A method for constructing a prediction model of soil freezing temperature

Abstract

A method for constructing a prediction model of soil freezing temperature belongs to the technical field of geotechnical engineering. The present invention proposes a prediction model of soil freezing temperature, comprehensively considering the influence of two factors: water content and dry density. These two factors are conventional macroscopic parameters in engineering and are easy to obtain. This prediction model does not require analysis of factors such as particle size content and mineral composition of the soil, and only requires two conventional physical parameters to make predictions, having the advantages of high efficiency and convenience. The freezing temperature of the soil in different physical states can be obtained based on the temperature-time history diagram of the monitored soil sample during the freezing process.

Description

Technical Field

[0001] The present invention belongs to the technical field of geotechnical engineering, especially the field of frozen soil engineering, and particularly relates to a method for constructing a prediction model of soil freezing temperature for predicting the freezing temperature of soil. Background Art

[0002] The freezing temperature of soil is a key index for determining whether the soil is in a frozen state, and is also the basis for determining the freezing depth and the thickness of an artificial frozen wall. In addition, the freezing temperature is also an important parameter in the soil freezing characteristic model (unfrozen water content, matric suction), the mechanical properties of frozen soil, and the permeability characteristics of frozen soil. During the construction of cold region projects, artificial freezing technology, and freezing tests, it is necessary to judge the freezing process of the site (or specimen). By using the temperature sensors arranged, non-destructive judgment of the temperature field distribution can be realized to obtain the freezing spatial distribution. In today's artificial freezing projects, especially in the fields of tunnel freezing construction, mine operation, and pollution waste treatment, etc., for judging whether the freezing reaches the predetermined target thickness and dynamically adjusting the freezing input or output is directly related to the safety of project construction.

[0003] For a specific soil, its freezing temperature is affected by the dry density and water content; for different soils, it is affected by multiple factors such as the content of soil particle size components (such as clay, silt, or sand, etc.), the type and content of minerals, the type and content of solutes, etc. If the freezing temperature of pure water is used as the freezing temperature of the soil, it will cause a large error. Using the continuous test method to measure the freezing temperature, on the one hand, precise sensors and data acquisition equipment are required, and on the other hand, the test is time-consuming, laborious, low in efficiency, and high in cost, and it is not convenient to quickly obtain the freezing temperature value. This prediction model can quickly and accurately predict the soil freezing temperature under the condition of knowing two basic macroscopic physical quantities of water content and dry density. Summary of the Invention

[0004] The present invention provides a method for constructing a prediction model of soil freezing temperature, which can quickly predict the freezing temperature of soils in different physical states.

[0005] This method can quickly obtain the freezing temperatures of different continuous physical states (such as water content and dry density) based on fewer test results (at least 3 groups). Research shows that the freezing temperature of soil is not affected by the freezing rate and the magnitude of the freezing ambient temperature. During the freezing process, the temperature of the soil shows a temperature jump due to the release of latent heat of phase change. Generally, the temperature drop process of the soil is also divided into four stages: the supercooling stage (Ⅰ), the heating jump stage (Ⅱ), the stable stage (Ⅲ), and the cooling stage (Ⅳ), as Figure 1 shown. The temperature corresponding to the end point of stage Ⅰ and the starting point of stage Ⅱ is called the supercooling temperature T c , and the end point of stage Ⅱ and the starting point of stage Ⅲ, that is, the jump temperature T of the temperature after the release of latent heatbf is called the freezing temperature. The determination of the freezing temperature is generally obtained from the cooling time - course curve of the phase - change object, and T bf is taken as the freezing temperature of this test item in this physical state.

[0006] 1), Prepare at least three groups of soil samples with different water contents, denoted as ω1, ω2... ωn (n≥3), prepare test soil samples according to the target dry density, record the dry densities ρ1 to ρn respectively. During the sample preparation process, place the temperature sensor in the center of the specimen in advance.

[0007] 2), Connect the temperature sensors in all specimens to the data collector, place the specimens in the temperature - control equipment at room temperature for freezing, and start temperature data acquisition simultaneously. The acquisition interval is 1 - 5 s.

[0008] 3), After the temperature data acquisition is completed, process the temperature data of all specimens to determine the freezing temperature of each physical state. A function is constructed in which the freezing temperature T f has the following functional relationship with the mass water content ω:

[0009] T f = a + b*e -c*ω (1).

[0010] Where a is the first fitting parameter, b is the second fitting parameter, c is the third fitting parameter, and ω≥0, c>0.

