A method for predicting the stability of high mountains under strong seismic forces

Abstract

This application discloses a method for predicting the strong seismic stability of high mountains, relating to the field of rock mass engineering geological dynamics. The method includes: constructing a two-dimensional model of the target mountain; determining the sliding surface of the two-dimensional model; dividing the two-dimensional model into multiple sliding body elements based on the sliding surface; constructing a permissible sliding velocity vector field for the two-dimensional model; calculating the external force power and internal energy dissipation of the two-dimensional model based on the permissible sliding velocity vector field and the internal structural surface strength parameters of the two-dimensional model after freeze-thaw cycle degradation; and predicting the strong seismic stability of the target mountain based on the external force power and the internal energy dissipation. This method solves the problem that existing limit analysis upper bound methods generally do not fully consider the synergistic effect of freeze-thaw cycles and fissure water seepage, leading to difficulties in accurately predicting the strong seismic stability of high mountains.

Description

Technical Field

[0001] This application relates to the field of rock mass engineering geology and dynamics technology, and in particular to a method for predicting the stability of high mountains under strong seismic forces. Background Technology

[0002] To ensure the safe construction and long-term operation of major projects, the challenge of evaluating the dynamic stability of high mountains under the combined effects of internal and external forces such as earthquakes, freeze-thaw cycles, and fissure water seepage urgently needs to be addressed.

[0003] Currently, the dynamic stability analysis of high mountains under strong earthquakes mainly employs methods such as the quasi-static method, the Newmark sliding block method, and the dynamic intensity reduction method. Among these, the upper limit method of limit analysis transforms the solution of the safety factor into a mathematical optimization problem by constructing a permissible velocity field, and has the advantages of clear physical concepts and rigorous theory. The amplification effect of seismic waves propagating within high mountains significantly alters their dynamic response distribution, having a crucial impact on dynamic stability. However, existing dynamic stability analyses generally neglect the amplification effect of the terrain on ground motion and fail to fully consider the synergistic effect of freeze-thaw cycles and fissure water seepage, making it difficult to accurately predict the dynamic stability of high mountains. Summary of the Invention

[0004] The purpose of this application is to provide a method for predicting the dynamic stability of high mountains under strong earthquakes. Based on the upper limit method of limit analysis, by considering the synergistic effect of freeze-thaw cycles and fissure water seepage, the method can solve for the external power and internal energy dissipation that more accurately reflect the actual state of the target mountain. The stability coefficient is calculated iteratively by the strength parameter reduction method that satisfies the limit equilibrium state. This solves the problem that the synergistic effect of freeze-thaw cycles and fissure water seepage is generally not fully considered, which makes it difficult to accurately predict the dynamic stability of mountains under strong earthquakes.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] Firstly, this application provides a method for predicting the stability of high mountains under strong seismic forces, including:

[0007] Construct a two-dimensional model of the target mountain, determine the sliding surface of the two-dimensional model, and divide the two-dimensional model into multiple sliding body units based on the sliding surface;

[0008] Construct the sliding velocity permit vector field of the two-dimensional model, the sliding velocity permit vector field including the sliding velocity of each sliding body unit and the relative sliding velocity between any two adjacent sliding body units;

[0009] The external force power and internal energy dissipation of the two-dimensional model are calculated based on the sliding velocity permissible vector field and the internal structural surface strength parameters of the two-dimensional model after deterioration by freeze-thaw cycles. The external force power includes the power of seismic force, fissure water pressure and self-weight. The internal structural surface strength parameters include the cohesion and internal friction angle of the bottom sliding surface of each sliding body element, and the cohesion and internal friction angle of the lateral structural surface between any two adjacent sliding body elements.

[0010] The strong seismic stability of the target mountain is predicted based on the external force power and the internal energy dissipation.

[0011] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for predicting the stability of high mountains under strong seismic forces as described above.

[0012] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for predicting the stability of high mountains under strong seismic forces as described above.

[0013] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method for predicting the stability of high mountains under strong seismic forces as described above.

