A "simulation-optimization" design method for optimizing the filter pipe length and depth of a foundation pit for lowering confined water

Abstract

The application discloses a kind of " simulation-optimization " design methods of foundation pit drawdown water, including the following steps: calculating drawdown requirement, obtaining safety water level drawdown;Make several schemes, initially determine the number and position of dewatering well;Simulate single well pumping, obtain single well dewatering influence coefficient, form influence coefficient matrix and block;Build influence coefficient prediction model, expand influence coefficient matrix;Linear programming model is constructed;Solve linear programming model, obtain each well optimal pumping amount;Check whether there is invalid well, if there is invalid well, exclude redundancy filter tube in invalid well, and linear programming model is constructed and solved again;Verify the calculation result by numerical simulation;Compare each scheme result, evaluate optimal scheme.The design method can determine the optimal filter tube length and depth of each well and pumping amount, can greatly reduce environmental effect and engineering cost, and can be widely applied to the optimization design of deep foundation pit engineering drawdown water.

Description

Technical Field

[0001] This invention relates to the field of underground engineering, and in particular to a "simulation-optimization" design method for reducing the pressure of foundation pits by optimizing the length and depth of filter pipes. Background Technology

[0002] Deep foundation pit construction in riverside and coastal areas often faces engineering challenges posed by high confined aquifer levels. Improper handling can easily lead to engineering accidents such as sudden water inrush, which can range from affecting construction progress and increasing costs to causing serious loss of life and property. Therefore, reasonable and efficient dewatering measures are of significant engineering importance in ensuring smooth foundation pit construction and protecting nearby sensitive buildings and structures, addressing the risks posed by confined aquifers. During foundation pit construction, depressurization of the confined aquifer is generally achieved through well pumping to ensure that the water pressure at the top of the aquifer does not exceed the weight of the overlying soil. Dewatering design plays a crucial guiding role in construction; a scientific dewatering design can ensure foundation pit safety while avoiding high engineering costs and significant environmental effects. Currently, dewatering design is generally carried out through theoretical calculations, numerical simulations, and a combination of both methods; however, each method has its limitations.

[0003] Theoretical calculations typically utilize the "equivalent well method," which treats the foundation pit as a circular well, estimating its total inflow based on dewatering requirements using the Dupuit formula. This, combined with the single-well output, roughly calculates the required number of wells and the length and depth of the filter pipes. However, because the theoretical formulas used in this method are ill-suited to account for complex foundation pit shapes and geological conditions, as well as the insertion of the cutoff wall into a confined aquifer to a certain depth, it usually significantly overestimates the total inflow.

[0004] With the development of computer technology, the application of numerical simulation methods in foundation pit dewatering has received increasing attention. Numerical simulation can consider relatively complex geological conditions, foundation pit shapes, and the insertion of cutoff walls into the target aquifer. Under the premise of reasonable parameter selection, it can accurately obtain the relationship between pumping volume and drawdown. For large-scale deep foundation pit projects, dewatering design is generally carried out by combining theoretical and numerical simulation methods. The theoretical calculation results are verified by numerical simulation, and the dewatering scheme is appropriately optimized. The traditional method of optimizing dewatering schemes using numerical simulation involves simulating several dewatering schemes and selecting the optimal one. This is currently the most commonly used method in dewatering design. However, the optimization process only involves comparing a limited number of schemes and lacks the guidance of optimization theory. Therefore, the dewatering scheme can be further optimized.

[0005] In recent years, a "simulation-optimization" dewatering design method combining numerical simulation and optimization theory has gradually developed. This method obtains the parameters needed for the optimization model through numerical simulation and solves the model to obtain the optimal pumping rate per well. Therefore, this method can fully utilize the advantages of numerical simulation and optimization theory to obtain a more accurate and efficient dewatering scheme. Existing research shows that the "simulation-optimization" dewatering design method can significantly reduce the number of wells opened, the total pumping volume, and the drawdown, thus further improving dewatering efficiency and significantly reducing construction costs and environmental impact. However, existing "simulation-optimization" methods struggle to optimize the length (vertical distance from top to bottom of the filter pipe) and depth (vertical distance from top of the filter pipe to the top of the confined aquifer) of the well. The length and depth of the filter pipe need to be set before optimization and used in the optimization results. The pre-set filter pipe length and depth may not be optimal. Existing research shows that changes in the length and depth of the well filter pipe affect dewatering efficiency; generally, the lower the filter pipe length and depth, the higher the dewatering efficiency. However, infinitely reducing the length and depth of the filter tube is not feasible, as this involves the issue of well capacity (or "maximum allowable pumping capacity"). The lower the length and depth of the filter tube, the lower the well capacity, so the required pumping capacity may not be achievable at a lower filter tube length and depth.

[0006] In conclusion, optimizing the length and depth of the filter pipe under the constraint of well volume can further improve dewatering efficiency and reduce environmental impact and construction costs. To achieve this goal, a relevant "simulation-optimization" design method needs to be proposed. Summary of the Invention

[0007] The technical problem to be solved by this invention is to propose a "simulation-optimization" design method for depressurization of foundation pits that can optimize the length and depth of filter pipes, addressing various problems existing in the existing dewatering design methods. This method determines the optimal length and depth of filter pipes based on the optimization of the single well pumping volume.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a "simulation-optimization" design method for reducing the pressure of foundation pits by optimizing the length and depth of filter pipes, comprising the following steps:

[0009] S1, calculate the drawdown requirement and obtain the safe drawdown level.

[0010] Within the excavation pit area, select a certain number of drawdown control points and calculate the safe water level drawdown according to the following formula based on item W.0.1 of the "Code for Design of Building Foundations" (GB50007-2011).

