Numerical method for slope stability analysis associated with displacement

Abstract

The invention discloses a numerical method for slope stability analysis associated with displacement. The technical problem that in the prior art, a traditional strength reduction method is not physically coordinated is solved. The numerical method comprises the following steps: establishing a slope numerical simulation analysis model; calculating and determining a strength reduction coefficient limit value corresponding to the limit state of the slope body and a corresponding potential sliding surface of the slope body by using a parameter synchronous change technology and a numerical simulation method; equally dividing the range between the numerical value 1 and the strength reduction coefficient limit value into an integer n to form a series of calculation intermediate reduction coefficients; synchronously changing the cohesive force, the internal friction angle, the Poisson's ratio and the elastic modulus of the slope rock-soil body according to the calculated intermediate reduction coefficient, and then calculating by adopting a numerical simulation method to obtain a corresponding slope body displacement field and the displacement of any point on the potential slip mass of the slope body; calculating a slope stability coefficient corresponding to each middle reduction coefficient; and obtaining the relationship between the slope stability coefficient F and the slope body displacement.

Description

Technical Field

[0001] The invention relates to the technical field of slope stability analysis, and in particular to a numerical method for slope stability analysis with associated displacement. Background Art

[0002] Slope stability is an important problem in geotechnical engineering practice. Reasonable analysis of slope stability is one of the key links in related engineering design. Subject to the elastic-plastic deformation and creep deformation characteristics of the slope rock and soil, as well as the changes in the external environment such as the geological environment and meteorological environment where the slope is located, the slope will produce displacement. With the occurrence of slope displacement, the stability of the slope will also change. However, traditional slope stability analysis methods including the limit equilibrium method and current specifications do not have a method that closely quantitatively associates slope stability with its displacement, and do not reflect the quantitative change characteristics of the slope stability coefficient with its displacement. There is a lack of reasonable calculation and analysis method reference in related actual projects, and most of them are based on experience, which is blind in design. Therefore, for those slopes that are prone to deformation due to the influence of internal and external conditions of the slope, a more reasonable quantitative method for slope stability analysis with associated displacement is urgently needed in engineering practice.

[0003] At present, the analysis of slope displacement generally adopts numerical simulation methods such as finite element method and finite difference method. Among them, in order to determine the stability characteristics of the slope, the shear strength reduction technology, commonly known as the strength reduction method, can be usually used. The traditional strength reduction method is to continuously reduce the strength parameters of the rock and soil body in the numerical simulation calculation process of the slope stability analysis until the limit state of the slope is reached. In particular, in this calculation and analysis process, only the strength parameters of the slope rock and soil body are reduced, while its deformation parameters remain unchanged. In fact, from the perspective of the physical properties of the rock and soil body, its deformation characteristics and strength characteristics are inherently correlated. Keeping the deformation parameters unchanged during the strength reduction process is obviously inconsistent with the physical properties of the actual rock and soil body, that is, the traditional strength reduction method is physically inconsistent. Summary of the invention

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

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

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

[0007] Step 10, establishing a slope numerical simulation analysis model;

[0008] Step 20: Using the parameter synchronous variation technology and numerical simulation method, calculate and determine the limit value of the strength reduction factor corresponding to the ultimate state of the slope ψ u and the corresponding potential sliding surface of the slope;

[0009] Step 30: Set the value 1 and the strength reduction factor limit value ψ u The range between is divided into n integer parts, forming a series of calculation intermediate reduction coefficients λ j ;

[0010] Step 40, calculating the intermediate reduction coefficient λ j The cohesion, internal friction angle, Poisson's ratio and elastic modulus of the slope rock and soil are changed synchronously, and then the corresponding slope displacement field and the displacement of any point on the potential sliding body of the slope are calculated by numerical simulation method;

[0011] Step 50, calculate each intermediate reduction factor λ j The corresponding slope stability factor F sj ;

[0012] Step 60, obtain the slope stability coefficient F sj The relationship between the displacement of the slope.

