Method for simulating and judging humidifying deformation coefficient of undisturbed loess

Abstract

The invention provides a method for simulating and judging the humidifying deformation coefficient of undisturbed loess, and relates to the technical field of geotechnical engineering.The method for simulating and judging the humidifying deformation coefficient of the undisturbed loess comprises the steps that on the basis of the undisturbed loess of a target area, a structure reinforcing component is added, preparing artificial structural loess meeting preset conditions and taking the artificial structural loess as a simulation sample; humidifying deformation tests under multi-stage pressure loads are conducted on the simulation samples with the different water contents respectively, and the humidifying deformation coefficient is recorded and determined according to the deformation stability height before and after humidifying; and constructing a loess humidifying deformation function model by taking the moisture content and the pressure load as independent variables and the humidifying deformation coefficient as a dependent variable. According to the method, the humidifying deformation of the loess in the unsaturated state can be measured, and the method has practical applicability and prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and more specifically, to a method for simulating and determining the wettability deformation coefficient of undisturbed loess. Background Technology

[0002] Loess, as a Quaternary sediment, differs from other soils in its morphology and composition. It possesses physical characteristics such as high porosity, low density, and high soluble salt content. Due to its unique formation mechanism, mineral composition, and mechanical properties, it has attracted widespread attention. Because of this special structure, collapsible loess often exhibits significant compressibility under the coupled effects of multiple factors such as water immersion and load, leading to problems such as local collapse and collapsing deformation of the foundation, which poses a great challenge to practical engineering.

[0003] In related technologies, the evaluation of loess collapsibility mainly relies on the collapsibility coefficient specified in the "Building Standard for Collapsible Loess Areas". This coefficient is obtained by measuring the deformation of the sample after it is saturated with water. However, for loess in unsaturated or other complex working conditions, the related technologies are difficult to accurately measure and evaluate the deformation of collapsible loess during the wetting process, especially in the unsaturated state. Moreover, the mechanical testing of unsaturated soil is complex, time-consuming, and costly, making it difficult to promote widely. In addition, the physical and mechanical properties and collapsibility characteristics of natural loess fluctuate significantly due to differences in the depositional environment, resulting in poor representativeness and repeatability of the test results. Summary of the Invention

[0004] The problem to be solved by this invention is at least one of the following technical issues: difficulty in accurately measuring humidification deformation under unsaturated conditions; complex and costly operation of unsaturated soil mechanics tests; and poor representativeness and repeatability of test results due to differences in the depositional environment of natural loess.

[0005] To address the above problems, this invention provides a method for simulating and determining the wettability deformation coefficient of undisturbed loess, comprising: Based on the original loess of the target area, structural reinforcement components are added to prepare artificial structural loess that meets the preset conditions and serve as a simulation sample. The physical and mechanical properties and collapsibility coefficient of the artificial structural loess that meets the preset conditions are consistent with the physical and mechanical properties and collapsibility coefficient of the original loess. The simulated samples with different moisture contents were subjected to humidification deformation tests under multi-level pressure loads. The results were recorded and the humidification deformation coefficient was determined based on the deformation stability height before and after humidification. The humidification deformation coefficient is used to characterize the deformation response of loess with increasing moisture content after the pressure load is applied in an unsaturated state. Using the moisture content and pressure load as independent variables and the humidification deformation coefficient as dependent variable, a loess humidification deformation function model is constructed. The undisturbed loess was subjected to a humidification deformation test under the same test conditions as the simulated sample to obtain the measured humidification deformation coefficient. The measured humidification deformation coefficient was compared with the predicted value of the loess humidification deformation function model. If the relative error between the two met the preset requirements, the model was deemed to be qualified and the qualified loess humidification deformation function model was obtained. The qualified loess humidification deformation function model was used to predict the humidification deformation coefficient of the undisturbed loess to be treated.

[0006] Optionally, the step of conducting multi-level pressure load humidification deformation tests on the simulated samples with different moisture contents, recording the results, and determining the humidification deformation coefficient based on the deformation stability height before and after humidification includes: Consolidation tests were conducted on the simulated specimens with different moisture content gradients and multiple pressure loads under multiple pressure loads, respectively. For each level of pressure load, the height of the simulated specimen after deformation stabilization is recorded. Based on the height of the height after deformation stabilization corresponding to the moisture content gradients of two adjacent levels under the same pressure load, the humidification deformation coefficient is determined.

[0007] Optionally, determining the humidification deformation coefficient based on the height after deformation stabilization corresponding to two adjacent moisture content gradients under the same pressure load includes: The humidification deformation coefficient is determined based on the following formula: = ( ) / ; in: Indicates the coefficient of deformation due to humidification; This represents the height of a soil sample with the current moisture content gradient after it has been immersed in water and moistened under a set pressure, once the deformation has stabilized. The height of the soil sample at the next level of moisture content gradient after deformation stabilization following immersion and wetting under the set pressure is indicated. This indicates the original height of the soil sample.

[0008] Optionally, the step of constructing a loess wetting deformation function model with the moisture content and the pressure load as independent variables and the wetting deformation coefficient as the dependent variable includes: Based on the test results of the humidification deformation test of the simulated sample, with the moisture content and the pressure load as independent variables and the humidification deformation coefficient as dependent variable, the test data are systematically classified and nonlinearly fitted to construct a three-dimensional response surface model that reflects the comprehensive effect of stress-humidification deformation-moisture content. The three-dimensional response surface model is fitted with nonlinear regression to establish the loess wetting deformation function model, which characterizes the combined influence of the pressure load and the moisture content on the wetting deformation coefficient.

[0009] Optionally, the loess wetting deformation function model is obtained by fitting a composite double exponential function.

[0010] Optionally, the loess wetting deformation function model is expressed by the following formula: ; in, This represents the humidification deformation coefficient. This indicates the moisture content. This indicates the pressure load. Based on the base intercept, B, C, D, E, F, G, and H are morphological parameters determined through nonlinear regression fitting.

[0011] Optionally, the undisturbed loess is subjected to a humidification deformation test under the same test conditions as the simulated sample to obtain a measured humidification deformation coefficient; the measured humidification deformation coefficient is compared with the predicted value of the loess humidification deformation function model, and if the relative error between the two meets a preset requirement, the model is deemed to be qualified; the qualified loess humidification deformation function model is used to predict the humidification deformation coefficient of the undisturbed loess, including: The loess wetting deformation function model is verified using the original loess in the target area. The wetting deformation test is carried out under the same water content gradient and pressure load as the simulated sample to obtain the measured wetting deformation coefficient of the original loess under different working conditions. The same water content gradient and pressure load are input into the loess wetting deformation function model to obtain the model prediction value. The measured humidification deformation coefficient under each of the aforementioned working conditions is compared with the model prediction value to determine the relative error under each of the aforementioned working conditions; If the relative error corresponding to each pressure load under all the moisture content gradients is less than the first preset threshold, the loess wetting deformation function model is deemed to have passed the verification.

[0012] Optionally, the method further includes: If the relative error corresponding to the pressure load under any of the moisture content gradients is greater than or equal to the first preset threshold, the verification of the loess wetting deformation function model is deemed unqualified. The proportioning and screening of the artificial structural loess is repeated, and the step of preparing artificial structural loess that meets the preset conditions and using it as a simulation sample is returned until the relative error corresponding to each pressure load under all the moisture content gradients is less than the first preset threshold, at which point the verification is deemed qualified.

[0013] Optionally, the step of preparing artificially structured loess as a simulation sample by adding structural reinforcing components to the undisturbed loess of the target area, and having physical and mechanical properties and collapsibility coefficients that meet the corresponding preset similarity to the undisturbed loess, includes: The original loess in the target area was sampled, and multiple groups of artificial structural loess mixed with structural reinforcement components were prepared based on the physical and mechanical properties of the original loess. The collapsibility coefficient of each group of artificial structural loess and the original loess under different pressure loads was measured. Based on the collapsibility coefficients under different pressure loads, the collapsibility coefficient-pressure fitting curves of the artificial structured loess and the undisturbed loess at a set moisture content were plotted respectively. The physical and mechanical properties of the artificially structured loess are compared with those of the original loess to select the artificially structured loess whose physical and mechanical properties meet the first preset similarity. The collapsibility coefficient-pressure fitting curve of the selected artificial structured loess at the set moisture content is compared with the collapsibility coefficient-pressure fitting curve of the undisturbed loess at the same moisture content. The artificial structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity is selected as the simulated sample.

