Slope slippage-bending damage judgment method under creep action

Abstract

The invention provides a method for judging sliding-bending damage of a side slope under the creep action, and relates to the technical field of side slope prevention and control engineering, and the method comprises the following steps: S1, obtaining rock mechanical parameters of thin-layer rocks; s2, establishing a slip-bending deformation mechanical model under the condition of considering the Burgers creep constitutive model, and analyzing a critical load; s3, establishing a bending axis timeliness equation of the rock beam with the initial deflection, and analyzing a long-term stable limit load enabling the compression bar to be unstable under the Burgers creep constitutive condition; and S4, enabling the critical load to be consistent with the long-term stable limit load, comparing the axial force of the rock beam with the instability critical force of the rock beam, and determining the conditions of instability failure of the side slope. The method has the advantages that the situation that the creep deformation characteristic of the lamellar rock mass is an important factor causing deformation and damage of the high and steep slope is considered, the slope slippage-bending damage criterion is more accurate and reasonable, and the method is more suitable for slope slippage-bending damage judgment of the lamellar rock high and steep slope under the creep action under the actual engineering condition.

Description

Technical Field

[0001] The present invention relates to the technical field of slope prevention and control engineering, and particularly to a method for judging slope slip-bending failure under creep action. Background Art

[0002] For the high-steep and bedding rock slopes in open-pit mining, due to their high-steep characteristics, they often undergo collapse or landslide failures induced by factors such as rainfall and blasting vibration. The failure modes of slopes include tensile failure, sliding failure of rock strata along weak structural planes, toppling failure, rolling failure of structural bodies, shear failure, bending failure, and buckling failure. Among them, the buckling failure refers to the slip-bending geomechanical model of landslides, which is a common failure mechanism in high-steep bedding slopes, especially common in layered rock masses composed of carbonate rocks with strong flexibility in thin layers. The layered slope body slides along the slip surface. Due to being blocked at the lower part, under the action of compressive stress in the reverse direction of smooth sliding, longitudinal bending deformation occurs. The reason for being blocked at the lower part is mostly that the slip surface is not in the air. Although the lower end of the slip surface is in the air, the slip surface presents a "deck chair" shape, with a steep upper part and a nearly horizontal lower part, significantly increasing the sliding resistance.

[0003] The essence of slope buckling failure is the mechanical and structural instability caused by the creep effect of rock strata (plates). This point is not considered in the currently proposed analysis models. That is to say, the mechanical analysis of the slip-bending deformation of thin-layered rock high-steep slopes in open-pit mining still mostly relies on the rock mass constitutive model based on the Mohr-Coulomb criterion.

[0004] These slope models do not consider that the essence of slope buckling failure is the mechanical and structural instability caused by the creep effect of rock strata (plates). However, rock strata often undergo slow buckling deformation under the influence of factors such as self-weight. And the slope failure caused by bending deformation is often affected by creep and shows a delayed characteristic. And only the influence of the component of the self-weight of the rock slab parallel to the direction of the rock slab, the interlayer friction force and the cohesion force is considered. At the same time, there is no consideration of how to consider the influence of the plasticity and rheological properties of the rock mass on its instability mechanism. In addition, the current slope slip-bending instability deformation failure criterion mainly uses the compression bar stability theory to establish the stress model during slope slip-bending deformation. However, rock strata often undergo slow buckling deformation under the influence of factors such as self-weight. And the slope failure caused by bending deformation is often affected by creep and shows a delayed characteristic. Summary of the Invention

[0005] In view of this, in order to solve the problems such as the unreasonable establishment of the landslide bending mechanical model, the inaccurate landslide bending deformation analysis of the mechanical model, and the inaccurate landslide bending deformation and failure criterion obtained, the embodiments of the present invention provide a method for judging slope slip-bending failure under creep action.

[0006] An embodiment of the present invention provides a method for judging slope slip-bending failure under creep action, including the following steps:

[0007] S1. Obtain the mechanical parameters of thin-layer rock mass;

[0008] S2. Based on the Burgers creep constitutive theory, establish a slip-bending deformation mechanical model considering the Burgers creep constitutive model, and analyze the critical load when the rock beam undergoes slip-bending failure;

[0009] S3. Combine the Burgers creep constitutive model with the theory of stability of compressed bars, establish the time-dependent equation of the bending axis of the rock beam with an initial deflection, and analyze the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition;

[0010] S4. Make the critical load when the rock beam undergoes slip-bending failure consistent with the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition, compare the axial force of the rock beam with the critical instability force of the rock beam, and determine the condition for slope instability failure.

