An evaluation method for shear buckling instability of dangerous rock on high and steep bank slope of reservoir area

Abstract

The application discloses an evaluation method for shear buckling instability of dangerous rock of high and steep bank slope in reservoir area, generalizes the dangerous rock of high and steep bank slope in reservoir area with shear buckling damage trend characteristics into a suitable geological structure model, carries out mechanical and deformation analysis on the deformation process of the rock mass of the buckling section of the slope surface in the drawdown area, constructs an energy conservation equation in the shear buckling deformation, constructs a stability coefficient calculation model of shear buckling deformation instability by calculating the critical parameters in the critical damage state of the rock mass of the buckling section, obtains the law of the attenuation of different rock mechanics parameters with the increase of the dry-wet cycle number based on the indoor dry-wet cycle rock mechanics test, substitutes the law into the stability calculation model, and calculates the shear buckling stability coefficient of the high and steep bank slope dangerous rock and the change trend after several hydrological years. The application can accurately and quantitatively calculate the stability of the shear buckling of the dangerous rock of the high and steep bank slope under the deterioration of the rock mass in the drawdown area, and reasonably predict the instability trend.

Description

Technical Field

[0001] This invention relates to the field of instability mechanism analysis and stability evaluation of geological disasters such as landslides and collapses on reservoir banks, and in particular to an evaluation method for the shear buckling instability of steep, water-eroded riverbanks in reservoir areas. Background Technology

[0002] Stability assessment and risk prediction of geological hazards caused by steep and unstable rock formations on reservoir banks are an important component of reservoir area geological safety risk assessment research. Some steep and unstable rock formations on reservoir banks will not experience overall instability due to drastic changes in pore water pressure caused by water level fluctuations; their stability is mainly controlled by the strength of the rock mass in the drawdown zone. During the annual periodic fluctuations of reservoir water levels in the drawdown zone, the rock mass within this zone undergoes long-term hydraulic erosion, resulting in significant macroscopic deterioration, a gradual decrease in rock mass mechanical strength, and a reduction in rock mass structural integrity. When the rock mass in the drawdown zone deteriorates to a certain extent, it may buckle and fail due to insufficient strength to support the load of the overlying rock mass, thus triggering instability and failure of the entire steep and unstable rock formation.

[0003] The catastrophic modes of steep slope instability caused by rock mass degradation in drawdown zones mainly include four types: toppling buckling, sliding buckling, fracturing buckling, and shear buckling. However, there are currently no specific studies or models for evaluating shear buckling instability of dangerous rock formations on steep slopes under the influence of rock mass degradation in drawdown zones. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention aims to provide an evaluation method for the shear buckling instability of steep, dangerous slopes in reservoir areas, so as to make accurate quantitative calculations on the stability of shear buckling of steep, dangerous slopes under the deterioration of rock mass in the drawdown zone, and to make reasonable predictions on their instability trends.

[0005] To achieve the above objectives, this invention proposes an evaluation method for the shear buckling instability of steep, water-eroded riverbanks in reservoir areas, comprising the following steps:

[0006] S1. Based on the shear buckling instability mode of high and steep banks of reservoirs, the geological structure of dangerous rocks on high and steep banks of reservoirs with shear buckling failure characteristics is generalized into a shear buckling geological model with overlying rock mass, drawdown zone rock mass and inundation zone rock mass, and there is a tectonic fracture zone on the shear buckling geological model.

[0007] S2. Since the rock mass near the upper side of the tectonic fracture zone will exhibit sliding along the tectonic fracture zone and pushing the rock mass in front, the rock mass in the drawdown zone in front of the tectonic fracture zone is generalized into the pushing section rock mass and the buckling section rock mass on the slope surface. The buckling section rock mass is located at the front edge of the pushing section rock mass.

[0008] S3. Perform mechanical and kinematic analysis on the deformation process of the buckling rock mass and list the energy conservation equations during the deformation process of the buckling rock mass;

[0009] S4. Based on the energy conservation equation, calculate the critical elastic modulus when the buckling rock mass is in a critical failure state. The ratio of this value to the current elastic modulus is used as the stability coefficient for the shear buckling deformation instability of dangerous rocks on steep slopes. This is the stability calculation model. The current elastic modulus is obtained by indoor rock mechanics test.

[0010] S5. Based on indoor wet-dry cycle rock mechanics tests, the law of decay of different rock mechanical parameters with the increase of wet-dry cycle number is obtained. The relevant mechanical parameters of the rock after different wet-dry cycle number are substituted into the stability calculation model proposed in step S4 to calculate the shear buckling stability coefficient and the changing trend of dangerous rocks on high and steep banks after different wet-dry cycle number, that is, after several hydrological years, so as to evaluate the shear buckling instability process of dangerous rocks on high and steep banks in the reservoir area.

