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

Abstract

The invention discloses a multi-factor coupling action slope dangerous rock mass instability starting speed determination method which comprises the following steps: establishing a dangerous rock mass generalization mechanical model, simplifying a dangerous rock mass main control structural plane into two parts, namely a through section and a non-through main control structural plane, and controlling dangerous rock mass instability damage by a rock mass corresponding to the dangerous rock mass main control structural plane; carrying out stress analysis on the dangerous rock mass and the locking section rock mass based on the external load effect and the generalized mechanical model of the dangerous rock mass; the external load effect comprises horizontal and vertical earthquake force, frost heaving force, fracture water pressure or excess pore water pressure; determining elastic strain energy released by potential energy reduction in crack propagation of the main control structural plane of the dangerous rock mass based on a multi-factor coupling effect; and on the basis of the assumption that elastic strain energy released by reduction of potential energy in crack propagation of the main control structural plane of the dangerous rock mass is instantaneously released and converted into kinetic energy of dangerous rock mass movement, the instability starting speed of slope dangerous rock mass severe movement under the multi-factor coupling effect is determined. The invention further discloses a system, electronic equipment and a computer readable storage medium.

Description

Technical Field

[0001] The invention relates to the technical field of roadbed slope protection, and in particular to a method and system for determining the instability starting speed of a dangerous rock mass on a slope under the action of multi-factor coupling. Background Art

[0002] The high mountain valleys are violently cut and the rock mass is broken. There are widespread distribution of unstable or even loose dangerous rock masses. Affected by the collision between different continental plates, active fault zones are densely distributed and earthquake activities are frequent. In addition, affected by the plateau climate, freeze-thaw effects are prominent. The coupling of multiple factors such as earthquakes and freeze-thaw can easily induce sudden instability of high-lying dangerous rock masses on steep slopes, seriously threatening the safety of life and property. How to calculate the starting speed of sudden instability of high-lying dangerous rock masses on steep slopes under the coupling of multiple factors such as earthquakes and freeze-thaw 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 destruction process of dangerous rock mass can be divided into three stages: start-up, operation, and stagnation. The start-up process of dangerous rock mass (i.e., the moment of dangerous rock mass destruction and instability) under the coupling of multiple factors such as earthquakes and freeze-thaw has the characteristics of sudden instability and large initial velocity. Accurately predicting the start-up velocity of dangerous rock instability is crucial for the reasonable assessment of the consequences of dangerous rock instability. Existing research mainly focuses on the study of the movement characteristics of dangerous rock after instability based on kinematic equations, and there is a lack of relevant research on the prediction of the initial velocity of dangerous rock instability under the coupling of earthquakes and freeze-thaw. Summary of the invention

[0004] The purpose of the present invention is to provide a method and system for determining the starting speed of instability of dangerous rock masses on slopes under the coupling of multiple factors such as earthquakes and freeze-thaw, in view of the defects of the prior art. The method for calculating the starting speed of dangerous rock masses on high and steep slopes under the coupling of multiple factors such as earthquakes and freeze-thaw proposed in the present invention can effectively solve the problem of difficulty in predicting the initial starting speed of sudden instability of dangerous rock masses.

[0005] The first aspect of the present invention is to provide a method for determining the instability starting speed of a dangerous rock mass on a slope due to the coupling of multiple factors, comprising:

[0006] S1, establishing a generalized mechanical model of dangerous rock mass, in which the main control structure surface of the dangerous rock mass is simplified into two parts: a through section and an unthrough main control structure surface, and the instability and failure of the dangerous rock mass is controlled by the rock mass corresponding to the main control structure surface of the dangerous rock mass;

[0007] S2, based on the external load and the generalized mechanical model of the dangerous rock mass, a force analysis is performed on the dangerous rock mass and the locked rock mass; wherein the external load includes one or more of horizontal and vertical seismic forces, frost heave force, fissure water pressure and excess pore water pressure;

[0008] S3, based on the conditions of multi-factor coupling, determining the elastic strain energy released by the reduction of the median potential energy of the crack extension of the main control structure surface of the dangerous rock mass;

[0009] S4, based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass is instantly released and converted into the kinetic energy of the dangerous rock mass movement, the instability starting speed of the dangerous rock mass movement on the slope under the coupling of multiple factors is determined.

