A numerical method for slope stability analysis related to displacement

Abstract

The present invention discloses a numerical method for analyzing the slope stability associated with displacement, which solves the technical problem of physical incoordination in the traditional strength reduction method in the prior art. The numerical method includes the steps of: establishing a numerical simulation analysis model for the slope; using the parameter synchronous variation technique and adopting the numerical simulation method to calculate and determine the ultimate value of the strength reduction coefficient corresponding to the ultimate state of the slope body and the corresponding potential slip surface of the slope body; equally dividing the range between the numerical value 1 and the ultimate value of the strength reduction coefficient into n integer parts to form a series of calculated intermediate reduction coefficients; synchronously varying the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass according to the calculated intermediate reduction coefficients, and then using the numerical simulation method to calculate the corresponding slope body displacement field and the displacement of any point on the potential sliding body of the slope body; calculating the slope stability coefficient corresponding to each intermediate reduction coefficient; and obtaining the relationship between the slope stability coefficient F and the slope body displacement.

Description

Technical Field

[0001] The present invention relates to the technical field of slope stability analysis. Specifically, it relates to a numerical method for slope stability analysis associated with displacement. Background Technique

[0002] The problem of slope stability is an important issue in geotechnical engineering practice. Reasonable analysis of slope stability is one of the key links in relevant engineering designs. Subject to the elastoplastic deformation, creep deformation characteristics of slope rock and soil masses, as well as the changes in external environments such as the geological environment and meteorological environment where the slope is located, the slope will generate displacement. Along with the occurrence of slope displacement, the stability of the slope also changes accordingly. However, in traditional slope stability analysis methods including the limit equilibrium method and current specifications, there is no method that closely and quantitatively associates slope stability with its displacement, and it does not reflect the quantitative change characteristics of the stability coefficient of the slope with its displacement. In relevant practical projects, there is a lack of reasonable calculation and analysis method references, mainly relying on experience, and there is blindness in design. Therefore, for slopes that are prone to deformation due to internal and external conditions of the slope body, there is an urgent need for a more reasonable quantitative method for slope stability analysis associated with displacement in engineering practice.

[0003] Currently, for the analysis of slope displacement, numerical simulation methods such as the finite element method and the finite difference method can generally be used. Among them, to determine the stability characteristics of the slope body, the shear strength reduction technique, commonly known as the strength reduction method, is usually used. The traditional strength reduction method is to continuously reduce the strength parameters of the rock and soil masses during the numerical simulation calculation of slope stability analysis until the ultimate state of the slope body is reached. In particular, during this calculation and analysis process, only the strength parameters of the slope rock and soil masses are reduced, while its deformation parameters remain unchanged all the time. In fact, from the perspective of the physical properties of rock and soil masses, its deformation characteristics and strength characteristics are intrinsically related. Keeping the deformation parameters unchanged during the strength reduction process obviously does not conform to the physical properties of actual rock and soil masses, that is, the traditional strength reduction method is physically inconsistent. Summary of the Invention

[0004] The main object of the present invention is to provide a numerical method for slope stability analysis associated with displacement to solve the technical problem of physical inconsistency of the traditional strength reduction method in the prior art.

[0005] To achieve the above object, the present invention provides a numerical method for slope stability analysis associated with displacement, and the technical solution is as follows:

[0006] A numerical method for slope stability analysis associated with displacement includes the following steps:

[0007] Step 10, establish a numerical simulation analysis model of the slope;

[0008] Step 20: Using the parameter synchronous variation technique, calculate and determine the ultimate value ψ of the strength reduction factor corresponding to the ultimate state of the slope body by means of numerical simulation u and the corresponding potential slip surface of the slope body;

[0009] Step 30: Divide the range between the numerical value 1 and the ultimate value ψ of the strength reduction factor into n equal integer parts to form a series of intermediate reduction factors λ for calculation u ; j ;

[0010] Step 40: Synchronously vary the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass according to the intermediate reduction factor λ for calculation j , and then calculate the corresponding displacement field of the slope body and the displacement of any point on the potential sliding mass of the slope body by means of numerical simulation;

[0011] Step 50: Calculate the corresponding slope stability coefficient F for each intermediate reduction factor λ j ; sj ;

[0012] Step 60: Obtain the relationship between the slope stability coefficient F sj and the displacement of the slope body.