[0011] In the above scheme: In step S3, it is assumed that the boundary fissures of the buckling section rock mass have been completely connected, and the buckling section rock mass controls the stability state of the entire steep slope rock mass;

[0012] The shear buckling deformation process of dangerous rocks on steep slopes can be generalized as follows: the overlying rock mass applies pressure to the pushing section rock mass, causing the pushing section rock mass to slide and deform along the structural fracture zone, and further pushes the buckling section rock mass on the slope surface of the drawdown zone, causing the buckling section rock mass to undergo elastic bending deformation under the pressure of the overlying rock mass and the pressure of the pushing section rock mass behind it.

[0013] The buckling section of the rock mass is generalized as a columnar body with height H and side lengths l and b. The original slope surface is assumed to be planar, and the slope angle is denoted as . The deflection at the point of maximum deformation during its buckling deformation is denoted as . ;

[0014] Let the overlying pressure on the buckling section of the rock mass be... Lateral thrust is Its buckling deformation exhibits a sinusoidal half-wave shape, so the equation for the bending deformation elastic curve of segment OA can be written as:

[0015]

[0016] In the formula, A is the amplitude of the sine function. The period number is 1 in the shear buckling instability mode. According to the characteristics of the sine function, the maximum bending deformation in segment OA will only occur in... Position, and its value is:

[0017]

[0018] Record the overlying load of the buckling section rock mass The axial compressive deformation under the action is Its expression is:

[0019]

[0020] In the above scheme: In step S3, according to the law of conservation of energy, the work done by the external force on the buckling rock mass is equal to the sum of the deformation energy and potential energy stored inside the structure. The buckling rock mass is subjected to gravity during the deformation process. Overhead pressure and lateral thrust Based on this, the energy conservation equation for the deformation process of the buckling section rock mass can be derived as follows:

[0021]

[0022] In the formula, The work done for the overlying load. The work done for the lateral thrust on the rear side, The work done by its own weight due to gravity. This refers to the elastic potential energy added or stored within the column. The increase in system potential energy, analyzed through the deformation process of shear buckling, is expressed by the following expression for each energy term:

[0023] Overhead load pressure Work done :

[0024]

[0025] In the formula, the overlying pressure The exerting force is the entire rock mass above the buckling section. The overburden pressure can be obtained by multiplying the geometric dimensions of the corresponding rock mass by its weight. The value of ;

[0026] Lateral thrust acting :

[0027]

[0028] In the formula, lateral thrust It is the force exerted by the pushing rock mass on the buckling rock mass, since it is numerically equal to the reaction force exerted by the buckling rock mass on the pushing rock mass. It is obtained by performing a force analysis on the pushing rock mass, listing the force balance equation and solving it.

[0029] Self-gravity acting :

[0030]

[0031] in,

[0032]

[0033] In the formula, Let be the unit weight of the rock mass, and be the product of the rock mass density and gravitational acceleration. Substituting the above equation into equation (7) yields the work done by gravity due to the rock mass's own weight. for:

[0034]

[0035] Stored elastic potential energy :

[0036]

[0037] In the formula, The elastic modulus of the rock was obtained through indoor rock mechanics tests. Let be the moment of inertia of the cross section of the buckling rock mass. The cross section of the buckling rock mass is equivalent to a rectangle with the same base and height. Therefore, its moment of inertia is:

[0038]

[0039] Increase in system potential energy :

[0040]

[0041] Substituting equations (5) to (12) into equation (4) yields the energy conservation equation for the buckling deformation process of the rock mass in the buckling section, expressed as:

[0042] .

[0043] In the above scheme: In step S4, when the buckling section of the rock mass fails due to buckling, its bending deformation will tend to infinity, that is... When the energy conservation equation satisfies the following condition (14), its corresponding solution is the critical parameter when the buckling rock mass is in the critical failure state.

[0044]

[0045] Based on the energy conservation equation, the critical elastic modulus that satisfies equation (14) is... Solving for the problem, we get:

[0046]

[0047] The ratio of the current elastic modulus to the critical elastic modulus of the buckling section rock mass is used as a stability quantification index for the shear buckling instability mode of dangerous rocks on steep slopes. Its expression is:

[0048]

[0049] when At that time, steep slopes will not experience shear buckling instability failure. At that time, steep and dangerous rock slopes are at risk of shear buckling and instability.

[0050] In the above scheme, the forces on the pushing section rock mass include its own weight, the pressure of the overlying rock mass, the supporting force of the underlying rock mass, the thrust of the buckling section rock mass on it, and the upward sliding resistance along the structural fracture zone. In the stress analysis, the upward sliding resistance along the structural fracture zone on the pushing section rock mass is related to the shear strength of the structural fracture zone, that is, it is related to the cohesion c and the internal friction angle φ on the structural fracture zone. The cohesion c and the internal friction angle φ can be obtained by indoor rock mechanics tests.

