CN116415425A - Calculation method and calculation system for cofferdam seepage field - Google Patents
Calculation method and calculation system for cofferdam seepage field Download PDFInfo
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- 239000002689 soil Substances 0.000 claims abstract description 34
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- 238000004590 computer program Methods 0.000 claims description 3
- 238000007789 sealing Methods 0.000 description 13
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- 238000005457 optimization Methods 0.000 description 2
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Abstract
The invention relates to the technical field of underground hydraulic engineering, and discloses a cofferdam seepage field calculation method and a cofferdam seepage field calculation system, wherein the method comprises the following steps: constructing a three-dimensional seepage analysis model of the target cofferdam based on the target cofferdam and soil surrounding the target cofferdam, and dividing the three-dimensional seepage analysis model into four areas; respectively constructing seepage balance equations of the four areas based on the three-dimensional seepage analysis model, and respectively calculating water head distribution explicit expressions of the four areas by combining boundary conditions of the four areas; respectively obtaining continuous conditions of the four areas, and respectively constructing a non-homogeneous equation set of the four areas based on the continuous conditions of the four areas; solving a non-homogeneous equation set of the four areas, introducing a solution result into a water head distribution explicit expression to obtain a calculation result of the water head distribution explicit expression, and taking the calculation result as a calculation result of a target cofferdam seepage field; the method solves the problem of lower calculation accuracy in the existing cofferdam seepage field calculation method.
Description
Technical Field
The invention relates to the technical field of underground hydraulic engineering, in particular to a cofferdam seepage field calculation method and a cofferdam seepage field calculation system.
Background
In recent years, a great deal of deep water area engineering is developed in the major engineering construction of high-rise buildings, underground space development, cross-sea tunnels, cross-sea bridges and the like in coastal or river-along areas of China. The cofferdam is used as a temporary enclosure structure and is widely applied to the foundation construction of bridge engineering, hydraulic structures and water supply and drainage engineering structures, and the cofferdam has the function of preventing water from entering a construction position so as to drain, excavate and construct the foundation engineering structures in a foundation pit enclosed by the cofferdam.
The stability of the cofferdam, seepage of the foundation thereof and the seepage damage of the sealing layer are studied, the occurrence of instability and weir-based seepage damage of the cofferdam is prevented, the method is an important content of cofferdam design, hydrostatic pressure is adopted when the instability of the sealing layer is judged at present, and certain errors exist on the actual pressure of the sealing layer, so that the calculation of seepage flow of the sealing layer and the pressure of the seepage flow is influenced, and the calculation accuracy of a seepage field is lower. Therefore, the existing cofferdam seepage field calculation method has the problem of low calculation accuracy.
Disclosure of Invention
The invention provides a calculation method and a calculation system of a cofferdam seepage field, which are used for solving the problem of lower calculation accuracy in the existing calculation method of the cofferdam seepage field.
In order to achieve the above object, the present invention is realized by the following technical scheme:
in a first aspect, the invention provides a method for calculating a cofferdam seepage field, which comprises the following steps:
and constructing a three-dimensional seepage analysis model of the target cofferdam based on the target cofferdam and the soil body around the target cofferdam, and dividing the three-dimensional seepage analysis model into four areas.
And respectively constructing seepage balance equations of the four areas based on the three-dimensional seepage analysis model, and respectively calculating water head distribution explicit expressions of the four areas by combining boundary conditions of the four areas.
And respectively acquiring continuous conditions of the four areas, and respectively constructing non-homogeneous equation sets of the four areas based on the continuous conditions of the four areas.
Solving a non-homogeneous equation set of the four areas, introducing the solving result into a water head distribution explicit expression to obtain a calculation result of the water head distribution explicit expression, and taking the calculation result as a calculation result of a target cofferdam seepage field.
In a second aspect, an embodiment of the present application provides a computing system for a cofferdam seepage field, including a processor and a memory.
And a memory for storing a computer program.
A processor for implementing the method steps of any one of the above first aspects when executing a program stored on a memory.
The beneficial effects are that:
according to the calculation method of the cofferdam seepage field, the peripheral seepage field of the cofferdam is divided into 4 areas, the water head distribution series solution form of the 4 areas under the cylindrical coordinate system is obtained respectively by using a separation variable method, continuous conditions among the areas are combined, and the analysis solution of the circular cofferdam steady-state seepage field considering the bottom sealing effect is obtained by using Bessel function orthogonality. By comparing with the calculation result of the numerical software, the simplified solution is verified to have good calculation precision.
