Slope infiltration and stability analysis method, medium and equipment

Abstract

The invention relates to the technical field of water and soil simulation analysis, and discloses a slope infiltration and stability analysis method, a medium and equipment. According to the method, seepage characteristics and a fractal theory are introduced, a GA model is improved, a new slope rainfall infiltration model is provided, the model is combined with groundwater distribution to establish a slope initial moisture content distribution model, a runoff-seepage coupling effect is introduced, and the influence of slope surface accumulated water on the infiltration rate is dynamically analyzed; the Mohr-Coulomb intensity criterion is optimized based on the saturated zone seepage effect and the fractal theory, the improved infiltration model is applied to limited slope stability analysis, and the limitation that a traditional model is only suitable for an infinite long slope is broken through; by comprehensively considering factors such as soil particle size characteristics, slope surface runoff, gradient, rainfall intensity and underground water level, the safety coefficient of each point position in the slope can be accurately calculated, and the accuracy of infiltration process description and the reliability of slope stability analysis under the heavy rainfall working condition are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of water and soil simulation analysis, and particularly relates to a slope infiltration and stability analysis method, medium and equipment. BACKGROUND

[0002] Landslide is one of the natural disasters widely distributed in the world, which has caused great loss to engineering construction and social economy. Existing researches have shown that rainfall is one of the main triggering factors of shallow landslide. On the one hand, rainwater infiltration increases the saturation degree of the slope soil, which increases the self-weight of the soil and in turn increases the sliding force of the slope; on the other hand, under the condition of rainfall infiltration, the matric suction in the unsaturated zone of the soil gradually decreases, which leads to the weakening of the anti-sliding force of the slope; in addition, after the formation of the wetting front, seepage will occur in the saturated zone of the slope, and the seepage force will further reduce the stability of the slope. Therefore, it is of great significance to strengthen the research on rainfall infiltration and slope stability analysis for the prevention and control of slope.

[0003] The feasibility of applying numerical simulation to analyze the rainfall infiltration of slope has been gradually proved by many scholars, but the numerical simulation research requires many model calculation parameters, has high requirements for parameter accuracy, and the model calculation principle is relatively complex, the calculation amount is large, at the same time, the model analysis result is easily affected by boundary conditions, element size and mesh division, and there is a difficult convergence situation. In terms of theory and experimental research, the common models for studying rainfall infiltration include Philips model, Mein-Larson model, Green-Ampt model (hereinafter referred to as GA model) and Horton empirical model. Among them, the GA model was proposed by Green and Ampt in 1911, compared with other methods, the calculation parameters of the GA model are easy to obtain, the principle is simple, and the GA model has been widely used in the research of rainfall infiltration of unsaturated soil.

[0004] However, since the GA model assumes that the soil is horizontal and the initial water content is uniformly distributed, it ignores the influence of the complex distribution of the initial water content of the soil and the seepage of the saturated zone on the slope infiltration law, and is only applicable to infinite slope, and does not consider the influence of the elliptical transition layer in the infiltration area. When analyzing rainfall infiltration, only the increase of the wetting front depth caused by the infiltration of rainwater is considered, and the decrease of the wetting front depth caused by the seepage of the saturated zone is ignored; when analyzing the stability of the slope, only the influence of rainfall on the factors such as specific gravity and matric suction of the slope is considered, and the influence of the seepage force of the saturated zone caused by rainfall on the stability of the slope is ignored, and the influence of the particle size distribution characteristics of the soil on the shear strength is not considered, which has certain limitations and is not conducive to practical application.

[0005] Therefore, there is a need for a slope infiltration and stability analysis method to solve the problems existing in the current slope rainfall infiltration and stability analysis. SUMMARY

[0006] The application aims to provide a slope infiltration and stability analysis method introducing seepage characteristics and fractal theory, to improve the accuracy of describing the infiltration process under heavy rainfall conditions and the precision of fitting and calculating the slope stability, and the specific technical scheme is as follows.

[0007] A slope infiltration and stability analysis method, comprising the following steps:

[0008] S1: According to the grading characteristics of soil, the soil-water characteristic curve model and the unsaturated hydraulic conductivity curve model of soil are established based on the fractal theory, and the initial groundwater influence slope water content distribution model is established considering the influence of initial groundwater;

[0009] S2: According to the infiltration characteristics of soil during rainfall, the influence of the transition layer between the saturated layer and the natural layer is considered, and the elliptical curve is used to describe the distribution law of the volumetric water content of the transition layer along the depth of the slope soil, to obtain the slope water content distribution model after rainfall;

[0010] S3: Considering the seepage of the saturated zone above the slope wetting front, the slope length L is introduced, and according to the rainfall conservation principle and Darcy's law, the actual depth change rate of the wetting front is obtained;

[0011] S4: According to the change law of rainfall infiltration rate, the rainfall process is considered in two stages, to obtain the expression of rainfall infiltration rate and the relationship between wetting front depth and rainfall time;

[0012] S5: Based on the seepage characteristics and fractal theory, the Mohr-Coulomb strength criterion is optimized, the improved infiltration model is applied to the stability analysis of the finite slope, and the stability coefficients of each point in the slope are obtained, and the minimum value of the stability coefficient is taken as the slope stability coefficient under the most unfavorable condition.

