Method and system for determining instability starting speed of slope dangerous rock mass under multi-factor coupling action

Abstract

The application discloses a method for determining a slope dangerous rock mass instability starting speed under multi-factor coupling effect, comprising: establishing a dangerous rock mass generalized mechanical model, simplifying a dangerous rock mass main control structure surface into two parts of a through section and a non-through main control structure surface, and dangerous rock mass instability and failure being controlled by a rock mass corresponding to the dangerous rock mass main control structure surface; performing stress analysis on the dangerous rock mass and a locking section rock mass based on external load action and the dangerous rock mass generalized mechanical model; the external load action comprises horizontal and vertical earthquake force, frost heaving force, fissure water pressure or excess pore water pressure; determining elastic strain energy released by crack extension mid-energy reduction of the dangerous rock mass main control structure surface based on multi-factor coupling effect; and determining the instability starting speed of the slope dangerous rock mass violent motion under the multi-factor coupling effect based on the assumption that the elastic strain energy released by the crack extension mid-energy reduction of the dangerous rock mass main control structure surface is instantaneously released and converted into kinetic energy of the dangerous rock mass motion. The application also discloses a system, an electronic device and a computer readable storage medium.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of roadbed slope protection, and particularly relates to a method and system for determining the instability starting speed of a slope dangerous rock mass under the coupling action of multiple factors. BACKGROUND

[0002] High mountain valleys are cut sharply, and rock masses are broken, and poor stability or even loose dangerous rock masses are widely distributed. In addition, affected by the collision between different continental plates, active fault zones are densely distributed, and earthquakes occur frequently. In addition, affected by plateau climate, freezing and thawing are prominent. Under the coupling action of earthquakes, freezing and thawing and other factors, high and steep slope high dangerous rock masses are prone to sudden instability, which seriously threatens the safety of life and property. How to calculate the sudden instability starting speed of high and steep slope high dangerous rock masses under the coupling action of earthquakes, freezing and thawing and other factors is an important prerequisite for reasonably predicting the movement path of dangerous rocks and accurately assessing potential losses.

[0003] The following technical problems exist in the prior art: The dangerous rock mass destruction process can be divided into three stages: starting, running and stalling. Under the coupling action of earthquakes, freezing and thawing and other factors, the starting process of the dangerous rock mass (i.e. the moment of destruction and instability of the dangerous rock mass) has the characteristics of sudden instability and large initial speed. Accurate prediction of the starting speed of the dangerous rock mass is crucial for reasonably assessing the consequences of dangerous rock instability. Existing research mainly focuses on the study of the movement characteristics of dangerous rocks after instability based on kinematic equations, and lacks relevant research on the prediction of the initial speed of dangerous rock instability under the coupling action of earthquakes, freezing and thawing and other factors. SUMMARY

[0004] The purpose of the present application is to provide a method and system for determining the instability starting speed of a dangerous rock mass on a slope under the coupling action of multiple factors to overcome the shortcomings of the prior art. The method for calculating the starting speed of a dangerous rock mass on a high and steep slope under the coupling action of earthquakes, freezing and thawing and other factors can effectively solve the problem of difficulty in predicting the initial starting speed of sudden instability of a dangerous rock mass.

[0005] The first aspect of the present application provides a method for determining the instability starting speed of a dangerous rock mass on a slope under the coupling action of multiple factors, comprising:

[0006] S1, establishing a dangerous rock mass generalized mechanical model, in which the main control structural plane of the dangerous rock mass is simplified into two parts: a through section and a non-through main control structural plane, and the instability and destruction of the dangerous rock mass are controlled by the rock mass corresponding to the main control structural plane;

[0007] S2, performing stress analysis on the dangerous rock mass and the locked segment rock mass based on the external load action and the dangerous rock mass generalized mechanical model; wherein the external load action includes one or more of horizontal and vertical earthquake force, frost heaving force, fissure water pressure and excess pore water pressure;

[0008] S3, determining the elastic strain energy released by the decrease of the potential energy in the crack propagation of the main control structural plane of the dangerous rock mass based on the conditions of the multi-factor coupling;

[0009] S4, determining the instability starting speed of the sudden movement of the slope dangerous rock mass under the multi-factor coupling based on the assumption that the instantaneous release of the elastic strain energy released by the decrease of the potential energy in the crack propagation of the main control structural plane of the dangerous rock mass is converted into the kinetic energy of the movement of the dangerous rock mass.

[0010] Preferably, the dangerous rock mass general mechanical model of S1 is established based on the following assumptions:

[0011] ①The seismic wave pull-shear effect is the fundamental power of the crack propagation of the dangerous rock mass;

[0012] ②The crack of the dangerous rock mass is a composite crack of type I and type II;

[0013] ③When the stress intensity factor at the crack tip under the action of the seismic load is greater than the fracture toughness of the rock mass, the crack starts to propagate;

[0014] ④The model is intercepted in unit width and is discussed and analyzed based on the plane strain problem;

[0015] ⑤It is assumed that the dangerous rock mass remains complete and unbroken during the movement after the instability starting.

