A method for analyzing infiltration of multi-layer soil and slope stability considering dynamic correction of infiltration coefficient

Abstract

The present application relates to the technical field of slope stability evaluation in geotechnical engineering, and particularly relates to a multi-layer soil infiltration and slope stability analysis method considering dynamic correction of infiltration coefficient, which can be used for prediction and prevention and control of shallow landslide disaster. S1: obtaining basic parameters of a multi-layer soil slope to be analyzed; S2: constructing a single-layer Green-Ampt infiltration model with transition layer correction; S3: constructing an enhanced multi-layer Green-Ampt infiltration model; S4: constructing a multi-layer soil slope stability analysis model; S5: result verification and comparative analysis. The method process of the present application is simple, the simulation accuracy is improved through dynamic correction of the transition zone infiltration coefficient, the retarding effect of the low-permeability interface on the wetting front is quantified, the stability coefficient is corrected by multiple factors, the traditional method is avoided to overestimate the safety of the slope, and the present application can directly provide quantitative basis for landslide early warning, anti-seepage design of the multi-layer soil slope.

Description

Technical Field

[0001] This invention relates to the field of slope stability assessment technology in geotechnical engineering, specifically to a multi-layer soil infiltration and slope stability analysis method that considers dynamic correction of the infiltration coefficient, which can be used for the prediction and prevention of shallow landslide disasters. Background Technology

[0002] Rainfall infiltration is a key factor inducing shallow landslides, and its mechanism is closely related to the seepage characteristics of unsaturated soil. Currently, research on rainfall infiltration in slopes mainly relies on theoretical analysis, experimental studies, and numerical simulations. Among these, the classic Green-Ampt (GA) model is widely used in slope stability analysis due to its easily obtainable parameters, clear physical meaning, and computational efficiency. However, the traditional GA model has significant limitations: it assumes that the soil above the wetting front is completely saturated, which is seriously inconsistent with the unsaturated transition layer phenomenon that exists in the actual infiltration process, leading to cumulative errors in infiltration rate, wetting front depth, and stability assessment results.

[0003] To improve the applicability of the GA model, existing studies have made improvements by optimizing the morphology of the wet zone (such as setting the wet front profile as a quarter ellipse), introducing stratification parameters, or considering soil properties (such as pore pressure and pore characteristics). However, there are still core defects: 1) Insufficient characterization of the dynamic effect of the proportion of the unsaturated transition zone on the infiltration coefficient; 2) Lack of response mechanism of rainfall intensity to the difference in infiltration between layers; 3) Ignoring the dynamic gradient effect of infiltration with the evolution of the wet zone in the stability assessment, resulting in an overestimation of the slope safety factor.

[0004] For multi-layered soil slopes, existing models struggle to accurately simulate the abrupt change in interfacial permeability during the advancement of wetting fronts across layers, and cannot quantify the impact of accumulated pore water pressure at low-permeability interfaces on slope stability. This makes it difficult to meet the needs of dynamic slope hazard risk assessment in engineering practice. Therefore, an integrated method is urgently needed that can couple dynamic correction of infiltration coefficients, simulation of interlayer interface effects, and stability analysis. Summary of the Invention