[0013] Preferably, S1 comprises:

[0014] The soil pore surface has fractal characteristics, and the soil pore surface is covered with spherical balls with equal radii; the relationship between the number of spherical balls N(r) and the void radius (r) is:

[0015] N(r)=Kr -D 1);

[0016] Wherein: -D represents the pore fractal dimension, Kr represents the proportionality coefficient, and (r represents the pore radius;

[0017] The relationship between the pore volume V(r) and the void radius r is:

[0018]

[0019] The relative water content Λ is defined as the difference between the volume water content θ of the unsaturated soil and the residual volume water content θ r The relative water content of the soil is shown in equation 3) due to the increment of the pore size of the unsaturated soil:

[0020]

[0021] Where: V t represents the initial pore volume of the soil;

[0022] Combining equations 1)-3), we get:

[0023] Λ = Ar 3-D 4);

[0024] Where: A = 4πK / [V t (3-D)], the relative volume water content when the soil is in a saturated state is as follows:

[0025] Λ s = θ s - θ r = AR 3-D 5);

[0026] Where: Λ s represents the relative volume water content when the soil is in a saturated state; θ s represents the saturated volume water content of the soil of the slope; R is the maximum pore radius;

[0027] Combining equations 4)-5) with the Young-Laplace equation ψ = (2Tcosβ) / r, and setting θ r = 0, we get the SWCC model described by the particle size distribution of the soil:

[0028]

[0029] Where: T represents the surface tension; β is the contact angle, which is 0; ψ a represents the air-entry suction head of the soil; ψ represents the matric suction head of the soil;

[0030] According to the pore distribution of the soil, the unsaturated hydraulic conductivity curve model is as follows:

[0031]

[0032] Where: k(θ) represents the unsaturated permeability coefficient function of the soil; ψ(θ) represents the matric suction function of the soil; ψ a represents the air-entry suction head of the soil; k s is the saturated permeability coefficient of the soil; S e represents the saturation degree;

[0033] The soil pore fractal dimension D is obtained according to the grading distribution characteristics of the soil, and the calculation formula is as follows:

[0034]

[0035] Wherein, M0 represents the total mass of soil particles; M(r i ) represents the soil mass with particle size less than d i ; d i represents the particle size of soil particles; d max represents the maximum particle size of soil particles;

[0036] According to the relationship between the soil matrix suction head ψ and the soil depth h, ignoring the influence of residual volume water content, the initial groundwater-affected slope water content distribution model is obtained by combining the soil-water characteristic curve model, and the expression is as follows:

[0037]

[0038] Wherein, θ i represents the water content of the slope before rainfall; θ i (h) represents the water content distribution of the slope before rainfall; ψ a represents the air entry value of the soil; b represents the height of the capillary water saturation zone, b = ψ a ; H represents the vertical distance between the slope surface and the groundwater level; λ represents the void distribution characteristic parameter of the soil;

[0039] The relationship between the soil matrix suction head ψ and the soil depth h is as follows:

[0040] ψ = H - h 10).

[0041] Preferably, S2 is specifically:

[0042] The distribution rule of the soil volume water content in the transition layer is assumed to be an elliptical curve, and the initial groundwater-affected slope water content distribution model is combined to obtain the corrected slope water content distribution model after rainfall as follows:

[0043]

[0044] Wherein, θ(h) represents the water content distribution of the slope after rainfall; θ i (h f ) represents the water content at the wetting front position of the slope before rainfall; h f represents the wetting front depth; h w represents the saturated layer depth; h t represents the transition layer depth;

[0045] With the infiltration process, the proportion of the transition layer to the wetting layer is constantly reduced, and the proportion of the transition layer has a linear relationship with the wetting peak depth, as shown in the following formula:

[0046] h t / h f =μ=ah f +b 12);

[0047] Wherein: μ represents the proportion of the transition layer to the entire wetting front depth; az and b are linear relationship correlation coefficients.

[0048] Preferably, the S3 comprises:

[0049] The change of the wetting front depth is divided into two parts, one part is the increase of the wetting front depth caused by the infiltration of rainwater, and the other part is the decrease of the wetting front depth caused by the seepage discharge of the saturated zone;

[0050] According to the characteristics of the rainfall infiltration of the slope, the change rate of the wetting front caused by the rainfall infiltration is The expression is as follows:

[0051]

[0052] Wherein: ψ f represents the matrix suction; α represents the slope angle;

[0053] In the dt time, the flow ΔQ discharged from the slope by the saturated zone seepage is equal to the decrease ΔI of the cumulative infiltration amount, that is:

[0054] ΔQ = ΔI = Δθdh f 14);

[0055] Wherein: Δθ represents the change amount of the water content of the soil in the dt time, when considering the saturated zone seepage above the wetting front of the slope, the slope length L is introduced, and according to the Darcy law, the saturated zone seepage rate v above the wetting front is:

[0056]

[0057] The change rate of the wetting front depth caused by the saturated zone seepage above the wetting front is obtained by combining the formula 14) and 15) as follows:

[0058]

[0059] Wherein: the difference between the formula 13) and 16) is the actual change rate of the wetting front depth That is:

[0060]

[0061] The matrix suction ψ f ​The relationship between the soil's unsaturated permeability coefficient K(ψ) and the soil's permeability coefficient is as follows:

[0062]

[0063] Where, ψ i The soil moisture content is represented by θ. i The matrix suction at time; k(ψ) represents the unsaturated permeability coefficient function of the soil.

