Method and system for simulating instability failure of soft and hard interbedding counter-tilt slope under rainfall condition

Abstract

The invention discloses an instability failure simulation method for a soft and hard interbedding counter-tilt slope under a rainfall condition, and relates to the technical field of rock mechanics and rock engineering. The method comprises the following steps: constructing an FDEM numerical model of a target soft and hard interbed counter-dip slope; setting boundary conditions for the numerical model, and applying initial gravity until a stress balance state is reached; based on the numerical model of stress balance, rainfall simulation is executed; according to a rainfall simulation result, judging whether slope instability failure occurs or not; if the slope instability failure does not occur and the load increasing condition is met, executing gravity load increasing simulation until the slope instability failure occurs while the rainfall simulation is maintained; and according to the critical gravity load when the slope is unstable, determining the slope safety coefficient of the target soft and hard interbed counter-tilt slope under the rainfall condition. According to the invention, fine simulation of the whole deformation and instability process of the soft and hard interbedding counter-dip slope under the rainfall condition can be realized.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and rock engineering, and in particular to a method and system for simulating the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions. Background Technology

[0002] Currently, numerous rock slopes have been formed in water conservancy and hydropower projects, road and transportation projects, and open-pit mining projects. These projects are mostly located in areas with sedimentary rock strata, where the rock masses exhibit significant layered structural characteristics, and the mechanical properties of adjacent rock strata differ markedly, forming a unique geological structure of alternating soft and hard layers. When the dip angle of the rock strata is opposite to the dip direction of the slope surface, it constitutes an alternating soft and hard layered reverse-dip slope. Its stability and failure mode are fundamentally different from those of homogeneous slopes, exhibiting unique deformation and instability mechanisms.

[0003] Rainfall, earthquakes, overloading at the top of the slope, and unloading at the toe of the slope are the main factors that induce slope slippage and instability. Among these, rainfall is particularly frequent and widespread in rainy areas such as the south, especially under prolonged periods of heavy rainfall, which often triggers landslides on roadside slopes. Rainwater infiltration leads to the continuous accumulation of groundwater and a rise in the water level, resulting in a continuous increase in transient groundwater dynamic and hydrostatic pressure, buoyancy, and seepage force. This leads to the continuous accumulation of sliding thrust, while prolonged water saturation causes softening of the embankment base and foundation, reducing shear strength and ultimately causing instability and failure.

[0004] To reveal the slippage and instability failure mechanism of interlayered soft and hard rock slopes and predict slope stability, numerical simulation methods are often used, such as the finite element method (FEM), discrete element method (DEM), finite difference method (FLAC), particle element method (PFC), numerical manifold method (NMM), and finite element-discrete element coupled method (FDEM). In recent years, the FDEM method has been proven to be well-suited for simulating the deformation, cracking, and macroscopic movement of rock materials. It can simulate the entire process of intact rock materials from continuous elastic-plastic deformation to discontinuous deformation leading to fracture failure and block contact, with no limit on the number of cracks, no need to assemble a total stiffness matrix, avoiding singular matrix problems, and can also characterize real cracks with geometric features such as aperture and roughness. Furthermore, it is easy to simulate large deformation anchoring reinforcement of soft rock.

[0005] However, while existing FDEM methods have been applied to simulate gravity-induced landslide instability of homogeneous rock slopes, they have not yet been applied to simulate rainfall-induced landslide instability of interbedded soft and hard slopes. Therefore, it is impossible to simulate, characterize, and accurately predict the sliding instability disaster mechanism of interbedded soft and hard slopes under rainfall conditions. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method and system for simulating the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions, which can achieve a detailed simulation of the entire process of deformation and instability of a reverse-dip slope with alternating soft and hard layers under rainfall conditions.

[0007] To achieve the above objectives, this invention provides a method for simulating the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions, comprising: Construct an FDEM numerical model of the target soft-hard interlayered reverse-dip slope; Boundary conditions are set for the numerical model, and initial gravity is applied until stress equilibrium is reached; Based on a numerical model of stress balance, rainfall simulation is performed. During the rainfall simulation, the infiltration depth of rainwater in the weak layer of the numerical model is calculated, and the strength degradation effect of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect and the slope runoff effect caused by rainwater infiltration are simulated simultaneously. Based on the results of the rainfall simulation, determine whether slope instability or failure has occurred; If no load increase occurs and the loading conditions are met, then while maintaining the rainfall simulation, a gravity loading simulation is performed until slope instability and failure occur; during the gravity loading simulation, the gravity load is gradually increased on the numerical model according to a preset increment; the loading conditions are reaching a preset rainfall duration and / or, the change in rainwater infiltration rate within a preset time period is less than or equal to a preset value. Based on the critical gravity load at which the slope becomes unstable, the slope safety factor of the target soft-hard interlayered reverse slope under rainfall conditions is determined. The boundary conditions include: the lateral boundary is free during the initial gravity loading stage, fixed in the horizontal direction during the rainfall simulation stage and the gravity loading simulation stage, the bottom boundary remains fixed in the vertical direction, and both the bottom boundary and the lateral boundary are impermeable boundaries.

[0008] Optionally, the quadrilateral elements located at the interface between the weak and hard layers in the numerical model adopt the mechanical parameters of the weak layer.

