CN114813820A - Method for constructing soil body freezing characteristic curve prediction model - Google Patents
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Abstract
A method for constructing a soil body freezing characteristic curve prediction model belongs to the technical field of geotechnical engineering, can rapidly obtain the unfrozen water content of different continuous physical states by using a plurality of groups of test results, and performs indoor tests and deduction of the correlation thereof based on a plurality of initial water contents. The factors such as particle size content, mineral composition and the like do not need to be analyzed, so that complex and expensive experimental equipment or instruments are not needed, and the measurement cost is low. So that the differential equation for controlling frozen soil freezing can be unified into an equation in the freezing area and the unfrozen area.
Description
Technical Field
The invention belongs to the technical field of geotechnical engineering, in particular to the field of frozen soil engineering, and particularly relates to a method for constructing a soil body freezing characteristic curve prediction model, which is used for predicting a freezing characteristic curve (relationship between unfrozen water content and temperature) of a soil body.
Background
After the soil is frozen, not all the liquid water in the soil is transformed into solid ice, but a certain amount of liquid water is still present as the freezing progresses, which is called unfrozen water, and even a certain amount of unfrozen water is still present at minus 70 ℃. The relationship between the content of unfrozen water and the temperature is in dynamic equilibrium, namely the content of unfrozen water is reduced along with the reduction of the temperature, and vice versa, and the relationship curve of the content of unfrozen water and the temperature is generally called as the freezing characteristic curve of a soil body. In the existing numerous frozen soil water-thermal coupling models, the unfrozen water content is the most critical quantitative index, and the migration states of water and heat in frozen soil are represented. A series of physical and mechanical properties of frozen soil, such as thermal conductivity, permeability, rigidity and strength, are related to the unfrozen water content of the frozen soil. For a particular soil mass, its unfrozen water content is affected by the initial water content and temperature. For different soil bodies, the soil body is influenced by a plurality of factors such as the content of the grain size components of the soil body (such as clay grains, powder grains, sand grains and the like), the type and the content of mineral substances, the type and the content of solute and the like. China has widely distributed seasonal frozen soil and permafrost regions and a large number of projects constructed by adopting an artificial freezing method. The existing monitoring and detecting technology can nondestructively acquire the temperature field distribution and the initial water content of the on-site soil body, and based on the conditions, the water content and the ice content of the soil body under different temperature conditions can be calculated more quickly and accurately by using the prediction model, so that key data support is provided for further evaluating frost heaving deformation of the soil body, and the safety of engineering construction is directly related.
Disclosure of Invention
The invention provides a method for constructing a soil body freezing characteristic curve prediction model, which is a method for calculating the unfrozen water content of frozen soil with different initial water contents.
The unfrozen water content of different continuous physical states (such as initial water content and dry density) can be quickly obtained by using 4-5 groups of test results, namely the upper limit of the unfrozen water content at any temperature in a general freezing state is defined.
The advantages are that:
(1) the invention carries out indoor tests and deduction of the mutual relation based on a plurality of initial water contents, provides a prediction model based on the powdery clay unfrozen water, can calculate the unfrozen water content under any freezing temperature condition of the conventional freezing state only by two conventional physical parameters of the initial water contents and the temperature, and has the advantages of high efficiency and convenience.
(2) The factors such as particle size content, mineral composition and the like do not need to be analyzed, so that complex and expensive experimental equipment or instruments are not needed, and the measurement cost is low.
(3) The water content of the model covers the positive temperature and negative temperature range, the condition that the numerical value is not converged during calculation due to the fact that the original model is infinite near the initial freezing temperature is avoided, and the curve is smoother integrally. So that the differential equation for controlling frozen soil freezing can be unified into an equation in the freezing area and the unfrozen area.
(4) The parameters of the model have clear physical significance, and the freezing characteristic curve can be determined by the conventional physical quantity forward direction.
Drawings
FIG. 1 shows the initial mass water content ω 0 ＝ω 1 Dry density is rho 1 And ρ 2 And (4) fitting the soil sample data.
Fig. 2 shows the model curves for different values of a (m-0.8, n-2). K is the temperature in Kelvin.
FIG. 3 shows a and T f Following omega 0 Trend of change and fitting thereof. Fitteda in the figure is a-omega 0 Fitting curve of the relation.
Fig. 4 shows model curves for different values of m (a-100, n-2).
FIG. 5 shows m as a function of ω 0 And (5) a trend of change.