[0064] Preferably, S4 includes:

[0065] There exists a critical moment t during slope rainfall. p When the rainfall lasts longer than t p At that time, rainwater cannot completely infiltrate, and runoff begins to occur on the slope surface;

[0066] Under heavy rainfall conditions, the slope rainfall infiltration rate i is obtained by measuring the actual depth change rate of the wetting front:

[0067]

[0068] Where: q represents rainfall intensity;

[0069] Based on the principle of conservation of rainfall, the critical time t is determined. p The corresponding critical wetting front depth h p and critical rainfall infiltration rate I p The expression is as follows:

[0070]

[0071] When the time it takes for the slope soil to reach the critical wetting front depth during heavy rainfall is relatively short, the critical time t is approximately considered to be... p Previous average infiltration rate i m =(i0+i p ) / 2; where the initial infiltration rate i0 = qcosα; i p The critical time t p The corresponding infiltration rate at that time;

[0072] At critical time t p Then, and before time t, the average rate of rainfall infiltration i is approximated by the slope rainfall infiltration rate. s for:

[0073]

[0074] Finally, the cumulative infiltration amount I at each stage and the relationship between the wetting front depth and rainfall time are obtained as follows:

[0075]

[0076] Preferably, the S5 comprises:

[0077] The total amount of each stage cumulative infiltration is applied to the rainfall infiltration and stability analysis of the subgrade slope, the Mohr-Coulomb strength criterion is optimized based on the seepage characteristics and fractal theory, the improved infiltration model is applied to the stability analysis of the finite slope, and the stability coefficient expression of each point inside the slope is obtained, as follows:

[0078] The effective stress σ' of the soil based on the fractal theory is:

[0079] σ' = (σ n -u a ) + Lγ w ψ c 3-D ψ D-2 24);

[0080] The shear strength τ s caused by the matric suction of the soil is represented as:

[0081]

[0082] The shear strength τ f of the unsaturated soil is corrected as:

[0083]

[0084] Wherein, c' represents the cohesion of the soil; φ' represents the internal friction angle of the soil; σ n represents the normal stress of the slope bottom; (σ n -u a ) represents the net normal force of the slope bottom; γ w represents the water density;

[0085] The wetting front of the slope body moves with the rainfall, the wetting front depth h f and the saturated layer depth h w under different rainfall times are obtained by formula 23), and the bulk density change γ m (h) of the slope body caused by the change of the water content of the slope body during the rainfall infiltration process is further obtained as:

[0086]

[0087] In the formula: γ d represents the dry density of the soil; γ s represents the saturated density of the soil

[0088] The seepage force j s parallel to the slope surface generated by the saturated zone seepage is represented as:

[0089] j s = γ w h w Lsinα 28);

[0090] Further, the weight W of the soil above the sliding surface is:

[0091]

[0092] In the formula, h i represents the depth of the sliding surface at each point of the slope body; γ m (h) represents the unit weight of the slope body after rainfall;

[0093] The normal stress σ n and the shear stress τ m at the bottom of the sliding surface are:

[0094]

[0095] Further, the safety factor F sn at each point in the slope is:

[0096]

[0097] The slope safety factor expression containing the safety factors of n points in the slope is:

[0098] F s = {F s1 , F s2 , …, F sn} min 33)。

[0099] The rainfall infiltration phenomenon of the slope body is a complex process, which is controlled by soil particle size characteristics, slope surface runoff, slope gradient, rainfall intensity, and underground water level and other factors. Clarifying the movement process of water in soil has important significance for slope disaster prevention. The slope infiltration and stability analysis method provided by the present application introduces seepage characteristics and fractal theory, considers the influence of various factors on the basis of the Green-Ampt model, obtains a new slope rainfall infiltration model, the model combines the distribution of underground water to determine the distribution model of the initial water content of the slope body, and on the basis of considering the influence of the runoff-seepage coupling effect, the influence of the dynamic change of the slope surface water caused by rainfall on the infiltration rate is analyzed. Based on the action of saturated zone seepage and fractal theory, the Mohr-Coulomb strength criterion is further optimized, and the improved rainfall infiltration model is applied to the rainfall infiltration and stability analysis of the roadbed slope, the model considers the influence of the slope length, and the model originally only applicable to the stability analysis of the infinite slope is extended to the stability analysis of the finite slope, so that the safety factor of each point in the slope is obtained, and the accuracy of describing the infiltration process under the strong rainfall working condition and the fitting calculation accuracy of the slope stability are effectively improved.

[0100] The application further provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the slope infiltration and stability analysis method.

[0101] The application further provides an electronic device, comprising a processor and a memory for storing executable instructions of the processor, wherein the processor is configured to execute the executable instructions to implement the slope infiltration and stability analysis method.

[0102] In addition to the purposes, features and advantages described above, the application has other purposes, features and advantages. The application will be further described below with reference to the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0103] The accompanying drawings, which form a part of the present application, are intended to provide further understanding of the application and are incorporated herein for explanation by illustrating the specific embodiments of the application. The present application is explained by the accompanying drawings and the description, but is not limited by the accompanying drawings and the description. In the drawings:

[0104] Figure 1 Flow chart of the method provided according to an exemplary embodiment of the application;

[0105] Figure 2 Slope initial water content distribution diagram provided for the embodiment;

[0106] Figure 3 Improved GA model rainfall infiltration analysis diagram provided for the embodiment;

[0107] Fig. 4(a) is a force analysis diagram of each point of the slope in the embodiment;

[0108] Fig. 4(b) is a force analysis diagram of the saturated zone in Fig. 4(a);

[0109] Fig. 4(c) is a force analysis diagram of the transition zone in Fig. 4(a);

[0110] Fig. 4(d) is a force analysis diagram of the natural soil layer 1 in Fig. 4(a);

[0111] Fig. 4(e) is a force analysis diagram of the natural soil layer 2 in Fig. 4(a);

[0112] Figure 5 Powdery clay shallow slope analysis model under the action of heavy rainfall in the embodiment;

[0113] Fig. 6(a) is a fractal fitting and diagram of powdery clay;

[0114] Fig. 6(b) is a soil-water characteristic curve diagram of powdery clay;

[0115] Fig. 7(a) is a schematic diagram of the change of wetting front;

[0116] Fig. 7(b) is a profile of volumetric water content;

[0117] Fig. 7(c) is a schematic diagram of stability analysis of each point in the slope;

[0118] Fig. 8(a) is a schematic diagram of the change of wetting front;

[0119] Fig. 8(b) is a profile of volumetric water content;

[0120] Fig. 8(c) is a schematic diagram of stability analysis of each point in the slope; DETAILED DESCRIPTION

[0121] The embodiments of the present application will be described in detail below with reference to the accompanying drawings, but the present application can be implemented in various different ways as defined and covered by the claims.