[0016] Preferably, S1 comprises: setting the crack height e of the main control structural plane of the dangerous rock mass, O point is the initial crack tip position, H is the total height of the dangerous rock mass, assuming h w is the filling height of the fissure water, and G is the gravity of the dangerous rock mass; when the seismic load exists, it is assumed that the angle between the action direction of the seismic force and the horizontal direction is α, wherein the horizontal seismic acceleration is a h , the vertical seismic acceleration is a v , and the angle between the action direction of the seismic acceleration and the horizontal direction is shown as formula (1):

[0017]

[0018] The seismic load P acting on the dangerous rock mass can be decomposed into horizontal seismic load P h and vertical seismic load P v , which is shown as formula (2):

[0019]

[0020] h and b are respectively the crack tip O and the gravity center of the dangerous rock mass, h w is the filling height of the fissure water; the dangerous rock mass considers the gravity G, the seismic load P, the fissure water pressure P w , the shear force F x along the initial crack direction, the normal tension T and the bending moment M OEqual load; gravity G corresponds to mass m;

[0021] According to the actual stress mode of dangerous rock, the xOy rectangular coordinate system is established with the crack tip O point as the origin and the initial crack direction as the x axis. Assuming that the horizontal and vertical distances between the dangerous rock mass center of gravity and the crack tip are l1 and h1, respectively, and the total height of the dangerous rock mass is H, the stress at the crack tip O point is solved as shown in the following formula (3)-(6):

[0022] Fracture water pressure P w :

[0023]

[0024] In the formula: P w is the fracture water pressure, γ w is the water density, h w is the fracture water height.

[0025] Shear force F along the initial crack direction x :

[0026] F x = P h cosβ+(G+P v )sinβ (4)

[0027] In the formula: F x is the shear force along the initial crack direction, P h is the horizontal seismic force, P v is the vertical seismic force, G is the rock mass gravity, and β is the angle between the rock mass structure surface and the horizontal plane.

[0028] Normal tension T:

[0029] T=P h sinβ+(P v -G)cosβ (5)

[0030] Bending moment M O :

[0031] M O =P h h1±(P v -G)l1 (6)

[0032] In the formula: M O is the bending moment, h1 is the vertical distance between the dangerous rock mass center of gravity and the crack tip, P h is the horizontal seismic force, P v is the vertical seismic force, G is the rock mass gravity, l1 is the horizontal distance between the dangerous rock mass center of gravity and the crack tip, and β is the angle between the rock mass structure surface and the horizontal plane.

[0033] In formula (3) - formula (6) : when the gravity center of the dangerous rock mass is inside the point O, the signs of all quantities are taken as ''-'';When the gravity center of the dangerous rock mass is outside the point O, the signs of all quantities are taken as ''+''.

[0034] Preferably, the S2 comprises: based on fracture mechanics, the failure of each type of dangerous rock is regarded as the fracture propagation problem of the main control structural plane of the dangerous rock mass under the combined action of loads, and the dangerous rock stability analysis is regarded as the solving process of the fracture model, comprising:

[0035] Assuming that the normal tension T and the shear force F along the initial crack direction x The fracture model is decomposed into four cases acted by the fissure water pressure P w , the shear force τ per unit length along the initial crack direction, and the bending moment M O and the unit height normal tension σ;Wherein τ = F x / L;σ = T / H;L is the total length of the dangerous rock mass;

[0036] Assuming that the fissure water pressure is uniformly distributed in the through section of the main control structural plane, the fracture strength factor generated thereby is represented by the following formula (7):

[0037]

[0038] In the formula: K I1 is the stress intensity factor generated by the fissure water pressure, is the fissure water pressure, and a0 is the crack length.

[0039] The crack fracture strength factor generated by the normal tension T is represented by the following formula (8):

[0040]

[0041] The crack fracture strength factor generated by the bending moment M O is represented by the following formula (9):

[0042]

[0043] In the formula: K I3 is the stress intensity factor generated by the bending moment M O , F(e) is a function related to the crack height of the main control structural plane of the dangerous rock mass, is the maximum normal stress generated by the bending moment.

[0044] The crack fracture strength factor generated by the shear force F along the initial crack direction x is represented by the following formula (10):

[0045]

[0046] According to the superposition of stress intensity factors, the first type fracture strength factor of the main control structural plane of the dangerous rock is calculated by the following formula (11):

[0047] K I = K I1 + K I2 + K I3 + K I4 (11).

[0048] Preferably, the S3 is based on the assumption that the initial crack of the main control structural plane expands along the original crack direction under the action of the load. According to the functional principle, when the crack of the main control structural plane expands, the potential energy of the crack body is reduced and the elastic strain energy is released; and for the plane fracture problem under the I-II type loading, the released elastic strain energy is equal to the assumption of the work done to make the crack re-close to the original state.