Fig. 6 shows the model curves for different values of n (a equals 100, m equals 0.8).
FIG. 7 shows n as ω 0 And (5) a trend of change.
FIG. 8 shows m following ω in the example of sinking yang soil 0 And (5) a trend of change.
FIG. 9 shows an example of sinking yang soil with n following ω 0 And (5) a trend of change.
Detailed Description
The core content of the patent of the invention is as follows:
(1) the unfrozen water content prediction model based on the composite function, namely the model described in the formula (1), is improved, and can be used for accurately predicting the unfrozen water content in any freezing temperature condition in the conventional freezing state.
(2) The prediction model considers the influence of two factors of the initial water content and the temperature of the soil body. For unknown soil bodies, relevant parameters can be determined by measuring changes of the unfrozen water content of the soil bodies under different groups of initial water contents, so that the change rule of the unfrozen water content in a continuous physical state is accurately predicted.
(3) For familiar silty clay, the model can be used for quickly calculating the content of unfrozen water without additional tests, and the method has the characteristics of accuracy and high efficiency and reduces the cost.
(4) And inverting the relation between the model parameters and the conventional physical quantity based on the experimental data, thereby giving the physical significance of the model parameters.
Comparison of similar patent methods:
a method for testing the content of unfrozen water in frozen soil based on a pressure plate instrument (patent No. 201610229165.5), a method for determining the content of the unfrozen water in frozen soil by measuring resistivity (patent No. 201710224095.9) and a method for measuring the content of the unfrozen water in frozen soil by piezoelectric ceramics (patent No. 202110880207.2) are all used for determining the content of the unfrozen water in a soil body by a test method and can only determine the content of the unfrozen water in the tested soil body in a certain physical state. However, after the unfrozen water content of the measured soil body in several physical states is determined by the three methods, the invention can be used for predicting the unfrozen water content of other physical states.
A system and a method for testing the content of unfrozen water in frozen soil by adopting pulse nuclear magnetic resonance (patent number 201010584539.8) calculate the content of the unfrozen water according to the proportional relation between signal intensity and liquid water by measuring the free induction attenuation of hydrogen nuclei in a magnetic field, calculate the content of the unfrozen water by measuring the heat conductivity coefficient of a soil body, and calculate the content of the unfrozen water by measuring the component content and the specific surface area of the soil body by a frozen soil unfrozen water content calculating method (202110613199.5) based on the ion concentration gradient of a clay diffusion layer. These methods are expensive to test.
A method for detecting the content of unfrozen water in frozen soil (patent number 201911332531.X) and a method for constructing a neural network model for detecting the content of the unfrozen water in frozen soil (patent number 201911332522.0) are all used for constructing a prediction model of the content of the unfrozen water by an artificial intelligent neural network method, but the method needs a large amount of test data to ensure the precision of the model.
The implementation method comprises the following steps:
when the change rule of the unfrozen water content of a certain soil body is unknown, a small amount of freezing tests can be carried out to obtain the change data of the unfrozen water content, and then a prediction model is constructed based on the test data, so that the unfrozen water content in other physical states can be predicted. The required testing instruments include small-sized high-precision temperature sensors and moisture sensors (TDR time domain reflectometer or other moisture sensors), acquisition instruments (known devices) capable of automatically recording according to certain frequency, computers and the like. The specific process is as follows:
(1) preparing not less than 4 groups of soil samples with different initial water contents (mass water contents) and marking as omega 1 、ω 2 、ω 3 ，ω 4 …, the initial water content for the initial determination of model parameters is recommended to be set above the plastic limit water content to ensure accuracy; the relation between the unfrozen water content of the soil body and the initial water content is researched, and the fact that a limit water content (or an interval) exists, above the limit water content, the unfrozen water content of the soil body is not influenced by the initial water content and the dry density any more, and the limit water content is close to a plastic limit. Preparing the test soil sample according to the target dry density, and preparing the same dry density rho or different dry densities, such as rho, according to the requirements 1 、ρ 2 、ρ 3 … is added. Through research, the influence of the dry density above the limit water content on the unfrozen water content is weak, and the dry density of the soil sample can be determined as required.
(2) Fixing probes of a temperature sensor and a moisture sensor into a soil sample, connecting the temperature sensor and the moisture sensor to an acquisition instrument, connecting the acquisition instrument to a computer, freezing the soil sample in a normal temperature state (positive temperature) in a temperature control device (known device) set to negative temperature, and simultaneously starting data acquisition at an acquisition interval of 1-30 s.