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

[0011] ① The shearing effect of seismic waves is the fundamental driving force for the expansion of cracks in dangerous rock masses;

[0012] ② The cracks in the dangerous rock mass are compound cracks of type I and type II;

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

[0014] ④ The model intercepts the unit width and discusses and analyzes based on the plane strain problem;

[0015] ⑤ Assume that after the dangerous rock instability starts, the dangerous rock mass remains intact and not broken during the movement.

[0016] Preferably, S1 includes: setting the crack height e of the main control structure surface of the dangerous rock mass, point O 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 fracture water, G is the gravity of the dangerous rock mass; when there is an earthquake load, it is assumed that the angle between the direction of the earthquake force and the horizontal direction is α, where the horizontal earthquake acceleration is a h , the vertical earthquake acceleration is a v , then the angle between the earthquake acceleration and the direction of earthquake force and the horizontal direction is as shown in formula (1):

[0017]

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

[0019]

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

[0021] According to the actual stress mode of the dangerous rock, the xOy rectangular coordinate system 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 dangerous rock mass 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 is solved as shown in the following equations (3) to (6):

[0022] Fracture water pressure P w :

[0023]

[0024] Where: P w is the fracture water pressure, γ w is the density of water, h w is the fissure water height.

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

[0026] F x =P h cosβ+(G+P v )sinβ (4)

[0027] Where: F x is the shear force along the initial crack direction, P h is the horizontal earthquake force, P v is the vertical seismic force, G is the weight of the rock mass, and β is the angle between the rock mass structural plane 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] Where: M O is the bending moment, h1 is the vertical distance between the center of gravity of the dangerous rock mass and the crack tip, P h is the horizontal earthquake force, P v is the vertical seismic force, G is the rock mass gravity, l1 is the horizontal distance between the center of gravity of the dangerous rock mass and the crack tip, and β is the angle between the rock mass structural surface and the horizontal plane.

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

[0034] Preferably, S2 includes: establishing a fracture model based on fracture mechanics, where the destruction of each type of dangerous rock is the fracture extension problem of the main control structure surface of the dangerous rock mass under the combined action of loads, and using the dangerous rock stability analysis as the solution process of the fracture model, including:

[0035] Assume that the normal tensile force T and the shear force F along the initial crack direction x The fracture model is evenly distributed along the main control structure surface of the dangerous rock mass, and the fracture model is decomposed into the fracture water pressure P w , shear force per unit length along the initial crack direction τ, bending moment M O and four cases of normal tension σ per unit height; where τ = F x / L; σ=T / H; L is the total length of the dangerous rock mass;

[0036] Assuming that the fracture water pressure is uniformly distributed in the main control structure through section, the resulting fracture strength factor is expressed by the following formula (7):

[0037]

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

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

[0040]

[0041] Bending moment M O The resulting crack fracture strength factor is expressed by the following formula (9):

[0042]

[0043] Where: K I3 is the bending moment M O The stress intensity factor F(e) generated is a function related to the crack height of the main controlling structural surface of the dangerous rock mass. is the maximum normal stress caused by the bending moment.

[0044] Shear force F along the initial crack direction x The resulting crack fracture strength factor is expressed by the following formula (10):

[0045]

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

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

[0048] Preferably, S3 is based on the assumption that the initial crack on the main control structure surface expands along the direction of the original crack under the action of load. According to the functional principle, when the crack on the main control structure surface expands, 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 released elastic strain energy is equal to the assumed realization of the work that should be done to reclose the crack to its original state.

