A multi-objective well group dewatering optimization calculation method based on intelligent algorithms

Abstract

The present invention discloses a calculation method for optimizing multi-target well group dewatering based on intelligent algorithms, comprising the following steps: constructing a mathematical model of foundation pit dewatering seepage-settlement in the study area; assigning and calibrating parameters for the model; establishing an objective function; establishing a judgment matrix; confirming the weights of each sub-objective of the objective function according to the judgment matrix to obtain the final objective function, and jointly constituting an optimization solution algorithm with the genetic algorithm. The optimization solution algorithm is coupled with the established MODFLOW groundwater foundation pit dewatering seepage-settlement mathematical model through Flopy. The optimization solution algorithm continuously reads the MODFLOW simulation results and performs iterative calculations until the optimization goal is achieved. The present invention can realize functions such as automatically optimizing the switching of wells and the pumping volume of single wells, and give corresponding solution sets, effectively reducing the impact of foundation pit dewatering construction on the environment, reducing construction costs, and providing a new technical means for modern foundation pit well group dewatering design.

Description

Technical Field

[0001] The present invention relates to a multi-object well group dewatering optimization calculation method based on intelligent algorithms, belonging to the fields of geological environmental protection and well group dewatering optimization design calculation. Background Technique

[0002] During the construction of various large-scale projects, dewatering construction is an important topic. Understanding the hydrogeological conditions of the construction site and formulating a reasonable well group dewatering plan in advance are the prerequisites for avoiding secondary disasters caused by dewatering construction and ensuring the safety and economy of project construction. With the continuous development of computers, numerical simulation methods have been widely applied to the simulation and solution of various engineering problems. Under complex boundary conditions and stratum conditions, the numerical method can obtain a better approximate solution, and the visualization platform can help customers intuitively understand the site conditions. However, in the current dewatering design scheme, most of them adopt the criterion of arranging wells at equal intervals and obtaining the designed number of wells by dividing the total pumping volume by the pumping volume of a single well. Although this method is simple and easy to implement, it is difficult to apply to complex geological environments. Setting "excessive" pumping volume increases the construction cost and may also cause various secondary geological disasters. Therefore, it is necessary to carry out the optimization design of the dewatering well group in advance to determine the reasonable number of wells and drainage volume, ensure the safe construction of the foundation pit, reduce the impact on the surrounding environment, and achieve the best dewatering effect.

[0003] In the optimization design of foundation pit dewatering, the problems faced are often composed of multiple conflicting and influencing objectives. For example, increasing the number of pumping wells, the greater the pumping volume, the safer the underground structure, but at the same time, the comprehensive dewatering cost will also increase. Excessive pumping volume will also cause ground settlement, which will affect the construction safety. This requires engineering decision-makers to comprehensively consider technical feasibility, economic benefits and environmental impacts, and by adjusting the weights of each objective, try to find the optimal solution to the problem to be optimized. With the rapid development of intelligent algorithms, the optimal design scheme can be quickly and intelligently selected by combining numerical simulation and optimization algorithms.

[0004] The well group dewatering method can generally be divided into the objective function method, the large well method, and the finite element method. The objective function method finds the optimal design parameters under the constraint conditions by taking the minimum or maximum value of a specific objective. However, in existing research, the optimization research and application of the pumping well group layout scheme are very limited. Researchers usually use the gradient descent method to solve the objective function problem, and the application of intelligent optimization methods in solving the objective function is less. Although MODFLOW has become the most mature program in groundwater simulation, its combination with intelligent optimization algorithms for coupled optimal design needs to be further improved. Therefore, the present invention constructs a multi-objective well group dewatering optimization model based on GA and FloPy, tightly couples the optimization algorithm with the numerical simulation model, and proposes a calculation method that can realize the automatic switching of pumping wells, the automatic optimization of the single well discharge, and the well location, and this optimization calculation method has good effectiveness and reliability, which can provide a new technical means for the optimal design of well group dewatering. Summary of the Invention

[0005] The present invention discloses a multi-objective well group dewatering optimization calculation method based on intelligent algorithms. In the optimal design of foundation pit dewatering, a multi-objective well group dewatering optimization model based on GA and FloPy is constructed to tightly couple the optimization algorithm with the numerical simulation model. At the same time, the weights of each objective in the function are determined by the analytic hierarchy process to realize an optimization calculation method that can realize the automatic switching of pumping wells, the automatic optimization of the single well discharge, and the well location. Based on a rigorous mathematical model and mature intelligent algorithms, the present invention avoids the problems of the conventional dewatering scheme design being overly conservative and the total shaft discharge being too large, and can also improve the economic benefits of the project, save groundwater resources, and provide a new technical means for the optimal design of well group dewatering.