[0009] Optionally, the infiltration depth is determined based on the weak layer exposed at the top of the slope. L Calculate using the following formula: Infiltration depth of weak layers exposed on slopes Calculate using the following formula: In the formula, f t For the weak layer exposed at the top of the slopet Infiltration rate at any given time f 0 represents the infiltration rate at the initial moment. f c To stabilize the infiltration rate, k For decreasing exponents, For the weak layer exposed on the slope t Infiltration rate at any given time θ The slope angle is... β The dip angle is the layer angle.

[0010] Optionally, the simulation includes the strength degradation effect of the weak layer caused by rainfall infiltration, including: For the weak layer in the rainwater infiltration area, it is considered to have reached the water saturation state instantaneously, and the parameter values ​​of elastic modulus, cohesion, internal friction angle and tensile strength are updated to the corresponding deterioration parameter values ​​under the water saturation state.

[0011] Optionally, the formula for calculating the slope mass increment in the rock mass weight gain effect is: In the formula, The increase in slope mass due to rainfall infiltration. The saturated water content of the weak layer, Rainwater density, For the first The infiltration depth of a weak layer For the first The thickness of a weak layer For the first The length of the layer of the weakest layer This represents the total number of weak layers.

[0012] Optionally, the formula for calculating the pore water pressure in the pore water pressure buoyancy effect is as follows: In the formula, Pore ​​water pressure, It is water-weighted. This refers to the water head height.

[0013] Optionally, the tangential stress on the slope caused by slope runoff in the slope runoff effect is calculated using the following formula: In the formula, The tangential stress on the slope is... It is water-weighted. For the thickness of the slope water flow, The slope angle is... For traffic, The velocity is the water flow velocity.

[0014] Optionally, based on the results of the rainfall simulation, determining whether slope instability or failure has occurred includes: Real-time monitoring of the system kinetic energy and the number of fractures of the quadrilateral elements in the numerical model; When the rate of change of the system's kinetic energy exceeds a first preset threshold, and / or the rate of change of the number of fractures exceeds a second preset threshold, slope instability and failure are determined to have occurred.

[0015] This invention also provides a simulation system for the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions, comprising: Model building unit, used to build FDEM numerical model of target soft-hard interlayered reverse slope; An initial configuration unit is used to set boundary conditions for the numerical model and apply initial gravity until a stress equilibrium state is reached. Simulation unit, used for: Based on a numerical model of stress balance, rainfall simulation is performed. During the rainfall simulation, the infiltration depth of rainwater in the weak layer of the numerical model is calculated, and the strength degradation effect of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect and the slope runoff effect caused by rainwater infiltration are simulated simultaneously. Based on the results of the rainfall simulation, determine whether slope instability or failure has occurred; If no load increase occurs and the loading conditions are met, then while maintaining the rainfall simulation, a gravity loading simulation is performed until slope instability and failure occur; during the gravity loading simulation, the gravity load is gradually increased on the numerical model according to a preset increment; the loading conditions are reaching a preset rainfall duration and / or, the change in rainwater infiltration rate within a preset time period is less than or equal to a preset value. Based on the critical gravity load at which the slope becomes unstable, the slope safety factor of the target soft-hard interlayered reverse slope under rainfall conditions is determined. The boundary conditions include: the lateral boundary is free during the initial gravity loading stage, fixed in the horizontal direction during the rainfall simulation stage and the gravity loading simulation stage, the bottom boundary remains fixed in the vertical direction, and both the bottom boundary and the lateral boundary are impermeable boundaries.

[0016] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The present invention provides a method for simulating the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions. By constructing an FDEM numerical model of the target reverse-dip slope with alternating soft and hard layers and setting displacement and impermeable boundary conditions that conform to its mechanical and hydrological characteristics, this method establishes for the first time an effective numerical analysis platform for simulating the instability behavior of such special slopes under rainfall conditions. During the rainfall simulation process, this method not only calculates the infiltration depth of rainwater into the weak layer in the numerical model, but also simultaneously simulates the strength degradation effect of the weak layer, the rock mass weight gain effect, the pore water pressure buoyancy effect, and the slope runoff effect caused by rainwater infiltration. This allows for a comprehensive characterization of the combined impact of rainfall infiltration on the mechanical properties and stress environment of the slope rock mass, achieving a refined simulation of the entire process of instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions. Furthermore, by maintaining the rainfall simulation while performing gravity loading simulation until slope instability occurs, and determining the slope safety factor based on the critical gravity load at the time of instability, this invention can quantitatively assess the stability reserve of slopes under the weakening effect of rainfall, accurately obtain the slope safety factor under rainfall conditions, and provide reliable technical support for the protection design and stability evaluation of slope engineering. Attached Figure Description

[0017] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same parts.

[0018] Figure 1 This is a schematic diagram of the method flow for simulating the instability and failure of a soft-hard interlayered reverse-dip slope under rainfall conditions, as shown in an embodiment of the present invention. Figure 2 This is a flowchart illustrating the simulation of deformation, instability, and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions, as shown in an embodiment of the present invention. Figure 3 This is a schematic diagram of the FDEM numerical model of a soft-hard interlayered reverse-dip slope shown in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the setting of displacement boundary conditions for a soft-hard interlayered anti-dip slope according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the slope runoff effect simulation in an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the simulation results of deformation, instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions, as shown in an embodiment of the present invention. Figure 7 This is a schematic diagram of the module structure of a simulation system for the instability and failure of a soft-hard interlayered reverse-dip slope under rainfall conditions, as shown in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Please see Figure 1 and Figure 2 , Figure 1 This is a schematic diagram of the method for simulating the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions.