[0011] Take the average value

[0012] And the parameter c is taken as a function of the dry density for freezing - temperature correction. Among them, ai and bi are the freezing - temperature parameters fitted at a certain dry density ρi.

[0013] Where i is a natural number (1, 2... n), and n is a natural number (1, 2... n).

[0014] By plotting the n points obtained (ρ1, c1), (ρ2, c2), (ρ3, c3) to (ρn, cn) in the rectangular coordinate system, it is found that the parameter c has a linear relationship with the dry density, and thus the linear relationship between the parameter c and the dry density is established:

[0015] c(ρ)= d + g*ρ (5).

[0016] Where d is the fourth fitting constant and g is the fifth fitting constant.

[0017] Thus, the prediction model of the freezing temperature of a certain soil under different dry densities and different water contents can be obtained as:

[0018]

[0019] Among them,

[0020]

[0021] c(ρ) = d + g * ρ.

[0022] Its advantages are as follows:

[0023] 1. The present invention proposes a prediction model for the freezing temperature of soil, comprehensively considering the influence of two factors, namely water content and dry density. These two factors are conventional macroscopic parameters in engineering and are easy to obtain.

[0024] 2. This prediction model does not need to analyze factors such as particle size content and mineral composition of the soil, and only requires two conventional physical parameters to make predictions, having the advantages of high efficiency and convenience.

[0025] 3. The freezing temperature of the soil in different physical states can be obtained based on the temperature-time graph of the monitored freezing process of the soil sample. Description of the Drawings

[0026] Figure 1 It is a soil temperature drop curve graph.

[0027] Figure 2 It is a freezing temperature prediction model with the same dry density.

[0028] Figure 3 It is a freezing temperature prediction model with different dry densities.

[0029] Figure 4 It is the relationship between c and dry density.

[0030] Figure 5 It is a freezing temperature curve graph with different dry densities and different water contents.

[0031] Figure 6 It is a graph of the relationship between c and dry density of Shenyang soil in the embodiment. Detailed Embodiment

[0032] The core content of this invention patent:

[0033] 1. A freezing temperature prediction model of an exponential function is constructed, that is, the model described in formula (1), which can be used to accurately predict the freezing temperature of the soil in different physical states.

[0034] 2. This prediction model takes into account the influence of two factors, namely the water content and dry density of the soil (it is also possible not to consider the influence of dry density, that is, only make predictions for different water contents at one dry density). For unknown soil, only the freezing temperatures of several different physical states need to be measured to determine the relevant parameters, so as to accurately predict the variation law of the freezing temperature of continuous physical states.

[0035] 3. For the freezing temperature of familiar soil, this model can be used to quickly obtain the freezing temperatures of different physical states without the need for additional tests, which is accurate, efficient, and reduces costs.

[0036] Comparison with similar patent methods:

[0037] "An experimental device for measuring the freezing temperature of soil" (Patent No. 202010546463.3) and "High-pressure soil freezing temperature test device" (201110218580.8) both determine the freezing temperature of soil through experimental methods, and can only determine the freezing temperature of the measured soil under a certain physical state. However, after determining the freezing temperatures of several physical states of the measured soil through these two methods, the content of this invention patent can be used to predict the freezing temperatures of other physical states.

[0038] "Non-contact freezing temperature determination" (201010280914.X) determines the freezing temperature of the ice-water mixture on the road surface through experimental methods, and cannot be used to determine the freezing temperature of soil, especially cannot be used to predict the freezing temperature of soil under different water contents and different dry densities.

[0039] This implementation method:

[0040] When there is no knowledge of the freezing temperature of a certain soil, several data points can be obtained through a small amount of cooling and freezing monitoring, and then the freezing temperatures of other physical states can be predicted based on this known freezing temperature state. The test objects used include small-volume high-precision temperature sensors (generally small-volume thermistors with an accuracy of 0.01 °C or above, which need to be calibrated with a mercury thermometer of grade two or above), data loggers that can automatically record at a certain frequency (any known device that can achieve automatic recording at a certain frequency), the test items, and computers, etc. The specific process is as follows:

[0041] 1. Prepare 3 groups of soil samples with different mass water contents, denoted as ω1, ω2, and ω3, and prepare test soil samples according to the target dry density. The dry densities of the three groups of tests are ρ1, ρ2, and ρ3 respectively. During the sample preparation process, place the temperature sensor in the center of the sample in advance.

[0042] 2. Connect the temperature sensors in all specimens to the data collector, and connect the data collector to the computer. Place the specimens in a temperature control device (a known device) at normal temperature (positive temperature) for freezing, and start collecting temperature data simultaneously. The collection interval is 1 - 5 s.

