A large-scale non-uniform stratum permeability parameter simulation method based on typical unit test

Abstract

The application discloses a large-scale non-uniform stratum permeation parameter simulation method based on typical unit test, which comprises the following steps: sampling a block in a region and setting a dipole pump, calculating the permeation coefficient spatial distribution of the region by using the water head data read by the sampling block, and obtaining the permeation coefficient distribution of the whole region by using Kriging interpolation according to the local distribution. Compared with the method for determining the permeation coefficient of a soil sample by means of drilling and indoor test, the method can more efficiently simulate the permeation coefficient of the whole stratum at a lower cost, and provides a new thought for simulating the permeation parameter of a non-uniform stratum under a large scale.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computing and predicting soil permeability coefficients, and in particular to a large-scale non-uniform stratum permeability parameter simulation method based on typical unit tests. BACKGROUND

[0002] In the fields of civil engineering and geology, accurately measuring the permeability coefficient of soil is crucial as it directly relates to groundwater flow, soil stability, and the design and construction of infrastructure. Currently, commonly used methods for measuring permeability coefficients include laboratory tests (such as constant head permeameter tests and variable head permeameter tests), field tests (such as conventional downhole permeability tests, vadose zone permeability tests, and Guelph permeameter tests), and indirect assessment methods based on soil physical properties. These methods each have their advantages and limitations, for example, laboratory tests can provide precise measurements under controlled conditions, while field tests can better reflect the permeability characteristics of actual soil layers. SUMMARY

[0003] The purpose of the present application is to provide a large-scale non-uniform stratum permeability parameter simulation method based on typical unit tests, which can more efficiently simulate the permeability coefficient of the entire stratum at a lower cost compared to traditional methods of determining the permeability coefficient of soil samples through drilling and laboratory testing, providing a new solution for simulating large-scale non-uniform stratum permeability parameters.

[0004] To achieve the above-mentioned purpose, the technical solution adopted by the present application is as follows:

[0005] A large-scale non-uniform stratum permeability parameter simulation method based on typical unit tests, characterized by the following steps:

[0006] Step 1: Select a block within the study area that can represent the characteristics of the entire area as a sampling block;

[0007] Step 2: Perform a dipole pump test in the sampling block, which includes a fixed-flow outlet and inlet located on both sides of the geometric center of the sampling block;

[0008] Step 3: Turn on the dipole pump and wait for the system to stabilize, then measure the spatially distributed water head data and record the coordinate positions;

[0009] Step 4: Use the objective function of the underdetermined inverse problem to solve the permeability coefficient distribution in the region using the water head distribution results measured by the dipole pump test;

[0010]

[0011] In formula (1), the optimized model is used to find the permeability coefficient spatial distribution corresponding to the least square target L(h, k); h represents the vector of water head measurement value; k represents the parameter value, i.e. the permeability coefficient; g is the function of calculating water head by using permeability coefficient; ΔH is the measurement accuracy; u is the auxiliary vector with the same length as the parameter k, u = γ -1 (k-k mean ), wherein the covariance matrix γ is the variation function related to the spatial distribution, and (k-k mean ) is the difference between the predicted permeability coefficient and the spatial weighted mean value thereof;

[0012] In step 6, the Kriging interpolation method is used to predict the permeability parameter of the non-uniform stratum at a large scale according to the water head spatial distribution result, and the specific form is as follows:

[0013]

[0014] is the predicted value calculated by using the Kriging interpolation function, λ i is the weight coefficient estimated by using the weighted summation of all known data points.

[0015] Further, the sampling blocks are selected at the edge of the research area (such as distributed in four directions of the sample) and the center of the research area, at least one sampling block is selected at the center of the research area, and the total number of sampling blocks is more than 5. The sampling blocks should have good representativeness.

[0016] Further, in step 2, the sampling block is a regular geometric shape with a symmetry axis passing through the geometric center, and the dipole pump should be placed on both sides of the symmetry axis of the sampling block, and at least two pairs of dipole pumps are placed in each sampling block.

[0017] Further, in step 2, the flow of the dipole pump should be controlled to a small extent to ensure that the water flow in the sample meets the Darcy flow.

[0018] Further, in step 3, the number of water head measuring devices should be at least more than 4, but not too much, to avoid excessive disturbance to the sample.

[0019] Further, in step 4, the target function L(h, k) is regarded as the combination of the fitting term and the penalty term function.

[0020] Further, in step 4, the fitting term is used to define the residual, and the target function is given as follows:

[0021]

[0022] The penalty term is used to punish the bad properties of the parameter field, and the target function is given as follows:

[0023] (h-h​mean ) T u = (h - h mean ) T gamma -1 (h - h mean ) (4)

[0024] h mean in formula (4) represents the weighted mean value of the vector of water head measurement.

