Earthquake-induced collapse type dangerous rock instability starting speed calculation method

Abstract

The invention discloses an earthquake-induced collapse type dangerous rock instability starting speed calculation method. The method comprises the steps that a sliding type dangerous rock mass simplified model of a rear-end locking section and a sliding type dangerous rock mass stress analysis model under the earthquake-rainfall-freeze thawing coupling effect are established; according to a semi-inverse solution method in elastic mechanics, an approximate stress solution of the locking section rock mass under the action of external force is solved, and then the starting speed of sudden instability of the earthquake-induced collapse type dangerous rock is deduced. According to the method, the collapse type dangerous rock is generalized into a mechanical model of rear-end locking section rock mass control, the influence of multi-load effects such as earthquake force, frost heaving force, fracture water pressure and excess pore water pressure on the collapse type dangerous rock mass instability starting speed can be comprehensively considered, and the earthquake-induced collapse type dangerous rock instability starting speed can be rapidly and accurately calculated; and a scientific basis is provided for motion path and influence range prediction and engineering influence evaluation after dangerous rock mass instability.

Description

Technical Field

[0001] This invention belongs to the field of roadbed slope protection technology and relates to a method for calculating the initiation speed of earthquake-induced landslide-type unstable rockfall. Background Technology

[0002] Western my country is characterized by its rugged mountainous valleys and fractured rock masses, with widespread unstable or even loose rock formations. Furthermore, the region is heavily influenced by collisions between continental plates, resulting in a dense network of active fault zones and frequent earthquakes. Landslide-type unstable rock formations are a common type of rockfall. Under seismic action, the anchored sections of these formations are highly susceptible to fracturing due to reciprocating forces, leading to sudden instability and posing a serious threat to life and property. Calculating the energy conversion mechanism and initial initiation velocity during the sudden instability of landslide-type unstable rock formations under seismic action is a crucial prerequisite for accurately predicting their movement paths and assessing potential losses.

[0003] The invention patent "Method and System for Determining the Initiation Speed ​​of Rock Mass Instability on Slopes under Multi-Factor Coupling Effects" derives the initiation speed of rock mass instability based on the assumption that the elastic strain performance of the potential energy released during the propagation of cracks on the structural surface of the rock mass is entirely converted into the kinetic energy of the rock mass. However, the mechanical model in the above method cannot reflect the control effect of the rock mass in the rear-end locking section on the stability of the rock mass in a landslide-type rock mass. Its core calculation parameter, the ultimate strength K of the structural surface of the rock mass, is insufficient. IC The values ​​are difficult to determine and often rely on experience, which has a significant impact on the accuracy of the results. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention discloses a method for calculating the initiation velocity of a sliding and collapsing unstable rock under seismic action, the technical solution of which is as follows:

[0005] A method for calculating the initiation velocity of a sliding and collapsing unstable rock under seismic action, characterized by:

[0006] Step 1: Establish a simplified model of the sliding unstable rock mass in the rear-end locking section and a stress analysis model of the sliding unstable rock mass under the coupled effects of earthquake, rainfall and freeze-thaw;

[0007] Step 2: Based on the semi-inverse solution method in elasticity, find the approximate stress solution of the unconsolidated rock mass under the action of external force, and then derive the initiation speed of sudden instability of earthquake-induced landslide-type unstable rock.

[0008] Beneficial effects

[0009] By generalizing landslide-type unstable rock masses into a mechanical model controlled by the rock mass in the rear-end locking section, the effects of multiple loads such as seismic force, frost heave force, fissure water pressure, and excess pore water pressure on the instability initiation speed of the landslide-type unstable rock mass can be comprehensively considered. This enables rapid and accurate calculation of the instability initiation speed of earthquake-induced landslide-type unstable rock masses, providing a scientific basis for predicting the movement path and impact range of unstable rock masses and assessing engineering impacts. Attached Figure Description

[0010] Figure 1 This is a simplified model diagram of a sliding unstable rock mass containing a rear locking section. As shown in the figure, the unstable rock mass consists of a rear locking section rock mass and an upper, already penetrated unstable rock mass. Its overall stability is controlled by the locking section rock mass.

[0011] Figure 2 The diagram shows the stress analysis of the penetrated dangerous rock mass. As shown in the figure, the stress analysis is performed on two adjacent sections of the penetrated dangerous rock mass (numbered ① and ②), including loads such as gravity, seismic load, frost heave force, and hydrostatic pressure.

