CN117251992A - Calculation method of infiltration line of anchorage circular foundation pit - Google Patents
Calculation method of infiltration line of anchorage circular foundation pit Download PDFInfo
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- 230000008595 infiltration Effects 0.000 title claims abstract description 58
- 238000001764 infiltration Methods 0.000 title claims abstract description 58
- 238000004364 calculation method Methods 0.000 title claims abstract description 28
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 65
- 238000004458 analytical method Methods 0.000 claims abstract description 32
- 239000002689 soil Substances 0.000 claims abstract description 17
- 239000003673 groundwater Substances 0.000 claims abstract description 8
- 238000000034 method Methods 0.000 claims description 24
- 239000010410 layer Substances 0.000 claims description 15
- 238000013178 mathematical model Methods 0.000 claims description 8
- 239000000725 suspension Substances 0.000 claims description 8
- 238000000926 separation method Methods 0.000 claims description 7
- 230000009189 diving Effects 0.000 claims description 6
- 239000002356 single layer Substances 0.000 claims description 3
- 238000010276 construction Methods 0.000 abstract description 8
- 238000010586 diagram Methods 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 238000009736 wetting Methods 0.000 description 2
- 230000008859 change Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
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- G06F30/00—Computer-aided design [CAD]
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- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A10/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
- Y02A10/40—Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping
Abstract
The invention belongs to the technical field of underground hydraulic engineering, in particular to a calculation method of an infiltration line of an anchorage circular foundation pit, which comprises the following steps: step one: constructing an anchorage circular foundation pit mathematical analysis model, selecting a limited area cylindrical soil body around the anchorage circular foundation pit, taking the center of the anchorage circular foundation pit as a Z axis, taking the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis, and constructing an axisymmetric three-dimensional seepage analysis model; step two: setting basic assumption conditions of a mathematical analysis model, and assuming that the water-bearing stratum in the calculation model is uniform in soil property and isotropic; groundwater seepage accords with Darcy's law; the position of the infiltration line is further determined based on the analytic solution, so that the water head at any position in the infiltration field of the circular anchorage foundation pit and the position of the infiltration line can be rapidly solved, convenience can be provided for solving other parameters of the infiltration field of the circular anchorage foundation pit, and a certain theoretical basis can be provided for the engineering construction and protection of the anchorage foundation pit in the coastal river-following area.
Description
Technical Field
The invention relates to the technical field of underground hydraulic engineering, in particular to a calculation method of an infiltration line of an anchorage circular foundation pit.
Background
In recent years, a large number of foundation pit projects are emerging in the major engineering construction of high-rise buildings, underground space development, cross-sea (river) tunnels, cross-sea bridges and the like in coastal or river-following areas of China. Wherein, circular (axisymmetric) anchorage foundation pit is a more common foundation pit type. In the engineering of bridge abutment, house construction and the like, round or round-like anchorage foundation pit is frequently encountered, the scale and depth of the foundation pit are continuously increased, and a plurality of new problems to be solved in the construction of the anchorage foundation pit engineering are generated. Groundwater seepage has a significant effect on the stability and deformation of foundation pit engineering, and data show that seepage is a main cause of many foundation pit engineering failures. Due to the fact that an aquifer is too thick or is in technical and economical reasons, a suspension type retaining wall is often adopted for designing an anchorage foundation pit, but the water impermeability of the retaining wall and the flow around characteristic of the bottom of the retaining wall enable the seepage mode of the anchorage circular foundation pit to be of special complexity. In order to reduce the risk of engineering and evaluate possible disasters, it is necessary to perform foundation stability analysis, calculate the foundation seepage and the seepage pressure of each part of the seepage field, determine the position of the seepage line, and the like. The determination of the position of the infiltration line is a core task, and has great engineering practical significance for the construction of the anchorage foundation pit.
Currently, research on groundwater seepage fields mainly comprises numerical calculation and analysis methods. Along with the gradual maturation of the numerical analysis means, many students utilize numerical methods such as finite elements, finite difference and the like to carry out seepage analysis on foundation pit engineering under the conditions of stable seepage and unstable seepage, and relatively accurate water head solution can be obtained. Compared with a numerical calculation analysis method, the analysis method can integrate factors such as the initial condition of the groundwater, the water level change and the like into a solving process, and expresses all the factors through a function expression, so that the further research of the motion rule of the groundwater is facilitated. The existing analysis solution of the seepage field is mainly used for researching rectangular anchorage foundation pits with larger length-width ratio, and the analysis research of round anchorage foundation pits is rare. In addition, a certain water level drop depth can be generated around the anchorage foundation pit, the formed free boundary of the diving surface is not only a streamline but also an isopipe, and the nonlinearity of the free boundary condition (due to the square value of the hydraulic gradient) prevents the conventional solution of the linear Laplace equation, so that the analysis research result of the seepage field on the round anchorage foundation pit is less at present.