[0051] The beneficial effects of this invention are:

[0052] This paper presents an evaluation method for shear buckling instability of dangerous rocks on steep, water-eroded slopes in reservoir areas. Based on a geological structure model of these rocks, the method divides the rock mass in the drawdown zone ahead of the tectonic fracture zone into two parts: a pushing section and a buckling section. According to the energy conservation relationship during the deformation of the buckling section, a shear buckling stability coefficient model for dangerous rocks on steep slopes is proposed. Finally, this model is combined with the rock mechanical strength reduction law in wet-dry cycle tests to predict the trend of shear buckling instability of dangerous rocks on steep slopes under the degradation of the drawdown zone. This method effectively fills the gap in the evaluation of shear buckling instability of dangerous rocks on steep, water-eroded slopes in reservoir areas. It can not only accurately and quantitatively calculate the shear buckling stability coefficient of dangerous rocks on steep slopes under the degradation of the drawdown zone, but also make reasonable predictions about their instability trends. Attached Figure Description

[0053] Figure 1 This is a flowchart of the present invention.

[0054] Figure 2 This is a schematic diagram of the computational model of the present invention.

[0055] Figure 3 This is a schematic diagram illustrating the calculation of the shear buckling stability of a steep, dangerous slope rock structure in an embodiment of the present invention.

[0056] Figure 4 This is a schematic diagram illustrating how the cohesion, internal friction angle, and elastic modulus change with the number of wet-dry cycles in both dry and saturated states, according to an embodiment of the present invention.

[0057] Figure 5 This is a schematic diagram illustrating the variation of the shear buckling stability coefficient of steep bank slopes with respect to different hydrological years in an embodiment of the present invention. Detailed Implementation

[0058] like Figure 1 As shown in Figure 5, an evaluation method for the shear buckling instability of steep, water-eroded riverbanks in reservoir areas mainly consists of the following steps:

[0059] S1. Based on the study of shear buckling instability mode, the geological structure of dangerous rocks on steep, water-eroded banks in reservoir areas with shear buckling failure characteristics is generalized into a shear buckling geological model with overlying rock mass, drawdown zone rock mass, and inundation zone rock mass.

[0060] Shear buckling failure typically occurs only on steep bank slopes of reservoirs where water levels fluctuate periodically (e.g., the Three Gorges Reservoir's water level fluctuates periodically between 145m and 175m). This periodically fluctuating water level area is known in the industry as the reservoir drawdown zone. Within this zone, the rock mass undergoes periodic wet-dry cycles, resulting in more significant surface deterioration and a substantial decrease in rock mass strength. This area is also referred to as the reservoir bank drawdown zone rock mass deterioration zone. The deterioration of the rock mass in the reservoir bank drawdown zone leads to four main modes of instability and failure. The essence of this instability is the loss of support for the overlying rock mass due to the decreased strength of the rock mass in the drawdown zone, causing the entire overlying rock mass to become unstable. While research has been conducted on the instability modes and stability calculation models for toppling buckling, sliding buckling, and fracturing buckling, this invention primarily proposes a stability calculation method for the fourth type of instability: shear buckling.

[0061] like Figure 2 In the model shown in (a), the rock mass in the drawdown zone refers to the rock mass within the periodic fluctuation range of the reservoir water level, which is the rock mass deterioration zone. The overlying rock mass specifically refers to the rock mass that will not be submerged for a long time. Because this part of the rock mass is not affected by water erosion for a long time, its rock mass strength parameters can be considered to remain unchanged. The rock mass in the range below the drawdown zone is called the submerged rock mass. Because the rock mass in this range is always submerged, its rock mass strength decreases at a very slow rate and can also be considered to remain unchanged. The tectonic fracture zone in the rock mass in the illustrated model exists in the rock mass due to tectonic activity. Only with the existence of this tectonic fracture zone structure can the rock mass of a high and steep bank slope potentially experience shear buckling instability, which corresponds to the shear buckling instability mode.

[0062] S2. The rock mass in the drawdown zone in front of the tectonic fracture zone is generalized into the thrust section rock mass and the buckling section rock mass on the slope surface.

[0063] As the rock mass within the drawdown zone gradually deteriorates and its strength decreases, the overlying rock mass will gradually slide down along the tectonic fracture zone and compress the rock mass within the drawdown zone. During this process, a tension fracture will naturally appear on the rear side of the overlying rock mass. Simultaneously, during the compression of the rock mass within the drawdown zone, the rock mass will exhibit different deformation characteristics in different areas due to the compression. Specifically, the rock mass near the upper side of the tectonic fracture zone will slide along the fracture zone and push against the rock mass in front, while the rock mass in the pushed-out area will undergo buckling deformation under the influence of overlying pressure and rear-side pushing force, and its surface rock mass will also show a certain degree of bulging. These two areas are named the pushing section rock mass and the buckling section rock mass, respectively, based on their different deformation characteristics.