Further, the water head of any point in the circular cofferdam seepage field is obtained through rapid solution by simplifying, the influence conditions of design parameters such as cofferdam radius, building envelope insertion depth and the like on the seepage field are rapidly and conveniently analyzed, and accurate basis is provided for construction and protection of cofferdam engineering; the seepage water pressure born by the bottom sealing layer can be accurately calculated, the thickness of the bottom sealing layer can be initially optimally designed, and the method has obvious engineering significance in ensuring the safe construction of the cofferdam.
Drawings
FIG. 1 is a flow chart of a method of calculating a cofferdam seepage field in accordance with a preferred embodiment of the present invention;
FIG. 2 is a schematic view of a three-dimensional seepage model of a cofferdam in accordance with a preferred embodiment of the present invention;
FIG. 3 is a graph showing the comparison and verification of the analysis solution and the numerical solution of the seepage field according to the preferred embodiment of the present invention;
FIG. 4 is a graph showing the flow calculation comparison between the calculation method and other methods according to the preferred embodiment of the present invention;
FIG. 5 is a graph showing the distribution of the seepage water pressure at different thicknesses of the back cover layer according to the preferred embodiment of the present invention;
fig. 6 is a view showing the evaluation of the optimization of the thickness of the back sheet according to the preferred embodiment of the present invention.
Detailed Description
The following description of the present invention will be made clearly and fully, and it is apparent that the embodiments described are only some, but not all, of the embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The terms "first," "second," and the like, as used herein, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. Likewise, the terms "a" or "an" and the like do not denote a limitation of quantity, but rather denote the presence of at least one. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", etc. are used merely to indicate a relative positional relationship, which changes accordingly when the absolute position of the object to be described changes.
It should be understood that the method for calculating the cofferdam seepage field of the present application can be applied to cofferdam construction, such as bridge engineering, hydraulic structure, water supply and drainage engineering structure, etc., and is only used as an example and not limited thereto
Example 1:
referring to fig. 1-6, an embodiment of the present application provides a method for calculating a cofferdam seepage field, including:
and constructing a three-dimensional seepage analysis model of the target cofferdam based on the target cofferdam and the soil body around the target cofferdam, and dividing the three-dimensional seepage analysis model into four areas.
And respectively constructing seepage balance equations of the four areas based on the three-dimensional seepage analysis model, and respectively calculating water head distribution explicit expressions of the four areas by combining boundary conditions of the four areas.
And respectively acquiring continuous conditions of the four areas, and respectively constructing non-homogeneous equation sets of the four areas based on the continuous conditions of the four areas.
Solving a non-homogeneous equation set of the four areas, introducing the solving result into a water head distribution explicit expression to obtain a calculation result of the water head distribution explicit expression, and taking the calculation result as a calculation result of a target cofferdam seepage field.
In the embodiment, the surrounding seepage field of the cofferdam is divided into 4 areas, the water head distribution series solution form of the 4 areas under the cylindrical coordinate system is obtained by using a separation variable method, continuous conditions among the areas are combined, and the analysis solution of the circular cofferdam steady-state seepage field considering the bottom sealing effect is obtained by using Bessel function orthogonality. By comparing with the calculation result of the numerical software, the simplified solution is verified to have good calculation precision.
In the embodiment, the periphery of the soil around the target cofferdam is a cylindrical soil body selected by taking the center of the bottom of the cofferdam as the center of the bottom surface of the cylinder, and the size of the cylinder can be adjusted according to actual requirements.
Optionally, constructing a three-dimensional seepage analysis model of the target cofferdam based on the target cofferdam and soil surrounding the target cofferdam comprises:
selecting a cylindrical soil body around the cofferdam, combining the soil body with a water body above the soil body, taking the center of the cofferdam as a Z axis, taking the top surface of a water impermeable layer at the bottom of the cofferdam as an r axis, and establishing an axisymmetric three-dimensional seepage analysis model.
Optionally, dividing the three-dimensional seepage analysis model into four regions includes:
taking the bottom layer inside the cofferdam enclosure as an area 1, taking the soil layer around the cofferdam enclosure as an area 2, taking the soil layer at the bottom of the cofferdam enclosure and the top of the watertight boundary as an area 3, taking the soil layer inside the cofferdam enclosure and below the bottom layer as an area 4, and dividing the three-dimensional seepage analysis model to obtain four divided areas.