[0011] Further, the slip-bending deformation mechanical model in step S2 is established based on the theory of stability of beam plates and considering the Burgers creep constitutive model.

[0012] Further, the slip-bending deformation mechanical model considering the Burgers creep constitutive model is as follows:

[0013]

[0014] where α is the slope and rock layer dip angle; φ is the internal friction angle of the sliding surface; c is the cohesion of the sliding surface; L is the slope length, l is the length of the bent section of the rock beam, U is the strain energy of the rock beam; f is the displacement at the midpoint of the bent section, J(t) is the creep compliance of the rock beam; I is the moment of inertia of the rock beam, G x and G y respectively represent the components of the self-weight G of the microelement of the rock beam in the bent section in the x and y directions.

[0015] Further, the critical load when the rock beam undergoes slip-bending failure where E M is the elastic modulus of the rock mass.

[0016] Further, step S3 is specifically: based on buckling, considering the case where the slope is damaged under ideal conditions, establish the bending axis equation of the rock beam with an initial deflection, and study the characteristic that the deflection of the system increases with time under a constant load, so as to obtain the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition.

[0017] Furthermore, the long-term stability limit load that causes the strut to lose stability under the Burgers creep constitutive condition where p2 is the differential operator of the viscoelastic constitutive relation.

[0018] Furthermore, when the axial force of the rock beam is equal to the critical force of the rock beam's instability, the slip-bending critical height of the vertical slope is Considering the toppling failure of the vertical slope, the critical height of toppling failure can be obtained as Comparing the critical heights of the two failure modes, considering the smaller critical height of toppling failure l cr ’ is the condition for the vertical slope not to undergo instability failure.

[0019] Furthermore, when the axial force of the rock beam is greater than the critical force of the rock beam's instability, when the slope undergoes slip-bending instability, the axial force P * = P cr , the length of the bending section satisfies the equation Al 3 + Bl 2 + C = 0, where

[0020]

[0021] C = -EIπ 2

[0022] In the above formulas, E is the elastic modulus of the rock mass, I is the moment of inertia of the rock beam, l is the length of the bending section of the rock beam, which can be regarded as the limit slope length l cr of the slip-bending instability deformation of the slope, γ is the unit weight of the rock mass, h is the thickness of the calculation unit body, α is the slope and rock layer dip angle, is the internal friction angle of the slip surface, c is the cohesion of the slip surface, and L is the slope length;

[0023] From this, the slip-bending critical height of the slope is calculated as

[0024] Comparing the slip-bending critical height of the slope with the actual slope length, when the slope length L > l cr then the slope is prone to slip-bending instability.

[0025] The beneficial effects brought by the technical solution provided by the embodiment of the present invention are as follows: A method for judging slope slip-bending failure under creep action of the present invention, based on the Burgers creep constitutive theory, establishes a creep mechanics model for slope slip-bending instability, analyzes the conditions for the occurrence of bending deformation in the rock beam. In view of the fact that the rock strata often undergo slow buckling deformation under the influence of factors such as self-weight, the Burgers constitutive model is used to fit the rock mechanics parameters of the thin-layered rock mass, and an accurate landslide bending mechanics model that conforms to the actual engineering situation can reflect the influence of the creep effect of the thin-layered rock mass on the long-term deformation of the project; the stability theory of compression bars is used to analyze and study the creep characteristics of the deflection of the rock beam; combined with the long-term strength of the rock mass, the slope slip-bending failure criterion under creep action is analyzed. Considering that the creep deformation characteristics of the thin-layered rock mass are an important factor causing the deformation and failure of high-steep slopes, the slope slip-bending failure criterion is more accurate and reasonable, and is more suitable for judging the slope slip-bending failure of thin-layered rocky high-steep slopes under creep action in actual engineering situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flow chart of a method for judging slope slip-bending failure under creep action of the present invention;

[0027] Figure 2 is a slip-bending deformation mechanics model considering the Burgers creep constitutive model;

[0028] Figure 3 is a schematic diagram of the deflection curve drawn by combining the corresponding deflection time-effect curve equation and considering the creep constitutive parameters of the thin-layered rock mass based on the Burgers model;

