A calculation method for slope stability analysis in association with displacement

Abstract

The application discloses a kind of calculation method of slope stability analysis associated with displacement, comprising the following steps: for any one strip block, establish horizontal and vertical static equilibrium equation and the moment equilibrium equation in the plane of the strip block;From the motion compatibility between each strip block, start from the first strip block, establish the displacement coordination relationship between each strip block in turn, determine the displacement expression of any one strip block;For the bottom surface of any one strip block, the relationship between its tangential stress and shear displacement is characterized by strain softening model;According to the condition that the inter-block force transmitted by the first strip block is zero, form the calculation control equation set;For the displacement of each strip block, start from zero, and form a series of displacement values with certain displacement increment;Under each displacement value of each strip block, the average value of the local stability coefficient of all strip blocks is used as the overall stability coefficient of the slope body, i.e. the relationship between the overall stability coefficient of the slope body and the potential sliding body displacement is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of slope stability analysis, in particular to a calculation method for slope stability analysis related to displacement. BACKGROUND

[0002] Reasonable analysis and evaluation of slope stability is one of the key links in related engineering design. Influenced by external environment such as geological environment and meteorological environment of the slope, and internal and external factors such as self-weight, elastic-plastic deformation and creep deformation characteristics of the slope rock-soil mass, displacement will occur in engineering slope and landslide. With the development of slope displacement, the stability of the slope also changes, which is manifested as the gradual decrease of the stability. However, the slope stability analysis method in the current relevant technical specification, which is typical of limit equilibrium method, mainly evaluates the stability coefficient of the slope as the index of slope stability, and there is no method to reflect the quantitative correlation between slope stability and slope displacement. Therefore, the quantitative change rule of slope stability coefficient with slope displacement cannot be represented, and there is a lack of reasonable calculation and analysis method for reference in related actual engineering, which is mainly based on engineering experience, and there is blindness in engineering design. Therefore, for the slope which is prone to deformation due to internal and external conditions, a more reasonable slope stability analysis method which can quantitatively correlate slope displacement with its stability coefficient is urgently needed in actual engineering.

[0003] At present, the displacement analysis of engineering slope or landslide can generally use numerical simulation methods such as finite element method and finite difference method. For numerical simulation method, numerical model needs to be established first, and the rationality of numerical model depends on model parameters, grid accuracy, material constitutive model, boundary conditions and other factors. The modeling process is complex, and there is human subjective operation interference. It is difficult to have "inheritance" (different people need to start from modeling operation), and it can be used as a reference for complex problems, but it is not conducive to the rapid analysis and operation of actual engineering and technical personnel. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a calculation method for slope stability analysis related to displacement, which can obtain the quantitative change relationship of slope stability coefficient with its displacement, and has simple calculation operation and small error.

[0005] In order to achieve the above purpose, the present application provides a calculation method for slope stability analysis related to displacement, and the technical scheme is as follows:

[0006] A calculation method for slope stability analysis related to displacement, comprising the following steps:

[0007] (1) the potential sliding body is divided into a plurality of vertical blocks, and the bottom surface of each block is kept as a plane or can be approximated as a plane, and the blocks are numbered from 1 in sequence from the back edge of the potential sliding body to the front;

[0008] (2) for any one block, a horizontal and vertical static equilibrium equation and a moment balance equation in the plane of the block are established;

[0009] (3) from the motion compatibility between the blocks, starting from the first block, the displacement coordination relationship between the blocks is established in sequence, and the displacement expression of any one block is determined;

[0010] (4) for the bottom surface of any one block, the relationship between the tangential stress and the shear displacement is represented by a strain softening model;

[0011] (5) according to the condition that the inter-block force transmitted from the first block is zero, a calculation control equation set is formed;

[0012] (6) for the displacement of each block, the displacement value is taken from zero, and a series of displacement values are formed with a certain displacement increment;

[0013] (7) at each displacement value of each block, the ratio of the tangential shear strength to the tangential stress of the sliding surface soil at the bottom of the block is taken as the local stability coefficient of the block, and then the average value of the local stability coefficients of all blocks is taken as the overall stability coefficient of the slope body, that is, the relationship between the overall stability coefficient of the slope body and the displacement of the potential sliding body is obtained, so as to quantitatively represent the stability of the slope body associated with the displacement.

[0014] The calculation method of the slope stability analysis associated with displacement of the present application has the following outstanding advantages:

[0015] Firstly, the calculation method of the present application reasonably introduces the displacement of the potential sliding body under the condition of static equilibrium, fully considers the strain softening characteristics of the sliding soil and the displacement coordination of each block.