[0012] Figure 3 This is a simplified mechanical model of the locked-in rock mass, as shown in the figure. For ease of analysis, a rectangular section of rock mass with length L, height H, and mass m is cut out from the locked-in section. Let F be the sliding thrust provided by the rock mass above the locked-in section, and let U1 and U2 be the hydrostatic pressure and the excess pore water pressure caused by the earthquake, respectively, and both be evenly distributed on the left side of the rock mass. The locked-in rock mass is subjected to horizontal and vertical seismic forces. The potential slip zone thickness of the locked-in slope is h.

[0013] Figure 4 The shear force-shear deformation curve of the potential sliding zone;

[0014] Figure 5 For the force model of the potential sliding surface element, an arbitrary element on the potential sliding surface is selected for force analysis;

[0015] Figure 6 The energy relationship between the locking segment and the potential sliding surface during minute deformation;

[0016] Figure 7 This is a diagram showing the energy relationship between the locked-in rock mass and the potential sliding surface;

[0017] Figure 8 The relationship between clinical energy accumulation on the slope and energy release during sliding deformation. Detailed Implementation

[0018] This invention is based on the following assumptions:

[0019] ① The deep failure of sliding unstable rock masses is controlled by the rock mass of the rear locking section;

[0020] ② Under the thrust of the upper fractured rock mass, the locked section of rock mass deforms, and the accumulated deformation energy is eventually converted into the kinetic energy of the entire landslide.

[0021] Based on the above assumptions, this invention discloses a method for calculating the initiation velocity of a sliding and collapsing unstable rock under seismic action, characterized by:

[0022] Step 1: Establish a simplified model of the sliding unstable rock mass in the rear locking section and a stress analysis model of the sliding unstable rock mass under the coupled effects of earthquake, rainfall and freeze-thaw.

[0023] Each as Figure 1 and Figure 2 As shown. Figure 2 After rainfall, the fissure water filling height is h1, the potential sliding surface height from the water surface is h1, and the structural surface width is B.

[0024] The horizontal seismic force on the soil above the slip surface is: Vertical seismic force is

[0025] In the formula, a h Horizontal seismic acceleration of the rock mass; a v denoted as , where is the vertical seismic acceleration of the rock mass; W is the weight of the landslide soil.

[0026] The hydrostatic pressure of the vertically opening fracture at the trailing edge is: The drag force is: η is the inclination angle of the sliding surface.

[0027] The uplift pressure on the sliding surface is perpendicular to the surface, and its effect reduces the slope's resistance to sliding. The pore water uplift pressure on the sliding surface is...

[0028] In the formula: γ w ρ is the specific weight of water; h1 is the height of the potential slip surface above the water surface; L1 is the length of the potential slip surface.

[0029] For plane strain problems, the increment of pore pressure can be expressed as the increment of the average principal stress and the constant increment of the shear stress:

[0030]

[0031] During an earthquake:

[0032] Δσ1=Δσ x =k h γ sat (4-8)

[0033] Δσ3=Δσ z =k v γ sat (4-9)

[0034] Δσ2=υ(Δσ1+Δσ3)=υ(k h +k v )γ sat (4-10)

[0035] The formula for calculating the pore pressure increment under seismic loading is as follows:

[0036]

[0037] In the formula: γ sat It is the unit weight (weighted average) of saturated soil; υ is the Poisson's ratio of the soil; α and β represent the pore water pressure coefficients; k h and k v These represent the horizontal and vertical seismic acceleration coefficients, respectively. ； σ1, σ1, and σ1 represent the increments of the major principal stress, the intermediate principal stress, and the minor principal stress, respectively.

[0038]

[0039]

[0040] In the formula: n is porosity; C v C and C are the volume compressibility coefficients of the pore fluid and soil, respectively (which are the reciprocals of the volumetric modulus); C q This is the shearing factor.

[0041] Establish a local coordinate system at the shear outlet of the sliding surface; therefore, the excess pore water pressure on the sliding surface is:

[0042]

[0043] In the formula: z is the height in the local coordinate system; L1 is the length of the unstable rock mass; η is the dip angle of the sliding surface; Δu is the excess pore water pressure on the sliding surface.