[0049] Preferably, S3 includes: the crack tip extension length Δa, during which the dangerous rock mass releases elastic strain energy; assuming that a uniformly distributed normal stress σ is applied on the crack surface Δa y and shear stress τ yx , so that the crack closes again, the uniformly distributed normal stress σ y and shear stress τ yx As the displacement of the force at each point increases linearly from zero, the maximum values ​​of the normal stress and shear stress applied to each point on the crack surface Δa are σ y (r,0) and τ yx (r, 0), the corresponding displacement on the crack surface Δa during the crack closing process is u(r, π) and v(r, π). Substituting r = x and θ = 0 into the stress field in the y direction of the crack end area, the maximum values ​​of the normal stress and shear stress applied to each point on the crack surface Δa are shown in equations (12) and (13), respectively:

[0050]

[0051] Where: y (r,0) is the normal stress at the polar radius r = r and 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 K is the first type fracture strength factor of the main controlling structural surface of dangerous rock; II It is the second type of fracture strength factor of the main controlling structural surface of dangerous rock;

[0052] Substituting r = Δa-x and θ = π into the displacement field in the y direction of the crack end region, the corresponding displacement on the crack surface Δa during the crack closing process can be obtained as shown in equations (14) and (15):

[0053]

[0054] Then, when the crack expands by Δa, the elastic strain energy ΔU released by the reduction of crack potential energy is expressed as follows (16):

[0055]

[0056] The expansion instability of the main control structure surface of the dangerous rock mass can be regarded as a plane strain problem.

[0057] Shear modulus The unit is kPa;

[0058] Crack extension area increment ΔA = bΔa, unit is m 2 ;

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

[0060]

[0061] Preferably, S4 includes:

[0062] As a brittle material, the stress K at the end of the crack in the main control structure of dangerous rock instability * Exceeding its strength limit K IC When K * >K IC , the crack begins to expand; when the dangerous rock loses stability, the elastic strain energy ΔU released by the crack potential energy reduction is instantly released and converted into the kinetic energy E of the dangerous rock mass movement k ; According to the kinetic energy theorem, we can get formula (18):

[0063]

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

[0065] Combining equations (17) and (18), the initial movement velocity of the dangerous rock mass is solved as shown in equation (19):

[0066]

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

[0068] The second aspect of the present invention is to provide a system for determining the instability starting speed of a dangerous rock mass on a slope under multi-factor coupling, which is used to implement the method of the first aspect, comprising:

[0069] A model building module (101) is used to build a generalized mechanical model of dangerous rock mass, in which the main control structure surface of the dangerous rock mass is simplified into two parts: a through section and an unthrough main control structure surface, and the instability and failure of the dangerous rock mass is controlled by the rock mass corresponding to the main control structure surface of the dangerous rock mass;

[0070] A stress analysis module (102) is used to perform stress analysis on the dangerous rock mass and the locked rock mass based on the external load and the generalized mechanical model of the dangerous rock mass; wherein the external load includes one or more of horizontal and vertical earthquake forces, frost heave force, fissure water pressure and excess pore water pressure;

[0071] A strain energy determination module (103) is used to determine the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass based on the conditions of the coupling effect of multiple factors;

[0072] The starting speed determination module (104) is used to determine the instability starting speed of the dangerous rock mass of the slope under the coupling of multiple factors based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack expansion of the main control structure surface of the dangerous rock mass is instantly released and converted into the kinetic energy of the dangerous rock mass movement.

[0073] A third aspect of the present invention provides an electronic device, comprising a processor and a memory, wherein the memory stores a plurality of instructions, and the processor is configured to read the instructions and execute the method described in the first aspect.

[0074] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a plurality of instructions, and the plurality of instructions can be read by a processor and execute the method described in the first aspect.

[0075] Beneficial effects of the method and system of the present invention:

[0076] Through the present invention, the potential dangerous rock mass on the high and steep slope is generalized into a mechanical model controlled by the rock mass of the unpenetrated main control structural surface. The influence of multiple loads such as horizontal and vertical seismic force, frost heave force, fissure water pressure, 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 coupling of multiple factors can be quickly and accurately calculated, providing a scientific basis for the prediction of the movement path and influence range of the dangerous rock mass after instability and the engineering impact assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the related technologies, the drawings required for use in the specific embodiments or the related technical descriptions will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0078] Figure 1 A flow chart of a method for determining the instability starting speed of a dangerous rock mass on a slope under the action of multiple coupling factors according to an embodiment of the present invention;

[0079] Figure 2 A generalized mechanical model of a typical dangerous rock mass provided according to an embodiment of the present invention;

