Reservoir water storage induced reservoir bank landslide prediction method and system based on refraction principle

Abstract

This application discloses a method and system for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction. The method includes: obtaining the natural slope angle above water in the natural state and the stable slope angle underwater in the saturated state of the target reservoir bank slope; introducing and calculating the refractive index to characterize the degree of difference between the natural slope angle above water and the stable slope angle underwater; the introduction of the refractive index is based on the understanding of landslide mechanisms: during reservoir impoundment, the water surface acts as an interface for abrupt changes in the physical and mechanical properties of the soil and rock mass, leading to a discontinuous reconstruction of the slope's stable morphology with the water surface as the boundary. The reservoir impoundment process follows the principle of mass conservation, and the actual inclination angle of the failure surface, instead of the natural slope angle above water, better reflects the mechanical state of the slope during instability; based on the value of the refractive index, the instability risk and progressive failure range of the target reservoir bank slope during reservoir impoundment are qualitatively or quantitatively predicted. This application improves the early risk identification and dynamic warning capabilities for reservoir bank landslides induced by impoundment.

Description

Technical Field

[0001] This application relates to the field of reservoir bank landslide prediction technology, and in particular to a method and system for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction. Background Technology

[0002] Currently, landslides pose a significant geological risk to the safety of transportation infrastructure in mountainous areas, and their occurrence is often significantly influenced by dynamic changes in hydrological conditions. During reservoir impoundment, the reservoir bank slopes are subjected to long-term infiltration, and the physical and mechanical parameters of the soil and rock mass (such as cohesion and internal friction angle) deteriorate due to the loss of matrix suction and water chemical softening, resulting in significant differences in stability between the above-water and underwater parts. Traditional reservoir bank landslide research has largely focused on the dynamic water pressure or seepage instability mechanism caused by a sudden drop in water level, paying insufficient attention to the gradual failure process induced by abrupt changes in soil and rock strength during the continuous rise in water level. Especially in high dam reservoir areas, the bank slopes often exhibit a discontinuous morphological reconstruction phenomenon of "steeper slope angle above water and gentler slope angle below water." Existing stability evaluation methods still generally use a uniform slope angle or static safety factor for analysis, making it difficult to accurately characterize the morphological evolution and instability mechanism caused by the water surface as an interface of abrupt changes in mechanical properties.

[0003] In recent years, although technologies such as integrated "space-air-ground" monitoring and point safety factor models have improved landslide early warning capabilities, quantitative understanding of the intrinsic mechanisms by which long-term, slow disturbances such as reservoir impoundment drive the transformation of riverbanks from a stable to an unstable state remains lacking during the survey and design phases of major engineering projects. For example, the right bank landslide of the Hongqi Grand Bridge at the Shuangjiangkou Hydropower Station occurred during the period of rising water levels. Its failure mode was characterized by a progressive, traction-driven collapse developing from the toe of the slope upwards, which is significantly different from the characteristics of conventional landslides, exposing the shortcomings of the current risk assessment system in mechanism modeling and process prediction. Therefore, it is urgent to establish a new prediction method that can reflect the differences in soil and rock conditions above and below water to improve the early risk identification and dynamic early warning capabilities for reservoir bank landslides induced by water impoundment. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies and establish a novel prediction method that can reflect the differences in soil and rock conditions above and below water, thereby improving the early risk identification and dynamic warning capabilities for reservoir bank landslides induced by water storage, this application provides a prediction method and system for reservoir bank landslides induced by water storage based on the principle of refraction.