[0011] The safe drawdown value is taken as the minimum s value that satisfies the following formula, and the safe drawdown at drawdown control point j is denoted as s. j,min .

[0012]

[0013] In the formula, h i Let be the thickness of the i-th soil layer between the bottom of the foundation pit and the top of the confined aquifer, in meters.

[0014] γ si The unit weight of the i-th soil layer between the bottom of the foundation pit and the top of the confined aquifer, in kN / m³. 3 ;

[0015] H0 is the initial pressure head at the top of the confined aquifer, in meters;

[0016] s represents the descent depth, m;

[0017] γ w The specific weight of water, kN / m 3 ;

[0018] F s For safety factor, it is set to 1.1 according to the specification.

[0019] When selecting drawdown control points, a certain number of representative points can be chosen. These control points must meet the following conditions: if the drawdown at all control points meets the drawdown requirements, it means that all points within the pit meet the drawdown requirements. When dewatering is carried out inside the pit, the corner points of the pit can be selected as drawdown control points; when dewatering is carried out outside the pit, in addition to the corner points of the pit, a certain number of control points should also be selected inside the pit.

[0020] S2. Develop several plans and preliminarily determine the number and location of dewatering wells for each plan.

[0021] Based on the required drawdown depth, a preliminary estimate of the pit's water inflow is made. Then, the required number of wells is calculated based on the single well's drainage capacity, and their locations are determined. Several dewatering schemes are developed by combining different numbers and locations of wells. The initial dewatering design only needs to determine the number and location of wells; the length and depth of the filter pipes do not need to be determined. The length and depth of the filter pipes are determined through subsequent optimization calculations. The calculation process is as follows:

[0022] According to Table B.0.3-2 of the "Technical Specification for Wells" (GB50296-2014), the inflow rate Q of the foundation pit can be calculated using the following formula. T :

[0023]

[0024] In the formula, K is the aquifer permeability coefficient, m / d; M a s is the aquifer thickness, in meters; s is the drawdown, in meters, taken from each control point s. j,minThe maximum value of; R is the radius of influence of precipitation, m; r0 is the equivalent radius of the foundation pit, m. If the foundation pit is circular, r0 is directly taken as the radius of the foundation pit. If the foundation pit is of other shapes, the value is taken according to Table B.0.1-1 in the "Technical Specification for Wells" (GB50296-2014); L is the length of the well filter pipe, m.

[0025] According to formula B.0.2-2 in the "Technical Specification for Wells" (GB50296-2014), the influence radius R of the dewatering well can be estimated using the following formula:

[0026]

[0027] According to Table B.0.1-1 of the "Technical Specification for Wells" (GB50296-2014), for rectangular foundation pits, the equivalent radius r0 can be calculated using the following formula:

[0028]

[0029] In the formula, a is the length of the rectangle, m; b is the width of the rectangle, m; and the values ​​of η are shown in the table below.

[0030] Table 2 η values ​​under different conditions

[0031] b / a 0.1～0.2 0.2～0.3 0.3～0.4 0.4～0.6 0.6～1.0 η 1.00 1.12 1.14 1.16 1.18

[0032] According to item 7.3.16 of the "Technical Specification for Foundation Pit Support" (JGJ120-2012), the water production capacity of a single well can be estimated using the following formula:

[0033]

[0034] In the formula, q represents the water production capacity of a single well, and m 3 / d; r is the radius of the filter tube, in meters.

[0035] The minimum number of wells is obtained by dividing the pit water inflow by the single well's water production capacity.

[0036] S3 simulates single-well pumping for a certain scheme, obtains a certain number of single-well dewatering influence coefficients, constructs influence coefficient matrices A and B, and divides the matrix into blocks according to different wells to facilitate subsequent processing of influence coefficients based on different wells.

[0037] A precipitation model is established for a specific scheme, and single-well pumping is simulated to obtain the single-well pumping influence coefficient.

[0038] To optimize the length and depth of the filter pipe for each well, a certain number of filter pipes with different lengths or depths need to be considered for each well, with each filter pipe treated as a separate well.

[0039] Each time, one filter pipe of a well is simulated for pumping water until all wells have been simulated.

[0040] The single-well pumping influence coefficient includes two types: one is the influence coefficient of single-well pumping on the drawdown control point; the other is the influence coefficient of single-well pumping on each well.

[0041] When different filter pipes of the same well are regarded as different wells, the influence coefficient of single-well pumping on the drawdown control point can be defined as follows.

[0042]

[0043] In the formula, α j,im denoted as the influence coefficient of the individual pumping of the m-th filter pipe of well i on the drawdown control point j;

[0044] s j,im The drawdown at drawdown control point j is the water level drawdown when the m-th filter pipe of well i is pumped out alone.

[0045] Q im Let m be the pumping volume of the m-th filter tube in well i.

[0046] Similarly, when different filter pipes of the same well are considered as different wells, the influence coefficient of single-well pumping on each well is defined as follows:

[0047]

[0048] In the formula, β kn,im Let be the influence coefficient of pumping water from the m-th filter pipe of well i alone on the n-th filter pipe of well k;

[0049] s kn,im The drawdown at the nth filter pipe of well k when the mth filter pipe of well i is pumped out alone;

[0050] H 0kn Let be the initial pressure head at the top of the nth filter tube in well k.

[0051] All α j,im Form matrix A, all β kn,im Form matrix B.

[0052] Each column element in the matrix represents the influence coefficient of a certain filter pipe in a certain well on each drawdown control point or each filter pipe in each well when a certain filter pipe is pumping water.

[0053] Matrix A and B are divided into blocks based on different wells to facilitate subsequent processing of influence coefficients according to different wells. The block division method is shown below.