[0043] 3. The temperature set by the temperature control device should be much lower than the freezing temperature. For example, set the final temperature to -10 to -20 °C. After collecting the temperature data of all specimens, process the temperature data to determine the freezing temperature of each physical state.

[0044] Based on the temperature monitoring during multiple freezing processes of soil samples with different dry densities and different water contents, it is found that the freezing temperature increases with the increase of water content. However, as the water content increases, the growth rate gradually decreases, approximately showing a hyperbolic / parabolic shape. In the present invention, a function of the freezing temperature T f showing the following functional relationship with the mass water content ω is constructed:

[0045] T f = a + b * e -c*ω (1). Wherein, a is the first fitting parameter, b is the second fitting parameter, c is the third fitting parameter, and ω ≥ 0, c > 0.

[0046] From the function graph, it can be seen that when the water content is large enough, the freezing temperature T f has an upper limit value of a. However, in fact, the water content ω cannot be infinitely large. Here, it is agreed that ω sat ≥ ω ≥ 0 (ω sat is the saturated water content). When the water content ω approaches 0, the lower limit of the freezing temperature is a + b. However, for soil with an approximate water content of 0, since the water content is extremely small, there is almost no phase change during freezing, so it has no practical significance to consider its freezing temperature.

[0047] For the above three groups of specimens, the water contents ω1 ≠ ω2 ≠ ω3, but the dry densities ρ1, ρ2, and ρ3 can be equal or not equal. The following discussions are carried out separately.

[0048] 1. When ρ1 = ρ2 = ρ3 (ω1 ≠ ω2 ≠ ω3).

[0049] When the dry densities are the same, at least 1 specimen is required for each group, that is, at least 3 specimens with the same dry density are required. Then the constructed prediction model can only describe the variation law of the freezing temperature with different water contents under one dry density condition. By using three water contents and three freezing temperatures, solve the following equation with three unknowns by numerical method:

[0050]

[0051] Where e is the base of the natural logarithm.

[0052] The numerical fitting solution gives:

[0053] T f = a1 + b1 * e -c1*ω (3).

[0054] The fitting results are as Figure 2 shown. FIT is the fitting.

[0055] It should be noted that at least 3 specimens with different water contents are required to solve for 3 unknowns. However, more test results can make the fitting of the three unknowns a, b, and c more accurate.

[0056] 2. When ρ1 ≠ ρ2 ≠ ρ3 (ω1 ≠ ω2 ≠ ω3).

[0057] When the water content of the specimens is different and the dry density is also different, theoretically 9 specimens are required for testing for 3 groups of specimens (each dry density is a group, and each group has 3 specimens with different water contents), that is, each dry density includes three tests with different water contents. The freezing temperature expressions for three different dry densities can be obtained through numerical solution (of course, there can also be n groups of dry density specimens, n ≥ 3):

[0058] T f = a1 + b1 * e -c1*ω , (4 - 1) corresponding to three cases with a density of ρ1.

[0059] T f = a2 + b2 * e -c2*ω , (4 - 2) corresponding to three cases with a density of ρ2.

[0060] T f = a3 + b3 * e -c3*ω , (4 - 3) corresponding to three cases with a density of ρ3.

[0061] The measured and fitting results are as Figure 3 shown. When there are more than 3 groups of dry densities, it is denoted as ρn.

[0062] Through comparative analysis, it is found that for the same soil at different water contents and dry densities, the fitting parameters a and b of the freezing temperature model change little and can be considered as fixed values.

[0063] Approximately, take the average value And the parameter c changes greatly and is taken as a function of the dry density, that is, the freezing temperature is corrected by taking the parameter c as a function of the dry density.

[0064] By plotting the three points (ρ1, c1), (ρ2, c2), and (ρ3, c3) obtained in the rectangular coordinate system, it is found that the parameter c has a linear relationship with the dry density, as Figure 4As shown in the figure, a linear relationship between parameter c and dry density is established as follows:

[0065] c(ρ) = d + g * ρ (5).

[0066] Where d is the fourth fitting constant and g is the fifth fitting constant.

[0067] Therefore, the freezing temperature prediction model of a certain soil under different dry densities and different water contents can be obtained as follows:

[0068]

[0069] Among them,

[0070]

[0071] c(ρ) = d + g * ρ.