[0029] Figure 4 is a comparison diagram of the critical slope lengths of bending deformation determined by three judgment methods for slopes with different slab crack thicknesses, where Figure 4 a, 4b, 4c, 4d are respectively comparison diagrams of the critical slope lengths of bending deformation determined by three judgment methods for slopes with slab crack inclinations of 30°, 45°, 60°, and 75°;

[0030] Figure 5 is a comparison diagram of the critical slope lengths of bending deformation determined by three judgment methods for slopes with different slab crack inclinations. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will further describe the embodiments of the present invention with reference to the drawings. The following describes a relatively optimal one among multiple possible embodiments of the present invention, aiming to provide a basic understanding of the present invention, but not aiming to identify the key or decisive elements of the present invention or limit the scope to be protected.

[0032] In all the examples shown and discussed here, any specific values should be construed as merely exemplary and not as a limitation. Thus, other examples of the exemplary embodiments may have different values.

[0033] Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such technologies, methods, and devices should be considered as part of the specification.

[0034] It should be noted that similar reference numerals and letters denote similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further discussed in subsequent figures. At the same time, it should be understood that, for the sake of convenience of description, the dimensions of the various parts shown in the figures are not drawn in actual proportional relationship.

[0035] Please refer to Figure 1 , embodiments of the present invention provide a method for judging slope slip-bending failure under creep action of a thin-layered rocky high-steep slope described in the following with reference to the accompanying drawings. In view of the related technologies mentioned in the above background art, it is found that the current mechanical analysis of the slip-bending deformation of thin-layered rock mass high-steep slopes is still mostly based on the rock mass constitutive model of the Mohr-Coulomb criterion. The present application uses the Burgers constitutive model to fit the rock mechanics parameters of thin-layered rock mass, which can reflect the influence of the creep effect of thin-layered rock mass on the long-term deformation of the project. Among them, in this method, a certain phyllite slope in Jiangxi is taken as the research object, and based on the Burgers creep constitutive theory, a creep mechanics model of slope slip-bending instability is established to analyze the conditions for the occurrence of bending section deformation of the rock beam; the stability theory of compression bars is used to analyze the creep characteristics of the deflection of the rock beam; combined with the long-term strength of the rock mass, a method for judging slope slip-bending failure under creep action is analyzed, providing a reference basis for the treatment design of similar slopes. Thus, in the related technologies, the mechanical analysis of the slip-bending deformation of the exposed thin-layered rocky high-steep slope is still mostly based on the rock mass constitutive model of the Mohr-Coulomb criterion, without considering that the creep deformation characteristics of the thin-layered rock mass are an important factor causing the deformation and failure of high-steep slopes and controlling engineering design, and the method for judging slope slip-bending failure under creep action and the reference basis provided for the treatment design of similar slopes need to be improved and other problems are solved.

[0036] Specifically, referring to Figure 1 the flowchart of a method for judging slope slip-bending failure under creep action provided by the embodiments of the present application in, which is applied to analyze the judgment of slope slip-bending failure under creep action and mainly includes the following steps:

[0037] S1. Obtain the rock mechanics parameters of thin-layered rock.

[0038] S2. Based on the Burgers creep constitutive theory, establish a slip-bending deformation mechanical model considering the Burgers creep constitutive model, and analyze the critical load when the rock beam undergoes slip-bending failure;

[0039] S3. Combine the Burgers creep constitutive model with the theory of stability of compressed bars, establish the time-dependent equation of the bending axis of the rock beam with an initial deflection, and analyze the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition;

[0040] S4. Make the critical load when the rock beam undergoes slip-bending failure consistent with the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition, compare the axial force of the rock beam and the critical force of the rock beam instability, and determine the conditions for the slope to undergo instability failure.

[0041] In step S1, obtain the actual length of the bent section of the rock slab in the thin-layer rock slope, the displacement at the midpoint (x = l / 2) of the bent section, the unit weight γ of the rock mass, calculate the thickness h of the unit body, the inclination angles α of the slope and the rock stratum, and the internal friction angle c of the sliding surface, the cohesion c of the sliding surface, the slope length (rock beam) L and other parameters.

[0042] In step S2, based on the Burgers creep constitutive theory, establish a slip-bending deformation mechanical model considering the Burgers creep constitutive model, as Figure 2 shown, and analyze the critical load when the rock beam undergoes slip-bending failure.

