A rapid prediction method for loess collapsibility in loess regions

Abstract

The present invention relates to a method for rapidly predicting the collapsibility of loess in a loess region, comprising the following steps: collecting basic physical and mechanical parameters of the loess in the region; conducting site sampling; conducting indoor experiments to obtain the collapsibility coefficient and basic physical parameters of a group of loess in the region through the experiments; determining a two-variable copula model for the loess parameters to characterize the relationship between the two-variable loess parameters; constructing a multi-dimensional variable Vine copula model; constructing a collapsibility prediction model based on the basic physical parameters based on the established multi-dimensional variable Vine copula model; validating the prediction model through experimentally obtained data; and realizing rapid prediction of the collapsibility of loess at a construction site through the validated model. The present invention establishes a prediction model based on the relationship between the loess physical parameters and the collapsibility, which can scientifically and rapidly evaluate the collapsibility of the loess, provide input parameters for the overall evaluation of the loess layer, and provide support for the formulation of construction plans and design schemes.

Description

Technical Field

[0001] The present invention relates to the field of physical state of soil in geotechnical engineering, and in particular to a method for quickly predicting the collapsibility of loess in loess areas, which can be used to accurately and quickly measure the collapsibility of loess in loess areas. Background Art

[0002] Loess, widely distributed in parts of Northeast, Northwest, Central, and East my country, is often collapsible. Collapsible loess is a special type of soil with relatively uniform texture, loose structure, and well-developed pores. When not wetted by water, it generally has high strength and low compressibility. When wetted by water under a certain pressure, the soil structure will quickly break down, resulting in significant additional settlement and a rapid decrease in strength. Therefore, when constructing on collapsible loess sites, comprehensive measures, mainly focusing on foundation treatment, should be adopted to prevent damage to the building caused by foundation collapse, based on the importance of the building, the likelihood of the foundation being wetted, and the strictness of restrictions on uneven settlement during use. More and more projects are being carried out in loess regions in my country, and loess collapsibility testing is a problem that must be addressed, especially in projects carried out in collapsible loess areas. Therefore, the evaluation and prevention of loess collapsibility has always been an important topic in loess research.

[0003] Currently, there are two main methods for predicting loess collapsibility in engineering practice. One is to obtain loess profile samples from the project area through exploratory wells, measure the collapsibility coefficient of the loess at different depths through indoor testing, and then calculate the cumulative collapsibility of the loess within the sampling depth range. The second method is to measure the actual collapsibility of the loess site through large-scale on-site immersion tests. The problem with the first method is that the test cycle is long and the test workload is huge, especially for large-scale projects, which require thousands of sets of samples. The second test faces the problem of a long test cycle and huge cost, but can only obtain experimental results from a single site, and the experimental results are not highly generalizable.

[0004] Therefore, it is urgent to invent a fast and effective technical method for predicting loess collapsibility, strike a balance between loess sampling volume, cost, and scientific evaluation, and be able to quickly evaluate loess collapsibility to provide a reference for engineering construction. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the purpose of the present invention is to provide a method for quickly predicting the collapsibility of loess in loess areas, which uses a small amount of loess measured data in a loess parameter data set to scientifically predict and evaluate loess collapsibility parameters.

[0006] To achieve the above objectives, the present invention is based on the following two insights: (1) the physical parameters and collapsibility of loess under the same geological background have an inherent unified law; (2) the workload of measuring the collapsibility of loess in large-scale projects is large, and a large number of loess collapsibility tests have been carried out in loess areas and a large amount of data has been accumulated.

