A method for predicting capillary water flux by capillary water rise height

Abstract

The present invention belongs to the field of capillary water rise flux testing and discloses a new method for predicting capillary water rise flux based on capillary water rise height. a , soil saturated permeability coefficient K s The capillary water rise flux is estimated by combining the derived mechanistic model with the correction coefficient λ for the modeled capillary water rise height and the fitting parameter β'. This paper divides capillary water rise into two stages. Based on Darcy's law under unsaturated conditions, a new mechanistic model for the variation of capillary water rise flux with height is derived and established. This model covers the entire water level rise process and has a wider range of applications compared to empirical models. The model fitting values ​​closely match the observed values.

Description

Technical Field

[0001] The invention belongs to the field of capillary water rising flux testing, and specifically provides a method for predicting capillary water rising flux based on capillary water rising height. Background Art

[0002] Soil capillary water refers to the liquid water maintained and moved in the capillary pores of the soil by capillary force. It is one of the main sources of water required for plant growth.

[0003] Two types of prediction models are commonly used in existing capillary water flux prediction methods. One type is a mechanistic model, which focuses on the rising range of capillary water flow and has poor prediction accuracy outside this range. The other type is an empirical model, which is applicable to specific conditions. When the actual situation deviates from the conditions on which the model is based, the model's prediction will be inaccurate. Summary of the Invention

[0004] Based on the problems existing in the existing technology, the present invention divides the capillary water rise process into two stages with the soil outgassing value as the threshold. According to Darcy's law under unsaturated conditions, a new mechanism model of the capillary water rise flux changing with height is derived, which is used to predict the capillary water rise flux at different capillary water rise heights.

[0005] The present invention is achieved by a method for predicting capillary water flux by capillary water rise height, comprising the following steps:

[0006] Step 1: Obtain soil outgassing value h a .

[0007] Step 2: Obtain soil saturated permeability coefficient K s .

[0008] Step 3: Obtain the correction coefficient λ and fitting parameter β' of the capillary water rise height of the model.

[0009] Step 4: Predict the capillary water upward flux based on the above parameters and the derived mechanism model.

[0010] Furthermore, in step 1, the soil to be tested is taken for a soil moisture absorption experiment. Before the experiment begins, the soil sample to be tested is dried until the soil moisture content is reduced to 0. Next, a certain volume of water is slowly added to the soil. After it is fully diffused, the volume moisture content and matrix suction in the soil are measured. The process of adding water and measuring the volume moisture content and matrix suction is then repeated until the volume moisture content reaches saturation and the matrix suction is reduced to 0KPa. The soil moisture absorption experiment is completed. The soil matrix suction measured in the experiment is converted into centimeters of water column height, and the moisture absorption curve of the soil moisture characteristic curve is plotted with matrix potential as the x-axis and volume moisture content as the y-axis.

[0011] The Gardner model (Gardner, 1958) was used as the fitting model for the soil-water characteristic curve:

[0012]

[0013] Where, θ, θ S are the average volumetric water content and saturated volumetric water content, respectively; h is the matrix suction, cm; θ r is the residual moisture content; c and m are the model shape parameters.

[0014] Using the soil moisture characteristic curve fitted by the model, draw the tangent line at the saturated volume moisture content and the tangent line at the inflection point, extend the two tangent lines, and the horizontal coordinate of their intersection is expressed as the soil outgassing value height h a , unit is cm.

[0015] Furthermore, in step 2, soil is filled into a cylindrical container and the column wall is tapped to restore the density of the soil in the column to that of the original soil. The column is then immersed in water. After reaching the saturation time, it is removed and secured using an iron stand. A beaker is placed below the column, and water is added above the column using a Marsh flask to maintain a constant water layer thickness and a constant water level.

[0016] The timer starts when the first drop of water appears below the soil column. The water seepage rate is measured at regular intervals thereafter, while the water temperature is recorded. The cumulative water seepage rate (V) for each measurement is plotted on the y-axis, and the time it takes for the cumulative water seepage to occur (t) is plotted on the x-axis. This yields a curve of cumulative soil water seepage over time. This curve gradually exhibits a linear correlation, indicating that the soil seepage rate remains constant over time, reaching a steady state.

[0017] The permeability coefficient is calculated according to Darcy's formula:

[0018]

[0019] in

[0020] Where: V is the cross-sectional area of ​​the soil column A (cm2) that penetrates within the time t (h) 2 ) of water, cm 3 ; I is the hydraulic gradient; K is the permeability coefficient, that is, the infiltration rate when the hydraulic gradient is 1, cm / h; L is the water infiltration distance between two specified points in the soil column, cm; Δh is the total head difference between the two specified points, cm.