[0021] Simulation methods for instability and failure of alternating soft and hard slopes under rainfall conditions include: S101: Construct the FDEM numerical model of the target soft-hard interlayered reverse slope.

[0022] In the application, based on the actual engineering geological conditions and exploration data of the target alternating soft and hard slope, its precise geometric structure information and rock mechanics parameters are obtained. Based on this information, a coupled finite element-discrete element (FDEM) numerical model is constructed for simulation. See also... Figure 3 This demonstrates a completed numerical model of a soft-hard interlayered reverse-dip slope. Figure 3 The dip angle in the numerical model β =45°, slope angle θ =80°, the layer thickness is 2 m, and the weak layer and the hard layer have the same thickness.

[0023] Specifically, in the model construction phase, a numerical geometric model reflecting the slope's geometry is first established based on the actual engineering geological survey data of the target slope. This geometric model needs to accurately depict the stratigraphic structure characteristics of alternating hard and soft rock layers, namely, the layered distribution of alternating hard and soft rock layers, and the reverse-dip structural characteristics where the rock layer dip direction is opposite to the slope surface dip direction. It also needs to include key geometric parameters such as slope dip angle, layer dip angle, and layer thickness. Based on this, the geometric model is discretized into mesh cells for numerical calculations. Subsequently, based on the rock mass parameters obtained from indoor physical and mechanical tests, the discretized mesh cells are assigned corresponding material properties. Considering the significant differences in lithology between the hard and soft interlayered layers, the model construction process needs to distinguish between soft and hard layers, assigning their corresponding physical and mechanical parameters to their respective stratigraphic units. These parameters cover the basic properties of the rock mass, such as density, elastic modulus, and Poisson's ratio, as well as the strength characteristics of the rock mass, such as cohesion, internal friction angle, and tensile strength. They also include parameters such as Type I fracture energy and Type II fracture energy used to describe the fracture characteristics of the rock mass, thereby establishing an FDEM numerical model that can realistically reproduce the geological structure and mechanical properties of the target slope.

[0024] For quadrilateral elements located at the interface between weak and hard layers in the numerical model, the material parameters should be set to be consistent with those of the adjacent weak layer, that is, the mechanical parameters of the weak layer should be adopted. This treatment can more reasonably simulate the transition of material mechanical properties near the interface or the behavior dominated by the weaker material, and ensure that the response of the interface region in the subsequent loading and deformation process is more consistent with the actual mechanical properties of such interlayered rock masses.

[0025] S102: Set boundary conditions for the numerical model and apply initial gravity until stress equilibrium is reached.

[0026] The boundary conditions include: the lateral boundary is free during the initial gravity loading stage, fixed in the horizontal direction during the rainfall simulation stage and the gravity loading simulation stage, the bottom boundary remains fixed in the vertical direction, and both the bottom boundary and the lateral boundary are impermeable boundaries.

[0027] After constructing the numerical model, boundary conditions need to be set to simulate real geological environment constraints and lay the foundation for subsequent simulations. The setting of displacement boundary conditions varies depending on the simulation stage. In the initial gravity loading stage, the lateral boundaries of the model remain free to allow the model to settle naturally under its own weight. In subsequent rainfall simulation and gravity loading simulation stages, the lateral boundaries are adjusted to be fixed in the horizontal direction, while the bottom boundary remains fixed in the vertical direction throughout all stages. To achieve this dynamic switching of boundary conditions, for example, it can be controlled through node attributes. For instance, the left and right node attributes can be set to 1, and the bottom node attribute can be set to 2. After entering the rainfall simulation and gravity loading stages, all nodes are checked cyclically. When the node attribute is 1, its horizontal velocity is constrained to be constant at 0; when the node attribute is 2, its vertical velocity is constrained to be constant at 0.

[0028] In addition, hydraulic boundary conditions need to be set, and the model should be set as an impermeable boundary condition, that is, the bottom boundary and the lateral boundary of the model are both impermeable boundaries, to ensure that the water flow is limited to infiltrating through the slope and flowing out or infiltrating from the lateral and bottom boundaries of the model.

[0029] Subsequently, initial gravity is applied to the numerical model with pre-defined boundary conditions to allow it to reach initial stress equilibrium under its own weight. The initial gravitational acceleration is applied to all nodes of the model, with the negative sign indicating a vertically downward direction. Since the initial loading will cause model oscillations and generate significant kinetic energy, hysteresis damping is used to quickly dissipate this kinetic energy until the model's monitoring indicators show that stress equilibrium has been reached, thus completing the simulation initialization preparation.

[0030] by Figure 3 Taking the numerical model in the example, the boundary conditions for slope displacement are as follows: Figure 4As shown, the following method is used to set the node attributes: set the left and right node attributes to 1, and the bottom node attribute to 2; loop through all nodes, and during the rainfall and gravity loading phases, when the attribute is 1, the horizontal velocity... Always 0; when the attribute is 2, the vertical speed. The water flow velocity is kept constant at zero at the lateral and bottom boundaries of the model, thus setting the hydraulic boundary conditions. Then, the initial gravitational acceleration is... =-9.8 m / s 2 Applied to all nodes of the model, the negative sign indicates a vertically downward direction. The model will oscillate, generating enormous kinetic energy, which will be rapidly dissipated through hysteresis damping. The hysteresis damping is as follows: In the formula, Indicates hysteresis damping, For nodes quality The hysteresis damping coefficient, For elastic modulus, This represents the material density.