[0122] Reference Figure 1 A slope infiltration and stability analysis method, comprising the following steps:

[0123] S1: According to the grading characteristics of the soil, the soil-water characteristic curve model and the unsaturated hydraulic conductivity curve model of the soil are established based on the fractal theory, and the initial groundwater influence slope water content distribution model is established considering the influence of the initial groundwater;

[0124] S2: According to the infiltration characteristics of the soil during the rainfall process, the influence of the transition layer between the saturated layer and the natural layer is considered, and an elliptical curve is used to describe the distribution of the volumetric water content of the transition layer along the depth of the slope soil body, so as to obtain the slope water content distribution model after the rainfall;

[0125] S3: Considering the seepage of the saturated zone above the slope wetting front, the slope length L is introduced, and according to the rainfall conservation principle and Darcy's law, the actual depth change rate of the wetting front is obtained;

[0126] S4: According to the change rule of the rainfall infiltration rate, the rainfall process is divided into two stages for consideration, and the expression of the rainfall infiltration rate and the relationship between the wetting front depth and the rainfall time are obtained;

[0127] S5: Based on the seepage characteristics and the fractal theory, the Mohr-Coulomb strength criterion is optimized, the improved infiltration model is applied to the stability analysis of the finite slope, the stability coefficients of each point in the slope are obtained, and the minimum value of the stability coefficient is taken as the slope stability coefficient under the most unfavorable condition.

[0128] The technical scheme of the present application is further described below by taking a certain region as an example. The overlying soil of the subgrade slope in the region is mostly silty clay, and there is stable initial underground water. The thickness of the overlying silty clay of the slope is d = 3 m, the lower part is an impermeable bedrock layer, the underground water level is parallel to the bedrock, and is located 2.4 m below the slope surface. The slope-related parameters are shown in Table 1:

[0129] Table 1: Slope-related parameters

[0130]

[0131] Details are as follows:

[0132] S1: According to the grading characteristics of the soil, the soil-water characteristic curve model and the unsaturated hydraulic conductivity curve model of the soil are established based on the fractal theory, and the initial underground water influence slope water content distribution model is established by considering the influence of the initial underground water. Details are as follows:

[0133] The soil pore surface has fractal characteristics, and the soil pore surface is covered with spherical balls with equal radii. The relationship between the number of spherical balls N(r) and the void radius r is as follows:

[0134] N(r) = Kr -D 1);

[0135] Wherein, D represents the pore fractal dimension, K represents the proportionality coefficient, and r represents the pore radius.

[0136] The relationship between the pore volume V(r) and the void radius r is as follows:

[0137]

[0138] The relative water content Λ is defined as the difference between the volume water content θ of the unsaturated soil and the residual volume water content θ r . Equation 3) shows that the relative water content of the soil changes due to the increase of the pore size of the unsaturated soil:

[0139]

[0140] Combining equations 1)-3), we have:

[0141] Λ = Ar 3-D 4);

[0142] Wherein, A = 4πK / [V t (3- D)], and the relative volume water content when the soil is in a saturated state is as follows:

[0143] Λ s = θ s - θ r = AR 3-D 5);

[0144] wherein: Λ s represents the relative volumetric water content when the soil is in a saturated state; θ s represents the saturated volumetric water content of the soil of the slope; R is the maximum pore radius.

[0145] Combining the equations 4) - 5) with the Young-Laplace equation ψ = (2Tcosβ) / r, let θ r = 0, the SWCC model describing the particle size distribution of the soil is obtained as follows:

[0146]

[0147] wherein, T represents the surface tension; β is the contact angle, and the value is 0; ψ c represents the air-entry suction head of the soil; ψ represents the matric suction head of the soil.

[0148] Further according to the pore distribution law of the soil, the non-saturated hydraulic conductivity curve model is as follows:

[0149]

[0150] wherein: k(θ) represents the non-saturated permeability coefficient function of the soil; ψ(θ) represents the matric suction function of the soil; ψ a represents the air-entry suction head of the soil; k s is the saturated permeability coefficient of the soil; S e represents the saturation.

[0151] According to the grading distribution characteristics of the soil, the pore fractal dimension D of the soil is obtained, and the calculation formula is as follows:

[0152]

[0153] wherein: M0 represents the total mass of the soil particles; M(r i ) represents the mass of the soil particles with the particle size less than d i ; d i represents the particle size of the soil particles; d max represents the maximum particle size of the soil particles.

[0154] In this embodiment, the particle size and mass distribution of the silty clay are obtained according to the survey data in the literature, as shown in Table 2.

[0155] Table 2 Percentage content of silty clay in each particle size range

[0156]

[0157] Substituting the existing particle size distribution (PSD) fractal model (Equation 2) into the model and performing linear regression fitting with a slope of 3-D, the fractal dimension D of the tailings sand particle size distribution can be obtained. The results are shown in Figure 6(a). Fitting the particle size test results of the silty clay with a linear fitting slope of approximately 0.205 yields an unsaturated soil pore fractal dimension D = 2.795. Based on Equations 5) and 7), the complete soil-water characteristic curve of the silty clay can be obtained, as shown in Figure 6(b).

[0158] Further establish a slope water content distribution model influenced by initial groundwater; such as Figure 2 The diagram shown is a schematic representation of the initial moisture content distribution of the slope provided in this embodiment.