[0080] Figure 3 A fracture mechanics model provided according to an embodiment of the present invention under the assumption that the fracture water pressure is uniformly distributed in the through section of the main control structure surface;

[0081] Figure 4 A mechanical model of the end load of the main control structure surface provided according to an embodiment of the present invention;

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

[0083] Figure 6 This is a diagram showing the architecture of a system for determining the instability starting speed of a dangerous rock mass on a slope under the action of multiple coupling factors according to an embodiment of the present invention;

[0084] Figure 7 A structural diagram of an electronic device provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0085] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0087] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0088] Embodiment 1

[0089] See also Figure 1 This embodiment provides a method for determining the instability starting speed of a dangerous rock mass on a slope due to the coupling of multiple factors, including:

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

[0091] In this embodiment, step S1 makes the following assumptions:

[0092] ① The shearing effect of seismic waves is the fundamental driving force for the expansion of cracks in dangerous rock masses;

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

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

[0095] ④ The model intercepts the unit width and discusses and analyzes based on the plane strain problem;

[0096] ⑤ Assume that after the dangerous rock instability starts, the dangerous rock mass remains intact and not broken during the movement.

[0097] Based on the above assumptions, a typical generalized mechanical model of dangerous rock mass is established, such as Figure 2 shown. Figure 2The height of the crack in the main control structure of the medium-risk rock mass is e, point O is the position of the initial crack tip, H is the total height of the dangerous rock mass, and it is assumed that h w is the filling height of the fracture water, and G is the gravity of the dangerous rock mass. Seismic waves are a function of time. Their magnitude is constantly increasing or decreasing over time, and their direction is also changing periodically. When there is an earthquake load, it is assumed that the angle between the direction of the earthquake force and the horizontal direction is α, where the horizontal earthquake acceleration is a h , the vertical earthquake acceleration is a v , then the angle between the earthquake acceleration and the direction of earthquake force and the horizontal direction is as shown in formula (1):

[0098]

[0099] The seismic load P acting on the dangerous rock mass can be decomposed into the horizontal seismic load P h and vertical seismic load P v , as shown in formula (2):

[0100]

[0101] h and b are the fracture tip O and the center of gravity of the dangerous rock mass, respectively. w is the filling height of the fissure water. The dangerous rock mass considers 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 tension T and bending moment M O Equal load.

[0102] According to the actual stress mode of dangerous rock ( Figure 2 As shown in ), the xOy rectangular coordinate system 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 dangerous rock mass and the crack tip are l1 and h1 respectively, and the total height of the dangerous rock mass is H, the force at the crack tip O is solved as shown in the following equations (3) to (6):

[0103] Fracture water pressure P w :

[0104]

[0105] Where: P w is the fracture water pressure, γ w is the density of water, h w is the fissure water height.

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

[0107] F x =P h cosβ+(G+P v)sinβ (4)

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

[0109] Normal tension 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 is the bending moment, h1 is the vertical distance between the center of gravity of the dangerous rock mass and the crack tip, P h is the horizontal earthquake force, P v

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

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

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

[0117] In this embodiment, based on fracture mechanics, the destruction of each type of dangerous rock is the problem of fracture extension of the main control structure surface of the dangerous rock mass under the combined action of loads. The stability analysis of dangerous rock can be regarded as the solution process of the fracture model. Assuming that the normal tensile force T and the shear force F along the initial crack direction x If the main control structure surface of the dangerous rock mass is evenly distributed, Figure 3 The fracture model shown can be further decomposed into the fracture water pressure P w , shear force per unit length along the initial crack direction τ, bending moment M O and four cases of normal tension σ per unit height. Among them, τ=F x / L; σ=T / H; where L is the total length of the dangerous rock mass.

