A calculation method for soil-water characteristic curve of unsaturated soil under drying and wetting cycles

Abstract

The present invention provides a calculation method for the soil-water characteristic curve of unsaturated soil, which includes: 1) collecting dewetting test data points and fitting them to obtain a continuous "initial dewetting curve"; 2) dividing the "initial dewetting curve" into N intervals equally within the soil suction range, and calculating the water content of each interval taking into account the hysteresis effect; 3) collecting test data points on the "main infiltration curve", fitting them with the calculated value in step 2, and determining the correction parameter k; 4) calculating the "infiltration scanning curve" or "dewetting scanning curve" under any initial state. The calculation results of this method are highly accurate and can effectively meet the engineering precision requirements. Compared with the use of experimental methods to obtain data throughout the process, this calculation method only requires part of the test data to calculate the "infiltration scanning curve" or "dewetting scanning curve" starting from any initial soil suction, which is relatively low in cost.

Description

Technical Field

[0001] The present invention belongs to the field of foundation engineering and ground treatment, and particularly relates to a method for calculating a soil-water characteristic curve of unsaturated soil under dry-wet cycles. Background Art

[0002] In practical projects such as foundation treatment and slope management, natural conditions such as groundwater level fluctuations, rainfall, and exposure to the sun are among the main factors affecting the long-term stability and safety of buildings and structures. Ensuring the safety of buildings and structures during their service life requires engineers to have a deep understanding of the physical and mechanical properties of soil. The soil-water characteristic curve is an important basis for determining the basic properties of unsaturated soil. Existing technologies require measuring every data point on each curve to obtain a complete wetting and dewetting scan curve. The test measurement process primarily involves varying the pore pressure, waiting for water-air equilibrium within the soil, and then reading the water content data within the unsaturated soil. Waiting for water-air equilibrium within the unsaturated soil typically takes a long time, ranging from several hours to several days for a single data point. Obtaining a complete scan curve that reflects the wetting and dewetting process requires dozens of test data points, which consumes considerable manpower and material resources. Summary of the Invention

[0003] Purpose of the Invention: This invention provides a method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles. This method requires only two sets of data points, the initial dewetting curve and the main wetting curve, and generates a series of scanned curves through numerical calculation. This method is characterized by a short computation time, a simple process, high accuracy, and intuitive graphical representation, resulting in high economic efficiency. The entire calculation process can be implemented using built-in functions in Excel, a common office software, for calculation, fitting, and plotting, facilitating its widespread application.

[0004] Technical solution: In order to solve the above technical problems, the present invention proposes a method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles, which includes the following specific steps:

[0005] (1) Collect the experimental data points of saturated soil dehumidification and fit the relationship curve between the continuous saturation S and soil suction ψ, which is called the initial dehumidification curve;

[0006] (2) Take N+1 points of the initial dehumidification curve on the soil suction axis at equal intervals, namely ψ0, ψ1, ψ2, ψ3, ..., ψ N , where, ψ0<ψ1<ψ2<ψ3<…<ψ N , soil suction ψ i and pore radius r i One-to-one correspondence, the water content ΔS in two adjacent soil suction intervals is determined by the initial dehumidification curve 1,i =S(ψ i-1 )-S(ψi );

[0007] (3) According to the test data points on the main infiltration curve, determine the initial infiltration soil suction ψ of the main infiltration curve 2,m , the soil suction of unsaturated soil is from ψ 2,m Start water absorption and infiltration, calculate the soil suction during the infiltration process to reduce to any suction ψ j The corresponding saturation S2(ψ j ), ψ j <ψ 2,m The obtained saturation S2 and soil suction ψ j The relationship curve is called the main infiltration curve; considering the hysteresis caused by the "entrained air" effect, "ink bottle effect" and "raindrop effect" in the infiltration process, the parameter k is introduced. During the infiltration process, the soil suction changes from ψ 2,m Reduce to any suction force ψ j When ψ 2,m to ψ j The water content in each adjacent interval ΔS 2,i The calculation formula is as follows, that is, ψ i-1 to ψ i , where ψ j <ψ i ≤ψ 2,m :

[0008] When kψ j >ψ i hour,

[0009] ΔS 2,i =0 (1)

[0010] When kψ j ≤ψ i When ΔS 1,i Taking into account the hysteresis, multiply the parameter Corrected to obtain ΔS 2,i ;

[0011] (4) Based on the initial dehumidification curve, the soil suction is reduced to any value ψ j Saturation S2(ψ j ) is expressed by formula (3), which contains the indefinite parameter k;

[0012]

