A method for constructing a prediction model of the soil freezing characteristic curve

Abstract

A method for constructing a prediction model of the freezing characteristic curve of soil belongs to the technical field of geotechnical engineering. It can quickly obtain the unfrozen water content in different continuous physical states by using several groups of test results. Based on multiple initial water contents, indoor tests and the deduction of their mutual relationships are carried out, and a prediction model based on the unfrozen water of cohesive soil is proposed. Only two conventional physical parameters, namely the initial water content and temperature, are required to calculate the unfrozen water content under any freezing temperature condition in the conventional freezing state, which has the advantages of high efficiency and convenience. There is no need to analyze factors such as particle size content and mineral composition of the soil, so there is no need for complex and expensive experimental equipment or instruments, and the measurement cost is low. Thus, the control differential equation of soil freezing can be unified into one equation in the frozen zone and the unfrozen zone.

Description

Technical Field

[0001] The present invention belongs to the technical field of geotechnical engineering, especially the field of frozen soil engineering. Specifically, it is a method for constructing a prediction model of the freezing characteristic curve of soil, which is used to predict the freezing characteristic curve (relationship between unfrozen water content and temperature) of soil. Background Art

[0002] After soil freezes, not all the liquid water in the soil completely changes into solid ice. Instead, there is still a certain amount of liquid water called unfrozen water during the freezing process. There is even a certain amount of unfrozen water at -70°C. There is a dynamic equilibrium relationship between the content of unfrozen water and temperature, that is, as the temperature decreases, the content of unfrozen water decreases, and vice versa. Generally, the relationship curve between unfrozen water content and temperature is called the freezing characteristic curve of soil. Among many existing coupled heat and water models of frozen soil, the unfrozen water content is the most crucial quantitative index, which characterizes the migration state of water and heat in frozen soil. A series of physical and mechanical properties of frozen soil, such as thermal conductivity, permeability, stiffness, and strength, are all related to its unfrozen water content. For a specific soil, its unfrozen water content is affected by the initial water content and temperature. For different soils, it is also affected by multiple factors such as the content of soil particle size components (such as clay particles, silt particles, and sand particles), the type and content of minerals, and the type and content of solutes. In China, there are extensive areas of seasonal frozen soil and permafrost, as well as a large number of projects constructed by the artificial freezing method. Existing monitoring and detection technologies can non-destructively obtain the temperature field distribution and initial water content of in-situ soil. Based on this condition, using this prediction model, the water content and ice content of soil under different temperature conditions can be calculated more quickly and accurately, providing key data support for further evaluating the frost heave deformation of soil, which is directly related to the safety of engineering construction. Summary of the Invention

[0003] The present invention provides a method for constructing a prediction model of the freezing characteristic curve of soil, which is a method for calculating the unfrozen water content of frozen soil with different initial water contents.

[0004] It can quickly obtain the unfrozen water content of different continuous physical states (such as initial water content and dry density) by using 4 - 5 groups of test results, that is, the upper limit of the unfrozen water content at any temperature under the general freezing state is defined.

[0005] Its advantages are as follows:

[0006] (1) Based on multiple initial water contents, the present invention conducts laboratory tests and deduces their mutual relationships, and proposes a prediction model based on the unfrozen water of silty clay. Only two conventional physical parameters, namely the initial water content and temperature, are required to calculate the unfrozen water content under any freezing temperature condition in the conventional freezing state, which has the advantages of high efficiency and convenience.

[0007] (2) There is no need to analyze factors such as particle size content and mineral composition of the soil mass, so there is no need for complex and expensive experimental equipment or instruments, and the measurement cost is low.

[0008] (3) The water content of this model covers the positive and negative temperature ranges, avoiding the situation where the previous model is infinite near the initial freezing temperature, resulting in non-convergence during numerical calculation, and the overall curve is smoother. Thus, the control differential equation of frozen soil freezing can be unified into one equation in the frozen zone and the unfrozen zone.

[0009] (4) The parameters of the model have clear physical meanings, and the freezing characteristic curve can be determined positively through conventional physical quantities. Description of the Drawings

[0010] Figure 1 Fitting of soil sample data with initial mass water content ω0 = ω1, dry densities ρ1 and ρ2.

[0011] Figure 2 Model curves for different values of a (m = 0.8, n = 2). K is the Kelvin temperature.