(3) The ambient temperature set by the temperature control device is slightly lower than the desired target temperature, for example, the change of unfrozen water content of 0 to-20 ℃ needs to be measured, and the final temperature can be set to-21 to-30 ℃. And after the soil body temperature measured by the temperature sensor approaches the set temperature of the temperature control equipment, taking out the soil sample, terminating the test and processing the temperature and water content test data.
(4) For the temperature control, two freezing models can be adopted, one is to test the water content change under discrete temperature states, for example, the unfrozen water content test can be carried out by adopting the freezing temperature of each stable state, namely, the temperature of the temperature control equipment is set to be T1, the unfrozen water content test of the T1 state is carried out and recorded when the soil sample temperature is constant to be T1, one temperature state can be tested for three times, each time is 5 minutes, then the test of the next temperature state is carried out in sequence, and the test sequence needs to be carried out according to a sequential cooling mode, and a repeated temperature changing mode of cooling-heating-cooling cannot be adopted, so that the hysteresis effect is avoided. The other testing method is to directly set the temperature control equipment to the lowest testing temperature and then test the unfrozen water content of the soil sample in the process of gradually and naturally freezing and cooling from the normal temperature state.
The existing research results and test data show that the unfrozen water content shows the following trend along with the temperature change: when the ambient temperature is in the positive temperature region, the liquid water content is theoretically constant. When the temperature just enters the freezing temperature (such as-5 ℃ to 0 ℃), the unfrozen water content in the violent phase change area is obviously reduced.
As the temperature continues to decrease (e.g., from-5 deg.C to-30 deg.C), the change in unfrozen water content is positively correlated with the change in temperature, with the rate of change decreasing gradually. At lower temperatures (e.g., below-30 ℃), it is less affected by temperature and gradually approaches a steady value. Thus, the rate of change of the water content exhibits a "S" type trend of "constant-rate drop-ramp-down" from the positive temperature region to the negative temperature region.
In the invention, the unfrozen water content theta is constructed u Dependent on initial water content theta 0 A function in the following functional relationship:
wherein, a, m and n are respectively a first fitting parameter, a second fitting parameter and a third fitting parameter, and e is the base number of the natural logarithm. T is the temperature.
The function has the following characteristics: the function is continuously derivable over the whole domain of definition, a, m, n>0. When the temperature T is>At 0 ℃ of theta u Quickly converge on theta 0 . When the temperature T is<At 0 deg.C,. theta. u Are all less than theta 0 And gradually decays as the temperature decreases rather than rapidly tending toward a lower asymptote.
It should be noted that the TDR sensors commonly used today often measure a volume water content θ u And the indoor soil sample and the test both adopt the mass water content omega u The conversion relationship is as follows:
ω u ＝θ u ρ w /ρ d formula (2).
Where ρ is w Is the density of water, p d I.e. the dry density rho or rho of the soil sample 1 、ρ 2 、ρ 3 …。
Therefore, the volume content data theta of the unfrozen water measured by the moisture sensor is measured u Conversion to mass water content omega u Then, formula (1) can also be written as:
in the fitting process using the formula (1) or the formula (3), in order to improve the fitting accuracy, it is necessary to adjust the fitting accuracy, as shown in the formula (4).
It can be readily seen that the normalized unfrozen water content y ∈ [0,1], with the following relationship between the various fitting parameters:
θ u ＝θ 0 y is represented by the formula (5).
m ═ k formula (6).
n-j formula (7).
a＝i 1/j Formula (8).
Where i, j, and k are scaled fitting parameters.
In the fitted model provided by equation (1), it is clear that the unfrozen water content is only related to the magnitude of the temperature, and is not related to the course and rate of change of the temperature. Therefore, the data to be fitted should be grouped at the same temperature interval (e.g. every 0.1C) and the same amount of data extracted in each group so that the weight of the temperature to the test data points is uniform.
For a certain initial water content omega 0 ＝ω 1 Dry density is rho 1 And ρ 2 The two groups of soil samples are subjected to normalization treatment on the content of unfrozen water. Observing soil samples of different dry densities at the same initial water contentThe data are very close, so the two sets of data are jointly fitted, as in fig. 1.
Similarly, fitting is performed on the soil sample data with different initial water contents respectively to obtain a plurality of groups of fitting parameters in the formula (1), as shown in table 1. (to improve accuracy, water content ω for the build model i It is recommended that above a threshold water content, about above the plastic limit water content, i.e. omega i ≥ω P )，ω P The plastic limit water content.