[0031] S103: A numerical model based on stress balance is used to perform rainfall simulation.

[0032] During the rainfall simulation, the infiltration depth of rainwater into the weak layer in the numerical model is calculated, and the strength degradation effect of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect and the slope runoff effect caused by rainwater infiltration are simulated simultaneously.

[0033] In the application, after the numerical model reaches stress equilibrium, rainfall simulation is performed based on the model. The impact of rainfall infiltration on a reverse-dip slope with alternating soft and hard layers is reproduced through numerical calculation. The focus is on calculating the infiltration depth of rainwater in the weak layer of the numerical model, and on this basis, the effects of rainwater infiltration on the strength degradation of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect, and the slope runoff effect are simulated simultaneously, thereby achieving a refined characterization of the evolution of the slope's mechanical state under rainfall.

[0034] When calculating rainwater infiltration depth, an algorithm based on the time-varying law of infiltration rate is employed. Rainwater infiltration depth is defined as the distance parallel to the bedding plane and the land surface. The infiltration rate of the weak layer exhibits an exponential decay trend over time, and its value is jointly controlled by the initial infiltration rate, the steady-state infiltration rate, and the decay exponent. The calculation logic also differs depending on the location of the weak layer: for a weak layer exposed at the top of a slope, the infiltration depth is directly obtained by integrating the infiltration rate that decays over time; for a weak layer exposed on the slope surface, the infiltration rate needs to be corrected according to the slope dip angle and the bedding angle to reflect the influence of the slope attitude on the infiltration process, and then the corrected rate is integrated. Through this process, the transport distance of the water front within the weak layer during rainfall can be obtained in real time.

[0035] Infiltration depth of the weak layer exposed at the top of the slope L Calculate using the following formula: Infiltration depth of weak layers exposed on slopes Calculate using the following formula: In the formula, f t For the weak layer exposed at the top of the slope t Infiltration rate at any given time f 0 represents the infiltration rate at the initial moment. f c To ensure a stable infiltration rate, all units are mm / h. k For decreasing exponents, For the weak layer exposed on the slope t Infiltration rate at any given time θ The slope angle is... β The dip angle is the layer angle.

[0036] The initial infiltration rate in the above infiltration rate formula With stable infiltration rate All of these are directly related to rainfall intensity. The greater the rainfall intensity, and The value of also increases accordingly. Therefore, within the same rainfall period, the infiltration depth of rainwater in the weak layer is also greater, thus more accurately reflecting the aggravating effect of water on the rock mass infiltration process under heavy rainfall conditions.

[0037] In practical simulation applications, rainfall intensity parameters can be determined according to the simulation objective. For stability evaluation of specific engineering slopes, the rainfall intensity value can be designed based on historical meteorological data of the slope location, or determined comprehensively based on data from typical rainfall events that have induced landslides. For parametric studies revealing general patterns, a series of representative rainfall intensity values ​​can be set for simulation to systematically analyze the influence trend and threshold of rainfall intensity on the stability of alternating soft and hard slopes.

[0038] While obtaining the infiltration depth, four key physical and mechanical effects are simultaneously simulated. It should be noted that the simulation of this invention is based on the following assumptions: the hard layer is an impermeable layer; when the hard layer is intact, rainfall has no effect on it; when cracks are generated, hydrostatic pressure exists; the infiltrated weak layer is in a saturated state, and the uninfiltrated rock mass is in a dry state, i.e., the initial water content is 0, and the unsaturation of the infiltration peak is ignored; the rock mass reaches a saturated state instantaneously after being infiltrated, and the process of the rock mass from dry to saturated is ignored; rainwater at the slope toe is drained away, and there is no water accumulation.

[0039] First, the strength degradation effect is simulated, which simulates the strength degradation effect of the weak layer caused by rainwater infiltration. This includes: for the weak layer in the rainwater infiltration area, it is regarded as instantaneously reaching the water saturation state, and the parameter values ​​of elastic modulus, cohesion, internal friction angle and tensile strength are updated to the corresponding degradation parameter values ​​under the water saturation state.

[0040] In the rainwater infiltration zone, the weak layer is considered to be instantaneously saturated, ignoring the existence of unsaturated zones and the process from dryness to saturation. Under this condition, the mechanical parameters of the weak layer, such as elastic modulus, cohesion, internal friction angle, and tensile strength, are instantaneously updated to their corresponding degradation parameter values ​​under water-saturated conditions. These degradation parameter values ​​can be obtained through indoor physical and mechanical tests; for example, the elastic modulus under saturation is determined by uniaxial compression testing, the tensile strength by Brazilian splitting test, and the internal friction angle and cohesion by triaxial compression testing, while neglecting changes in Poisson's ratio.

[0041] by Figure 3 Taking the numerical model as an example, the parameters of the weak layer and the hard layer in the model are shown in Table 1 and Table 2 below.

[0042] Table 1 Input parameters for weak and hard layers

[0043] Table 2 Parameters of the weak layer under saturation state

[0044] Specifically, at each calculation step, the wetting state of each weak layer is determined based on the real-time calculated infiltration depth. For areas determined to have been infiltrated by rainwater, the material parameters (such as elastic modulus, cohesion, internal friction angle, and tensile strength) of all quadrilateral elements within that area are immediately updated from their initial dry state values ​​(see Table 1) to preset saturated degradation values ​​(see Table 2). For elements that have not yet been infiltrated, their original parameters are retained. This parameter update mechanism can directly affect the element attribute database of the numerical model, ensuring that subsequent mechanical calculations are based on the updated degradation strength, thereby accurately coupling the strength degradation effect caused by rainfall into the FDEM solution process in real time.