[0012] Figure 3 For a and T f Variation trend of a with ω0 and its fitting. In the figure, Fitteda is the fitting curve of the a~ω0 relationship.

[0013] Figure 4 Model curves for different values of m (a = 100, n = 2).

[0014] Figure 5 Variation trend of m with ω0.

[0015] Figure 6 Model curves for different values of n (a = 100, m = 0.8).

[0016] Figure 7 Variation trend of n with ω0.

[0017] Figure 8 Variation trend of m with ω0 in the Shenyang soil example.

[0018] Figure 9 Variation trend of n with ω0 in the Shenyang soil example. Detailed Implementation Manner

[0019] Core content of this invention patent:

[0020] (1) An unfrozen water content prediction model based on a composite function is improved, that is, the model described in formula (1), which can be used to accurately predict the unfrozen water content under any freezing temperature condition in the conventional freezing state.

[0021] (2) The influence of two factors, namely the initial water content and temperature of the soil mass, is considered in this prediction model. For unknown soil masses, only a few sets of unfrozen water content changes of the soil mass under different initial water contents need to be measured to determine the relevant parameters, so as to accurately predict the change law of the unfrozen water content in the continuous physical state.

[0022] (3) For the familiar silty clay, this model can be used to quickly calculate the unfrozen water content without the need for additional tests, which is accurate and efficient, reduces costs.

[0023] (4) Based on the inversion of the relationship between the model parameters and conventional physical quantities from the test data, the physical meaning of the model parameters is given.

[0024] Comparison with similar patent methods:

[0025] "Test Method for Unfrozen Water Content of Frozen Soil Based on Pressure Plate Apparatus" (Patent No. 201610229165.5), "Method for Determining Unfrozen Water Content of Frozen Soil by Measuring Resistivity" (Patent No. 201710224095.9), and "Method for Measuring Unfrozen Water Content of Frozen Soil with Piezoelectric Ceramics" (Patent No. 202110880207.2) all determine the unfrozen water content of the soil mass through experimental methods, and can only determine the unfrozen water content of the measured soil mass under a certain physical state. However, after determining the unfrozen water content of the measured soil mass in several physical states by these three methods, the content of this invention patent can be used to predict the unfrozen water content in other physical states.

[0026] "System and Method for Measuring Unfrozen Water Content of Frozen Soil by Using Pulsed Nuclear Magnetic Resonance" (Patent No. 201010584539.8) calculates the unfrozen water content by measuring the free induction decay of hydrogen nuclei in a magnetic field and according to the proportional relationship between the signal intensity and liquid water. "Calculation Method for Unfrozen Water Content Based on Thermal Conductivity of Frozen Soil" calculates the unfrozen water content by measuring the thermal conductivity of the soil mass. "Calculation Method for Unfrozen Water Content of Frozen Soil Based on Ion Concentration Gradient in Clay Diffusion Layer" (202110613199.5) calculates the unfrozen water content by measuring the component content and specific surface area of the soil mass. The test costs of these methods are relatively high.

[0027] "A Detection Method for Unfrozen Water Content of Frozen Soil" (Patent No. 201911332531.X) and "Construction Method for Neural Network Model for Detecting Unfrozen Water Content of Frozen Soil" (Patent No. 201911332522.0) both construct a prediction model for the unfrozen water content through artificial intelligence neural network methods, but this method requires a large amount of test data to ensure the model accuracy.

[0028] This implementation method:

[0029] When the variation law of unfrozen water content in a certain soil mass is unknown, a small number of freezing tests can be carried out to obtain the data of unfrozen water content variation. Then, a prediction model can be constructed based on the test data to predict the unfrozen water content under other physical states. The required testing instruments include small-volume high-precision temperature sensors and moisture sensors (TDR time domain reflectometers or other moisture sensors), a data collector that can automatically record at a certain frequency (known equipment), a computer, etc. The specific process is as follows:

[0030] (1) Prepare no less than 4 groups of soil samples with different initial water contents (mass water contents), denoted as ω1, ω2, ω3, ω4… For the initial water content for initially determining the model parameters, it is recommended to set it above the plastic limit water content to ensure accuracy; studying the relationship between the unfrozen water content and the initial water content of the soil mass reveals that there is a critical water content (or range). Above the critical water content, the unfrozen water content of the soil mass is no longer affected by the initial water content and dry density, and this critical water content is near the plastic limit. Prepare the test soil samples according to the target dry density. The same dry density ρ or different dry densities, such as ρ1, ρ2, ρ3… can be prepared as needed. Through research, above the critical water content, the influence of dry density on the unfrozen water content is weak, and the dry density of the soil samples can be determined as needed.