[0013] (5) fitting the calculated value in step (4) with the experimental data points of the main wetting curve, and determining the parameter k value through planning and solving;

[0014] (6) The process of unsaturated soil undergoing dewetting-infiltration and then rewetting-infiltration is called a dry-wetting cycle. The S3 obtained during the rewetting process is related to the soil suction ψj The relationship curve is called the infiltration scanning curve, and the S4 obtained by dehumidification is related to the soil suction ψ j The relationship curve is called the dewetting scanning curve. When the above correction parameter k is determined, the soil suction is calculated according to formula (3) from any other initial wet soil suction ψ 3,m The infiltration scanning curve S3 (ψ j ), where ψ 3,m Replace ψ 2,m Perform calculations;

[0015] (7) The saturation S4 during the re-dewetting process and the initial soil suction ψ during the previous infiltration process 3,m Closely related, soil suction from the initial dehumidification suction ψ 4,m The dehumidification scanning curve is obtained to construct the saturation S4 and soil suction ψ j The relationship between ψ 4,m >ψ j >ψ 3,m .

[0016] Furthermore, the pore radius corresponds to the soil suction in a one-to-one relationship, as shown in formula (5):

[0017]

[0018] Among them, T s is a coefficient related to the environment, α is the contact angle between water and soil particles, r i is the pore radius.

[0019] Furthermore, the fitting formula in step 1 adopts the Fredlund & Xing model, as shown in formula (6):

[0020]

[0021] Among them, S(ψ) is the saturation, which is a function of soil suction ψ, C r is a constant, which is 1500 for sand, e is a natural constant, and a, m, and n are fitting parameters in the model.

[0022] Furthermore, in step 3, ΔS 2,i The calculation of is shown in formula (2);

[0023]

[0024] Where S0 is the maximum saturation after entrainment; ψ 2,m The initial soil suction on the main infiltration curve; S0 and ψ 2,m They are all determined by the experimental data points of the main wetting curve.

[0025] Furthermore, the saturation S4 and soil suction ψ j The relationship is shown in formula (4):

[0026]

[0027] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0028] This paper provides a numerical calculation method that, using only a subset of data points on the initial dewetting curve and the main wetting curve, can generate a complete and continuous initial dewetting curve, a main wetting curve, and a series of wetting and dewetting sweep curves. This method simulates the water-holding characteristics of unsaturated soils under different initial conditions during wetting-drying cycles. This calculation method eliminates the traditional reliance on experimental techniques, significantly reducing experimental costs and data acquisition cycles. It also provides a more comprehensive understanding of unsaturated soil properties and improves engineering efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of soil-water characteristic curve for unsaturated soil drying and wetting cycles;

[0030] Figure 2 Initial dewetting curve of unsaturated soil;

[0031] Figure 3 ψ 2,m = "main wetting curve" of 500kPa, ψ 4,m = "Dehumidification scanning curve" of 1.118kPa. DETAILED DESCRIPTION

[0032] The implementation of the present invention will be described in detail below in conjunction with specific experimental data.

[0033] The present invention proposes a method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles, which includes the following specific steps:

[0034] (1) Collect the experimental data points of saturated soil dehumidification and fit the relationship curve between the continuous saturation S and soil suction ψ, which is called the initial dehumidification curve;

[0035] (2) Take N+1 points of the initial dehumidification curve on the soil suction axis at equal intervals, namely ψ0, ψ1, ψ2, ψ3, ..., ψ N , where, ψ0<ψ1<ψ2<ψ3<…<ψ N , soil suction ψ i and pore radius r i One-to-one correspondence, the water content ΔS in two adjacent soil suction intervals is determined by the initial dehumidification curve 1,i =S(ψ i-1 )-S(ψi );

[0036] (3) According to the test data points on the main infiltration curve, determine the initial infiltration soil suction ψ of the main infiltration curve 2,m , the soil suction of unsaturated soil is from ψ 2,m Start water absorption and infiltration, calculate the soil suction during the infiltration process to reduce to any suction ψ j The corresponding saturation S2(ψ j ), ψ j <ψ 2,m The obtained saturation S2 and soil suction ψ j The relationship curve is called the main infiltration curve; considering the hysteresis caused by the "entrained air" effect, "ink bottle effect" and "raindrop effect" in the infiltration process, the parameter k is introduced. During the infiltration process, the soil suction changes from ψ 2,m Reduce to any suction force ψ j When ψ 2,m to ψ j The water content in each adjacent interval ΔS 2,i The calculation formula is as follows, that is, ψ i-1 to ψ i , where ψ j <ψ i ≤ψ 2,m :