[0049] Preferably, the S3 includes: crack tip extension length Δa, during which the dangerous rock body releases elastic strain energy; and assumption that uniform normal stress σ y and shear stress τ yx are applied on the crack face Δa, so that the crack re-closes, the uniform normal stress σ y and shear stress τ yx gradually increase from zero according to the linear variation law of the displacement of the force acting on each point; the maximum values of the normal stress and shear stress applied on each point on the crack face Δa are σ y (r, 0) and τ yx (r, 0), respectively, and the corresponding displacement amounts of the crack on the crack face Δa during the closing process are u(r, π) and v(r, π). The maximum values of the normal stress and shear stress applied on each point on the crack face Δa are shown in the following formula (12) and formula (13) by bringing r=x and θ=0 into the stress field in the y direction of the crack end region:

[0050]

[0051] In the formula, σ y (r, 0) is the normal stress at the polar radius r=r and the polar angle θ=0 in the polar coordinate system; τ yx (r, 0) is the shear stress at the polar radius r=r and the polar angle θ=0 in the polar coordinate system; K I is the first type fracture strength factor of the main control structural plane of the dangerous rock; and K II is the second type fracture strength factor of the main control structural plane of the dangerous rock.

[0052] The displacement amounts of the crack on the crack face Δa during the closing process are shown in the following formula (14) and formula (15) by bringing r=Δa-x and θ=π into the displacement field in the y direction of the crack end region:

[0053]

[0054] The elastic strain energy ΔU released by the crack energy reduction Δa is shown in the following formula (16):

[0055]

[0056] The crack extension instability of the main control structural plane of the dangerous rock mass can be regarded as a plane strain problem,

[0057] The shear modulus is kPa;

[0058] The crack extension area increment ΔA = bΔa, and the unit is m 2 ;

[0059] Then, formula (16) is converted into formula (17):

[0060]

[0061] Preferably, the S4 comprises:

[0062] As a brittle material, the stress K * of the crack end of the main control structural plane of the dangerous rock exceeds the strength limit K IC , that is, K * >K IC , the crack starts to expand; when the dangerous rock is unstable, the elastic strain energy ΔU released by the crack energy reduction is instantaneously released and converted into the kinetic energy E k of the dangerous rock movement; according to the kinetic energy theorem, formula (18) is obtained:

[0063]

[0064] In formula (18), E k is the initial kinetic energy of the dangerous rock; m is the mass of the dangerous rock; v0 is the initial movement speed of the dangerous rock;

[0065] By combining formula (17) and formula (18), the initial movement speed of the dangerous rock is shown in the following formula (19):

[0066]

[0067] The initial movement speed of the dangerous rock is the instability starting speed of the slope dangerous rock.

[0068] The second aspect of the present application provides a multi-factor coupling slope dangerous rock instability starting speed determination system for implementing the method of the first aspect, comprising:

[0069] The model establishing module (101) is configured to establish a dangerous rock mass generalized mechanical model, in which a main control structural plane of the dangerous rock mass is simplified into two parts of a through section and a non-through main control structural plane, and instability and failure of the dangerous rock mass are controlled by the rock mass corresponding to the main control structural plane of the dangerous rock mass.

[0070] The stress analysis module (102) is configured to perform stress analysis on the dangerous rock mass and the locked segment rock mass based on external load action and the dangerous rock mass generalized mechanical model, wherein the external load action includes one or more of horizontal and vertical earthquake force, frost heaving force, fissure water pressure and excess pore water pressure.

[0071] The strain energy determination module (103) is configured to determine elastic strain energy released in crack propagation of the main control structural plane of the dangerous rock mass under the condition of multi-factor coupling.

[0072] The starting speed determination module (104) is configured to determine instability starting speed of the dangerous rock mass under the multi-factor coupling based on the assumption that instantaneous release of the elastic strain energy released in crack propagation of the main control structural plane of the dangerous rock mass is converted into kinetic energy of the dangerous rock mass movement.

[0073] The third aspect of the present application provides an electronic device including a processor and a memory, the memory stores a plurality of instructions, and the processor is configured to read the instructions and execute the method according to the first aspect.

[0074] The fourth aspect of the present application provides a computer readable storage medium, the computer readable storage medium stores a plurality of instructions, and the plurality of instructions can be read and executed by a processor to execute the method according to the first aspect.

[0075] The method and system of the present application have the following advantages:

[0076] According to the present application, the potential dangerous rock mass of the high and steep slope is generalized into a mechanical model of the rock mass controlled by the non-through main control structural plane, the influence of multi-load action such as horizontal and vertical earthquake force, frost heaving force, fissure water pressure and excess pore water pressure on the instability starting speed of the dangerous rock mass can be comprehensively considered, and the instability starting speed of the dangerous rock mass under the multi-factor coupling can be quickly and accurately calculated, thereby providing a scientific basis for prediction of the movement path and influence range of the dangerous rock mass after instability and engineering influence evaluation. BRIEF DESCRIPTION OF DRAWINGS

[0077] In order to more clearly illustrate the technical solutions in the specific embodiments or related art, the following will briefly introduce the drawings needed to be used in the specific embodiments or related art description. Obviously, the drawings described below are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0078] Figure 1 A flow chart of a method for determining the instability starting speed of a dangerous rock mass of a slope under the multi-factor coupling effect according to an embodiment of the present application is provided.