[0014] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0015] This application provides a method for predicting the stability of high mountains under strong seismic forces. First, a two-dimensional model of the target mountain is constructed and divided into multiple sliding body elements. Then, the sliding velocity of each sliding body element and the relative sliding velocity between any two adjacent sliding body elements are calculated to obtain the permissible sliding velocity vector field. The sliding velocity of a sliding body element refers to its relative velocity to the stable mountain below it, constrained by the rock mass structure. After obtaining the permissible sliding velocity vector field, the external force power of the two-dimensional model, consisting of seismic forces, fissure water pressure, and gravity power, is calculated based on the permissible sliding velocity vector field and the internal structural surface strength parameters of the two-dimensional model after freeze-thaw cycles. This paper proposes a method to predict the dynamic stability of a target mountain under strong earthquakes by analyzing the internal energy dissipation of a two-dimensional model and the limit equilibrium state of external force power and internal energy dissipation. Specifically, the calculation of external force power and internal energy dissipation in the two-dimensional model considers the degradation effect caused by freeze-thaw cycles, thus making the calculated results more consistent with the actual state. Furthermore, the calculation of external force power comprehensively considers the power of seismic forces, fissure water pressure, and self-weight, further improving the consistency between the calculated results and the actual state. This method solves the problem in existing limit analysis upper bound methods that generally do not fully consider the synergistic effect of freeze-thaw cycles and fissure water seepage, making it difficult to accurately predict the dynamic stability of mountains under strong earthquakes. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a method for predicting the stability of high mountains under strong seismic forces, provided in an embodiment of this application;

[0018] Figure 2 This is a schematic diagram of seismic forces and self-weight in one embodiment of this application;

[0019] Figure 3 This is a schematic diagram of cohesion and internal friction angle in one embodiment of this application;

[0020] Figure 4 This is a schematic diagram illustrating the effect of fissure water pressure in one embodiment of this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] In one exemplary embodiment, such as Figure 1 As shown, a method for predicting the stability of high mountains under strong seismic forces is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is described using a terminal device as an example, including steps 110 to 140. Wherein:

[0024] Step 110: Construct a two-dimensional model of the target mountain, determine the sliding surface of the two-dimensional model, and divide the two-dimensional model into multiple sliding body units based on the sliding surface.

[0025] Step 120: Construct the sliding velocity permitting vector field of the two-dimensional model. The sliding velocity permitting vector field includes the sliding velocity of each sliding body element and the relative sliding velocity between any two adjacent sliding body elements. The lateral structural surface is the contact surface between two adjacent sliding body elements.

[0026] Step 130: Calculate the external force power and internal energy dissipation of the two-dimensional model based on the sliding velocity permissible vector field and the internal structural surface strength parameters of the two-dimensional model after deterioration by freeze-thaw cycles. The external force power includes seismic force, fissure water pressure and self-gravity power. The internal strength parameters include the cohesion and internal friction angle of the bottom sliding surface of each sliding body element, and the cohesion and internal friction angle of the lateral structural surface between any two sliding body elements.

[0027] Step 140: Predict the strong seismic stability of the target mountain based on the external force power and internal energy dissipation.

[0028] In steps 110 to 140 above: First, a two-dimensional model of the target mountain is constructed and divided into multiple sliding body elements; then, the sliding velocity of each sliding body element and the relative sliding velocity between any two adjacent sliding body elements are calculated to obtain the sliding velocity permissible vector field; where the sliding velocity of a sliding body element refers to the relative velocity of the sliding body element relative to the stable mountain below it under the constraint of the rock mass structure. Therefore, the bottom surface of the sliding body element is called the bottom sliding surface. The key point of the above steps is that after obtaining the sliding velocity permissible vector field, the external force power of the two-dimensional model composed of seismic force, fissure water pressure and self-gravity power and the internal energy dissipation of the two-dimensional model are calculated based on the sliding velocity permissible vector field and the internal strength parameters of the two-dimensional model after deterioration by freeze-thaw cycles, and the strong seismic stability of the target mountain is predicted based on the external force power and internal energy dissipation. In calculating the external force power and internal energy dissipation of the two-dimensional model, the degradation effect caused by freeze-thaw cycles was considered, which made the calculated results of external force power and internal energy dissipation more consistent with the actual state. Furthermore, the power of external force power was comprehensively considered by seismic force, fissure water pressure and self-weight, which further made the calculated results of external force power more consistent with the actual state.