[0044] In winter, the research area is covered by snow. During the day, the temperature rises due to sunlight, and some of the snow melts and seeps into the cracks, or rainwater seeps into the cracks. At night, the temperature drops sharply, and the water in the cracks turns into ice, expanding in volume and creating frost heave force on both sides of the crack. The formula for calculating frost heave force is as follows:

[0045]

[0046] In the formula: k is the volume expansion coefficient of water freezing; Δt is the freezing temperature difference; E is the elastic modulus; μ is Poisson's ratio; b is the crack opening; R is the radius of the tip of the main control structural surface; and l is the freezing depth.

[0047] The remaining landslide thrust F6 of block ⑥, calculated using the transfer coefficient method, is the thrust acting on the locked rock mass. Combining the effects of earthquakes, rainfall, and freeze-thaw cycles on slope stress discussed in the previous section with the transfer coefficient method, the thrust acting on the locked section by the upper fractured rock mass can be derived as follows:

[0048]

[0049]

[0050] When i is greater than 1, P i5 =0.

[0051] When the slip zone medium in the upper and middle parts of the rock mass is in the residual strength stage, its influence is ignored. This section of the rock mass provides thrust to the lower rock mass while also undergoing elastic deformation. The lower rock mass has a reaction effect on the downward trend of the entire rock mass, i.e., a locking effect; this section of the rock mass is called the locked section. The potential slip surface dip angle of the locked section is α, and the average height is H. For ease of analysis, a rectangular section with length L, height H, and mass m is cut from the locked section. Let the downward thrust provided by the rock mass above the locked section be F, and the hydrostatic pressure and the excess pore water pressure caused by the earthquake be U1 and U2, respectively, and uniformly distributed on the left side of the rock mass. The locked-in rock mass is subjected to horizontal and vertical seismic forces. The potential slip zone thickness of the locked-in slope is h, and a simplified model is shown below. Figure 2 As shown.

[0052] When the potential slip zone is sheared and fractured under the action of the upper thrust, the lower locked section of rock mass will spring out from the shear exit as a whole. The instability mode of the upper and middle rock masses is different, and they slide down in the form of potential-kinetic energy conversion.

[0053] The locked rock mass before instability is considered as an elastic body with a shear modulus of G. The weight of the locked rock mass per unit width is mg = 0.5 * H * L * 1 * (ρg), where ρ is the water-bearing density of the rock mass. Due to precipitation, the water saturation of the rock mass changes continuously, and the value of ρ also varies. The relationship between the shear resistance of the potential sliding zone of the locked rock mass and its shear deformation (i.e., the displacement on the upper side of the potential sliding zone) u is assumed to be:

[0054]

[0055] In the formula: G0 is the initial shear modulus of the subslip zone; denoted as , where is the initial shear stiffness of the latent slip zone; m is the family index of the curves, with a larger m value indicating stronger brittleness and rigidity of the material. The relationship between u0 and the shear deformation uc at the peak of the Q(u) curve is as follows:

[0056] (1 / r) 1 / r u0 = u c (4-192)

[0057] From the above equation, we can see that when r = 1, u0 = uc

[0058] Horizontal seismic force on the locked-in rock mass:

[0059] P h =k h mg (4-193)

[0060] Vertical seismic force:

[0061] P v =k v mg (4-194)

[0062] like Figure 2 As shown, establish a coordinate system along the direction of the sliding surface and its normal direction, and establish the equilibrium equations in the x-direction:

[0063]

[0064] The locked-in rock mass is located above the potential slip zone, and its displacement is the sum of the shear deformation of the slip zone and the displacement of the slip zone itself, that is:

[0065] u y =u+u1(y) (4-196)

[0066] In the formula: uy is Figure 4 The total displacement at any point y in the coordinate system is equal to the displacement of points with the same y value; u is the shear deformation of the subsurface slip zone; u1(y) is the displacement of the rock mass in the locked section, which is caused by the combined action of the volume forces X and Y and the downward thrust F of the rock mass in the locked section.

[0067] The volume forces X and Y in the x and y directions of the locked rock mass are respectively:

[0068]

[0069] The potential slip reaction force caused by the forces and volume forces transmitted from the upper rock mass is

[0070]

[0071] The force analysis of the subsurface slip unit is shown in the figure below, and the equilibrium equations in the x and y directions are obtained:

[0072]

[0073] Step 2: Based on the semi-inverse solution method in elasticity, find the approximate stress solution of the unconsolidated rock mass under the action of external force, and then derive the initiation speed of sudden instability of earthquake-induced landslide-type unstable rock.