[0025] Further, gamma represents the variation function related to the spatial distribution, which is defined by the following formula:

[0026]

[0027] where sigma 2 is the base station parameter, taking the value of 1, r is the range parameter, taking the value related to the model size, and l is the distance between the point to be solved and other points in the spatial distribution.

[0028] Further, the definition of the parameter l is given by the following formula:

[0029]

[0030] The parameter u is an auxiliary vector, which is solved by using the distributed ordinary differential equation f:

[0031]

[0032] Further, in step 6, the Kriging interpolation method can meet the optimal coefficient of the minimum difference between the estimated value and the true value The Kriging interpolation method meets the unbiased estimation condition

[0033] The present application proposes a new permeability coefficient measurement method, that is, using the dipole pump technology to measure the water head change in the local area to calculate the soil permeability coefficient. By taking the sampling block in the area and setting the dipole pump, the water head data read by the sampling block is used to calculate the permeability coefficient spatial distribution of the area, and according to the local distribution, the Kriging interpolation is used to obtain the permeability coefficient distribution of the whole area.

[0034] The core of this method is to use a dipole pump system, where one side injects water while the other side extracts water at the same rate, forming a local water circulation system. By measuring the water head at different positions in the soil after the system reaches a steady state, and by changing the position of the dipole pump and the layout of the measurement points to obtain multiple sets of data, the permeability coefficient of the soil can be accurately solved using mathematical methods. This method has several unique advantages: first, by changing the position of the dipole pump and the layout of the measurement points, it can adapt to different soil conditions and testing requirements. Second, this method can accurately measure the permeability coefficient of local areas in the soil, which helps better understand the spatial variability of soil permeability. Third, unlike traditional methods that require water head changes over a large range, the dipole pump technology relies on controlled water head changes in local areas, reducing environmental disturbance and experimental complexity, and reducing measurement costs. In summary, although traditional permeability coefficient measurement methods have been widely used in many fields, the newly proposed method using dipole pump technology demonstrates its unique advantages and potential, especially in applications that require high precision and efficiency in measuring soil permeability coefficients.

[0035] Compared with the prior art, the present application has the following beneficial effects:

[0036] (1) By changing the position of the dipole pump and the layout of the measurement points, it can adapt to different soil conditions and testing requirements;

[0037] (2) By increasing the number of dipole pumps, this method can accurately measure the permeability coefficient of local areas in the soil, which helps better understand the spatial variability of soil permeability;

[0038] (3) Unlike traditional methods that require water head changes over a large range, the dipole pump technology relies on controlled water head changes in local areas, reducing environmental disturbance and experimental complexity;

[0039] (4) Compared with traditional soil sampling and experimental measurement, this technology can obtain permeability coefficient distribution with sufficient accuracy at a higher efficiency. The calculation results show that two sets of dipole pump experiments at different positions can solve the permeability coefficient distribution with sufficient accuracy.

[0040] (5) The Kriging interpolation method considers the correlation between different positions, which can improve the accuracy and reliability of the results compared with the traditional linear interpolation method. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 Flow chart of the large-scale non-uniform stratum permeability parameter simulation method based on typical unit test involved in the present application;

[0042] Figure 2This is a schematic diagram of the selected typical blocks and dipole pump test setup involved in the embodiments of the present invention;

[0043] Figure 3 The permeability coefficient results are calculated from the four sets of head data involved in the embodiments of the present invention;

[0044] Figure 4 This refers to the permeability coefficient of the actual distribution involved in the embodiments of the present invention. Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0046] (1) As Figure 2 As shown, a typical square block representing the characteristics of the entire study area was selected as the sampling block, and multiple dipole pump experiments were conducted within the sampling block. During the dipole pump experiments, two points within the sampling block were used as the inlet and outlet of the dipole pump to maintain a consistent inflow and outflow rate. Then, the head height at the other six points was measured.

[0047] (2) After setting up the dipole pump and reaching steady state, measure the following 6 sets of water heads at the marked points.

[0048] Points Coordinates First group Second group Third group Fourth group 1 (-50,-50) Water outlet 0.115m -0.731m 0.513m 8 (50,50) Water inlet -0.549m -0.771m -0.092m 2 (-50,0) 0.462m Water outlet -0.023m 0.203m 7 (50,0) -0.202m Water inlet -1.208m 0.452m 3 (-50,50) -0.011m 0.566m Water outlet -0.548m 6 (50,-50) -0.050m -0.618m Water inlet 0.582m 4 (0,-50) 0.108m -0.486m -1.207m Water outlet 5 (0,50) -0.497m -0.238m -0.077m Water inlet

[0049] (4) Define the initial permeability coefficient within the region according to K0 = 10. -5 The m / s is uniformly distributed.