[0029] In summary, through steps 110 to 140 above, the external force power and internal energy dissipation that better reflect the actual state of the target mountain can be calculated. The stability is analyzed by iterative calculation using the strength parameter reduction method that satisfies the limit equilibrium state. This solves the problem that it is difficult to accurately predict the dynamic stability of mountains under strong earthquakes because the synergistic effect of freeze-thaw cycles and fissure water seepage is generally not fully considered.

[0030] Specifically, the upper bound method of limit analysis can be used to construct the sliding velocity allowable vector field of the two-dimensional model. The following example illustrates steps 110 and 120.

[0031] First, key engineering geological survey data of the target mountain are collected, including topographic contour lines, geometric coordinates of the mountain surface, borehole information, the occurrence and location of rock mass structural planes, and rock mass quality grading indicators. During the mountain planar generalization, the summit, foot, and slope lines are defined based on the actual contour to ensure that the two-dimensional model reflects the main topographic trends of the target mountain.

[0032] Then, combining the structural surface data, key weak surfaces (such as fault zones or major fracture zones) are identified and designated as potential sliding surfaces. Based on the non-linear geometric characteristics of the sliding surface, inflection points or turning points are used as discrete control points. The two-dimensional model above the sliding surface is discretized into different sliding body elements according to the sliding surface and lateral structural surfaces. The sliding velocity of a sliding body element is the sliding velocity of the sliding body element relative to the stable mountain below (the top surface of the stable mountain and the bottom sliding surface of the sliding body element are in contact).

[0033] Based on discrete sliding body elements, a velocity field with maneuverability is constructed using the upper bound method of limit analysis. i-1 , i , ,like Figure 3 As shown. The velocity polygons of adjacent sliding body elements must be vector-closed to ensure that the movement of adjacent sliding body elements does not cause them to overlap or separate, which can be expressed by the formula:

[0034]

[0035] In the formula, Indicates the first i The and the first i -1 relative sliding velocity between sliding body units i Indicates the first i The sliding speed of each sliding body unit. i-1 Indicates the first i -1 sliding speed of a sliding body unit.

[0036] The associated flow rule defines the angle between the sliding velocity of a sliding body element and its bottom sliding surface as the internal friction angle of its bottom sliding surface, and defines the angle between the relative sliding velocity between adjacent sliding body elements and the lateral structural surface as the internal friction angle of the lateral structural surface. Based on the geometric relationship of the closed triangle formed by the velocity vectors of adjacent sliding body elements, it can be... After scalarization, it is represented as:

[0037]

[0038] In short:

[0039]

[0040] In the formula:

[0041]

[0042] In the formula: , and They are respectively , , and x The angle between the axes is defined as the angle from the axis. x Starting from the negative direction of the axis, counterclockwise rotation is positive, and 0 ≤ ≤2 π In calculation At that time, i When =1, let m 1=1; in calculation hour,i ≥2. and The calculation formula is:

[0043]

[0044] In the formula, , The first i The and the first i -1 The angle between the bottom sliding surface of a sliding body element and the horizontal direction. If the bottom sliding surface of the sliding body element is parallel to the slope direction, then Take a positive value, otherwise take a negative value.

[0045] Reference Figure 3 , No. i The first sliding body unit is the upper sliding body unit, the... i -1 is the lower sliding body element, for the -1 sliding body element i The sliding body unit and the first i -1 Angle between the lateral structural planes of the sliding body units and the horizontal direction It has different calculation methods in different situations.

[0046] when When this occurs, it indicates that the lower sliding body element moves upward relative to the upper sliding body element. In this case, the lower sliding body element acts as a resisting element against the upper sliding body element, and this situation accounts for the majority of landslide analyses. The calculation formula is:

[0047]

[0048] In the formula, For the first i -1 sliding body unit and the first i The inclination angle of the lateral structural surfaces between the sliding body units, so as to... y Negative direction of the axis clockwise x Rotation in the negative direction of the axis is positive. For the first i -1 sliding unit and the first i The internal friction angle of the lateral structural surfaces between sliding body units.