[0054]

[0055]

[0056] In the formula, the block matrix A iA represents the influence coefficient matrix of different filter tubes pumping water individually from well i on different drawdown control points. i The elements in the same row represent the influence coefficients of different filter pipes of well i on a certain drawdown control point, and the elements in the same column represent the influence coefficients of a certain filter pipe of well i on different drawdown control points.

[0057] N cw To optimize the number of wells considered in the calculation;

[0058] N s The number of filter tubes to consider for each well;

[0059] N cp This represents the number of depth control points.

[0060] The remaining parameters are the same as those described above.

[0061]

[0062]

[0063] In the formula, the block matrix B ki This represents the influence coefficient matrix of each filter pipe in well k on the pumping of water by different filter pipes in well i. The other parameters are the same as described above.

[0064] Additionally, it is necessary to partition the matrix B along its main diagonal. ki (k = i = 1, 2, ..., N) cw (B) will be processed. ki (k = i = 1, 2, ..., N) cw The elements in ) represent the influence of each filter pipe in a certain well on each filter pipe in the same well.

[0065] B needs to be ki (k = i = 1, 2, ..., N) cw All elements outside the main diagonal of the diagram are changed to 0 to prevent different filter pipes from pumping water from the same well from affecting each other, thus reducing the number of calculations. The processing method is shown below.

[0066]

[0067] S4 uses mathematical methods to construct an influence coefficient prediction model and expands the influence coefficient matrices A and B, thereby considering more filter pipes for each well.

[0068] In optimization calculations, multiple filter pipes are considered for the same well, especially when the increments in filter pipe length and depth are small. In this case, simulating every filter pipe for all wells is too labor-intensive. Therefore, mathematical methods such as machine learning or multiple regression can be used, selecting data from a representative set of filter pipes as the training set, with filter pipe length and depth as input variables, and the influence coefficient (α) as the input variable. j,imβ kn,im Using the output variable, an influence coefficient prediction model is constructed to expand the influence coefficient matrices A and B, thereby allowing more filter pipes to be considered for each well and reducing the workload of numerical simulation calculations.

[0069] S5, Construct a linear programming model.

[0070] A linear programming model consists of two parts: an objective function and constraints. The objective function represents the maximum or minimum value of the linear combination of variables to be solved, and the constraints, denoted as st, represent the conditions that the variables to be solved must satisfy.

[0071] Using the influence coefficients in matrices A and B and the safe drawdown s j,min Construct a linear programming model in the following form.

[0072]

[0073]

[0074] In the formula, Q total Total pumping volume; s j,min Let s be the safe drawdown depth for point j. nkn The normalized drawdown at the nth filter pipe of well k is the sum of the drawdown at that filter pipe (the total drawdown of the nth filter pipe of well k when all wells are pumping water together) and the initial pressure head H at the top of the filter pipe. 0kn The ratio. The other parameters are the same as described above.

[0075] The meanings of the objective function and constraints in a linear programming model are explained below:

[0076] The objective function of the model is to find the minimum total pumping volume of all wells. The model has three constraints: first, the drawdown at the control points must satisfy the safe drawdown s. j,min Secondly, the normalized drawdown of each well must be less than 1 to avoid excessive drawdown at each well, which would cause the calculated pumping volume to be unattainable in actual conditions. Thirdly, the pumping volume of each well must not be less than 0 to ensure that it is pumping water rather than reinjection.

[0077] The first two constraints can also be described in matrix form, as shown below:

[0078]

[0079]

[0080]

[0081]

[0082] S n =(11…1)T

[0083] In the formula, vector Q stores the pumping volume of all filter pipes in all wells. Q can be divided into blocks according to different wells, and the block vector is denoted as Q_block. i (i = 1, 2, ..., N) cw Each element in the block vector represents the pumping volume of different filter tubes in the same well;

[0084] Vector S n The elements in the array are all 1s, and the number of elements in the array is N. cw ·N s The total number of filter tubes in all wells.

[0085] S6, Solve the linear programming model to obtain the optimal pumping rate for each well and filter pipe, and store it in vector Q;

[0086] The constructed linear programming model can be solved using the linprog function built into Matlab software. The calculation result is the optimal pumping rate for all filter pipes in each well. The result is stored in vector Q.

[0087] S7, Check for invalid wells.

[0088] An invalid well is defined as follows: if the location of the same well in the optimization calculation results has more than one filter pipe with a pumping volume greater than 0, the well is invalid, because in the real world, only one filter pipe can be opened for the same well when pumping.

[0089] The method for checking for invalid wells is as follows: check each block vector Q. i If the number of elements in the well exceeds ε (ε is a small value close to 0 defined by an individual, such as 1E-4), the corresponding well is considered invalid.

[0090] S8. If there are invalid wells, remove the redundant filter tubes in the invalid wells and return to S5 until there are no invalid wells in the results.

[0091] The method for identifying redundant filters in invalid wells is as follows: multiply matrix B by vector Q to obtain vector C. The elements of vector C are the normalized drawdown s at different filters in different wells. nkn The vector C is divided into blocks according to different wells, resulting in a block matrix C0. k (k = 1, 2, ..., N) cw ).

[0092]

[0093]

[0094] Record the C corresponding to the invalid well k The middle satisfies |Ck Elements with (n)-1|<ε are considered redundant and should be excluded.