[0013] The technical concept and technical effect of the present invention are as follows:

[0014] The simple strength reduction method has little influence on the result of the slope stability coefficient, but has a great influence on the result of the slope displacement, and the latter is a very critical value for the problem of slope stability analysis related to displacement. Therefore, a practical approach should be to reasonably process the deformation parameters synchronously during the strength reduction process of the rock and soil mass so that they change synchronously and coordinately. However, there is currently no method for reasonably and coordinately processing the strength parameters and deformation parameters of the rock and soil mass, making the relevant engineering designs lack scientificity and rationality in specific application analysis.

[0015] Therefore, the present invention overcomes the deficiencies of the traditional method and proposes a simple and reasonable numerical method for analyzing the slope stability related to displacement. Based on the numerical simulation method, this method uses the parameter synchronous coordination variation technique to reasonably and coordinately process the strength parameters and deformation parameters of the slope rock and soil mass, with sufficient physical coordination. While analyzing the slope stability, it can also reasonably obtain the corresponding displacement, making the calculation of the slope body displacement corresponding to different strength reduction factors more reasonable. The quantitative variation relationship between the slope stability coefficient and its displacement can be obtained, enabling engineers to more easily analyze the slope stability related to displacement and providing a fast and effective technical means and algorithm basis for the design calculation operation of relevant practical projects, having important technical significance and engineering application value.

[0016] Furthermore, the method for determining the slope stability coefficient in different intermediate calculation states according to the present invention is simple and convenient for quick operation. By using the method of the present invention, the quantitative characteristics of the change of the slope stability coefficient with its displacement development can be simply calculated without time-consuming, laborious and costly tests, and the relationship between the slope stability coefficients and the corresponding slope displacements can be quickly obtained, which is convenient for rapid engineering design analysis.

[0017] The following further describes the present invention in conjunction with the drawings and specific embodiments. Some of the additional aspects and advantages of the present invention will be given in the following description, some will become obvious from the following description, or will be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The content provided in the drawings and the related descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention. In the drawings:

[0019] Figure 1 It is a schematic diagram of a typical slope analysis object of the present invention.

[0020] Figure 2 It is a schematic diagram of the slope in the embodiment of the present invention.

[0021] Figure 3 It is a schematic diagram of the geometric range of the slope numerical simulation analysis model in the embodiment of the present invention.

[0022] Figure 4 It is a schematic diagram of the mesh division and boundary conditions of the slope numerical simulation analysis model in the embodiment of the present invention.

[0023] Figure 5 It is a schematic diagram of the potential slip surface of the slope body in the embodiment of the present invention.

[0024] Figure 6 It is the intermediate reduction coefficient λ j = 1.012 of the slope displacement contour map.

[0025] Figure 7 It is the intermediate reduction coefficient λ j = 1.037 of the slope displacement contour map.

[0026] Figure 8 It is the intermediate reduction coefficient λ j = 1.062 of the slope displacement contour map.

[0027] Figure 9 It is the intermediate reduction coefficient λ j = 1.087 of the slope displacement contour map.

[0028] Figure 10 is the intermediate reduction coefficient λ of the embodiment of the present invention j when = 1.112, the slope displacement nephogram.

[0029] Figure 11 is the slope stability coefficient F of the embodiment of the present invention sj and the relationship curve of the horizontal displacement of point A at the slope toe.

[0030] Figure 12 is the slope stability coefficient F of the embodiment of the present invention sj and the relationship curve of the vertical displacement of point A at the slope toe.

[0031] Figure 13 is the slope stability coefficient F of the embodiment of the present invention sj and the relationship curve of the horizontal displacement of point B at the slope top.

[0032] Figure 14 is the slope stability coefficient F of the embodiment of the present invention sj and the relationship curve of the vertical displacement of point B at the slope top. Detailed implementation manners

[0033] The present invention will be described clearly and completely below with reference to the accompanying drawings. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the accompanying drawings, it should be particularly noted that:

[0034] The technical solutions and technical features provided in each part including the following description in the present invention can be combined with each other without conflict.

[0035] In addition, the embodiments of the present invention involved in the following description are usually only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts should fall within the protection scope of the present invention.