[0064] S3. Perform mechanical and kinematic analysis on the deformation process of the buckling rock mass, and list the energy conservation equations during the deformation process of the buckling rock mass; specifically:

[0065] To facilitate stability analysis, this model directly assumes that the boundary of the buckling section rock mass is completely continuous. Therefore, in the geological structure model of shear buckling instability of dangerous rocks on steep slopes in this invention, the relationship between the pushing section rock mass and the buckling section rock mass can be generalized as follows: Figure 2 As shown in (b), the buckling section of the rock mass controls the stability of the entire steep slope rock mass.

[0066] The buckling section of the rock mass is generalized as a columnar body with height H and side lengths l and b. The original slope surface is assumed to be planar, and the slope angle is denoted as . The deflection at the point of maximum deformation during its buckling deformation is denoted as . .

[0067] Taking point O of the buckling section rock mass as the origin, the direction of the line connecting point O and point A is the X-axis direction.

[0068] The OA segment is the edge of the buckling rock mass in the height direction. Its shape is initially straight, but gradually bends as the rock mass buckles and deforms. l is the projected length of the OA segment in the X-axis direction; b is the length of OO', which is the length of the buckling rock mass in the depth direction.

[0069] Let the overlying pressure on the buckling section of the rock mass be... Lateral thrust is Its buckling deformation exhibits a sinusoidal half-wave shape, so the equation for the bending deformation elastic curve of segment OA can be written as:

[0070] ;

[0071] In the formula, ω is the lateral deflection (bending displacement) of segment OA at position x, reflecting the amplitude of bending deformation; x represents the spatial coordinate along the line OA, used to describe the distribution of deflection along the length direction. A is the amplitude of the sine function. The period number is 1 in the shear buckling instability mode. According to the characteristics of the sine function, the maximum bending deformation in segment OA will only occur in... Position, and its value is:

[0072] ;

[0073] Record the overlying load of the buckling section rock mass The axial compressive deformation under the action is Its expression is:

[0074] ;

[0075] ω' represents the equation of the elastic curve of bending deformation in segment OA. The first derivative with respect to the spatial coordinate x corresponds to the rotation angle (rotation angle, slope) of segment OA at that position.

[0076] According to the law of conservation of energy, the work done by external forces on the buckling rock mass is equal to the sum of the deformation energy and potential energy stored within the structure. The buckling rock mass is subjected to gravity during deformation. Overhead pressure and lateral thrust Based on this, the energy conservation equation for the deformation process of the buckling section rock mass can be derived as follows:

[0077] ;

[0078] In the formula, The work done for the overlying load. The work done for the lateral thrust on the rear side, The work done by its own weight due to gravity. This refers to the elastic potential energy added or stored within the column. The increase in system potential energy, analyzed through the deformation process of shear buckling, is expressed by the following expression for each energy term:

[0079] Overhead load pressure Work done :

[0080] ;

[0081] In the formula, the overlying pressure The exerting force is the entire rock mass above the buckling section. The overburden pressure can be obtained by multiplying the geometric dimensions of the corresponding rock mass by its weight. The value of ;

[0082] Lateral thrust acting :

[0083]

[0084] In the formula, lateral thrust This is the force exerted by the pushing rock mass on the buckling rock mass, as it is numerically equal to the reaction force of the buckling rock mass on the pushing rock mass. It is obtained by analyzing the forces acting on the pushing rock mass, establishing and solving the force equilibrium equations. These equations are related to the rock mass's own weight, the pressure from the overlying rock mass, the support force from the underlying rock mass, the thrust from the buckling rock mass, and the upward sliding resistance along the tectonic fracture zone. It is important to note that the upward sliding resistance along the tectonic fracture zone is related to the shear strength of the tectonic fracture zone, specifically the cohesion *c* and the internal friction angle *φ*, which can be obtained through laboratory rock mechanics tests. Specific calculation and solution methods can be derived from fundamental rock mechanics force equilibrium analysis and solutions for specific examples.