[0037] When kψ j >ψ i hour,

[0038] ΔS 2,i =0 (1)

[0039] When kψ j ≤ψ i When ΔS 1,i Taking into account the hysteresis, multiply the parameter Corrected to obtain ΔS 2,i ;

[0040] (4) Based on the initial dehumidification curve, the soil suction is reduced to any value ψ j Saturation S2(ψ j ) is expressed by formula (3), which contains the indefinite parameter k;

[0041]

[0042] (5) fitting the calculated value in step (4) with the experimental data points of the main wetting curve, and determining the parameter k value through planning and solving;

[0043] (6) The process of unsaturated soil undergoing dewetting-infiltration and then rewetting-infiltration is called a dry-wetting cycle. The S3 obtained during the rewetting process is related to the soil suction ψj The relationship curve is called the infiltration scanning curve, and the S4 obtained by dehumidification is related to the soil suction ψ j The relationship curve is called the dewetting scanning curve. When the above correction parameter k is determined, the soil suction is calculated according to formula (3) from any other initial wet soil suction ψ 3,m The infiltration scanning curve S3 (ψ j ), where ψ 3,m Replace ψ 2,m Perform calculations;

[0044] (7) The saturation S4 during the re-dewetting process and the initial soil suction ψ during the previous infiltration process 3,m Closely related, soil suction from the initial dehumidification suction ψ 4,m The dehumidification scanning curve is obtained to construct the saturation S4 and soil suction ψ j The relationship between ψ 4,m >ψ j >ψ 3,m .

[0045] Furthermore, the pore radius corresponds to the soil suction in a one-to-one relationship, as shown in formula (5):

[0046]

[0047] Among them, T s is a coefficient related to the environment, α is the contact angle between water and soil particles, r i is the pore radius.

[0048] The fitting formula in step 1 adopts the Fredlund & Xing model, as shown in formula (6):

[0049]

[0050] Among them, S(ψ) is the saturation, which is a function of soil suction ψ, C r is a constant, which is 1500 for sand, e is a natural constant, and a, m, and n are fitting parameters in the model.

[0051] In step 3, ΔS 2,i The calculation of is shown in formula (2);

[0052]

[0053] Where S0 is the maximum saturation after entrainment; ψ 2,m The initial soil suction on the main infiltration curve; S0 and ψ 2,m They are all determined by the experimental data points of the main wetting curve.

[0054] The saturation S4 and soil suction ψj The relationship is shown in formula (4):

[0055]

[0056] Case Analysis

[0057] 1. Dehumidification test data of saturated soil specimens were collected, as shown in Table 1. Using the Fredlund & Xing model and the built-in planning solver function in Excel, the best fitting parameters a = 67.78, m = 0.78, and n = 1.319 were obtained.

[0058] Table 1 Dehumidification test data of a saturated soil sample

[0059]

[0060] 2. Divide the soil suction axis into equal parts. The more intervals there are, the higher the calculation accuracy. In this embodiment, the number of divisions is 40.

[0061] 3. From the infiltration test data points, it can be seen that the initial infiltration value ψ 2,m is 500kPa, S0 is 0.868. During the calculation of the infiltration process, the soil suction is reduced to any soil suction ψ j When ψ 2,m =500kPa to ψ j Each adjacent interval between (i.e., from ψ i-1 to ψ i , where ψ j <ψ i ≤ψ 2,m ) Water content ΔS 2,i The calculation formula is as follows:

[0062] When kψ j >ψ i hour,

[0063] ΔS 2,i =0 (1)

[0064] When kψ j ≤ψ i hour,

[0065]

[0066] 4. Based on the “initial dehumidification curve”, the soil suction is reduced to any value. j Saturation S2(ψ j ) can be calculated by formula (3);

[0067]

[0068] 5. Based on the collected infiltration test data, as shown in Table 2, use the built-in planning solver in Excel, select the parameter k in "By Variable Cell", fit the calculated value with the infiltration test value, and determine k = 1.57.

[0069] Table 2 Infiltration test data of a saturated soil sample

[0070]

[0071] 6. At the initial infiltration value ψ 2,m Under the condition of 500kPa,

[0072]

[0073] 7.ψ 3,m =500kPa, S(ψ 3,m )=0.426, unsaturated soil from ψ 4,m =1.118kPa and dehumidified again. The calculated water content values ​​of each soil suction range are shown in Table 3.