[0031] (2) Fix the temperature sensor and moisture sensor probes into the soil samples, connect the temperature sensor and moisture sensor to the data collector, and connect the data collector to the computer. Place the soil samples at normal temperature (positive temperature) into a temperature control device (known equipment) set to negative temperature for freezing, and start data collection simultaneously. The collection interval is 1 - 30 s.

[0032] (3) The ambient temperature set by the temperature control device should be slightly lower than the required target temperature. For example, if the unfrozen water content variation from 0 to -20 °C needs to be measured, the final temperature can be set to -21 °C to -30 °C. After the soil temperature measured by the temperature sensor is close to the temperature set by the temperature control device, the soil samples can be taken out, the test can be terminated, and the temperature and water content test data can be processed.

[0033] (4) For temperature control, two freezing models can be adopted. One is to test the water content variation at discrete temperature states. For example, the unfrozen water content can be tested at the freezing temperature of each stable state, that is, first set the temperature of the temperature control device to T1. When the soil sample temperature is constant at T1, test and record the unfrozen water content at the T1 state. One temperature state can be tested three times, with an interval of 5 minutes each time, and then the next temperature state can be tested in sequence. The test sequence should be in the order of decreasing temperature, and the repeated temperature change mode of decreasing - increasing - decreasing temperature cannot be adopted to avoid the hysteresis effect. Another test method is to directly set the temperature control device to the lowest test temperature, and then test the unfrozen water content of the soil samples during the process of gradually freezing and cooling from the normal temperature state.

[0034] Both existing research results and experimental data indicate that the unfrozen water content shows the following trend with temperature changes: when the ambient temperature is in the positive temperature range, theoretically, the liquid water content is constant. When the temperature just enters the freezing temperature range (such as -5°C to 0°C), that is, in the severe phase change range, the unfrozen water content decreases significantly.

[0035] When the temperature continues to decrease (for example, from -5°C to -30°C), the change in the unfrozen water content is positively correlated with the temperature change, and the change rate gradually decreases. When the temperature is even lower (for example, below -30°C), it is less affected by temperature and gradually approaches a stable value. Therefore, the change rate of the water content shows an "S"-shaped trend of "constant - rapid decrease - slow decrease" from the positive temperature range to the negative temperature range.

[0036] In the present invention, a function is constructed for the unfrozen water content θ u showing the following functional relationship with the initial water content θ0:

[0037]

[0038] where a, m, and n are the first fitting parameter, the second fitting parameter, and the third fitting parameter respectively, e is the base of the natural logarithm, and T is the temperature.

[0039] This function has the following characteristics: the function is continuously differentiable over the entire domain, and a, m, n > 0. When the temperature T > 0°C, θ u rapidly converges to θ0. When the temperature T < 0°C, θ u is all less than θ0, and gradually decays as the temperature decreases, rather than rapidly approaching the lower asymptote.

[0040] It should be noted that the volume water content θ u measured by the commonly used TDR sensor is often used, while the indoor soil samples and tests all adopt the mass water content ω u , and their conversion relationship is as follows:

[0041] ω u = θ u ρ w / ρ d Equation (2).

[0042] where ρ w is the density of water, and ρ d is the dry density ρ of the soil sample or ρ1, ρ2, ρ3...

[0043] Therefore, after converting the unfrozen water volume content data θ u measured by the moisture sensor into the mass water content ω u , Equation (1) can also be recorded as:

[0044]

[0045] In the process of fitting using Equation (1) or Equation (3), in order to improve the fitting accuracy, it is necessary to adjust it, as shown in Equation (4).

[0046]

[0047] It is not difficult to see that the normalized unfrozen water content y ∈ [0, 1], and the following relationships exist among the fitting parameters:

[0048] θ u = θ0y Equation (5).

[0049] m = -k Equation (6).

[0050] n = -j Equation (7).

[0051] a = i 1 / j Equation (8).

[0052] Where i, j, and k are the converted fitting parameters.