[0007] The technical solution adopted by the present invention to solve its technical problem is:

[0008] A method for quickly predicting loess collapsibility in loess regions comprises the following steps:

[0009] Step 1: Determine the regional geological background of the loess area and collect the basic physical and mechanical parameters of the loess in the area;

[0010] Step 2: Conduct site sampling;

[0011] Step 3: Conduct indoor experiments to obtain the collapsibility coefficient and basic physical properties of a group of loess in the area;

[0012] Step 4: Based on the basic physical and mechanical parameters collected in step 1, determine the two-variable copula model of loess parameters to characterize the relationship between the two-variable loess parameters;

[0013] Step 5: Construct a multi-variable Vine copula model based on the two-variable copula model to establish the mathematical relationship between loess collapsibility and basic physical properties of loess;

[0014] Step 6: Construct a collapsibility prediction model based on basic physical property parameters according to the multi-dimensional variable Vine copula model established in step 5;

[0015] Step 7: Verify the collapsibility prediction model using the data obtained from the experiment in step 3;

[0016] Step 8: Rapidly predict the collapsibility of loess at the engineering site through the verified model.

[0017] As a specific improvement, in step 1, the basic physical parameters include liquid limit and plastic limit (WL&WP), porosity (e), saturation (Sr), and water content (w), and the mechanical parameters include compression coefficient (a) and wetting coefficient (δ).

[0018] As a specific improvement, in step 2, site sampling includes undisturbed sampling of exploration wells and sampling of basic physical properties of loess. The undisturbed sampling location of the exploration wells is the control engineering site location, which is used to obtain the collapsibility coefficient of the loess in the area for model verification. The sampling location of basic physical properties of loess is all points along the project where collapsibility needs to be calculated, which are used to calculate the basic physical properties of loess.

[0019] As a specific improvement, the undisturbed sampling depth of the exploration well is based on the bottom depth of the engineering construction, the sampling interval is 1m, and the undisturbed sampling size is 15cm×15cm×15cm.

[0020] As a specific improvement, the basic physical property sampling of loess is casing sampling, and a ring knife sample with a diameter of 6.2 cm and a height of 2 cm is obtained.

[0021] As a specific improvement, step 4 includes:

[0022] (1) First, a mathematical model is constructed. Five different copula models are selected, including Gaussian distribution, t distribution, Clayton distribution, Frank distribution, and Gumbel distribution. Gaussian distribution and t distribution are used to characterize positive correlation, while Clayton distribution, Frank distribution, and Gumbel distribution are used to characterize negative tail correlation.

[0023] (2) Using the AIC and BIC evaluation methods, the AIC and BIC values ​​were calculated in the five models, and the optimal two-dimensional copula model was determined with the minimum value.

[0024] As a specific improvement, in step 4, when building the mathematical model, four different marginal distribution models are also selected, including normal distribution, lognormal distribution, Weibull distribution and Johnson-SB. The marginal distribution is used to characterize the original distribution form of the data.

[0025] As a specific improvement, in step 5, the mathematical expression of the Vine copula model of multidimensional variables is:

[0026]

[0027] Where f represents the marginal distribution of different parameters;

[0028] c represents the two-variable copula model, c 1，2 refers to the best copula model that fits X1 and X2, c 1，4|2 It refers to the optimal copula model of X1 and X4 when X2 is the conditional probability. Similarly, all c are two-dimensional copula models, which are combined into a multidimensional Vine copula model.

[0029] As a specific improvement, step 6 includes:

[0030] (1) Invert the multi-variable Vine copula model obtained in step 5;

[0031] (2) The conditional probability distribution formula for loess collapsibility is obtained through the conditional probability formula P(A|B=P(AB) / P(B)):

[0032]

[0033] Represents the probability of collapsibility coefficient based on physical property parameters;

[0034] The joint probability distribution of the representative physical property parameters and the collapsibility coefficient;

[0035] Represents the joint probability of physical property parameters.

[0036] As a specific improvement, in step 8, the moisture content, specific gravity and liquid limit data of soil samples at different stratum depths at the test point are obtained and input into the calculation model constructed in step 6 to obtain the collapsibility of loess in the original stratum unit at different stratum depths at the test point.

[0037] The beneficial effects of the technical solution of the present invention are: based on the relationship between loess physical properties and collapsibility, the present invention collects and analyzes a large amount of data in advance and establishes data correlations. This allows for a scientific and rapid evaluation of loess collapsibility, providing input parameters for the overall evaluation of loess strata and supporting the formulation of construction and design plans. The present invention provides rapid evaluation and a wide range of applications. Specifically, the present invention has at least the following practical effects:

[0038] (1) Based on the preliminary research on loess physical property parameters, collapsibility parameters and their correlation, this paper realizes a joint model (high-dimensional model) of loess physical property indicators and collapsibility. Based on this, a rapid evaluation method for loess collapsibility is developed. The model is verified by experimental data and can make an accurate and rapid evaluation of collapsibility based on only the physical property parameters.