[0005] Firstly, the objective of this invention is achieved through the following technical solution: Methods for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction include: Obtain the natural slope angle and soil parameters of the target reservoir bank slope in its natural state, and the relationship between the stable slope angle and soil parameters in the underwater state under saturated water conditions. Based on the difference between the natural slope angle above water and the stable slope angle underwater, a refractive index characterizing the degree of difference is introduced and calculated; The introduction of the refractive index is based on the following understanding of the slope mechanism: During the reservoir impoundment process, the water surface serves as the interface for the abrupt change in the physical and mechanical properties of the soil and rock, resulting in a discontinuous reconstruction of the slope stability mode with the water surface as the boundary. The above-water and underwater parts tend to the limit equilibrium slope angle controlled by their respective effective strength parameters. The reservoir impoundment process follows the principle of mass conservation, and the actual failure surface inclination angle, instead of the natural slope angle above the water, can better reflect the mechanical state when the slope is unstable. Based on the value of the refractive index, the instability risk and progressive damage range of the target reservoir bank slope during the reservoir impoundment process can be qualitatively or quantitatively predicted.

[0006] By adopting the above technical solution, this application introduces the dimensionless parameter "refractive index" to quantitatively characterize the discontinuous reconstruction characteristics of the above-water and underwater stable morphology caused by the water surface as a sudden interface of abrupt changes in the mechanical properties of soil and rock. This effectively solves the prediction bias problem caused by neglecting the difference in strength parameters before and after immersion in existing stability analyses, and breaks through the limitations of the traditional assumption of the same slope angle. Simultaneously, to reveal and model the progressive failure mechanism of reservoir bank landslides during the water storage rise period, based on the principle of mass conservation, a physical relationship is established between the collapse of the above-water slope and the reshaping of the underwater slope. This allows the prediction results to not only determine whether instability has occurred, but also to quantitatively assess the expansion trend of the landslide damage range and the critical water level threshold, significantly improving the early risk identification capability for "gradual traction" landslides. This application uses the actual failure surface dip angle (β) instead of the natural above-water slope angle (θ) as a representative parameter of the above-water state, more realistically reflecting the mechanical response state when the slope becomes unstable. This is particularly suitable for complex reservoir banks that have already deformed or have historical sliding traces, avoiding the underestimation of risk caused by using the initial topographic slope angle. This application, with physical mechanisms at its core, measurable parameters as its foundation, and quantitative indicators (refractive index, limiting water level) as its output, can be integrated into a "space-air-ground" monitoring and early warning system. It provides dynamic risk assessment criteria with clear physical meaning and engineering operability for major transportation infrastructure (such as bridges, tunnels, and pipelines) traversing reservoir areas, supporting scientific decision-making and resilient design. Therefore, this application enhances the early risk identification and dynamic early warning capabilities for reservoir bank landslides induced by water storage.

[0007] In a preferred embodiment of this application, the refractive index is calculated using the following formula: Alternatively, when the actual failure surface dip angle β is known, the expression used is: The natural slope angle θ above water and the stable slope angle α underwater are determined through the following steps: Samples were taken from the target reservoir bank soil and rock mass, and the shear strength parameters of the target reservoir bank soil and rock mass under natural water content and saturated conditions were tested respectively. The cohesion c and internal friction angle under natural conditions were obtained. γ, unit weight, and effective cohesion under saturation. Effective internal friction angle buoyancy ; (b) Determine the representative height h and pore water pressure of the potential sliding body based on the plane sliding assumption. The maximum slope angles of the target reservoir bank rock and soil mass that reach the limit equilibrium state under the natural water content state and the saturated state are obtained by using the limit equilibrium conditions, and are respectively taken as θ and α. Based on the ultimate height of the soil column above the shear surface with an actual failure angle of β, the potential sliding body is analyzed using limit equilibrium conditions. The value of the most unfavorable shear surface angle β is calculated through the characteristics of the soil and rock mass. The expression for calculating angle β is: .

