A correction method for wetting deformation of earth-rockfill dam based on in-situ measured water content and density of rockfill
By conducting triaxial wet deformation tests on the moisture content and density of rockfill materials in the field, a corrected formula was established, which solved the problem of accuracy in predicting wet deformation of earth-rock dams, realized efficient prediction and control of dam deformation, and reduced test costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- POWERCHINA HUADONG ENG CORP LTD
- Filing Date
- 2025-07-09
- Publication Date
- 2026-06-30
AI Technical Summary
Existing technologies cannot accurately predict the wet deformation of earth-rock dams, especially when considering changes in the moisture content and density of the rockfill material on site. This can lead to design deviations and potentially cause engineering risks such as dam deformation and cracks.
By conducting triaxial wetting deformation tests on the moisture content and density of riprap in the field, a correction formula was established. Combined with a conventional wetting model, a correction coefficient was introduced to achieve accurate prediction of wetting deformation.
It improves the accuracy and engineering applicability of wet deformation prediction, reduces testing costs, and provides a reliable means of predicting dam deformation and controlling compaction quality.
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Figure CN120740534B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of geotechnical engineering technology and relates to a method for correcting the wet deformation of earth-rock dams based on field-measured moisture content and density of rockfill. Background Technology
[0002] With the rapid development of new energy sources (such as wind and photovoltaic power) in my country, the demand for power grid regulation capabilities and energy storage systems is increasing daily. Pumped storage power stations, due to their advantages such as low construction and operating costs, long service life, and mature technology, have become the mainstream large-scale energy storage method. Currently, pumped storage power stations are widely deployed throughout my country, and their installed capacity continues to grow. In the design and construction of pumped storage power stations, earth-rock dams are typically chosen as the water storage structure for the upper and lower reservoirs.
[0003] Wetting deformation of rockfill refers to the deformation that occurs when it changes from a dry to a wet state. During the construction and operation of earth-rock dams, the dam materials inevitably undergo a wetting process due to factors such as rainfall, floods, or reservoir impoundment. In severe cases, this can lead to dam deformation, cracks, or even leakage, threatening the safety of the entire pumped storage power station project. Therefore, accurately predicting and rationally controlling the wetting deformation of rockfill is a crucial aspect of the design and construction process.
[0004] Currently, research on the wet deformation characteristics of rockfill mainly relies on indoor wet testing, with common methods including the "double-line method" and the "single-line method." The single-line method is widely considered more reasonable because it better reflects the actual immersion deformation process. However, the single-line method can only obtain wet deformation data under one stress state each time. To comprehensively study the wet deformation of rockfill under different stress states and with different physical properties (density, moisture content, etc.), numerous repeated tests are required, resulting in extremely high testing costs and workload. Furthermore, during actual earth-rock dam construction, the density and initial moisture content of the rockfill fluctuate due to differences in construction technology, equipment efficiency, and climatic conditions, and the moisture content of the dam material also changes continuously over time. Using wet deformation parameters obtained from traditional indoor wet testing based on single-density dry samples to guide the design of earth-rock dams often leads to certain deviations. On the one hand, it may overestimate wet deformation, leading to over-compaction after construction adjustments; on the other hand, it may underestimate wet deformation, lacking corresponding countermeasures, resulting in excessive local deformation and engineering risks such as cracks.
[0005] In conclusion, wetting deformation is an issue that cannot be ignored in earth-rock dam engineering, and its impact extends throughout the entire process of earth-rock dam construction, water impoundment, and even long-term operation. To improve the accuracy and practicality of prediction, there is an urgent need to establish a correction method for wetting deformation that can take into account the moisture content and density of the rockfill on site, thereby providing more reliable technical support for the design and construction of earth-rock dams. Summary of the Invention
[0006] To address the problems existing in the prior art, this invention proposes a correction method for the wetting deformation of earth-rock dams based on field-measured moisture content and density of the rockfill. This method considers the influence of the actual moisture content and density of the rockfill on the wetting deformation, solving the problem of accurately predicting the wetting deformation of earth-rock dams under existing technical conditions. It balances high accuracy, low testing cost, and good field applicability, making it suitable for the engineering design and evaluation of various large-scale dams, such as pumped storage dams.