[0006] To solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0007] A calculation method for multi-objective well group dewatering optimization based on intelligent algorithms, comprising the following steps:

[0008] (1) According to factors such as the on-site topography and geomorphology, stratum lithology, hydrogeological conditions, and engineering geological conditions, comprehensively determine the scope of the study area, determine the aquifer structure, boundary conditions, and initial conditions around the foundation pit, and construct a seepage-settlement mathematical model for foundation pit dewatering in the study area;

[0009] The seepage-settlement mathematical model for foundation pit dewatering is established as follows:

[0010] ① Mathematical model of groundwater flow movement

[0011]

[0012] In the formula: W is the source-sink term function, m / d; when the type of groundwater is confined water, F = KM and E = μ* , where K is the permeability coefficient of the aquifer, m / d; M is the thickness of the aquifer, m; μ * is the elastic storage coefficient; when the type of groundwater is phreatic water, F = K(H - Z) and E = μ , H is the phreatic surface height, m; Z is the height of the impermeable bottom plate of the aquifer, m; μ is the specific yield; t is the simulation time, t = 0 represents the initial moment; Ω1 is the first type of boundary; Ω2 is the second type of boundary; n is the normal direction of the boundary Ω2; K is the permeability coefficient in the normal direction of the boundary Ω2, m / d; q(x, y, z, t) is the flow rate per unit area cross-section of the boundary, m 3 / (d·m 2 ), q = 0 represents a zero-flow boundary, which is an impermeable boundary in this study; H0(x, y, z) is the initial water level of the aquifer, m; H1(x, y, z, t) is the known function on the boundary Ω1;

[0013] ② Formation settlement model

[0014] Based on Terzaghi's effective stress principle, only the stress in the vertical direction of the formation is considered, and the stress in the horizontal direction is ignored. The total stress on any plane in the soil mass is composed of effective stress and pore water pressure; the vertical settlement model is:

[0015]

[0016] In the formula: Δb is the settlement amount, mm; Ω is the seepage area; S sf is the skeleton storage rate, m -1 , when the water level in the formation is lower than the previous lowest water level, S sf is the inelastic skeleton storage rate (S sfv ), when the water level is higher than the previous lowest water level, S sf is the elastic skeleton storage rate (S sfe ); Δh is the change in water head, m; b is the corresponding formation thickness, m;

[0017] (2) Determine the initial values of the hydrogeological parameters and physical and mechanical parameters of the study area based on the basic data of the study area, previous field tests, and laboratory tests, and assign values to the parameters of the established seepage-settlement mathematical model for the foundation pit dewatering in the study area;

[0018] (3) Run the seepage-settlement mathematical model for the foundation pit dewatering obtained after the assignment in step (2), and correct the parameters through the measured data of the water level observation points to ensure that the simulated groundwater seepage field model is relatively consistent with the natural situation;

[0019] (4) Establish the objective function: The solution of the well group dewatering optimization model can be transformed into an optimization problem. Taking factors such as the well construction economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost of the dewatering scheme as sub-objectives to form the objective function, and taking the minimum total value of the objective function as the overall optimization goal;

[0020] (5) Establish the judgment matrix: Since there are multiple sub-objectives in the objective function established in step (4), and these sub-objectives of the dewatering optimization model often affect each other, different weights can be multiplied according to the importance degree between each sub-objective;

[0021] (6) Model coupling and optimization solution: Confirm the weights of each sub-objective of the objective function in step (4) according to the judgment matrix in step (5) to obtain the final objective function. Combine the final objective function with the genetic algorithm to form an optimization solution algorithm. Couple the optimization solution algorithm with the MODFLOW groundwater foundation pit dewatering seepage-settlement mathematical model established in step (3) through Flopy. The optimization solution algorithm continuously reads the MODFLOW simulation results (such as the settlement amount and water head at the observation point) and performs iterative calculations until the optimization goal is achieved.

[0022] The aquifer structure of the model in the above step (1) includes the unconfined aquifer and the confined aquifer, the boundary conditions include the first type of constant head boundary, the second type of constant flow boundary, and the third type of mixed boundary, and the initial conditions include the initial water head condition and the initial stress condition.

[0023] In the above step (2), the initial values of the hydrogeological parameters and physical and mechanical parameters required for calculation are obtained according to the on-site investigation research report, on-site pumping test, micro-water test, injection test, indoor constant head test, variable head test, and geotechnical test; the hydrogeological parameters include permeability coefficient, porosity, volume compressibility, and specific weight, etc.

[0024] In the above step (3), the means of parameter correction include but are not limited to: setting up simulated observation wells to fit and adjust parameters with the measured data of on-site observation wells and using the PEST module to invert parameters, etc.