[0043] Specifically, as Figure 2 shown, when the bent section deformation appears in the slip section of the rock beam, the rotation angles at both ends A and B are 0°, and the displacements at both ends A and B are both 0, and the rotation angles are both 0°, that is:

[0044] x = 0, y = 0, y'' = 0; x = l, y = 0, y'' = 0,

[0045] Adopt the following deflection curve equation for analysis:

[0046]

[0047] l is the length of the bent section of the rock slab; f is the displacement at the midpoint (x = l / 2) of the bent section,

[0048] Take a micro-element hdl for the rock beam in the bent section, and the self-weight of the slope body:

[0049] dG = γhdx; dG x = γhsinαdx; dG y = γhcosαdx,

[0050] dG is the self-weight of the micro-element; Gx and G y respectively represent the components of the self-weight G of the infinitesimal element in the x and y directions; γ is the unit weight of the rock mass; h is the thickness of the infinitesimal element; dx is the length of the infinitesimal element.

[0051] The thrust P of the sliding segment BC on the bending segment is:

[0052]

[0053] α is the slope and rock stratum dip angle; is the internal friction angle of the sliding surface; c is the cohesion of the sliding surface; L is the slope length (rock beam), l is the length of the bending segment of the rock beam,

[0054] For an elastic rock beam, the strain energy U during bending includes bending strain energy and shear strain energy. Taking an infinitesimal element of the bending segment with a length of dx, then:

[0055]

[0056] U is the strain energy of the rock beam; E is the elastic modulus of the rock mass; I is the moment of inertia of the rock beam,

[0057] Taking its Laplace transform and using to replace E, the bending strain energy of the Burgers rock beam is obtained, and considering that there is in the transform space, then there is

[0058]

[0059] is the strain energy of the rock beam; J(t) is the creep compliance of the rock beam,

[0060] The work done by the external force on the infinitesimal element includes the work done by the axial concentrated force P (T1), the work done by the axial body force (T2), and the work done by the normal force (T3). The axial differential shortening during the bending of the rock beam:

[0061]

[0062] When the strain energy during the bending of the rock beam is equal to the work done by the external force, it can be obtained:

[0063]

[0064] is the axial pressure on the simply supported rock beam; The critical force of the rock beam is then simplified to:

[0065]

[0066] Among them,

[0067] P crLet \(N_{cr}\) be the critical axial force when the bending section deformation begins to appear in the sliding section of the rock beam. Then, we have:

[0068]

[0069] In step S3, considering that the slope surface of the open-pit mine is non-ideal, combining the Burger's creep constitutive model with the theory of compression bar stability, the time-dependent equation of the bending axis of the rock beam with an initial deflection is established, and the long-term stability limit load that causes the compression bar to lose stability under the Burgers creep constitutive condition is analyzed.

[0070] Since the material conforms to the strain characteristics of the Burgers material, it is described by the following stress-strain differential law:

[0071]

[0072] In the formula: \(p_1\), \(p_2\), \(q_1\), and \(q_2\) are all differential operators of the viscoelastic constitutive relationship, where:

[0073]

[0074] For a rod with an initial deflection, the external moment \(M = Fy_0+Fy(t)\),

[0075] where \(F\) is the axial pressure applied to the rod; \(y_0\) is the initial deflection of the rod; \(y(t)\) is the additional deflection that increases with time during the creep process.

[0076] According to the plane-section assumption of the bending deformation of the element, we have

[0077]

[0078] where \(\varepsilon\) is the strain generated by the bending stress at a distance \(z\) from the neutral axis; \(\rho\) is the radius of curvature of the cross-section axis; \(\kappa\) is the curvature of the rod axis.