[0016] Secondly, the stability coefficient of the calculation method of the present application uses the average value of the local stability coefficients of each block, which simplifies the definition of the stability coefficient and facilitates the calculation operation.

[0017] Then, the calculation method of the present application has clear concept and simple calculation operation, without the need of numerical simulation modeling for calculation, and without the need of time-consuming, laborious and expensive experiments or monitoring, avoiding the complicated numerical modeling process, and the quantitative characteristics of the development and change of the slope stability coefficient with the displacement of the slope body can be quickly and efficiently calculated and determined through simple programming.

[0018] It can be seen that the calculation method of the associated displacement slope stability analysis of the application can more reasonably and efficiently calculate and determine the characteristics of the development and change of the slope stability coefficient with the displacement of the slope body, and provides a convenient method and scientific basis for the stability design and analysis of the deformation evolution of the slope, facilitates the design and analysis of the slope reinforcement control or landslide prevention engineering, and has important technical method significance and engineering application value.

[0019] The application will be further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0020] The accompanying drawings, which form a part of the present application, are used to help explain the present application and are provided along with the description given below to further facilitate understanding of the present application. The drawings described are provided only for the purpose of illustrating an embodiment of the present application and are not intended to limit the present application in any way. In the drawings:

[0021] Figure 1 A schematic diagram of the potential sliding surface position and morphology in the embodiment of the present application.

[0022] Figure 2 A schematic diagram of the potential sliding body segmentation in the embodiment of the present application.

[0023] Figure 3 A curve of the overall stability coefficient of the slope body changing with displacement in the embodiment of the present application.

[0024] Figure 4 A comparison diagram of the results of the method of the present application and the numerical simulation method in the embodiment of the present application. DETAILED DESCRIPTION

[0025] The application will be further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the application.

[0026] The technical solutions and technical features provided in each part of the present application, including the following description, can be combined with each other without conflict.

[0027] In addition, the embodiments of the application involved in the following description are generally only a part of the embodiments of the application, not all the embodiments. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments in the present application without creative labor should belong to the scope of protection of the present application.

[0028] With respect to the terms and units in the present application. The terms "comprising", "having", and any variations thereof in the specification and claims of the present application and related parts are intended to cover non-exclusive inclusion.

[0029] The specific embodiment of the calculation method of the slope stability analysis of the associated displacement of the present application comprises the following steps:

[0030] (1) The potential sliding body is divided into a plurality of vertical strips, and the bottom surface of each strip is kept as a plane or can be approximated as a plane, and the strips are numbered from small to large from 1 to the front edge of the potential sliding body;

[0031] Preferably, the position and shape of the potential sliding surface of the slope body are determined by using the limit equilibrium method or the numerical simulation method, and then the potential sliding body is determined.

[0032] The potential sliding body is divided into n vertical strips, n≥20, and the number of any strip is represented by i, 1≤i≤n.

[0033] The limit equilibrium method is preferably but not limited to the slice method, and the numerical simulation method is preferably but not limited to the finite element strength reduction method.

[0034] After the division, the self-weight, bottom surface inclination angle, and bottom surface length of each strip are determined.

[0035] (2) For any one strip, the horizontal and vertical static equilibrium equations and the moment balance equation in the plane of the strip are established.

[0036] The expressions of the horizontal and vertical static equilibrium equations and the moment balance equation in the plane of strip i are:

[0037]

[0038] In the formula, W i , N i , and T i are the self-weight of strip i, the normal force acting on the bottom surface of strip i, and the tangential force acting on the bottom surface of strip i, respectively; q i is the full load on the top surface of strip i; H i and P i are the tangential force and normal force acting on the vertical strip interface of the front side of strip i, collectively referred to as inter-strip force; α i is the horizontal inclination angle of the sliding surface soil of strip i; b i is the width of strip i; z i is the distance of normal force P i from the bottom surface of strip i along the vertical strip interface direction; and λ is a constant to be determined.

[0039] The inter-slice force meets H i = λf i P i ;

[0040] f i is a function representing the inter-slice force coefficient, a semi-sine function related to the slice position is adopted to obtain the expression of f i The expression of f

[0041]

[0042] In the formula, L x is the projection length of the entire potential sliding surface in the horizontal direction, x i is the horizontal distance from the front side inter-slice interface of slice i to the starting point of the potential sliding surface of the potential sliding body rear edge, where the front side refers to the downhill side.