[0049] when When this occurs, it indicates that the lower sliding body element moves downward relative to the upper sliding body element. In this case, the lower sliding body element is at risk of sliding down relative to the upper sliding body element. This situation is rare in landslide analysis. The calculation formula is:

[0050]

[0051] The above describes the element division process of the two-dimensional model and the construction process of the sliding velocity permissible vector field. Through this process, the sliding velocity of each sliding body element and the relative sliding velocity between any two adjacent sliding body elements can be obtained. In the formula, the... i The sliding speed of each sliding body unit is i , No. i The and the first i The relative sliding speed between -1 sliding body units is .

[0052] Reference Figure 2 and Figure 3 Specifically, the external force power in the two-dimensional model for:

[0053]

[0054]

[0055]

[0056]

[0057] In the formula, , and These represent the power of seismic force, fissure water pressure, and self-weight, respectively. n This represents the total number of sliding body elements. Indicates the horizontal quasi-static coefficient. Indicates the vertical quasi-static coefficient. Indicates the first i The weight of each sliding body unit i Indicates the first i The sliding speed of each sliding body unit. Indicates the first i The angle between the bottom sliding surface of each sliding unit and the horizontal plane. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit after being deteriorated by freeze-thaw cycles; Indicates the action in the i The fissure water pressure on the bottom sliding surface of each sliding body unit. Indicates the first i The and the first i -1 relative sliding velocity between sliding body units Indicates the action in the i The and the first i- The fissure water pressure at the lateral structural surface between a single sliding body unit. Indicates the first i The and the firsti -1 The internal friction angle of the lateral structural surface between sliding body units after being deteriorated by freeze-thaw cycles.

[0058] In the external force power model, the influence of each external force on the rock mass properties needs to be considered separately. The quasi-static method is used to apply horizontal and vertical forces to the sliding body element to take into account the influence of seismic action.

[0059] The formula for calculating the horizontal pseudo-static coefficient is:

[0060]

[0061] The formula for calculating the vertical pseudo-static coefficient is:

[0062]

[0063] In the formula, This represents the reduction factor for seismic action effects, typically taken as 0.25. This represents the peak ground acceleration (PGA) of the horizontal ground motion corresponding to the earthquake intensity. Indicates the first i The seismic acceleration-elevation dynamic amplification factor of the sliding body element is the first... i The ratio of the peak acceleration at the center of gravity of an individual sliding body element to the peak acceleration at the center of gravity of the sliding body element at the toe of the slope. Indicates the coefficient or multiple.

[0064] Because the dynamic response modes of various high mountains differ significantly under different seismic conditions, the dynamic amplification coefficients of seismic acceleration-elevation vary among different sliding blocks. This embodiment fully considers this factor, calculating the dynamic amplification coefficients of seismic acceleration-elevation for different sliding body elements, making the calculation results more consistent with reality. Therefore, it overcomes the deficiency in existing dynamic stability analyses that generally neglect the amplification effect of high mountain terrain on seismic motion.

[0065] Fissure water pressure is an important factor that must be considered in the stability analysis of high mountains under strong seismic forces, so it is included in the calculation process in this embodiment.

[0066] No. i Water pressure on the bottom sliding surface of each sliding unit The calculation formula is:

[0067]

[0068] The effect of the i The and the first i Water pressure on the lateral structural surface between -1 sliding body units The calculation formula is:

[0069]

[0070] In the formula, Indicates the specific gravity of water. Indicates the first i -1 sliding body unit and the first i Water depth in the cracks of the lateral structural surfaces between sliding body units Indicates the first i The sliding body unit and the first i +1 Crack water depth at the lateral structural surface between sliding body units Indicates the first i The length of the bottom sliding surface of each sliding body unit. Indicates the first i -1 sliding body unit and the first i The length of the portion of the lateral structural surface below the water level between each sliding body unit.