[0118] Figure 3 It is assumed that the fracture water pressure is uniformly distributed in the main control structure through section, and the resulting fracture strength factor can be expressed by the following formula (7):

[0119]

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

[0121] The crack fracture strength factor generated by the normal tensile force T can be expressed by the following formula (8):

[0122]

[0123] Bending moment M O The resulting crack fracture strength factor can be expressed by the following formula (9):

[0124]

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

[0126] Shear force F along the initial crack direction x The resulting crack fracture strength factor can be expressed by the following formula (10):

[0127]

[0128] According to the superposition of stress intensity factors, the first type of fracture intensity factor of the main control structure surface of dangerous rock 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 multi-factor coupling, determining the elastic strain energy released by the reduction of the median potential energy of the crack extension of the main control structure surface of the dangerous rock mass;

[0131] In this embodiment, Figure 4As shown in Figure 1, the load at the end of the main control structure surface A of the dangerous rock mass is mainly manifested as the bending moment and shear force generated by the deadweight of the dangerous rock mass and the earthquake load, and the tensile stress generated by the fracture water pressure. According to fracture mechanics, the stress intensity factor K generated by the fracture water pressure is I1 , stress intensity factor K generated by normal force I2 , stress intensity factor K caused by bending moment I3 , stress intensity factor K generated by shear force I4 It can be obtained by the calculation in step S2.

[0132] Assuming that the initial crack on the main control structure surface expands along the original crack direction under the action of load, according to the functional principle, when the crack on the main control structure surface expands, the potential energy of the crack body decreases and the elastic strain energy is released. For the plane fracture problem under type I-II loading, the released elastic strain energy is equal to the work that should be done to close the crack to its original state. Figure 5 Schematic diagram of calculation of elastic strain energy released by crack extension Δa under I-II type loading. Figure 5 (a) Schematic diagram of calculation of elastic strain energy released corresponding to crack extension state a under type I-II loading; Figure 5 (b) Schematic diagram of calculation of elastic strain energy released corresponding to crack extension state b under type I-II loading; Figure 5 (c) Schematic diagram of the calculation of the elastic strain energy released corresponding to the crack extension state c under type I-II loading.

[0133] The crack tip extension length Δa is given by Figure 5 In (a), state a becomes Figure 5 (b) State b, during this process, the dangerous rock mass releases elastic strain energy; Figure 5 As shown in state c in (c), it is assumed that a uniform normal stress σ is applied on the crack surface Δa. y and shear stress τ yx , so that the crack in state b closes and returns to the original state a, the uniformly distributed normal stress σ y and shear stress τ yx The displacement of the force at each point gradually increases from zero according to the linear law. The maximum values ​​of the normal stress and shear stress applied to each point on the crack surface Δa in state c are σ y (r,0) and τ yx (r, 0), the corresponding displacement on the crack surface Δa during the crack closing process is u(r, π) and v(r, π). Substituting r = x and θ = 0 into the stress field in the y direction of the crack end area, the maximum values ​​of the normal stress and shear stress applied to each point on the crack surface Δa in state c are shown in equations (12) and (13), respectively:

[0134]

[0135] Where:y (r,0) is the normal stress at the polar radius r = r and 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 K is the first type fracture strength factor of the main controlling structural surface of dangerous rock; II It is the second type of fracture strength factor of the main controlling structural surface of dangerous rock;

[0136] Substituting r = Δa-x and θ = π into the displacement field in the y direction of the crack end region, the corresponding displacement on the crack surface Δa during the crack closing process can be obtained as shown in equations (14) and (15):

[0137]

[0138] Then, when the crack expands by Δa, the elastic strain energy ΔU released by the reduction of crack potential energy is expressed as follows (16):

[0139]

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

[0141] Shear modulus The unit is kPa;

[0142] Crack extension area increment ΔA = bΔa, unit is m 2 ;

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

[0144]

[0145] S4, based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass is instantly released and converted into the kinetic energy of the dangerous rock mass movement, the instability starting speed of the dangerous rock mass movement on the slope under the coupling of multiple factors is determined.

[0146] In this embodiment, as a brittle material, the stress K at the end of the crack on the main control structure surface of the dangerous rock instability * Exceeding its strength limit K IC When K * >K IC , the crack begins to expand. When the dangerous rock loses stability, the elastic strain energy ΔU released by the reduction of crack potential energy is instantly released and converted into the kinetic energy E of the dangerous rock mass movement k According to the kinetic energy theorem, we can get equation (18):

[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; v0 is the initial movement speed of the dangerous rock mass.