[0005] The technical problem to be solved by the invention is to provide a method for analyzing the infiltration and slope stability of multi-layer soils that considers dynamic correction of the infiltration coefficient, in order to address the shortcomings mentioned in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution, comprising the following steps: S1: Obtain the basic parameters of the multi-layered soil slope to be analyzed, including slope geometric parameters, rainfall infiltration parameters, and physical, mechanical, and hydraulic parameters of each soil layer; S2: Construct a single-layer Green-Ampt infiltration model with a transition layer correction. To address the shortcomings of the traditional GA model that ignores the unsaturated transition layer, the VanGenuthen model and the equivalent permeability algorithm of the transition zone are introduced to achieve accurate simulation of the single-layer soil infiltration process. Specifically, it includes three sub-steps: (a) describing soil water content and unsaturated permeability, (b) calculating the equivalent permeability of the transition zone, and (c) dividing the infiltration stage and deriving the cumulative infiltration amount. S3: Construct an enhanced multi-layer Green-Ampt infiltration model. In response to the abrupt change in interlayer permeability of multi-layer soil slopes, the model achieves accurate simulation of the cross-layer advance of wetting fronts through layered control and cross-layer iteration. Specifically, it includes three sub-steps: (a) defining the foundation parameters of multi-layer soil, (b) simulating the cross-layer advance of wetting fronts, and (c) iteratively calculating the infiltration depth of multi-layer soil. S4: Construct a multi-layer soil slope stability analysis model. Based on the infinite slope model, couple the seepage force gradient effect to quantify the stability of two types of potential sliding surfaces. Specifically, it includes two sub-steps: (a) calculate key physical quantities and (b) calculate stability coefficients. S5: Results verification and comparative analysis, including (a) comparative analysis of wetting front depth and (b) comparative analysis of slope stability coefficient.

[0007] Furthermore, in step S2, the specific formula describing soil water content and unsaturated permeability is as follows:

[0008] In the formula, Residual water content in the soil, Soil saturated water content, a , n , m Soil hydraulic fitting parameters ( m =1-1 / n ), Negative pore water pressure;

[0009] In the formula, For soil saturation permeability, For effective saturation ( ), l This is an empirical coefficient.

[0010] Furthermore, in step S2, the specific formula for calculating the equivalent permeability of the transition zone is as follows: The unsaturated transition zone is considered as a "superimposed body of thin layers with different permeabilities." Based on the layered soil equivalent permeability algorithm, the formula for calculating the transition zone (depth range) is derived. z s < z < zf Equivalent penetration rate :

[0011] In the formula, z s For slope surface depth, z f The depth of the moist front; Meanwhile, considering that the water content in the transition zone during the initial stage of rainfall is elliptical, the average water content in the transition zone is derived. :

[0012] In the formula, The initial volumetric water content of the soil, z t This refers to the depth of the transition zone.

[0013] Furthermore, in step S2, the specific formula for dividing the infiltration stages and deriving the cumulative infiltration amount is as follows: Based on the relationship between rainfall intensity and soil infiltration capacity, the infiltration of a single soil layer is divided into two stages, and the correlation between the cumulative infiltration amount and the wetting front depth is derived respectively: Phase 1: Rainfall Intensity Control Phase ( ) Rainfall intensity during this period q Less than the soil's infiltration capacity, rainwater completely infiltrates, cumulative infiltration amount Based on the conservation of water volume, the following derivation is made: and Relationship:

[0014] In the formula, This is the critical moment for water accumulation. α For slope gradient, This is the critical wetting front depth; Phase 2: Soil Infiltration Rate Control Phase ) During this stage, rainfall intensity exceeds soil infiltration capacity, leading to water accumulation on the slope surface. The total cumulative infiltration is the sum of the infiltration from the saturated zone and the transition zone. (6) In the formula, The depth of the saturation region. The suction force is due to the moistening front matrix.

[0015] Furthermore, in step S3, the parameters for defining multi-layer soil foundations are defined: for an n-layer soil slope, the parameters for the first layer are specified. m Layered soil ( m =1,2,..., nKey parameter: thickness d m Initial water content saturated water content saturation permeability Matrix suction This provides the basic data for subsequent calculations.