[0085] Self-gravity acting :

[0086] ;

[0087] in,

[0088] ;

[0089] In the formula, Let be the unit weight of the rock mass, and be the product of the rock mass density and gravitational acceleration. Substituting the above equation into equation (7) yields the work done by gravity due to the rock mass's own weight. for:

[0090] ;

[0091] Stored elastic potential energy :

[0092] ;

[0093] In the formula, W m The internal work done by the bending moment is the elastic strain energy stored in the bending deformation; M is the bending moment (internal force bending moment) at the section of the member, which varies with the x position and reflects the bending effect caused by the external load. ω'' is the rotation angle of the beam section, equal to the slope of the deflection curve; ω'' is the equation of the elastic curve of the bending deformation of segment OA. The second derivative with respect to spatial coordinate x is related to curvature and bending moment; The elastic modulus of the rock was obtained through indoor rock mechanics tests. Let be the moment of inertia of the cross section of the buckling rock mass. The cross section of the buckling rock mass is equivalent to a rectangle with the same base and height. Therefore, its moment of inertia is:

[0094] ;

[0095] Increase in system potential energy :

[0096] ;

[0097] is the self-weight component along the deflection direction per unit length; h is the equivalent weight-bearing height per unit length.

[0098] Substituting equations (5) to (12) into equation (4) yields the energy conservation equation for the buckling deformation process of the rock mass in the buckling section, expressed as:

[0099] .

[0100] S4. Based on the energy conservation equation, calculate the critical elastic modulus when the buckling rock mass is in a critical failure state. The ratio of this critical modulus to the current elastic modulus is used as the stability coefficient for shear buckling deformation instability of dangerous rock masses on steep slopes, which constitutes the stability calculation model. The current elastic modulus is obtained from indoor rock mechanics tests. Specifically:

[0101] When the buckling section of the rock mass undergoes buckling failure, its bending deformation will tend to infinity, that is... When the energy conservation equation satisfies the following condition (14), its corresponding solution is the critical parameter when the buckling rock mass is in the critical failure state.

[0102] ;

[0103] Considering the variables mentioned above, As a geometric structure variable, it remains almost unchanged; As a thrust variable, it is mainly affected by gravity and friction. Gravity is calculated by measuring the actual side length of the mountain, and friction is obtained from the actual mountain structure, gravity, and shear strength of the tectonic fracture zone. The rock mass is relatively small, and its variation is also very small; Can be directly from Calculation yielded; As the elastic modulus, it exhibits significant strength degradation during the periodic fluctuations and erosion of the water level in the drawdown zone. Therefore, based on the energy conservation equation, the critical elastic modulus satisfying equation (14) is... Solving for the problem, we get:

[0104] ;

[0105] The ratio of the current elastic modulus to the critical elastic modulus of the buckling section rock mass is used as a stability quantification index for the shear buckling instability mode of dangerous rocks on steep slopes. Its expression is:

[0106] ;

[0107] when At that time, steep slopes will not experience shear buckling instability failure. At that time, steep and dangerous rock slopes are at risk of shear buckling and instability.

[0108] S5. Based on indoor wet-dry cycle rock mechanics tests, the law of decay of different rock mechanical parameters with the increase of wet-dry cycle number is obtained. The relevant mechanical parameters of the rock after different wet-dry cycle number are substituted into the stability calculation model proposed in step S4 to calculate the shear buckling stability coefficient and the changing trend of dangerous rocks on high and steep banks after different wet-dry cycle number, that is, after several hydrological years, so as to evaluate the shear buckling instability process of dangerous rocks on high and steep banks in the reservoir area.

[0109] Example 1

[0110] The dangerous rock embankment of a steep, wading bank in the Three Gorges Reservoir area, exhibiting characteristics of shear buckling failure, is generalized as follows: Figure 3 The geological structure model shown.

[0111] The rock mass in the drawdown zone ahead of the tectonic fracture zone is divided into a thrusting section and a buckling section. It is assumed that the boundary fractures of the buckling section are fully connected, and the buckling section controls the stability of the entire steep slope rock mass.

[0112] The shear buckling deformation process of dangerous rocks on steep slopes can be generalized as follows: the overlying rock mass applies pressure to the pushing section of the rock mass, causing the pushing section of the rock mass to slide and deform along the tectonic fracture zone, and further pushes the buckling section of the rock mass on the slope surface of the drawdown zone, causing the buckling section of the rock mass to undergo elastic bending deformation under the pressure of the overlying rock mass and the pushing pressure from the rear side.

[0113] The buckling section of the rock mass is generalized as a primitive slope surface in a plane, with a height... slope angle The side lengths are respectively and The columnar rock mass, with its density based on the average density of limestone. Calculation. For example... Figure 3 As shown, the buckling deformation of the OA segment of the slope surface in the drawdown zone exhibits a sinusoidal half-wave shape, and its bending deformation elastic curve equation is:

[0114] ;

[0115] In the formula, A is the amplitude of the sine function. The period number is the number of cycles. In the shear buckling instability mode, the period number can be directly taken as 1. Based on the characteristics of the sine function, the maximum bending deformation of segment OA is... It will only appear in Position, and its value is:

[0116] ;

[0117] Record the overlying load of the buckling section rock mass The axial compressive deformation under the action is Its expression is:

[0118] ;

[0119] Furthermore, considering that the elastic modulus of the rock mass will decrease year by year with the erosion of the periodic rise and fall of reservoir water, and the decrease is relatively large, therefore, when analyzing the shear buckling stability of the steep slope in the embodiments of the present invention, we first directly use... This is used to represent the elastic modulus of the rock mass.