[0074] The approximate stress solution for the unconsolidated rock mass under external forces is as follows:

[0075]

[0076] Substituting equations (4-204), (4-205), and (4-206) into equations (4-202) and (4-203) yields the following results. In these equations: x and y are the abscissa and ordinate of any point (x, y), respectively; L and H are the length and height of the rock mass section to which the rock is locked, respectively; σ xThe normal stress on the x-plane, σ y H is the normal stress in the y-plane. S For any point of height, For the major principal stress, τ xy and τ yx These are the shear stresses in the xy and yx directions, respectively;

[0077] In the simplified model, the boundary conditions for the stress solution are:

[0078]

[0079] σ x (L)=0 (4-208)

[0080] σ y (H)=0 (4-209)

[0081]

[0082] τ xy (H)=τ yx (H)=0 (4-212)

[0083] When the displacement of the subsurface along the sliding direction is u1(y), the corresponding displacement in the vertical direction is v1(y).

[0084] Combining the constitutive equations under plane strain conditions in elasticity, we can obtain:

[0085]

[0086] When y = 0, the displacement in the vertical direction is 0, i.e., v1(0) = 0. Integrating equation (4-213) and substituting the point (0, 0) into it, we get:

[0087]

[0088] After taking the partial derivative of equation (4-214) with respect to x, substituting it into the plane geometric equations, and then, based on the shear stress-strain relationship, after deformation and rearrangement, we can finally obtain the displacement equation with respect to y:

[0089]

[0090] In the formula, u1(y) is the displacement value of the locked rock mass, G is the shear modulus, kv and kh are the horizontal and vertical seismic acceleration coefficients, respectively, and U1 is the excess pore water pressure on the slip surface. For, μ is Poisson's ratio, kv and kh are the horizontal and vertical seismic acceleration coefficients, respectively; α is the dip angle of the unstable rock mass sliding surface. It is the ultimate shear stress;

[0091] Integrating u1(y) with respect to y and then dividing by the height H, we can obtain the average displacement of any cross section caused by the deformation of the rock mass in the locked section. for

[0092]

[0093] For common rocks, the Poisson's ratio is μ≈0.2. Therefore, it can be ignored. Combining this with equation (1-63), equation (4-216) can be simplified and rearranged as follows:

[0094]

[0095] Rearranging equation (4-217), we can obtain the relationship between the average displacement μ of any cross section and the increment of Q(u) as follows:

[0096]

[0097] in,

[0098] The shear stress in the locked slope is:

[0099]

[0100] The shear failure of the subslip zone in a locked slope is related to shear stress and shear deformation energy. The shear deformation energy per unit width of the locked slope is:

[0101]

[0102] As the deformation u of the subsurface slip zone increases, the shear deformation energy UP accumulated and consumed per unit width of the subsurface slip zone is:

[0103]

[0104] When the deformation increment δu of the subslip zone is greater than 0, the energy required is δU. P =Q(u)δu; Before the Q(u) curve reaches its peak, if the deformation δu of the slip zone is greater than 0, the deformation increment of the locked slope is... Locking slope deformation energy After the Q(u) curve reaches its peak, the deformation of the slip zone δu > 0, the deformation increment of the locked slope δu < 0, and the deformation energy released by the locked slope is... In addition, when That is, the deformation energy released by the locked slope is less than the energy δU required to cause deformation δu in the subslip zone. PWhen Q(u)δu, external forces, gravity, and seismic forces are required to do work (δW) to replenish energy so that the subslip zone can continue to deform. Assuming the system is in a quasi-static state and neglecting the influence of kinetic energy, the energy conservation principle can be used to obtain the energy increment balance relationship of the slope system when the subslip zone undergoes slight deformation:

[0105]

[0106] Energy change value of locked section slope

[0107]

[0108] The energy required to achieve a unit deformation of the potential sliding zone is

[0109] δU P =Q(u)δu (4-224)

[0110]

[0111] in The energy required to induce unit deformation in the potential slip zone within the locked slope system can be termed the energy input rate. From the above derivation and the physical meaning of each parameter, it can be observed that: when the input rate J1 > 0, the slip zone undergoes quasi-static deformation; when J ≤ 0, the locked rock mass requires no external energy input, and the slip zone will deform by a magnitude of u, at which point the system is in a critical instability state. Therefore, J1 can be used as a criterion for the stability of the locked rock mass.