[0079] Figure 2 A typical dangerous rock mass generalized mechanical model according to an embodiment of the present application is provided.

[0080] Figure 3 A fracture mechanics model under the assumption that the fissure water pressure is uniformly distributed in the through section of the main control structural plane according to an embodiment of the present application is provided.

[0081] Figure 4 A mechanical model of the end load of the main control structural plane according to an embodiment of the present application is provided.

[0082] Figure 5 A calculation diagram of the elastic strain energy released by the crack extension Δa under the I-II type loading according to an embodiment of the present application is provided. Figure 5 (a) a calculation diagram of the elastic strain energy released by the crack extension state a under the I-II type loading; Figure 5 (b) a calculation diagram of the elastic strain energy released by the crack extension state b under the I-II type loading; Figure 5 (c) a calculation diagram of the elastic strain energy released by the crack extension state c under the I-II type loading;

[0083] Figure 6 A system architecture diagram of a system for determining the instability starting speed of a dangerous rock mass of a slope under the multi-factor coupling effect according to an embodiment of the present application is provided.

[0084] Figure 7 An electronic device structure diagram according to an embodiment of the present application is provided. DETAILED DESCRIPTION

[0085] The technical solutions of the present application will be described clearly and completely below with reference to the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0086] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, which are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second", "third" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0087] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0088] Embodiment one

[0089] Reference Figure 1 , the present embodiment provides a method for determining the instability starting speed of a slope dangerous rock mass under the action of multiple factors, comprising:

[0090] S1, a dangerous rock mass generalized mechanical model is established, in which the main control structure surface of the dangerous rock mass is simplified into two parts of a through section and a non-through main control structure surface, and the instability and failure of the dangerous rock mass are controlled by the rock mass corresponding to the main control structure surface of the dangerous rock mass;

[0091] In the present embodiment, the following assumptions are made in step S1:

[0092] ① The seismic wave tensile shear action is the fundamental driving force for crack propagation of the dangerous rock mass;

[0093] ② The cracks of the dangerous rock mass are I-type and II-type composite cracks;

[0094] ③ When the stress intensity factor at the crack tip under the action of the seismic load is greater than the fracture toughness of the rock mass, the crack begins to expand;

[0095] ④ The model is intercepted in unit width, and is discussed and analyzed based on the plane strain problem;

[0096] ⑤ It is assumed that the dangerous rock mass remains complete and unbroken during the movement process after the instability starting of the dangerous rock.

[0097] Based on the above assumptions, a typical dangerous rock mass generalized mechanical model is established, as shown in Figure 2 . Figure 2The crack height e is the main controlling structural plane of the medium-risk rock mass, point O is the initial crack tip position, H is the total height of the dangerous rock mass, and h is assumed to be... w Let G be the height of the fissure water filling the rock, and G be the weight of the unstable rock. Seismic waves are a function of time; their magnitude increases or decreases over time, and their direction changes periodically. When a seismic load is present, assume the angle between the direction of the seismic force and the horizontal direction is α, where the horizontal seismic acceleration is a. h The vertical earthquake acceleration is a v Then the angle between the direction of seismic acceleration and seismic force and the horizontal direction is as shown in equation (1):

[0098]

[0099] The seismic load P acting on the unstable rock mass can be decomposed into a horizontal seismic load P h and vertical seismic load P v As shown in equation (2):

[0100]

[0101] h and b are the crack tip O and the center of gravity of the unstable rock, respectively. w This represents the height of the fissure water filling the rock mass. The unstable rock mass is considered to have gravity G (corresponding to m in the formula), seismic load P, and fissure water pressure P. w Shear force F along the initial crack direction x Normal tensile force T and bending moment M O Equal load.

[0102] Based on the actual stress mode of the unstable rock ( Figure 2 As shown in the figure, a rectangular coordinate system xOy is established with the crack tip O as the origin and the initial crack direction as the x-axis. Assuming that the horizontal and vertical distances between the center of gravity of the unstable rock mass and the crack tip are l1 and h1 respectively, and the total height of the unstable rock mass is H, the force at the crack tip O is calculated as shown in equations (3)-(6):

[0103] fissure water pressure P w :

[0104]

[0105] In the formula: P w For the fracture water pressure, γ w h represents the specific gravity of water. w This represents the height of the fissure water.

[0106] Shear force F along the initial crack direction x :

[0107] F x =P h cosβ+(G+P vsinβ (4)

[0108] In the formula: F x P is the shear force along the initial crack direction. h For horizontal seismic force, P v G represents the vertical seismic force, G represents the weight of the rock mass, and β represents the angle between the rock mass structural plane and the horizontal plane.