[0025] In step (4) above, the optimal design objective function of well group dewatering contains two types of variables: decision variables and state variables. The decision variables are the objects to be optimized, including the number, location, and water inflow of pumping wells. By adjusting the combination among them, the best dewatering effect can be achieved. Due to the environmental restrictions of the engineering site, the locations of pumping wells cannot be set arbitrarily. Therefore, before the optimization model runs, it is necessary to select the possible locations of pumping wells in advance and determine the maximum number of pumping wells. The optimization algorithm will search for the optimal solution among the possible locations of pumping wells, and then determine the best layout plan of the pumping well group. This process is completed by defining the opening or closing of pumping wells as binary variables. Some decision variables in the objective function can only be selected from 0 or 1, which is called 0-1 integer programming. In the genetic algorithm used this time, 0-1 integer programming represents the on-off state of pumping wells. If a pumping well is encoded as 1 in the algorithm, it means that the pumping well is working, otherwise it means that the pumping well has stopped pumping. The groundwater level in the aquifer and the maximum settlement amount restricted by the observation points are used as the state variables of the optimization model. They are the output results after the decision variables are input into the MODFLOW model and change with the change of the decision variables. The state variables and decision variables serve as the bridge connecting the MODFLOW program and the genetic algorithm program in the dewatering optimization model.

[0026] Taking the well completion economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost of the dewatering plan as sub-objectives to form the objective function, and taking the minimum total value of the objective function as the overall optimization goal. Since there are multiple sub-objectives in the objective function, it is necessary to solve them by assigning reasonable weight values to each sub-objective. The established objective function formula is as follows:

[0027]

[0028] The constraint conditions corresponding to the objective function:

[0029] n z ≥n w (4)

[0030] Q max ≥Q i ≥Q min (5)

[0031] In the formula, Y is the value of the objective function, α1 is the weight coefficient of the well completion economic cost, and c1 is the cost of drilling and cementing the pumping well; α2 is the weight coefficient of the pumping economic cost, and c2 is the cost consumed per unit water inflow; X i is a binary variable, X i =1 represents that the pumping well is working normally, X i =0 represents that the pumping well is not working; Q i is the water inflow of the pumping well working normally, n obsis the number of observation points, β1 is the weight coefficient of the target water level of the observation point, β2 is the weight coefficient of the maximum allowable settlement of the observation point, h i is the water level value of the observation point, H i is the target water level value, S i is the settlement of the observation point, n z is the maximum allowable number of pumping wells, n w is the number of actually operating pumping wells, Q min Q max are the minimum and maximum water inflows of a single well respectively.

[0032] In the above step (5), the analytic hierarchy process (AHP) is adopted to analyze the weights of each sub-goal. AHP can not only transform the decision maker's judgment into the comparison of the importance between pairs of several factors, thus transforming the qualitative judgment that is difficult to quantify into the operable comparison of importance; AHP can also reflect the basic characteristics of decision-making thinking, that is, based on the observation of the research goal, the collection, statistical analysis and summary of data, and finally obtaining a quantitative weight result evaluation, overcoming the shortcoming of other analysis methods that avoid the decision maker's subjective judgment.

[0033] In the above step (5), taking the four sub-goals in the objective function: well completion economic cost, operation economic cost, target water level value and maximum allowable settlement as the elements of each index layer, and the weight analysis of each sub-goal as the target layer, thus constructing a hierarchical structure model for the weight analysis of sub-goals in the objective function.

[0034] In the above step (5), define the n-order judgment matrix a ij , compare the importance of each pair of sub-goals in the index layer, and take the mutual ratio between each index as the element in the matrix. The importance scale is quantified in the form of expert scoring. The judgment matrix scale is shown in Table 1. At this time, the judgment matrix A is obtained:

[0035]

[0036] Table 1 Judgment matrix scale

[0037]

[0038] In the above step (5), after constructing the judgment matrix A, it is necessary to solve the maximum eigenvalue and its eigenvector of A, and conduct a test according to the consistency test index:

[0039]

[0040] In the formula, CI is the consistency test index of matrix A; λ maxis the largest eigenvalue of matrix A; n is the order of matrix A; CR is the consistency ratio. When CR < 0.1, the judgment matrix is consistent; RI is the average random consistency index of order n. RI is the average random consistency index of order n, and the corresponding relationship between the two can be obtained from the average random consistency test index table, as shown in Table 2;

[0041] Table 2 Average Random Consistency Test Index Table

[0042]

[0043] In the above step (6), Flopy is used to couple and solve the foundation pit dewatering seepage-settlement mathematical model established by MODFLOW with the genetic algorithm. The genetic algorithm gradually adjusts and evolves the population towards the direction containing the optimal solution by performing operations such as selection, crossover, and mutation on the initial population. In practical applications, the genetic algorithm can obtain a definite global optimal solution according to the objective function; the on-off of the well is defined as a binary problem, and the decision variable can only be selected from 0 or 1. Compared with other algorithms, the genetic algorithm can well accommodate this optimization requirement. When using the model, first create a MODFLOW groundwater model using FloPy according to the hydrogeological model, and then use the genetic algorithm to solve the objective function established based on FloPy. The objective function value will read the MODFLOW simulation results (such as the settlement amount and water head at the observation point) for iterative calculation.