[0036] Regarding the terms and units in the present invention. The terms "including", "having" and any variations thereof in the specification, claims and relevant parts of the present invention are intended to cover non-exclusive inclusion.

[0037] Figure 1 is a schematic diagram of the typical slope analysis object of the present invention.

[0038] As Figure 1 shown, the specific implementation manner of the numerical method for slope stability analysis of associated displacements of the present invention includes steps 10 - 600, specifically as follows:

[0039] Step 10, establish a numerical simulation analysis model for the slope.

[0040] According to the basic data such as the geometry and geology of the slope, use FLAC3D software or ABAQUS software to establish the numerical simulation analysis model of the slope;

[0041] The geometric range of the numerical simulation analysis model of the slope is taken as follows: the horizontal distance from the rear boundary of the slope top to the slope top is not less than 2 times the slope height, and the horizontal distance from the outer boundary of the slope toe to the slope toe is not less than 1 time the slope height;

[0042] The boundary of the numerical simulation analysis model of the slope adopts the standard static boundary, that is: the bottom surface is fixed and constrained, and the horizontal displacements on both sides are constrained.

[0043] Step 20, use the parameter synchronous change technology and adopt the numerical simulation method to calculate and determine the ultimate value ψ of the strength reduction coefficient corresponding to the ultimate state of the slope body u and the corresponding potential slip surface of the slope body.

[0044] The parameter synchronous change technology is as follows: for the established numerical simulation analysis model of the slope, a series of synchronous changes are made to the strength parameters and deformation parameters of the slope rock and soil mass. Among them, the strength parameters are reduced, and the deformation parameters are synchronously adjusted with the reduction of the strength parameters.

[0045] The numerical simulation method is as follows: comprehensively judge the ultimate state of the slope body through the judgment conditions including the penetration of the plastic zone, the inflection point of the displacement-vs.-strength reduction coefficient curve, and the non-convergence of the calculation, so as to determine the ultimate value ψ of the strength reduction coefficient corresponding to the ultimate state of the slope body u and the corresponding potential slip surface of the slope body.

[0046] The calculation expressions for the synchronous change of cohesion, internal friction angle, elastic modulus, and Poisson's ratio with the strength reduction coefficient are respectively:

[0047]

[0048] In the formula, ψ is the strength reduction coefficient, ψ i is the coefficient of the i-th strength reduction, and the ultimate value ψ of the strength reduction coefficient u is ψ i is the maximum value; c, μ, E are respectively the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass; c i , μ i , E i are respectively the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass corresponding to the coefficient ψ i of the i-th strength reduction; β is an intermediate calculation parameter, and its expression is

[0049] Step 30: Divide the range between the value 1 and the ultimate value of the strength reduction factor ψ u into n equal integer parts to form a series of intermediate reduction factors λ for calculation j .

[0050] Preferably, take n≥10 to form a series of intermediate reduction factors λ for calculation j , and its calculation expression is:[[]]

[0051]

[0052] where j is the calculation process identification number, j = 0, 1, 2, 3, …, n.[[]]

[0053] Step 40: Synchronously vary the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass according to the intermediate reduction factor λ for calculation j , and then use the numerical simulation method to calculate the corresponding slope displacement field and the displacement of any point on the potential sliding mass of the slope.[[]]

[0054] The calculation expressions for synchronously varying the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass according to the intermediate reduction factor λ for calculation are respectively:[[]] j [[]]

[0055]

[0056] where c j , μ j , E j are respectively the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass corresponding to the intermediate reduction factor λ for calculation j .

[0057] Then, use the FLAC3D software or the ABAQUS software to calculate the corresponding slope displacement field by the numerical simulation method, and the displacement of any point on the potential sliding mass of the slope can be obtained synchronously, including the horizontal displacement u j and the vertical displacement v j .

[0058] Step 50: Calculate the slope stability factor F j corresponding to each intermediate reduction factor λ for calculation sj .

[0059] According to the ultimate value ψ of the strength reduction factor corresponding to the ultimate state of the slope obtained in Step 20 u , and the intermediate reduction factor λ obtained from Equation (6)[[]] j , the slope stability factor F corresponding to λ j can be obtainedsj , and its calculation expression is:

[0060]

[0061] Correspondingly, when j = 0, λ j = 1, which is the initial state of the slope body without changes in strength parameters and deformation parameters. The corresponding slope stability coefficient F sj is ψ u ;

[0062] When j = n, λ j = ψ u , which is the final state where the strength parameters and deformation parameters change synchronously to the limit of the slope body. The corresponding slope stability coefficient F sj is 1.