[0109] Normal tensile force T:

[0110] T = P h sinβ+(P v -G)cosβ (5)

[0111] Bending moment M O :

[0112] M O =P h h1±(P v -G)l1 (6);

[0113] Where: M O P is the bending moment, h1 is the vertical distance between the center of gravity of the unstable rock and the tip of the crack, and P is the bending moment. h For horizontal seismic force, P v

[0114] G is the vertical seismic force, l1 is the weight of the rock mass, β is the horizontal distance between the center of gravity of the unstable rock mass and the tip of the crack, and β is the angle between the rock mass structure plane and the horizontal plane.

[0115] In equations (3) to (6): when the center of gravity of the unstable rock mass is inside point O, all quantities are marked with "-"; when the center of gravity of the unstable rock mass is outside point O, all quantities are marked with "+".

[0116] S2, based on the external load and the generalized mechanical model of the unstable rock mass, perform a stress analysis on the unstable rock mass and the locked rock mass; wherein, the external load includes one or more of the following: horizontal and vertical seismic forces, frost heave forces, fissure water pressure, and excess pore water pressure;

[0117] In this embodiment, based on fracture mechanics, the failure of each type of unstable rock mass is a fracture propagation problem of the main controlling structural plane of the unstable rock mass under combined loads. The stability analysis of the unstable rock mass can then be viewed as a solution process for the fracture model. Assume a normal tensile force T and a shear force F along the initial crack direction. x If the rock mass is evenly distributed along its main structural plane, then... Figure 3 The fracture model shown can be further decomposed into a system based on the fracture water pressure P. w Shear force τ and bending moment M per unit length along the initial crack direction O Four cases involving a normal tensile force σ per unit height. Where τ = F xL;σ=T / H; wherein, L is the total length of the dangerous rock mass.

[0118] Figure 3 Assuming that the fissure water pressure is uniformly distributed in the through section of the main controlling structural plane, the fracture strength factor generated thereby can be represented by the following formula (7):

[0119]

[0120] wherein: K I1 is the stress intensity factor generated by the fissure water pressure, is the fissure water pressure, and a0 is the crack length.

[0121] The fracture strength factor of the crack generated by the normal tension T can be represented by the following formula (8):

[0122]

[0123] The bending moment M O generated by the fracture strength factor of the crack can be represented by the following formula (9):

[0124]

[0125] wherein: K I3 is the stress intensity factor generated by the bending moment M O , and F(e) is a function related to the crack height of the main controlling structural plane of the dangerous rock mass, is the maximum normal stress generated by the bending moment.

[0126] The shear force F x generated by the fracture strength factor of the crack can be represented by the following formula (10):

[0127]

[0128] According to the superposition of the stress intensity factors, the first type fracture strength factor of the main controlling structural plane of the dangerous rock mass can be calculated by the following formula (11):

[0129] K I = K I1 + K I2 + K I3 + K I4 (11).

[0130] S3, based on the conditions of the multi-factor coupling, determine the elastic strain energy released by the energy reduction in the crack propagation of the main controlling structural plane of the dangerous rock mass;

[0131] In this embodiment, as Figure 4As shown, the load of the end of the main control structural plane A of the dangerous rock mass mainly presents the bending moment and shear force generated by the gravity and seismic load of the dangerous rock mass, and the tensile stress generated by the fissure water pressure. According to fracture mechanics, the stress intensity factor K I1 generated by the normal force, the stress intensity factor K I2 generated by the bending moment, the stress intensity factor K I3 generated by the shear force, and the stress intensity factor K I4 generated by the fissure water pressure can be obtained by the calculation of step S2.

[0132] It is assumed that the initial crack of the main control structural plane expands along the original crack direction under the action of the load. According to the functional principle, when the crack of the main control structural plane expands, the potential energy of the crack body decreases and the elastic strain energy is released. For the plane fracture problem under I-II type loading, the released elastic strain energy is equal to the work done to make the crack re-close to the original state. Figure 5 The calculation schematic diagram of the elastic strain energy released by the crack expansion Δa under I-II type loading. Wherein Figure 5 (a) the calculation schematic diagram of the elastic strain energy released by the crack expansion state a under I-II type loading; Figure 5 (b) the calculation schematic diagram of the elastic strain energy released by the crack expansion state b under I-II type loading; Figure 5 (c) the calculation schematic diagram of the elastic strain energy released by the crack expansion state c under I-II type loading.