[0039] (2) The present invention has low cost. In the past, it was necessary to dig a well to manually take samples and then test the collapsibility (the collapsibility test is time-consuming and costly). Now, it only requires drilling sampling (drilling sampling is continuous sampling, which can be based on actual needs, generally taking a sample every 1m, with low sampling cost and fast speed) and then measuring the physical property indicators (the physical property indicators are simple and easy to measure), which reduces the workload of the test.

[0040] (3) It can balance the errors of traditional collapsible tests (indoor tests and on-site immersion tests) and correct the error coefficients of indoor tests and immersion tests;

[0041] (4) The method of the present invention is generalizable and can evaluate physical property parameters based on other parameters. For example, after establishing a multidimensional model, we are concerned about collapsibility and then develop a method for calculating collapsibility. Then, other physical property indices, such as pore water content, can also be calculated by developing analogy models based on other physical property indicators. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0043] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, provided they do not affect the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0044] Figure 1 This is a flow chart of a method for predicting loess collapsibility according to one embodiment of the present invention;

[0045] Figure 2 A diagram showing a data relationship of modeling of a subway project in accordance with a method for predicting loess collapsibility according to an embodiment of the present invention;

[0046] Figure 3 A diagram showing the structure of a two-dimensional copula model for a subway project modeling method for predicting loess collapsibility according to one embodiment of the present invention (displays of X4 and X7 under different copula models);

[0047] Figure 4 This is a structural diagram of an R-vinecopula model for modeling a subway project in a method for predicting loess collapsibility according to an embodiment of the present invention;

[0048] Figure 5 This is a schematic diagram of the inversion results of the R-vinecopula model for modeling a subway project in a method for predicting loess collapsibility according to an embodiment of the present invention;

[0049] Figure 6 This is a diagram of the prediction results of the R-vinecopula model for modeling a subway project in a loess collapsible prediction method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0051] In the present invention, unless otherwise expressly specified or limited, terms such as "disposed," "installed," "connected," "connected," and "fixed" should be understood in a broad sense. For example, they may refer to any reasonable and feasible arrangement, including fixed connection, detachable connection, or integration; mechanical connection or electrical connection; direct connection or indirect connection through an intermediate medium; and internal communication between two components or interaction between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0052] It should be understood that the terms "comprises / comprising," "consisting of," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a product, apparatus, process, or method comprising a list of elements includes not only those elements but also, if necessary, other elements not explicitly listed, or elements inherent to such product, apparatus, process, or method. In the absence of further limitations, the elements defined by the phrases "comprises / comprising," "consisting of," do not preclude the presence of additional identical elements in the product, apparatus, process, or method comprising the elements.

[0053] It should also be understood that terms such as "upper", "lower", "front", "back", "left", "right", "top", "bottom", "inside", "outside", "center", and "central" to indicate directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device, component or structure referred to must have a specific direction, be constructed or operate in a specific direction, and should not be understood as limiting the present invention.

[0054] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature identified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0055] Loess is formed after certain geological processes. Therefore, in the same region, under similar genetic backgrounds, the basic physical properties and physical and mechanical parameters of loess also have certain similarities.

[0056] The macro-engineering properties of loess are the external manifestations of its inherent fundamental properties influenced by external factors. Current understanding of loess collapsibility suggests that this is influenced by its composition and internal particle structure, manifesting under the action of water. Selecting appropriate loess parameters to reflect the inherent particle structure and establishing a relationship between these parameters and collapsibility provides a new approach to predicting loess collapsibility.

[0057] Based on the above principles, the present invention provides a method for quickly predicting the collapsibility of loess in loess areas. Figure 1 This method can greatly expand the scope of use of a large amount of current survey data in the loess region and reduce the cost of loess collapsibility measurement in the loess region. It is of great significance, especially for large-scale linear projects in the loess region that need to carry out a large number of collapsibility tests, and can minimize the time and economic costs of collapsibility tests.