[0072] Model evaluation:

[0073] The prediction effect of the predicted values of this model can be evaluated by the following four parameters, namely the root mean square error (RMSE), the average error (AD), the mean absolute percentage error (MAPE), and the Nash efficiency coefficient (NSE), so as to evaluate the prediction ability of the model. Their definitions are as follows:

[0074] Root mean square error (RMSE):

[0075] Average error (AD):

[0076] Mean absolute percentage error (MAPE):

[0077] Nash efficiency coefficient (NSE):

[0078] In formulas (7), (8), (9), and (10): N is the number of data, Y j is the measured freezing temperature value in the experiment, is the average value of Y j and is the predicted freezing temperature value calculated using formula (3) or formula (6).

[0079] The closer the root mean square error (RMSE) is to 0, the closer the average error (AD) is to 0, the closer the mean absolute percentage error (MAPE) is to 0%, and the closer the Nash efficiency coefficient (NSE) is to 1, the better the prediction effect.

[0080] Case reference:

[0081] Taking the analysis of the freezing temperature 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 the freezing temperatures measured at three dry densities of 1.4 g / cm 3 , 1.5 g / cm 3 and 1.6 g / cm 3 and water contents (by weight) ranging from 15% to 34.4% as an example, the model construction analysis is carried out. The measured freezing temperatures in the experiment are shown in Table 1.

[0082] Table 1 Freezing Temperature Test Results (°C)

[0083]

[0084] According to formula (1) and the test results in Table 1, parameter fitting is carried out by numerical methods. The freezing temperatures at three dry densities are as follows:

[0085] T f = -0.4518 - 2.5460*e -0.1944*ω , R 2 = 0.998, ρ = 1.4 g / cm 3 .

[0086] T f = -0.4557 - 2.5584*e -0.16836*ω , R 2 = 0.998, ρ = 1.5 g / cm 3 .

[0087] T f = -0.4583 - 2.5095*e -0.1458*ω , R 2 = 0.999, ρ = 1.6 g / cm 3 .

[0088] R 2 is the goodness of fit.

[0089] As shown in Table 2, through analysis, it can be considered that the T f (ω) fitted by formula (1) should have

[0090] the same a and b under different dry density conditions. Approximately, taking the average value, we get:

[0091] Table 2 Predicted Model Limit Values

[0092]

[0093] We get Figure 5 Freezing Temperature Curves for Different Dry Densities and Different Water Contents

[0094] However, different dry densities change the curvature of the function in the range of [15, 35](%) through different c values, that is

[0095] T f =-0.4553 - 2.5380*e -c(ρ)*ω (11).

[0096] To obtain the expression of c(ρ), the c-ρ curve is plotted Figure 6 :

[0097] It is not difficult to see that c-ρ approximately shows a linear relationship, and the fitting result is:

[0098] c = -0.243ρ + 0.534, R 2 = 0.997.

[0099] Therefore, the prediction model of the freezing temperature of this silty clay is:

[0100] T f =-0.4553 - 2.5380*e (0.243ρ-0.534)*ω .

Claims

1. A method for constructing a prediction model of soil freezing temperature, comprising the following steps: 1), Prepare at least three groups of soil samples with different water contents, denoted as ω1, ω2... ωn, n≥3, and prepare test soil samples according to the target dry density, and record the dry densities ρ1 to ρn respectively. During the sample preparation process, place the temperature sensor in the center of the sample in advance; 2), Connect the temperature sensors in all samples to the collector, place the samples in the temperature control device at room temperature for freezing, and start collecting temperature data at the same time. The collection interval is 1-5 s; 3), After the temperature data collection is completed, process the temperature data of all samples to determine the freezing temperature of each physical state; A function was constructed for the freezing temperature T f varying as a function of the mass water content ω as follows: T f = a + b * e -c*ω (1); Among them, a is the first fitting parameter, b is the second fitting parameter, c is the third fitting parameter, and ω≥0, c>0; Take the average value Among them, a1, a2, a3... an are the first fitting parameters with different water contents; The parameter c is taken as a function of the dry density, and the freezing temperature is corrected as a function of the dry density; Among them, b1, b2, b3... bn are the second fitting parameters with different water contents; Plot the obtained n points of (ρ1, c1), (ρ2, c2), (ρ3, c3) to (ρn, cn) in the rectangular coordinate system, and find that the parameter c has a linear relationship with the dry density, so as to establish a linear relationship between the parameter c and the dry density: c(ρ) = d + g*ρ (5); Where d is the fourth fitting constant and g is the fifth fitting constant; Therefore, the prediction model of the freezing temperature of a certain soil under different dry densities and different water contents can be obtained as: Among them, c(ρ) = d + g*ρ.

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