[0159] The specific steps are as follows:

[0160] Based on the relationship between the soil matrix suction head ψ and the soil depth h, and ignoring the influence of residual volumetric water content, the slope water content distribution model under the influence of initial groundwater is obtained by combining the soil-water characteristic curve model. Its expression is:

[0161]

[0162] Where: θ i θ represents the water content of the slope before rainfall; i (h) represents the moisture content distribution of the slope before rainfall; ψ a The value of soil air intake is represented by b; the height of the capillary water saturation zone is represented by b = ψ. a H represents the vertical distance between the slope surface and the groundwater level; λ represents the characteristic parameter of soil porosity distribution.

[0163] The relationship between the soil matrix suction head ψ and the soil depth h is as follows:

[0164] ψ=Hh 10).

[0165] S2: Based on the soil infiltration characteristics during rainfall, the influence of the transition layer between the saturated and natural layers is considered. An elliptic curve is used to describe the distribution law of the volumetric water content of the transition layer along the depth of the slope soil, resulting in the slope water content distribution model after rainfall, as follows:

[0166] Using an elliptic curve to assume the distribution pattern of soil volumetric moisture content in the transition layer, and combining it with the slope moisture content distribution model influenced by initial groundwater, the modified slope moisture content distribution model after rainfall is obtained as follows:

[0167]

[0168] Where: θ(h) represents the slope moisture content distribution after rainfall; θ i (h f) represents the water content at the position of the wetting front peak before rainfall; h f represents the wetting front depth; h w represents the saturated layer depth; h t represents the transition layer depth.

[0169] As the infiltration process proceeds, the proportion of the transition layer to the wetting layer decreases, and the proportion of the transition layer has a good linear relationship with the wetting front depth, as shown in the following formula:

[0170] h t / h f = μ = ah f + b 12);

[0171] wherein: μ represents the proportion of the transition layer to the entire wetting front depth; az and b are linear relationship correlation coefficients.

[0172] S3: Considering the seepage of the saturated zone above the slope wetting front, introducing the slope length L, according to the rainfall conservation principle and Darcy's law, the actual depth change rate of the wetting front is obtained, which is as follows:

[0173] The change of the wetting front depth is divided into two parts, one part is the increase of the wetting front depth caused by the rainfall infiltration, and the other part is the decrease of the wetting front depth caused by the saturated zone seepage;

[0174] According to the characteristics of the rainfall infiltration of the slope, the expression of the change rate of the wetting front caused by the rainfall infiltration is obtained as follows:

[0175]

[0176] wherein: ψ f represents the matrix suction; α represents the slope angle;

[0177] In dt time, the flow ΔQ discharged from the slope by the saturated zone seepage is equal to the decrease ΔI of the cumulative infiltration amount, that is:

[0178] ΔQ = ΔI = Δθdh f 14);

[0179] wherein: Δθ represents the change amount of the water content of the soil in dt time, when considering the seepage of the saturated zone above the slope wetting front, introducing the slope length L, according to Darcy's law, the saturated zone seepage rate v above the wetting front is obtained as follows:

[0180]

[0181] The change rate of the wetting front depth caused by the saturated zone seepage above the wetting front is obtained by combining formula 14) and 15) as follows:

[0182] ​​

[0183] wherein the difference between formula 13) and 16) is the actual depth variation rate of the wetting front i.e.

[0184]

[0185] the matrix suction ψ f The relationship between the unsaturated permeability coefficient K(ψ) of the soil and the matrix suction ψ is:

[0186]

[0187] wherein ψ i represents the matrix suction of the soil when the water content of the soil is θ i ; and k(ψ) represents the unsaturated permeability coefficient function of the soil.

[0188] S4: According to the change rule of the rainfall infiltration rate, the rainfall process is divided into two stages for consideration, the expression of the rainfall infiltration rate and the relationship between the wetting front depth and the rainfall time are obtained, which are specifically:

[0189] In the rainfall process of the slope, there is a critical time t p , when the rainfall time exceeds t p , the rainwater cannot be completely infiltrated, and the surface of the slope begins to produce runoff.

[0190] Under the condition of heavy rainfall, the rainfall infiltration rate i of the slope is obtained through the actual depth variation rate of the wetting front, which is:

[0191]

[0192] wherein q represents the rainfall intensity;

[0193] According to the principle of rainfall conservation, the critical time t p corresponding to the critical wetting front depth h p and the critical rainfall infiltration amount I p are obtained, and the expressions are as follows:

[0194]

[0195] When the time for the slope soil to reach the critical wetting front depth is short at the moment of heavy rainfall, it is approximately considered that the average infiltration rate i p = (i0+i m ) / 2 before the critical time t p ; wherein the infiltration rate i0 at the initial moment is qcosα; i p is the infiltration rate corresponding to the critical time t p ;

[0196] At the critical time tp After and at time t, the average rate of rainfall infiltration i is approximately obtained by the rainfall infiltration rate of the slope s is:

[0197]

[0198] Finally, the total amount of cumulative infiltration I in each stage is obtained, and the relationship between the wetting front depth and the rainfall time is:

[0199]

[0200] As shown in Figure 3 Fig. 4(a)-(e), specifically, Fig. 4(a) is a force analysis diagram of each point of the slope in the embodiment, Fig. 4(b) is a force analysis diagram of the saturated zone in Fig. 4(a), Fig. 4(c) is a force analysis diagram of the transition zone in Fig. 4(a), Fig. 4(d) is a force analysis diagram of natural soil layer 1 in Fig. 4(a), and Fig. 4(e) is a force analysis diagram of natural soil layer 2 in Fig. 4(a); Figure 5 is a model for analyzing a silty clay shallow slope under the action of heavy rain; and the improved rainfall infiltration model is further applied to the analysis of rainfall infiltration and stability of a roadbed slope.