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

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

[0015] To this end, the present invention overcomes the shortcomings of traditional methods and proposes a simple and reasonable numerical method for slope stability analysis with associated displacement. The method is based on a numerical simulation method and adopts parameter synchronous coordinated change technology to synchronously and reasonably coordinate the strength parameters and deformation parameters of the slope rock and soil body. It has sufficient physical coordination and can reasonably obtain the corresponding displacement while analyzing the slope stability, making the slope displacement calculation corresponding to different strength reduction factors more reasonable. The quantitative change relationship between the slope stability coefficient and its displacement can be obtained, so that engineering designers can more easily analyze the slope stability with associated displacement, and provide a fast and effective technical means and algorithm basis for the design and calculation operations of related actual projects, which has important technical significance and engineering application value.

[0016] Furthermore, the method of the present invention is simple to determine the slope stability coefficient in different intermediate calculation states, and is convenient for quick operation. The method of the present invention can be used to simply calculate and determine the quantitative characteristics of the slope stability coefficient as it develops with its displacement without time-consuming, labor-intensive, and costly experiments. The relationship between each slope stability coefficient and the corresponding slope displacement can be quickly obtained, which is convenient for quick engineering design analysis.

[0017] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned 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 contents provided in the drawings and their related descriptions in the present invention can be used to explain the present invention, but do not constitute improper limitations on 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 Schematic diagram of a slope according to an embodiment of the present invention.

[0021] Figure 3 Schematic diagram of the number and range of the slope numerical simulation analysis model according to an embodiment of the present invention.

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

[0023] Figure 5 Schematic diagram of a potential sliding surface of a slope according to an embodiment of the present invention.

[0024] Figure 6 is the intermediate reduction coefficient λ of the embodiment of the present invention j Slope displacement cloud diagram when =1.012.

[0025] Figure 7 is the intermediate reduction coefficient λ of the embodiment of the present invention j Slope displacement cloud diagram when =1.037.

[0026] Figure 8 is the intermediate reduction coefficient λ of the embodiment of the present invention j Slope displacement cloud diagram when =1.062.

[0027] Fig. 9 is the intermediate reduction coefficient λ of the embodiment of the present invention j =1.087 when the slope displacement cloud diagram.

[0028] Fig.10 is the intermediate reduction coefficient λ of the embodiment of the present invention j Slope displacement cloud diagram when =1.112.

[0029] Fig.11 is the slope stability coefficient F of the embodiment of the present invention sj Relationship curve with the horizontal displacement of point A at the toe of the slope.

[0030] Fig.12 is the slope stability coefficient F of the embodiment of the present invention sj Relationship curve with the vertical displacement of point A at the toe of the slope.

[0031] Fig.13 is the slope stability coefficient F of the embodiment of the present invention sj Relationship curve with the horizontal displacement of point B at the top of the slope.

[0032] Fig.14 is the slope stability coefficient F of the embodiment of the present invention sj Relationship curve with the vertical displacement of point B at the top of the slope. DETAILED DESCRIPTION

[0033] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0034] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0035] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0036] About the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusions.

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

[0038] like Figure 1 As shown, the specific implementation of the numerical method for slope stability analysis with associated displacement of the present invention includes steps 10-600, which are as follows:

[0039] Step 10: Establish a slope numerical simulation analysis model.

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

[0041] The geometric range of the slope numerical simulation analysis model is 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 foot to the slope foot is not less than 1 times the slope height;

[0042] The boundary of the slope numerical simulation analysis model adopts the standard static boundary, that is, fixed constraint on the bottom and horizontal displacement constraint on both sides.

[0043] Step 20: Using the parameter synchronous variation technology and numerical simulation method, calculate and determine the limit value of the strength reduction factor corresponding to the ultimate state of the slope ψ u And the corresponding potential sliding surface of the slope.

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

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

[0046] The calculation expressions of cohesion, internal friction angle, elastic model and Poisson's ratio changing synchronously with the strength reduction coefficient are:

[0047]

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

[0049] Step 30: Set the value 1 and the strength reduction factor limit value ψ u The range between is divided into n integer parts, forming a series of calculation intermediate reduction coefficients λ j .

[0050] It is preferred to take n≥10, so as to form a series of calculation intermediate reduction coefficients λ j , its calculation expression is:

[0051]

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

[0053] Step 40, calculating the intermediate reduction coefficient λ j The cohesion, internal friction angle, Poisson's ratio and elastic modulus of the slope rock and soil are changed synchronously, and then the corresponding slope displacement field and the displacement of any point on the potential sliding body of the slope are calculated using numerical simulation methods.