[0008] By adopting the above technical solution, the calculation method of refractive index n is determined, and it is stipulated that the slope angle above or below water must be obtained through limit equilibrium condition inversion based on measured soil and rock strength parameters (c, φ, γ and their corresponding values ​​in saturation state), which significantly improves the scientific nature and operability of parameter acquisition. Compared with the rough estimation relying on empirical slope angles or remote sensing inversion, this method establishes the refractive index on the basis of physical and mechanical testing, ensuring the authenticity of the input parameters; at the same time, the actual failure surface dip angle β is introduced as a better alternative, so that the refractive index can dynamically reflect the mechanical state of the slope after deformation, avoiding misjudgment of the stability of potential landslides due to excessive optimism.

[0009] In a preferred embodiment of this application, the natural slope angle above water and the stable slope angle underwater are determined by the strength parameters of the soil and rock mass under the corresponding states through limit equilibrium conditions. For a given actual failure surface dip angle β, the corresponding slope limit height satisfy: in, These represent the unit weight, cohesion, and angle of internal friction in their natural state; when used underwater, they are replaced with buoyant unit weight. Effective cohesion and effective internal friction angle .

[0010] By adopting the above technical solution, the determination of the natural slope angle above water and the stable slope angle underwater is combined with the classical limit equilibrium equation. This direct correlation enables analytical derivation from soil and rock strength parameters to critical slope angles. It eliminates reliance on subjective experience or static topographic data, allowing slope angles to be determined by multiple measurable physical quantities such as unit weight, cohesion, and internal friction angle. This is particularly suitable for analyzing potential sliding surfaces at different heights or depths. When applied to underwater conditions, the influence of buoyancy and pore water pressure is accurately considered by replacing these parameters with buoyant unit weight and effective strength parameters.

[0011] In a preferred embodiment of this application, the prediction method further includes: Based on the principle of mass conservation, an equivalence relationship is established between the mass of rock and soil lost above the water surface due to instability and the mass of rock and soil required below the water surface to form a new stable slope. Using the aforementioned quantitative relationships, combined with the current reservoir water level and depth, the natural slope angle above water, the stable slope angle underwater, and the actual inclination angle of the failure surface, the critical instability range of the above-water slope is calculated. Based on the changing trend of the critical instability range with the rise of water level, the location of the landslide failure front in the next stage is predicted to determine whether the risk of stepwise instability is triggered, and the landslide instability prediction result is output.

[0012] By adopting the above-mentioned technical solution and based on the principle of mass conservation, an equivalence relationship between the above-water collapse volume and the underwater filling volume was established, and this relationship was transformed into a calculable tool for predicting the critical instability range. This breaks through the limitation of traditional landslide analysis, which only focuses on the overall safety factor, and for the first time incorporates the physical essence of "progressive failure"—material migration and morphological reconstruction—into a quantitative prediction framework. By combining the current water level, slope angle parameters, and the actual inclination angle of the failure surface, the system can dynamically output the location of the next stage of failure front, achieving a forward-looking assessment of the "step-by-step" landslide evolution process.

[0013] In a preferred embodiment of this application, the method further includes: calculating the limiting water level depth. The extreme water level depth refers to the critical water depth corresponding to the extent that the landslide damage extends to the top of the slope; Among them, the Calculate using the following steps: Obtain the total height H, the natural slope angle θ above water, and the stable slope angle underwater of the target reservoir bank slope. and the actual dip angle of the damaged surface. ; (b) Based on the limit equilibrium condition, calculate the slope limit height corresponding to the actual failure surface dip angle β. ,satisfy: or , make Solving using geometric compatibility relations The geometric compatibility relationship is as follows: , The geometric compatibility relationship can be verified by the horizontal compensation distance OR at the water surface, where OR represents the horizontal projection offset formed by the intersection of the original slope, the actual failure surface, and the underwater stable slope under extreme water level conditions: .