[0201] In this embodiment, the working condition of a rainfall intensity of 4 mm / h is selected for analysis. With different types of slope soil, the particle size distribution characteristics of the soil are also different, and the model parameter λ also changes accordingly. This embodiment can be used for slope infiltration and stability analysis under different soil pore distribution characteristics (fractal dimension). Fig. 7(a) is a schematic diagram of the change of the wetting front, i.e., the change of the slope wetting front with rainfall time under different soil pore distribution characteristics (fractal dimension). This figure is derived from equation 19) of this embodiment. As can be seen from the figure, the smaller the parameter λ, the better the water conductivity of the soil, and the higher the initial moisture content of the slope soil, resulting in a larger wetting front depth under the same rainfall duration. In addition, the smaller the λ, the smaller the critical time t p , and the earlier the runoff is formed on the slope surface.

[0202] S5: Based on the seepage characteristics and the fractal theory, the Mohr-Coulomb strength criterion is optimized, the improved infiltration model is applied to the stability analysis of the finite slope, the stability coefficients of each point inside the slope are obtained, and the minimum value of the stability coefficients is taken as the slope stability coefficient under the most unfavorable condition, specifically:

[0203] The cumulative infiltration volume at each stage was applied to the analysis of rainfall infiltration and stability of the roadbed slope. Based on seepage characteristics and fractal theory, the Mohr-Coulomb strength criterion was optimized. The improved infiltration model was applied to the stability analysis of finite slopes, and the expressions for the stability coefficients at various points inside the slope were obtained, as follows:

[0204] The effective stress σ' of soil based on fractal theory is:

[0205] σ'=(σ n -u a )+Lγ w ψ c 3-D ψ D-2 twenty four);

[0206] Shear strength τ caused by soil matrix suction s Represented as:

[0207]

[0208] Corrected shear strength τ of unsaturated soil f for:

[0209]

[0210] Where c' represents the cohesion of the soil; The internal friction angle of the soil is represented by σ. n This represents the normal stress at the bottom of the slope; (σ) n -u a ) represents the net normal force at the bottom of the slope; γ w Indicates the specific gravity of water;

[0211] The moistening front of the slope moves continuously with rainfall. The depth h of the moistening front at different rainfall times can be obtained using Equation 23). f and saturation layer depth h w Furthermore, the change in unit weight γ at various points on the slope caused by the change in slope moisture content during rainfall infiltration was derived. m (h) is:

[0212]

[0213] In the formula: γ d Indicates the dry unit weight of the soil; γ s Indicates the saturated unit weight of the soil;

[0214] Saturated zone seepage will generate seepage force j parallel to the slope surface. s Its expression is:

[0215] j s =γ w h wLsinα 28) ;

[0216] Further, the weight of the soil above the sliding surface W is:

[0217]

[0218] wherein h i represents the depth of the sliding surface at each point of the slope; γ m (h) represents the bulk density of each point of the slope after rainfall;

[0219] The normal stress σ n and the shear stress τ m at the bottom of the sliding surface are:

[0220]

[0221] Further, the safety factor of each point in the slope is:

[0222]

[0223] The safety factor expression of the slope containing n points in the slope is:

[0224] F s = {F s1 , F s2 ,..., F sn} min 33).

[0225] In this embodiment, the evaluation criteria are set as follows:

[0226] Table 3 Evaluation criteria set in this embodiment

[0227] Slope stability factor Fs Fs < 1.00 1.00 < Fs < 1.05 1.05 < Fs < Fst Fs≥Fst Slope stability state Unstable Unstable Unstable Stable Stable

[0228] Fig. 7(b) is a profile of the volumetric water content, i.e., the profile of the volumetric water content of the slope at different rainfall times, which is obtained on the basis of Fig. 7(a) and formula 9). On this basis, the Mole-Coulomb strength criterion optimized by considering the action of the saturated zone seepage and the fractal theory is further applied to the rainfall infiltration and stability analysis of the embankment slope, the safety factors of each point in the slope are obtained, and the most dangerous point of the slope can be known according to formula 29), as shown in Fig. 7(c). For the natural soil layer, the initial water contents of each point of the slope are different due to the influence of the initial underground water level, and the generated matrix suction is also different, so the influence of τ s needs to be considered, but as a whole, the safety factors F sStill with the slope body with the passage of depth and decrease, and in the depth H = 4m of impermeable bedrock layer reaches the minimum. Slope angle on the slope stability is more obvious, the steeper the slope, the same conditions, the greater the slope safety factor, the slope is more prone to instability and damage.

[0229] The influence of slope angle on slope rainfall infiltration has always been one of the focuses of research, and the embodiment aims to provide an analysis method which can be used to study the influence of different soil slope angles on slope infiltration and stability. Figure 8(a) shows the change rule of the slope wetting front with rainfall time under different slope angles, which is derived from formula 19) of the embodiment. As can be seen from the figure, under the same rainfall conditions, the size of the slope angle has a more significant influence on the moving rate of the slope wetting front, and the moving rate of the slope wetting front decreases with the increase of the slope angle. Figure 8(b) shows the slope volume water content profile under different rainfall times, which is derived on the basis of figure 8(a) and formula 9); on this basis, further considering the action of saturated zone seepage and the optimized Mohr-Coulomb strength criterion based on fractal theory, it is applied to the analysis of rainfall infiltration and stability of roadbed slope, and the safety factor of each point in the slope is obtained, and combined with formula 29), the most dangerous point of the slope can be known, as shown in figure 8(c). For natural soil layer, due to the influence of initial groundwater level, the initial water content of each point in the slope is different, and the generated matrix suction is different, the influence of τ s needs to be considered, but as a whole, the safety factor F s of each point in the natural soil layer decreases with the passage of the depth of the slope body, and reaches the minimum at the depth H = 4m of the impermeable bedrock layer. The influence of soil particle pore distribution on the slope stability is smaller, and the parameter λ mainly affects the infiltration rate of the slope and further affects the slope stability, and is more likely to affect the stability of the soil layer in the wetting front transition zone.