[0095] The reason for excluding it is: it satisfies |C k The filter pipe corresponding to the element (n)-1|<ε is often the one with the highest pumping efficiency among all the filter pipes in that well. The higher the pumping efficiency, the lower the pumping volume required to achieve a certain drawdown. However, to satisfy the second constraint, the maximum pumping volume that can be applied is also smaller. Therefore, the pumping volume allocated to this well will be preferentially allocated to this filter pipe, resulting in its normalized drawdown s. nkn The value reaches 1. At this point, according to the second constraint, it is impossible to continue allocating pumping volume to this filter pipe. However, continuing to allocate pumping volume to this well would still help reduce the total pumping volume, and the additional pumping volume would be allocated to the relatively less efficient filter pipe in this well. If s nkn Filter tubes with a value of 1 are excluded. The pumping volume allocated to this well may be handled by the remaining most efficient filter tube alone, at which point the well becomes an effective well.

[0096] Suppose that the y-th filter pipe of the x-th well needs to be removed, the removal method is: divide the block matrix A x The element in column y is replaced with 0, as shown below. Through this process, the excluded filter tube, regardless of its pumping volume, cannot produce any drawdown, meaning its pumping efficiency is 0. According to the optimization principle, no pumping volume will be allocated to this filter tube, effectively excluding it.

[0097] yth column

[0098]

[0099] After eliminating redundant filter pipes from all invalid wells, return to S5.

[0100] S9 verifies the optimized calculation results through numerical simulation.

[0101] The optimal single-well pumping rate obtained from the optimization calculation is substituted into the corresponding well and filter pipe in the previously established numerical model to carry out calculations and verify whether the water level drawdown at the drawdown control point meets the requirements.

[0102] S10: After all schemes have been verified, compare the calculation results of each scheme and evaluate the optimal scheme. If there are still schemes that have not completed the optimization calculation, return to S3.

[0103] If all schemes have been verified, compare the total pumping volume, number of wells opened, drawdown depth, and surface settlement of each scheme. Based on the comparison results and actual construction requirements, select the best scheme. Otherwise, if any scheme has not yet been optimized and verified, return to S3.

[0104] Beneficial effects:

[0105] Compared with existing dewatering design methods, this invention, while ensuring the safety of the foundation pit, can not only determine the optimal pumping volume of a single well, but also the optimal filter pipe length and depth of each well, thereby further reducing the total pumping volume and water level drawdown, achieving more efficient dewatering, and reducing project costs and environmental effects caused by dewatering. Attached Figure Description

[0106] Figure 1 This is a flowchart of the method described in this invention;

[0107] Figure 2 This is a plan view of the foundation pit according to an embodiment of the present invention;

[0108] Figure 3 This is a schematic diagram of the finite element model of an embodiment of the present invention;

[0109] Figure 4 The different filter tubes included in different training sets of the influence coefficient prediction model in the embodiments of the present invention;

[0110] Figure 5 This is a comparison chart of cross-validation results of different MARS models in embodiments of the present invention;

[0111] Figure 6 The depth reduction at each depth reduction control point is calculated by substituting the optimization results into the finite element model in this embodiment of the invention.

[0112] Figure 7 The different cross-sectional depths and surface subsidences are calculated by substituting the optimization results into the finite element model in this embodiment of the invention. Detailed Implementation

[0113] To better understand the present invention, further detailed description is provided below with reference to specific embodiments and accompanying drawings. The accompanying drawings illustrate embodiments of the present invention. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, the embodiments are provided to make the disclosure of the present invention more thorough and complete.

[0114] Specific embodiments of the present invention are as follows: Figures 1-7 As shown. Figure 1 This is a flowchart of a "simulation-optimization" design method for reducing the pressure of foundation pits by optimizing the length and depth of filter pipes, according to the present invention. Figure 2 This is a plan view of the foundation pit according to an embodiment of the present invention. Figure 3 This is a schematic diagram of a single-well pumping finite element model according to an embodiment of the present invention; Figure 4 These are different filter tubes included in different training sets of the influence coefficient prediction model in the embodiments of the present invention; Figure 5 This is a comparison chart of cross-validation results of different MARS models in embodiments of the present invention; Figure 6The depth reduction at each depth reduction control point is calculated by substituting the optimization results into the finite element model in this embodiment of the invention. Figure 7 The different cross-sectional depths and surface subsidences are calculated by substituting the optimization results into the finite element model in this embodiment of the invention.

[0115] Figure 2 This is a schematic diagram of the foundation pit according to an embodiment of the present invention. The foundation pit project is a hypothetical project, and the foundation pit has a rectangular shape with a planar dimension of 50m × 30m.

[0116] The strata where the foundation pit is located include ① fill soil, ② silty clay, ③ silty sand, and ④ silty clay. The thickness and physical and mechanical parameters of each soil layer are shown in Table 1. Among them, layer ③, silty sand, is a confined aquifer with a confined water level 2m below the ground surface.

[0117] The excavation depth of the foundation pit is 25.21m. A diaphragm wall is used as a water-stop curtain. The depth of the diaphragm wall is 40m, which means it is inserted 10m deep into the silty sand layer ③ (as shown in Table 1). The insertion ratio is 0.5.

[0118] During the excavation of the foundation pit, in order to prevent sudden gushing of water in the foundation pit, it is required to depressurize the pressurized water in the silty sand layer ③.

[0119] Table 1 Soil physical and mechanical parameters

[0120]

[0121]

[0122] Note: γ is the soil weight; μ is the soil Poisson's ratio; e0 is the initial void ratio of the soil; λ is the compression index of the modified Cambridge model; κ is the rebound index of the modified Cambridge model; M is the critical stress ratio of the modified Cambridge model; e1 is the void ratio when the average effective principal stress p′ of the soil is 1 kPa; K v K is the vertical permeability coefficient of the soil. h is the horizontal permeability coefficient of the soil.