[0071] The resistance (internal forces) on the sliding surface (the bottom sliding surface of the sliding body element) and the lateral structural surfaces include shear force and normal force (see reference). Figure 3 , For the first i The normal force on the bottom sliding surface of each sliding body unit. For the first i -1 sliding body unit and the first i Normal forces on the lateral structural surfaces between sliding body units For the first i The sliding body unit and the first i +1 normal force on the lateral structural surface between sliding body units), where the shear force consists of two parts, one of which is cohesion. c One part is known; the other part is friction, whose value is... It and normal force N Together, they form an angle with the direction of the normal to the sliding surface. The combined force P —Combined frictional force. The magnitude of this combined frictional force is usually unknown, but its direction is known, i.e., the angle between it and the normal direction of the sliding surface is θ. Since the sliding velocity of the sliding body element is... V The angle between the sliding surface and the sliding surface is This combination of friction forces P With sliding speed V Orthogonal, therefore P sliding speed V The power generated is 0. Therefore, the internal energy dissipation generated by the internal forces is calculated. When internal energy is dissipated, only the cohesion on the sliding surface and lateral structural surfaces generates the internal energy dissipation rate in the permissible vector field of the sliding velocity. The formula for this rate is:

[0072]

[0073]

[0074]

[0075] In the formula, This represents the internal energy dissipation caused by the cohesion of the bottom sliding surface of the sliding body element in the sliding velocity permissible vector field. This represents the internal energy dissipation caused by the cohesion of the lateral structural surfaces between two adjacent sliding body elements in the sliding velocity permissible vector field. n This represents the total number of sliding body elements. i Indicates the first i The sliding speed of each sliding body unit. Indicates the first i The cohesion of the bottom sliding surface of each sliding body unit after being deteriorated by freeze-thaw cycles. Indicates the first i The length of the bottom sliding surface of each sliding body unit. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit after being degraded by freeze-thaw cycles. Indicates the first i The and the first i -1 relative sliding velocity between sliding body units Indicates the first i The and the first i -1 Cohesion of the lateral structural surfaces between sliding body units after deterioration due to freeze-thaw cycles Indicates the first i The and the first i -1 lateral structural surface length of a sliding body unit Indicates the first i The and the first i -1 The internal friction angle of the lateral structural surface between sliding body units after being deteriorated by freeze-thaw cycles.

[0076] As explained above, the external power and internal energy dissipation of the two-dimensional model can be calculated using the cohesion and internal friction angle of the bottom sliding surface of each sliding body element, the cohesion and internal friction angle of the lateral structural surfaces between any two adjacent sliding body elements, and the permissible vector field of sliding velocity. It should be noted that this embodiment considers the degradation effect of freeze-thaw cycles on the strength parameters of the internal structural surfaces. Therefore, the calculation uses the internal friction angle of the bottom sliding surface of the sliding body element after freeze-thaw cycle degradation, the internal friction angle of the lateral structural surfaces between sliding body elements after freeze-thaw cycle degradation, the cohesion of the bottom sliding surface of the sliding body element after freeze-thaw cycle degradation, and the cohesion of the lateral structural surfaces between sliding body elements after freeze-thaw cycle degradation to calculate the external power and internal energy dissipation of the two-dimensional model.

[0077] Specifically, and as well as and They are respectively:

[0078]

[0079] In the formula, Indicates the first i The cohesion of the bottom sliding surface of each sliding body unit before degradation due to freeze-thaw cycles. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit before degradation by freeze-thaw cycles. Indicates the first i The and the first i -1 The cohesion of the lateral structural surfaces between sliding body units before degradation due to freeze-thaw cycles. Indicates the first i The and the first i -1 The internal friction angle of the lateral structural surfaces between sliding body units before degradation due to freeze-thaw cycles. This represents the degradation coefficient, which is determined experimentally.

[0080] The degradation coefficient is the total degree of degradation after different saturations and freeze-thaw cycles under each group of test conditions, and its expression is as follows:

[0081]

[0082] In the formula, and These are the saturation influence coefficient and the freeze-thaw cycle number influence coefficient, respectively, and their expressions are as follows:

[0083]

[0084]

[0085] In the formula, and n These represent different saturation levels and the number of freeze-thaw cycles, respectively. and These represent the convergence values ​​of the saturation influence coefficient and the freeze-thaw cycle number influence coefficient, respectively. a and b These are undetermined coefficients, obtained through fitting specific experimental data.