[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0008] A correction method for the wetting deformation of earth-rock dams based on field-measured moisture content and density of rockfill material is proposed. First, a typical rockfill material is selected for scale-down testing. Through systematic wetting deformation tests at different initial moisture contents and densities, the variation of the wetting deformation characteristics of the rockfill material with dry density and moisture content is obtained. Then, based on a conventional wetting model, a correction coefficient is introduced to establish a correction formula for wetting deformation under moisture content and density control. Finally, by substituting the field-measured moisture content and density data into the correction formula, the correction coefficient can be obtained, thereby achieving accurate prediction of the wetting deformation amount in different dam areas. The specific steps include:
[0009] Step 1: Select the rockfill material for the main rockfill zone of the rockfill dam body. Following the "Standard for Geotechnical Testing Methods GB / T50123-2019", scale down the material using the similar gradation method. The maximum particle size after scaling down is 60mm. Measure the specific gravity and natural moisture content of the scaled-down rockfill material in an indoor laboratory.
[0010] The specific gravity and natural moisture content of the riprap were determined according to the "Standard for Geotechnical Testing Methods GB / T 50123-2019", using the flotation method and the drying method respectively.
[0011] Step 2: For the rockfill material with a maximum particle size of 60mm obtained in Step 1, triaxial wet deformation tests were conducted on the rockfill material under different densities and moisture contents to obtain the wet deformation characteristics of the rockfill material and to obtain the law of variation of the wet deformation characteristics of the rockfill material with dry density and moisture content.
[0012] Furthermore, in the second step, the triaxial wetting test of the riprap was conducted. The sample preparation and test operation were carried out in accordance with the specifications of the triaxial wetting deformation test chapter in the "Test Procedure for Coarse-grained Soils T / CHES 29-1019". The sample size was a cylinder with a diameter of 300 mm and a height of 700 mm. During the test, the wetting shear strain and wetting volumetric strain of the riprap sample were recorded.
[0013] Furthermore, in the second step, when designing triaxial wet deformation tests of riprap with different densities and initial moisture contents under different working conditions, orthogonal design may be omitted to reduce the workload of the tests. It is recommended to divide the tests into two main working conditions: Working condition 1, where the initial moisture content of the samples is controlled at 0%, involves designing triaxial wet deformation tests of riprap with low, medium (fill design density), and high density levels, and at least 3-5 density gradients; Working condition 2, where the test density is controlled at the fill design density, involves triaxial wet deformation tests of riprap with low, medium, and high moisture contents, and at least 3-5 moisture content gradients.
[0014] Furthermore, in the second step, the density control index is determined based on the properties of the riprap. If the riprap is blasted material, porosity or void ratio is used for control; if the riprap is gravel, compaction degree is used for control. The moisture content mentioned is the mass moisture content.
[0015] Furthermore, in the second step, the variation of the wet deformation characteristics of the riprap with dry density and moisture content is mainly characterized by wet shear strain. , strain of humidified body With stress level Confining pressure (kPa), porosity n (%), water content The changing pattern of (%).
[0016] Step 3: Establish a modified formula based on the conventional wetting model, taking into account moisture content and density, to describe the variation of the wetting deformation characteristics of riprap with dry density and moisture content.
[0017] Furthermore, the recommended form for the correction formula based on the conventional wetting model that considers moisture content and density is as follows, where formula (1) is the corrected wetting shear strain model, formula (2) is the corrected wetting volume strain model, and formula (3) is the formula for calculating the correction coefficient:
[0018] (1)
[0019] (2)
[0020] (3)
[0021] in, For humidified shear strain, Stress level; These are the undetermined coefficients in the wetted shear strain model; The index to be determined for the wetted shear strain model is K; K is the correction coefficient obtained from the experiment. For the strain of the humidified body; Given the humidification shear dilatation ratio, the humidification volumetric strain can be calculated from the humidification shear strain. Therefore, only the correction factor K for the humidification shear strain needs to be considered during the correction. For the wet shear dilatation ratio of riprap The undetermined coefficients; p' is the stress ratio when the humidification dilatation ratio is 0; p' is the average effective principal stress; p a The pressure is one atmosphere (101.2 kPa), used for dimensionless stress unit conversion; m is the humidification shear dilatation ratio. The undetermined stress index; The stress ratio is the ratio of the deviatoric stress q to the mean principal stress p. The fitting index is the correction coefficient; The effective water absorption rate (i.e., the rate at which no wetting deformation occurs even as the water content increases beyond this level) is obtained by fitting data. The design porosity for the filling is the baseline porosity used in the wetting test. The moisture content of the riprap material undergoing wetting deformation is to be corrected. Density of the wetted and deformed riprap to be corrected.