[0123] This embodiment provides a "simulation-optimization" design method for depressurization of foundation pits that can optimize the length and depth of filter pipes, applicable to the aforementioned project. The method includes the following steps S1-S10:

[0124] S1, calculate the drawdown requirement and obtain the safe drawdown level.

[0125] Select a certain number of drawdown control points within the excavation pit area.

[0126] Since this case involves dewatering within the pit, the drawdown curve is generally funnel-shaped, meaning the drawdown decreases as you get closer to the outer edge. Therefore, control points can be selected at several points on the outermost edge of the pit excavation area to ensure that all points within the pit meet the requirements when the drawdown at all control points meets the safe drawdown requirement.

[0127] In this case, the control points selected are marked as CP1-CP9, a total of 9 points, as follows: Figure 2 As shown, in addition to the outermost part of the excavation area, another control point (CP5) was selected in the middle of the excavation pit.

[0128] According to Article W.0.1 of the "Code for Design of Building Foundations" (GB50007-2011), the safe drawdown can be calculated using the following formula. The safe drawdown value is taken as the minimum s value that satisfies the following formula, and the safe drawdown at drawdown control point j is denoted as s. j,min .

[0129]

[0130] In the formula, h i Let be the thickness of the i-th layer of soil between the bottom of the foundation pit and the top of the confined aquifer (③ silt), in meters. In this example, since the excavation depth of the foundation pit is 25.21 meters (the bottom of the foundation pit is located in ② silty clay), there is only one layer of soil between the foundation and the top of ③ silt, with a thickness of 4.79 meters.

[0131] γ si The unit weight of the i-th soil layer between the bottom of the foundation pit and the top of the confined aquifer (③ silt) is given in kN / m³. 3 In this example, the soil between the base and the top of ③ silty sand is ② silty clay, with a unit weight of 18.0 kN / m³. 3 .

[0132] H0 is the initial pressure head at the top of the confined aquifer, in meters (m); s is the drawdown, in meters (m); γ w The specific weight of water, kN / m 3 ;F s For safety factor, we take 1.1.

[0133] Based on the various settings in this case, it can be known that ∑h i γ si The pressure is 86.22 kPa; H0 is 30-2 = 28 m; γ w 9.8 kN / m 3 ;F s The value is 1.1. Calculations show that the required drawdown at each control point is 20m, i.e., s j,min =20m.

[0134] S2, formulate several plans and preliminarily determine the number and location of dewatering wells for each plan;

[0135] Based on the required drawdown depth, a preliminary estimate of the pit's water inflow is made. Then, the required number of wells is calculated based on the single well's water output capacity, and their locations are determined. Several dewatering schemes are developed by combining different numbers and locations of wells.

[0136] According to Table B.0.3-2 of the "Technical Specification for Wells" (GB50296-2014), the inflow rate Q of the foundation pit can be calculated using the following formula. T :

[0137]

[0138] In the formula, K is the aquifer permeability coefficient, m / d;

[0139] M a s is the aquifer thickness, in meters; s is the drawdown, in meters, taken from each control point s. j,min The maximum value, in this embodiment, s j,min The maximum value is 20m. In other embodiments, if s 1,min =20m,s 2,min =22m, then s j,min The maximum value is 22m, at which point s = 22m.

[0140] R is the radius of influence of precipitation, m; r0 is the equivalent radius of the foundation pit, m. If the foundation pit is circular, r0 is directly taken as the radius of the foundation pit. If the foundation pit is of other shapes, the value is taken according to Table B.0.1-1 in the "Technical Specification for Wells" (GB50296-2014); L is the length of the well filter pipe, m.

[0141] According to formula B.0.2-2 in the "Technical Specification for Wells" (GB50296-2014), the influence radius R of the dewatering well can be estimated using the following formula:

[0142]

[0143] According to Table B.0.1-1 of the "Technical Specification for Wells" (GB50296-2014) (which summarizes many types of foundation pit shapes, and can be directly consulted during design), for a rectangular foundation pit, the equivalent radius r0 can be calculated using the following formula:

[0144]

[0145] In the formula, a is the length of the rectangle, m; b is the width of the rectangle, m; and the values ​​of η are shown in the table below.

[0146] Table 2 η values ​​under different conditions

[0147] b / a 0.1～0.2 0.2～0.3 0.3～0.4 0.4～0.6 0.6～1.0 η 1.00 1.12 1.14 1.16 1.18

[0148] According to item 7.3.16 of the "Technical Specification for Foundation Pit Support" (JGJ120-2012), the water production capacity of a single well can be estimated using the following formula:

[0149]

[0150] In the formula, q represents the water production capacity of a single well, and m 3 / d; r is the radius of the filter tube, in meters.

[0151] In this embodiment of the invention, the parameters required for the preliminary design are summarized in the table below.

[0152] Table 3 Summary of Preliminary Design Parameters

[0153]

[0154] Calculations show that when the length of the well filter pipe varies from 3 to 18 meters, the water inflow rate Q in the foundation pit is... T The range is 6077.08 to 7694.73 m. 3 / d(When the length of the well filter pipe is 3m, Q T It is 6077.08m 3 / d, when the well filter pipe length is 18m, Q T It is 7694.73m 3 / d), the single-well water production capacity is 332.60~1995.58m. 3 / d(When the filter pipe length of the well is 3m, the single well water output capacity is 332.60m³ / d) 3 / d, when the filter pipe length is 18m, the single well water output capacity is 1995.58m³ / d. 3 / d), therefore at least 4 wells need to be installed.

[0155] It should be noted here that the water inflow rate Q in the foundation pit... T The calculation formula does not consider the case where the cutoff wall is inserted into the confined aquifer to a certain depth (the theoretical formula cannot account for this situation). Since the presence of the cutoff wall increases the seepage path and reduces the seepage area, the same pumping volume will result in a greater drawdown compared to the case without a cutoff wall. Therefore, without considering the insertion of the cutoff wall, the Q calculated using the formula... T It will be too large.