[0014] Optionally, the step of comparing the collapsibility coefficient-pressure fitting curve of the selected artificially structured loess at the set moisture content with the collapsibility coefficient-pressure fitting curve of the undisturbed loess at the same moisture content, and selecting the artificially structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity as the simulated sample includes: The collapsibility coefficient-pressure fitting curve of the selected artificial structured loess at the set moisture content is compared with the collapsibility coefficient-pressure fitting curve of the undisturbed loess to determine the first error between the two. When the first error is less than the second preset threshold, it is determined that the similarity between the collapsibility coefficient-pressure fitting curve of the selected artificial structured loess and the collapsibility coefficient-pressure fitting curve of the undisturbed loess meets the second preset similarity, and the corresponding artificial structured loess is used as the simulated sample.

[0015] This invention prepares artificially structured loess as a simulation sample by adding structural reinforcement components to the original loess of the target area. The artificially structured loess exhibits physical and mechanical properties and a collapsibility coefficient that are similar to the original loess at a predetermined level. Because the artificially structured loess is precisely controllable, it can replace natural original soil for benchmark testing. This not only reproduces the chemical cementation and dissolution mechanisms of natural loess but also eliminates testing errors caused by the inhomogeneity of natural soil samples, providing a repeatable standard physical benchmark and reducing exploration costs and experimental cycles. By conducting multi-level pressure load humidification deformation tests on the simulation samples with different moisture contents, and determining the humidification deformation coefficient based on the deformation stability height before and after humidification, the invention accurately characterizes the progressive deformation response of loess in the unsaturated state with increasing moisture content, overcoming the limitation that the traditional collapsibility coefficient is only applicable to the saturated state. Using the experimental data of the artificially structured loess, with moisture content and pressure load as the basis, the invention further refines the simulation. A variable-based loess wetting deformation function model is constructed, transforming discrete experimental data into a continuous mathematical function expression. This model reflects the deformation response law of soil under unsaturated conditions caused by water-mechanical coupling, avoiding the technical limitations of simplifying the unsaturated wetting deformation process to a saturated collapsing process. This improves the pertinence and accuracy of unsaturated loess deformation evaluation. The model is validated using undisturbed loess under the same experimental conditions as the simulated sample. The relative error between the measured and predicted values ​​determines the model's qualification. Using the validated loess wetting deformation function model, the wetting deformation response of unsaturated loess can be directly predicted under known site moisture content and design load conditions. This provides a supplementary quantitative index, distinct from the traditional collapsibility coefficient, for foundation deformation analysis and engineering design in collapsible loess areas. It is applicable to engineering deformation evaluation under unsaturated conditions, ensuring the model's practical applicability and predictive accuracy for natural loess. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the method for simulating and determining the wettability deformation coefficient of undisturbed loess in an embodiment of the present invention; Figure 2 The curves showing the variation of various physical and mechanical properties with depth in the embodiments of the present invention are shown. Figure 3 This is a flowchart of the large ring cutter sample preparation process in an embodiment of the present invention; Figure 4 The figures show the fitting curves of the collapsibility coefficients of structured loess and undisturbed loess prepared with different materials in the embodiments of the present invention. Figure 5 This is a curve showing the relationship between the wettability deformation coefficient of loess and pressure in an embodiment of the present invention (taking 5% salt and 2% cement as an example); Figure 6 This is a graph showing the humidification deformation coefficient of undisturbed loess under vertical pressure and the curves of various pressure levels in an embodiment of the present invention; Figure 7The original loess δ under different moisture contents in the embodiments of the present invention SW curve; Figure 8 This is a surface showing the humidification deformation coefficient of undisturbed loess with different moisture contents in an embodiment of the present invention; Figure 9 The embodiments of the present invention show undisturbed loess and artificially structured loess under different pressures. SW curve; Figure 10 This is a surface showing the load and moisture content humidification deformation coefficient of artificially structured loess in this embodiment of the invention; Figure 11 This is a surface fitting diagram showing the influence of artificial structural loess load and moisture content on the humidification deformation coefficient in an embodiment of the present invention. Figure 12 This is a flowchart of a method for simulating and determining the wettability deformation coefficient of undisturbed loess in another embodiment of the present invention. Detailed Implementation

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0018] It should be noted that relational terms such as "first" and "second" in this invention are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0019] In the description of this specification, references to terms such as "embodiment," "one embodiment," and "one implementation" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or implementation is included in at least one embodiment or illustrative implementation of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or implementation. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or implementations.

[0020] Reference Figure 1As shown in the figure, this invention proposes a method for simulating and determining the wettability deformation coefficient of undisturbed loess, including: S100: Based on the original loess of the target area, add structural reinforcement components to prepare artificial structural loess that meets preset conditions and use it as a simulation sample. The physical and mechanical properties and collapsibility coefficient of the artificial structural loess that meets the preset conditions are similar to those of the original loess.

[0021] Specifically, undisturbed loess samples were collected from the target area, and their physical and mechanical properties (such as dry density, void ratio, liquid limit, and plastic limit) and collapsibility coefficient were measured. Using these properties as a benchmark, remolded soil was mixed with structural reinforcing components such as cement and soluble salts to prepare multiple groups of artificial structural loess with different proportions. The physical and mechanical properties and collapsibility coefficient of each group of artificial soil were measured. The collapsibility coefficient is a quantitative indicator characterizing the degree of additional deformation that loess undergoes after being soaked in water. This coefficient reflects the sensitivity of loess to structural damage and compressive deformation under water conditions. The physical and mechanical properties of the artificial soil were compared with those of the undisturbed loess to select proportions with similar physical properties. The collapsibility characteristics of the selected artificial soil (e.g., the law of change of the collapsibility coefficient with pressure at a certain moisture content) were then comprehensively compared with those of the undisturbed loess, and the artificial soil with the collapsibility characteristics closest to that of the undisturbed loess was selected as the simulation sample. Since artificial samples are prepared uniformly according to a preset ratio under laboratory conditions, their material composition and structural distribution are highly homogeneous. This avoids the significant fluctuations in physical properties and collapsibility characteristics between different samples caused by factors such as differences in depositional environment and random particle arrangement of natural loess, thereby eliminating heterogeneity interference caused by uneven sampling of natural loess.

[0022] S200: Perform humidification deformation tests on the simulated samples with different moisture contents under multi-level pressure loads, record the results and determine the humidification deformation coefficient based on the deformation stability height before and after humidification. The humidification deformation coefficient is used to characterize the deformation response of loess with increasing moisture content after applying the pressure load in an unsaturated state.

[0023] Specifically, according to multiple moisture content gradients (such as several gradients from low to high) and multiple pressure loads (such as several levels from low to high), consolidation tests are conducted on simulated specimens with different moisture content gradients under multiple pressure loads. For each simulated specimen with each moisture content gradient under each pressure load, the height after deformation stabilization is recorded. Then, under the same pressure load, the deformation stabilization heights corresponding to two adjacent moisture content gradients are taken. By calculating the ratio of the difference between the two to the original height of the specimen, the humidification deformation coefficient during the process of increasing from the current moisture content to the next moisture content is determined, thereby obtaining a dataset of humidification deformation coefficients under different combinations of moisture content and pressure loads.

[0024] It should be noted that the collapsibility coefficient characterizes the sudden collapse deformation of a soil sample when it is directly soaked in water from its natural state to saturation, reflecting the extreme situation under saturated conditions; while the humidification deformation coefficient characterizes the gradual deformation of a soil sample in an unsaturated state as the water content increases step by step, reflecting the gradual deformation law of loess in actual engineering when it is exposed to water, which is more in line with the actual situation of loess water content changes under natural conditions. Through the humidification deformation coefficient, the sensitivity of loess to water content changes and deformation response characteristics under different pressure loads can be quantitatively described.

[0025] S300: Construct a loess humidification deformation function model with the moisture content and pressure load as independent variables and the humidification deformation coefficient as dependent variable.