[0133] The crack tip expansion length Δa, that is, from Figure 5 state a in (a) to Figure 5 state b in (b), in which process the dangerous rock mass releases elastic strain energy; as shown in Figure 5 state c, it is assumed that the uniform normal stress σ y and shear stress τ yx are applied to the crack face Δa, so that the crack in state b re-closes to the original state a, and the uniform normal stress σ y and shear stress τ yx gradually increase from zero according to the linear variation law of the displacement of the force acting on each point. The maximum values of the normal stress and shear stress applied to the crack face Δa in state c are σ y (r, 0) and τ yx (r, 0), and the corresponding displacement amounts of the crack face Δa in the closing process are u(r, π) and v(r, π). By bringing r=x and θ=0 into the stress field in the crack end area y direction, the maximum values of the normal stress and shear stress applied to the crack face Δa in state c are shown as formula (12) and formula (13):

[0134]

[0135] In the formula: σy (r,0) is the normal stress at the polar radius r = r, polar angle θ = 0 in the polar coordinate system; τ yx (r,0) is the shear stress at the polar radius r = r, polar angle θ = 0 in the polar coordinate system; K I is the first type of fracture strength factor of the main control structural plane of the dangerous rock; K II is the second type of fracture strength factor of the main control structural plane of the dangerous rock;

[0136] The r = Δa - x, θ = π is brought into the crack end area y direction displacement field, and the displacement amount corresponding to the crack face Δa in the closing process of the crack is respectively shown as formula (14) and formula (15):

[0137]

[0138] The elastic strain energy ΔU released by the crack energy reduction when the crack expands Δa is shown as formula (16):

[0139]

[0140] The expansion instability of the main control structural plane of the dangerous rock mass can be regarded as a plane strain problem,

[0141] The shear modulus G = 0.75E , unit: kPa;

[0142] The crack expansion area increment ΔA = bΔa, unit: m 2 ;

[0143] Then formula (16) can be converted into formula (17):

[0144]

[0145] S4, based on the assumption that the elastic strain energy released by the potential energy reduction in the crack expansion of the main control structural plane of the dangerous rock mass is instantaneously released and converted into the kinetic energy of the dangerous rock mass movement, the instability starting speed of the slope dangerous rock mass under the multi-factor coupling effect is determined.

[0146] In this embodiment, as a brittle material, the stress K * of the crack end of the main control structural plane of the dangerous rock instability exceeds the strength limit K IC , that is, K * >K IC , and the crack starts to expand. When the dangerous rock instability occurs, the elastic strain energy ΔU released by the crack energy reduction is instantaneously released and converted into the kinetic energy E k of the dangerous rock mass movement. According to the kinetic energy theorem, formula (18) can be obtained:

[0147]

[0148] In formula (18), Ek is the initial kinetic energy of the dangerous rock mass; m is the mass of the dangerous rock mass; and v0 is the initial movement speed of the dangerous rock mass.

[0149] By combining formula (17) and formula (18), the initial movement speed of the dangerous rock mass is solved as shown in the following formula (19):

[0150]

[0151] The initial movement speed of the dangerous rock mass is the instability starting speed of the dangerous rock mass of the slope.

[0152] Embodiment Two

[0153] As shown in Figure 6 The embodiment provides a system for determining an instability starting speed of a dangerous rock mass of a slope under multi-factor coupling, which is used for implementing the method in embodiment one and comprises the following steps of:

[0154] A model establishing module 101 is configured to establish a dangerous rock mass generalized mechanical model, in which a main control structural plane of the dangerous rock mass is simplified into two parts of a through section and a non-through main control structural plane, and instability and failure of the dangerous rock mass are controlled by the rock mass corresponding to the main control structural plane of the dangerous rock mass.

[0155] A stress analysis module 102 is configured to perform stress analysis on the dangerous rock mass and the locked segment rock mass based on an external load effect and the dangerous rock mass generalized mechanical model; and the external load effect comprises one or more of horizontal and vertical earthquake force, frost heaving force, fissure water pressure and excess pore water pressure.

[0156] An elastic strain energy determining module 103 is configured to determine elastic strain energy released by a mid-energy reduction in crack propagation of the main control structural plane of the dangerous rock mass based on a condition of multi-factor coupling.

[0157] An instability starting speed determining module 104 is configured to determine an instability starting speed of the dangerous rock mass under multi-factor coupling based on an assumption that the elastic strain energy released by the mid-energy reduction in crack propagation of the main control structural plane of the dangerous rock mass is instantaneously released and converted into kinetic energy of movement of the dangerous rock mass.

[0158] The embodiment further provides a memory storing a plurality of instructions for implementing the method in embodiment one.

[0159] As shown in Figure 7 The embodiment further provides an electronic device comprising a processor 301 and a memory 302 connected to the processor 301, wherein the memory 302 stores a plurality of instructions, the instructions can be loaded and executed by the processor, so that the processor can execute the method in embodiment one.