[0149] Combining equations (17) and (18), the initial movement velocity of the dangerous rock mass is solved as shown in equation (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 2

[0153] like Figure 6 As shown, this embodiment provides a system for determining the instability starting speed of dangerous rock mass on a slope under multi-factor coupling, which is used to implement the method of embodiment 1, including:

[0154] The model building module 101 is used to build a generalized mechanical model of dangerous rock mass, in which the main control structure surface of the dangerous rock mass is simplified into two parts: a through section and an unthrough main control structure surface, and the instability and failure of the dangerous rock mass is controlled by the rock mass corresponding to the main control structure surface of the dangerous rock mass;

[0155] A stress analysis module 102 is used to perform stress analysis on the dangerous rock mass and the locked rock mass based on the external load and the generalized mechanical model of the dangerous rock mass; wherein the external load includes one or more of horizontal and vertical seismic forces, frost heave force, fissure water pressure and excess pore water pressure;

[0156] The strain energy determination module 103 is used to determine the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass based on the conditions of the coupling effect of multiple factors;

[0157] The starting speed determination module 104 is used to determine the instability starting speed of the dangerous rock mass of the slope under the coupling of multiple factors based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass is instantly released and converted into the kinetic energy of the dangerous rock mass movement.

[0158] The present invention also provides a memory storing a plurality of instructions, wherein the instructions are used to implement the method as in the first embodiment.

[0159] like Figure 7 As shown, the present invention also provides an electronic device, including a processor 301 and a memory 302 connected to the processor 301, the memory 302 stores a plurality of instructions, and the instructions can be loaded and executed by the processor so that the processor can execute the method as in the first embodiment.

[0160] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the instability starting speed of dangerous rock mass on slope under multi-factor coupling, characterized in that: include: S1, establishing a generalized mechanical model of dangerous rock mass, in which the main control structure surface of the dangerous rock mass is simplified into two parts: a through section and an unthrough main control structure surface, and the instability and failure of the dangerous rock mass is controlled by the rock mass corresponding to the main control structure surface of the dangerous rock mass; S2, based on the external load and the generalized mechanical model of the dangerous rock mass, a force analysis is performed on the dangerous rock mass and the locked rock mass; wherein the external load includes one or more of horizontal and vertical seismic forces, frost heave force, fissure water pressure and excess pore water pressure; S3, based on the conditions of multi-factor coupling, determining the elastic strain energy released by the reduction of the median potential energy of the crack extension of the main control structure surface of the dangerous rock mass; S4, based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass is instantly released and converted into the kinetic energy of the dangerous rock mass movement, the instability starting speed of the dangerous rock mass movement on the slope under the coupling of multiple factors is determined.

2. The method for determining the instability starting speed of dangerous rock mass on slope due to multi-factor coupling according to claim 1 is characterized in that: The generalized mechanical model of the dangerous rock mass in S1 is established based on the following assumptions: ① The shearing effect of seismic waves is the fundamental driving force for the expansion of cracks in dangerous rock masses; ② The cracks in the dangerous rock mass are compound cracks of type L and type II; ③ When the stress intensity factor at the crack tip under the action of earthquake load is greater than the fracture toughness of the rock mass, the crack begins to expand; ④ The model intercepts the unit width and discusses and analyzes based on the plane strain problem; ⑤ Assume that after the dangerous rock instability starts, the dangerous rock mass remains intact and not broken during the movement.