Optionally, a seepage balance equation of the four areas is respectively constructed based on the three-dimensional seepage analysis model, which comprises the following steps:
and constructing a seepage balance equation based on the three-dimensional seepage analysis model, wherein the equation is as follows:
wherein H is 1 、H 2 、H 3 、H 4 The total head functions for zone 1, zone 2, zone 3 and zone 4 are shown,
representing differential symbols, r, z represent two independent variables in the head function.
Optionally, the boundary conditions of the four regions are respectively:
the boundary conditions for region 1 are as follows:
upper boundary:
(z＝h 1 ),H 1 ＝h 1 。
outer boundary:
the boundary conditions for region 2 are as follows:
upper boundary:
(z＝T 2 ),H 2 ＝h 2 。
outer boundary:
the boundary conditions for region 3 are as follows:
the lower boundary:
outer boundary:
the boundary conditions for region 4 are as follows:
outer boundary:
wherein h is 1 Represents the water level in the enclosure structure, h 2 Represents the water level outside the enclosure, b represents the distance from the enclosure to the outer boundary of the model, c represents the cofferdam radius, T 2 And the thickness of the soil layer outside the enclosure structure is shown.
Optionally, calculating the water head distribution explicit expression of the four areas respectively in combination with the boundary conditions of the four areas includes:
the boundary conditions of the four areas are taken into a seepage flow equation, and the water head distribution explicit expression of the four areas is calculated by using a separation variable method, wherein the expressions are respectively as follows:
wherein A is in the formula 10 、A n 、B 10 、B m 、C 10 、C i 、D 10 、D n 、E n Is a constant term that can be determined with continuous boundary conditions on the area interface; j (J) 0 (x)、Y 0 (x) Respectively zero-order Bessel functions of the first class and the second class, lambda m Represents the separation constant lambda m Representing the separation constant, sinh (x) represents a sine hyperbola function, and cosh (x) represents a cosine hyperbola function.
Alternatively, the four regions are respectively in continuous condition:
wherein k is 0 Represents the permeability coefficient, k, of the back cover layer 1 Represents the permeability coefficient, k, of soil layer 1 2 Represents the permeability coefficient of the soil layer. Alternatively, a system of non-homogeneous equations for the four regions is constructed based on continuous conditions for the four regions, respectively, including: a non-homogeneous system of equations is constructed using the continuous conditions of the four regions, the system of equations of which is shown below:
wherein a represents the distance from the enclosure to the bottom watertight boundary, lambda i Represents the separation constant, d represents the thickness of the back cover layer, T 1 Represents the thickness of soil layer inside the enclosure structure, Y 1 (x) Represents a Bessel function of the second class, J 1 (x) Represents the second class of 1 st order Bessel function.
Example 2:
referring to fig. 2-6, the method for calculating the cofferdam seepage field can specifically further include:
step S100: and constructing a mathematical analysis model. Selecting a cylindrical soil body in a limited area around the cofferdam, taking the center of the circular cofferdam as a Z axis, taking the top surface of a water impermeable layer at the bottom of the cofferdam as an r axis, and establishing an axisymmetric three-dimensional seepage analysis model as shown in figure 1. The outer boundary of the cofferdam is infinite and can be approximately regarded as watertight; the envelope is considered to be watertight and has a thickness that is small relative to the overall width of the mold, and therefore has a negligible thickness. The model is divided into 4 areas, wherein the area 1 is a bottom sealing layer, the area 2 is a cofferdam outer column annular soil layer, the area 3 is a cofferdam bottom column soil layer, and the area 4 is a bottom sealing layer bottom soil layer.
Step S200: and solving a water head distribution function expression. Assuming that the soil quality of the calculation area on the upper part of the impermeable layer is uniform, and the soil seepage isotropy accords with Darcy's law, the water heads of all areas meet the seepage balance equation:
wherein H1, H2, H3 and H4 are the total water heads of the area 1, the area 2, the area 3 and the area 4 respectively, and the water head calculation reference is the bottom surface of the permeable layer. The coordinate system takes the center of a round cofferdam as a Z axis, and the top surface of a water-impermeable layer at the bottom of the cofferdam as an r axis.