[0230] In summary, the embodiment is used to solve the model limitation problem caused by ignoring the complex distribution of initial water content of soil, the seepage effect of saturated zone, the transition layer of infiltration area and the soil particle size grading characteristics and other factors in the prior art, the embodiment improves the GA model by introducing the seepage characteristics and the fractal theory on the basis of the traditional Green-Ampt model, and proposes a new slope rainfall infiltration model, the model establishes a slope initial water content distribution model combined with the groundwater distribution, and the runoff-seepage coupling effect is included, and the influence of slope surface water on the infiltration rate is dynamically analyzed; further, the Mohr-Coulomb strength criterion is optimized based on the saturated zone seepage effect and the fractal theory, the improved infiltration model is applied to the finite slope stability analysis, and the limitation that the traditional model is only applicable to the infinite long slope is broken; by comprehensively considering the soil particle size characteristics, the slope surface runoff, the slope, the rainfall intensity and the groundwater level and other factors, the safety factor of each point in the slope can be accurately calculated, the accuracy of the description of the infiltration process under the condition of heavy rainfall and the reliability of the slope stability analysis are significantly improved, and effective theoretical support is provided for the slope disaster prevention and control.

[0231] The embodiment also discloses a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and the computer program is executed by a processor to realize the slope infiltration and stability analysis method.

[0232] The embodiment also discloses an electronic device, which comprises:

[0233] a processor; and a memory for storing executable instructions of the processor;

[0234] The processor is configured to execute the executable instructions to perform the slope infiltration and stability analysis method.

[0235] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and the present application can have various changes and variations for those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for analyzing the infiltration and stability of a slope, characterized by, It comprises the following steps: S1: According to the grading characteristics of soil, the soil-water characteristic curve model and the unsaturated hydraulic conductivity curve model of soil are established based on fractal theory, and the initial groundwater influence slope water content distribution model is established considering the influence of initial groundwater; S2: According to the soil infiltration characteristics during rainfall, the influence of the transition layer between the saturated layer and the natural layer is considered, and the elliptical curve is used to describe the distribution of the volumetric water content of the transition layer along the depth of the slope soil, and the slope water content distribution model after rainfall is obtained; S3: Considering the saturated zone seepage above the slope wetting front, the slope length L is introduced, and according to the rainfall conservation principle and Darcy's law, the actual depth change rate of the wetting front is obtained; S4: According to the change rule of rainfall infiltration rate, the rainfall process is divided into two stages for consideration, and the expression of rainfall infiltration rate and the relationship between wetting front depth and rainfall time are obtained; S5: Based on the seepage characteristics and the fractal theory, the Mohr-Coulomb strength criterion is optimized, the improved infiltration model is applied to the stability analysis of the finite slope, and the stability coefficient of each point in the slope is obtained, and the minimum value of the stability coefficient is taken as the slope stability coefficient under the most unfavorable condition.

2. The method for analyzing the infiltration and stability of a slope according to claim 1, wherein The S1 comprises: The soil pore surface has fractal characteristics, and the soil pore surface is covered with spherical balls with equal radius; the relationship between the number of spherical balls N(r) and the void radius (r) is: N(r) = Kr -D 1) Wherein: -D represents the pore fractal dimension, K represents the proportionality coefficient, and r represents the pore radius; The relationship between the pore volume V(r) and the void radius r is: The relative water content Λ is defined as the difference between the volume water content θ of the unsaturated soil and the residual volume water content θ r ; and equation 3) represents the change in the relative water content of the soil due to the increase in the pore size of the unsaturated soil: where: V t represents the initial pore volume of the soil; Combined with formulas 1)-3), we have: Λ = Ar 3-D 4); where: A = 4πK / [V t (3-D) and the relative volumetric water content when the soil is saturated is given by: Λ s = θ s - θ r = AR 3-D 5); where: Λ s represents the relative volume water content when the soil is in a saturated state; θ s represents the saturated volume water content of the soil of the slope; R is the maximum pore radius; Combining Eqs. 4) - 5) with the Young-Laplace equation ψ = (2T cos β) ( / r, let θ r = 0, the SWCC model describing the soil particle size distribution is obtained: where: T represents surface tension; β is the contact angle, which is taken as 0; ψ a represents the air entry suction head of the soil; and ψ represents the matric suction head of the soil. According to the pore distribution of the soil, the unsaturated hydraulic conductivity curve model is as follows: where: k(0) represents the unsaturated hydraulic conductivity function of the soil; ψ(0) represents the matric suction function of the soil; ψ a represents the air-entry suction head of the soil; k s is the saturated hydraulic conductivity of the soil; S e represents the degree of saturation According to the grading distribution characteristics of the soil, the pore fractal dimension -D of the soil is obtained, and the calculation formula is as follows: Where: M0 represents the total mass of soil particles; M(r <d i ) indicates that the particle size is less than d i Soil quality; d i Indicates soil particle size; d max Indicates the maximum soil particle size; According to the relationship between the matric suction head ψ of the soil and the soil depth h, ignoring the influence of residual volume water content, combined with the soil-water characteristic curve model, the initial groundwater influence slope water content distribution model is obtained, and the expression is: where: θ i represents the water content of the slope before rainfall; θ i (h) represents the water content distribution of the slope before rainfall; ψ a represents the air entry value of the soil; b represents the height of the capillary water saturation zone, b = ψ a ; H represents the vertical distance between the slope surface and the groundwater level; λ represents the void distribution characteristic parameter of the soil; The relationship between the matric suction head ψ of the soil and the soil depth h is: ψ=H-h10)。 3. The method according to claim 2, wherein, The S2 specifically comprises: The elliptical curve is used to assume the distribution of soil volumetric water content in the transition layer, combined with the initial groundwater influence slope water content distribution model, and the corrected slope water content distribution model after rainfall is obtained as follows: where: θ(h) represents the soil moisture profile after rainfall; θ i (h f ) represents the soil moisture at the location of the wetting front before rainfall; h f represents the depth of the wetting front; h w represents the depth of the saturated layer; h t represents the depth of the transition layer; With the progress of the infiltration process, the proportion of the transition layer to the wetting layer decreases, and the proportion of the transition layer to the wetting peak depth has a linear relationship, as shown in the following formula: h t / h f = μ = a h f + b 12); Wherein: μ represents the proportion of the transition layer to the entire wetting front depth; a and b are linear relationship correlation coefficients.