[0016] Furthermore, in step S3, the specific formula for simulating the cross-layer advance of the wetting front is as follows: A layered permeability control function is used to calculate the infiltration intensity and critical time of each soil layer in stages: ① Calculate the first m Critical moment of water accumulation in soil layers : like , For the moist front to reach the first m If the time for +1 layer is taken, then take This indicates that the layer only has a rainfall intensity-controlled phase; conversely, the layer has two infiltration phases. ② Calculate the first m Infiltration strength of the soil layer: Rainfall intensity control phase ( ):

[0017] Soil infiltration control stage ( ):

[0018] In the formula, The middle is the first m Equivalent permeability of the moist zone of the soil layer; ③ Calculate the time it takes for the wetting front to reach the soil interface. : Based on the difference in infiltration strength between layers and the thickness of the soil layer, the derivation is... ( =0, ):

[0019] Furthermore, in step S3, the specific formula for iteratively calculating the infiltration depth of multi-layered soil is as follows: using a time step... Iterative calculation at any time t depth of the moist front The judgment logic is as follows: ①If The moist front only advances in the first layer:

[0020] ②If The moist front is in the first m Layer-by-layer advancement:

[0021] ③If The moist front reaches the lowest layer (or bedrock):

[0022] Furthermore, in step S4, the specific formula for calculating the key physical quantity is as follows: Based on the infiltration results in step S3, the derivation of slope at any depth is performed. z Physical quantities related to the force at the point: Volumetric weight :

[0023] In the formula, Soil dry weight, The specific weight of pore water; Volumetric water specific gravity :

[0024] Normal stress at the bottom of the sliding surface :

[0025] Soil Damage Shear Stress :

[0026] Effective normal stress at the bottom of the sliding surface :

[0027] In the formula, Pore ​​pressure, This refers to the pore water pressure.

[0028] Furthermore, in step S4, the specific formula for calculating the stability coefficient is as follows: Calculate the stability coefficients for the two types of potential sliding surfaces separately, and take the minimum value as the overall slope stability coefficient. Indicating slope instability: ① When the wetting front acts as the sliding surface, based on Fredlund's formula for the shear strength of unsaturated soil, the stability coefficient is... :

[0029] ②The soil interface acts as the sliding surface, at which point the stability coefficient... :

[0030] ③Total stability coefficient :

[0031] Compared with the prior art, the advantages of the present invention are: The method of this invention has a simple process. It improves the simulation accuracy by dynamically correcting the infiltration coefficient of the transition zone, quantifies the blocking effect of the low-permeability interface on the wetting front, and corrects the stability coefficient by multiple factors. It avoids overestimating the slope safety of traditional methods and can directly provide a quantitative basis for landslide early warning and seepage prevention design of multi-layer soil slopes. Attached Figure Description

[0032] Figure 1 This is a flowchart of a multi-layer soil infiltration and slope stability analysis method that considers dynamic correction of the infiltration coefficient according to the present invention. Figure 2 This is a schematic diagram of a multi-layer slope model in one embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the change of the wetting front over time in one embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the variation of slope stability coefficient with wetting front depth in one embodiment of the present invention. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0034] 1) Obtain the foundation parameters of multi-layer soil slopes A typical three-layer soil slope on the A1 section of the Huangmei-Huangshi Expressway was selected as the implementation subject. The slope is 90m wide, 60m high, and has a slope of 1:1.5. The rainfall intensity is 0.2m / h. The thickness of each soil layer was determined through geological survey, and the physical and mechanical parameters of each soil layer were determined based on laboratory geotechnical tests. The results are shown in Table 1. Table 1 Physical properties of the soil layer

[0035] The hydraulic parameters of each soil layer were determined through soil moisture characteristic curve tests and infiltration tests. The results are shown in Table 2. Table 2 Hydraulic parameters of the soil layer

[0036] 2) Substitute into the infiltration model (EML-GA) for calculation (a) Calculate the critical time and infiltration strength of the first soil layer. The parameters of the first layer ( i s1 =0.357, i i1 =0.128, i r =0.05, a =1.935, n =2.45, m Substituting 0.59 into formula (1), the negative pore water pressure is calculated. ψ f1 =15.7cm.

[0037] Then the parameters of the first layer (( i s1 =0.357, i i1 =0.128, i r =0.05, k s1 Substituting 165 mm / h into formula (2) calculates different moisture contents. i Permeability coefficient below k .

[0038] Substitute the parameters of the first layer into formula (5) to calculate the critical moment of water accumulation. t p1 =1.86h.