[0026] Specifically, the experimental data on the humidification deformation coefficient obtained from simulated samples under different moisture contents and pressure load combinations were systematically organized. A three-dimensional data space was constructed with moisture content as one dimension, pressure load as another dimension, and the humidification deformation coefficient as the response value. Nonlinear regression fitting was performed on the discrete data points using AI and other tools to establish a continuous function model that reflects the combined influence of moisture content and pressure load on the humidification deformation coefficient. This model can characterize the evolution of the humidification deformation coefficient under water-mechanical coupling.

[0027] S400: The undisturbed loess is subjected to a humidification deformation test under the same test conditions as the simulated sample to obtain the measured humidification deformation coefficient; the measured humidification deformation coefficient is compared with the predicted value of the loess humidification deformation function model; if the relative error between the two meets the preset requirements, the model is deemed to be qualified and the qualified loess humidification deformation function model is obtained, wherein the qualified loess humidification deformation function model is used to predict the humidification deformation coefficient of the undisturbed loess to be treated.

[0028] Specifically, by conducting humidification deformation tests under the same experimental conditions as undisturbed loess, the measured humidification deformation coefficients of undisturbed loess under different working conditions are obtained. The measured values ​​are compared with the model prediction values, and the prediction accuracy of the model is evaluated by calculating the relative error between the two. When the relative error under all working conditions meets the preset requirements, it proves that the model can accurately reflect the real humidification deformation law of undisturbed loess, thus determining that the model is qualified for verification. The qualified loess humidification deformation function model is obtained. The qualified model has reliable prediction ability and can be directly applied to actual engineering. Based on the natural moisture content and design load conditions of the target area, it can quickly predict the humidification deformation coefficient of undisturbed loess under any given moisture content and pressure load, providing a quantitative basis for foundation deformation analysis and engineering design in collapsible loess areas, and effectively reducing the workload of repeated sampling and indoor testing.

[0029] In practical application, this embodiment uses undisturbed loess from the target area as a base, adding structural reinforcement components to prepare artificially structured loess samples with physical and mechanical properties and collapsibility coefficients that meet preset similarity to the undisturbed loess. Because the artificially structured loess is precisely controllable, it replaces natural undisturbed soil for benchmark testing. This not only reproduces the chemical cementation and dissolution mechanisms of natural loess but also eliminates testing errors caused by the inhomogeneity of natural soil samples, providing a repeatable standard physical benchmark and reducing exploration costs and experimental cycles. By conducting multi-level pressure load humidification deformation tests on simulated samples with different moisture contents, and determining the humidification deformation coefficient based on the deformation stability height before and after humidification, the progressive deformation response of loess under unsaturated conditions with increasing moisture content is accurately characterized, overcoming the limitation that the traditional collapsibility coefficient is only applicable to saturated conditions. Using the experimental data of the artificially structured loess, with moisture content and pressure... A loess wetting deformation function model is constructed with load as the independent variable, transforming discrete experimental data into a continuous mathematical function expression. This model reflects the deformation response law of soil under unsaturated conditions caused by water-mechanical coupling, avoiding the technical limitations of simplifying the unsaturated wetting deformation process into a saturated collapsing process. This improves the pertinence and accuracy of unsaturated loess deformation evaluation. The model is validated using undisturbed loess under the same experimental conditions as the simulated sample. The relative error between the measured and predicted values ​​determines the model's qualification. Using the validated loess wetting deformation function model, the wetting deformation response of unsaturated loess can be directly predicted under known site moisture content and design load conditions. This provides a supplementary quantitative index, distinct from the traditional collapsibility coefficient, for foundation deformation analysis and engineering design in collapsible loess areas. It is applicable to engineering deformation evaluation under unsaturated conditions, ensuring the model's practical applicability and predictive accuracy for natural loess.

[0030] This invention provides an economical, efficient, scientific, and reliable quantitative evaluation method for foundation deformation analysis and engineering design in collapsible loess areas.

[0031] like Figure 2 and Figure 3 As shown, in an optional embodiment of the present invention, the preparation of artificially structured loess as a simulation sample, which uses the original loess of the target area as a base and adds structural reinforcing components to prepare an artificially structured loess with physical and mechanical properties and a collapsibility coefficient that satisfy a preset similarity to the original loess, includes: The original loess in the target area was sampled, and multiple groups of artificial structural loess mixed with structural reinforcement components were prepared based on the physical and mechanical properties of the original loess. The collapsibility coefficient of each group of artificial structural loess and the original loess under different pressure loads was measured. Specifically, undisturbed loess samples were collected from the target area, and their physical and mechanical properties (such as dry density, void ratio, liquid limit, and plastic limit) were measured to serve as the physical benchmark for artificial loess preparation. Cement and soluble salts were added to the remolded soil to prepare multiple groups of artificial structural loess with different proportions. The collapsibility coefficients of each group of artificial soil and undisturbed loess under different pressure loads were measured according to the "Standard for Geotechnical Testing Methods" to obtain basic test data.

[0032] For example, undisturbed loess from a specific site is sampled to obtain data, which determines the physical benchmark for artificially prepared soil samples. Based on the determined physical benchmark, artificially structured loess is then prepared. Due to differences in sampling location and depth, undisturbed soil exhibits different physical and mechanical properties.

[0033] The undisturbed loess samples taken from a specific site were subjected to liquid and plastic limit tests in accordance with the "Standard for Geotechnical Testing Methods" (GB / T50123-2019): a 76g cone was used for a sinking test, and the water content recorded when the cone sank to a depth of 2mm was determined as the plastic limit water content; the water content recorded when the cone sank to a depth of 10mm was determined as the liquid limit water content.

[0034] Based on the moisture content data, the dry density is calculated using Formula 1. After multiple iterations, the arithmetic mean is taken as the final result, and the value must be accurate to one decimal place. This is how the calculation result is standardized.

[0035] According to the dry density in the "Standard for Geotechnical Testing Methods" (GB / T50123-2019) The calculation formula 1 is as follows: (1) In the formula: Dry density; Wet density (natural density); Moisture content (%).

[0036] Among them, soil samples No. 1 and No. 8 have the most typical physical indicators and the most complete data. Soil sample No. 1 was taken from the 0m-16m soil layer. Its physical and mechanical parameters were relatively homogeneous: water content 10.8%-25.1% (mean 16.31%), dry density 1.26g / cm³-1.66g / cm³ (mean 1.41g / cm³), void ratio 0.636-1.155 (mean 0.93); liquid limit 27.0%-30.1%, plastic limit 16.4%-17.7%, plasticity index 11.2; compressibility coefficient 0.27MPa. - ¹-0.96MPa -¹, the collapse coefficient is 0.002-0.067. Its physical properties are the most typical, the data are the most complete, and it meets the simulation conditions.

[0037] Soil sample No. 8 exhibits a significant parameter gradient within the depth range of 0m-16m (e.g. Figure 2 As shown in (a) and (b): the moisture content fluctuates between 7.7% and 22.8% with increasing depth, and the dry density fluctuates between 1.27 g / cm³ and 1.60 g / cm³ with increasing depth. Its physical indices are basically consistent with and similar to those of natural loess in Xi'an, meeting the similarity criteria. With increasing soil depth, the void ratio decreases between 0.698 and 1.141, while the liquid limit and plastic limit moisture contents remain stable with depth. The collapsibility coefficient decreases with increasing depth.

[0038] Based on the above data, the dry density range used was consistent with the measured dry density of the undisturbed soil, set at 1.42 g / cm³ to 1.53 g / cm³; the moisture content gradient was set at 15%, 18%, 21%, 24%, 27%, 30%, and saturation, and corresponding structural loess comparative samples were prepared accordingly. Simultaneously, to simulate the structural characteristics of the undisturbed soil, different contents of cement (1.0%, 2.0%, 4.0%) and edible salt (2%, 3%, 5%) were added. The sample preparation steps for the structural loess test are as follows... Figure 3 As shown, we first obtained soil samples from the construction site, dried and milled them, and then sieved them through a 1 mm sieve to remove coarse particles and impurities, obtaining homogenized fine-grained soil. The treated soil samples were then dried to constant weight at 105±2℃. Salt (NaCl) and 52.5R ordinary Portland cement were added according to a preset ratio, with dosages ranging from 2% to 5% and 1% to 4%, respectively, and dry-mixed to form 9 different 3×3 mix proportions. Seven parallel samples were prepared for each mix proportion. The moisture content was controlled using a gravimetric method (w = 15%), with distilled water added evenly in three stages and thoroughly mixed to stabilize the soil moisture content. The prepared soil samples were then left to stand in sealed plastic bags for 24 hours. The moisture content was measured again before the test. If a large deviation in moisture content was found, the soil samples were re-prepared, and the above steps were repeated. Through these steps, we successfully prepared artificially structured loess samples, providing a reliable material basis for subsequent experiments.