[0014] By adopting the above technical solution, the extreme water level depth is constructed. The complete calculation process deeply integrates geotechnical mechanics parameters, geometric morphology, and failure mechanisms, achieving precise positioning of the "critical point of total instability." The core lies in: firstly, using the limit equilibrium equations to solve for the limit height corresponding to the actual failure surface dip angle β. On the other hand, the mechanical results are mapped to the real slope space through geometric compatibility relations (including horizontal compensation distance OR). This method overcomes the existing practice of relying on historical statistics or safety margins for setting water level thresholds, and instead derives critical water depths with clear engineering significance based on physical mechanisms.

[0015] In a preferred embodiment of this application, the method further includes verifying and calibrating the refractive index calculation model through physical model experiments, wherein the physical model experiments employ immersion-controlled water operation to simulate the dynamic change process of soil and rock cohesion. First, the artificially prepared loose slope model is completely submerged in still water to saturate the loose slope model and form a stable underwater slope angle α. Subsequently, the drainage rate is controlled to slowly lower the water level, allowing the surface moisture of the loose slope model to evaporate or be discharged, restoring the apparent cohesion generated by capillary negative pressure, so as to form a natural slope angle θ on the water. By comparing the slope evolution parameters and collapse variation range at different water level stages, the actual failure surface dip angle β is inverted and used to correct the calculation parameters of refractive index n.

[0016] By employing the above technical solution, the dynamic change of soil cohesion with water content was simulated, providing a verifiable experimental platform for the refractive index calculation model. The problem of quantifying "apparent cohesion" in the theoretical model was solved: by first immersing the soil to eliminate capillary forces and form a stable underwater slope angle α, and then controlling the water flow to restore negative pressure and reconstruct the natural surface slope angle θ, the mechanical response of the reservoir bank slope during the water storage-drawdown cycle was realistically reproduced. The slope evolution and collapse range obtained from the experiment can be used to invert the actual failure surface dip angle β, and then calibrate the refractive index parameters.

[0017] Secondly, the objective of this invention is achieved through the following technical solution: A reservoir impoundment-induced landslide prediction system based on the principle of refraction, the system comprising: The data acquisition module is used to acquire the natural slope angle and soil parameters of the target reservoir bank slope in its natural state, and the relationship between the underwater stable slope angle and soil parameters in the saturated state. The refractive index calculation module is used to introduce and calculate the refractive index that characterizes the degree of difference between the natural slope angle above water and the stable slope angle below water, based on the difference between the natural slope angle above water and the stable slope angle below water. The introduction of the refractive index is based on the following understanding of the slope mechanism: During the reservoir impoundment process, the water surface serves as the interface for the abrupt change in the physical and mechanical properties of the soil and rock, resulting in a discontinuous reconstruction of the slope stability mode with the water surface as the boundary. The above-water and underwater parts tend to the limit equilibrium slope angle controlled by their respective effective strength parameters. The reservoir impoundment process follows the principle of mass conservation, and the actual failure surface inclination angle, instead of the natural slope angle above the water, can better reflect the mechanical state when the slope is unstable. The risk prediction module is used to qualitatively or quantitatively predict the instability risk and progressive damage range of the target reservoir bank slope during the reservoir impoundment process, based on the value of the refractive index.

[0018] Thirdly, the objective of this invention is achieved through the following technical solution: A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-described method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction.

[0019] Fourthly, the objective of this invention is achieved through the following technical solution: A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction.