[0063] Step 60: Obtain the relationship between the slope stability coefficient F sj and the displacement of the slope body.

[0064] According to the stability coefficient F sj obtained in Step 50 and the horizontal displacement u j and vertical displacement v j of the slope body determined in Step 40, the relationship between the slope stability coefficient F s and the horizontal displacement u or vertical displacement v of the slope body can be determined, preferably represented in the form of a relationship curve.

[0065] The beneficial effects of the present invention are illustrated below through specific embodiments.

[0066] Such as Figure 2 a slope shown, with the unit weight of soil being 19.63 kN / m 3 , and its relevant calculation parameters are shown in Table 1.

[0067] Table 1

[0068]

[0069] Step 10:

[0070] According to the basic data such as the geometry and geology of the slope, use FLAC3D software to establish a numerical simulation analysis model. The geometric range of the model is shown in Figure 3 , and the model boundary adopts the standard static boundary. The numerical model including mesh division and boundary conditions is shown in Figure 4 .

[0071] Step 20:

[0072] Substitute the relevant parameters into Equation (5) to obtain:

[0073]

[0074] By performing synchronous variation calculations on relevant parameters according to equations (1) to (4), we can obtain:

[0075]

[0076]

[0077] Using the parameter synchronous variation technique and numerical simulation method, the ultimate value ψ of the strength reduction factor corresponding to the limit state of the slope body is calculated. u = 1.124, and the corresponding potential slip surface of the slope body is as Figure 5 shown.

[0078] Step 30:

[0079] Take the integer n = 10, and the intermediate reduction factor λ can be obtained according to equation (6) j :

[0080]

[0081] where j = 0, 1, 2, 3,..., 10.

[0082] Step 40:

[0083] By performing synchronous variation calculations on relevant parameters according to equations (7) to (10), we can obtain:

[0084]

[0085] Calculate the displacement field of the corresponding slope for each intermediate reduction factor λ j . Among them, the contour maps of the slope displacement field when the typical λ j = 1.012, 1.037, 1.062, 1.087, 1.112 are as Figures 6 - 10 shown.

[0086] Step 50:

[0087] According to equation (11), the stability factor F of the slope corresponding to the calculated intermediate reduction factor λ j can be calculated. sj is:

[0088]

[0089] Step 60:

[0090] Finally, the horizontal displacement u j and vertical displacement v j at point A at the slope toe, and the horizontal displacement u j and vertical displacement v j at point B at the slope top are obtained under different calculated intermediate reduction factors λ jand the slope stability coefficient F sj The results are shown in Table 2.

[0091] Table 2

[0092]

[0093] The relationship curves between the slope stability coefficient determined according to the results in Table 2 and the slope displacement are as Figures 11 - 14 shown. Among them, Figure 11 , Figure 12 are the relationship curves between the slope stability coefficient and the horizontal displacement and vertical displacement of point A at the slope toe respectively; Figure 13 , Figure 14 are the relationship curves between the slope stability coefficient and the horizontal displacement and vertical displacement of point B at the slope top respectively.

[0094] To specifically present the differences between the method of the present invention and the calculation results of the traditional strength reduction method, Table 3 gives a comparison of the two methods for the relationship between the slope stability coefficient and the horizontal displacement and vertical displacement of point A at the slope toe, and Table 4 gives a comparison of the two methods for the relationship curves between the slope stability coefficient and the horizontal displacement and vertical displacement of point B at the slope top.

[0095] It can be seen from Tables 3 - 4 that under the same slope stability coefficient, the displacement results of the method of the present invention are all greater than those of the traditional method, indicating that the slope stability coefficient obtained by the traditional method based on the strength reduction technology is relatively too sensitive to displacement, while the method of the present invention is more reasonable. Its essence reflects the elastoplastic deformation characteristics of general geotechnical bodies, which is more in line with the actual situation; for the calculation results of the traditional method, under the same slope stability coefficient, the slope displacement is smaller than the results of the present method, and its essence tends to reflect the brittle fracture characteristics of materials, which does not conform to the deformation characteristics of general geotechnical bodies (especially soil and loose fragmented rock masses).