[0058] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0059] This paper uses an example to illustrate the method for predicting loess collapsibility. This example uses the Dongshan Loess Plateau area in Taiyuan as the engineering background site and a project in Taiyuan as the engineering entity. The following steps are followed:

[0060] Step 1: Determine the regional geological background of the loess area and collect the basic physical and mechanical parameters of the loess in the area;

[0061] The existing engineering density and scientific research achievements in the loess region have generated a large amount of survey data, meeting the requirements for data collection. In this step, based on the geological background of the project site, relevant historical research parameters, and the progress of previous projects, we collected historical survey and literature research data for engineering sites with similar geological backgrounds. This includes basic physical properties: liquid limit and plastic limit (WL&WP), porosity (e), saturation (Sr), water content (w), and mechanical parameters: compressibility (a), collapsibility (δ), etc.

[0062] In this case, we collected the water immersion test data and some survey data from the Dongshan Loess Plateau area in Taiyuan. The data relationship is as follows: Figure 2 As shown, X1=W L &X2=W P (Liquid limit), X3=w (water content), X4=Sr (saturation), X5=e (porosity), X6=a (compressibility), X7=δ (collapsibility). Figure 2It shows that there is a correlation between loess parameters, but this correlation is not very strong. There are linear, nonlinear, and strong tail correlations. For multidimensional modeling with complex correlations, the traditional normal distribution is no longer applicable. For this complex correlation, the present invention proposes a modeling method based on vine-copula, which will be explained in detail later.

[0063] Step 2: sampling at different construction sites within the construction area;

[0064] In this step, loess samples are taken according to the requirements for testing the basic physical properties of loess, and according to the sampling requirements, field sampling includes undisturbed sampling of the exploration well and sampling of the basic physical properties of loess.

[0065] Traditional collapsible tests require taking undisturbed 15×15×15cm samples (minimum standard). Sampling requires digging a well with a diameter of no less than 500m (the depth is determined by the depth of the soil layer, generally around 30m). Then people go down into the well and chisel out the samples.

[0066] The sampling depth for undisturbed sampling in this invention is based on the depth of the construction site, with a sampling interval of 1 meter and a sample size of 15 cm × 15 cm × 15 cm. Sample moisture content is tested on-site using the combustion method. The undisturbed sampling location for the exploration well is the control project site, used to determine the collapsibility coefficient of the loess in the area. This is used to modify the collapsibility calculation model established based on previous project data, conduct model verification, and improve model accuracy.

[0067] Loess basic physical property sampling locations are located at all points along the project where collapsibility calculations are needed. Casing sampling is used, requiring only a single cutter ring sample (6.18 cm diameter, 2 cm height). A common small-diameter drill (127 mm) is used, eliminating the need for a Luoyang shovel to dig a well. Sampling is fast and easy with a standard small-diameter drill rig (127 mm). Loess basic physical property sampling is used to calculate the basic physical parameters of the loess. Once these basic physical parameters are obtained, the collapsibility of the corresponding points can be calculated.

[0068] The above sampling operation requires a small amount of sample, the sampling method is simple and easy to operate, and the sampling cost is greatly reduced.

[0069] Step 3: Conduct indoor tests to measure the collapsibility coefficient of undisturbed samples from the exploration well and the basic physical properties of all samples;

[0070] This step involves conducting different tests based on the samples obtained in Step 2 for different purposes. The test standards refer to the Standard for Geotechnical Test Methods (GB / T 50123-2019). The collapsibility coefficient of the loess in the area is obtained by taking undisturbed soil samples from exploration wells for model validation. The basic physical property test group obtains the basic physical properties of the loess at the collapsible points to be tested, which are used to perform collapsible calculations required for the project.