[0039] ①Rainfall intensity control stage ( t < t p1 According to formula (7), calculate the infiltration intensity of the first layer before the critical time. i 1(1) =16.64mm / h.

[0040] ② Soil infiltration control stage ( t ≥ t p1 According to formula (8), the infiltration intensity of the first layer at different depths before the critical time is calculated. i 1(2) .

[0041] (b) Iterative calculation of infiltration depth in multi-layer soil Repeat step (a) to calculate the infiltration intensity of different soil layers before and after the critical moment.

[0042] According to formula (9), the time for the wetting front to reach the interface of different soil layers is calculated: the time for the wetting front to reach the interface of layer 1-2. t 1 = 4.07h, time for the moist front to reach the 2nd-3rd layer interface t2 = 36.87h, the time it takes for the wetting front to reach the interface between the third layer and the bedrock. t 3 = 692.45h.

[0043] Using time step Δ t =5min, calculate any time step using formulas (10)-(12) iteratively. t depth of the moist front z f For example, when rainfall lasts 3.87 hours, the depth of the moist front is... z f =1.38m, located in the first soil layer; depth of the wetting front after 34.54 hours of rainfall. z f =4.3m, close to the bottom of the second soil layer; depth of the wetting front after 473.52 hours of rainfall. z f =8m, close to the bottom of the 3rd layer of soil.

[0044] 3) Construct a multi-layer soil slope stability analysis model (EML-GA-SSA) (a) Calculate key physical quantities Based on the infiltration results from step two, the slope depth at any point is calculated using formulas (13)-(17). z The physical quantities related to the forces acting at the location. These are based on rainfall over 31.05 hours and depth. z Taking a location at 4m as an example: Specific gravity γ(z) =18.2kN / m³; Volumetric water specific gravity c w (z) =9.8kN / m³; Normal stress at the bottom of the sliding surface s n =128.6 kPa; Soil damage shear stress t =65.3kPa; Effective normal stress at the bottom of the sliding surface s n ' =93.7 kPa.

[0045] (b) Calculate the stability coefficient Based on the calculation results of step (a), when the wetting front is used as the sliding surface, according to formula (18), the stability coefficient is... F st =1.162; Taking the soil interface as the sliding surface, according to formula (19), the stability coefficient is F sm = 1.062; The overall stability coefficient is calculated according to formula (20). F s =min( F st , Fsm =1.062.

[0046] 1) Result verification and comparative analysis (a) Comparative analysis of the depth of moist fronts like Figure 2 , 3 As shown, in the initial stage of rainfall infiltration, due to the high permeability coefficient of the surface soil, the water infiltration rate is relatively fast, the transition zone is narrow, and its impact on the overall infiltration rate is small. The trend of the wetting front depth calculated by the model of this invention over time is relatively consistent with that of the traditional Green-Ampt model. When the wetting front reaches the interface between silty clay and silty mudstone, the soil permeability coefficient decreases significantly, and the influence range of the transition zone increases. The model of this invention considers the influence of the soil infiltration transition zone on the permeability coefficient, while the traditional GA model (Huang et al. 2024) still assumes that the wetting zone is completely saturated, thus underestimating the soil infiltration capacity and the initial wetting front formation time, resulting in a gradual increase in the difference between the calculated wetting front depth and the results of this model and numerical analysis.

[0047] The development patterns of the wetting front calculated by the three methods are similar, but the results calculated by the model of this invention are closer to the numerical analysis. The infiltration time required to reach a wetting front depth of 4m is as follows: 31.05 hours for the EML-GA model of this invention, 30.01 hours for numerical analysis, and 23 hours for the traditional GA model. The infiltration time required to reach a wetting front depth of 8m is as follows: 473.53 hours for the EML-GA model, 480.24 hours for numerical analysis, and 640.17 hours for the GA model. The results show that the calculation results of the model of this invention are in significantly better agreement with the numerical analysis than the traditional GA model, demonstrating consistency and accuracy.