[0160] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for determining the initiation rate of slope instability due to multi-factor coupling effects, characterized in that, include: S1. Establish a generalized mechanical model of the unstable rock mass. In the generalized mechanical model of the unstable rock mass, the main controlling structural surface of the unstable rock mass is simplified into two parts: the through section and the non-through main controlling structural surface. The instability and failure of the unstable rock mass is controlled by the rock mass corresponding to the main controlling structural surface of the unstable rock mass. S2, based on the external load and the generalized mechanical model of the unstable rock mass, perform a stress analysis on the unstable rock mass and the locked rock mass; wherein, the external load includes one or more of the following: horizontal and vertical seismic forces, frost heave forces, fissure water pressure, and excess pore water pressure; S2 includes: establishing a fracture model based on fracture mechanics, where the failure of each type of unstable rock mass is considered as the fracture propagation problem of the main controlling structural plane of the unstable rock mass under combined loads; and using unstable rock stability analysis as the solution process for the fracture model, including: Assume normal tensile force T and shear force along the initial crack direction The fracture model is uniformly distributed along the main structural plane of the unstable rock mass, and is decomposed into a system based on fracture water pressure. Shear force per unit length along the initial crack direction Bending moment and unit height normal tensile force Four possible scenarios for its effect; among which = / L; =T / H; L is the total length of the unstable rock mass; Assuming that the fissure water pressure is uniformly distributed throughout the main structural surface, the resulting fracture strength factor is expressed by the following equation (7): （7）； In the formula: The stress intensity factor generated by fissure water pressure. For fissure water pressure, The length of the crack; Normal tension The resulting crack fracture strength factor is expressed by the following equation (8): （8）； In the formula: The stress intensity factor generated by the normal tensile force. To exert force in the direction of the law, This represents the total height of the unstable rock mass. The length of the crack; Bending moment The resulting crack fracture strength factor is expressed by the following equation (9): （9）； In the formula: For bending moment The resulting stress intensity factor A function related to the crack height on the main structural surface of the unstable rock mass. The height of the cracks on the main structural surface controlling the unstable rock mass. This represents the maximum normal stress generated by the bending moment; Shear force along the initial crack direction The resulting crack fracture strength factor is expressed by the following equation (10): （10）； In the formula: For shear force The resulting stress intensity factor For shear force The resulting shear stress; Based on the superposition of stress intensity factors, the first type of fracture intensity factor of the main structural plane controlling the unstable rock mass. Calculated by the following formula (11): + （11）; S3, based on the condition of multi-factor coupling, determine the elastic strain energy released by the reduction of the median potential energy of crack propagation on the main structural surface of the unstable rock mass; S4. Based on the assumption that the elastic strain energy released by the reduction of the median potential energy of the crack propagation of the main structural surface of the unstable rock mass is instantaneously released and converted into the kinetic energy of the unstable rock mass movement, the instability initiation speed of the unstable rock mass under the coupling effect of multiple factors is determined.

2. The method for determining the initiation rate of slope instability due to multi-factor coupling effects as described in claim 1, characterized in that, The generalized mechanical model of the unstable rock mass in S1 is established based on the following assumptions: ①The tensile and shearing action of seismic waves is the fundamental driving force for the propagation of cracks in unstable rock masses; ②The cracks in the unstable rock mass are a combination of Type I and Type II cracks; ③ When the stress intensity factor at the crack tip is greater than the fracture toughness of the rock mass under seismic load, the crack begins to propagate; ④ The model is cut off at a unit width, and the discussion and analysis are based on the plane strain problem; ⑤ Assume that after the unstable rock mass is initiated, it remains intact and does not break during the movement process.

3. The method for determining the initiation rate of slope instability due to multi-factor coupling effects as described in claim 2, characterized in that, S1 includes: setting the crack height of the main control structural surface of the unstable rock mass. Point O is the initial crack tip location, and H is the total height of the unstable rock mass. Assuming... G represents the height of the fissure water filling the rock, and G represents the weight of the unstable rock mass. When seismic loads are present, it is assumed that the angle between the direction of the seismic force and the horizontal direction is θ. The horizontal seismic acceleration is Vertical earthquake acceleration is Then the angle between the direction of seismic acceleration and seismic force and the horizontal direction is shown in equation (1): （1）； Seismic loads acting on unstable rock masses It can be decomposed into horizontal seismic loads. and vertical seismic loads As shown in equation (2): （2）； and These are the crack tip O and the center of gravity of the unstable rock, respectively. The height of the fissure water filling; the unstable rock mass is considered in terms of gravity G and seismic load. Fissure water pressure Shear force along the initial crack direction Normal tensile force and bending moment Gravity G corresponds to mass m; Based on the actual stress pattern of the unstable rock, a rectangular coordinate system xOy is established with the crack tip O as the origin and the initial crack direction as the x-axis; it is assumed that the horizontal and vertical distances between the center of gravity of the unstable rock and the crack tip are respectively... and Given the total height H of the unstable rock mass, the force at the crack tip O is calculated as shown in equations (3) to (6): fissure water pressure : （3） In the formula: For fissure water pressure, The density of water, The height of the fissure water; Shear force along the initial crack direction : （4） In the formula: Shear force along the initial crack direction, For horizontal seismic forces, For vertical seismic forces, For the weight of the rock, The angle between the rock mass structural plane and the horizontal plane; Normal tension : （5） Bending moment : （6）； In the formula: For bending moment, This represents the vertical distance between the center of gravity of the unstable rock and the tip of the crack. For horizontal seismic forces, For vertical seismic forces, For the weight of the rock, The horizontal distance between the center of gravity of the unstable rock and the tip of the crack. The angle between the rock mass structural plane and the horizontal plane; In equations (3) to (6): when the center of gravity of the unstable rock mass is inside point O, all quantities are marked with "-"; when the center of gravity of the unstable rock mass is outside point O, all quantities are marked with "+".