[0054] According to the calculation of the intermediate reduction factor λ j The calculation expressions for synchronous changes in the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil are:

[0055]

[0056] In the formula, c j , μ j 、E j are respectively and calculated as the intermediate reduction factor λ j The corresponding cohesion, internal friction angle, Poisson's ratio and elastic modulus of the slope rock and soil.

[0057] Then, the corresponding slope displacement field can be calculated by numerical simulation using FLAC3D software or ABAQUS software, and the displacement of any point on the potential sliding body of the slope can be obtained simultaneously, including the horizontal displacement u j and vertical displacement v j .

[0058] Step 50, calculate each intermediate reduction factor λ j The corresponding slope stability factor F sj .

[0059] According to the limit value of the strength reduction factor ψ corresponding to the ultimate state of the slope obtained in step 20 u , and the intermediate reduction coefficient λ obtained by formula (6) j , we can get j The corresponding slope stability factor Fsj , its calculation expression is:

[0060]

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

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

[0063] Step 60, obtain the slope stability coefficient F sj The relationship between the displacement of the slope.

[0064] According to the stability factor F obtained in step 50 sj The horizontal displacement u of the slope determined in step 40 j and vertical displacement v j , the slope stability factor F can be determined s The relationship between the horizontal displacement u or vertical displacement v of the slope is preferably expressed in the form of a relationship curve.

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

[0066] like Figure 2 The slope shown has a soil density of 19.63 kN / m 3 The relevant calculation parameters are shown in Table 1.

[0067] Table 1

[0068]

[0069] Step 10:

[0070] According to the basic data of slope geometry and geology, the numerical simulation analysis model was established using FLAC3D software. The geometric range of the model is shown in Figure 3 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] Substituting the relevant parameters into formula (5) we can get:

[0073]

[0074] According to equations (1) to (4), the synchronous change calculation of relevant parameters can be obtained:

[0075]

[0076]

[0077] The strength reduction factor limit value ψ corresponding to the ultimate state of the slope is calculated by using the parameter synchronous variation technology and numerical simulation method. u =1.124, and the corresponding potential sliding surface of the slope is as follows Figure 5 shown.

[0078] Step 30:

[0079] Taking the integer n = 10, the intermediate reduction coefficient λ can be calculated according to formula (6): j :

[0080]

[0081] Among them, j=0,1,2,3,…,10.

[0082] Step 40:

[0083] According to equations (7) to (10), the synchronous change calculation of relevant parameters can be obtained:

[0084]

[0085] Calculate the intermediate reduction coefficient λ j The displacement field of the corresponding slope is j =1.012, 1.037, 1.062, 1.087, 1.112 when the slope displacement field cloud diagram is as follows Figures 6 to 10 shown.

[0086] Step 50:

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

[0088]

[0089] Step 60:

[0090] Finally, we get different calculation intermediate reduction coefficients λ j The horizontal displacement u of the slope foot point A is j and vertical displacement v j , horizontal displacement u of point B at the top of the slope j and vertical displacement v jand the slope stability factor F sj The results are shown in Table 2.

[0091] Table 2

[0092]

[0093] The relationship curve between the slope stability coefficient and the slope displacement determined according to the results in Table 2 is as follows: Figure 11 to Figure 14 As shown. Among them, Fig.11 , Fig.12 They are the relationship curves between the slope stability coefficient and the horizontal and vertical displacements of point A at the slope foot; Fig.13 , Fig.14 They are the relationship curves between the slope stability coefficient and the horizontal displacement and vertical displacement of point B at the top of the slope.

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

[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 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 the displacement, while the method of the present invention is more reasonable, and its essence reflects the elastic-plastic deformation characteristics of general rock and soil, 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 result of the method, and its essence tends to reflect the brittle fracture characteristics of the material, which is not in line with the deformation characteristics of general rock and soil (especially soil and loose and fragmented rock).

[0096] Table 3

[0097]

[0098] Table 4

[0099]

[0100] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without creative work shall fall within the scope of protection of the present invention.