[0022] Step 4: Based on the wet deformation characteristics of the rockfill obtained from the triaxial wet deformation test of the rockfill in Step 2, fit the formula parameters of the correction formula considering moisture content and density established in Step 3 based on the conventional wet deformation model. Then, substitute the actual moisture content and density of the rockfill material of the earth-rock dam that needs to be corrected for wet deformation into formula (3) to obtain the correction coefficient K. And the correction of the wet deformation of the earth-rock dam based on the measured moisture content and density of the rockfill material in the field can be completed through formulas (1) and (2).
[0023] Furthermore, in step four, the process of fitting parameters to the corrected formula considering moisture content and density based on the conventional humidification model is as follows:
[0024] Step 4.1: Based on working condition 1 in step 2, control the initial moisture content of the sample to be 0%, the density to be the filling design density, and the simplification coefficient K=1. Degenerate the modified model into a conventional wetting model. Use the nonlinear regression function of the statistical analysis software SSPS to fit the parameters in formula (1). , The parameters in formula (2) , m;
[0025] Step 4.2, based on the fitting results of Step 4.1, according to working condition 1 in the second step, the initial moisture content of the sample is controlled to be 0%. Wet deformation tests of riprap with different densities are conducted. The parameters in formula (3) are fitted using the nonlinear regression function of the statistical analysis software SSPS. ;
[0026] Step 4.3, based on working condition 2 in step 2, control the test density to the filling design density, including triaxial wet deformation tests of rockfill with low, medium and high levels and at least 3-5 moisture content gradients, and the parameter fitting results of steps 2) and 3), and use the nonlinear regression function of the statistical analysis software SSPS to fit the parameters in formula (3). .
[0027] Compared with the prior art, the beneficial effects of the present invention are:
[0028] (1) This invention establishes a correction formula based on the conventional wetting model that considers moisture content and density, which solves the limitation of traditional wetting deformation prediction that fails to consider the actual on-site changes in the density and initial moisture content of dam construction materials, and can significantly improve the prediction accuracy;
[0029] (2) The design method of the triaxial wet deformation test of riprap proposed in this invention can significantly reduce the workload of sample preparation while ensuring that the wet deformation characteristics of riprap can be obtained with respect to density and moisture content. It has good engineering applicability.
[0030] (3) The correction method for the wet deformation of earth-rock dam based on the measured moisture content and density of rockfill material proposed in this invention can be directly applied to earth-rock dam engineering practice. By substituting the measured moisture content and density on site, the correction result of the wet deformation adapted to the region can be obtained, providing a reliable technical means for dam body zonal deformation prediction and compaction quality control.
[0031] (4) The test process of the method of the present invention strictly follows the "Standard for Geotechnical Test Methods GB / T 50123-2019" and "Test Procedure for Coarse-grained Soil T / CHES 29-2019". The parameter determination method is clear and has broad engineering application and promotion value. Attached Figure Description
[0032] Figure 1 This is a typical asphalt concrete core wall dam filling zoning diagram;
[0033] Figure 2 A gradation curve of riprap material;
[0034] Figure 3 The curve shows the change of wetted shear strain over time.
[0035] Figure 4 The curve showing the strain of the humidified body over time;
[0036] Figure 5 The variation of wetting shear strain with stress level under different porosity conditions;
[0037] Figure 6The variation of strain in the humidified body with stress level under different porosity conditions;
[0038] Figure 7 The variation of wetted shear strain with moisture content;
[0039] Figure 8 The variation of strain in a humidified body with water content;
[0040] Figure 9 These are fitting results of wetted shear strain under different porosities;
[0041] Figure 10 This is a graph showing the fitting effect of the humidification shear dilatation ratio;
[0042] Figure 11 The fitting effect of wetted shear strain;
[0043] Figure 12 The fitting effect of the humidified volume change;
[0044] Figure 13 This is a histogram of the frequency distribution of porosity in the measured rockfill material.