[0120] Stress analysis of the rock mass in the buckling section of the slope in the drawdown zone revealed that the rock mass in the buckling section is only subjected to gravity. Overhead pressure and rear thrust .

[0121] Among them, gravity It can be calculated by multiplying volume, density, and gravitational acceleration. In this embodiment of the invention, gravitational acceleration is taken as... Gravity can be calculated. The value is:

[0122] ;

[0123] Overhead pressure Numerically equal to the weight of the rock mass in the AA'D'D region above section AA'. The AA'D'D rock mass has an average width of 6.3m, an average height of 51.4m, and a density of [missing value]. Calculations show that the overlying pressure... The value can be:

[0124] ;

[0125] Rear thrust The calculations are relatively complex, but since they are not the focus of this invention, they will only be briefly introduced here. Figure 3 Yes, rear thrust Provided by the CBA rock mass in the thrust zone. A stress analysis was performed on the CBA rock mass in the thrust zone, considering the reaction force generated by the buckling segment. The CBA rock mass is also subject to overlying pressure. Support of CB segment Self-gravity And the anti-slip force acting upwards along the CB segment. The overburden pressure was calculated. Self-gravity Length of the tectonic fracture zone on the CB side of the CBA rock mass. ,inclination Considering that the shear strength of the CB section fracture zone shows a relatively significant downward trend over the years due to rock mass deterioration, it is advisable to first use... and The cohesion and internal friction angle of the CB segment are used to characterize these properties, respectively. According to Newton's first and second laws, the rear thrust can be obtained. The formula for calculation is:

[0126] ;

[0127] In the formula, only and Let be the variable. Based on the force relationships, the above equation applies only when ... Valid at that time. This indicates that there is no interaction force between the thrusting section and the shear buckling section of the rock mass in the CBA area. The value should be 0.

[0128] In determining gravity Overhead pressure and rear thrust Based on the magnitude or calculation formula, the work done by the buckling rock mass during deformation is further calculated. Through analysis of the shear buckling deformation process, the overlying load... Work done for:

[0129] ;

[0130] Lateral thrust work :

[0131] ;

[0132] Work done by its own weight :

[0133] ;

[0134] in,

[0135] ;

[0136] In the formula, The unit weight of the rock mass. Substituting the above formula into equation (9), we can obtain the work done by gravity due to its own weight. for:

[0137] ;

[0138] According to the law of conservation of energy, the work done by external forces on the buckling section of the rock mass in the drawdown zone is equal to the sum of the deformation energy and potential energy stored within the structure. Analysis shows that the stored elastic potential energy... :

[0139] ;

[0140] Increase in system potential energy :

[0141] ;

[0142] Therefore, the energy conservation equation for the buckling rock mass during the deformation process can be derived:

[0143] ;

[0144] It can also be expressed as:

[0145] ;

[0146] When the rock mass in the buckling section of the drawdown zone undergoes buckling failure, its bending deformation will tend to infinity, that is... That is, when the energy conservation equation satisfies the following condition (16), its corresponding solution is the critical parameter when the buckling rock mass is in a critical failure state.

[0147] ;

[0148] Considering the variables mentioned above, The geometric structure variables remain almost unchanged; As a thrust variable, it is mainly affected by gravity and friction. The rock mass is relatively small, and its variation is also very small; Can be directly from Calculation yielded; As the elastic modulus, it exhibits significant strength degradation during the periodic fluctuations and erosion of the water level in the drawdown zone. Therefore, based on the aforementioned energy conservation equation, this section defines the critical elastic modulus that satisfies equation (14). Solving for the problem, we get:

[0149] ;

[0150] Based on this, the ratio of the elastic modulus of the buckling section rock mass to the critical elastic modulus is used as a stability quantification index for the shear buckling instability mode of dangerous rocks on steep slopes. Its specific expression is as follows:

[0151] ;

[0152] The above formula is the stability coefficient calculation model for shear buckling instability in the embodiment of the present invention.

[0153] Furthermore, when the rock mass in the drawdown zone is in a state of submersion saturation in the case study, it is best to consider the influence of both the rock mass strength parameters and pore water pressure under saturation conditions. Under saturation conditions, the elastic modulus of the buckling section rock mass... The saturation value can be directly used for calculation; the back thrust is calculated. At that time, the corresponding strength parameters of the submerged area are also calculated using saturated values. Regarding pore water pressure, a conservative approach is adopted, assuming that pore water pressure participates in the entire buckling process of the rock column; therefore, the work done by pore water pressure also needs to be calculated. Since the direction of pore water pressure is perpendicular to the action surface, it can be directly used as thrust. One component of the force is calculated by referring to equation (8).