[0086] The above is the complete calculation process for external power and internal energy dissipation. Through this process, specific external power and internal energy dissipation can be quantitatively calculated, and calculation models for external power and internal energy dissipation can also be constructed.

[0087] When the external force power and internal energy dissipation of the target mountain are equal, it indicates that the target mountain is in a state of limit equilibrium. This can be used to determine the strong seismic stability of the target mountain.

[0088] In this embodiment, a reduction factor is introduced. K The strength parameters of the internal structural surfaces of the two-dimensional model after being deteriorated by freeze-thaw cycles are reduced. Based on the reduced internal structural surface strength parameters, the external force power and internal energy dissipation of the target mountain are calculated, and the reduction coefficient value that makes the external force power and internal energy dissipation of the target mountain equal is determined, i.e., the stability coefficient. Finally, the strong seismic stability of the target mountain can be judged based on this value.

[0089] Specifically, the strong seismic stability of the target mountain is predicted based on the external force power and internal energy dissipation. This includes: introducing a reduction factor to reduce the strength parameters of the internal structural surface of the two-dimensional model after it has been deteriorated by freeze-thaw cycles in order to update the external force power and internal energy dissipation; determining the reduction factor that makes the external force power and internal energy dissipation equal as the stability factor; and predicting the strong seismic stability of the target mountain based on the stability factor.

[0090] In the formula, the reduction formula is:

[0091]

[0092] In the formula, Indicates the first i The bottom sliding surface of each sliding body unit has deteriorated and reduced cohesion due to freeze-thaw cycles. Indicates the first i The and the first i -1 Cohesion of the lateral structural surfaces between sliding body units after deterioration and reduction due to freeze-thaw cycles. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit is degraded and reduced by freeze-thaw cycles. Indicates the first i The and the first i -1 The internal friction angle of the lateral structural surface between sliding body units after being degraded and reduced by freeze-thaw cycles.

[0093] The calculation process is as follows: Substitute the internal structural surface strength parameters of the two-dimensional model after it has been deteriorated by freeze-thaw cycles into the reduction formula to obtain the internal structural surface strength parameters of the two-dimensional model after it has been deteriorated and reduced by freeze-thaw cycles. Then, use the internal structural surface strength parameters after it has been deteriorated and reduced by freeze-thaw cycles to calculate the external force power and internal energy dissipation of the two-dimensional model, establish the limit equilibrium equation (virtual power equation) for external force power and internal energy dissipation, and inversely calculate the specific value of the corresponding reduction coefficient. This specific value is the stability coefficient.

[0094] Since the sliding velocity of each sliding body element and the relative sliding velocity of the lateral structural surfaces between sliding body elements can both be expressed as linear functions of the sliding velocity of the first sliding body element, all velocity terms can be eliminated from the virtual power equation. After simplification, the expression for the reduction coefficient in the limit analysis method is obtained as follows:

[0095]

[0096]

[0097]

[0098]

[0099] Reduction factor K The implicit equations require an iterative algorithm to solve. During the calculation, an initial reduction factor is first assumed. K Apply iterative calculations until the reduction factor is reached. K The final reduction factor is calculated until the required accuracy is achieved. K The value is the stability coefficient.

[0100] The stability coefficient calculated using the above method can accurately reflect the stability of the target mountain. In other embodiments, a simpler method can also be used to estimate the stability coefficient. In this case, predicting the strong seismic stability of the target mountain based on external force power and internal energy dissipation specifically includes: using the ratio of internal energy dissipation to external force power when they are equal as the stability coefficient; and predicting the strong seismic stability of the target mountain based on the stability coefficient.

[0101] Furthermore, after obtaining the stability coefficient, the stability of the target mountain can be judged based on the specific value of the stability coefficient. Specifically, when the stability coefficient is greater than 1, the target mountain is predicted to be in a stable state; when the stability coefficient is equal to 1, the target mountain is predicted to be in a limiting equilibrium state; when the stability coefficient is less than 1, the target mountain is predicted to be in an unstable state.