4. The method according to claim 3, wherein, The S3 comprises: The change of the wetting front depth is divided into two parts, one part is the increase of the wetting front depth caused by the rainfall infiltration, and the other part is the decrease of the wetting front depth caused by the saturated zone seepage; According to the characteristics of rainfall infiltration of the slope, the change rate of the wetting front caused by rainwater infiltration is obtained The expression is: where: ψ f represents the matrix suction; a represents the slope angle; In dt time, the flow ΔQ discharged from the slope by the saturated zone seepage is equal to the decrease ΔI of the cumulative infiltration amount, that is: ΔQ = ΔI = Δθdh f 14) Wherein: Δθ represents the change of soil water content in dt time, when considering the saturated zone seepage above the slope wetting front, the slope length L is introduced, and according to Darcy's law, the saturated zone seepage rate v above the wetting front is obtained as: Simultaneous equations 14) and 15) give the rate of change of the depth of the wetting front due to the flow in the saturated zone above the wetting front is: wherein: the difference between formula 13) and 16) is the actual rate of change of wetting front depth i.e. Matrix suction ψ f The relationship between the unsaturated permeability coefficient K(ψ) of the soil body is: where ψ i represents the matric suction of the soil when the water content of the soil is θ i ; and k(ψ) represents the unsaturated hydraulic conductivity function of the soil.

5. The method for analyzing the infiltration and stability of a slope according to claim 4, wherein The S4 comprises: There is a critical time t p When the rainfall time exceeds t p , the rainwater cannot completely infiltrate, and the surface of the slope begins to produce runoff; Under the condition of heavy rainfall, the rainfall infiltration rate i of the slope is obtained by the actual depth variation rate of the wetting front: wherein q represents the rainfall intensity; According to the rain conservation principle, the critical time t p The corresponding critical wetting front depth h p And the critical rainfall infiltration I p , the expression is as follows: When the time it takes for the slope soil to reach the critical wetting front depth during heavy rainfall is relatively short, the critical time t is approximately considered to be... p Previous average infiltration rate i m =(i0+i p ) / 2; where the initial infiltration rate i0 = qcosα; i p The critical time t p The corresponding infiltration rate at that time; At the critical time t p After time t and before time t, the average rate of rainfall infiltration i is approximately obtained by the rainfall infiltration rate of the slope s is: Finally, the total amount of cumulative infiltration I of each stage and the relationship between the wetting front depth and the rainfall time are obtained as follows:

6. The method for analyzing the infiltration and stability of a slope according to claim 5, wherein The S5 comprises: The total amount of cumulative infiltration of each stage is applied to the rainfall infiltration and stability analysis of the subgrade slope, the improved infiltration model is applied to the stability analysis of the finite slope based on the seepage characteristics and the fractal theory optimization Mohr-Coulomb strength criterion, and the stability coefficient expression of each point in the slope is obtained as follows: The effective stress σ' of the soil based on the fractal theory is: σ' = (σ n - u a + Lγ w ψ c 3-D ψ D-2 24); Shear strength τ caused by matric suction of soil s is expressed as: Amending the shear strength τ of unsaturated soils f is: wherein c' represents the cohesion of the soil; represents the internal friction angle of the soil; σ n represents the normal stress at the toe of the slope; (σ n -y a ) represents the net normal force at the toe of the slope; γ w represents the unit weight of water; The wetting front of the slope body continuously moves with the rainfall, and the wetting front depth hf and the saturated layer depth h at different rainfall times are obtained by formula 23) w Further, the change of the unit weight γ of each point of the slope body caused by the change of the water content of the slope body during the rainfall infiltration process is obtained m (h) is: where: γ d represents the dry density of the soil mass; γ s represents the saturated density of the soil mass; Saturated zone flow will produce a seepage force j parallel to the slope surface s The expression for this is j s = γ w h w Lsinα 28); The weight W of the soil above the sliding surface is further obtained as follows: where: h i represents the depth of the slip surface at each point of the slope; γ m (h) represents the bulk density of each point of the slope after rainfall; Normal stress σ at the bottom of the sliding surface n and shear stress τ m is: Further, the safety factor F at each point in the slope is obtained sn is: The slope safety coefficient expression containing the safety coefficients of n points in the slope is obtained as follows: F s = {F s1 , F s2 ,..., F sn} min 33).

7. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the slope infiltration and stability analysis method in any one of claims 1-6.

8. An electronic device, comprising: comprises: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to execute the executable instructions to perform the slope infiltration and stability analysis method in any one of claims 1-6.

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