[0045] Secondly, there is the rock mass weight gain effect, where rainwater infiltration increases the mass of the slope rock mass. Based on the saturated water content of the weak layer, the calculated infiltration depth, the thickness of the weak layer, and the extension length of the bedding plane, the increase in slope mass caused by rainfall infiltration is calculated by summing up, thus reflecting the dynamic change of the rock mass's self-weight in the model.

[0046] The formula for calculating the slope mass increment in the rock mass weight gain effect is: In the formula, The increase in slope mass due to rainfall infiltration. The saturated water content of the weak layer, Rainwater density, For the first The infiltration depth of a weak layer For the first The thickness of a weak layer For the first The length of the layer of the weakest layer This represents the total number of weak layers.

[0047] In the application, at each calculation step, it is determined which weak layers are wetted by rainwater based on the real-time updated infiltration depth. For these identified wetted units, their material density is determined from the density value under the initial dry state. (As shown in Table 1) Updated in real time The calculation formula is as follows: in, To increase the density of the rock mass, The initial rock mass density, For density increment, The saturated water content of the weak layer, This represents the density of rainwater. For elements not infiltrated by rainwater, the density remains unchanged. The update of this density parameter directly participates in the gravity load calculation of the numerical model, thus accurately coupling the rock mass weight gain effect caused by rainwater infiltration into the dynamic solution process of FDEM in the form of distributed load.

[0048] The third is the pore water pressure buoyancy effect, which generates pore water pressure perpendicular to the action surface within a saturated weak layer. This pressure value is calculated based on the water's unit weight and hydraulic head, simulating the buoyancy effect of groundwater on the rock mass skeleton and reducing effective stress.

[0049] The formula for calculating pore water pressure in the pore water pressure buoyancy effect is as follows: In the formula, Pore ​​water pressure, It is water-weighted. This refers to the water head height.

[0050] The pore water pressure buoyancy effect is realized in the FDEM numerical model by calculating the shear strength of the rock mass elements in real time. The calculation formula is as follows: In the formula, For the shear strength of the rock mass, To account for the normal stress due to the buoyancy effect of rainwater, It is the internal friction angle. It is cohesive force; The normal stress is caused by the weight of the rock mass. , The rock mass is of high density. The depth of the rock mass represents the vertical distance from the top of the slope, which is also the water head height. This refers to the pore water pressure.

[0051] In application, the rainwater infiltration status of each unit is dynamically determined based on the real-time updated infiltration depth. For units identified as infiltrated, a formula is used... Calculate its normal stress considering the rainwater buoyancy effect. This allows for real-time updates of shear strength; for unwetted elements, the effective normal stress is directly calculated using their self-weight stress. Through this coupling mechanism based on dynamic correction of effective stress in unit state, the buoyancy effect of pore water pressure changing with the advance of the infiltration front is simulated, thus realistically reflecting the weakening effect of rainfall infiltration on the anti-sliding capacity of slope rock mass.

[0052] Finally, there is the slope runoff effect, which simulates the tangential scouring effect on a slope caused by rainfall flowing across it. The tangential stress generated by slope runoff depends on the slope runoff thickness and the slope angle, where the slope runoff thickness is determined by the flow rate and velocity, and the flow rate is obtained based on the set rainfall intensity.

[0053] The tangential stress exerted on the slope by slope runoff in the slope runoff effect is calculated using the following formula: In the formula, The tangential stress on the slope is... γ w It is water-weighted. For the thickness of the slope water flow, The slope angle is... For traffic, The velocity is the water flow velocity.

[0054] In the slope runoff effect, flow rate It is determined by the rainfall intensity. The greater the rainfall intensity, the more rainwater reaches the slope per unit time, and the higher the flow rate. The corresponding increase leads to a thickness of the slope water flow. The increase leads to a greater tangential stress on the slope caused by runoff. Increase. Therefore, rainfall intensity not only regulates the infiltration process, but also directly determines the intensity of the scouring effect of slope runoff on the slope surface.

[0055] See Figure 5 The shear force caused by slope runoff will be calculated in the application. It can be applied directly to the edges of the triangular units on the slope, that is, directly to the exposed outer edges of all the triangular units that constitute the slope boundary.

[0056] Through the above-mentioned synchronous coupling simulation of multiple effects, the combined effects of the softening of the weak layer, the increase of its own weight, the pore water pressure and the scouring of the slope on the slope stability under rainfall conditions can be fully reflected.

[0057] It should be noted that, based on the geological characteristics of alternating soft and hard layers in a reverse-dip slope, this simulation method follows the fundamental assumption that the hard layer is an impermeable layer. Therefore, in the dynamic simulation process, rainfall infiltration and its directly caused strength degradation, rock mass weight gain, and pore water pressure buoyancy effect are only calculated and applied to the weak layer; for the hard layer, it is assumed that rainwater will not infiltrate, so the above effects are not simulated. However, the slope runoff effect acts on all rock layers exposed on the slope surface, thus generating tangential scouring forces on the slope boundary between the weak and hard layers. For the simulation of mechanical processes such as gravity loading and rock mass fracture evolution, the specific implementation method can be found in the prior patent application number 2025111833318, entitled "An FDEM Simulation Method and System for Rock Slope Fracture and Instability," which will not be elaborated here.