[0021] Furthermore, in step 3, a new dry soil column was prepared, and a stable groundwater level and sufficient water source were provided using a Malchnitz flask. At the beginning of the experiment, water was supplied from the Malchnitz flask to flow into the soil column. When the water level in the soil column rose to the stable groundwater level, the capillary water rise height at this time was recorded as 0 cm, the rise time was 0 h, and the rise volume was 0 cm. 3 In the first stage of capillary water rise (the capillary water rise height is less than the soil gas value h a ), every time the capillary water rises to a certain height, record the rising time and the scale of the water tank until the capillary water rises to 1 / 3h a The capillary water rise flux (q0) is estimated by using the rising water volume and rising time, and then combined with the capillary water rise height (z T ) and soil outgassing value h a and soil saturated permeability coefficient K s , substituting into the following formula, we can get the correction coefficient λ of the capillary water rise height:

[0022]

[0023] In formula (3), q0 is the capillary water flux, cm / h; K s is the saturated permeability coefficient (cm / h); z T is the capillary water rise height, cm; λ is the correction coefficient of the capillary water rise height; h a is the soil gasification value.

[0024] In the second stage of capillary water rising (the capillary water rising height is greater than the soil gas release value h a ), every time the capillary water rises to a certain height, record the rising time and the scale of the water tank until the capillary water rises to 4 / 3h a The capillary water rise flux is estimated by using the rising water volume and rising time, and then combined with the multiple discrete values ​​of the capillary water rise height and the soil outgassing value h a and soil saturated permeability coefficient K s , substituting into the following formula, we can get the model fitting parameter β':

[0025]

[0026] In formula (4), β' is the model fitting parameter.

[0027] Furthermore, in step 4, the model parameters estimated in steps 1 to 3 and formulas (3) and (4) are used to estimate the capillary water rising flux at other heights during the capillary water rising process.

[0028] In summary, the advantages and positive effects of the present invention are:

[0029] The capillary rise is divided into two stages. Based on Darcy's law under unsaturated conditions, a new mechanistic model for the variation of capillary water flux with altitude is derived and established. This model covers the entire process of water level rise and has a wider range of applications compared to empirical models. The model fitting values ​​closely match the observed values. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Schematic diagram of the method for predicting capillary water flux;

[0031] Figure 2 The first stage of capillary water rising flux (the capillary water rising height is less than h a ) prediction graph;

[0032] Figure 3 The second stage of capillary water rising flux (the capillary water rising height is greater than h a ) prediction graph. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present method is further described in detail below in conjunction with embodiments.

[0034] An embodiment of the present invention provides a method for predicting capillary water flux by capillary water rise height, comprising the following steps:

[0035] Step 1: Obtain soil outgassing value h a .

[0036] Step 2: Obtain soil permeability coefficient K s .

[0037] Step 3: Obtain the correction coefficient λ and fitting parameter β' of the capillary water rise height of the model.

[0038] Step 4: Predict the capillary water upward flux based on the above parameters and the derived mechanism model.

[0039] In the step 1, 0.075mm quartz sand is taken to carry out the soil moisture absorption experiment. Before the experiment begins, the quartz sand sample needs to be dried until the soil moisture content is reduced to 0. Next, a certain volume of water is slowly added to the soil. After it is fully diffused, the volumetric moisture content and matrix suction in the soil are measured. The process of adding water and measuring the volumetric moisture content and matrix suction is then repeated until the volumetric moisture content reaches saturation and the matrix suction is reduced to 0Kpa. The soil moisture absorption experiment is completed. The soil matrix suction measured in the experiment is converted into centimeters of water column height, and the moisture absorption curve of the soil moisture characteristic curve is drawn with matrix potential as the x-axis and volumetric moisture content as the y-axis.

[0040] The Gardner model (Gardner, 1958) was used as the fitting model for the soil-water characteristic curve:

[0041]

[0042] Where, θ, θ S are the average volumetric water content and saturated volumetric water content, respectively; h is the matrix suction, cm; θ r is the residual moisture content; c and m are the model shape parameters.

[0043] Using the soil moisture characteristic curve fitted by the model, the tangent line at the saturated volume moisture content and the tangent line at the inflection point are drawn and extended. The horizontal coordinate of the intersection of the two tangents represents the soil gasification value height, h a The unit is 69, cm.

[0044] In the step 2, 0.075 mm quartz sand is filled into a columnar container, and the soil density in the soil column is restored to the density of the original soil by knocking on the column wall. The soil column is immersed in water, taken out after reaching the saturation time, fixed with an iron stand, and water is added on top of the soil column using a Martens flask, and a beaker is placed below to maintain a water layer thickness of 5 cm while maintaining a constant water level. The timing is started when the first drop of water appears below the soil column from the start of water supply from the Martens flask, and the water seepage is measured every 5 minutes thereafter, while recording the water temperature. The cumulative water seepage V measured each time is set to the y-axis, and the time t spent by the cumulative water seepage is set to the x-axis to obtain a curve of the cumulative water seepage of the soil over time.