[0050] (5) Define the variogram function, where σ 2 is the base parameter, taken as 1. r is the range parameter, taken as 50m, and l is the distance between the point to be determined and other points in the spatial distribution.

[0051]

[0052] (6) Define l i Let be the distance from any point on the sample to the origin, be the auxiliary vector u, be the penalty function, and be the residual. Solve for the corresponding auxiliary vector using partial differential equations, and further define the residual.

[0053]

[0054]

[0055] (hh mean ) T u

[0056] (7) Based on this, the residual and penalty function are incorporated into the least squares iterative calculation, and the permeability coefficient distribution of the sampling area is solved in reverse using the head data. The calculation results are as follows: Figure 3The true distribution of the permeability coefficient is shown. The comparison Figure 4 The true distribution of the permeability coefficient is shown. It can be seen that as the number of measurement groups increases, the calculation result is more accurate.

[0057] (8) To quantitatively evaluate the calculation error, the area-weighted mean square error is defined as the sum of the square of the difference between the calculated value of the permeability coefficient and the true value multiplied by the proportion of the corresponding area to the total area. It can also be seen from the defined area-weighted mean square error that as the water head data increases, the calculation accuracy improves.

[0058] Number of groups Area-weighted mean squared error 1 0.07880 2 0.02847 3 0.01134 4 0.01097

[0059] (9) Repeat the above steps to conduct a dipole pump test on the soil in other areas to obtain the permeability coefficient, and then use Kriging interpolation to obtain the permeability coefficient distribution of the entire area.

Claims

1. A method for simulating large-scale non-uniform formation permeability parameters based on typical unit tests, characterized in that, Includes the following steps: Step 1: Select a block within the study area that can represent the characteristics of the entire area as the sampling block; Step 2: Conduct a dipole pump test in the sampling block. The dipole pump consists of a fixed flow outlet and an inlet, located on either side of the geometric center of the sampling block. Step 3: After turning on the dipole pump and waiting for the system to stabilize, measure the head data distributed along the space and record the coordinates. Step 4: Using the objective function of the underdetermined inverse problem, solve for the permeability coefficient distribution in the region using the head distribution results measured by the dipole pump test; In equation (1), the spatial distribution of the permeability coefficient corresponding to the least squares objective L(h,k) is found using the optimization model; h represents the vector of the measured head value; k represents the vector of the parameter value to be obtained, i.e., the permeability coefficient; g is the function for calculating the head using the permeability coefficient; ΔH is the measurement accuracy; u is an auxiliary vector with the same length as the parameter k to be obtained, u=γ -1 (kk mean ), where the covariance matrix γ is a variogram function related to the spatial distribution, (kk mean The difference between the predicted permeability coefficient and its spatially weighted mean is denoted as . Step 5: Based on the spatial distribution of hydraulic head, predict the permeability parameters of large-scale heterogeneous strata using the Kriging interpolation method. The specific representation is as follows: in It is the predicted value calculated using the Kriging interpolation function, λ i It is the weighting coefficient estimated by weighted summation of all known data points.

2. The method as described in claim 1, characterized in that: In step 1, sampling blocks are selected at the edge and center of the study area, and at least one sampling block is selected at the center of the study area, with a total of more than 5 sampling blocks.

3. The method as described in claim 1, characterized in that: In step 2, the sampling blocks are of regular geometric shape and have an axis of symmetry passing through the geometric center. The dipole pumps should be placed on both sides of the axis of symmetry of the sampling blocks, and at least two pairs of dipole pumps should be placed in each sampling block.

4. The method as described in claim 1, characterized in that: In step 2, the flow rate of the dipole pump should be controlled to a low level to ensure that the water flow in the sample conforms to Darcy flow.

5. The method as described in claim 1, characterized in that: In step 4, the objective function L(h,k) is considered as a combination of the fitting term and the penalty term function.

6. The method as described in claim 5, characterized in that: In step 4, the fitting term is used to define the residuals, and the objective function is given by the following equation: The penalty term is used to penalize undesirable properties of the parameter field, and the objective function is given below: (h-h mean ) T u=(h-h mean ) T γ -1 (h-h mean ) (4) In equation (4) h mean The weighted average of the vector representing the water head measurements.

7. The method as described in claim 6, characterized in that: γ represents the variogram related to spatial distribution, and its definition is given by the following equation: Where σ 2 is the base parameter, with a value of 1; r is the range parameter, with a value related to the model size; and l is the distance between the point to be determined and other points in the spatial distribution.

8. The method as described in claim 7, characterized in that: The parameter l is defined as follows: The parameter u is an auxiliary vector, which is solved using the distributed ordinary differential equation f:

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