Wherein the zone 1 boundary conditions are as follows: upper boundary (z=h) 1 )，H 1 ＝h 1 The method comprises the steps of carrying out a first treatment on the surface of the The outer boundary (r=c),
the zone 2 boundary conditions are as follows: upper boundary (z=t) 2 )，H 2 ＝h 2 The method comprises the steps of carrying out a first treatment on the surface of the The outer boundary (r=b+c) can be approximately seen when b has a large value
The zone 3 boundary conditions are as follows: the lower boundary (z=0),
outer boundary (r=b+c), +.>
The boundary conditions for region 4 are as follows: the outer boundary (r=c),
and combining boundary conditions of all areas of the foundation pit seepage field. The explicit expression of the water head distribution of each region when the number of the stage number item is 1 can be obtained by using a separation variable method:
step S300: unknown coefficients in the head function expression are determined. Continuous conditions exist among the areas, and the conditions are respectively as follows:
constructing a non-homogeneous equation set by using continuous conditions among four regions:
all undetermined coefficients in the head function obtained in step S200 can be determined by solving the equation set using matlab code.
Example 3:
on the basis of the calculation method of the cofferdam seepage field, a back cover layer thickness optimization design system based on the calculation method is provided, and the system comprises the following components:
and a seepage field calculation module. Establishing a three-dimensional seepage steady-state model of the circular cofferdam, dividing the seepage field around the circular cofferdam into 4 areas, solving a seepage balance equation in each area by using a separation variable method, respectively obtaining the water head distribution series solution form of the 4 areas under a cylindrical coordinate system, combining continuous conditions among the areas, and obtaining a circular cofferdam steady-state seepage field analytic solution considering the bottom sealing effect by utilizing the orthogonality of Bessel functions.
And a seepage flow calculation module. And according to the definition of the seepage flow, combining with the analysis solution of the seepage flow field, and deducing a cofferdam excavation surface seepage flow calculation formula by adopting a calculus method.
According to Darcy's law, the seepage flow of cofferdam excavation face department is:
Q＝Sυ＝Sk zz i (1)
q is water inflow m 3 S; s is the seepage cross-sectional area m 2 The method comprises the steps of carrying out a first treatment on the surface of the V is the seepage flow velocity m/s; i is a hydraulic gradient; the cofferdam opening can be obtained by analyzing the water head of the area 1 by H1 (r, z)Hydraulic gradient at any point of the digging surface.
The hydraulic gradient is axisymmetric as shown in the formula (2), namely, the hydraulic gradient is equal to the hydraulic gradient with the distance r from the central axis z of the cofferdam, and the total seepage at the excavation surface can be understood as superposition of seepage of any circular ring areas with the z axis as the center. Wherein the seepage rate per unit annular area can be expressed as:
q h ＝2πk zz irdr (3)
pair q h And integrating from 0 to c to obtain the total seepage flow at the excavation surface.
And the water pressure calculation module. And according to the Bernoulli equation, solving a calculation formula of the seepage water pressure born by the sealing layer based on the analytic solution of the module 1.
And the back cover layer instability limit judging module. According to the technical standard GB/T51295-2018 of steel cofferdam engineering, a bottom layer instability limit discrimination formula considering the osmotic force is provided.
And a back cover layer thickness evaluation module. Based on the discrimination formula obtained by the back cover layer instability limit discrimination module, a relation diagram describing the seepage flow of the back cover layer and the thickness change of the back cover layer is drawn for thickness evaluation of the back cover layer.
In the seepage flow calculation module, the calculated considered seepage flow calculation formula of the excavation surface of the circular cofferdam is as follows:
in the water pressure calculation module, the calculated calculation formula of the seepage water pressure born by the bottom sealing layer is as follows:
in the back cover layer instability limit judging module, a back cover layer instability limit judging formula considering the osmotic force is provided.
The embodiment of the application also provides a calculation system of the cofferdam seepage field, which comprises a processor and a memory.
And a memory for storing a computer program.
And the processor is used for realizing any one of the method steps of the cofferdam seepage field calculation method when executing the program stored in the memory.
The calculation system of the cofferdam seepage field can realize each embodiment of the calculation method of the cofferdam seepage field, can achieve the same beneficial effects, and is not described in detail here.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (9)
1. The method for calculating the cofferdam seepage field is characterized by comprising the following steps of:
constructing a three-dimensional seepage analysis model of the target cofferdam based on the target cofferdam and soil surrounding the target cofferdam, and dividing the three-dimensional seepage analysis model into four areas;
respectively constructing seepage balance equations of four areas based on the three-dimensional seepage analysis model, and respectively calculating water head distribution explicit expressions of the four areas by combining boundary conditions of the four areas;
respectively obtaining continuous conditions of the four areas, and respectively constructing a non-homogeneous equation set of the four areas based on the continuous conditions of the four areas;
solving a non-homogeneous equation set of the four areas, introducing the solving result into a water head distribution explicit expression to obtain a calculation result of the water head distribution explicit expression, and taking the calculation result as a calculation result of a target cofferdam seepage field.