[0044] Technologies not mentioned in the present invention shall refer to the prior art.

[0045] A calculation method for multi-objective well group dewatering optimization based on intelligent algorithms according to the present invention. By using the MODFLOW module to establish an accurate three-dimensional groundwater seepage model of the research area, and then constructing an objective function with sub-objectives such as well completion cost, operation cost, water level drawdown at the observation point, and environmental cost, using the AHP method to assign weights according to the importance of each sub-objective and its impact on the project, and constructing a multi-objective well group dewatering optimization model based on GA and FloPy, which tightly couples the optimization algorithm and the numerical simulation model, and proposes a calculation method that can realize the automatic on-off of pumping wells, the automatic optimization of the single-well water inflow and the position of the well. This optimization calculation method has good effectiveness and reliability, effectively reduces the impact of foundation pit dewatering construction on the environment, reduces construction costs, and provides a new technical means for the optimization design of well group dewatering. Brief Description of the Drawings

[0046] Figure 1 is a schematic flow chart of the calculation method for multi-objective well group dewatering optimization based on intelligent algorithms according to an embodiment of the present invention;

[0047] Figure 2 is a setting diagram of the well group dewatering optimization verification model in an embodiment of the present invention;

[0048] Figure 3 This is the contour map of the site water level and settlement under the multi-objective well group dewatering optimization calculation based on the intelligent algorithm in the embodiment of the present invention;

[0049] Figure 4 This is the contour map of the site water level and settlement under the "large well method" calculation in the embodiment of the present invention;

[0050] Figure 5 This is the comparison chart of each index under different method calculations in the embodiment of the present invention; Detailed implementation manners

[0051] To better understand the present invention, the content of the present invention will be further clarified below in conjunction with embodiments, but the content of the present invention is not limited to the following embodiments only.

[0052] A multi-objective well group dewatering optimization calculation method based on an intelligent algorithm first uses the MODFLOW module to establish an accurate three-dimensional groundwater seepage model of the research area. A target function is constructed with sub-objectives such as well completion economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost. The AHP method is used to assign weight scores according to the importance of each sub-objective and its impact on the project. Finally, the Flopy is coupled with the MODFLOW model and the GA, and the genetic algorithm's good compatibility and optimization ability are used for solution to obtain the best well group dewatering scheme. The present invention will be further described below in conjunction with the drawings and embodiments.

[0053] Example 1: This example provides a multi-objective well group dewatering optimization calculation method based on an intelligent algorithm, and the calculation process is schematically shown as Figure 1 shown, and is implemented by the following steps.

[0054] (1) To verify the effectiveness and superiority of the multi-objective well group dewatering optimization calculation method based on the intelligent algorithm, an ideal well group dewatering optimization verification model was designed by simulating the actual situation of the foundation pit dewatering project. The model is a single-layer unconfined aquifer with a thickness of 80m, and the model extends 105m in the X and Y directions and is divided into 441 units by grids with a side length of 5m. The model boundaries are all set as constant head boundaries, the constant head and the initial head are both set as 80m, the bottom is set as an impermeable boundary, and the site is divided into three regions with different hydrogeological parameters. A square foundation pit with a side length of 25m is set in the site, and 8 alternative pumping wells are arranged around the foundation pit. All the pumping wells are unconfined complete wells. A water level observation point is made at the center point of the foundation pit, and a settlement observation point is arranged on the east side of the model to simulate and observe the settlement of important locations caused by the foundation pit dewatering. The goal of this dewatering is that the water level drawdown at the center point of the foundation pit reaches 3m within 10 days, and the settlement value of the settlement observation point is less than 5mm. The specific settings of the model are as Figure 2 shown.

[0055] (2) Establishment of the foundation pit dewatering seepage-settlement mathematical model

[0056] ①Mathematical model of groundwater flow movement

[0057] The type of groundwater in the model is phreatic water, and its control equation is

[0058]

[0059] In the formula: D is the seepage area; H is the water level elevation, m; K x , K y , K z are the main permeability coefficients in the x, y, and z-axis directions respectively, m / d; h is the height of the phreatic surface, m; ε is the source-sink term function, m / d; μd is the specific yield; t is the simulation time, t = 0 represents the initial moment; Ω1 is the first type of boundary; Ω2 is the second type of boundary; n is the normal direction of the boundary Ω2; K is the permeability coefficient in the normal direction of the boundary Ω2, m / d; q(x, y, z, t) is the flow rate of the unit area cross-section of the boundary, m 3 / (d·m 2 ), when q = 0, it represents a zero-flow boundary, which is an impermeable boundary in this study; H0(x, y, z) is the initial water level of the aquifer, m; H1(x, y, z, t) is the known function on the boundary Ω1.