[0112] The entire rock mass system consists of lock-section rock mass and subslip zone, with uniformly distributed thrust. The volume force X of the locked segment rock mass is an external force of the system. The fractured rock mass is located above the subsurface slip zone. Therefore, when the subsurface slip zone produces a deformation increment of δu, at any height y of the locked segment rock mass, in addition to the deformation displacement increment δu1(y) force, there is also a system rigid body displacement δu. Therefore, when the deformation of the subsurface slip zone δu>0, the increment δW of the work done by the uniformly distributed thrust F and the volume force X is:

[0113]

[0114] because X=(mg(1+k v sinα+mgk h cosα) / HL and equation (3-99) can be obtained

[0115]

[0116] After sorting, we can obtain:

[0117]

[0118] Figure 4-5 The slope Q'(u) of the Q(u) curve reaches a negative extreme value at the inflection point t of the softening segment of the curve under the following conditions:

[0119] Q'(u)+k1<0 (4-229)

[0120] As u increases, there must exist a point j between point c and point t, and at point j, the following relationship holds:

[0121] Q'(u)+k1=0 (4-230)

[0122] And at uj:

[0123]

[0124] After point j, the energy relationship for a unit displacement u is: After this, slippage can occur solely based on the shear deformation properties accumulated in the released locked rock mass, and the subslip zone is in a state of dynamic fracturing.

[0125] exist Figure 7 It can also be seen that there is a point 's' at this time.

[0126]

[0127] And there exists the same relationship as point t.

[0128] Q'(u)+k1=0 (4-233)

[0129] The energy relationship for unit displacement after point t is as follows: From formula (4-191), the shear resistance of the locked section is:

[0130]

[0131] The components of the sliding force in the x-direction, consisting of the seismic load, gravity, and overlying pressure, are as follows:

[0132] G T =mg(1+k) v sinα+mgk h cosα+F (4-235)

[0133] Under load, a safety factor is introduced to determine whether the slope is stable.

[0134]

[0135] Substituting T and GT into the above equation, we get:

[0136]

[0137] From the preceding theoretical derivation, we can conclude that:

[0138]

[0139] Substituting the conditions for the initiation point of dynamic fracture of the locked segment and the termination point of instantaneous release of elastic energy into equation (4-238), we can obtain:

[0140]

[0141] For the locked segment, at points j and s, there are

[0142]

[0143] From equations (4-239) to (4-240), it can be seen that... and At points j and s, the values ​​are the same but the signs are opposite.

[0144] Substituting into equation (4-238) and dividing by k1 u0, we can obtain the dimensionless energy change rate of the locked segment:

[0145]

[0146] in

[0147] Substituting the values, we obtain the dimensionless rate of change of energy in the locked segment:

[0148]

[0149] Given that the initial elastic modulus G0 of the locked-in rock mass is approximately equal to the slope elastic modulus G, we can obtain:

[0150]

[0151] Taking the effective height H of the locking section as 6m and the thickness h of the sliding band as 0.2m, according to equation (4-245), we can obtain... Taking m=1 in equation (4-244), the curve of the rate of change of deformation potential energy of the slope with dimensionless mass is plotted using MATLAB. and The curve is as follows Figure 8 As shown.

[0152] As can be seen from the figure, the energy released by the landslide rupture is the area of ​​the shaded region enclosed by the two curves. Multiply Right now:

[0153]

[0154] Since it involves the release of energy, ΔE < 0. Figure 8 The area ΔE of the shaded region is located at The same applies below the axis. ΔE will be converted into sliding body kinetic energy, which can be calculated from equation (4-246).

[0155]

[0156] u s It is the point at which the slope deformation energy is released instantaneously. The locked section is a hard rock mass, like a rock burst; the dynamic fracturing of the locked section is completed instantaneously, corresponding to (u j ,u s ) Δt = t during the deformation stage s -t j This is an extremely short time period. Let the mass of the sliding body be M. From dynamics, we can obtain the sliding body's position in u... s The velocity of the projectile at that point is:

[0157]

[0158] The explosive velocity obtained based on equation (4-248) is the initial velocity of the unstable rock mass induced by earthquake-induced landslide. It can be used to predict the initial velocity of the unstable rock mass induced by earthquake-induced landslide and provide a basis for predicting the movement path after the unstable rock mass becomes unstable.

[0159] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A method for calculating the initiation rate of earthquake-induced landslide-type unstable rockfall, characterized by: Step 1: Establish a simplified model of the sliding unstable rock mass in the rear-end locking section and a stress analysis model of the sliding unstable rock mass under the coupled effects of earthquake, rainfall and freeze-thaw; Step 2: Based on the semi-inverse solution method in elasticity, find the approximate stress solution of the unconsolidated rock mass under the action of external force, and then derive the initiation speed of sudden instability of earthquake-induced landslide-type unstable rock.