3. The method for determining the instability starting speed of dangerous rock mass on slope due to multi-factor coupling according to claim 2 is characterized in that: S1 includes: setting the crack height e of the main control structure surface of the dangerous rock mass, point 0 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 fracture water, G is the gravity of the dangerous rock mass; when there is an earthquake load, it is assumed that the angle between the direction of the earthquake force and the horizontal direction is α, where the horizontal earthquake acceleration is a h , the vertical earthquake acceleration is a v , then the angle between the earthquake acceleration and the direction of earthquake force and the horizontal direction is as shown in formula (1): The seismic load P acting on the dangerous rock mass can be decomposed into the horizontal seismic load P h and vertical seismic load P v , as shown in formula (2): h and b are the crack tip 0 and the center of gravity of the dangerous rock mass, respectively. w is the filling height of the fissure water; the dangerous rock mass considers gravity G, seismic load P, and fissure water pressure P w , shear force F along the initial crack direction x , normal tension T and bending moment M O Equal load; gravity G corresponds to mass m; According to the actual stress mode of the dangerous rock, the x0y rectangular coordinate system is established with the crack tip 0 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 dangerous rock mass 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 0 is solved as shown in the following equations (3) to (6): Fracture water pressure P w : Where: P w is the fracture water pressure, γ w is the density of water, h w is the height of fracture water; Shear force F along the initial crack direction x : F x =P h cosβ+(G+P v )sinβ (4) Where: F x is the shear force along the initial crack direction, P h is the horizontal earthquake force, P v is the vertical seismic force, G is the weight of the rock mass, and β is the angle between the rock mass structural plane and the horizontal plane; Normal tension T: T=P h sinβ+(P v -G)cosβ (5) Bending moment M O : M O =P h h1±(P v -G)l1 (6); Where: M O is the bending moment, h1 is the vertical distance between the center of gravity of the dangerous rock mass and the crack tip, P h is the horizontal earthquake force, P v is the vertical seismic force, G is the rock mass gravity, l1 is the horizontal distance between the center of gravity of the dangerous rock mass and the crack tip, and β is the angle between the rock mass structural surface and the horizontal plane; In formula (3) to formula (6): when the center of gravity of the dangerous rock mass is inside the 0 point, the signs of all quantities are "-"; when the center of gravity of the dangerous rock mass is outside the 0 point, the signs of all quantities are "+".

4. The method for determining the instability starting speed of a dangerous rock mass on a slope due to multi-factor coupling according to claim 3 is characterized in that: The S2 includes: establishing a fracture model based on fracture mechanics, taking the destruction of each type of dangerous rock as the fracture extension problem of the main control structure surface of the dangerous rock mass under the combined action of loads, and taking the stability analysis of the dangerous rock as the solution process of the fracture model, including: Assume that the normal tensile force T and the shear force F along the initial crack direction x The fracture model is evenly distributed along the main control structure surface of the dangerous rock mass, and the fracture water pressure P w , shear force per unit length along the initial crack direction τ, bending moment M O and four cases of normal tension σ per unit height; where τ = F x / L; σ=T / H; L is the total length of the dangerous rock mass; Assuming that the fracture water pressure is uniformly distributed in the main control structure through section, the resulting fracture strength factor is expressed by the following formula (7): Where: K I1 is the stress intensity factor generated by fracture water pressure, is the fracture water pressure, a0 is the crack length; The crack fracture strength factor generated by the normal tensile force T is expressed by the following formula (8): Where: K I2 is the stress intensity factor generated by the normal tensile force, T is the normal force, H is the total height of the dangerous rock mass, and a0 is the crack length; Bending moment M O The resulting crack fracture strength factor is expressed by the following formula (9): Where: K I3 is the bending moment M O The stress intensity factor generated, F(e), is a function related to the crack height of the main controlling structural surface of the dangerous rock mass, e is the crack height of the main controlling structural surface of the dangerous rock mass, is the maximum normal stress generated by the bending moment; Shear force F along the initial crack direction x The resulting crack fracture strength factor is expressed by the following formula (10): Where: K I4 is the shear force F x The resulting stress intensity factor, is the shear force F x The shear stress generated; According to the superposition of stress intensity factors, the first type fracture intensity factor K of the main control structure surface of dangerous rock is I Calculated by the following formula (11): K I =K I1 +K I2 +K I3 +K I4 (11)。 5. The method for determining the instability starting speed of dangerous rock mass on slope due to multi-factor coupling according to claim 4 is characterized in that: The S3 is based on the assumption that the initial crack of the main control structure surface expands along the original crack direction under the action of load. According to the functional principle, when the crack of the main control structure surface expands, the potential energy of the crack body decreases and the elastic strain energy is released; And for the plane fracture problem under type 1-ll loading, the elastic strain energy released is equal to the assumed realization of the work that should be done to close the crack to its original state.