Therefore, the calculation method of the infiltration line of the anchorage circular foundation pit is provided.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description summary and in the title of the application, to avoid obscuring the purpose of this section, the description summary and the title of the invention, which should not be used to limit the scope of the invention.
The present invention has been made in view of the above-mentioned and/or problems existing in the prior art in solving the defects existing in the flow field of an anchored circular foundation pit.
Therefore, the invention aims to provide a calculation method of infiltration lines of an anchorage circular foundation pit, which constructs a mathematical analysis model of the anchorage circular foundation pit infiltration field, divides the circular anchorage foundation pit steady-state infiltration field into 3 areas, respectively represents the water heads of the 3 areas as series solutions by using a separation variable method, combines continuous conditions among the areas, utilizes Bessel function orthogonality to integrate and transform the water head expression, constructs a non-homogeneous linear equation set, and solves the equation set to obtain the circular anchorage foundation pit steady-state infiltration field analysis solution. The position of the infiltration line is further determined based on the analytic solution, so that the water head at any position in the infiltration field of the circular anchorage foundation pit and the position of the infiltration line can be rapidly solved, convenience can be provided for solving other parameters of the infiltration field of the circular anchorage foundation pit, and a certain theoretical basis can be provided for the engineering construction and protection of the anchorage foundation pit in the coastal river-following area. In order to solve the technical problems, according to one aspect of the present invention, the following technical solutions are provided:
a calculation method of the infiltration line of an anchorage circular foundation pit comprises the following steps:
step one: constructing an anchorage circular foundation pit mathematical analysis model, selecting a limited area cylindrical soil body around the anchorage circular foundation pit, taking the center of the anchorage circular foundation pit as a Z axis, taking the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis, and constructing an axisymmetric three-dimensional seepage analysis model;
step two: setting basic assumption conditions of a mathematical analysis model, and assuming that the water-bearing stratum in the calculation model is uniform in soil property and isotropic; groundwater seepage accords with Darcy's law; the anchorage foundation pit is in a stable seepage state, and the water level in the foundation pit is reduced to the bottom of the foundation pit; the suspension retaining wall is impermeable to water; the lower soil layer of the aquifer is a watertight boundary, and the upper part of the aquifer is a infiltration line;
step three: deriving a foundation pit seepage field water head distribution expression, and combining boundary conditions of all areas of the foundation pit seepage field, and obtaining a mathematical expression of water head distribution of all areas of the anchorage circular foundation pit by utilizing a separation variable method and the property of Bessel functions;
step four: solving unknown coefficients of a water head distribution expression, constructing a non-homogeneous equation set by utilizing continuous conditions among areas of the anchorage circular foundation pit mathematical model 3, and solving the equation set to determine coefficients to be determined in the water head mathematical expression;
step five: and determining the infiltration line of the anchorage circular foundation pit, and determining the position of the infiltration line by utilizing the condition that the pressure at the submerged surface is zero and the water head height is equal to the position height.
As a preferable scheme of the calculation method of the infiltration line of the anchorage circular foundation pit, the invention comprises the following steps: in the first step, a mathematical analysis model of the seepage field of the anchorage foundation pit in the isotropic single-layer soil layer under the steady-state seepage condition is shown in fig. 1, and a seepage balance equation describing the model is as follows:
wherein H1, H2 and H3 are the total water heads of the region (1), the region (2) and the region (3), and the water head calculation reference is the bottom surface of the permeable layer. The coordinate system takes the center of a round anchorage foundation pit as a Z axis, and the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis.