[0043] (3) From the motion compatibility between each slice, starting from the first slice, the displacement coordination relationship between each slice is established in sequence to determine the displacement expression of any slice;

[0044] The expression of the sliding displacement υ i of slice i is:

[0045]

[0046] The expression of the tangential displacement Δ i of slice i along the potential sliding surface is:

[0047]

[0048] The expressions of the horizontal displacement u i of slice i are respectively:

[0049]

[0050] The expressions of the vertical displacement v i of slice i are respectively:

[0051]

[0052] In the formula, ψ i is the dilatancy angle of the sliding surface soil of slice i, and is taken as is the internal friction angle of the sliding surface soil of slice i.

[0053] (4) For the bottom surface of any slice, the relationship between the tangential stress and the shear displacement is represented by a strain softening model;

[0054] The relationship expression between the tangential stress of the bottom surface of the strip i and the shear displacement is represented by the strain softening model as follows:

[0055] τ i = G i Δ i (1+Δ i m / s i ) ρ Equation 6

[0056] In the equation, τ i is the tangential stress of the bottom surface of the strip i; G i represents the linear shear modulus or shear stiffness of the slip surface soil of the strip i; m and ρ are respectively the strain softening coefficient and the strain softening index, which are fitting parameters of the test curve, and are both dimensionless coefficients, which can be obtained by fitting the shear test data, wherein the value of m is generally taken as 2, and the value of ρ is generally between -0.5 and -1.0;

[0057] s i is a derived quantity related to the normal force of the bottom surface of the strip i, and the calculation expression of s i can be obtained by satisfying the condition of the Coulomb strength theorem for the peak value of the tangential stress of the bottom surface of the strip i as follows:

[0058]

[0059] In the equation, c i and l i are respectively the cohesion of the slip surface soil of the strip i and the bottom surface length, and l i = b i / cosα i .

[0060] (5) According to the condition that the inter-strip force transmitted forward by the first strip is zero, the calculation control equation set is formed;

[0061] According to the condition that the inter-strip force transmitted forward by the first strip is zero, it is obtained as follows:

[0062] H n = P n = 0 Equation 8

[0063] The tangential force expression acting on the bottom surface of the strip i is as follows:

[0064] T i = τ i l i Equation 9

[0065] Considering the unified strength weakening coefficient of the slip surface soil, and by combining Equation 1, Equation 5 and Equation 8, it is obtained as follows:

[0066]

[0067] In the formula, κ is a unified strength weakening coefficient of the introduced sliding surface soil body, κ is a positive real number, and generally, κ≥1.

[0068] Thus, by combining formula 3, formula 7 and formula 9, the calculation control equation set is obtained as:

[0069]

[0070] Thus, by solving the calculation control equation set shown in formula 11, the unified strength weakening coefficient, the normal force and the tangential force of any block bottom surface under the specified block displacement condition can be obtained. The block displacement can be represented by the displacement of any block, and preferably, the vertical displacement v1 of the first block is used to represent the displacement, and the displacements of the remaining blocks can be obtained by formula 2-5.

[0071] (6) The displacement of each block starts from zero and forms a series of displacement values with a certain displacement increment, and preferably, the displacement increment is 1-5 cm.

[0072] (7) The ratio of the tangential shear strength of the sliding surface soil body at the bottom of each block to the tangential stress is used as the local stability coefficient of the block, and then the average value of the local stability coefficients of all blocks is used as the overall stability coefficient of the slope body, i.e., the relationship between the overall stability coefficient of the slope body and the potential sliding body displacement is obtained, so as to quantitatively represent the stability of the slope body associated with the displacement;

[0073] The calculation expression of the local stability coefficient of block i is:

[0074]

[0075] The calculation expression of the overall stability coefficient of the slope body is:

[0076]

[0077] In the formula, F si is the local stability coefficient of block i; F s is the overall stability coefficient of the slope body.

[0078] Thus, the corresponding overall stability coefficient F s of the slope body under each specified displacement v1 is calculated according to formula 11 and formula 13, and further, the overall stability coefficient F sThe relationship between the other displacements and the relationship that determines the overall stability coefficient of the slope body with the displacement of the potential sliding body is determined, so as to quantitatively characterize the slope stability of the associated displacement. Among them, the overall stability coefficient of the slope body corresponding to the displacement of the potential sliding body being zero is the overall stability coefficient of the slope body obtained by the traditional calculation method without considering the displacement and stability correlation of the slope body, and the displacement of the potential sliding body corresponding to the overall stability coefficient of the slope body being 1 is the limit displacement of the slope body that can slide.