4. The method for determining the initiation rate of slope instability due to multi-factor coupling effects as described in claim 3, characterized in that, S3 is based on the assumption that the initial crack on the main control structural surface propagates along the original crack direction under load. According to the functional principle, when the crack on the main control structural surface propagates, the potential energy of the crack body decreases and releases elastic strain energy. And for the plane fracture problem under type I-II loading, the assumption that the released elastic strain energy is equal to the work required to close the crack back to its original state is realized.

5. The method for determining the initiation rate of slope instability due to multi-factor coupling effects as described in claim 4, characterized in that, The S3 includes: crack tip propagation length During this process, the unstable rock mass releases elastic strain energy; assuming at the crack surface... Apply uniformly distributed normal stress and shear stress This causes the crack to close again, resulting in a uniform distribution of normal stress. and shear stress The displacement of each point of force increases gradually from zero according to a linear variation law; applied to the crack surface The maximum values ​​of normal stress and shear stress at each point are respectively and During the crack closure process, the crack surface The corresponding displacement is , ; with r=x, Substituting 0 into the stress field in the y-direction of the crack tip region, we obtain the stress applied to the crack surface. The maximum values ​​of normal stress and shear stress at each point are shown in equations (12) and (13), respectively: （12）； （13）； In the formula: Polar radius in polar coordinate system Polar angle Normal stress at =0; Polar radius in polar coordinate system Polar angle Shear stress at point = 0; The first type of fracture strength factor for the main structural plane of the unstable rock; The second type of fracture strength factor for the main structural plane controlling the unstable rock; Will , Substituting π into the displacement field in the y-direction of the crack tip region, we can obtain the crack surface during the crack closure process. The corresponding displacements are shown in equations (14) and (15), respectively: （14）； （15）； Then the crack will propagate. The crack potential energy reduces the released elastic strain energy. As shown in equation (16): （16）； The expansion and instability of the main structural plane controlling the unstable rock mass can be regarded as a plane strain problem. ; shear modulus The unit is kPa; Crack propagation area increment The unit is m2; Equation (16) is then transformed into equation (17): （17）。 6. The method for determining the initiation rate of slope instability due to multi-factor coupling effects as described in claim 5, characterized in that, S4 includes: As a brittle material, the stress at the crack tip of the main structural surface controlling the instability of unstable rocks... Exceeding its strength limit At that time, that is The crack begins to propagate; when the unstable rock becomes unstable, the crack potential energy reduces the released elastic strain energy. The kinetic energy released instantaneously is transformed into the movement of the unstable rock mass. According to the work-energy theorem, we can obtain equation (18): （18）； In formula (18): The initial kinetic energy of the unstable rock mass; For the quality of the unstable rock mass; This represents the initial velocity of the unstable rock mass. Combining equations (17) and (18), the initial velocity of the unstable rock mass is calculated as shown in equation (19): （19）； The initial movement velocity of the unstable rock mass is the initiation velocity of the unstable rock mass on the slope.

7. A system for determining the initiation rate of slope instability due to multi-factor coupling, used to implement the method described in any one of claims 1-6, characterized in that, include: The model building module (101) is used to build a generalized mechanical model of the dangerous rock mass. In the generalized mechanical model of the dangerous rock mass, the main control structural surface of the dangerous rock mass is simplified into two parts: the through section and the non-through main control structural surface. The instability and failure of the dangerous rock mass is controlled by the rock mass corresponding to the main control structural surface of the dangerous rock mass. The stress analysis module (102) is used to perform stress analysis on the unstable rock mass and the locked rock mass based on the external load and the generalized mechanical model of the unstable rock mass; wherein, the external load includes one or more of horizontal and vertical seismic forces, frost heave forces, fissure water pressure and excess pore water pressure; The strain energy determination module (103) is used to determine the elastic strain energy released by the reduction of the median potential energy of crack propagation on the main structural surface of the unstable rock mass based on the condition of multi-factor coupling. The instability initiation speed determination module (104) is used to determine the instability initiation speed of the unstable rock mass under the coupling effect of multiple factors based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack propagation of the main control structural surface of the unstable rock mass is instantly released and converted into the kinetic energy of the unstable rock mass movement.

8. An electronic device, characterized in that, It includes a processor and a memory, the memory storing multiple instructions, and the processor being used to read the instructions and execute the method as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a plurality of instructions, which can be read by a processor and executed as described in any one of claims 1-6.

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