[0154] Based on indoor wet-dry cycle rock mechanics tests, the law of decay of different rock mechanics parameters with increasing number of wet-dry cycles was obtained.

[0155] In this example, the elastic modulus of the buckling segment is... Cohesion of the CB section fracture zone and internal friction angle Under wet-dry cycling, there will be a significant decrease in strength. Consider using... , and To describe The elastic modulus and shear strength in the dry state after one wet-dry cycle, using , and To characterize The saturation strength parameters corresponding to the saturated state after 30 indoor wet-dry cycle rock mechanics tests. The changes of the above six parameters with increasing number of wet-dry cycles were obtained, as follows: Figure 4 As shown, this also represents the changes in six intensity indicators over 30 hydrological years.

[0156] By substituting each set of parameters into equation (16) for calculation, the corresponding shear buckling stability coefficient under dry or saturated conditions can be obtained. and Furthermore, it is assumed that the water level fluctuates sinusoidally between 175m and 145m. This fluctuation extends to arbitrary elevations. At this point, the elastic modulus, cohesion of the fractured zone, and internal friction angle of the rock mass are equivalent to the arithmetic mean of their dry and saturated state values, respectively. Therefore, the water level at any elevation can be calculated. Equivalent shear buckling stability coefficient at time Calculations show that over the next 30 hydrological years,

[0157] , and The changes are as follows: Figure 5 As shown.

[0158] At the moment before experiencing a wet-dry cycle, the shear buckling stability coefficients of the steep slope unstable rock in this invention example under dry and saturated conditions are as follows:

[0159]

[0160] With the increase of hydrological years, the shear buckling stability coefficient of steep bank slopes shows a decreasing trend. At the saturation point of the 12th hydrological year, the shear buckling stability coefficient of steep bank slopes will decrease to less than 1.0, indicating that the steep bank slopes will undergo shear buckling instability and failure at that time.