[0102] The stability coefficient is a reduction factor for a two-dimensional model under the condition that the external power and internal energy dissipation are equal. Generally speaking, the larger the stability coefficient, the more stable the target mountain.

[0103] In summary, this embodiment provides a specific method for predicting the dynamic stability of high mountains under strong seismic forces. It is a method for solving the dynamic stability of mountains by comprehensively considering earthquakes, seepage, and freeze-thaw cycles. First, the geological model of the mountain is generalized and discretely divided into blocks. Then, a permissible velocity field is constructed that simultaneously considers seismic inertial force (characterized by introducing dynamic acceleration distribution to represent the topographic amplification effect), fissure water seepage (through the fissure water pressure term), and rock mass strength degradation caused by freeze-thaw cycles (through the reduction of mechanical strength parameters by the degradation coefficient). Based on this, the solution for the stability coefficient (reduction coefficient) is transformed into a mathematical optimization problem with the constraint that internal energy dissipation equals external force power, aiming to find the minimum upper bound solution, thereby calculating the final stability coefficient. This method achieves the integrated analysis of seismic dynamic amplification, fissure water pressure, and freeze-thaw cycle evolution within the framework of the limit analysis upper bound method, overcoming the shortcomings of traditional methods that isolate or simplify various factors. The solution process avoids complex assumptions about constitutive relations, directly capturing the most dangerous sliding mechanism and critical state during mountain instability, ensuring both theoretical rigor and computational efficiency. This method significantly enhances the engineering application depth of the stability coefficient. The obtained stability coefficient is not only an evaluation index for the strong-motion stability of mountains, but also a core tool for quantitatively guiding engineering decisions. This provides quantitative scientific basis for the site selection of major projects, the formulation of seismic fortification standards, and long-term monitoring and early warning during operation, effectively connecting theoretical analysis with disaster prevention and control practices.

[0104] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0105] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0106] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0107] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0108] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0109] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0110] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0111] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the stability of high mountains under strong seismic forces, characterized in that, include: Construct a two-dimensional model of the target mountain, determine the sliding surface of the two-dimensional model, and divide the two-dimensional model into multiple sliding body units based on the sliding surface; Construct the sliding velocity permit vector field of the two-dimensional model, the sliding velocity permit vector field including the sliding velocity of each sliding body unit and the relative sliding velocity between any two adjacent sliding body units; The external force power and internal energy dissipation of the two-dimensional model are calculated based on the sliding velocity permissible vector field and the internal structural surface strength parameters of the two-dimensional model after deterioration by freeze-thaw cycles. The external force power includes the power of seismic force, fissure water pressure and self-weight. The internal structural surface strength parameters include the cohesion and internal friction angle of the bottom sliding surface of each sliding body element, and the cohesion and internal friction angle of the lateral structural surface between any two adjacent sliding body elements. Predict the strong seismic stability of the target mountain based on the external force power and the internal energy dissipation; The external force power of the two-dimensional model for: In the formula, , and These represent the power of seismic force, fissure water pressure, and self-weight, respectively. n This represents the total number of the sliding body units. Indicates the horizontal quasi-static coefficient. Indicates the vertical quasi-static coefficient. Indicates the first i The weight of each sliding body unit i Indicates the first i The sliding speed of each sliding body unit. Indicates the first i The angle between the bottom sliding surface of each sliding unit and the horizontal plane. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit after being degraded by the freeze-thaw cycle; Indicates the action in the i The fissure water pressure on the bottom sliding surface of each sliding body unit. Indicates the first i The and the first i -1 relative sliding velocity between sliding body units Indicates the action in the i The and the first i -1 The fissure water pressure on the lateral structural surface between sliding body units. Indicates the first i The and the first i -1 The internal friction angle of the lateral structural surface between sliding body units after being deteriorated by the freeze-thaw cycle; The formula for calculating the horizontal pseudo-static coefficient is as follows: The formula for calculating the vertical pseudo-static coefficient is as follows: In the formula, This represents the reduction factor for the effect of earthquake action. This represents the peak ground acceleration (PGA) of the horizontal ground motion corresponding to the earthquake intensity. Indicates the first i The seismic acceleration-elevation dynamic amplification factor of the sliding body element is the first... i The ratio of the peak acceleration at the center of gravity of an individual sliding body element to the peak acceleration at the center of gravity of the sliding body element at the toe of the slope. Indicates the coefficient multiple; The first i The formula for calculating the fissure water pressure on the bottom sliding surface of a sliding body element is: The action in i The and the first i The formula for calculating the fissure water pressure on the lateral structural surface between -1 sliding body elements is: In the formula, Indicates the specific gravity of water. Indicates the first i -1 sliding body unit and the first i Water depth in the cracks of the lateral structural surfaces between sliding body units Indicates the first i The sliding body unit and the first i +1 Crack water depth at the lateral structural surface between sliding body units Indicates the first i The length of the bottom sliding surface of each sliding body unit. Indicates the first i -1 sliding body unit and the first i The length of the lateral structural surface between each sliding body unit below the water level.