The boundary conditions for region I are as follows: upper boundary (z=h) 1 )，H＝h 1 The method comprises the steps of carrying out a first treatment on the surface of the The outer boundary (r=c),
the boundary conditions for region II are as follows: the upper boundary head drop is much smaller than b, the hydraulic gradient is approximately 0 in the r direction, so that it is approximately a watertight boundary, i.e. the upper boundary (z=h 2 )，H 2 ＝h 2 The method comprises the steps of carrying out a first treatment on the surface of the The inner boundary (r=c),outer boundary (r=b+c), H 2 ＝h 2 。
The boundary conditions for region III are as follows: the lower boundary (z=0),outer boundary (r=b+c), H 3 ＝h 2 。
As a preferable scheme of the calculation method of the infiltration line of the anchorage circular foundation pit, the invention comprises the following steps: in the second step, the seepage boundary conditions of the seepage line in the set mathematical model are as follows:
the boundary condition is obtained by simplifying the condition (the following formula) that the two-dimensional diving surface boundary meets
The method comprises the following steps: 1) Isotropic foundation pit considering two-dimensional steady-state upper-free replenishmentW is zero; 2) The submergence level delta is generally relatively small; 3) Neglecting the higher order infinitesimal item +.>
As a preferable scheme of the calculation method of the infiltration line of the anchorage circular foundation pit, the invention comprises the following steps: the water head expression obtained in the third step is as follows:
in the above formula A 0 ,A n ,B m ,C i Is a constant term that can be determined with continuous boundary conditions on the area interface; j0 And (x) and Y0 (x) are zero-order Bessel functions of the first class and the second class respectively.
As a preferable scheme of the calculation method of the infiltration line of the anchorage circular foundation pit, the invention comprises the following steps: in the fourth step, the continuous conditions between the areas are as follows:
as a preferable scheme of the calculation method of the infiltration line of the anchorage circular foundation pit, the invention comprises the following steps: in the fourth step, the constructed non-homogeneous linear equation set is:
as a preferable scheme of the calculation method of the infiltration line of the anchorage circular foundation pit, the invention comprises the following steps: in the fifth step, the equation of the wetting line is defined as H (r, z) =z, because the water pressure p at the submergence surface is zero, and thus the water head H is equal to the submergence surface position height.
Compared with the prior art: the invention constructs an anchorage circular foundation pit seepage field mathematical analysis model, divides a circular anchorage foundation pit steady state seepage field into 3 areas, respectively represents the water heads of the 3 areas as a series solution by using a separation variable method, combines continuous conditions among the areas, utilizes Bessel function orthogonality to integrate and transform the water head expression, constructs a non-homogeneous linear equation set, and solves the equation set to obtain a circular anchorage foundation pit steady state seepage analysis solution. The position of the infiltration line is further determined based on the analytic solution, so that the water head at any position in the infiltration field of the circular anchorage foundation pit and the position of the infiltration line can be rapidly solved, convenience can be provided for solving other parameters of the infiltration field of the circular anchorage foundation pit, and a certain theoretical basis can be provided for the engineering construction and protection of the anchorage foundation pit in the coastal river-following area.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following detailed description of the embodiments of the present invention will be given with reference to the accompanying drawings, which are to be understood as merely some embodiments of the present invention, and from which other drawings can be obtained by those skilled in the art without inventive faculty. Wherein:
FIG. 1 is a schematic diagram of a seepage model of a circular anchorage foundation pit;
FIG. 2 is a water head distribution diagram of an anchorage circular foundation pit seepage field calculated by analysis and solution according to the invention;
FIG. 3 is a diagram showing the comparison and verification of the analysis solution and the numerical solution of the seepage field provided by the invention.
Detailed Description
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present invention is not limited to the specific embodiments disclosed below.
Next, the present invention will be described in detail with reference to the drawings, wherein the sectional view of the device structure is not partially enlarged to general scale for the convenience of description, and the drawings are only examples, which should not limit the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in actual fabrication.
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
The invention provides a calculation method of infiltration lines of an anchorage circular foundation pit, which constructs a mathematical analysis model of the infiltration field of the anchorage circular foundation pit, divides the steady-state infiltration field of the circular anchorage foundation pit into 3 areas, respectively represents the water heads of the 3 areas in the form of series solutions by using a separation variable method, combines continuous conditions among the areas, utilizes Bessel function orthogonality to integrate and transform the water head expression, constructs a non-homogeneous linear equation set, and solves the equation set to obtain the steady-state infiltration field analysis solution of the circular anchorage foundation pit. The position of the infiltration line is further determined based on the analytic solution, so that the water head at any position in the infiltration field of the circular anchorage foundation pit and the position of the infiltration line can be quickly solved, convenience can be provided for solving other parameters of the infiltration field of the circular anchorage foundation pit, a certain theoretical basis can be provided for the engineering construction and protection of the anchorage foundation pit in coastal along-river areas, and referring to fig. 1-3, the main body part of the calculation method of the infiltration line of the circular anchorage foundation pit in the embodiment comprises;
step one: and constructing an anchorage circular foundation pit mathematical analysis model. Selecting a cylindrical soil body in a limited area around the anchorage foundation pit, taking the center of the circular anchorage foundation pit as a Z axis, taking the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis, and establishing an axisymmetric three-dimensional seepage analysis model as shown in figure 1. The outer side of the anchorage foundation pit is an infinite diving condition, can be approximately regarded as watertight, the enclosure structure is regarded as watertight, and compared with the whole width of the model, the thickness of the enclosure structure is smaller, so that the thickness is negligible. Dividing the mathematical model into 3 areas by using a suspension type retaining wall and a horizontal line at the bottom of the suspension type retaining wall, wherein the area 1 is cylindrical soil in the suspension type retaining wall, the area 2 is annular soil of an outer column of the retaining wall, and the area 3 is cylindrical soil at the bottom of the suspension type retaining wall;
in the first step, a mathematical analysis model of the seepage field of the anchorage foundation pit in the isotropic single-layer soil layer under the steady-state seepage condition is shown in fig. 1, and a seepage balance equation describing the model is as follows:
wherein H1, H2 and H3 are the total water heads of the region (1), the region (2) and the region (3), and the water head calculation reference is the bottom surface of the permeable layer. The coordinate system takes the center of a round anchorage foundation pit as a Z axis, and the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis.