6. The method for determining the instability starting speed of dangerous rock mass on slope due to multi-factor coupling according to claim 5 is characterized in that: The S3 includes: the crack tip extension length Δa, during which the dangerous rock mass releases elastic strain energy; assuming that a uniformly distributed normal stress σ is applied on the crack surface Δa y and shear stress τ yx , so that the crack closes again, the uniformly distributed normal stress σ y and shear stress τ yx As the displacement of the force at each point increases linearly from zero, the maximum values ​​of the normal stress and shear stress applied to each point on the crack surface Δa are σ y (r, 0) and τ yx (r, 0), the corresponding displacement on the crack surface Δa during the crack closing process is u(r, π) and v(r, π); substituting r = x, θ = 0 into the stress field in the y direction of the crack end area, the maximum values ​​of the normal stress and shear stress applied to each point on the crack surface Δa are shown in equations (12) and (13), respectively: Where: y (r, 0) is the normal stress at the polar radius r = r and 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 K is the first type fracture strength factor of the main controlling structural surface of dangerous rock; II It is the second type of fracture strength factor of the main controlling structural surface of dangerous rock; Substituting r = Δa-x and θ = π into the displacement field in the y direction of the crack end region, the corresponding displacement on the crack surface Δa during the crack closing process can be obtained as shown in equations (14) and (15): Then, when the crack expands by Δa, the elastic strain energy ΔU released by the reduction of crack potential energy is expressed as follows (16): The expansion instability of the main control structure surface of the dangerous rock mass can be regarded as a plane strain problem. Shear modulus The unit is kPa; Crack extension area increment ΔA = bΔa, unit is m 2 ; Then formula (16) is transformed into formula (17):

7. The method for determining the instability starting speed of dangerous rock mass on slope due to multi-factor coupling according to claim 6 is characterized in that: The S4 includes: As a brittle material, the stress K at the end of the crack on the main control surface of the dangerous rock instability * Exceeding its strength limit K IC When K * >K IC , the crack begins to expand; when the dangerous rock loses stability, the elastic strain energy ΔU released by the crack potential energy reduction is instantly released and converted into the kinetic energy E of the dangerous rock mass movement k ; According to the kinetic energy theorem, we can get formula (18): In formula (18): E k is the initial kinetic energy of the dangerous rock mass; m is the mass of the dangerous rock mass; v0 is the initial movement speed of the dangerous rock mass; Combining equations (17) and (18), the initial movement velocity of the dangerous rock mass is solved as shown in equation (19): The initial movement speed of the dangerous rock mass is the instability starting speed of the dangerous rock mass of the slope.

8. A system for determining the instability start-up speed of dangerous rock mass on slopes under multi-factor coupling, used for implementing the method described in any one of claims 1 to 7, characterized in that: include: A model building module (101) is used to build a generalized mechanical model of dangerous rock mass, in which the main control structure surface of the dangerous rock mass is simplified into two parts: a through section and an unthrough main control structure surface, and the instability and failure of the dangerous rock mass is controlled by the rock mass corresponding to the main control structure surface of the dangerous rock mass; A stress analysis module (102) is used to perform stress analysis on the dangerous rock mass and the locked rock mass based on the external load and the generalized mechanical model of the dangerous rock mass; wherein the external load includes one or more of horizontal and vertical earthquake forces, frost heave force, fissure water pressure and excess pore water pressure; A strain energy determination module (103) is used to determine the elastic strain energy released by the reduction of the potential energy of the crack extension of the main control structure surface of the dangerous rock mass based on the conditions of the coupling effect of multiple factors; The starting speed determination module (104) is used to determine the instability starting speed of the dangerous rock mass of the slope under the coupling of multiple factors based on the assumption that the elastic strain energy released by the reduction of the potential energy of the crack expansion of the main control structure surface of the dangerous rock mass is instantly released and converted into the kinetic energy of the dangerous rock mass movement.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores a plurality of instructions, and the processor is used to read the instructions and execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a plurality of instructions, and the plurality of instructions can be read by a processor to execute the method according to any one of claims 1 to 7.

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