[0058] S104: Based on the results of rainfall simulation, determine whether slope instability or failure has occurred.

[0059] Throughout the rainfall simulation process, it is necessary to continuously monitor and dynamically assess the stability of the slope based on the simulation results to determine whether instability or failure has occurred. This assessment is not conducted only after the simulation ends, but rather throughout each calculation step of the rainfall simulation. The basic principle is to identify key inflection points that indicate overall slope instability by analyzing the dynamic response characteristics of the numerical model under the influence of rainfall. In numerical simulations, slope instability and failure typically manifest as a dynamic abrupt process from localized damage and deformation accumulation to the eventual occurrence of overall, irreversible sliding or collapse. This process leaves clear signals in the model's macroscopic mechanical response.

[0060] Specifically, the above-mentioned determination of whether slope instability or failure has occurred based on rainfall simulation results includes: Real-time monitoring of the system kinetic energy and the number of fractures of quadrilateral elements in the numerical model; When the rate of change of the system's kinetic energy exceeds the first preset threshold, and / or the rate of change of the number of fractures exceeds the second preset threshold, slope instability and failure are determined to have occurred.

[0061] In the application, while numerical calculations are being performed, the system kinetic energy of the numerical model and the number of fractures in the quadrilateral elements within the model are continuously tracked and recorded. System kinetic energy is a comprehensive indicator reflecting the motion state of the entire model system. When the slope is in a stable state, the kinetic energy usually remains at a low level or fluctuates only around the equilibrium position. The number of fractures in the quadrilateral elements directly quantifies the initiation, propagation, and penetration of cracks within the rock mass, characterizing the cumulative degree of rock mass damage.

[0062] To accurately and sensitively capture the critical moment when a slope transitions from a stable to an unstable state, a judgment criterion based on the rate of change is introduced. Based on the real-time acquisition of the aforementioned monitoring data, the rate of change of the system's kinetic energy and the rate of change of the number of fractured quadrilateral elements over time are further calculated. Since slope instability is often accompanied by abrupt changes in physical state—for example, the instantaneous release of gravitational potential energy leading to a sharp increase in kinetic energy, or the rapid propagation and penetration of cracks within the rock mass leading to a surge in the number of fractures—corresponding thresholds are set as criteria. Specifically, when the rate of change of the system's kinetic energy exceeds the first preset threshold, it indicates a sudden increase in the model's kinetic energy, meaning the slope rock mass has begun to undergo violent macroscopic sliding or collapse; or, when the rate of change of the number of fractured quadrilateral elements exceeds the second preset threshold, it indicates that cracks within the model have rapidly expanded in a short period, and the rock mass structure has lost its integrity. If either of these conditions is met, the slope is judged to have become unstable. By monitoring the rate of change of these indicators and comparing them with preset thresholds, the sudden characteristics of rainfall-induced slope disasters can be effectively identified, ensuring the accuracy and reliability of the determination of the instability moment.

[0063] S105: If no load increase occurs and the loading conditions are met, then while maintaining the rainfall simulation, execute the gravity loading simulation until slope instability and failure occur.

[0064] During the gravity loading simulation, the gravity load is gradually increased according to the preset increment logarithmic model; the above loading conditions are to reach the preset rainfall duration and / or, the change in rainwater infiltration rate within the preset time period is less than or equal to the preset value.

[0065] During the rainfall simulation phase, after each calculation time step, the rate of change of the system's kinetic energy and the number of fracture elements is monitored in real time to determine whether the slope is unstable. If instability is determined, the simulation is terminated and the results are analyzed. If instability is not determined, it is further determined whether the loading conditions are met. It is understandable that if slope instability occurs before the loading conditions are met, it indicates that the target slope is in an unstable state under the set rainfall conditions and is a dangerous slope, so there is no need to perform subsequent gravity loading simulations and safety factor calculations.

[0066] Regarding the conditions for adding load, they can be determined in two ways depending on the simulation objective. One method is when a specific engineering example exists, using the actual total rainfall duration of that project as the preset rainfall duration; reaching this preset duration signifies the simulation of the rainfall event is complete. The other method is when no actual engineering case is available for reference, or when the simulation is not limited to the rainfall duration of the engineering example and simply aims to study or predict slope stability under different rainfall durations. In this case, the timing of adding gravity load is determined by monitoring the dynamic changes in the rainwater infiltration rate. Since the rainwater infiltration rate decays over time and gradually approaches stability, when its change over multiple consecutive calculation steps is less than or equal to the preset value, the infiltration effect is considered to have fully developed and stabilized, and further extending the simulation time has negligible impact on the slope condition. At this point, the stable influence state of rainfall infiltration can be determined to have been achieved.

[0067] The rainfall infiltration rate can be expressed by the above formula. and The calculation process involves automatically selecting an appropriate formula based on the actual exposure location of the weak layer during execution. During the simulation, the infiltration rate of each weak layer within the slope is calculated and monitored independently according to its exposure category. When there is no specific rainfall duration as a basis, the infiltration status of all weak layers must be determined simultaneously. Only when the change in the infiltration rate of all weak layers within a preset time period (e.g., two consecutive calculation time steps) is less than or equal to a preset value can it be determined that the rainfall infiltration effect of the entire numerical model has generally stabilized.