The boundary conditions for region I are as follows: upper boundary (z=h) 1 )，H＝h 1 The method comprises the steps of carrying out a first treatment on the surface of the The outer boundary (r=c),
the boundary conditions for region II are as follows: the upper boundary head drop is much smaller than b, the hydraulic gradient is approximately 0 in the r direction, so that it is approximately a watertight boundary, i.e. the upper boundary (z=h 2 )，H 2 ＝h 2 The method comprises the steps of carrying out a first treatment on the surface of the The inner boundary (r=c),outer boundary (r=b+c), H 2 ＝h 2 。
The boundary conditions for region III are as follows: the lower boundary (z=0),outer boundary (r=b+c), H 3 ＝h 2 。
Step two: setting basic assumption conditions of a mathematical model. Assuming that the aquifer in the calculation model is uniform in soil texture and isotropic; groundwater seepage accords with Darcy's law; the anchorage foundation pit is in a stable seepage state, and the water level in the foundation pit is reduced to the bottom of the foundation pit; the suspension retaining wall is impermeable to water; the lower soil layer of the aquifer is a watertight boundary, the upper part of the aquifer is a infiltration line, and the diving condition is assumed according to Neuman;
in the second step, the seepage boundary condition of the seepage line in the set mathematical model is that
The boundary condition is obtained by simplifying the condition (the following formula) that the two-dimensional diving surface boundary meets
The method comprises the following steps: 1) Consider the direction and direction of two-dimensional steady-state upper-free replenishmentSex foundation pitW is zero; 2) The submergence level delta is generally relatively small; 3) Neglecting the higher order infinitesimal item +.>
Step three: deriving a foundation pit seepage field water head distribution expression, and combining boundary conditions of all areas of the foundation pit seepage field, and obtaining a mathematical expression of water head distribution of all areas of the anchorage circular foundation pit by utilizing a separation variable method and the property of Bessel functions;
the water head expression obtained in the third step is as follows:
in the above formula A 0 ,A n ,B m ,C i Is a constant term that can be determined with continuous boundary conditions on the area interface; j0 And (x) and Y0 (x) are zero-order Bessel functions of the first class and the second class respectively.
Step four: solving unknown coefficients of a water head distribution expression, constructing a non-homogeneous equation set by utilizing continuous conditions among areas of the anchorage circular foundation pit mathematical model 3, and solving the equation set to determine coefficients to be determined in the water head mathematical expression;
in the fourth step, the continuous conditions among the areas are as follows:
in the fourth step, the constructed non-homogeneous linear equation set is:
step five: and determining the infiltration line of the anchorage circular foundation pit, and determining the position of the infiltration line by utilizing the condition that the pressure at the submerged surface is zero and the water head height is equal to the position height.
In step five, the equation of the wetting line is defined as H (r, z) =z, because the water pressure p at the surface of the submergence is zero, and thus the water head H is equal to the position height of the submergence.
Solving an equation set by using matlab codes to determine all undetermined coefficients in the water head function obtained in the step four; fig. 2 is a water head distribution diagram of the anchorage circular foundation pit seepage field drawn by adopting the calculation result.
Dividing the seepage field around the anchorage circular foundation pit into 3 areas, respectively obtaining the water head distribution series solution form of the 3 areas under the cylindrical coordinate system by using a separation variable method, combining continuous conditions among the areas, obtaining explicit analysis solutions of the seepage field of each area by using Bessel function orthogonality, and then combining the explicit solution of the seepage field water head, and solving the infiltration line according to the infiltration line condition. By comparing with the calculation result of the numerical software, the simplified solution is verified to have good calculation precision.