[0079] Processing the above formula gives

[0080]

[0081] Since the deflection of the rod can be ignored compared to its length, the second derivative of the deflection with respect to the length can be used to replace the curvature \(\kappa\), and we get

[0082]

[0083] For a rod with an initial deflection (\(F\) is a constant),

[0084]

[0085] For a pinned rod, the initial deflection and the bending axis can be represented by the following sine curve:

[0086]

[0087] Then, for a hinged rod with an initial deflection

[0088]

[0089] Discussion Compare with 0, that is Substitute the differential operator of Burgers material to obtain the discriminant Δ=(2q2 - p1q1) 2 -(p1 2 -4p2)q1 is always less than 0, that is is always greater than 0,

[0090] Therefore, in step S2, the differential equation The solution is

[0091] When

[0092]

[0093] When

[0094]

[0095] When

[0096]

[0097] Compare the relationship between the axial force of the rock beam and the critical buckling force of the rock beam. Combining the corresponding deflection time-effect curve equation and considering the creep constitutive parameters of phyllite based on the Burgers model, the deflection curve can be plotted from the graphical illustration of the above relationship, as Figure 3 shown

[0098] From Figure 3 it can be seen that the curve characteristics of the maximum bending deflection of the rock beam change with the magnitude of the axial force of the rock beam, and its critical load is

[0099] When the force acting on the rock beam is greater than the critical load, that is, F>F cr At this time, the deflection increase rate accelerates, and when a certain time is reached, it will suddenly become unstable;

[0100] When the force acting on the rock beam is equal to the critical load, that is, F = F cr At this time, the growth rate of the rod deflection is approximately a constant;

[0101] When the force acting on the rock beam is less than the critical load of the rock beam, that is, F<Fcr When the time is cr , the growth rate of the deflection of the rod member increases slowly with time.

[0102] In the case where the material creep shows linear attenuation, when the growth rate of the deflection slows down with time, it can be considered as the stable state of the rock beam. Therefore, regarding the development of the deflection at an accelerating rate as the characteristic of the unstable state, it can be considered that is the long-term stability limit of the rock beam.

[0103] In step S4, make the critical load when the rock beam undergoes slip-bending failure consistent with the long-term stability limit load that causes the compression bar to lose stability under the Burgers creep constitutive condition. Discuss the slip-bending failure situation of the slope under this condition and establish a slope instability failure criterion.

[0104] The critical load when the rock beam undergoes slip-bending failure is consistent with the long-term stability limit load that causes the compression bar to lose stability under the Burgers creep constitutive condition is consistent. The discussion of the slip-bending failure situation of the slope is as follows:

[0105] Discuss that the axial force of the rock beam is equal to the critical force of the rock beam's instability.

[0106] When the axial pressure P of the rock beam * the rock beam reaches the critical force P k At this time, the normal force on the rock beam is zero, and the slope and rock layer inclination angle is α = 90°, that is, the slope is in an upright state. From P * = P cr the slip-bending critical height of the upright slope can be obtained as

[0107] Considering the toppling failure of the upright slope, the toppling failure critical height can be obtained as

[0108] Comparing the critical heights of the two failure modes, the smaller toppling failure critical height l cr ' should be considered as the condition for the upright slope not to undergo instability failure.

[0109] Discuss that the axial force of the rock beam is greater than the critical force of the rock beam's instability.

[0110] When the axial force on the rock mass is greater than the critical force and instability occurs, the slip-bending critical height of the slope is When the slope length L > l cr the slope is prone to slip-bending instability.

[0111] The following uses an embodiment to verify the effectiveness of the embodiments of the present application.

[0112] The embodiments of this application can be verified by a site with thin-layered high-steep rocky mass, comparing and analyzing the rationality and applicable conditions of three calculation methods for slope slip and bending deformation. The parameters of the site can be shown in Table 1 and Table 2. Among them, Table 1 is the recommended value table of the slope parameters of the site, and Table 2 is the recommended value table of the rock mass parameters of the site.

[0113] Table 1

[0114]

[0115] Table 2

[0116]

[0117] There are three calculation methods:

[0118] Criterion of Sun Guangzhong's empirical method:

[0119] Sun Guangzhong et al. obtained the critical load of the bending deformation of slab-cracked rock mass through the static method as:

[0120]

[0121] Combined with the empirical elastic deformation curve equation, the limit slope length when the slope undergoes slip and bending deformation is:

[0122]

[0123] In the formula: q is the weight of the rock mass slab-cracked structural unit; E is the elastic modulus of the slab beam; I is the section moment coefficient of the slab beam strip.

[0124] Criterion of Sun Guangzhong's equation:

[0125] Sun Guangzhong et al. obtained that the limit slope length when the slope undergoes slip and bending deformation satisfies the following equation through the energy balance equation:

[0126] Al 3 +Bl 2 +C = 0

[0127] Among them:

[0128] In the formula: E is the elastic modulus of the rock mass, I is the moment of inertia of the rock beam, l is the length of the bent section of the rock beam, and it can be regarded as the limit slope length l of the slope slip and bending instability deformation cr , γ is the unit weight of the rock mass, h is the thickness of the calculation unit, α is the dip angle of the slope rock stratum, is the internal friction angle of the sliding surface, c is the cohesion of the sliding surface, and L is the slope length (rock beam).