[0068] If no slope instability or failure is determined during the rainfall simulation phase (i.e., the slope remains intact under continuous rainfall and the loading conditions are met), then the gravity loading simulation phase begins to further assess its stability. During this gravity loading simulation, the rainfall simulation conditions are maintained, meaning the model remains in a rainfall environment. This ensures that rainfall infiltration and its resulting effects, such as the degradation of weak layers, rock mass weight gain, and pore water pressure, continue to exist or be calculated, thereby simulating the complex coupling of rainfall and loading.

[0069] Based on this, a gravity loading simulation is performed, gradually increasing the gravity load on the numerical model according to a preset increment. For example, a constant gravity acceleration loading rate can be set, so that the gravity acceleration applied to the model increases linearly with time. At each calculation step, the gravity acceleration value corresponding to the current moment is used for the solution. Simultaneously, throughout the entire loading simulation process, the same judgment method as during the rainfall phase must be continuously used to monitor the rate of change of the model system's kinetic energy and the number of fracture elements in real time, monitoring the slope's stability until slope instability and failure are detected.

[0070] When the slope remains intact during the rainfall phase, gravity is added to the model in the following manner: In the formula, Given the current gravitational acceleration, For the current computation time step, This is the calculation time step when the rainfall phase simulation is completed, that is, the time step when the load increase conditions are met. The rate of increase in gravity load.

[0071] S106: Determine the slope safety factor of the target soft-hard interlayered reverse slope under rainfall conditions based on the critical gravity load at which the slope becomes unstable.

[0072] When it is confirmed that the slope will become unstable and fail under sustained rainfall conditions while gradually increasing gravity load, the gravity loading simulation process is terminated. At this point, the gravity load value borne by the numerical model is recorded as the critical gravity load. To determine the slope safety factor of the target soft-hard interbedded reverse-dip slope under rainfall conditions, the final gravity acceleration value at this critical state needs to be extracted. The safety factor is determined based on the ratio of the final gravity acceleration value to the initial gravity acceleration value. This ratio quantifies the surcharge multiple that the slope can withstand relative to the initial state under the background of deterioration of rock mechanical properties due to rainfall infiltration. Through the above calculations, the specific impact of rainfall on slope stability can be accurately assessed. When the slope becomes unstable and fails, the critical gravity load data at the moment of stopping the loading is used to solve for the safety factor, thus providing a quantitative stability evaluation index for engineering protection.

[0073] The formula for calculating the slope safety factor is as follows: In the formula: For the slope safety factor, This represents the final gravitational acceleration value.

[0074] by Figure 3 Taking the numerical model in the text as an example, the failure mode of a soft-hard interlayered reverse-dip slope under rainfall conditions is as follows: Figure 6 As shown, the slope safety factor can be calculated. =1.80.

[0075] Corresponding to the aforementioned application function implementation method embodiments, the present invention also provides a simulation system for the instability and failure of a soft-hard interlayered reverse-dip slope under rainfall conditions and corresponding embodiments.

[0076] Please see Figure 7 , Figure 7 This is a schematic diagram of the module structure of a simulation system for the instability and failure of a reverse-dip slope with alternating soft and hard layers under rainfall conditions.

[0077] A simulation system for the instability and failure of alternating soft and hard slopes under rainfall conditions includes: Model building unit 71 is used to build the FDEM numerical model of the target soft-hard interlayered reverse slope; The initial configuration unit 72 is used to set boundary conditions for the numerical model and apply initial gravity until stress equilibrium is reached. Analog unit 73 is used for: Based on a numerical model of stress balance, rainfall simulation is performed. During the rainfall simulation, the infiltration depth of rainwater in the weak layer of the numerical model is calculated, and the strength degradation effect of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect and the slope runoff effect caused by rainwater infiltration are simulated simultaneously. Based on the results of rainfall simulation, determine whether slope instability or failure has occurred; If no load increase occurs and the loading conditions are met, then while maintaining the rainfall simulation, a gravity loading simulation is performed until slope instability and failure occur. During the gravity loading simulation, the gravity load is gradually increased according to the preset incremental logarithmic model. The loading conditions are reaching the preset rainfall duration and / or the change in the rainwater infiltration rate within the preset time period is less than or equal to the preset value. Based on the critical gravity load at which the slope becomes unstable, the slope safety factor of the target soft and hard interlayered reverse slope under rainfall conditions is determined. The boundary conditions include: the lateral boundary is free during the initial gravity loading stage, fixed in the horizontal direction during the rainfall simulation stage and the gravity loading simulation stage, the bottom boundary remains fixed in the vertical direction, and both the bottom boundary and the lateral boundary are impermeable boundaries.

[0078] In one embodiment, when simulating the strength degradation effect of a weak layer caused by rainfall infiltration, the simulation unit 73 is specifically used for: For the weak layer in the rainwater infiltration area, it is considered to have reached the water saturation state instantaneously, and the parameter values ​​of elastic modulus, cohesion, internal friction angle and tensile strength are updated to the corresponding deterioration parameter values ​​under the water saturation state.

[0079] In one embodiment, when determining whether slope instability or failure has occurred based on rainfall simulation results, the simulation unit 73 is specifically used for: Real-time monitoring of the system kinetic energy and the number of fractures of quadrilateral elements in the numerical model; When the rate of change of the system's kinetic energy exceeds the first preset threshold, and / or the rate of change of the number of fractures exceeds the second preset threshold, slope instability and failure are determined to have occurred.