Although the invention has been described hereinabove with reference to embodiments, various modifications thereof may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In particular, the features of the disclosed embodiments may be combined with each other in any manner as long as there is no structural conflict, and the exhaustive description of these combinations is not given in this specification merely for the sake of omitting the descriptions and saving resources. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (7)
1. The calculation method of the infiltration line of the anchorage circular foundation pit is characterized by comprising the following steps of:
step one: constructing an anchorage circular foundation pit mathematical analysis model, selecting a limited area cylindrical soil body around the anchorage circular foundation pit, taking the center of the anchorage circular foundation pit as a Z axis, taking the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis, and constructing an axisymmetric three-dimensional seepage analysis model;
step two: setting basic assumption conditions of a mathematical analysis model, and assuming that the water-bearing stratum in the calculation model is uniform in soil property and isotropic; groundwater seepage accords with Darcy's law; the anchorage foundation pit is in a stable seepage state, and the water level in the foundation pit is reduced to the bottom of the foundation pit; the suspension retaining wall is impermeable to water; the lower soil layer of the aquifer is a watertight boundary, and the upper part of the aquifer is a infiltration line;
step three: deriving a foundation pit seepage field water head distribution expression, and combining boundary conditions of all areas of the foundation pit seepage field, and obtaining a mathematical expression of water head distribution of all areas of the anchorage circular foundation pit by utilizing a separation variable method and the property of Bessel functions;
step four: solving unknown coefficients of a water head distribution expression, constructing a non-homogeneous equation set by utilizing continuous conditions among areas of the anchorage circular foundation pit mathematical model 3, and solving the equation set to determine coefficients to be determined in the water head mathematical expression;
step five: and determining the infiltration line of the anchorage circular foundation pit, and determining the position of the infiltration line by utilizing the condition that the pressure at the submerged surface is zero and the water head height is equal to the position height.
2. The method for calculating the infiltration line of the anchorage circular foundation pit according to claim 1, wherein in the first step, a mathematical analysis model of the infiltration field of the anchorage circular foundation pit in the isotropic single-layer soil layer under the steady state infiltration condition is shown in fig. 1, and an infiltration balance equation describing the model is as follows:
wherein H1, H2 and H3 are the total water heads of the region (1), the region (2) and the region (3), and the water head calculation reference is the bottom surface of the permeable layer. The coordinate system takes the center of a round anchorage foundation pit as a Z axis, and the top surface of a water impermeable layer at the bottom of the anchorage foundation pit as an r axis.
The boundary conditions for region I are as follows: upper boundary (z=h) 1 )，H＝h 1 The method comprises the steps of carrying out a first treatment on the surface of the The outer boundary (r=c),
the boundary conditions for region II are as follows: the upper boundary head drop is much smaller than b, the hydraulic gradient is approximately 0 in the r direction, so that it is approximately a watertight boundary, i.e. the upper boundary (z=h 2 )，H 2 ＝h 2 The method comprises the steps of carrying out a first treatment on the surface of the The inner boundary (r=c),outer boundary (r=b+c), H 2 ＝h 2 。
The boundary conditions for region III are as follows: the lower boundary (z=0),outer boundary (r=b+c), H 3 ＝h 2 。
3. The method for calculating the seepage line of the anchorage circular foundation pit according to claim 1, wherein in the second step, the seepage boundary condition of the seepage line in the set mathematical model is as follows
The boundary condition is obtained by simplifying the condition (the following formula) that the two-dimensional diving surface boundary meets
The method comprises the following steps: 1) Isotropic foundation pit considering two-dimensional steady-state upper-free replenishmentW is zero; 2) The submergence level delta is generally relatively small; 3) Neglecting the higher order infinitesimal item +.>
4. The method for calculating the infiltration line of the anchorage circular foundation pit according to claim 1, wherein the water head expression obtained in the third step is as follows,
in the above formula A 0 ,A n ,B m ,C i Is a constant term that can be determined with continuous boundary conditions on the area interface; j0 And (x) and Y0 (x) are zero-order Bessel functions of the first class and the second class respectively.
5. The method for calculating the infiltration line of the anchorage circular foundation pit according to claim 1, wherein in the fourth step, the continuous conditions between the areas are as follows:
6. the method for calculating the infiltration line of the anchorage circular foundation pit according to claim 1, wherein in the fourth step, the constructed non-homogeneous linear equation set is:
7. the method of claim 1, wherein in the fifth step, the equation of the determination of the infiltration line is H (r, z) =z, because the water pressure p at the submergence surface is zero, and the water head H is equal to the submergence surface position height.
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