[0053] In the fitting model provided by Equation (1), obviously the unfrozen water content is only related to the magnitude of the temperature, and is independent of the temperature change process and change rate. Therefore, the data to be fitted should be grouped at the same temperature interval (for example, every 0.1 °C), and the same number of data should be extracted in each group to make the weight of the temperature on the test data points uniform.

[0054] For two groups of soil samples with an initial water content ω0 = ω1, dry densities of ρ1 and ρ2, the unfrozen water content is normalized. It is observed that under the condition of the same initial water content, the data of soil samples with different dry densities are very close. Therefore, the two groups of data are jointly fitted, as Figure 1 .

[0055] Similarly, the data of soil samples with different initial water contents are respectively fitted to obtain several groups of fitting parameters in Equation (1), as shown in Table 1. (To improve the accuracy, for the water content ω used to construct the model i it is recommended that above the liquid limit water content, approximately above the plastic limit water content, that is, ω i ≥ ω P ), ω P is the plastic limit water content.

[0056] Table 1 Summary of fitting parameters (a, m, n have been converted from i, j, k).

[0057]

[0058] In Figure 2In this case, taking m = 0.8 and n = 2 as an example, as a gradually increases from 10 to 1000, the curve as a whole gradually shifts to the left. However, according to the experimental data, for most soil masses, the "climbing section" (intense phase change interval) of the curve is concentrated in the range of (-5°C to 0°C) (corresponding to 268.15K to 273.15K). In other words, for soil masses, 0 < a << 10.

[0059] In Table 1, as ω0 changes, the generally obtained a has a very small change range, and the values change around 0.67 - 0.94. Therefore, it has a small impact on the left - right position of the curve. Analyzing from the perspective of parameter deduction, the left - right horizontal position of the curve originates from the initial freezing temperature T f 's influence, and the initial freezing temperature T f in turn depends on the initial water content ω0. Therefore, the following relationship is obtained:

[0060]

[0061] where g, h, and f are the third fitting parameter, the fourth fitting parameter, and the fifth fitting parameter respectively.

[0062] See Figure 3 .

[0063] If the slight influence of the change in a on the curve position is ignored, a can also be considered as a constant, taking the average value of a in Table 1. That is, it is considered that in Equation (1):

[0064]

[0065] Taking a = 100 and n = 2 as an example, as m gradually increases, the curve gradually decreases in the negative temperature region, that is, the normalized unfrozen water content becomes smaller and smaller, as Figure 4 shown.

[0066] As the initial mass water content continuously increases, m continuously decreases, and the change rate gradually decreases. In particular, when ω0 exceeds the critical water content ω c , m hardly decreases any more. According to this characteristic, a hyperbolic function or a logarithmic function can be used for fitting to obtain:

[0067] Hyperbolic function:

[0068] where b and c are the sixth fitting parameter and the seventh fitting parameter respectively.

[0069] Logarithmic function:

[0070]

[0071] where b1 and b2 are the eighth fitting parameter and the ninth fitting parameter respectively.

[0072] See Figure 5 .

[0073] Taking a = 100 and m = 0.8 as an example, the smaller the n, the smaller the slope of the curve at a temperature of 0 °C (273.15 K). As shown in Equation (12), the curve is relatively flat in the "climbing section", the change range of the unfrozen water content of the soil body is small, and the change rate is low, that is, the difficulty of soil freezing is greater / slower, which macroscopically corresponds to a lower initial water content of the soil body. Vice versa, when n is larger, it macroscopically corresponds to a higher initial water content of the soil body.

[0074] Figure 6 See Figure 6 .

[0075]

[0076] Accordingly, by plotting the curve of the change relationship between n and ω0, an exponential function can be used for fitting, that is:

[0077]

[0078] where d, p, and q are the tenth fitting parameter, the eleventh fitting parameter, and the twelfth fitting parameter, respectively.

[0079] See Figure 7 .

[0080] Combining Equation (1), Equation (2), Equation (9), Equation (11), and Equation (13), the calculation formula of the unfrozen water content prediction model can be obtained, that is:

[0081]

[0082] Or based on Equation (1), (2)(10), (11), and (13), it can be obtained:

[0083]

[0084] Volume ice content θ i :

[0085]

[0086] Mass ice content ω i :

[0087]

[0088] Case reference:

[0089] Taking the freezing temperature analysis of silty clay in a certain place in Shenyang as an example. The plastic limit of the measured soil is 18.5, the liquid limit is 31.3, and the plasticity index is 12.8. Taking ρ1 = 1.4 g / cm 3, ρ2 = 1.5 g / cm 3 and ρ3 = 1.6 g / cm 3 Three kinds of dry densities, taking the initial mass water content θ0 of 15% - 34.4% as an example, the freezing test was carried out.