[0071] Step 4, characterize the relationship between the loess parameters of the two variables;

[0072] The implementation of step 1, step 2 and step 3 completes the data preparation basis for the application of the invention. In this step, the first step of mathematical model construction is required. Figure 2 It shows that there is a correlation between loess parameters, but this correlation is not very strong. There are linear, nonlinear, and strong tail correlations. Therefore, for multidimensional modeling with complex correlations, the traditional normal distribution is no longer applicable. In response to this complex correlation, the present invention proposes a modeling method based on vine-copula (mathematical method; code implementation), which can establish relationships layer by layer through two-dimensional iteration, overcome the tail correlation, nonlinear correlation, and negative correlation of data, and has strong practicality in loess parameter modeling.

[0073] Therefore, the first step in building the mathematical model is to determine the copula model for the two-dimensional loess parameters. Five different copula models and four different marginal distribution models (Note: Probability analysis is represented as PDF model below and in the accompanying figures) were selected (Tables 1 and 2). The copula models are used to characterize positive correlation (Gaussian distribution, t distribution) and negative tail correlation (Clayton distribution, Frank distribution, Gumbel distribution), respectively. The marginal distributions are used to characterize the original distribution of the data. This is the basis for data inversion after copula modeling. The data calculated in the copula space are transformed into the measured space through the marginal distributions.

[0074] It should be noted that in actual operation, the copula model and marginal distribution model here are determined according to the distribution form of the data. The model selection can be diverse, and different choices can be made according to the data distribution form in different regions and different geological backgrounds. The ones listed here are limited to use in this example. Different copula models and marginal distribution models have no effect on the core method of the present invention. They can be flexibly selected according to the actual data set situation in the future, and are not intended to limit the present invention.

[0075] Table 1 Five different copula models selected

[0076]

[0077] Table 2 Marginal distribution model

[0078]

[0079] by Figure 2 The X4 and X7 in the example are used to illustrate the model selection of two-dimensional copula. The application results of five different copula models on X4 and X7 are shown in Figure 3 In this step, the maximum likelihood estimation is used to calculate the model parameters. This method is easy to implement mathematically and the results are reliable. Figure 3 A rotated copula model is also presented. This model is an extension of the Frank and Clayton model (a rotated form of the model space). Among the five models, the most appropriate one must be selected to characterize the relationship between loess parameters. Here, the AIC and BIC evaluation methods are used to determine the optimal model parameters. The model with the lowest AIC and BIC values ​​is the most appropriate. The same applies to selecting copula models between any two parameters.

[0080]

[0081]

[0082] Where: c is one of the five copula models, n represents the number of model parameters, are the copula model parameters.

[0083] Taking X4 and X7 as examples, we can calculate the values ​​of five different copulas:

[0084]

[0085] The Frank model that obtains the minimum AIC and BIC is the best two-dimensional copula model.

[0086] Step 5: Construct a Vine copula model of multi-dimensional variables based on the results of step 4;

[0087] The core of the present invention is to explore the correlation between all data. Therefore, this step is to build a multi-dimensional copula model (vine copula) based on the two-variable copula model on the basis of step 4 until a vine copula model containing all parameters is formed.

[0088] The copula model structure used in this example is as follows Figure 4As shown. The order of the first-level variables in the figure is just a demonstration in this example. This order has little effect on the model results, so in actual operation, you can arbitrarily order them as needed. After determining the copula model between each adjacent parameter according to the solution in step 4, you can determine the second-level copula model based on the new copula model until all two variables are determined to have deviated from the model (see step 4 for the determination method). The mathematical expression of the multidimensional model can be written according to the recursive formula. In this example, the expression is:

[0089]

[0090] Each factor in the formula corresponds to Figure 4 An elliptical unit in .

[0091] f represents the marginal distribution of different parameters;

[0092] c represents the two-variable copula model, c 1，2 refers to the best copula model that fits X1 and X2, c 1，4|2 This refers to the optimal copula model for X1 and X4, with X2 as the conditional probability. Similarly, all c copula models are two-dimensional, combined into a multidimensional Vine copula model. The multidimensional Vine copula model can fit diverse correlations between data, overcoming the limitations of the traditional multivariate normal distribution, which cannot capture negative correlations and exhibits tail correlations.