[0156] The present invention initially formulated two schemes, which are distinguished by the number and location of the precipitation wells.

[0157] The dewatering wells considered in each scheme are shown in Table 4, and the locations of the dewatering wells are as follows: Figure 2 As shown.

[0158] Meanwhile, it is stipulated that the minimum length of the filter pipe in this case is 3m and the minimum depth is 1m. The length and depth of the filter pipe are controlled to increase in increments of 1m to form filter pipes with different lengths or depths. It is also ensured that the sum of the length and depth of the filter pipe does not exceed 19m (the thickness of the target aquifer is 20m). Therefore, 136 filter pipes are considered for each well.

[0159] Table 4 shows the precipitation wells considered for each scheme.

[0160] plan Precipitation wells one J2, J4, J6, J8 two J1~J9 (all wells)

[0161] S3 simulates single-well pumping for a certain scheme, obtains a certain number of single-well dewatering influence coefficients, constructs influence coefficient matrices A and B, and divides the matrix into blocks according to different wells to facilitate subsequent processing of influence coefficients based on different wells.

[0162] Figure 3 This is a finite element model of a single well pumping system built using the finite element software Abaqus.

[0163] in, Figure 3 (a) shows the overall finite element model. Figure 3 (b) shows a partial grid plan view near the foundation pit.

[0164] The model includes all the precipitation wells from the two schemes mentioned above.

[0165] According to the specific description in the instruction manual, a single-well pumping (existing technology) is simulated to obtain a certain number of single-well pumping influence coefficients, forming influence coefficient matrices A and B, and then the matrices are divided into blocks according to different well pairs.

[0166] Meanwhile, according to the specific description in the instruction manual, the block matrix B will be... ki (k = i = 1, 2, ..., N) cw Replace the non-main diagonal elements in the text with 0.

[0167] Since matrices A and B contain a large number of elements, they are not convenient to display and therefore will not be shown in this embodiment of the invention.

[0168] S4 uses mathematical methods to construct an influence coefficient prediction model and expands the influence coefficient matrices A and B, thereby considering more filter pipes for each well.

[0169] This invention employs a multivariate adaptive regression spline (MARS) machine learning method. The accuracy of the MARS model's prediction results is closely related to the selection of the training set. Generally, the wider the range and the larger the quantity of data in the training set, the higher the prediction performance of the constructed MARS model. However, if the amount of data is too large, the workload is too heavy. Therefore, it is necessary to find a training set that can balance the prediction performance of the MARS model with a relatively small amount of data.

[0170] To achieve this objective, this embodiment studies the impact of different training sets on the model's predictive performance. Since the distances of the precipitation well J2 to both the control point and the cutoff wall are relatively close, its influence coefficient varies considerably, making J2 the most representative.

[0171] This invention embodiment sets four training sets based on different filter tubes of J2, such as... Figure 4As shown.

[0172] MARS models were constructed using each training set, and cross-validation was performed using a test set that was different from the training set. Figure 5 To compare the predicted and simulated values ​​of the influence coefficients for different filter tubes in the test set.

[0173] Combination Figure 4 and Figure 5 It can be seen that Model 3 and Model 4 have good prediction results with little difference. However, Model 4 requires a large number of filters in its training set. Therefore, in subsequent steps when constructing the MARS model, the length and depth of the filters in the training set should be selected from the combination in the Model 3 training set.

[0174] In the constructed MARS model, the length and depth of the 136 filter pipes considered for each well are input to obtain the corresponding influence coefficients. These influence coefficients are then stored in the expanded matrices A and B for use in the construction of subsequent linear programming models.

[0175] S5, Construct a linear programming model.

[0176] Using the influence coefficients in matrices A and B and the safe drawdown s j,min Construct a linear programming model in the following form.

[0177]

[0178]

[0179] The first two constraints can also be described in matrix form, as shown below:

[0180]

[0181]

[0182] Q i =(Q i1 Q i2 … Q i,136 ) T i = 1, 2, ..., N cw

[0183] S = (20 20 ... 20) T

[0184] S n =(1 1 ... 1) T

[0185] In the formula, vector S n The elements in the array are all 1s, and the number of elements in the array is N. cw• 136, which is the total number of filter pipes in all wells; for Scheme 1, N cw The value is 4. For scheme two, N cw The value is 9.

[0186] S6 solves the linear programming model to obtain the optimal pumping rate for each well and filter pipe, which is stored in vector Q.

[0187] The constructed linear programming model was solved using the linprog function built into Matlab software. The result is the optimal pumping rate for all filter pipes in each well. The result is stored in vector Q.

[0188] S7, check for invalid wells.

[0189] An invalid well is defined as follows: if the location of the same well in the optimization calculation results has more than one filter pipe with a pumping volume greater than 0, the well is invalid, because in the real world, only one filter pipe can be opened for the same well when pumping.

[0190] The method for checking for invalid wells is as follows:

[0191] Examine each block vector Q i If the number of elements in the well exceeds ε (ε is a small value close to 0 defined by an individual, such as 1E-4), the corresponding well is considered invalid.

[0192] S8. If there are invalid wells, remove the redundant filter tubes in the invalid wells and return to S5 until there are no invalid wells in the results.

[0193] The method for identifying redundant filters in invalid wells is as follows: multiply matrix B by vector Q to obtain vector C. The elements of vector C are the normalized drawdown s at different filters in different wells. nkn The vector C is divided into blocks according to different wells, resulting in a block matrix C0. k (k = 1, 2, ..., N) cw ).