[0060] ②Stratum settlement model. Based on Terzaghi's effective stress principle, only the vertical stress of the stratum is considered, and the horizontal stress is ignored. The total stress on any plane in the soil mass consists of effective stress and pore water pressure. The vertical settlement model is:

[0061]

[0062] In the formula: Δb is the settlement amount, mm; Ω is the seepage area; S sf is the skeleton water storage rate, m -1 , when the water level in the stratum is lower than the previous lowest water level, S sf is the inelastic skeleton water storage rate (S sfv ), when the water level is higher than the previous lowest water level, S sf is the elastic skeleton water storage rate (S sfe ); Δh is the change in water head, m; b is the corresponding stratum thickness, m.

[0063] (3) Obtain the initial values of the hydrogeological parameters and physical and mechanical parameters required for calculation according to the on-site investigation research report, on-site pumping test, micro-water test, injection test, indoor constant-head test, variable-head test, and geotechnical test, and assign values to the parameters of the established seepage-settlement mathematical model of the foundation pit dewatering in the study area; among them, the hydrogeological parameters include permeability coefficient, porosity, volume compressibility, and specific weight.

[0064] (4) Run the foundation pit dewatering seepage-settlement mathematical model obtained in step (3), and calibrate the parameters through the measured data of the water level observation points to ensure that the simulated groundwater seepage field model is consistent with the natural situation; among them, the means of parameter correction include: setting up a simulated observation well to fit and adjust the parameters with the measured data of the on-site observation well and using the PEST module to invert the parameters.

[0065] (5) Establish an objective function: The solution of the well group dewatering optimization model can be transformed into an optimization problem. Taking factors such as the well completion economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost of the dewatering plan as sub-objectives to form an objective function, and taking the minimum total value of the objective function as the overall optimization goal;

[0066] The objective function of the well group dewatering optimization design contains two types of variables: decision variables and state variables; the decision variables are the objects to be optimized, including the number, location, and water inflow of the pumping wells, and by adjusting the combination between them to achieve the best dewatering effect; due to the environmental restrictions of the engineering site, the location of the pumping wells cannot be set arbitrarily; therefore, before running the optimization model, it is necessary to select the possible locations of the pumping wells in advance and determine the maximum number of pumping wells; the optimization algorithm will search for the best solution among the possible locations of the pumping wells, and then determine the best layout plan of the pumping well group. This process is completed by defining the opening or closing of the pumping wells as binary variables. Some decision variables in the objective function can only be selected from 0 or 1, which is called 0-1 integer programming. In the genetic algorithm used this time, 0-1 integer programming represents the on-off state of the pumping wells. If the pumping well is encoded as 1 in the algorithm, it means that the pumping well is working, otherwise it means that the pumping well has stopped pumping water; the groundwater level in the aquifer and the maximum settlement amount restricted by the observation point are used as the state variables of the optimization model. They are the output results after the decision variables are input into the MODFLOW model and change with the change of the decision variables; the state variables and decision variables serve as the bridge between the MODFLOW program and the genetic algorithm program in the dewatering optimization model.

[0067] Taking the well completion economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost of the dewatering plan as sub-objectives to form an objective function, and taking the minimum total value of the objective function as the overall optimization goal; since there are multiple sub-objectives in the objective function, it is necessary to solve them by assigning reasonable weight values to each sub-objective. The established objective function formula is as follows:

[0068]

[0069] The constraint conditions corresponding to the objective function:

[0070] n z ≥n w (4)

[0071] Qmax ≥Q i ≥Q min (5)

[0072] Wherein, Y is the objective function value, α1 is the weight coefficient of the well completion economic cost, and c1 is the cost of the pumping well drilling and cementing; α2 is the weight coefficient of the pumping economic cost, and c2 is the cost consumed per unit of pumped water volume; X i is a binary variable, X i = 1 represents that the pumping well is working properly, X i = 0 represents that the pumping well is not working; Q i is the water inflow of the pumping well working properly, n obs is the number of observation points, β1 is the weight coefficient of the target water level of the observation point, β2 is the weight coefficient of the maximum allowable settlement of the observation point, h i is the water level value of the observation point, H i is the target water level value, S i is the settlement of the observation point, n z is the maximum allowable number of pumping wells, n w is the number of pumping wells actually working, Q min ,Q max are the minimum and maximum water inflows of a single well respectively.