Table 1 summary of the fitting parameters (a, m, n have been scaled from i, j, k).
In fig. 2, for example, m is 0.8 and n is 2, and the entire curve gradually moves to the left as a gradually increases from 10 to 1000. However, according to the experimental data, the "climbing segment" (sharp phase transition interval) of the curve is concentrated in the range (-5 ℃ to 0 ℃) corresponding to 268.15K to 273.15K for most soils. In other words, 0< a < 10 for the soil mass.
In Table 1, with ω 0 And the fitting obtained a generally has small change amplitude, and the value changes from about 0.67 to about 0.94, so that the influence on the left and right positions of the curve is small. Analysis of the left and right horizontal positions of the curve, from a parameter deductive point of view, results from the onset freezing temperature T f To the initial freezing temperature T f Again depending on the initial water content omega 0 Thus, the following relationship is obtained:
wherein g, h and f are respectively a third fitting parameter, a fourth fitting parameter and a fifth fitting parameter.
See fig. 3.
If the slight influence of the change of a on the position of the curve is neglected, a can be considered as a constant and is taken as the average value of a in table 1, namely, the value is considered as in the formula (1):
taking a as 100 and n as 2 as an example, the curve gradually decreases in the negative temperature region as m gradually increases, i.e., the normalized unfrozen water content becomes smaller and smaller, as shown in fig. 4.
As the initial mass water content increases, m decreases and the rate of change decreases. In particular, when ω 0 Exceeding critical water content omega c At this time, m hardly decreases any more. According to the characteristic, a hyperbolic function or a logarithmic function can be adopted for fitting to obtain:
hyperbolic function:
wherein b and c are respectively a sixth fitting parameter and a seventh fitting parameter.
Logarithmic function:
wherein b1, b2 are the eighth fitting parameter and the ninth fitting parameter, respectively.
See fig. 5.
For example, when a is 100 and m is 0.8, the smaller n is, the slope of the curve at 0 ℃ (273.15K) is
The smaller the value is, as shown in formula (12), the curve is flatter in a climbing section, the variation amplitude of the unfrozen water content of the soil body is small, the variation rate is low, namely the difficulty of freezing the soil body is higher/slower, and the initial water content corresponding to the soil body in a macroscopic view is lower. Conversely, and in the same way, when n is larger, the initial water content macroscopically corresponding to the soil body is higher.
See fig. 6.
Accordingly, by plotting n- ω 0 Can be fitted by using an exponential function, namely:
wherein d, p, q are the tenth fitting parameter, the eleventh fitting parameter, and the twelfth fitting parameter, respectively.
See fig. 7.
By integrating the formula (1), the formula (2), the formula (9), the formula (11) and the formula (13), the calculation formula of the unfrozen water content prediction model can be obtained, namely:
or are obtainable based on formulae (1), (2) (10), (11) and (13):
volumetric ice content θ i ：
Mass ice content omega i ：
Case reference:
next, Shenyang powdered clay freezing temperature analysis is taken as an example. The plastic limit of the soil body is 18.5, the liquid limit is 31.3, and the plasticity index is 12.8. By rho 1 ＝1.4g/cm 3 、ρ 2 ＝1.5g/cm 3 And ρ 3 ＝1.6g/cm 3 Three kinds of stemsDensity, initial mass water content theta of 15-34.4% 0 For example, a freezing test was performed.
As shown in table 2.
TABLE 2 soil sample conditions for the freezing test
Note: in table 2, "√" indicates that the test under the set of conditions was performed, and "-" indicates that the test under the set of conditions was not performed.
And (3) processing and normalizing the volume content data of the unfrozen water measured by the moisture sensor according to the formula (1) and the formula (2), and fitting according to different initial moisture content conditions to form corresponding model fitting parameters.
As shown in table 3.
TABLE 3 model fitting parameters of test data
According to formula (9) and table 3:
or
Fitting m- ω of Table 2 with a hyperbolic function according to equation (10) and FIG. 8 0 The relationship of (a) yields:
or:
R 2 is the goodness of fit.