[0079] The beneficial effects of the present application are illustrated by specific examples below.

[0080] The calculation parameters of a certain slope are shown in Table 1.

[0081] Table 1

[0082]

[0083]

[0084] Step (1), based on the geometric parameters of the slope body, the physical and mechanical parameters of the stratum, etc., the Morgenstern-Price method in the traditional limit equilibrium method is used to determine the position and shape of the potential sliding surface of the slope body, as shown in Figure 1 . Then, according to the position and shape of the potential sliding surface of the slope body, the potential sliding body 200 is divided into 20 vertical blocks with a width of b=3.048m, and the bottom surface of each block is kept as an approximate plane, as shown in Figure 2 . The basic geometric and self-weight information of each block is shown in Table 2.

[0085] Table 2

[0086] Block number Base inclination (°) Base length (m) Block self-weight (kN / m) 1 55 5.35 147.42 2 50 4.76 417.22 3 45 4.35 643.60 4 41 4.05 837.19 5 37 3.83 1004.41 6 33 3.65 1134.37 7 30 3.51 1163.22 8 26 3.40 1162.36 9 23 3.31 1146.29 10 20 3.23 1116.02 11 16 3.18 1072.51 12 13 3.13 1016.46 13 10 3.09 948.43 14 7 3.07 868.80 15 4 3.05 777.86 16 1 3.05 676.75 17 -3 3.05 562.51 18 -12 3.11 427.21 19 -22 3.29 254.89 20 -33 3.49 65.92

[0087] Step (2), the force balance equation of block i is:

[0088]

[0089] H i = λf i P i

[0090]

[0091] Step (3), the expressions of the horizontal displacement u i and the vertical displacement v i of block i are respectively:

[0092]

[0093] Step (4), the relationship expression between the tangential stress and the shear displacement of the bottom surface of block i is:

[0094] τ i = G i Δ i (1+Δ i m / s i ) ρ = 200Δ i (1+Δ i 2 / s i ) -0.7

[0095]

[0096] Step (5), the corresponding calculation control equation group is obtained as follows:

[0097]

[0098] By solving the calculation control equation group, when v1=0, 2cm, 4cm, 6cm, the unified intensity weakening coefficient is 2.09, 1.72, 1.41, 1.25 respectively, and the normal force and the tangential force of each block bottom surface are shown in Table 3.

[0099] Table 3

[0100]

[0101] Step (6), the relevant displacement increment is 2cm, that is, v1=0, 2cm, 4cm, 6cm, 8cm, ….

[0102] Step (7), according to formula 12 and formula 13, the corresponding overall stability coefficient of the slope body is 2.589, 2.129, 1.624, 1.293, 1.080, ….

[0103] Further, the overall stability coefficient F of the slope body is determined s The relationship curve of the potential sliding body vertical displacement v1 and the horizontal displacement u1 is shown in Figure 1, wherein the negative sign represents the vertical downward direction. Figure 3

[0104] In order to further illustrate the rationality of the method of the present application, Figure 4 ​The comparison of the slope overall stability coefficient change curve with displacement obtained by the method of the embodiment and the FLAC3D numerical simulation method is given. It can be seen that the calculation result of the method of the embodiment is basically consistent with the FLAC3D numerical simulation result, the slope stability coefficient change curves with displacement obtained by the two methods almost coincide, the maximum relative deviation of the corresponding vertical displacement and horizontal displacement is 11.9% and 8.2% respectively, which all belong to the acceptable error range in the related engineering practice, further illustrating the rationality of the method of the embodiment.

[0105] The above describes the relevant content of the present application. The person skilled in the art can implement the present application based on the above description. Based on the above content of the present application, all other embodiments obtained by the person skilled in the art without creative labor should belong to the protection scope of the present application.