[0093] Step 6: constructing a collapsibility prediction model based on physical property parameters;

[0094] In the previous step 5, the initial construction of the model is basically achieved. Here, we first need to perform a preliminary inversion of the model. The purpose of the preliminary inversion is to verify the correctness and robustness of the multi-dimensional model. If the preliminary inversion is effective, we can then perform the derivation calculation. The inversion result is as follows Figure 5 As shown, the core of this step is to obtain the method of collapsibility prediction based on the conditional probability formula (P(A|B=P(AB) / P(B))), that is, the conditional probability distribution formula:

[0095]

[0096] Represents the probability of collapsibility coefficient based on physical property parameters;

[0097] The joint probability distribution of the representative physical property parameters and the collapsibility coefficient;

[0098] represents the joint probability of physical property parameters;

[0099] Based on this formula and the method and formula obtained in step 5, the conditional probability distribution of collapsibility based on physical property parameters is obtained through conditional probability calculation. Accordingly, under different physical property parameters, the probability distribution of collapsibility will present a corresponding distribution form. Taking the peak value of the partition curve as the predicted value, the prediction of collapsibility is preliminarily realized.

[0100] Step 7: Model verification based on the measured data of the verification profile;

[0101] In step 3, the measured values ​​of collapsibility and basic physical parameters of two points on the site were obtained through experiments. In this step, the data of these two points are substituted into the calculation formula of step 6 to obtain the probability distribution curve of the predicted collapsibility values ​​of the two points ( Figure 6 In verification conditions 1 and 2, the 95% confidence intervals of the peak values ​​of the probability distribution curves of the measured and predicted values ​​are completely consistent, and the prediction error is within the range allowed by the project, indicating that the method is feasible and the prediction results are reliable.

[0102] It should be noted that undisturbed sampling in exploratory wells is performed to validate the model, and theoretically, only a single point is required. The principle for basic physical property sampling is that large engineering projects often require collapsibility measurements at numerous locations. For example, along a subway line, hundreds of locations often require collapsibility measurements. Therefore, if collapsibility needs to be calculated at a specific point, a basic physical property sample (drilling sample) can be collected at the corresponding point.

[0103] Step 8: Implement collapsibility prediction for other remaining points on the project site;

[0104] The data of the verification points show that the method proposed in the present invention is feasible, and the collapsibility of all other points can be quickly obtained by bringing the physical property parameters of other points into the model.

[0105] It can be concluded that the present invention realizes rapid prediction of loess collapsibility based on engineering practice, big data mining and mathematical methods: determining the geological background of the engineering site, collecting past engineering and scientific research literature data in the regional loess area; obtaining corresponding related parameters of a small number of loess profile samples in the area to be evaluated and loess profile physical parameters of the collapsibility points to be measured through experiments; by constructing a mathematical relationship between loess collapsibility and basic physical parameters of loess: multidimensional probability modeling between loess parameters is realized through the vine copula method, which can overcome the tail correlation between loess parameters and characterize the intrinsic connection between loess parameters to the greatest extent; the conditional probability distribution relationship between the basic physical parameters of regional loess and collapsibility is obtained through conditional probability formula calculation, and the loess collapsibility calculation model is obtained; the calculation model is verified by experimentally measured profile data; the verified model can be widely used in the prediction and evaluation of loess collapsibility in loess areas with the same geological conditions.

[0106] It is easy for those skilled in the art to understand that, under the premise of no conflict, the above preferred solutions can be freely combined and superimposed.

[0107] At this point, those skilled in the art will recognize that, although exemplary embodiments of the present invention have been shown and described in detail herein, many other variations or modifications consistent with the principles of the present invention may be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the present invention. Therefore, the scope of the present invention should be understood and deemed to cover all such other variations or modifications.