[0073] (6) Establish a judgment matrix: Since there are multiple sub-goals in the objective function established in step (5), and these sub-goals of the precipitation optimization model often affect each other, different weights can be multiplied according to the importance of each sub-goal;

[0074] The analytic hierarchy process (AHP) is adopted to analyze the weights of each sub-goal. AHP can not only transform the decision-maker's judgment into the comparison of the importance between pairs of several factors, thus transforming the qualitative judgment that is difficult to quantify into the operable comparison of importance; AHP can also reflect the basic characteristics of the decision-making thinking, that is, based on the observation of the research goal, the collection and statistical analysis and summary of data, and finally obtaining a quantitative weight result evaluation, overcoming the shortcoming of other analysis methods that avoid the decision-maker's subjective judgment.

[0075] Taking the four sub-goals in the objective function: well completion economic cost, operation economic cost, target water level value, and maximum allowable settlement as the elements of each index layer, and the weight analysis of each sub-goal as the target layer, thus constructing a hierarchical structure model for the weight analysis of sub-goals in the objective function.

[0076] Define an n-order judgment matrix a ij , compare the importance of each pair of sub-goals in the index layer, and take the mutual ratio between each index as the element in the matrix. The importance scale is quantified in the form of expert scoring. The judgment matrix scale is shown in Table 1. At this time, the judgment matrix A is obtained:

[0077]

[0078] Table 1 Judgment Matrix Scale

[0079]

[0080] After constructing the judgment matrix A, it is necessary to solve the maximum eigenvalue and its eigenvector of A, and conduct an inspection according to the consistency inspection index:

[0081]

[0082] In the formula, CI is the consistency inspection index of matrix A; λ max is the maximum eigenvalue of matrix A; n is the order of matrix A; CR is the consistency ratio. When CR < 0.1, the judgment matrix is consistent; R is the average random consistency index of the nth order. The corresponding relationship between the two can be obtained from the average random consistency inspection index table, as shown in Table 2. When n = 4, RI = 0.89.

[0083] Table 2 Average Random Consistency Inspection Index Table

[0084]

[0085] (7) Model coupling and optimization solution: According to the judgment matrix in step (6), confirm the weights of each sub-objective of the objective function in step (5) to obtain the final objective function. Combine the final objective function with the genetic algorithm to form an optimization solution algorithm. Couple the optimization solution algorithm with the MODFLOW groundwater foundation pit dewatering seepage-settlement mathematical model established in step (4) through Flopy. The optimization solution algorithm continuously reads the MODFLOW simulation results (such as the settlement amount and water head of the observation point) and conducts iterative calculations until the optimization goal is achieved.

[0086] In this example, call the coupled model to calculate the verification model. In this verification, assign the same weight coefficients to each item in the objective function. The proposed optimization model will automatically optimize the well group pumping parameters according to the limiting conditions. If parallel tests are carried out under the same conditions, the optimization model will give the corresponding series of solution sets. Conduct 10 parallel calculations on the verification model. On the premise of ensuring that the water level at the center point of the foundation pit drops by 3m, minimize the impact of pumping on the settlement observation point as much as possible, and at the same time reduce the comprehensive dewatering cost, including construction cost and operation cost.

[0087] Use the traditional large well method to arrange the dewatering well group for calculation and comparison

[0088] At present, the "large well method" is mainly used in engineering to calculate the total inflow of the foundation pit, and then the total inflow is evenly distributed to each pumping well to determine the dewatering well group of the foundation pit. The advantage of this method is simple calculation and easy operation. It is calculated according to the complete well formula of the unconfined aquifer stipulated in the specification:

[0089]

[0090] In the formula: Q is the inflow of the foundation pit (m 3 ); K is the permeability coefficient of the aquifer (m / d); S is the drawdown (m); H is the thickness of the aquifer (m); r w is the equivalent radius (m); when the shape of the foundation pit is rectangular, a and b are the length and width of the rectangle (m).

[0091] The results of the large well method and ten parallel optimization calculations are shown in Table 3. Examples of the site water level and ground settlement contour maps are Figure 3 shown as follows. The "large well method" is used to calculate the total inflow of the foundation pit of the verification model, and the total inflow (808 m 3 ) is evenly distributed to 8 standby pumping wells. After 10 days of pumping work of the well group, the site water level and ground settlement contour maps are Figure 4 shown as follows. The well completion cost is 500 yuan per well, and the pumping operation cost is 1 yuan / m 3 , and the comprehensive calculation results are compared as Figure 5 shown as follows.