[0045] Figure 14 This is a histogram showing the frequency distribution of the measured moisture content of the rockfill.
[0046] Figure 15 This is a flowchart of the method of the present invention. Detailed Implementation
[0047] The following detailed description of the relevant design of this invention, in conjunction with the accompanying drawings, illustrates the specific implementation process of a method for correcting the wetting deformation of an earth-rock dam based on on-site measured moisture content and density of the rockfill material.
[0048] Step 1: The zoning of the asphalt concrete core wall dam project is shown in the attached figure. Figure 1 As shown, the dam body consists of upstream rockfill zone I, downstream rockfill zone I, downstream rockfill zone II, a grouting gallery, and a concrete core wall. Considering the wetting deformation behavior of the upstream dam body, the rockfill material from upstream rockfill zone I was used as the test material. Following the "Standard for Geotechnical Testing Methods GB / T 50123-2019," a similar gradation method was used for scale-down testing. The dam material gradation curves before and after scale-down are shown in the appendix. Figure 2 The maximum particle size was 60 mm. In an indoor laboratory, the specific gravity and moisture content of the scaled-down riprap were measured using both the flotation method and the drying method. The measured specific gravity was 2.97, and the natural moisture content was 0.3%.
[0049] Step 2: Triaxial wet deformation tests were conducted on the riprap material with a maximum particle size of 60 mm obtained in Step 1, under different densities and moisture contents. Three confining pressure gradients were used in the tests: 500 kPa, 1500 kPa, and 2500 kPa. Stress level S l The values were taken as 0.2, 0.5, and 0.8. To reduce the workload of the experiment, based on the design porosity of 19% and the design filling moisture content of 1.9% for the upstream rockfill I zone, Case 1 was adopted, where the initial moisture content of the sample was controlled at 0%, and the rockfill porosity was taken as 18%, 19%, and 20% respectively; Case 2 was adopted, where the test density was controlled at the filling design density of 19%, and the initial mass moisture content w was taken as 1.2%, 1.9%, and 2.6% respectively. The detailed test plan is shown in Table 1 below:
[0050] Table 1
[0051]
[0052] Specimen preparation and testing procedures were conducted according to the triaxial wetting deformation test chapter of the "Test Procedure for Coarse-grained Soils T / CHES 29-1019". The specimens were cylindrical with a diameter of 300 mm and a height of 700 mm. After preparation, a preset confining pressure was applied according to the test design. Consolidation was considered complete when the volume change curve over time approached a horizontal line. Axial stress was then applied to the corresponding stress level. The wetting shear strain and wetting volumetric strain of the riprap specimens were immediately recorded. A stability criterion was a change in axial strain of less than 0.01% within 30 minutes. After stabilization of dry or samples with a certain moisture content, the confining pressure and axial stress were kept constant, and saturation was achieved with a 2 m water head difference. The stability criterion for wetting deformation was also a change in axial strain of less than 0.01% within 30 minutes; the test was considered complete once deformation stabilized.
[0053] Finally, the curves showing the changes in humidified volumetric strain and humidified shear strain over time obtained in step two are attached. Figure 3 , Figure 4 As shown in the figure. The wet deformation characteristics of the obtained riprap vary with dry density and moisture content. (See attached figure.) Figure 5 , Figure 6 , attached Figure 7 , Figure 8 As shown.
[0054] Step 3: Establish a modified formula based on the conventional wetting model, taking into account moisture content and density, to describe the variation of the wetting deformation characteristics of riprap with dry density and moisture content:
[0055] (1)
[0056] (2)
[0057] (3)
[0058] in, For humidified shear strain, Stress level; These are the undetermined coefficients in the wetted shear strain model; The index to be determined for the wetted shear strain model is K; K is the correction coefficient obtained from the experiment. For the strain of the humidified body, Given the humidification shear dilatation ratio, the humidification volumetric strain can be calculated from the humidification shear strain. Therefore, only the correction factor K for the humidification shear strain needs to be considered during the correction. For the wet shear dilatation ratio of riprap The undetermined coefficients; p' is the stress ratio when the humidification dilatation ratio is 0; p' is the average effective principal stress; p a The pressure is one atmosphere (101.2 kPa), used for dimensionless stress unit conversion; m is the humidification shear dilatation ratio. The undetermined stress index; The stress ratio is the ratio of the deviatoric stress q to the mean principal stress p. These are the fitting parameters for the correction coefficients; The effective water absorption rate (i.e., the rate at which no wetting deformation occurs even as the water content increases beyond this level) is obtained by fitting data. The design porosity for the filling is the baseline porosity used in the wetting test. The moisture content of the riprap to be predicted and corrected for wetting deformation; The density of the riprap to be predicted and corrected for wet deformation.