[0129] Criterion of this paper:

[0130] When the slope undergoes slip-bending instability, the length l of the bending section satisfies the following equation:

[0131] Al 3 +Bl 2 +C=0

[0132] Where:

[0133] In the formula: E is the elastic modulus of the rock mass, I is the moment of inertia of the rock beam, l is the length of the bending section of the rock beam, which can be regarded as the ultimate slope length l of the slope slip-bending instability deformation cr 、γ is the unit weight of the rock mass, h is the thickness of the calculation unit body, α is the dip angle of the slope rock stratum, is the internal friction angle of the slip surface, c is the cohesion of the slip surface, and L is the slope length (rock beam).

[0134] Assume that the slope length is 60m, and the slab crack thickness h increases from 0.8m to 1.8m at a growth rate of 0.1m / time; when the slope length is certain, the calculation results when the slab crack dip angles are 30°, 45°, 60° and 75° are as Figure 4 , Figure 5 shown, where Figure 4 is the comparison diagram of the critical slope length of the bending deformation for different slab crack thicknesses, Figure 5 is the comparison diagram of the critical slope length of the bending deformation for different slab crack dip angles.

[0135] Sun Guangzhong's empirical method formula is calculated based on the assumption that the entire slope length of the slope undergoes bending deformation. The calculation result obtained by Sun Guangzhong's empirical method actually means that when the slope length is greater than the calculated critical slope length, the slopes in the entire calculation area undergo bending deformation. The deformation condition assumptions based on both Sun Guangzhong's equation method formula and the formula in this paper are: when the remaining sliding force generated by the upper sliding section of the slope is equal to the critical load required for the lower arching section to undergo bending deformation, the slope will undergo bending deformation, and the latter is more in line with the actual situation.

[0136] The calculation results of Sun Guangzhong's equation method formula and the formula in this paper are relatively close. The former adopts the constraint condition that the slope toe is a fixed end and the upper end of the bending section is a fixed slider, while the formula in this paper adopts the constraint condition that the slope toe is a hinge support end and the upper end of the bending section is simply supported. Therefore, when the rock slab is thin, the results of the two formulas are closer; while in the thick rock slab, the critical slope length calculated by the formula in this paper is smaller than that of Sun Guangzhong's equation method formula, and it is safer to use it to judge whether the slope will undergo slip-bending deformation in practical engineering.

[0137] In summary, this shows that the criterion of the embodiment of this application can be better applied to the actual engineering situation.

[0138] The slope slip-bending failure judgment method under creep action proposed according to the embodiments of the present application is applied to the judgment of slope slip-bending deformation failure of thin-layered rocky high-steep slopes under creep action, and can obtain the actual rock slab bending section length of the thin-layered rocky slope, the displacement at the midpoint (x = l / 2) of the bending section, the unit weight γ of the rock mass, the thickness h of the calculation unit, the slope and rock layer dip angles α, the internal friction angle of the slip surface parameters such as the cohesion C of the slip surface, the slope length (rock beam) L, etc. Based on the Burgers creep constitutive theory, a slip-bending deformation mechanical model is established considering the Burgers creep constitutive model, and the critical load when the rock beam undergoes slip-bending failure is analyzed. Considering that the slope surface of the open-pit mine slope is in a non-ideal shape, combining the Burgers creep constitutive model with the theory of the stability of compressed bars, the time-dependent equation of the bending axis of the rock beam with an initial deflection is established, and the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition is analyzed. Let the critical load when the rock beam undergoes slip-bending failure be consistent with the long-term stability limit load that causes the compressed bar to lose stability under the Burgers creep constitutive condition. In this case, the slope slip-bending failure situation is discussed, and a slope instability failure criterion is established, taking into account the fact that the essence of slope buckling failure is the mechanical and structural instability of the rock layer (plate) caused by creep action. Thus, the problems in the related art that the establishment of the landslide bending mechanical model is unreasonable, the landslide bending deformation analysis of this mechanical model and the obtained landslide bending deformation and failure criterion need to be improved are solved.