2. The method for calculating the initiation rate of earthquake-induced landslide-type unstable rockfall as described in claim 1, characterized in that: The stress analysis model structure of the sliding unstable rock mass in step 1 is as follows: the sliding unstable rock mass is divided into a rear-end locking section and a front-end section of rock mass with several structural planes that have been penetrated; while the penetrated rock mass provides thrust to the lower rock mass, it also undergoes elastic deformation; the rear-end locking section plays a opposite locking role on the downward trend of the entire unstable rock mass; when the locking section is sheared and fractured under the action of the upper thrust, the unstable rock mass will become unstable and bounce out from the shear outlet as a whole.

3. The method for calculating the initiation rate of earthquake-induced landslide-type unstable rockfall as described in claim 1, characterized in that: The coupled loads in step 1 include: seismic load, hydrostatic pressure, excess pore water pressure, frost heave force, drag force, and gravity.

4. The method for calculating the initiation rate of earthquake-induced landslide-type unstable rockfall as described in claim 1, characterized in that: In step 2, the derivation of the starting speed must meet the energy criterion: when the potential sliding surface undergoes a unit deformation δu, it needs to provide energy J1 to the rock mass of the locking section, that is, the energy input rate. When J1>0, the potential sliding surface fractures and the unstable rock becomes unstable.

5. The method for calculating the initiation rate of earthquake-induced landslide-type unstable rockfall as described in claim 1, characterized in that: The calculation of shear deformation energy of the locked section rock mass satisfies: the approximate stress solution of the locked section rock mass under external force is derived; In the formula: x and y are the abscissa and ordinate of any point (x, y), respectively; L and H are the cut-off length and height of the locked-in rock mass, respectively; σ x The normal stress on the x-plane, σ y H is the normal stress in the y-plane. S For any point of height, For the major principal stress, τ xy and τ yx These are the shear stresses in the xy and yx directions, respectively; Assuming the displacement of the slip zone along the sliding direction is u1(y), then the corresponding displacement in the vertical direction is v1(y). According to the shear stress-strain relationship, the displacement equation for y is obtained as follows: In the formula, u1(y) is the displacement value of the locked rock mass, G is the shear modulus, kv and kh are the horizontal and vertical seismic acceleration coefficients, respectively, and U1 is the excess pore water pressure on the slip surface. For, μ is Poisson's ratio, kv and kh are the horizontal and vertical seismic acceleration coefficients, respectively; α is the dip angle of the unstable rock mass sliding surface. It is the ultimate shear stress; Integrating u1(y) with respect to y and then dividing by the height H, we can obtain the average displacement of any cross section caused by the deformation of the rock mass in the locked section. for Then the average displacement of any cross section The incremental relationship with Q(u) is as follows: In the formula: δQ is the increment of shear deformation energy; G is the average displacement increment; L is the shear modulus; H is the length of the locked section rock mass; and L is the height of the locked section rock mass. The shear stress in the locked slope is In the formula: F is the sliding thrust provided by the rock mass above the locking section, U1 is the excess pore water pressure on the sliding surface, m is the mass of the unstable rock mass, g is the gravitational acceleration, kv and kh are the horizontal and vertical seismic acceleration coefficients, respectively; α is the dip angle of the unstable rock mass sliding surface, L is the length of the locking section rock mass, and H is the height of the locking section rock mass; The shear failure of the subslip zone of a locked slope is related to the shear stress and shear deformation energy. Therefore, the shear deformation energy per unit width of the locked slope is: In the formula: dV represents the shear deformation energy per unit width of the locked slope, dy represents the unit volume increment, k1 represents the unit length increment in the y-direction, and k1 is a coefficient.

6. A non-volatile storage medium, characterized in that, The non-volatile storage medium includes a stored program, wherein the program, when executed, controls the device where the non-volatile storage medium is located to perform the method described in any one of claims 1 to 5.

7. A terminal device, characterized in that, The terminal device includes: a processor, a memory, a communication interface, and a bus; the processor, the memory, and the communication interface are connected through the bus and communicate with each other; the memory stores executable program code; the processor reads the executable program code stored in the memory to run a program corresponding to the executable program code, so as to perform the method as described in any one of claims 1-5 above.

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