[0039] According to the "Standard for Geotechnical Testing Methods" (GB / T50123-2019), the prepared artificial structural loess was tested to determine the basic physical properties of the soil sample, such as dry density, void ratio, particle specific gravity, liquid limit, and plastic limit, as well as the collapsibility coefficient.

[0040] Based on the test results (as shown in Table 1), the liquid limit moisture content of the sample ranged from 28.1% to 28.8% (mean 28.45%), and the plastic limit moisture content ranged from 16.8% to 17.1% (mean 16.9%). The calculated plasticity index was 11.0 to 12.1 (mean 11.42).

[0041] Table 1 Physical properties of artificially prepared collapsible loess

[0042] During the experiment, it was observed that the physical properties of the four types of artificially structured loess samples (A1-A4) prepared in this embodiment were as shown in Table 1. The dry density was limited to the range of 1.42 g / cm³ to 1.53 g / cm³, and the specific gravity ranged from 2.69 to 2.71. These values ​​are consistent with the physical properties of undisturbed loess under natural conditions. Comparative measurement results show that the physical properties of the four types of artificial soil samples are close to those of undisturbed soil samples No. 1 and No. 8, meeting the experimental benchmark requirements for artificially simulating structured loess.

[0043] According to Formula 2 of the "Standard for Geotechnical Testing Methods" (GB / T50123-2019), the collapsibility coefficient is calculated as follows: (2) Where: δs—collapse coefficient; —The height (mm) of the specimen after deformation stabilizes under a certain pressure level. —The height (mm) of the sample after it has stabilized after being immersed in water and undergoing wet deformation under a certain pressure. —The original height of the soil sample (mm). The degree of collapsibility of loess can be represented by the collapsibility coefficient δs mentioned above. Among them, the collapsibility coefficient is used to characterize the collapsibility deformation characteristics of loess under saturated conditions; the humidification deformation coefficient is used to characterize the deformation response of loess under unsaturated conditions as the water content increases. The two are independent of each other in terms of physical meaning and applicable working conditions.

[0044] The collapsibility deformation characteristics of structural loess were determined, and the control effect of different additive ratios on the collapsibility performance of the soil was determined. The specific operation strictly followed the collapsibility coefficient test procedure in the "Standard for Geotechnical Testing Methods" (GB / T50123-2019). The collapsibility coefficient was calculated by measuring the height change of the sample before and after collapsibility deformation.

[0045] Based on the collapsibility coefficients under different pressure loads, the collapsibility coefficient-pressure fitting curves of the artificial structured loess and the undisturbed loess at a set moisture content were plotted respectively. Specifically, the collapsibility coefficient data under each pressure load were organized and fitted, and the collapsibility coefficient-pressure relationship curves (δs-p curves) of artificial structured loess and undisturbed loess under the same set water content conditions were plotted to provide a visual basis for subsequent curve comparison and morphological analysis.

[0046] The physical and mechanical properties of the artificially structured loess are compared with those of the original loess to select the artificially structured loess whose physical and mechanical properties meet the first preset similarity. Specifically, the physical and mechanical properties (dry density, void ratio, liquid limit, plastic limit, etc.) of each group of artificially structured loess were compared one by one with the corresponding properties of undisturbed loess. The artificially structured loess mixes with physical properties close to those of undisturbed loess and meeting the first preset similarity requirement were selected to ensure that they are representative on a physical basis.

[0047] The collapsibility coefficient-pressure fitting curve of the selected artificial structured loess at the set moisture content is compared with the collapsibility coefficient-pressure fitting curve of the undisturbed loess at the same moisture content. The artificial structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity is selected as the simulated sample.

[0048] Specifically, by comparing the collapsibility coefficient-pressure fitting curves of artificially structured loess selected through physical index screening with the corresponding curves of undisturbed loess under the same moisture content, and by comparing the overall trend, variation trend, fitting parameters, and degree of deviation of the two curves, the similarity of the two in the law of collapsibility coefficient change with pressure is comprehensively evaluated. When the overall shape of the two curves is similar, the variation trend is consistent, and the quantitative deviation is within the preset range, it can be determined that the collapsibility evolution law of the two has sufficient similarity. Artificially structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity requirement is selected as the simulation sample, thereby ensuring that the selected simulation sample is not only close to the undisturbed loess in physical properties, but also consistent with the typical evolution law of undisturbed loess in collapsibility characteristics, providing a highly representative test carrier for subsequent humidification deformation tests.

[0049] For example, the physical and mechanical properties of undisturbed loess were determined by testing the undisturbed loess according to the "Standard for Geotechnical Testing Methods". The dry density ranged from 1.26 to 1.66 g / cm³, the void ratio ranged from 0.636 to 1.155, the liquid limit ranged from 27.0% to 30.1%, the plastic limit ranged from 16.4% to 17.7%, the plasticity index was 11.2, and the collapsibility coefficient ranged from 0.002 to 0.067.

[0050] The preparation and screening of artificially structured loess: Based on the physical and mechanical properties of undisturbed loess, cement (1%-4%) and NaCl (2%-5%) were added to the remolded soil as structural reinforcement components to prepare multiple groups of artificially structured loess with different proportions. The physical and mechanical properties of each group of artificially structured loess were measured, and the proportion with dry density, void ratio, liquid limit, plastic limit, and plasticity index that are similar to those of undisturbed loess was screened.

[0051] In practical application, this embodiment involves collecting undisturbed loess from the target area and preparing multiple groups of artificially structured loess based on its physical and mechanical properties. The collapsibility coefficients of these artificially structured loess samples under different pressures are measured, and collapsibility coefficient-pressure fitting curves are plotted at the same moisture content. First, artificial soils whose physical properties meet the first preset similarity are selected by comparing their physical and mechanical properties. Then, artificial soils whose collapsibility evolution law meets the second preset similarity are selected as simulation samples by comparing the shape and peak range of the collapsibility coefficient-pressure fitting curves. This ensures that the simulation samples are highly consistent with the undisturbed loess in terms of physical properties and collapsibility characteristics, providing a reliable physical benchmark for subsequent humidification deformation tests.

[0052] As an optional embodiment of the present invention, the step of comparing the collapsibility coefficient-pressure fitting curve of the screened artificially structured loess at the set moisture content with the collapsibility coefficient-pressure fitting curve of the undisturbed loess at the same moisture content, and selecting the artificially structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity as the simulated sample includes: The collapsibility coefficient-pressure fitting curve of the selected artificial structured loess at the set moisture content is compared with the collapsibility coefficient-pressure fitting curve of the undisturbed loess to determine the first error between the two. Specifically, the pre-screened artificial structured loess was placed alongside the undisturbed loess in the target area under the same moisture content conditions. The collapsibility coefficient-pressure fitting curves of the two were then compared side-by-side. This direct comparison allowed for a visual observation of the overall trend and degree of agreement between the two curves under the same conditions, laying the foundation for subsequent morphological determination. Based on the curve comparison, the morphological characteristics of the fitting curves were further analyzed, mainly in two dimensions: first, the overall shape of the curve, i.e., the trend, steepness, and evolution law of the collapsibility coefficient changing with pressure; and second, the peak range, i.e., the pressure range corresponding to the maximum value of the collapsibility coefficient and its peak value. Through these two dimensions of morphological determination, the similarity between the artificial soil and the undisturbed soil in terms of collapsibility evolution law could be assessed.

[0053] When the first error is less than the second preset threshold, it is determined that the similarity between the collapsibility coefficient-pressure fitting curve of the selected artificial structured loess and the collapsibility coefficient-pressure fitting curve of the undisturbed loess meets the second preset similarity, and the corresponding artificial structured loess is used as the simulated sample.