[0045] The permeability coefficient can be calculated according to Darcy's formula to get K s It is 3.23cm / h.

[0046]

[0047] in

[0048] Where: V is the cross-sectional area of ​​the soil column A (cm2) that penetrates within the time t (h) 2 ) of water, cm 3 ; I is the hydraulic gradient; K is the permeability coefficient, that is, the infiltration rate when the hydraulic gradient is 1, cm / h; L is the water infiltration distance between two specified points in the soil column, cm; Δh is the total head difference between the two specified points, cm.

[0049] In step 3, a new dry soil column was prepared, and a stable groundwater level and sufficient water source were provided by a Malchow flask. At the beginning of the experiment, water was supplied by the Malchow flask to flow into the soil column. When the water level in the soil column rose to the stable groundwater level, the capillary water rise height at this time was recorded as 0 cm, the rise time was 0 h, and the rise volume was 0 cm 3In the first stage of capillary water rise (the capillary water rise height is less than the soil gas value h a ), record the rising time and the scale of the water tank every 2cm, until the capillary water rises to 1 / 3h a The capillary water rise flux (q0) is estimated by using the rising water volume and rising time, and then combined with the capillary water rise height (z T ) and soil outgassing value h a and soil saturated permeability coefficient K s , substituting into the following formula, we can get the correction coefficient λ of the capillary water rise height as 0.7475.

[0050]

[0051] In the above formula: q0 is the capillary water flux, cm / h; z T is the capillary water rise height, cm; λ is the correction coefficient of the capillary water rise height; β' is the fitting parameter.

[0052] In the second stage of capillary water rising (the capillary water rising height is greater than the soil gas release value h a ), record the rising time and the scale of the water tank every time the capillary water rises 2cm, until the capillary water rises to 4 / 3h a The capillary water rise flux is estimated by using the rising water volume and rising time, and then combined with the multiple discrete values ​​of the capillary water rise height and the soil outgassing value h a and soil saturated permeability coefficient K s , substituting into the following formula, we can get the model fitting parameter β' to be 0.086.

[0053]

[0054] In step 4, the model parameters estimated in steps 1 to 3 and formulas (7) and (8) are used to estimate the capillary water rising flux at other heights during the capillary water rising process.

[0055] The above embodiments are only for illustrating the technical concept and features of the present invention. Its purpose is to enable people familiar with this technology to understand the content of the present invention and implement it. It cannot be used to limit the scope of protection of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting capillary water flux by capillary water rise height, characterized in that Follow the steps below: Step 1: Obtain the soil outgassing value h through soil moisture absorption experiment a ; Step 2: Use the soil column experiment to calculate the soil saturated permeability coefficient K according to Darcy's formula s ; Step 3: In the first stage of capillary water rise, the correction coefficient λ of the model capillary water rise height is obtained according to the capillary water rise experimental data and formula (1); in the second stage of capillary water rise, the model fitting parameter β' is obtained according to the capillary water rise experimental data and formula (2); Step 4: Substitute the model parameters h estimated in steps 1 to 3 a , K s , λ, β' are substituted into formulas (1) and (2) to predict the capillary water rising flux; Where q0 represents the capillary water flux, unit is cm / h; h a is the soil gasification value; K s is the saturated permeability coefficient, unit is cm / h; z T is the capillary water rise height, unit is cm; λ is the correction coefficient of the capillary water rise height; β' is the model fitting parameter; In step 1, the soil to be tested is subjected to a soil moisture absorption experiment. The soil moisture characteristic curve is fitted using the Gardner model. The tangent line at the saturated volume moisture content and the tangent line at the inflection point are drawn and extended. The horizontal coordinate of the intersection of the two tangent lines is represented as the soil outgassing value height h. a .

2. The method for predicting capillary water flux by capillary water rise height according to claim 1, characterized in that: In step 3, the capillary water rise flux q0 and the capillary water rise height z are obtained by using a Malvern flask to conduct an experiment. T Multiple discrete values ​​of soil gasification value h a and soil saturated permeability coefficient K s , and substituted into the derived multi-stage capillary water flux mechanism model to obtain the correction coefficient λ of the capillary water rise height and the fitting parameter β'.

3. The method for predicting capillary water flux by capillary water rise height according to claim 1, characterized in that: In step 4, the model parameters estimated in steps 1 to 3 and the derived multi-stage capillary water flux mechanism model are used to estimate the capillary water rising flux at other heights during the capillary water rising process.

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