[0194]

[0195]

[0196] Record the C corresponding to the invalid well k The middle satisfies |C k Elements with (n)-1|<ε are considered redundant and should be excluded.

[0197] The reason for excluding it is: it satisfies |C kThe filter pipe corresponding to the element (n)-1|<ε is often the one with the highest pumping efficiency among all the filter pipes in that well. The higher the pumping efficiency, the lower the pumping volume required to achieve a certain drawdown. However, to satisfy the second constraint, the maximum pumping volume that can be applied is also smaller. Therefore, the pumping volume allocated to this well will be preferentially allocated to this filter pipe, resulting in its normalized drawdown s. nkn The value reaches 1. At this point, according to the second constraint, it is impossible to continue allocating pumping volume to this filter pipe. However, continuing to allocate pumping volume to this well would still help reduce the total pumping volume, and the additional pumping volume would be allocated to the relatively less efficient filter pipe in this well. If s nkn Filter tubes with a value of 1 are excluded. The pumping volume allocated to this well may be handled by the remaining most efficient filter tube alone, at which point the well becomes an effective well.

[0198] Suppose that the y-th filter pipe of the x-th well needs to be removed, the removal method is: divide the block matrix A x The element in column y is replaced with 0, as shown below. Through this process, the excluded filter tube, regardless of its pumping volume, cannot produce any drawdown, meaning its pumping efficiency is 0. According to the optimization principle, no pumping volume will be allocated to this filter tube, effectively excluding it.

[0199] yth column

[0200]

[0201] After eliminating redundant filter pipes from all invalid wells, return to S5.

[0202] After several iterations of calculations from S5 to S8, the optimal filter pipe length, filter pipe depth, and pumping rate for each well in each scheme were obtained and summarized in Table 5.

[0203] Table 5 Optimization Calculation Results of Each Scheme

[0204]

[0205] S9 verifies the optimized calculation results through numerical simulation.

[0206] Substitute the optimal pumping rates of each well obtained from the optimization calculations into the corresponding wells and filter pipes in the previously established finite element model, and perform calculations to verify whether the drawdown at the control points of each scheme meets the requirements. At this point, the pumping rates of all wells corresponding to each scheme should be simultaneously applied to the finite element model. Figure 6 The water level drawdown at the control points for each scheme is shown in the figure. As can be seen from the figure, the water level drawdown (at least 20m) for each scheme is not less than the required drawdown.

[0207] S10: After all schemes have been verified, compare the calculation results of each scheme and evaluate the optimal scheme. If there are still schemes that have not completed the optimization calculation, return to S3.

[0208] By comparing the total pumping volume, number of wells opened, drawdown depth, and surface settlement of each scheme, the best scheme is selected based on the comparison results and actual construction needs.

[0209] Figure 7 For the surface settlement and drawdown outside the pit corresponding to each scheme, sections I and II in the figure are shown. Figure 2 Defined in the table. (Refer to Table 5) Figure 6 and Figure 7 It can be seen that:

[0210] The total pumping volume is: Option 1 > Option 2; the number of wells opened is: Option 1 < Option 2; the length and depth of the filter pipe are: Option 1 > Option 2; the drawdown and surface subsidence are: Option 1 > Option 2. Based on the number of wells opened for each option, the construction cost of the dewatering wells is: Option 1 < Option 2; based on the total pumping volume, the long-term operating cost is: Option 1 > Option 2; based on the drawdown and surface subsidence, the environmental impact is: Option 1 > Option 2.

[0211] Taking into account construction costs and environmental effects, if the foundation pit project has a short construction period and the surrounding environment is not sensitive, then Option 1 is the optimal choice; conversely, if the foundation pit project has a long construction period and the surrounding environment is sensitive, then Option 2 is the optimal choice. This completes the evaluation of the optimal option.

[0212] The foregoing has shown and described the basic principles and main features of the present invention. Those skilled in the art should understand that the present invention is not limited to the above examples; the examples and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A simulation-optimization design method for reducing confined water level in foundation pits, characterized in that: Includes the following steps: S1, calculate the drawdown requirement and obtain the safe drawdown level; S2, formulate several plans and preliminarily determine the number and location of dewatering wells for each plan; S3. For a certain scheme, simulate single-well pumping, obtain a certain number of single-well dewatering influence coefficients, construct influence coefficient matrices A and B, and divide the matrix into blocks according to different wells. S4. Using mathematical methods, an influence coefficient prediction model is constructed, and the influence coefficient matrices A and B are expanded to consider more filter pipes for each well. S5, Construct a linear programming model; S6, Solve the linear programming model to obtain the optimal pumping rate for each well and filter pipe, and store it in vector Q; S7, check for invalid wells; S8. If there are invalid wells, remove the redundant filter tubes in the invalid wells and return to S5 until there are no invalid wells in the results. S9, the optimized calculation results are verified through numerical simulation; S10: After all schemes have been verified, compare the calculation results of each scheme and evaluate the optimal scheme. If there are still schemes that have not completed the optimization calculation, return to S3. In step S5, the influence coefficients in matrices A and B and the safe water level drawdown s need to be used. j,min Construct a linear programming model of the following form: ， Q total -Total pumping volume; N cw - The number of wells considered in the optimization calculation; N s - The number of filter pipes to be considered for each well; Q im - The pumping capacity of the m-th filter tube in well i; α j,im - The influence coefficient of the individual pumping of the m-th filter tube of well i on the drawdown control point j; s j,min -Safe water level drawdown at point j; N cp - Number of depth control points; s nkn - The normalized drawdown at the nth filter tube of well k, i.e., the drawdown at that filter tube and the initial pressure head H at the top of the filter tube. 0kn The ratio; β kn,im - The influence coefficient of pumping water from the m-th filter pipe of well i alone on the n-th filter pipe of well k; The objective function of the model is to find the minimum total pumping volume of all wells; There are three constraints on the model: first, the drawdown at the control points must meet the safe water level drawdown sj,min; second, the normalized drawdown of each well must be less than 1 to avoid the calculated pumping volume being unattainable in reality due to excessive drawdown at each well; and third, the pumping volume of each well must be no less than 0 to ensure that it is pumping water rather than reinjecting it. The first two constraints can also be described in matrix form, as shown below: ， Vector Q stores the pumping volume of all filter pipes in all wells. Q can be divided into blocks according to different wells, and the block vector is denoted as Q0. i (i = 1, 2, ..., N) cw Each element in the block vector represents the pumping volume of different filter tubes in the same well; Vector S n The elements in the array are all 1s, and the number of elements in the array is N. cw ·N s The total number of filter tubes in all wells.

