computer programs.

[0082] When the processor executes the program stored in the memory, it implements any of the method steps in the above-described method for calculating the seepage field of the cofferdam.

[0083] The above-described calculation system for the cofferdam seepage field can implement various embodiments of the above-described calculation method for the cofferdam seepage field and achieve the same beneficial effects, which will not be elaborated here.

[0084] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for calculating the seepage field of a cofferdam, characterized in that, include: A three-dimensional seepage analysis model of the target cofferdam and the surrounding soil is constructed, and the three-dimensional seepage analysis model is divided into four regions. Based on the three-dimensional seepage analytical model, seepage equilibrium equations for four regions were constructed respectively, and explicit expressions of head distribution for the four regions were calculated respectively in combination with the boundary conditions of the four regions. Obtain the continuity conditions for the four regions respectively, and construct the non-homogeneous equation systems for the four regions based on the continuity conditions of the four regions respectively; The non-homogeneous equations for the four regions are solved, and the results are substituted into the explicit expression of head distribution to obtain the calculation result of the explicit expression of head distribution. This calculation result is then used as the calculation result of the seepage field of the target cofferdam. Based on the aforementioned three-dimensional seepage analytical model, seepage equilibrium equations were constructed for four regions, including: Based on the aforementioned three-dimensional seepage analytical model, a seepage equilibrium equation is constructed, as shown below: ； in, , , , Let these represent the total head functions for regions 1, 2, 3, and 4, respectively. Represents the differential symbol. r , z This represents the two independent variables in the head function; The boundary conditions for the four regions are as follows: The boundary conditions for region 1 are shown in the following equation: Upper boundary: ； Outer boundary: ； The boundary conditions for region 2 are as follows: Upper boundary: ； Outer boundary: ； The boundary conditions for region 3 are as follows: Lower boundary: ； Outer boundary: ； The boundary conditions for region 4 are as follows: Outer boundary: ； in, Indicates the water level inside the enclosure structure. This indicates the water level outside the enclosure structure. This represents the distance from the enclosure structure to the outer boundary of the model. Indicates the radius of the cofferdam. Indicates the thickness of the soil layer outside the retaining structure; The explicit expressions for calculating the head distribution in the four regions by combining the boundary conditions of the four regions include: Substituting the boundary conditions of the four regions into the seepage equilibrium equation, and using the method of separation of variables, the explicit expressions for the head distribution in the four regions are calculated, as shown below: ； ； ； ； Where, in the formula , It is a constant term that can be determined by continuous boundary conditions on the region interface; J 0( x () is a zero-order Bessel function of the first kind. Y 0( x () is a zero-order Bessel function of the second kind. Represents the separation constant. Represents the separation constant. Represents a sine hyperbolic function. This represents a cosine hyperbolic function.

2. The method for calculating the seepage field of a cofferdam according to claim 1, characterized in that, The three-dimensional seepage analytical model of the target cofferdam, constructed based on the target cofferdam and the surrounding soil, includes: A cylindrical soil mass surrounding the cofferdam is selected, and the soil mass is combined with the water mass above it. An axisymmetric three-dimensional seepage analytical model is established with the center of the cofferdam as the Z-axis and the top surface of the impermeable layer at the bottom of the cofferdam as the r-axis.

3. The method for calculating the seepage field of a cofferdam according to claim 1, characterized in that, The three-dimensional seepage analysis model is divided into four regions, including: The three-dimensional seepage analysis model is divided into four regions: the inner sealing layer of the cofferdam retaining structure is designated as region 1, the soil layer around the cofferdam retaining structure is designated as region 2, the soil layer at the bottom of the cofferdam retaining structure and the top of the impermeable boundary is designated as region 3, and the soil layer inside the cofferdam retaining structure and below the sealing layer is designated as region 4.

4. The method for calculating the seepage field of a cofferdam according to claim 1, characterized in that, The continuity conditions for the four regions are as follows: ； ； ； in, Indicates the permeability coefficient of the sealing layer. Indicates the permeability coefficient of soil layer 1. This represents the soil permeability coefficient, and 'a' represents the distance from the retaining structure to the bottom impermeable boundary. This indicates the thickness of the soil layer inside the retaining structure.

5. The method for calculating the seepage field of a cofferdam according to claim 4, characterized in that, The construction of non-homogeneous equation systems for the four regions based on the continuity conditions of the four regions includes: A non-homogeneous system of equations is constructed using the continuity conditions of the four regions, as shown below: ； ； ； in, The separator represents the separation constant, and d represents the thickness of the sealing layer. Represents the first-order Bessel function of the second kind. This represents a first-order Bessel function of the first kind.

6. A calculation system for the seepage field of a cofferdam, characterized in that, Including processor and memory; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the steps of the method described in any one of claims 1-5.

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