[0054] Specifically, based on morphological determination, the deviation between the fitted curves of the two is measured using quantitative calculation methods to obtain a quantified first error. This first error is then compared with a pre-set second threshold. When the first error is less than this threshold, it indicates that the collapsibility coefficient-pressure fitted curve of the artificially structured loess has a sufficiently high similarity to the corresponding curve of the undisturbed loess in terms of morphological characteristics and overall trend; that is, the collapsibility evolution law of the artificial soil is basically consistent with that of the undisturbed soil. At this point, the artificially structured loess with this mix ratio is determined as the simulated sample for subsequent humidification deformation tests.

[0055] For example, consolidation tests were conducted on preliminarily selected artificially structured loess and undisturbed loess at moisture contents of 8% and 12%, respectively. The collapsibility coefficients under different pressures were measured, and their respective collapsibility coefficient-pressure fitting curves were plotted. Figure 4 As shown, the peak value of the collapsibility coefficient gradually increases with the increase of vertical load; and the peak value of the collapsibility coefficient gradually decreases with the increase of cement content. The collapsibility coefficient-pressure fitting curves of artificially structured loess with various proportions at moisture contents of 8% and 12% were compared with the collapsibility coefficient-pressure fitting curves of undisturbed loess at the same moisture content. The shape of the curves and the peak range were determined, and the error between the two fitting curves was calculated. The results show that the collapsibility coefficient-pressure fitting curve of artificially structured loess with a salt content of 5% and a cement content of 2% is closest to the corresponding curve of undisturbed loess, with an error of less than 5%. The judgment rule that "when the error between the artificially structured curve and the natural loess curve is within 10%" is applied, the deformation response of the artificially structured loess under collapsibility conditions is consistent with the typical collapsibility evolution law of natural undisturbed loess. Therefore, the collapsibility evolution law of the artificially structured loess with this proportion is consistent with that of undisturbed loess. It was used as a simulation sample for subsequent humidification deformation tests, realizing the effect of simulating undisturbed soil with prepared structured soil.

[0056] The collapsibility coefficient data of artificial structured loess and undisturbed loess after the test were fitted, and the δs-P curve of artificial structured loess at a fixed moisture content was compared with that of undisturbed loess at a fixed moisture content to determine the ratio of artificial structured loess with undisturbed loess with a similar collapsibility coefficient.

[0057] like Figure 4As shown, the peak value of the collapsibility coefficient gradually increases with the increase of vertical load; the peak value of the collapsibility coefficient gradually decreases with the increase of cement content. Comparing the fitting curves of the collapsibility coefficient of the structural loess under various mix proportions, it was found that the fitting curve of the structural loess with 5% salt content and 2% cement content is closest to that of the loess in the drainage canal, with an error value of less than 5%. Therefore, the structural characteristics of the structural loess with 5% salt content and 2% cement content are most similar to those of the loess in the drainage canal, achieving the effect of simulating undisturbed soil with prepared structural soil.

[0058] In practical application, this embodiment determines the shape and peak range of the collapsibility coefficient-pressure fitting curves of artificially structured loess and undisturbed loess at the same moisture content, and quantifies the first error between the two as a screening criterion. This can accurately identify the artificially structured loess mix ratio that is closest to the collapsibility evolution law of undisturbed loess, ensuring that the simulated sample is highly representative in terms of collapsibility characteristics. This provides a reliable physical basis for subsequent humidification deformation tests and model construction, thereby significantly improving the accuracy and applicability of humidification deformation coefficient prediction.

[0059] As an optional embodiment of the present invention, the step of conducting humidification deformation tests on the simulated samples with different moisture contents under multi-level pressure loads, recording the results, and determining the humidification deformation coefficient based on the deformation stability height before and after humidification includes: Consolidation tests were conducted on the simulated specimens with different moisture content gradients and multiple pressure loads under multiple pressure loads, respectively. Specifically, based on the above-mentioned optimal artificial structure loess sample and undisturbed loess test, consolidation and wet deformation tests were conducted on them respectively, and the consolidation test scheme is shown in Table 2 below.

[0060] The dry density range used in the experiment was consistent with that of Xi'an loess, set at 1.42 g / cm³ to 1.53 g / cm³. The moisture content gradients were set at 15%, 18%, 21%, 24%, 27%, 30%, and saturation. Following the requirements of GB / T50123-2019 "Standard for Geotechnical Testing Methods," soil samples were placed in large-diameter ring cutters (79.8 mm in diameter and 20 mm in height) and compacted in layers. The moisture content settings were the same as above, with a total of 7 gradients. Three parallel samples were prepared for each group, and the samples were sealed and cured for 24 hours after compaction.

[0061] Table 2 Standard Consolidation Test Scheme

[0062] In this embodiment, a one-dimensional consolidation apparatus was used to perform compression tests on the prepared specimens. The molded specimens were placed in the consolidation apparatus, and preset vertical loads were applied sequentially under radial constraint of a ring cutter. The load levels were set to 12.5 kPa, 25 kPa, 50 kPa, 100 kPa, 200 kPa, 300 kPa, 400 kPa, 600 kPa, and 800 kPa. Each load level was maintained until the specimen's deformation rate stabilized to less than 0.01 mm / h, or the loading time reached 24 hours, and the corresponding vertical deformation was recorded. After completing one load level, the next load level was introduced, and this process was repeated until the test was completed. After one round of consolidation tests was completed, the same operation was performed on specimens with a different moisture content (e.g., the next gradient after 15% was 18%), and this process was repeated until all moisture content gradient tests were completed. Finally, the collected data were used to calculate the corresponding moisture deformation coefficient using the moisture deformation coefficient formula.

[0063] For each level of pressure load, the height of the simulated specimen after deformation stabilization is recorded. Based on the height of the height after deformation stabilization corresponding to the moisture content gradients of two adjacent levels under the same pressure load, the humidification deformation coefficient is determined.

[0064] Specifically, for each simulated specimen under each pressure load and moisture content gradient, the height after deformation stabilization is recorded. Then, under the same pressure load, the heights corresponding to two adjacent moisture content gradients are taken and the difference is calculated to determine the humidification deformation coefficient during the process of increasing from the current moisture content to the next moisture content.

[0065] It should be further explained that the consolidation test is the fundamental operation for obtaining basic data in this embodiment. It is conducted on simulated specimens under a single fixed moisture content gradient. Multiple levels of vertical pressure loads are applied sequentially under radial constraint of a ring cutter, and the height of the specimen after deformation stabilization under each load level is recorded to establish the pressure-deformation relationship under that moisture content condition. The humidification deformation test, on the other hand, involves completing the above consolidation test under multiple different moisture content gradients. Then, at the same pressure load level, the stable heights of specimens from adjacent moisture content gradients are compared laterally to calculate the additional deformation caused by the increase in moisture content, and the humidification deformation coefficient is determined accordingly. Therefore, the consolidation test and the humidification deformation test constitute a relationship between basic data acquisition and comprehensive parameter characterization. The former provides the original deformation data support for the latter, and the latter, based on this, enables a quantitative evaluation of the deformation response under the influence of moisture changes.

[0066] In practical applications, this embodiment expands the traditional single-point collapsibility coefficient test into a humidification deformation test system covering all working conditions by conducting consolidation tests on simulated samples with different moisture content gradients under multiple levels of pressure load. By comparing the deformation stability height of samples with adjacent moisture content levels laterally under the same pressure load, the deformation increment caused by moisture content change can be independently separated, avoiding the coupling interference between pressure load change and moisture content change. This provides systematic and accurate experimental data support for the subsequent construction of a humidification deformation function model under water-mechanical coupling.

[0067] like Figure 5 , Figure 6 , Figure 7 , Figure 8 and Figure 9 As shown, in an optional embodiment of the present invention, determining the humidification deformation coefficient based on the height after deformation stabilization corresponding to two adjacent moisture content gradients under the same pressure load includes: The humidification deformation coefficient is determined based on the following formula: = ( ) / (3) in: Indicates the coefficient of deformation due to humidification; This represents the height of a soil sample with the current moisture content gradient after it has been immersed in water and moistened under a set pressure, once the deformation has stabilized. The height of the soil sample at the next level of moisture content gradient after deformation stabilization following immersion and wetting under the set pressure is indicated. This indicates the original height of the soil sample.