[0074] Table 3ψ 3,m =500kPa,ψ 4,m =1.118kPa corresponds to the water content of each soil suction range

[0075]

[0076]

[0077] Soil suction increases to ψ j When , the water content corresponding to the dehumidification scanning curve can be calculated by the formula:

[0078]

[0079] Under different suction conditions, from ψ 4,m =1.118kPa The calculated values ​​of the scanning curve for dehumidification are shown in Table 4:

[0080]

[0081]

[0082] From this, a set of "main wetting curves" and "dewetting scanning curves" can be calculated and the curves can be drawn in Excel as follows: Figure 3 shown.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, rather than to limit it. Any changes made based on the technical solution in accordance with the technical ideas proposed by the present invention fall within the scope of protection of the present invention.

Claims

1. A method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles, characterized in that: The method comprises the following specific steps: (1) Collect the experimental data points of saturated soil dehumidification and fit the relationship curve between the continuous saturation S and soil suction ψ, which is called the initial dehumidification curve; (2) Take N+1 points of the initial dehumidification curve on the soil suction axis at equal intervals, namely ψ0, ψ1, ψ2, ψ3, ..., ψ N , where, ψ0<ψ1<ψ2<ψ3<…<ψ N , soil suction ψ i and pore radius r i One-to-one correspondence, the water content ΔS in two adjacent soil suction intervals is determined by the initial dehumidification curve 1,i =S(ψ i-1 )-S(ψ i ); (3) According to the test data points on the main infiltration curve, determine the initial infiltration soil suction ψ of the main infiltration curve 2,m , the soil suction of unsaturated soil is from ψ 2,m Start water absorption and infiltration, calculate the soil suction during the infiltration process to reduce to any suction ψ j The corresponding saturation S2(ψ j ), ψ j <ψ 2,m The obtained saturation S2 and soil suction ψ j The relationship curve is called the main infiltration curve; considering the hysteresis caused by the "entrained air" effect, "ink bottle effect" and "raindrop effect" in the infiltration process, the parameter k is introduced. During the infiltration process, the soil suction changes from ψ 2,m Reduce to any suction force ψ j When ψ 2,m to ψ j The water content in each adjacent interval ΔS 2,i The calculation formula is as follows, that is, ψ i-1 to ψ i , where ψ j <ψ i ≤ψ 2,m : When kψ j >ψ i hour, ΔS 2,i =0 (1) When kψ j ≤ψ i When ΔS 1,i Considering the hysteresis, ΔS 1,i Multiply by the parameter to correct for ΔS 2,i , where ΔS 2,i The calculation of is shown in formula (2); Where S0 is the maximum saturation after entrainment; ψ 2,m The initial soil suction on the main infiltration curve; S0 and ψ 2,m They are all determined by the experimental data points of the main wetting curve; (4) Based on the initial dehumidification curve, the soil suction is reduced to any value ψ j Saturation S2(ψ j ) is expressed by formula (3), which contains the indefinite parameter k; (5) fitting the calculated value in step (4) with the experimental data points of the main wetting curve, and determining the parameter k value through planning and solving; (6) The process of unsaturated soil undergoing dewetting-infiltration and then rewetting-infiltration is called a dry-wetting cycle. The S3 obtained during the rewetting process is related to the soil suction ψ j The relationship curve is called the infiltration scanning curve, and the S4 obtained by dehumidification is related to the soil suction ψ j The relationship curve is called the dewetting scanning curve. When the above correction parameter k is determined, the soil suction is calculated according to formula (3) from any other initial wet soil suction ψ 3,m The infiltration scanning curve S3 (ψ j ), where ψ 3,m Replace ψ 2,m Perform calculations; (7) The saturation S4 during the re-dewetting process and the initial soil suction ψ during the previous infiltration process 3,m Closely related, soil suction from the initial dehumidification suction ψ 4,m The dehumidification scanning curve is obtained to construct the saturation S4 and soil suction ψ j The relationship between ψ 4,m >ψ j >ψ 3,m .

2. The method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles according to claim 1, characterized in that: The pore radius corresponds to the soil suction in a one-to-one relationship, as shown in formula (5): Among them, T s is a coefficient related to the environment, α is the contact angle between water and soil particles, r i is the pore radius.

3. The method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles according to claim 1, characterized in that: The fitting formula in step 1 adopts the Fredlund & Xing model, as shown in formula (6): Among them, S(ψ) is the saturation, which is a function of soil suction ψ, C r is a constant, which is 1500 for sand, e is a natural constant, and a, m, and n are fitting parameters in the model.

4. The method for calculating the soil-water characteristic curve of unsaturated soil under dry-wet cycles according to claim 1, characterized in that: The saturation S4 and soil suction ψ j The relationship is shown in formula (4):

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