[0020] In summary, this application includes at least one of the following beneficial technical effects: 1. This paper proposes for the first time the physical analogy model of "slope refraction effect," abstracting the difference in stable slope angle caused by abrupt changes in strength parameters between the above-water and underwater soil and rock masses during reservoir impoundment into a quantifiable "refractive index" parameter. It breaks through the limitations of traditional slope stability analysis that relies on a uniform slope angle or static safety factor. Starting from the mechanical essence, it reveals the slope reconstruction mechanism triggered by the water surface as a discontinuous interface, achieving a mechanistic description of reservoir bank landslides during the rising water level period, especially the cascading traction-type failure. This provides a completely new theoretical framework for explaining the long-neglected problem of "disasters caused by slowly rising water levels." 2. A quantitative prediction system integrating limit equilibrium theory, the principle of mass conservation, and geometric compatibility relations was constructed: the stable slope angle above / below water was inverted through measured soil and rock parameters, and the actual failure surface dip angle was introduced to improve the calculation accuracy; the expansion trend of the instability range was predicted using volume equality relationships; and the ultimate water level depth was derived. As a key early warning threshold. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the "refraction" principle of slope immersion in a water storage-induced landslide prediction method based on the principle of refraction in one embodiment of this application. Figure 2 This is a stability zoning diagram of soil column height and different shear surface inclination angles in a reservoir impoundment-induced landslide prediction method based on the principle of refraction in one embodiment of this application. Figure 3 This is a geometric diagram of slope refraction failure in a reservoir impoundment-induced landslide prediction method based on the principle of refraction in one embodiment of this application; Figure 4 This is an experimental diagram showing the contribution of cohesion to slope angle in a method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, according to an embodiment of this application. Figure 5 This is a schematic diagram of a device according to one embodiment of this application. Detailed Implementation

[0022] The present application will be further described in detail below with reference to the accompanying drawings.

[0023] In one embodiment, this application discloses a method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, which specifically includes the following steps: S1: Obtain the natural slope angle and soil parameters of the target reservoir bank slope in its natural state, and the relationship between the stable slope angle and soil parameters underwater in a saturated state.

[0024] In this embodiment, the above-water natural slope angle θ refers to the ultimate stable slope angle that the target reservoir bank slope can maintain due to the strength of its own rock and soil when it is not affected by the current reservoir water storage and is in a state of natural water content; the underwater stable slope angle α refers to the new ultimate stable slope angle that the same slope can maintain after being fully submerged and saturated, under the influence of buoyancy, pore water pressure and rock and soil softening effect; the rock and soil parameters include the above-water natural slope angle, the underwater stable slope angle, etc.

[0025] This embodiment proposes a conceptual model based on the actual soil and rock parameters and morphological characteristics of the landslide body, using the water surface as the boundary, where the morphology of the landslide body undergoes a "refractive" change. Based on the landslide phenomenon that occurs during a period of continuous rise in reservoir water levels, the technical characteristic of the "refractive" effect of the slope is introduced; refraction is a common phenomenon in physics. For example... Figure 1 As shown in (a), the original slope line is CB; when the water level rises to height h, the water surface and the slope intersect at point O. According to the principles of soil mechanics, due to the difference between the underwater slope angle α and the natural slope angle θ above water, the slope morphology will undergo a change similar to "refraction" with the water surface as the boundary. Its physical essence lies in the significant difference in the stability mechanisms of the soil and rock masses above and below water. This difference is the result of the combined effects of factors such as unit weight (γ), cohesion (c), internal friction angle (φ), and the hydrochemical properties of the cementing substances between particles, ultimately manifesting as a difference between the natural slope angle θ above water and the stable slope angle α below water. Given the similarity of this phenomenon to optical refraction, it is called the "refraction" effect of slopes.

[0026] Under the influence of refraction, the slope is submerged by still water from its toe. As the water depth h increases, material compensation is needed to maintain a stable underwater slope angle. Under natural conditions, this compensation can only be achieved through the collapse and displacement of the near-water slope surface, which weakens the support of the above-water slope angle. As the water level rises, this phenomenon gradually expands, leading to a larger-scale landslide. Figure 1 As shown in (b), the higher the water level, the greater the mass required to rebuild underwater stability and equilibrium, and the greater the amount of landslides caused by the resulting water slope collapses.

[0027] Specifically, to analyze the impact of water level fluctuations on slope stability, the following simplified model is used for derivation: the natural geological body is considered as a homogeneous semi-infinite spatial body, and its cross-section is used for two-dimensional analysis. Under the combined influence of internal factors such as unit weight, cohesion, internal friction angle, and intergranular bonding mineral characteristics, as well as external factors such as gravity, buoyancy, and water, there are significant differences between the natural slope angle (θ) above water and the underwater stable slope angle (α) of the same soil mass.