[0068] Specifically, the deformation stability heights corresponding to two adjacent moisture contents under the same pressure load are substituted into the above formula for calculation. The difference between the deformation stability height of the soil sample at the current moisture content and the height of the soil sample at the next moisture content after humidification deformation stability under the same pressure is divided by the original height of the soil sample to obtain the humidification deformation coefficient during the process of increasing from the current moisture content to the next moisture content. Formula 3 is fundamentally different from the traditional formula 2 for the wet collapse coefficient (which uses a deformation after immersion in water saturation), and is specifically designed for the humidification process under unsaturated conditions; The collapsibility coefficient is used to characterize the collapsibility deformation characteristics of loess under saturated conditions (saturation of the sample by water immersion); The humidification deformation coefficient is used to characterize the deformation response of loess under unsaturated conditions as the water content increases. The two are independent of each other in terms of physical meaning and applicable working conditions.

[0069] The results of the wettation deformation test of the optimal ratio of artificial structured loess (e.g., artificial structured loess with a salt content of 5% and a cement content of 2%) calculated according to the formula are shown in Table 3. Table 3 Statistical table of the results of the wettation deformation test of artificially structured loess

[0070] Generate from the data in Table 3 as follows Figure 5 The optimal ratio of artificially structured loess under pressure δ SP relationship diagram Figure 5 This mainly demonstrates the effect of changes in water content on δ The influence of the SP curve is investigated. Under the same water content conditions, this method sets the water content of loess greater than 20% as the technical criterion point for entering the non-collapse state. The sample with a water content of w=24% is used as the calibration benchmark, and the measurement range of its humidification deformation coefficient is locked in the range of 0.0015-0.014. When the experimental data of the target undisturbed soil falls into this value range, it can be technically determined that the soil has lost its collapsibility. This provides a standardized artificial simulation method and quantitative judgment basis for engineering sites.

[0071] The results of the wet deformation test of the original loess soil are shown in Table 4. Table 4 Statistical Table of Wet Deformation Test Results of Unsaturated Loess

[0072] The data in Table 4 was generated as follows Figure 6 The coefficient of δ for wetting deformation of undisturbed loess under different vertical loads is shown. The graph showing the relationship between s and water content w. This includes the vertical load... At that time, the humidification deformation coefficient δ s decreases with increasing water content w, and the sample's trapping properties remain stable; when At that time, δ The decrease in s increases. The wetting deformation coefficient of soils with low water content is more sensitive to changes in vertical load, while the δ of soils with high water content... The fluctuation range of s converges, which shows that the wetting deformation law of artificial structured loess can reflect the wetting deformation law of undisturbed loess and the curves are similar. Therefore, the structural characteristics of structured loess with 5% salt content and 2% cement admixture have achieved the effect of simulating undisturbed soil, providing a reference basis.

[0073] Table 4 shows the humidification deformation coefficient - vertical pressure (δ) covering different initial moisture content gradients (18%, 21%, 24%, 27%, 30%, 34%). SP) relationship curve (e.g. Figure 7 (As shown).

[0074] When performing the quantitative characterization step, the humidification deformation coefficient δ s is set as a bivariate function of vertical pressure P and initial water content w. By fitting the stress-humidification deformation coefficient path under different hydraulic coupling sequences in the P-ε-w three-dimensional coordinate system, the stress-humidification deformation coefficient surface of undisturbed loess is constructed (e.g., Figure 8 (As shown). This step utilizes a three-dimensional curved surface structure to spatially characterize the deformation evolution trajectory of undisturbed loess under multiple working conditions, providing standard reference data for determining the applicability of subsequent artificial structured loess fitting models.

[0075] The data in Table 3 and Table 4 were used to generate the following data: Figure 9 The δ values ​​of undisturbed loess and artificially structured loess under different stress levels are shown. Comparison of SW curves shows that within a certain humidity range, the amount of humidification deformation decreases with increasing water content, and then stabilizes after a certain critical point. Under medium pressure, when the humidification deformation coefficient reaches its maximum value, both artificially structured loess and remolded loess exhibit significant collapsibility. The experimental results show that when the cement content is 2%, the variation law of the humidification deformation coefficient is closest to that of undisturbed loess. Therefore, the structural characteristics of structured loess with a salt content of 5% and a cement content of 2% achieve the effect of simulating undisturbed soil, providing a reference basis for its application.

[0076] like Figure 10 and Figure 11 As shown, in an optional embodiment of the present invention, the construction of the loess wetting deformation function model, with the moisture content and the pressure load as independent variables and the wetting deformation coefficient as the dependent variable, includes: Based on the test results of the humidification deformation test of the simulated sample, with the moisture content and the pressure load as independent variables and the humidification deformation coefficient as dependent variable, the test data are systematically classified and nonlinearly fitted to construct a three-dimensional response surface model that reflects the comprehensive effect of stress-humidification deformation-moisture content. Specifically, the experimental data on the humidification deformation coefficient obtained from simulated samples under different moisture content gradients and pressure load combinations are systematically organized and categorized to form a three-dimensional data space with moisture content as the X-axis, pressure load as the Y-axis, and humidification deformation coefficient as the Z-axis. By performing nonlinear fitting on these discrete data points, a continuous three-dimensional response surface model (such as...) is constructed. Figure 10 As shown in the figure, this surface can intuitively reflect the variation law of the humidification deformation coefficient under the combined action of moisture content and pressure load, as well as the coupling effect between the two.

[0077] The three-dimensional response surface model is fitted with nonlinear regression to establish the loess wetting deformation function model, which characterizes the combined influence of the pressure load and the moisture content on the wetting deformation coefficient.

[0078] Specifically, based on the three-dimensional response surface model, a mathematical fitting is further performed using a nonlinear regression method to obtain a specific functional expression as the loess wetting deformation function model. This nonlinear regression fitting employs optimization algorithms from the field of artificial intelligence (such as gradient descent and backpropagation) for parameter optimization, minimizing the error between the model's predicted values ​​and the experimental data through iterative calculations, thereby achieving a high-precision mapping from discrete experimental data to a continuous function expression. Alternatively, tools such as the Extreme Cum model in Origin plotting software can be used for fitting, as their underlying mathematical logic is consistent with AI nonlinear regression methods, yielding results such as... Figure 11 The surface fitting results of the wetting deformation coefficient of artificially structured loess under different pressure loads and moisture contents are used to intuitively characterize the comprehensive influence relationship between load and moisture content on the wetting deformation coefficient. This function model can quantitatively describe the comprehensive influence of moisture content and pressure load on the wetting deformation coefficient, transforming discrete experimental data into continuous mathematical expressions, and realizing the prediction calculation of the wetting deformation coefficient under any given combination of moisture content and pressure load.

[0079] In practical application, this embodiment systematically classifies the simulated sample humidification deformation test data and constructs a three-dimensional response surface model with water content and pressure load as independent variables. This transforms the discrete test data into an intuitive spatial surface, clearly demonstrating the evolution law of the humidification deformation coefficient under water-force coupling. Furthermore, a loess humidification deformation function model is obtained through nonlinear regression fitting, which can be used to quickly calculate the humidification deformation coefficient under any given combination of water content and pressure load.

[0080] As an optional embodiment of the present invention, the loess wetting deformation function model is obtained by fitting a composite double exponential function. The composite double exponential function is used to describe the nonlinear law of the influence of water content and pressure load on the wetting deformation coefficient. For example, from experimental results ( Figure 5 , Figure 6 , Figure 7 It can be seen that the humidification deformation coefficient exhibits obvious nonlinear characteristics as it changes with moisture content and pressure load: Figure 6 The data shows that when the vertical load P < 50 kPa, the humidification deformation coefficient decreases gradually with increasing moisture content; when P ≥ 50 kPa, the decrease in the humidification deformation coefficient increases, exhibiting a rapid change phase. Figure 5Setting a moisture content greater than 20% as the technical criterion for entering a non-collapsed state indicates that the humidification deformation coefficient tends to converge and stabilize at high moisture content. This nonlinear evolution law of "gradual change - rapid change - tendency to stabilize" is precisely what the composite double exponential function excels at describing.