Claims

1. A numerical method for slope stability analysis with associated displacements, characterized by: The following steps are involved: Step 10, establishing a slope numerical simulation analysis model; Step 20: Using the parameter synchronous variation technology and numerical simulation method, calculate and determine the limit value of the strength reduction factor corresponding to the ultimate state of the slope ψ u and the corresponding potential sliding surface of the slope; Step 30: Set the value 1 and the strength reduction factor limit value ψ u The range between is divided into n integer parts, forming a series of calculation intermediate reduction coefficients λ j ; Step 40, calculating the intermediate reduction coefficient λ j The cohesion, internal friction angle, Poisson's ratio and elastic modulus of the slope rock and soil are changed synchronously, and then the corresponding slope displacement field and the displacement of any point on the potential sliding body of the slope are calculated by numerical simulation method; Step 50, calculate each intermediate reduction factor λ j The corresponding slope stability factor F sj ; Step 60, obtain the slope stability coefficient F sj The relationship between the displacement of the slope.

2. A numerical method for slope stability analysis with associated displacements as claimed in claim 1, characterized in that: In step 10: using FLAC3D software or ABAQUS software to establish the slope numerical simulation analysis model; The geometric range of the slope numerical simulation analysis model is 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 foot to the slope foot is not less than 1 times the slope height; The boundary of the slope numerical simulation analysis model adopts the standard static boundary.

3. A numerical method for slope stability analysis with associated displacements as claimed in claim 1, characterized in that: In step 20, the parameter synchronous change technology is: for the established slope numerical simulation analysis model, a series of synchronous changes are made to the strength parameters and deformation parameters of the slope rock and soil, wherein the strength parameter is reduced and the deformation parameter is synchronously adjusted with the reduction of the strength parameter; The numerical simulation method is: comprehensively judge the limit state of the slope through the three judgment conditions including the penetration of the plastic zone, the inflection point of the displacement versus strength reduction coefficient curve, and the non-convergence of the calculation, so as to determine the limit value of the strength reduction coefficient ψ corresponding to the limit state of the slope u And the corresponding potential sliding surface of the slope.

4. A numerical method for slope stability analysis with associated displacements as claimed in claim 3, characterized in that: In step 20: the calculation expressions for the cohesion, internal friction angle, elastic model, and Poisson's ratio changing synchronously with the strength reduction coefficient are: Where ψ is the strength reduction factor, ψ i is the coefficient of the i-th strength reduction, and the limit value of the strength reduction coefficient ψ u is i The maximum value of μ and E are the cohesion, internal friction angle, Poisson's ratio and elastic modulus of the slope rock and soil respectively; c i , μ i 、E i are the coefficients ψ of the i-th strength reduction i The corresponding slope rock and soil cohesion, internal friction angle, Poisson's ratio, and elastic modulus; β is an intermediate calculation parameter, and its expression is 5. A numerical method for slope stability analysis with associated displacements as claimed in claim 4, characterized in that: In step 30: take n ≥ 10, thereby forming a series of calculation intermediate reduction coefficients λ j , its calculation expression is: In the formula, j is the calculation process identification number, j = 0, 1, 2, 3,…, n.

6. A numerical method for slope stability analysis with associated displacements as claimed in claim 5, characterized in that: In step 40: according to the calculation of the intermediate reduction coefficient λ j The calculation expressions for synchronous changes in the cohesion, internal friction angle, Poisson's ratio, and elastic modulus of the slope rock and soil are: In the formula, c j , μ j 、E j are respectively and calculated as the intermediate reduction factor λ j The corresponding cohesion, internal friction angle, Poisson's ratio and elastic modulus of the slope rock and soil.

7. A numerical method for slope stability analysis with associated displacements as claimed in claim 6, characterized in that: Step 50: Slope stability factor F sj The calculation expression is: When j = 0, λ j =1, which is the initial state of the slope without changes in strength parameters and deformation parameters. The corresponding slope stability coefficient F sj is u ; When j = n, λ j =ψ u , that is, the final state where the strength parameter and deformation parameter change synchronously to the slope limit, and the corresponding slope stability coefficient F sj is 1.

8. The numerical method for slope stability analysis with associated displacements according to claim 1, characterized in that: In step 60: the displacement includes horizontal displacement and vertical displacement, and the slope stability factor F s The relationship between the horizontal displacement or vertical displacement of the slope is expressed by a relationship curve.

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