[0028] Taking a conical slope as an example (its half-section is as follows) Figure 1 As shown in (a), when the still water level rises to height h, the submerged portion needs to maintain stability with a gentler slope angle α. To re-establish stability underwater, the OBD slope area requires additional soil replenishment, which is ideally supplied by the slope above the water surface (assuming total material conservation). Under the influence of gravity, the above-water slope near the water surface transports material to the underwater slope toe (OBD area) through sliding, rolling, and collapse until the entire system is re-equilibrium.

[0029] As the water level continues to rise ( Figure 1(b) The above process occurs repeatedly: as the water depth increases from 0 to h1, h2, and h3, in order to meet the requirements of the underwater stable slope angle at different water depths, the corresponding unstable supply area of ​​the water surface slope also expands from S1 to S2 and S3 along the slope surface, and the scale gradually increases.

[0030] Furthermore, taking the right bank of the Hongqi Grand Bridge at the Shuangjiangkou Hydropower Station as an example, a high-precision digital elevation model (DEM) of the area was first obtained through UAV aerial surveying or ground laser scanning to preliminarily identify the potential unstable slope range. Subsequently, boreholes or trenches were laid at different elevations on the slope to collect undisturbed soil samples. The soil samples were divided into two groups: one group maintained at its natural moisture content, and the other group was saturated according to standard procedures. The shear strength parameters of the two groups of samples were tested using a direct shear tester or a triaxial apparatus, obtaining the cohesion c=12.5kPa and the internal friction angle under natural conditions. , bulk density and effective cohesion under saturation. Effective internal friction angle buoyancy .

[0031] S2: Based on the difference between the natural slope angle above water and the stable slope angle below water, a refractive index is introduced and calculated to characterize the degree of difference. The introduction of the refractive index is based on the following understanding of the slope mechanism: During the impoundment of a reservoir, the water surface serves as the interface for the abrupt change in the physical and mechanical properties of the soil and rock mass, resulting in a discontinuous reconstruction of the slope stability mode with the water surface as the boundary. The above-water and underwater parts tend to reach the limit equilibrium slope angle controlled by their respective effective strength parameters. The impoundment process of the reservoir follows the principle of mass conservation, and the actual failure surface inclination angle can better reflect the mechanical state of the slope when it becomes unstable, rather than the natural slope angle above water.

[0032] In this embodiment, the refractive index *n* is a dimensionless parameter used to quantify the degree of discontinuous slope reconstruction caused by the water surface as an interface of abrupt changes in mechanical properties. Specifically, to quantify the difference in stable slope angles above and below water, an optical analogy is used to introduce a "refractive index" parameter *n*, defined as the ratio of the tangent of the natural slope angle above water to the tangent of the stable slope angle below water. The calculation expression is as follows: Alternatively, when the actual failure surface dip angle β is known, the expression used is: The parameter n directly reflects the degree of change of the slope above and below water, and also reflects the amount of material transport required to maintain slope stability. If there are signs of deformation such as cracks or displacement on site, the actual inclination angle β of the failure surface is used; otherwise, the natural slope angle θ above water is used. The larger the value of n, the more significant the impact of the water environment, and the larger the range of slope instability above water that may be caused by rising water levels. During reservoir impoundment, the above-water portion tends to be controlled by the limiting slope angle θ, which is controlled by (c, φ, γ), while the underwater portion tends to be controlled by (c, φ, γ). The transition between the two, which involves a gentler slope angle α controlled by the water, is achieved through the collapse of the near-shore slope, a process that follows the principle of mass conservation.