[0048] (b) Comparative analysis of slope stability coefficients The slope stability coefficients were calculated based on the EML-GA-SSA model, the LIGA model (Huang et al. 2024), and numerical simulation analysis (Huang et al. 2024). F s The curves related to the wetting front depth are shown in the figure. In the initial stage of rainfall, the slope stability coefficient decreases rapidly with increasing wetting front depth; in the middle and later stages of rainfall, the slope stability coefficient gradually stabilizes. A significant change in the curve was observed at the soil interface. This phenomenon stems from a sudden change in the permeability coefficient at the soil interface. The hydraulic gradient in the low-permeability soil layer increases significantly, intensifying the downward seepage force. Simultaneously, the sudden increase in effective stress directly improves the soil's shear strength, leading to the abrupt change in the stability coefficient at the interface.

[0049] like Figure 4As shown, the EML-GA-SSA model exhibits significant advantages in slope stability prediction: in the sandy clay layer (0-1.5m), its stability coefficient is reduced by an average of 18% compared to the LIGA model; in the silty clay transition layer (1.5-4.5m), the difference increases to 27%. The core breakthrough occurs in the silty mudstone layer (4.5-9.5m), where the EML-GA-SSA model accurately captures the critical instability state at a wetting depth of 9.1m, a state that the LIGA model fails to identify. Compared to numerical analysis, the deep prediction error rate of the EML-GA-SSA model is only 4.7%, significantly lower than the 12.3% of the LIGA model. This advantage stems from the accurate description of the seepage force correction effect by the EML-GA-SSA model, and at the same wetting front location, the calculation results of the EML-GA-SSA model are closer to the numerical analysis results.

[0050] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for analyzing the infiltration and slope stability of multi-layered soils considering dynamic correction of the infiltration coefficient, characterized in that, Includes the following steps: S1: Obtain the basic parameters of the multi-layered soil slope to be analyzed, including slope geometric parameters, rainfall infiltration parameters, and physical, mechanical, and hydraulic parameters of each soil layer; S2: Construct a single-layer Green-Ampt infiltration model with a transition layer correction. To address the shortcomings of the traditional GA model that ignores the unsaturated transition layer, the VanGenuthen model and the equivalent permeability algorithm of the transition zone are introduced to achieve accurate simulation of the single-layer soil infiltration process. Specifically, it includes three sub-steps: (a) describing soil water content and unsaturated permeability, (b) calculating the equivalent permeability of the transition zone, and (c) dividing the infiltration stage and deriving the cumulative infiltration amount. S3: Construct an enhanced multi-layer Green-Ampt infiltration model. In response to the abrupt change in interlayer permeability of multi-layer soil slopes, the model achieves accurate simulation of the cross-layer advance of wetting fronts through layered control and cross-layer iteration. Specifically, it includes three sub-steps: (a) defining the foundation parameters of multi-layer soil, (b) simulating the cross-layer advance of wetting fronts, and (c) iteratively calculating the infiltration depth of multi-layer soil. S4: Construct a multi-layer soil slope stability analysis model. Based on the infinite slope model, couple the seepage force gradient effect to quantify the stability of two types of potential sliding surfaces. Specifically, it includes two sub-steps: (a) calculate key physical quantities and (b) calculate stability coefficients. S5: Results verification and comparative analysis, including (a) comparative analysis of wetting front depth and (b) comparative analysis of slope stability coefficient.

2. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S2, the specific formula describing soil water content and unsaturated permeability is as follows: In the formula, Residual water content in the soil, Soil saturated water content, a , n , m Soil hydraulic fitting parameters ( m =1-1 / n ), Negative pore water pressure; In the formula, For soil saturation permeability, For effective saturation ( ), l This is an empirical coefficient.

3. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S2, the specific formula for calculating the equivalent permeability of the transition zone is as follows: The unsaturated transition zone is considered as a "superimposed body of thin layers with different permeabilities." Based on the layered soil equivalent permeability algorithm, the formula for calculating the transition zone (depth range) is derived. z s < z < z f Equivalent penetration rate : In the formula, z s For slope surface depth, z f The depth of the moist front; Meanwhile, considering that the water content in the transition zone during the initial stage of rainfall is elliptical, the average water content in the transition zone is derived. : In the formula, The initial volumetric water content of the soil, z t This refers to the depth of the transition zone.

4. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S2, the specific formulas for dividing the infiltration stages and deriving the cumulative infiltration amount are as follows: Based on the relationship between rainfall intensity and soil infiltration capacity, the infiltration of a single soil layer is divided into two stages, and the correlation between the cumulative infiltration amount and the wetting front depth is derived respectively: Phase 1: Rainfall Intensity Control Phase ( ) Rainfall intensity during this period q Less than the soil's infiltration capacity, rainwater completely infiltrates, cumulative infiltration amount ; Based on the law of conservation of water volume, the following derivation is made. and Relationship: In the formula, This is the critical moment for water accumulation. α For slope gradient, This is the critical wetting front depth; Phase 2: Soil Infiltration Rate Control Phase ) During this stage, rainfall intensity exceeds soil infiltration capacity, leading to water accumulation on the slope surface. The total cumulative infiltration is the sum of the infiltration from the saturated zone and the transition zone. （6） In the formula, The depth of the saturation region. For the suction of the moist front matrix.

5. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S3, the definition of multi-layer soil foundation parameters is as follows: For an n-layer soil slope, the parameters of the first layer are specified. m Layered soil ( m =1,2,..., n Key parameter: thickness d m Initial water content saturated water content saturation permeability Matrix suction This provides the basic data for subsequent calculations.

6. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S3, the specific formula for simulating the cross-layer advance of the wetting front is as follows: A layered permeability control function is used to calculate the infiltration intensity and critical time of each soil layer in stages: ① Calculate the first m Critical moment of water accumulation in soil layers : like , For the moist front to reach the first m If the time for +1 layer is taken, then take This indicates that the layer only has a rainfall intensity-controlled phase; conversely, the layer has two infiltration phases. ② Calculate the first m Infiltration strength of the soil layer: Rainfall intensity control phase ( ): Soil infiltration control stage ( ): In the formula, The middle is the first m Equivalent permeability of the moist zone of the soil layer; ③ Calculate the time it takes for the wetting front to reach the soil interface. : Based on the difference in infiltration strength between layers and the thickness of the soil layer, the derivation is... ( =0, ): 。 7. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S3, the specific formula for iteratively calculating the infiltration depth of multi-layered soil is as follows: using a time step... Iterative calculation at any time t depth of the moist front The judgment logic is as follows: ①If The moist front only advances in the first layer: ②If The moist front is in the first m Layer-by-layer advancement: ③If The moist front reaches the lowest layer (or bedrock): 。 8. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S4, the specific formula for calculating the key physical quantity is as follows: Based on the infiltration results in step S3, the derivation of slope at any depth is performed. z Physical quantities related to the force at the point: Volumetric weight : In the formula, Soil dry weight, The specific weight of pore water; Volumetric water specific gravity : Normal stress at the bottom of the sliding surface : Soil Damage Shear Stress : Effective normal stress at the bottom of the sliding surface : In the formula, Pore ​​pressure, This refers to the pore water pressure.

9. The method for analyzing multi-layer soil infiltration and slope stability considering dynamic correction of infiltration coefficient according to claim 1, characterized in that: In step S4, the specific formula for calculating the stability coefficient is as follows: Calculate the stability coefficients for the two types of potential sliding surfaces separately, and take the minimum value as the overall slope stability coefficient. Indicating slope instability: ① When the wetting front acts as the sliding surface, based on Fredlund's formula for the shear strength of unsaturated soil, the stability coefficient is... : ②The soil interface acts as the sliding surface, at which point the stability coefficient... : ③Total stability coefficient : 。

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