Claims

1. A method for rapid prediction of loess collapsibility in loess regions, characterized in that: The steps include: Step 1: Determine the regional geological background of the loess area and collect the basic physical and mechanical parameters of the loess in this loess area; Step 2: Conduct site sampling; Step 3: Conduct indoor experiments to obtain the collapsibility coefficient and basic physical properties of a group of loess in this loess region; Step 4: Based on the basic physical and mechanical parameters collected in step 1, determine the two-variable copula model of loess parameters to characterize the relationship between the two-variable loess parameters; Step 5: Construct a multi-variable Vine copula model based on the two-variable copula model to establish the mathematical relationship between loess collapsibility and basic physical properties of loess; Step 6: Construct a collapsibility prediction model based on basic physical property parameters according to the multi-dimensional variable Vine copula model established in step 5; Step 7: Verify the collapsibility prediction model using the data obtained from the experiment in step 3; Step 8: Rapidly predict the collapsibility of loess at the engineering site using the validated model; in Step 4 includes: (1) First, a mathematical model is constructed. Five different copula models are selected, including Gaussian distribution, t distribution, Clayton distribution, Frank distribution, and Gumbel distribution. Gaussian distribution and t distribution are used to characterize positive correlation, while Clayton distribution, Frank distribution, and Gumbel distribution are used to characterize negative tail correlation. (2) Using the AIC and BIC evaluation methods, the AIC and BIC values ​​were calculated among the five models, and the optimal two-dimensional copula model was determined by taking the minimum value; Step 6 includes: (1) Invert the multi-variable Vine copula model obtained in step 5; (2) The conditional probability distribution formula for loess collapsibility is obtained through the conditional probability formula P(A|B=P(AB) / P(B)): ； Where: Represents the probability distribution of collapsibility coefficient based on physical property parameters; The joint probability distribution of the representative physical property parameters and the collapsibility coefficient; Represents the joint probability distribution of physical property parameters.

2. The method for rapid prediction of loess collapsibility in loess regions according to claim 1, wherein: In step 1, the basic physical properties include liquid limit W L , plastic limit W P , porosity e, saturation Sr, water content w, and mechanical parameters include compression coefficient a and collapsibility coefficient δ.

3. The method for rapid prediction of loess collapsibility in loess regions according to claim 1, characterized in that: In step 2, site sampling includes undisturbed sampling of exploration wells and sampling of basic physical properties of loess. The undisturbed sampling location of the exploration wells is the control project site location, which is used to obtain the collapsibility coefficient of loess in the loess area for model verification. The sampling location of basic physical properties of loess is all points along the project where collapsibility needs to be calculated, which are used to calculate the basic physical properties of loess.

4. The method for rapid prediction of loess collapsibility in loess regions according to claim 3, characterized in that: The undisturbed sampling depth of the exploration well is based on the bottom boundary depth of the engineering construction, the sampling interval is 1m, and the undisturbed sampling size is 15cm×15cm×15cm.

5. The method for rapid prediction of loess collapsibility in loess regions according to claim 3, characterized in that: The basic physical property sampling of loess is performed by casing sampling, and a ring knife sample with a diameter of 6.2 cm and a height of 2 cm is obtained.

6. The method for rapid prediction of loess collapsibility in loess regions according to claim 1, characterized in that: In step 4, when building the mathematical model, four different marginal distribution models are selected, including normal distribution, lognormal distribution, Weibull distribution and Johnson-SB. The marginal distribution is used to characterize the original distribution form of the data.

7. The method for rapid prediction of loess collapsibility in loess regions according to claim 1, characterized in that: In step 5, the mathematical expression of the Vine copula model of multidimensional variables is: ； Where: f represents the marginal probability distribution of different parameters; X1=Liquid limit W L , X2=plastic limit W P , X3=water content w, X4=saturation Sr, X5=porosity e, X6=compression coefficient a, X7=wetting coefficient δ; c represents the two-variable copula model, c 1,2 refers to the best copula model that fits X1 and X2, c 1,4|2 It refers to the optimal copula model of X1 and X4 when X2 is the conditional probability. And so on, all c are combined into a multi-dimensional variable Vinecopula model.

8. The method for rapid prediction of loess collapsibility in loess regions according to claim 1, characterized in that: In step 8, the moisture content, specific gravity and liquid limit data of soil samples at different stratum depths at the test point are obtained and input into the calculation model constructed in step 6 to obtain the collapsibility of loess in the original stratum unit at different stratum depths at the test point.

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