Claims

1. A method for evaluating the shear buckling instability of dangerous rock on a high and steep bank slope of a reservoir area, characterized in that: The method comprises the following steps: S1, according to the shear buckling instability mode of the high and steep slope of the reservoir, the geological structure of the dangerous rock of the high and steep slope in the reservoir area is generalized into a shear buckling geological model with overlying rock mass, drawdown area rock mass and submerged area rock mass, and a structural fracture zone exists on the shear buckling geological model; S2, because the rock mass near the upper side of the structural fracture zone will slide along the structural fracture zone and push the front rock mass, the drawdown area rock mass in front of the structural fracture zone is generalized into a pushing section rock mass and a buckling section rock mass on the slope surface, and the buckling section rock mass is located in front of the pushing section rock mass; S3, the deformation process of the buckling section rock mass is analyzed in mechanics and kinematics, and an energy conservation equation in the deformation process of the buckling section rock mass is listed; S4, according to the energy conservation equation, the critical elastic modulus of the buckling section rock mass in the critical failure state is calculated, and the ratio of the critical elastic modulus to the current elastic modulus is taken as the stability coefficient of the shear buckling deformation instability of the dangerous rock of the high and steep slope, that is, a stability calculation model, wherein the current elastic modulus is obtained by indoor rock mechanics test; S5, based on the indoor dry-wet cycle rock mechanics test, the attenuation law of different rock mechanics parameters with the increase of dry-wet cycle times is obtained, the related mechanics parameters of the rock after different dry-wet cycle times are substituted into the stability calculation model in step S4, and the shear buckling stability coefficient of the dangerous rock of the high and steep slope after different dry-wet cycle times, that is, after a certain number of hydrological years, and the change trend are calculated, so that the evaluation of the shear buckling instability process of the dangerous rock of the high and steep slope in the reservoir area is realized; In step S3, it is assumed that the boundary crack of the buckling section rock mass is completely penetrated, the buckling section rock mass controls the stability state of the whole high and steep slope rock mass, and the shear buckling deformation process of the dangerous rock of the high and steep slope is generalized as: The overlying rock mass exerts pressure on the pushing section rock mass, causing the pushing section rock mass to slide and deform along the structural fracture zone, and further pushing the buckling section rock mass on the drawdown area slope surface, causing the buckling section rock mass to elastically bend and deform under the pressure of the overlying rock mass and the pressure of the pushing section rock mass behind; The buckling segment rock mass is generalized into a high H columnar body with side length l and b, the original slope surface is assumed to be a plane, and the slope angle is denoted as The deflection of the maximum deformation in the buckling deformation process of the rock mass is denoted as ; Taking the O point of the buckling section rock mass as the origin, and the connecting line direction of the O point and the A point as the X axis direction; OA section is the edge of the buckling section rock mass in the height direction, which is initially a straight line, gradually bends with the buckling deformation of the rock mass, and l is the projection length of OA section in the X axis direction; b is the length of OO', that is, the length of the buckling section rock mass in the longitudinal direction; The overlying pressure on the flexural segment rock mass is , the lateral thrust is , and the flexural deformation of the flexural segment rock mass is in the shape of a sine half wave. Thus, the elastic curve equation of the bending deformation of the OA segment is ； In the formula, x represents the spatial coordinate in the X-axis direction, ω is the transverse deflection of the OA segment at position x, reflecting the bending deformation amplitude, A is the amplitude of the sine function, and is the number of periods, and in the shear buckling instability mode, the number of periods is 1. According to the characteristics of the sine function, the maximum bending deformation of the OA segment only occurs at the position , and the value is: ； The axial compression deformation of the flexural segment rock mass under the overlying load is The expression is: ； ω' represents the bending deformation elastic curve equation of the OA segment the first derivative of the spatial coordinate x, corresponding to the turning angle of the OA segment at this position; According to the law of conservation of energy, the work done by external forces on the buckling segment rock mass is equal to the sum of the deformation energy and potential energy stored inside the structure. The buckling segment rock mass is subjected to the action of gravity , overburden pressure and lateral thrust during deformation, and thus the energy conservation equation during deformation of the buckling segment rock mass can be listed as: ； wherein the work done by the overburden load, the work done by the lateral thrust on the back side, the work done by the dead weight gravity, the elastic potential energy added or stored in the column, the increase in the system potential energy, the analysis of the deformation process by shear buckling, the expression of each energy is as follows: Overburden pressure Work done : ； In the formula, the overburden pressure The force applying body is the whole rock mass above the buckling segment rock mass. According to the product of the corresponding rock mass geometric size and the rock mass weight, the overburden pressure value can be obtained. lateral thrust work : ； wherein the lateral thrust force is the action force of the push segment rock mass on the buckling segment rock mass, and its value is equal to the reaction force of the buckling segment rock mass on the push segment rock mass, which is obtained by analyzing the stress of the push segment rock mass, listing the stress balance equation and solving it. Self-weight gravity Work : ； Wherein, ； wherein is the specific weight of the rock mass, which is the product of the density of the rock mass and the acceleration of gravity, and substituting the above equation into equation (7) gives the work done by the self-weight gravity is: ； Stored elastic potential energy : ； where W m is the internal work done by the bending moment, i.e. the elastic strain energy stored by the bending deformation; M is the bending moment at the cross-section of the member, which varies with the x position and reflects the bending effect caused by external loads; is the rotation angle of the beam cross-section, equal to the slope of the deflection curve; ω’’ is the second derivative of the deflection curve with respect to the spatial coordinate x, related to the curvature and bending moment; is the second derivative of the deflection curve with respect to the spatial coordinate x, related to the curvature and bending moment; is the elastic modulus of the rock, measured by indoor rock mechanics test, is the moment of inertia of the buckling segment rock mass cross-section, the cross-section of the buckling segment rock mass is equivalent to a rectangle with the same base and height, so its moment of inertia is: ； System potential energy increase amount : ； is the self-weight component in the deflection direction per unit length; h is the corresponding equivalent height of the self-weight per unit length; Substituting formula (5) to formula (12) into formula (4) to obtain the energy conservation equation of the buckling section rock mass in the buckling deformation process, and the expression is: 。 2. The method according to claim 1, wherein the method is characterized in that: When the buckling segment rock mass occurs buckling failure, its bending deformation will tend to infinity, that is When the energy conservation equation satisfies the following formula (14) condition, the corresponding solution is the critical parameters when the buckling segment rock mass is in the critical failure state; ； Based on the energy conservation equation, the critical elastic modulus satisfying equation (14) is solved to be: ； The ratio of the current elastic modulus of the buckling section rock mass to the critical elastic modulus is taken as the stability quantitative index of the shear buckling instability mode of the dangerous rock of the high and steep slope, and the expression is: ； When the high and steep slope does not occur shear buckling instability failure, when the high and steep slope dangerous rock exists the risk of shear buckling instability.

3. The method according to claim 1, wherein the method is characterized by: The stress of the pushing and squeezing rock mass includes its own gravity, the pressure of the overlying rock mass, the support force of the underlying rock mass, the pushing force of the buckling rock mass and the anti-sliding force along the tectonic fracture zone, wherein the anti-sliding force along the tectonic fracture zone is related to the shear strength of the tectonic fracture zone, i.e., the cohesion c and the internal friction angle φ of the tectonic fracture zone, which can be obtained by indoor rock mechanics test.

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