[0081] The composite double exponential function, through its special mathematical structure—the double exponential terms characterize the single-factor effects of moisture content and pressure load respectively, and the coupling term characterizes the synergistic effect of the two—can accurately fit the nonlinear characteristics observed in the above experiments, and realize a continuous functional expression of the humidification deformation coefficient under any combination of moisture content and pressure load.

[0082] As an optional embodiment of the present invention, the loess wetting deformation function model is expressed by the following formula: (4) in, This represents the humidification deformation coefficient. This indicates the moisture content. This indicates the pressure load. Based on the base intercept, B, C, D, E, F, G, and H are morphological parameters determined through nonlinear regression fitting.

[0083] Specifically, the nonlinear regression analysis method uses the ExtremeCum model from Origin plotting software for fitting, constructing a composite double exponential function model as the target fitting equation, which is then determined through nonlinear regression fitting. After obtaining morphological parameters such as B, C, D, E, F, G, and H, this formula can be used to predict the humidification deformation coefficient under any given combination of water content and pressure load. This realizes the transformation of discrete experimental data into a continuous mathematical function expression. These parameters are obtained by fitting the humidification deformation data of the optimally proportioned artificial structured loess.

[0084] The value ranges of these parameters are as follows: ; : ; : ; : ; : ; : ; ; .

[0085] The validity of the model is validated by calculating the coefficient of determination R², based on the statistical test results; the formula for calculating R² is as follows: (5) In the formula, These are the true values ​​(actual observation data). These are the model's predicted values. The mean of the true values. This represents the total number of samples. If... If the value is less than 1, the model is considered valid. This model transforms discrete physical test data into a continuous mathematical function expression, which is used to quantitatively predict the loess wetting deformation coefficient under any given moisture content and load condition. As can be seen from the above relational equations, within the applicable range of the model, when different moisture content and pressure load parameters are input, the humidification deformation coefficient under the corresponding working conditions can be predicted and calculated. The relational equations are established based on experimental data, and their fitting correlation coefficient R² is 0.9615, used to characterize the degree of correlation between the model calculation results and the experimental data. This embodiment transforms the traditional method of obtaining the humidification deformation coefficient based on a large number of repeated experiments into a parameter prediction method based on a mathematical model, realizing the transformation of the humidification deformation coefficient from discrete experimental data to a continuous function expression form.

[0086] In practical applications, this embodiment can obtain the natural moisture content and foundation bearing capacity of the proposed site through on-site surveys. By substituting the parameters into the aforementioned relational equations, the corresponding predicted value of the humidification deformation coefficient can be quickly obtained. This provides a basis for foundation deformation and settlement calculations and engineering design in collapsible loess areas. Compared with related technologies, this method can effectively reduce the workload of repeated sampling and indoor testing, lower engineering costs, shorten the design cycle, and improve the efficiency and reliability of foundation deformation prediction and engineering design in collapsible loess areas.

[0087] As an optional embodiment of the present invention, the undisturbed loess is subjected to a humidification deformation test under the same test conditions as the simulated sample to obtain a measured humidification deformation coefficient; the measured humidification deformation coefficient is compared with the predicted value of the loess humidification deformation function model, and if the relative error between the two meets a preset requirement, the model is deemed to be qualified; the qualified loess humidification deformation function model is used to predict the humidification deformation coefficient of the undisturbed loess, including: The loess wetting deformation function model is verified using the original loess in the target area. The wetting deformation test is carried out under the same water content gradient and pressure load as the simulated sample to obtain the measured wetting deformation coefficient of the original loess under different working conditions. The same water content gradient and pressure load are input into the loess wetting deformation function model to obtain the model prediction value. Specifically, undisturbed loess from the same target area as the simulated sample was used to conduct a humidification deformation test under identical test conditions (the same moisture content gradient series and the same pressure load level). The actual humidification deformation coefficient of the undisturbed loess under different moisture contents and different pressure load combinations was measured as the measured value. At the same time, these working condition parameters (moisture content and pressure load) were substituted into the constructed loess humidification deformation function model to calculate the predicted value of the model under this working condition, providing a data basis for subsequent comparative verification.

[0088] The measured humidification deformation coefficient under each of the aforementioned working conditions is compared with the model prediction value to determine the relative error under each of the aforementioned working conditions; Specifically, for each test condition (i.e., each combination of moisture content and pressure load), the measured wettability deformation coefficient of the undisturbed loess is compared with the model prediction value point by point, the relative error between the two is calculated, the prediction accuracy of the model under each specific condition is quantified, and error distribution data covering all conditions is formed.

[0089] If the relative error corresponding to each pressure load under all the moisture content gradients is less than the first preset threshold, the loess wetting deformation function model is deemed to have passed the verification.

[0090] Specifically, the relative error under all working conditions is comprehensively judged: only when the relative error corresponding to each pressure load point in each moisture content gradient is less than the first preset threshold, is the model considered to have sufficient prediction accuracy under all possible working conditions, thus the model is deemed to be qualified for verification and can be used to predict the wet deformation coefficient of undisturbed loess in actual engineering.

[0091] For example, from the obtained undisturbed loess wetting deformation test results (Table 4), a moisture content gradient is randomly selected as the verification input, and its wetting deformation coefficient under the same pressure load is extracted. Taking a moisture content of w=18% as an example, its measured wetting deformation coefficient under a pressure load P=200kPa is... It is 0.0525.

[0092] The predicted sequence is compared point by point with the measured sequence, the relative error is calculated, and the correctness of the fitting formula and the fitting model is determined accordingly.

[0093] The relative error can be calculated using the following formula 6: (6) In the formula, The measured wet deformation coefficients corresponding to the wet deformation test results of the loess in Table 4 are shown in Table 4. The predicted value is the one fitted to Equation 4.

[0094] When the error at each pressure point under the same moisture content gradient satisfies η≤5%, it is determined that the model prediction sequence and the measured sequence under that moisture content gradient are consistent, indicating that the established fitting formula and fitting model are correct and effective under that working condition; for example, the above measured humidification deformation coefficient The corresponding independent variable pairs (x=w, y=P) are substituted point by point into the humidification deformation function model (Equation 4), and the given fitting parameters are used for calculation to obtain the predicted humidification deformation coefficient under the same moisture content gradient and pressure load. The value is 0.054888, or 4.55%, which meets the full tolerance. The above verification results show that the artificial structural loess determination model constructed in this invention can accurately invert the wetting and deformation characteristics of natural loess. This method not only proves the feasibility of artificially prepared soil samples in simulating the structure of natural loess, but also demonstrates its engineering effectiveness and accuracy in predicting collapsibility in complex engineering sites.

[0095] When the error exceeds 5%, it indicates that there is an anomaly in the experimental input data. The experimental data acquisition and calculation process should be traced back and refitted for correction. For details, please refer to the next example.

[0096] In practical application, this embodiment uses undisturbed loess from the same region as the simulated sample to conduct a humidification deformation test under the same test conditions to obtain measured values. These values ​​are then compared with the model's predicted values ​​point by point under all conditions, and relative errors are calculated. The model is deemed qualified only when the relative error of each pressure load point under all moisture content gradients is less than the first preset threshold. This ensures that the verified loess humidification deformation function model has reliable prediction accuracy across the entire range of conditions.

[0097] like Figure 12 As shown, in an optional embodiment of the present invention, the method further includes: If the relative error corresponding to the pressure load under any of the moisture content gradients is greater than or equal to the first preset threshold, the verification of the loess wetting deformation function model is deemed unqualified. The proportioning and screening of the artificial structural loess is repeated, and the step of preparing artificial structural loess that meets the preset conditions and using it as a simulation sample is returned until the relative error corresponding to each pressure load under all the moisture content gradients is less than the first preset threshold, at which point the verification is deemed qualified.