2. The method for predicting the stability of high mountains under strong seismic forces according to claim 1, characterized in that, The internal energy dissipation of the two-dimensional model under freeze-thaw cycle for: In the formula, This represents the internal energy dissipation generated by the cohesion of the bottom sliding surface of the sliding body unit in the sliding velocity permissible vector field. This represents the internal energy dissipation caused by the cohesion of the lateral structural surfaces between two adjacent sliding body units in the sliding velocity permissible vector field. n This represents the total number of the sliding body units. i Indicates the first i The sliding speed of each sliding body unit. Indicates the first i The cohesion of the bottom sliding surface of each sliding body unit after being degraded by the freeze-thaw cycle. Indicates the first i The length of the bottom sliding surface of each sliding body unit. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit after being degraded by the freeze-thaw cycle. Indicates the first i The and the first i -1 relative sliding velocity between sliding body units Indicates the first i The and the first i -1 The cohesion of the lateral structural surfaces between sliding body units after being deteriorated by the freeze-thaw cycle. Indicates the first i The and the first i -1 is the length of the lateral structural surface between sliding body units. Indicates the first i The and the first i -1 The internal friction angle of the lateral structural surface between sliding body units after being deteriorated by the freeze-thaw cycle.

3. The method for predicting the stability of high mountains under strong seismic forces according to claim 2, characterized in that, The and and the and They are respectively: In the formula, Indicates the first i The cohesion of the bottom sliding surface of each sliding body unit before degradation due to freeze-thaw cycles. Indicates the first i The internal friction angle of the bottom sliding surface of each sliding body unit before degradation by freeze-thaw cycles. Indicates the first i The and the first i -1 The cohesion of the lateral structural surfaces between the sliding body units before deterioration due to the freeze-thaw cycle. Indicates the first i The and the first i -1 The internal friction angle of the lateral structural surfaces between sliding body units before deterioration due to the freeze-thaw cycle. This represents the degradation coefficient, which is determined experimentally.

4. The method for predicting the stability of high mountains under strong seismic forces according to claim 1, characterized in that, Predicting the strong seismic stability of the target mountain based on the external force power and the internal energy dissipation specifically includes: A reduction factor is introduced to reduce the internal structural surface strength parameters of the two-dimensional model after it has been deteriorated by freeze-thaw cycles, so as to update the external force power and the internal energy dissipation. The reduction factor when the external force power and the internal energy dissipation are equal is determined as the stability coefficient; The stability of the target mountain is predicted based on the stability coefficient.

5. The method for predicting the stability of high mountains under strong seismic forces according to claim 1, characterized in that, Predicting the strong seismic stability of the target mountain based on the external force power and the internal energy dissipation specifically includes: The ratio of the internal energy dissipation to the external force power is used as the stability coefficient; The stability of the target mountain under strong seismic forces is predicted based on the stability coefficient.

6. The method for predicting the stability of high mountains under strong seismic forces according to claim 4 or 5, characterized in that, Predicting the strong seismic stability of the target mountain based on the stability coefficient specifically includes: When the stability coefficient is greater than 1, the target mountain is predicted to be in a stable state; When the stability coefficient is equal to 1, the target mountain is predicted to be in a state of extreme equilibrium. When the stability coefficient is less than 1, the target mountain is predicted to be in an unstable state.

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