[0090] As shown in Table 2.

[0091] Table 2 Soil sample conditions for the freezing test

[0092]

[0093] Note: In Table 2, "√" indicates that the test under this group of conditions was carried out, and "-" indicates that the test under this group of conditions was not carried out.

[0094] According to equations (1) and (2), the unfrozen water volume content data measured by the moisture sensor were processed and normalized, and fitting was carried out according to different initial water content conditions to form the corresponding model fitting parameters.

[0095] As shown in Table 3.

[0096] Table 3 Model fitting parameters of the test data

[0097]

[0098] According to equation (9) and Table 3: Or

[0099] R 2 = 0.908.

[0100] According to equation (10) and Figure 8 , the relationship between m - ω0 in Table 2 was fitted with a hyperbolic function, and we got:

[0101] R 2 = 0.986.

[0102] Or:

[0103] R 2 = 0.976.

[0104] R 2 is the goodness of fit.

[0105] According to equation (12) and Figure 9 , the relationship between n - ω0 in Table 2 was fitted with an exponential function, that is: R 2 = 0.984.

[0106] Therefore, the calculation formula for the prediction model of the unfrozen water content of the soil in this test is:

[0107]

[0108] Or:

[0109]

[0110] When the accuracy requirement for a is relatively low:

[0111]

Claims

1. A method for constructing a prediction model of the soil freezing characteristic curve, characterized in that It includes the following steps: 1) Prepare no less than 4 groups of soil samples with different initial mass water contents, denoted as ω1, ω2, ω3, ω4…, and the initial mass water content is set above the plastic limit water content; prepare test soil samples according to the target dry density, and prepare soil samples with the same dry density ρ or different dry densities, such as ρ1, ρ2, ρ3… as needed; 2) Fix the temperature sensor and moisture sensor probes into the soil samples, connect the temperature sensor and moisture sensor to the data collector, place the soil samples at positive temperature into the temperature control device set at negative temperature for freezing, stepwise freezing or continuous freezing, and start data collection simultaneously, with the collection interval being 1 - 30 s; 3) The environmental temperature set by the temperature control device should be lower than the required target temperature. After the soil temperature measured by the temperature sensor approaches the temperature set by the temperature control device, take out the soil samples, terminate the test and process the temperature and water content test data; Constructed the unfrozen water content θ u As a function of the initial volumetric water content θ0 as follows: where a, m, n are the first fitting parameter, the second fitting parameter, and the third fitting parameter respectively, e is the base of the natural logarithm; T is the temperature; When the moisture sensor measures the volumetric water content θ u , while the indoor soil samples and tests all use the gravimetric water content ω u , their conversion relationship is as follows: ω u = θ u ρ w / ρ d Equation (2); where ρ w is the density of water, and ρ d is the dry density of the soil sample, i.e., ρ or ρ1, ρ2, ρ3...; Therefore, after converting the unfrozen water volume content data θ measured by the moisture sensor u into the mass water content ω u , Equation (1) is also denoted as: ω0 is the initial mass water content of the soil sample; Then, use Equation (1) or Equation (3) for fitting, normalization, and deduction to obtain the following relationship: where g, h, and f are the third fitting parameter, the fourth fitting parameter, and the fifth fitting parameter respectively; Take the average value of a, that is, it is considered in Equation (1): a1, a2, a3…a n are the first fitting parameters of soil samples with different initial mass water contents; Use the hyperbolic function for fitting to obtain: Hyperbolic function: where b and c are the sixth fitting parameter and the seventh fitting parameter respectively; Exponential function: where b1 and b2 are the eighth fitting parameter and the ninth fitting parameter respectively; The slope of the curve at a temperature of 0°C is smaller, as shown in Equation (12); The variation relationship between n and ω0 is fitted by the exponential function, that is: where d, p, q are the tenth fitting parameter, the eleventh fitting parameter, and the twelfth fitting parameter respectively; Combining Equation (1), Equation (2), Equation (9), Equation (11), and Equation (13), the calculation formula for the unfrozen water content prediction model is obtained, that is: Or based on Equation (1), (2), (10), (11), and (13), we get:

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