[0092] Table 3 Results of 10 - time parallel optimization

[0093]

[0094] The multi - objective well group dewatering optimization calculation method based on intelligent algorithms shows good calculation results. Compared with the calculation results of the "large well method", the target water level obtained at the water level observation points is more accurate, and at the same time, the settlement amount at a certain point of the site can be accurately controlled purposefully. The optimization algorithm will give a solution set under the restricted conditions. Generally, compared with the calculation results of the large well method, the water extraction volume of the optimization algorithm is reduced by 20.3%, the settlement is reduced by 53.7%, and the construction cost is reduced by 45.9%. Using the optimization algorithm to optimize the calculation of the foundation pit pumping well group is more accurate, safe and economical.

[0095] The multi - objective well group dewatering optimization calculation method based on intelligent algorithms can realize functions such as automatically optimizing the opening and closing of wells and the pumping volume of single wells, and give the corresponding solution set, effectively reducing the impact of foundation pit dewatering construction on the environment, reducing the construction cost, and providing a new technical means for modern foundation pit well group dewatering design.

Claims

1. A calculation method for optimizing multi-objective well group precipitation based on intelligent algorithms, characterized in that: It includes the following steps: (1) Based on the on-site topography and geomorphology, stratum lithology, hydrogeological conditions, and engineering geological conditions, comprehensively determine the scope of the study area, determine the aquifer structure, boundary conditions, and initial conditions around the foundation pit, and construct a mathematical model for seepage - settlement of foundation pit dewatering in the study area; The mathematical model for seepage - settlement of foundation pit dewatering is established as follows: ① Mathematical model of groundwater flow movement Where: W is the source term function, m / d; when the groundwater type is confined water, F = KM and E = μ * , at this time K is the aquifer permeability coefficient, m / d; M is the aquifer thickness, m; μ * is the elastic storage coefficient; when the groundwater type is unconfined water, F = K(H - Z) and E = μ, H is the height of the water table, m; Z is the height of the impermeable bottom plate of the aquifer, m; μ is the specific yield; t is the simulation time, t = 0 represents the initial time; Ω1 is the first type of boundary; Ω2 is the second type of boundary; n is the normal direction of the boundary Ω2; K is the permeability coefficient in the normal direction of the boundary Ω2, m / d; q(x, y, z, t) is the flow rate per unit area cross-section of the boundary, m 3 / (d·m 2 ), q = 0 represents a zero-flow boundary, which is an impermeable boundary in this study; H0(x, y, z) is the initial water level of the aquifer, m; H1(x, y, z, t) is the known function on the boundary Ω1; ② Stratum settlement model Based on Terzaghi's effective stress principle, only consider the stress in the vertical direction of the stratum, ignore the stress in the horizontal direction, and the total stress on any plane in the soil body is composed of effective stress and pore water pressure; the vertical settlement model is: Where: Δb is the settlement amount, in mm; Ω is the seepage area; S sf is the skeleton water storage rate, in m -1 . When the water level in the formation is lower than the lowest water level in the previous period, S sf is the inelastic skeleton water storage rate S sfv . When the water level is higher than the lowest water level in the previous period, S sf is the elastic skeleton water storage rate S sfe ; Δh is the change in water head, in m; b is the corresponding formation thickness, in m; (2) Based on the basic data of the study area, previous on-site tests, and laboratory tests, comprehensively determine the initial values of hydrogeological parameters and physical and mechanical parameters in the study area, and assign values to the parameters of the established mathematical model for seepage - settlement of foundation pit dewatering in the study area; (3) Run the mathematical model for seepage - settlement of foundation pit dewatering obtained after the assignment in step (2), and correct the parameters through the measured data of the water level observation points to ensure that the simulated groundwater seepage field model is relatively consistent with the natural situation; (4) Take the well - forming economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost of the dewatering plan as sub - objectives to form an objective function, and take the minimum total value of the objective function as the overall optimization goal; (5) According to the importance degree among the sub - objectives, multiply different weights to each sub - objective to form a judgment matrix; (6) Confirm the weights of each sub - objective of the objective function in step (4) according to the judgment matrix in step (5) to obtain the final objective function. Combine the final objective function with the genetic algorithm to form an optimization solution algorithm. Couple the optimization solution algorithm with the MODFLOW groundwater foundation pit dewatering seepage - settlement mathematical model established in step (3) through Flopy. The optimization solution algorithm continuously reads the MODFLOW simulation results and performs iterative calculations until the optimization goal is reached; In step (4), there are two types of variables in the objective function: decision variables and state variables; The decision variables are the objects to be optimized, including the number, location, and pumping volume of the pumping wells. By adjusting the combinations among them, the best dewatering effect can be achieved. Due to the environmental restrictions of the engineering site, the locations of the pumping wells cannot be set arbitrarily. Therefore, before the optimization model runs, it is necessary to select the possible locations of the pumping wells in advance and determine the maximum number of pumping wells. The optimization algorithm will search for the optimal solution among the possible locations of the pumping wells, and then determine the best layout plan of the pumping well group. This process is completed by defining the opening or closing of the pumping wells as binary variables. Some decision variables in the objective function can only be selected from 0 or 1, which is called 0-1 integer programming. In the genetic algorithm used in this study, 0-1 integer programming represents the on / off state of the pumping wells. If a pumping well is encoded as 1 in the algorithm, it means that the pumping well is working; otherwise, it means that the pumping well has stopped pumping. The groundwater level in the aquifer and the maximum settlement amount restricted by the observation points are used as the state variables of the optimization model. They are the output results after the decision variables are input into the MODFLOW model and change with the change of the decision variables. The state variables and decision variables serve as the bridge between the MODFLOW program and the genetic algorithm program in the dewatering optimization model. The objective function is composed of sub-objectives such as the well completion economic cost, operation economic cost, water level drawdown at the observation point, and environmental cost of the dewatering plan. The overall optimization goal is to minimize the total value of the objective function. Since there are multiple sub-objectives in the objective function, it is necessary to solve them by assigning reasonable weight values to each sub-objective. The established objective function is as follows: Constraints corresponding to the objective function: n z ≥ n w (4) Q max ≥Q i ≥Q min (5) In the formula, Y is the objective function value, α1 is the weight coefficient of the well completion economic cost, and c1 is the cost of the pumping well drilling and cementing; α2 is the weight coefficient of the pumping economic cost, and c2 is the cost consumed per unit of pumped water volume; X i is a binary variable, and X i = 1 represents that the pumping well is working normally, and X i = 0 represents that the pumping well is not working; Q i is the water inflow of the pumping well working normally, n obs is the number of observation points, β1 is the weight coefficient of the target water level of the observation point, β2 is the weight coefficient of the maximum allowable settlement of the observation point, h i is the water level value of the observation point, H i is the target water level value, S i is the settlement of the observation point, n z is the maximum allowable number of pumping wells, n w is the actual number of pumping wells working, Q min , Q max are respectively the minimum and maximum water inflows of a single well; In step (5), an \(n\)-order judgment matrix \(a\) is defined ij , pairwise comparison of the importance of each sub-goal in the index layer is carried out, and the mutual ratio between each index is used as the element in the matrix. The importance scale is quantified in the form of expert scoring. The judgment matrix scale is shown in Table 1. At this time, the judgment matrix \(A\) is obtained: Table 1 Judgment matrix scale 2. The calculation method for optimizing multi-objective well group precipitation based on intelligent algorithms according to claim 1, characterized in that: In step (2), according to the on-site investigation research report, on-site pumping test, mini-water test, injection test, indoor constant-head test, variable-head test, and geotechnical test, the initial values of the hydrogeological parameters and physical and mechanical parameters required for calculation are obtained. The hydrogeological parameters include permeability coefficient, porosity, volume compressibility, and specific weight.