[0098] Specifically, when validating the loess humidification deformation function model, if it is found that under any moisture content gradient, the relative error between the measured humidification deformation coefficient and the model prediction value at a certain pressure load point exceeds or equals a pre-set first threshold, it indicates that the model's prediction accuracy under that working condition fails to meet the requirements, and the overall applicability of the model is questionable. Therefore, the model is deemed unqualified for validation. When the model validation fails, it is necessary to go back to the source for adjustment, re-screen the proportions of artificially structured loess, and possibly adjust the cement and soluble salt content to obtain a simulated sample that is closer to the collapsible characteristics of undisturbed loess. Then, humidification deformation tests are conducted again on the new simulated sample to obtain new humidification deformation coefficient data. Based on the new data, nonlinear regression fitting is performed again to construct a new loess humidification deformation function model, and validation is performed again. The above iterative process of backtracking, screening, testing, fitting, and validation is repeated until the relative error between the measured and predicted values ​​at all moisture content gradients and all pressure load points is less than the first preset threshold, that is, when the model's prediction accuracy under all working conditions meets the requirements, the model is finally deemed qualified for validation and can be used for actual engineering prediction.

[0099] In practical application, this embodiment uses a backtracking correction mechanism to address verification failures. When the relative error of a pressure load point under any moisture content gradient exceeds a preset threshold, the model is promptly deemed unqualified, and artificial soil mix selection, humidification deformation tests, and data refitting are performed again. Through iterative optimization, the prediction errors under all working conditions meet the requirements, ensuring that the final loess humidification deformation function model has high accuracy and reliability across the entire working condition range.

[0100] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

[0101] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for simulating and determining the deformation coefficient of undisturbed loess due to moisture absorption, characterized in that, include: Based on the original loess of the target area, structural reinforcement components were added to prepare artificial structural loess that met the preset conditions and used as a simulation sample. The physical and mechanical properties and collapsibility coefficient of the artificial structural loess that met the preset conditions were consistent with the physical and mechanical properties and collapsibility coefficient of the original loess. The simulated samples with different moisture contents were subjected to humidification deformation tests under multi-level pressure loads. The results were recorded and the humidification deformation coefficient was determined based on the deformation stability height before and after humidification. The humidification deformation coefficient is used to characterize the deformation response of loess with increasing moisture content after the pressure load is applied in an unsaturated state. Using the moisture content and pressure load as independent variables and the humidification deformation coefficient as dependent variable, a loess humidification deformation function model is constructed. The measured wet deformation coefficient was obtained by conducting a humidification deformation test on the undisturbed loess under the same test conditions as the simulated sample. The measured humidification deformation coefficient is compared with the predicted value of the loess humidification deformation function model. If the relative error between the two meets the preset requirements, the model is deemed to be qualified and the qualified loess humidification deformation function model is obtained. The qualified loess humidification deformation function model is used to predict the humidification deformation coefficient of the undisturbed loess to be treated.

2. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to claim 1, characterized in that, The process of conducting multi-level pressure load humidification deformation tests on the simulated samples with different moisture contents, recording the results, and determining the humidification deformation coefficient based on the deformation stability height before and after humidification includes: Consolidation tests were conducted on the simulated specimens with different moisture content gradients and pressure loads under multiple pressure loads, respectively. For each level of pressure load, the height of the simulated specimen after deformation stabilization is recorded. Based on the height of the height after deformation stabilization corresponding to the moisture content gradients of two adjacent levels under the same pressure load, the humidification deformation coefficient is determined.

3. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to claim 2, characterized in that, The step of determining the humidification deformation coefficient based on the height after deformation stabilization corresponding to two adjacent moisture content gradients under the same pressure load includes: The humidification deformation coefficient is determined based on the following formula: =（ ） / ； in: Indicates the coefficient of deformation due to humidification; This represents the height of a soil sample with the current moisture content gradient after deformation stabilization following immersion and wetting under a set pressure level. The height of the soil sample at the next level of moisture content gradient after deformation stabilization following immersion and wetting under the set pressure is indicated. This indicates the original height of the soil sample.

4. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to any one of claims 1-3, characterized in that, The construction of the loess wetting deformation function model, using the moisture content and pressure load as independent variables and the wetting deformation coefficient as the dependent variable, includes: Based on the test results of the humidification deformation test of the simulated sample, with the moisture content and the pressure load as independent variables and the humidification deformation coefficient as dependent variable, the test data are systematically classified and nonlinearly fitted to construct a three-dimensional response surface model that reflects the comprehensive effect of stress-humidification deformation-moisture content. The three-dimensional response surface model is fitted with nonlinear regression to establish the loess wetting deformation function model, which characterizes the combined influence of the pressure load and the moisture content on the wetting deformation coefficient.

5. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to claim 4, characterized in that, The loess wetting deformation function model is obtained by fitting a composite double exponential function, which is used to describe the nonlinear law of the influence of the moisture content and the pressure load on the wetting deformation coefficient.

6. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to claim 5, characterized in that, The loess wetting deformation function model is expressed by the following formula: ； in, This represents the humidification deformation coefficient. This indicates the moisture content. This indicates the pressure load. Based on the base intercept, B, C, D, E, F, G, and H are morphological parameters determined through nonlinear regression fitting.

7. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to any one of claims 1-3, characterized in that, The undisturbed loess is subjected to a humidification deformation test under the same test conditions as the simulated sample to obtain the measured humidification deformation coefficient; the measured humidification deformation coefficient is compared with the predicted value of the loess humidification deformation function model, and if the relative error between the two meets the preset requirements, the model is deemed to be qualified. The validated loess wetting deformation function model used to predict the wetting deformation coefficient of the undisturbed loess includes: The loess wetting deformation function model is verified using the original loess in the target area. The wetting deformation test is carried out under the same water content gradient and pressure load as the simulated sample to obtain the measured wetting deformation coefficient of the original loess under different working conditions. The same water content gradient and pressure load are input into the loess wetting deformation function model to obtain the model prediction value. The measured humidification deformation coefficient under each of the aforementioned working conditions is compared with the model prediction value to determine the relative error under each of the aforementioned working conditions; If the relative error corresponding to each pressure load under all the moisture content gradients is less than the first preset threshold, the loess wetting deformation function model is deemed to have passed the verification.

8. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to claim 7, characterized in that, Also includes: If the relative error corresponding to the pressure load under any of the moisture content gradients is greater than or equal to the first preset threshold, the verification of the loess wetting deformation function model is deemed unqualified. The proportioning and screening of the artificial structural loess is repeated, and the step of preparing artificial structural loess that meets the preset conditions and using it as a simulation sample is returned until the relative error corresponding to each pressure load under all the moisture content gradients is less than the first preset threshold, at which point the verification is deemed qualified.

9. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to any one of claims 1-3, characterized in that, The process of preparing artificially structured loess as a simulation sample, based on the original loess of the target area with the addition of structural reinforcing components, and possessing physical and mechanical properties and a collapsibility coefficient that are similar to the original loess to a predetermined level, includes: The original loess in the target area was sampled, and multiple groups of artificial structural loess mixed with structural reinforcement components were prepared based on the physical and mechanical properties of the original loess. The collapsibility coefficient of each group of artificial structural loess and the original loess under different pressure loads was measured. Based on the collapsibility coefficients under different pressure loads, the collapsibility coefficient-pressure fitting curves of the artificial structured loess and the undisturbed loess at a set moisture content were plotted respectively. The physical and mechanical properties of the artificially structured loess are compared with those of the original loess, and the artificially structured loess whose physical and mechanical properties meet the first preset similarity is selected. The collapsibility coefficient-pressure fitting curve of the selected artificial structured loess at the set moisture content is compared with the collapsibility coefficient-pressure fitting curve of the undisturbed loess at the same moisture content. The artificial structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity is selected as the simulated sample.

10. The method for simulating and determining the wettability deformation coefficient of undisturbed loess according to claim 9, characterized in that, The step of comparing the collapsibility coefficient-pressure fitting curve of the selected artificially structured loess at the set moisture content with the collapsibility coefficient-pressure fitting curve of the undisturbed loess at the same moisture content, and selecting the artificially structured loess whose collapsibility coefficient-pressure fitting curve meets the second preset similarity as the simulated sample includes: The collapsibility coefficient-pressure fitting curve of the selected artificial structured loess at the set moisture content is compared with the collapsibility coefficient-pressure fitting curve of the undisturbed loess to determine the first error between the two. When the first error is less than the second preset threshold, it is determined that the similarity between the collapsibility coefficient-pressure fitting curve of the selected artificial structured loess and the collapsibility coefficient-pressure fitting curve of the undisturbed loess meets the second preset similarity, and the corresponding artificial structured loess is used as the simulated sample.

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