2. The "simulation-optimization" design method for depressurization of foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S2, the preliminary dewatering design only needs to determine the number and location of wells, and does not need to determine the length and depth of the filter pipe; the length and depth of the filter pipe are obtained from subsequent optimization calculations.

3. The "simulation-optimization" design method for depressurization of foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S3, the single-well pumping influence coefficient includes two types: one is the influence coefficient of single-well pumping on the drawdown control point; the other is the influence coefficient of single-well pumping on each well. To optimize the length and depth of the filter pipe for each well, a certain number of filter pipes with different lengths or depths need to be considered for each well, and each filter pipe is regarded as a separate well. At this point, the influence coefficient of single-well pumping on the drawdown control point is: ， α j,im - The influence coefficient of the individual pumping of the m-th filter tube of well i on the drawdown control point j; s j,im - When the m-th filter tube of well i is pumped out alone, the water level drawdown at the drawdown control point j is ; Q im - The pumping capacity of the m-th filter tube in well i; When each filter pipe is considered as a separate well, the impact coefficient of single-well pumping on each well is: ， β kn,im - The influence coefficient of pumping water from the m-th filter pipe of well i alone on the n-th filter pipe of well k; s kn,im - When the m-th filter pipe of well i is pumped out alone, the water level drawdown at the n-th filter pipe of well k is as follows: H 0kn -The initial pressure head at the top of the nth filter tube in well k; All α j,im Form matrix A, all β kn,im Form matrix B; Each column element in the matrix represents the influence coefficient of a certain filter pipe in a certain well on each drawdown control point or each filter pipe in each well when a certain filter pipe is pumping water.

4. The "simulation-optimization" design method for depressurization of foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S3, matrices A and B need to be divided into blocks according to different wells to facilitate subsequent processing of influence coefficients based on different wells. The block division method is as follows: ， Block matrix A i - The influence coefficient matrix of different filter pipes of the i-th well on different drawdown control points when pumping water individually. A i Elements in the same row represent the influence coefficients of different filter pipes of well i on a certain drawdown control point, and elements in the same column represent the influence coefficients of the same filter pipe of well i on different drawdown control points. N cw - The number of wells considered in the optimization calculation; N s - The number of filter pipes considered for each well; N cp - Number of depth control points; ， Block matrix B ki - The influence coefficient matrix of the individual pumping of different filter tubes in well i on the filter tubes of well k; Additionally, it is necessary to partition the matrix B along its main diagonal. ki (k=i=1, 2, …, N cw B) will be processed. ki (k=i=1,2, …, N cw The elements in () represent the influence of each filter pipe in a well on different filter pipes in the same well. B needs to be included. ki (k=i=1, 2,…, N cw To prevent different filter pipes from interfering with each other during pumping from the same well, all elements not on the main diagonal are changed to 0, thus reducing the number of calculations. The method is as follows: 。 5. The "simulation-optimization" design method for depressurization of foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S4, mathematical methods such as machine learning or multiple regression are used to select data from several representative filter pipes as training sets, with filter pipe length and depth as input variables and influence coefficients as output variables, to construct an influence coefficient prediction model to expand the influence coefficient matrices A and B, thereby allowing more filter pipes to be considered for each well and reducing the workload of numerical simulation calculations.

6. The "simulation-optimization" design method for depressurization of foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S7, an invalid well is defined as follows: if there are more than one filter pipe with a pumping volume greater than 0 at the same location in the optimization calculation results, the well is invalid, because in the real world, only one filter pipe can be opened for the same well when pumping. The method for checking for invalid wells is as follows: check each block vector Q. i If the number of elements in the well exceeds ε, and there are more than 1 such elements, the corresponding well is considered invalid; where ε is a human-defined value.

7. The "simulation-optimization" design method for reducing confined water in foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S8, the method for identifying redundant filter pipes in invalid wells is as follows: multiply matrix B by vector Q to obtain vector C; divide vector C into blocks according to different wells to obtain block matrix C. k (k=1, 2, …, N cw ): ， Record the C corresponding to the invalid well k The middle satisfies |C k The filter tubes corresponding to the elements (n)-1|<ε are considered redundant and should be excluded, where ε is a human-defined value; Suppose that the y-th filter pipe of the x-th well needs to be removed, the removal method is: divide the block matrix A x Replace the element in column y with 0: ， After eliminating redundant filter pipes from all invalid wells, return to S5.

8. The "simulation-optimization" design method for depressurization of foundation pits with optimized filter pipe length and depth as described in claim 1, characterized in that: In step S10, the comparison of the calculation results of each scheme includes the total pumping volume, the number of wells opened, the drawdown, and the surface settlement. Based on the comparison results and the actual construction needs, the best scheme is selected.

Images