[0059] Step 4: Based on the humidification deformation characteristics of the riprap obtained from the triaxial humidification deformation test in Step 2, fit the formula parameters of the modified formula considering moisture content and density established in Step 3 based on the conventional humidification model. The fitting process is as follows:
[0060] 1) Based on working condition 1 in step 2, the initial moisture content of the sample is controlled to be 0%, the density is 19% of the design porosity, and the simplification coefficient K=1. The modified model is degenerated into a conventional wetting model. The parameters in formula (1) are fitted by the nonlinear regression function of the statistical analysis software SSPS. , The parameters in formula (2) , m;
[0061] 2) Based on the fitting results of a, according to working condition 1 in step 2, the initial moisture content of the sample was controlled to be 0%, and the initial density was 18%, 19%, and 21% for the wet deformation test of the riprap. The parameters in formula (3) were fitted by the nonlinear regression function of the statistical analysis software SSPS. The shear strain fitting results of humidification tests with different porosities are shown in the attached figure. Figure 9 As shown in the attached figure, the fitting results of the shear dilatation ratio for different humidification tests are as follows. Figure 10 As shown;
[0062] 3) Based on working condition 2 in step 2, the test density is controlled at 19% of the filling design density, and the initial moisture content is 1.2% (1.9.2.6). The corresponding working condition 1, with a controlled test density of 19% of the filling design density and an initial moisture content of 0%, is used to perform a triaxial wet deformation test on the riprap. The parameter fitting results of steps 2) and 3) are used, and the parameters in formula (3) are fitted using the nonlinear regression function of the statistical analysis software SSPS. The fitting results of the humidification tests at different moisture contents are attached. Figure 11 , Figure 12 As shown.
[0063] The final parameters of the wetting deformation correction model for the rockfill in this engineering example are shown in Table 2:
[0064] Table 2
[0065]
[0066] The cumulative frequency distribution histograms of moisture content and density of the rockfill material measured on-site for this project are attached. Figure 13 , Figure 14 As shown, by substituting the actual moisture content and density of the rockfill material in the earth-rock dam that requires wetting deformation correction into formula (3), the correction coefficient K can be obtained. For example, if the porosity on site is 19.5% and the mass moisture content is 1%, then the wetting deformation correction coefficient K for this area is calculated as 0.63 by substituting it into formula (3). Then, the correction of the wetting deformation of the earth-rock dam based on the measured moisture content and density of the rockfill material on site can be completed by formulas (1) and (2).
[0067] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.