[0033] The natural slope angle θ above water and the stable slope angle α underwater are determined through the following steps: (a) Samples were taken from the target reservoir bank soil and rock mass, and the shear strength parameters of the target reservoir bank soil and rock mass under natural water content and saturated conditions were tested respectively. The cohesion c, internal friction angle ϕ, and unit weight γ under natural conditions were obtained, as well as the effective cohesion c', effective internal friction angle ϕ', and buoyant unit weight γ' under saturated conditions. (b) Determine the representative height h and pore water pressure of the potential sliding body based on the plane sliding assumption. The maximum slope angles of the target reservoir bank rock and soil mass that reach the limit equilibrium state under the natural water content state and the saturated state are obtained by using the limit equilibrium conditions, and are respectively taken as θ and α.

[0034] Based on the ultimate height of the soil column above the shear surface with an actual failure angle of β, the potential sliding body is subjected to equilibrium analysis using limit equilibrium conditions, and the value of the most unfavorable shear surface angle β is calculated through the characteristics of the soil and rock mass.

[0035] For example, taking the landslide area on the right bank of the Hongqi Grand Bridge at the Shuangjiangkou Hydropower Station as the research object, three exploratory wells were set up at different elevations to collect undisturbed weathered residual soil samples from granite. Each sample group was divided into two parts: one part was kept at its natural moisture content (approximately 18.5%), and the other part was vacuum saturated according to the "Standard for Geotechnical Testing Methods" (GB / T 50123). Subsequently, shear tests were conducted using a strain-controlled direct shear apparatus under normal stresses of 100 kPa, 200 kPa, and 300 kPa. The following parameters were obtained by fitting the Mohr-Coulomb envelope: Natural moisture content: cohesion c = 12.5 kPa, internal friction angle bulk density ; Saturated state: effective cohesion Effective internal friction angle buoyancy (in (The density of water). Secondly, in step (b), the planar sliding assumption simplifies the potential sliding surface to a plane with a constant inclination angle, applicable to homogeneous or near-homogeneous loose-body slopes. The representative height h refers to the average thickness of the potential sliding body in the direction perpendicular to the sliding surface, which can be initially estimated through geological profiles or monitoring data.

[0036] Furthermore, the mass conservation violation mechanism under the refraction effect includes: based on the aforementioned slope angle "refraction" effect, consider a homogeneous slope whose initial profile is a triangle ABC in static equilibrium, such as... Figure 1As shown in (a), when the water body is submerged to depth h (to point O), the underwater slope, under the combined effects of buoyancy, weakening of water chemistry, and gravity, adjusts the stable slope angle from θ to a gentler α. The pore water pressure u is typically small under natural conditions and can be approximated as 0; under saturated conditions, if it is still water, then... Where z is the burial depth of the sliding surface. However, in the infinite slope model, the buoyancy effect is often directly represented by the buoyant unit weight. This avoids explicit calculation of u. θ is the limit stability slope angle (not the measured topographic slope angle) inverted from (c, φ, γ) under natural conditions; β is the actual main slip surface dip angle inverted by monitoring only when there are signs of deformation such as cracks and displacement on site.

[0037] A gentler slope angle causes the length of the underwater slope surface OB to increase from OD, thus forming an additional wedge-shaped region OBD (the area of ​​which can be expressed as...) within a unit width, which needs to be filled by rock and soil. Under the ideal assumption of no external material replenishment and neglecting lateral extrusion of the underwater slope, the additional material required to fill this area must all come from the near-water surface portion of the above-water slope.

[0038] Therefore, the water-surface slope near point O will continuously replenish the underwater portion with material through sliding, rolling, and collapse. This process will continue until a new slope morphology is formed that can maintain its static equilibrium under the current (after water-rock interaction) strength parameters.

[0039] In this idealized closed system, the law of conservation of mass applies, meaning that the mass lost by the above-water portion due to erosion (m1) is equal to the mass gained by the underwater portion to construct the new slope (m2).