Fitting n- ω in Table 2 using an exponential function according to equation (12) and FIG. 9 0 The relationship of (1), namely:
R 2 ＝0.984。
therefore, the calculation formula of the unfrozen water content prediction model of the soil body in the test is as follows:
or:
when the accuracy requirement for a is relatively low:
Claims (2)
1. a method for constructing a soil body freezing characteristic curve prediction model is characterized by comprising the following steps:
1) preparing not less than 4 groups of soil samples with different initial mass water contents, and recording as omega 1 、ω 2 、ω 3 ，ω 4 …, setting the initial mass water content at or above the plastic limit water content; preparing a test soil sample according to the target dry density, and preparing the same dry density rho or different dry densities such as rho according to requirements 1 、ρ 2 、ρ 3 …；
2) Fixing probes of a temperature sensor and a moisture sensor in a soil sample, connecting the temperature sensor and the moisture sensor to an acquisition instrument, putting the soil sample into temperature control equipment with negative temperature at positive temperature for freezing, freezing in a stepped manner or continuously freezing, and simultaneously starting data acquisition at an acquisition interval of 1-30 s;
3) the environmental temperature set by the temperature control equipment is lower than the required target temperature, and after the soil body temperature measured by the temperature sensor approaches the set temperature of the temperature control equipment, the soil sample can be taken out, the test is terminated, and the temperature and water content test data are processed;
the unfrozen water content theta is constructed u Water content theta with initial volume 0 A function in the following functional relationship:
wherein a, m and n are respectively a first fitting parameter, a second fitting parameter and a third fitting parameter, and e is the base number of a natural logarithm; t is the temperature.
2. The method for constructing the soil mass freezing characteristic curve prediction model according to claim 1, which is characterized by comprising the following steps:
when the moisture sensor measures the volume water content theta u And the indoor soil sample and the test both adopt the mass water content omega u The conversion relationship is as follows:
ω u ＝θ u ρ w /ρ d formula (2);
where ρ is w Is the density of water, p d I.e. the dry density rho or rho of the soil sample 1 、ρ 2 、ρ 3 …；
Therefore, the volume content data theta of the unfrozen water measured by the moisture sensor is measured u Conversion to mass water content omega u Then, formula (1) is also noted:
fitting, normalizing and deducting by using the formula (1) or the formula (3) to obtain the following relation:
wherein g, h and f are respectively a third fitting parameter, a fourth fitting parameter and a fifth fitting parameter;
taking the average value of a, namely considering that in the formula (1):
fitting by adopting a hyperbolic function to obtain:
hyperbolic function:
wherein b and c are respectively a sixth fitting parameter and a seventh fitting parameter;
exponential function:
wherein b1, b2 are the eighth fitting parameter and the ninth fitting parameter, respectively;
slope of the curve at a temperature of 0 DEG C
The smaller, as shown in formula (12);
n-ω 0 is fitted with an exponential function, i.e.:
wherein d, p and q are a tenth fitting parameter, an eleventh fitting parameter and a twelfth fitting parameter, respectively;
by integrating the formula (1), the formula (2), the formula (9), the formula (11) and the formula (13), the calculation formula of the unfrozen water content prediction model can be obtained, namely:
or are obtainable based on formulae (1), (2), (10), (11) and (13):
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115270515A (en) * | 2022-08-31 | 2022-11-01 | 中国长江三峡集团有限公司 | Soil body state data prediction method, device and equipment based on boundary surface model |
| CN115684240A (en) * | 2022-09-09 | 2023-02-03 | 中国科学院西北生态环境资源研究院 | Method for obtaining initial freezing temperature of water-containing rock mass |
| CN116975788A (en) * | 2023-09-21 | 2023-10-31 | 吉林大学 | Calculation method of unfrozen water content of turfy soil based on fitting function |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115270515A (en) * | 2022-08-31 | 2022-11-01 | 中国长江三峡集团有限公司 | Soil body state data prediction method, device and equipment based on boundary surface model |
| CN115270515B (en) * | 2022-08-31 | 2023-07-07 | 中国长江三峡集团有限公司 | Soil body state data prediction method, device and equipment based on boundary surface model |
| CN115684240A (en) * | 2022-09-09 | 2023-02-03 | 中国科学院西北生态环境资源研究院 | Method for obtaining initial freezing temperature of water-containing rock mass |
| CN116975788A (en) * | 2023-09-21 | 2023-10-31 | 吉林大学 | Calculation method of unfrozen water content of turfy soil based on fitting function |
| CN116975788B (en) * | 2023-09-21 | 2023-12-12 | 吉林大学 | Calculation method of unfrozen water content of turfy soil based on fitting function |
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