[0096] Table 3

[0097]

[0098] Table 4

[0099]

[0100] The above has described the relevant content of the present invention. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above content of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

Claims

1. A numerical method for analyzing the stability of slopes associated with displacement, characterized in that: It includes the following steps: Step 10: Establish a numerical simulation analysis model for the slope; Step 20, using the parameter synchronous change technology, adopt the numerical simulation method to calculate and determine the ultimate value ψ of the strength reduction factor corresponding to the ultimate state of the slope body u and the corresponding potential slip surface of the slope body; Step 30, equally divide the range between the value 1 and the limit value ψ of the strength reduction factor into n integer parts to form a series of intermediate reduction factors λ for calculation u ; j ; Step 40: Calculate the intermediate reduction coefficient λ j Synchronously vary the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass, and then use the numerical simulation method to calculate the corresponding slope displacement field and the displacement of any point on the potential sliding mass of the slope; Step 50, calculate each intermediate reduction coefficient λ j The corresponding slope stability coefficient F sj ; Step 60, obtaining the relationship between the slope stability coefficient F sj and the slope displacement; In Step 20: The calculation expressions for the cohesion, internal friction angle, elastic modulus, and Poisson's ratio that vary synchronously with the strength reduction factor are respectively: In step 30: take n≥10, so as to form a series of intermediate reduction coefficients λ j , and its calculation expression is: In step 40: According to the calculated intermediate reduction coefficient λ j The calculation expressions for the synchronous variation of the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass are respectively: where ψ i is the coefficient of the i-th strength reduction, and the limit value of the strength reduction coefficient ψ u is the maximum value of ψ i ; c, μ, and E are the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass, respectively; c i , μ i , and E i are the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass corresponding to the coefficient ψ i of the i-th strength reduction, respectively; β is an intermediate calculation parameter, and its expression is j is the calculation process identification number, j = 0, 1, 2, 3, …, n; c j , μ j , and E j are the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil mass corresponding to the intermediate reduction coefficient λ j , respectively.

2. The numerical method for analyzing the slope stability related to displacement according to claim 1, wherein: In Step 10: Use FLAC3D software or ABAQUS software to establish the numerical simulation analysis model for the slope; The geometric range of the numerical simulation analysis model for the slope is taken as follows: The horizontal distance from the rear boundary of the slope top to the slope top is not less than 2 times the slope height, and the horizontal distance from the outer boundary of the slope toe to the slope toe is not less than 1 times the slope height; The boundary of the numerical simulation analysis model for the slope adopts the standard static boundary.

3. The numerical method for analyzing the slope stability related to displacement according to claim 1, characterized in that: In Step 20: The parameter synchronous variation technique is as follows: For the established numerical simulation analysis model for the slope, a series of synchronous variations are carried out on the strength parameters and deformation parameters of the slope rock and soil mass. Among them, the strength parameter is reduced, and the deformation parameter is synchronously adjusted with the reduction of the strength parameter; The numerical simulation method is as follows: The ultimate state of the slope body is comprehensively judged through judgment conditions including three conditions: the penetration of the plastic zone, the inflection point appears in the curve of displacement varying with the strength reduction coefficient, and the calculation does not converge, so as to determine the ultimate value ψ of the strength reduction coefficient corresponding to the ultimate state of the slope body. u and the corresponding potential slip surface of the slope body.

4. A numerical method for analyzing the stability of slopes related to displacement according to claim 1, characterized in that: In step 50: the slope stability factor F sj The calculation expression is: When j = 0, λ j = 1, which is the initial state of the slope body without changes in strength parameters and deformation parameters. The corresponding slope stability coefficient F sj is ψ u ; When j = n, λ j = ψ u , that is, the strength parameter and the deformation parameter synchronously change to the ultimate state of the slope body, and the corresponding slope stability coefficient F sj is 1.

5. A numerical method for analyzing the slope stability related to displacement according to claim 1, characterized in that: In step 60: The displacement includes horizontal displacement and vertical displacement, and the relationship between the slope stability factor F s and the horizontal or vertical displacement of the slope body is represented by a relationship curve.

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