3. A calculation method for optimizing multi-target well group precipitation based on intelligent algorithms according to claim 1 or 2, characterized in that: In step (3), the means of parameter correction include, but are not limited to: setting up simulated observation wells to fit and adjust parameters with the measured data of on-site observation wells and using the PEST module to invert parameters.

4. A calculation method for optimizing multi-target well group precipitation based on an intelligent algorithm according to claim 1 or 2, characterized in that: In step (5), the analytic hierarchy process (AHP) is adopted to analyze the weights of each sub-objective. AHP can not only transform the decision maker's judgment into the comparison of the importance between two factors, thus transforming the qualitative judgment that is difficult to quantify into the operable comparison of importance, but also reflect the basic characteristics of decision-making thinking, that is, based on the observation of the research objective, data collection, statistical analysis, and summary, and finally obtaining a quantitative weight result evaluation.

5. A calculation method for optimizing multi-target well group precipitation based on an intelligent algorithm according to claim 1 or 2, characterized in that: In step (5), taking the four sub-objectives in the objective function: well completion economic cost, operation economic cost, target water level value, and maximum settlement amount limit as the elements of the index layer, and the weight analysis of each sub-objective as the target layer, the hierarchical structure model of the sub-objective weight analysis in the objective function is constructed accordingly.

6. A calculation method for optimizing multi-target well group precipitation based on intelligent algorithms according to claim 1 or 2, characterized in that: In step (5), after the judgment matrix A is constructed, it is necessary to solve the maximum eigenvalue and its eigenvector of A, and conduct a test according to the consistency test index: In the formula, CI is the consistency test index of matrix A; λ max is the maximum eigenvalue of matrix A; n is the order of matrix A; CR is the consistency ratio. When CR < 0.1, the judgment matrix is consistent; RI is the average random consistency index of order n. The corresponding relationship between the two can be obtained from the average random consistency test index table, as shown in Table 2; Table 2 Average Random Consistency Test Index Table

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