Claims
1. A method for correcting the wetting deformation of earth-rock dams based on field-measured moisture content and density of rockfill, characterized in that, The correction method includes the following steps: Step 1: Select the rockfill material for the main rockfill section of the rockfill dam body, scale it down using the similar gradation method, and measure the specific gravity and natural moisture content of the scaled-down rockfill material. Step 2: Conduct triaxial wet deformation tests on the scaled-down riprap at different densities and moisture contents to obtain the wet deformation characteristics of the riprap and to obtain the law of variation of the wet deformation characteristics of the riprap with dry density and moisture content. Step 3: Establish a modified formula based on the conventional wetting model, taking into account moisture content and density, to describe the variation of the wetting deformation characteristics of riprap with dry density and moisture content. In the third step, the modified wetting shear strain model is shown in formula (1), the modified wetting volume strain model is shown in formula (2), and the formula for calculating the correction coefficient is shown in formula (3); specifically: （1） （2） （3） in, For wetted shear strain; Stress level; These are the undetermined coefficients in the wetted shear strain model; The undetermined exponents for the wetted shear strain model; K The correction factor is obtained from the experiment; For the strain of the humidified body; The wetted shear dilatation ratio; For the wet shear dilatation ratio of riprap The undetermined coefficients; This represents the stress ratio when the humidification shear dilatation ratio is 0. p ' is the average effective principal stress; p a Atmospheric pressure; m is the humidification shear dilatation ratio. The undetermined stress index; The stress ratio, i.e., the deviatoric stress. q With mean principal stress p The ratio; The fitting index is the correction coefficient; For effective water absorption rate; The design porosity of the filling; The moisture content of the riprap material undergoing wetting deformation is to be corrected. Density of the wetted and deformed riprap to be corrected; The correction formula includes the corrected humidification shear strain model, the corrected humidification body strain model, and the calculation formula for the correction coefficient; Step 4: Based on the wet deformation characteristics of the rockfill obtained from the triaxial wet deformation test in Step 2, fit the formula parameters of the correction formula established in Step 3; then, substitute the actual moisture content and density of the rockfill material in the earth-rock dam that needs wet deformation correction into the calculation formula of the correction coefficient in Step 3 to obtain the correction coefficient. K Furthermore, through the modified wetted shear strain model and the modified wetted volume strain model in the third step, the wetted deformation of the earth-rock dam based on the measured moisture content and density of the rockfill material is corrected, thereby achieving accurate prediction of the wetted deformation in different dam areas.
2. The method for correcting the wetting deformation of earth-rock dams based on the measured moisture content and density of rockfill material according to claim 1, characterized in that, In the first step, the maximum particle size after scaling down is 60mm.
3. The method for correcting the wetting deformation of earth-rock dams based on the measured moisture content and density of rockfill material according to claim 1, characterized in that, In the second step, when designing triaxial wet deformation tests of rockfill with different densities and initial moisture contents under different working conditions, orthogonal design is not performed to reduce the workload of the tests.
4. The method for correcting the wetting deformation of earth-rock dams based on field-measured moisture content and density of rockfill as described in claim 1, characterized in that, In the second step, the different working conditions include two main working conditions: Working condition 1 is to control the initial moisture content of the sample to 0%, and design triaxial wet deformation tests of rockfill with low, medium and high levels and at least 3-5 density gradients; Working condition 2 is to control the test density to the filling design density, and design triaxial wet deformation tests of rockfill with low, medium and high levels and at least 3-5 moisture content gradients.
5. The method for correcting the wetting deformation of earth-rock dams based on field-measured moisture content and density of rockfill as described in claim 1, characterized in that, In the second step: the density index is determined according to the properties of the riprap. If the riprap is blasted material, porosity or void ratio is used for control. If the riprap is gravel, compaction degree is used for control. The moisture content is the mass moisture content.
6. The method for correcting the wetting deformation of earth-rock dams based on field-measured moisture content and density of rockfill as described in claim 1, characterized in that, In the second step: the variation of the wet deformation characteristics of the riprap with dry density and moisture content is mainly due to the wet shear strain. , strain of humidified body With stress level Confining pressure The unit is kPa and porosity. n Unit: %, Moisture content The variation pattern is expressed in percentage (%).
7. The method for correcting the wetting deformation of earth-rock dams based on field-measured moisture content and density of rockfill as described in claim 1, characterized in that, In the fourth step, the process of fitting parameters based on the modified formula considering moisture content and density according to the conventional humidification model is as follows: Step 4.1, based on working condition 1 in step 2, control the initial moisture content of the sample to be 0%, the density to be the design density for filling, and the simplification factor. K =1, degenerate the modified model into a conventional humidification model, and fit the parameters in formula (1). , The parameters in formula (2) , m; Step 4.2, based on the fitting results of Step 4.1, according to working condition 1 in the second step, the initial moisture content of the sample is controlled to be 0%, and the wet deformation test of riprap with different densities is performed. The parameters in the fitting formula (3) are used. ; Step 4.3: Based on working condition 2 in step 2, control the test density to the filling design density, including triaxial wet deformation tests of rockfill with low, medium and high levels and at least 3-5 moisture content gradients, and the parameter fitting results of steps 4.2 and 4.3, the parameters in the fitting formula (3) are... .