Claims

1. A calculation method for slope stability analysis with associated displacement, characterized by: The following steps are involved: (1) Divide the potential sliding body into multiple vertical strips, and keep the bottom surface of each strip flat or approximately flat. Number the strips in ascending order from the trailing edge of the potential sliding body; (2) For any bar, establish the horizontal and vertical static equilibrium equations and the moment equilibrium equation within the plane of the bar; (3) Based on the kinematic compatibility between the blocks, starting from the first block, the displacement coordination relationship between the blocks is established in sequence, and the displacement expression of any block is determined; (4) For the bottom surface of any bar, the relationship between its tangential stress and shear displacement is characterized by the strain softening model; (5) Based on the condition that the inter-bar force transmitted forward by the first bar is zero, a group of computational control equations is formed; (6) For the displacement of each bar, the value is taken from zero and a series of displacement values ​​are formed with a certain displacement increment; (7) At each displacement value of each strip, the ratio of the tangential shear strength of the sliding surface soil at the bottom of the strip to the tangential stress is used as its local stability coefficient. Then, the average value of the local stability coefficients of all strips is used as the overall stability coefficient of the slope. In other words, the relationship between the overall stability coefficient of the slope and the displacement of the potential sliding body is obtained, which can quantitatively characterize the slope stability associated with the displacement. In step (1), the position and shape of the potential sliding surface of the slope are determined by the limit equilibrium method or numerical simulation method, and then the potential sliding body is determined; the potential sliding body is divided into n A vertical strip, n ≥20, any block number is i Indicates that 1≤ i ≤ n； In step (5), the control equations are calculated as: ； In step (7), the strips i The calculation expression of the local stability coefficient is: ； The calculation expression of the overall stability coefficient of the slope is: ； Where, Δ i For strips i tangential displacement along the potential slip surface; α i For strips i The inclination of the bottom surface; ψ i It's a strip i The shear dilatancy angle of the sliding surface soil is taken as φ i / 4~ φ i / 3, φ i For strips i The internal friction angle of the sliding surface soil; v i For strips i The vertical displacement of , with vertical downward as positive; W i 、 N i and T i Separately into strips i The weight of the bar i The normal force on the bottom surface and the force acting on the bar i Tangential force on the bottom surface; q i For strips i Full load on the top surface; H i and P i Acting on bars i The tangential force and normal force at the front vertical strip interface are collectively referred to as the inter-strip force. Using the assumption of the Morgenstern-Price method, the inter-strip force satisfies ; λ is an undetermined constant; f i is the function that characterizes the inter-strip force coefficient; c i 、 l i Separately into strips i The cohesion and bottom length of the sliding surface soil, and l i = b i / cos α i ; G i Represents a bar i The linear shear modulus or shear stiffness of the sliding surface soil; m and ρ are the strain softening coefficient and strain softening index, respectively, which are the fitting parameters of the test curve. Both are dimensionless coefficients and can be obtained by fitting the shear test data. s i For strips i Derived quantities related to the normal force on the bottom surface; z i Normal force P i Distance from strips along the vertical strip interface direction i Distance to the bottom surface; b i For strips i width; κ is the uniform strength weakening coefficient of the sliding surface soil, κ is a positive real number, κ ≥1; F si For strips i The local stability coefficient; F s is the overall stability coefficient of the slope.

2. The calculation method for slope stability analysis with associated displacement according to claim 1, characterized in that: In step (2), the strips i The expressions of the horizontal and vertical static equilibrium equations and the moment equilibrium equation in the plane are: 。 3. The calculation method for slope stability analysis with associated displacement according to claim 2, characterized in that: Using the half-sine function related to the position of the bar, we get f i The expression is: ； Where, L x is the horizontal projection length of the entire potential sliding surface, x i For strips i The horizontal distance between the front side inter-strip interface and the starting point of the potential sliding surface at the trailing edge of the potential sliding body, , where the front side refers to the downhill side.

4. The calculation method for slope stability analysis with associated displacement according to claim 3, characterized in that: In step (3), the strips i Sliding displacement The expression is: ； strips i Tangential displacement along the potential slip surface Δ i The expression is: ； The slope is positive from the back to the front. i Horizontal displacement u i The expressions are: ； Take vertical downward as positive, strips i Vertical displacement v i The expressions are: 。 5. The calculation method for slope stability analysis with associated displacement according to claim 4, characterized in that: In step (4), the strain softening model is used to characterize the strips i The relationship between the tangential stress and shear displacement of the bottom surface is expressed as: ； Where, τ i For strips i Tangential stress at the bottom surface.

6. The calculation method for slope stability analysis with associated displacement according to claim 5, characterized in that: Through the blocks i The peak value of the tangential stress at the bottom surface satisfies the conditions of Coulomb's strength theorem, and we can get s i The calculation expression is: 。 7. The calculation method for slope stability analysis with associated displacement according to claim 6, characterized in that: In step (6), the displacement increment is 1 to 5 cm.

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