[0139] In this article, the front, back, up, down and other orientation words are defined based on the positions of the components in the drawings and the positions of the components relative to each other, only for the sake of clarity and convenience in expressing the technical solution. It should be understood that they are relative concepts and can change accordingly according to different usage and placement methods. The use of the orientation words should not limit the scope of protection claimed in the present application.

[0140] Without conflict, the above embodiments and the features in the embodiments in this article can be combined with each other. The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for judging slope slip-bending failure under creep, characterized in that: The following steps are involved: S1. Obtain rock mechanics parameters of thin rock layers; S2. Based on the Burgers creep constitutive theory, a slip-bending deformation mechanical model considering the Burgers creep constitutive model is established to analyze the critical load that causes the rock beam to fail in slip-bending. S3. Combining the Burgers creep constitutive model with the compression bar stability theory, the time-effect equation of the bending axis of the rock beam with initial deflection is established, and the long-term stable limit load that causes the compression bar to become unstable under the Burgers creep constitutive condition is analyzed; S4. The critical load that causes the rock beam to slip-bending failure is consistent with the long-term stable limit load that causes the compression bar to become unstable under the Burgers creep constitutive condition. The axial force of the rock beam and the critical force of rock beam instability are compared to determine the conditions for the slope to become unstable.

2. The method for determining slope slip-bending failure under creep as claimed in claim 1, characterized in that: The slip-bending deformation mechanical model in step S2 is established based on the beam-slab stability theory and taking into account the Burgers creep constitutive model.

3. The method for determining slope slip-bending failure under creep as claimed in claim 2, characterized in that: The slip-bending deformation mechanics model considering the Burgers creep constitutive model is: Among them, α is the inclination angle of the slope and rock layer; φ is the internal friction angle of the sliding surface; c is the cohesion of the sliding surface; L is the slope length, l is the length of the bending section of the rock beam, U is the strain energy of the rock beam; f is the displacement of the midpoint of the bending section, J(t) is the creep compliance of the rock beam; I is the moment of inertia of the rock beam, G x and G y They represent the x- and y-direction components of the deadweight G of the microelement of the rock beam in the curved section respectively.

4. The method for determining slope slip-bending failure under creep as claimed in claim 3, characterized in that: Critical load of rock beam when it fails due to slip-bending Where E M is the elastic modulus of the rock mass.

5. The method for determining slope slip-bending failure under creep as claimed in claim 1, characterized in that: The step S3 is specifically as follows: based on buckling and considering the ideal condition that the slope is destroyed, a bending axis equation of the rock beam with initial deflection is established, and the characteristics of the deflection increasing with time under a constant load are studied, so as to obtain the long-term stable limit load that makes the compression rod unstable under the Burgers creep constitutive condition.

6. A method for determining slope slip-bending failure under creep as claimed in claim 5, characterized in that: Long-term stable limit load that causes the compression bar to become unstable under the Burgers creep constitutive condition Among them, q2 and p2 are differential operators of the viscoelastic constitutive relation.

7. The method for determining slope slip-bending failure under creep as claimed in claim 1, characterized in that: When the axial force of the rock beam is equal to the critical force of rock beam instability, the sliding-bending critical height of the vertical slope is Considering the collapse of the vertical slope, the critical height of collapse is: Comparing the critical heights of the two failure modes, the smaller critical height of the overturning failure l is considered. cr ' is the condition for the vertical slope not to fail.

8. A method for determining slope slip-bending failure under creep as claimed in claim 1 or 7, characterized in that: When the axial force of the rock beam is greater than the critical force of rock beam instability, the axial force P on the bending section will be * =P cr , the length of the bending section satisfies the equation Al 3 +Bl 2 + C = 0, where C=-EIπ 2 In the above formula, E is the elastic modulus of the rock mass, I is the moment of inertia of the rock beam, and l is the length of the bending section of the rock beam, which can be regarded as the limit slope length l of the slope sliding bending instability deformation cr , γ is the rock mass density, h is the thickness of the calculation unit, α is the slope and rock layer inclination, is the internal friction angle of the sliding surface, c is the cohesion of the sliding surface, and L is the slope length; The slope sliding-bending critical height is calculated as follows: Compare the critical height of slope slip-bending and the actual slope length. When the slope length L>l cr When the load is too high, the slope is prone to slip-bending instability.

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