[0080] Regarding the system in the above embodiments, the specific manner in which each unit module performs operations has been described in detail in the embodiments related to the method, and will not be elaborated further here.

[0081] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, characterized in that, include: Construct an FDEM numerical model of the target soft-hard interlayered reverse-dip slope; Boundary conditions are set for the numerical model, and initial gravity is applied until stress equilibrium is reached; Based on a numerical model of stress balance, rainfall simulation is performed. During the rainfall simulation, the infiltration depth of rainwater in the weak layer of the numerical model is calculated, and the strength degradation effect of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect and the slope runoff effect caused by rainwater infiltration are simulated simultaneously. Based on the results of the rainfall simulation, determine whether slope instability or failure has occurred; If no load increase occurs and the conditions for load increase are met, then while maintaining the rainfall simulation, a gravity load increase simulation is performed until slope instability and failure occur; during the gravity load increase simulation, the gravity load is gradually increased on the numerical model according to the preset increment; The loading conditions are reaching a preset rainfall duration and / or the change in rainwater infiltration rate within a preset time period being less than or equal to a preset value. Based on the critical gravity load at which the slope becomes unstable, the slope safety factor of the target soft-hard interlayered reverse slope under rainfall conditions is determined. The boundary conditions include: the lateral boundary is free during the initial gravity loading stage, fixed in the horizontal direction during the rainfall simulation stage and the gravity loading simulation stage, the bottom boundary remains fixed in the vertical direction, and both the bottom boundary and the lateral boundary are impermeable boundaries.

2. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... The quadrilateral elements located at the interface between the weak and hard layers in the numerical model adopt the mechanical parameters of the weak layer.

3. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... Infiltration depth of the weak layer exposed at the top of the slope L Calculate using the following formula: Infiltration depth of weak layers exposed on slopes Calculate using the following formula: In the formula, f t For the weak layer exposed at the top of the slope t Infiltration rate at any given time f 0 represents the infiltration rate at the initial moment. f c To stabilize the infiltration rate, k For decreasing exponents, For the weak layer exposed on the slope t Infiltration rate at any given time θ The slope angle is... β The dip angle is the layer angle.

4. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... Simulation of the strength degradation effect of weak layers caused by rainfall infiltration includes: For the weak layer in the rainwater infiltration area, it is considered to have reached the water saturation state instantaneously, and the parameter values ​​of elastic modulus, cohesion, internal friction angle and tensile strength are updated to the corresponding deterioration parameter values ​​under the water saturation state.

5. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... The formula for calculating the slope mass increment in the rock mass weight gain effect is as follows: In the formula, The increase in slope mass due to rainfall infiltration. The saturated water content of the weak layer, Rainwater density, For the first The infiltration depth of a weak layer For the first The thickness of a weak layer For the first The length of the layer of the weakest layer This represents the total number of weak layers.

6. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... The formula for calculating the pore water pressure in the pore water pressure buoyancy effect is as follows: In the formula, Pore ​​water pressure, It is water-weighted. This refers to the water head height.

7. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... The tangential stress on the slope caused by slope runoff in the slope runoff effect is calculated using the following formula: In the formula, The tangential stress on the slope is... It is water-weighted. For the thickness of the slope water flow, The slope angle is... For traffic, The velocity is the water flow velocity.

8. The method for simulating the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, as described in claim 1, is characterized in that... Based on the results of the rainfall simulation, determine whether slope instability or failure has occurred, including: Real-time monitoring of the system kinetic energy and the number of fractures of the quadrilateral elements in the numerical model; When the rate of change of the system's kinetic energy exceeds a first preset threshold, and / or the rate of change of the number of fractures exceeds a second preset threshold, slope instability and failure are determined to have occurred.

9. A simulation system for the instability and failure of a reverse-dip slope with alternating layers of soft and hard layers under rainfall conditions, characterized in that, include: Model building unit, used to build FDEM numerical model of target soft-hard interlayered reverse slope; An initial configuration unit is used to set boundary conditions for the numerical model and apply initial gravity until a stress equilibrium state is reached. Simulation unit, used for: Based on a numerical model of stress balance, rainfall simulation is performed. During the rainfall simulation, the infiltration depth of rainwater in the weak layer of the numerical model is calculated, and the strength degradation effect of the weak layer, the weight gain effect of the rock mass, the pore water pressure buoyancy effect and the slope runoff effect caused by rainwater infiltration are simulated simultaneously. Based on the results of the rainfall simulation, determine whether slope instability or failure has occurred; If no load increase occurs and the conditions for load increase are met, then while maintaining the rainfall simulation, a gravity load increase simulation is performed until slope instability and failure occur; during the gravity load increase simulation, the gravity load is gradually increased on the numerical model according to the preset increment; The loading conditions are reaching a preset rainfall duration and / or the change in rainwater infiltration rate within a preset time period being less than or equal to a preset value. Based on the critical gravity load at which the slope becomes unstable, the slope safety factor of the target soft-hard interlayered reverse slope under rainfall conditions is determined. The boundary conditions include: the lateral boundary is free during the initial gravity loading stage, fixed in the horizontal direction during the rainfall simulation stage and the gravity loading simulation stage, the bottom boundary remains fixed in the vertical direction, and both the bottom boundary and the lateral boundary are impermeable boundaries.

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