2. The method for calculating a cofferdam seepage field according to claim 1, wherein the constructing a three-dimensional seepage analysis model of the target cofferdam based on the target cofferdam and the soil surrounding the target cofferdam comprises:
selecting a cylindrical soil body around the cofferdam, combining the soil body with a water body above the soil body, taking the center of the cofferdam as a Z axis, taking the top surface of a water impermeable layer at the bottom of the cofferdam as an r axis, and establishing an axisymmetric three-dimensional seepage analysis model.
3. The method for calculating a cofferdam seepage field according to claim 1, wherein the dividing the three-dimensional seepage analysis model into four areas comprises:
taking the bottom layer inside the cofferdam enclosure as an area 1, taking the soil layer around the cofferdam enclosure as an area 2, taking the soil layer at the bottom of the cofferdam enclosure and the top of the watertight boundary as an area 3, taking the soil layer inside the cofferdam enclosure and below the bottom layer as an area 4, and dividing the three-dimensional seepage analysis model to obtain four divided areas.
4. The method for calculating a cofferdam seepage field according to claim 1, wherein the method for respectively constructing seepage balance equations of four areas based on the three-dimensional seepage analysis model comprises the following steps:
and constructing a seepage balance equation based on the three-dimensional seepage analysis model, wherein the equation is as follows:
wherein H is 1 、H 2 、H 3 、H 4 The total head functions for zone 1, zone 2, zone 3 and zone 4 are shown,
representing differential symbols, r, z represent two independent variables in the head function.
5. The method for calculating a cofferdam seepage field according to claim 1, wherein the boundary conditions of the four areas are respectively:
the boundary conditions for region 1 are as follows:
upper boundary:
(z＝h 1 ),H 1 ＝h 1 ；
outer boundary:
the boundary conditions for region 2 are as follows:
upper boundary:
(z＝T 2 ),H 2 ＝h 2 ；
outer boundary:
the boundary conditions for region 3 are as follows:
the lower boundary:
outer boundary:
the boundary conditions for region 4 are as follows:
outer boundary:
wherein h is 1 Represents the water level in the enclosure structure, h 2 Represents the water level outside the enclosure, b represents the distance from the enclosure to the outer boundary of the model, c represents the cofferdam radius, T 2 And the thickness of the soil layer outside the enclosure structure is shown.
6. The method for calculating a cofferdam seepage field according to claim 1 or 5, wherein the calculating the water head distribution explicit expression of the four areas by combining the boundary conditions of the four areas comprises:
the boundary conditions of the four areas are taken into a seepage flow equation, and the water head distribution explicit expression of the four areas is calculated by using a separation variable method, wherein the expressions are respectively as follows:
wherein A is in the formula 10 、A n 、B 10 、B m 、C 10 、C i 、D 10 、D n 、E n Is a constant term that can be determined with continuous boundary conditions on the area interface; j (J) 0 (x)、Y 0 (x) Respectively zero-order Bessel functions of the first class and the second class, lambda n Represents the separation constant lambda m Representing the separation constant, sinh (x) represents a sine hyperbola function, and cosh (x) represents a cosine hyperbola function.
7. The method for calculating a cofferdam seepage field of claim 1, wherein the four areas are respectively:
wherein k is 0 Represents the permeability coefficient, k, of the back cover layer 1 Represents the permeability coefficient, k, of soil layer 1 2 Represents the permeability coefficient of the soil layer.
8. The method for calculating a cofferdam seepage field according to claim 1 or 7, wherein the constructing a non-homogeneous equation set of four areas based on the continuous condition of the four areas respectively comprises:
a non-homogeneous system of equations is constructed using the continuous conditions of the four regions, the system of equations of which is shown below:
wherein a represents the distance from the enclosure to the bottom watertight boundary, lambda i Represents the separation constant, d represents the thickness of the back cover layer, T 1 Represents the thickness of soil layer inside the enclosure structure, Y 1 (x) Represents a Bessel function of the second class, J 1 (x) Representing a first class of bezier functions.
9. The computing system of the cofferdam seepage field is characterized by comprising a processor and a memory;
a memory for storing a computer program;
a processor for implementing the method steps of any one of claims 1-8 when executing a program stored on a memory.
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