[0040] In natural environments, soil and rock masses typically possess both cohesion and an internal friction angle, and their shear strength conforms to the Mohr-Coulomb criterion. Therefore, a slope with an angle of (θ) is a slope angle that temporarily maintains the slope body in a stable state under natural conditions (or artificially formed conditions). It is jointly controlled by internal factors such as the unit weight (γ), cohesion (c), and internal friction angle (φ) of the soil and rock mass, and external factors such as load, water, and morphology.

[0041] Consider a simple and representative model—an infinite slope. Take an arbitrary vertical column of soil on the slope with an angle of (θ). For example... Figure 2As shown, let the horizontal cross-sectional area of ​​the soil column be A. There is a shear plane with a full cross-section and an inclination angle of β within the soil column. Ignoring the interaction between the surrounding soil and the soil column, under the interaction of the maximum ultimate height hmax of the stable soil column above the shear plane, the inclination angle β of the shear plane, the unit weight γ, the cohesion c, and the internal friction φ, the soil above the shear plane reaches a limit stability state on the shear plane, i.e., when the sliding force equals the resisting force, reaching a limit equilibrium state. Let A be the cross-sectional area of ​​the soil column. Taking a unit width A = 1, for a given actual failure surface inclination angle β, what is the corresponding slope limit height? satisfy: in, These represent the unit weight, cohesion, and angle of internal friction in their natural state; when used underwater, they are replaced with buoyant unit weight. Effective cohesion and effective internal friction angle .

[0042] From equation (2), we can see that the shear surface inclination angle β and the limit height of the soil column above the shear surface are mutually restrictive. When the soil and rock properties (γ, c, φ) are constant, the soil column on the shear surface is stable in region I where β < φ and the soil column height is less than hmax; the soil column on the shear surface is unstable in region III where the shear surface inclination angle β > φ and the soil column height is greater than hmax; if a natural slope is in this state, it will be damaged to adjust to a stable region; a slope that is naturally stable for a long time usually falls in region I or region II.

[0043] Next, we need to analyze the relationship between the natural slope angle θ, the shear plane inclination angle β, and the refractive index n: Under the influence of internal and external factors of soil and rock, a homogeneous slope in its natural state usually has a relatively stable slope angle θ. However, field investigations have found that due to differences in soil and rock properties and environmental conditions, the natural slope angle θ varies and is not unique, for example, in zigzag slopes, parabolic slopes, etc.

[0044] Under certain conditions, when a slope is infiltrated by water and the water level is at a certain height on the slope, the portion above the water surface may become unstable and fail. For example... Figure 3 As shown, for a slope with a natural slope angle of θ, failure occurs in still water at a depth of h. The actual slip surface is located at EK, and its dip angle β is one of the many potential slip surfaces that ultimately fail. After failure, a new slope surface EKO is formed, and the original natural slope surface EO no longer exists.

[0045] When the water level rises above KG, it is not advisable to continue using θ in the slope angle calculation related to slope stability. Instead, the dip angle β of the actual failure surface (or the newly formed slope angle) should be used. As for the KO section, which is an extension of the OD underwater slope angle, the influence of its slope change is extremely weak within this range, that is, the slope angle of the above-water part is similar to that of the underwater part α.

[0046] Figure 3 In the diagram, ∠EKJ=β is the dip angle corresponding to the actual failure surface, and the slope failure limit height corresponding to this dip angle is hmax. Using equation (2) and the sum and difference angle relationships of trigonometric functions, the dip angle β of the failure surface is solved as follows: .

[0047] During the process of slope failure due to water immersion, the inclination angle of the new slope shear surface formed by the collapse is often inconsistent with the natural slope angle. In this inconsistency, it is more reasonable to use the inclination angle β of the new slope failure surface to calculate the refractive index than to use the natural slope angle. Assuming that the soil and rock properties above water are (γ, c, φ) and the soil and rock properties after water immersion are (γ', c', φ'), the relationship between the refractive index and the main soil and rock properties above and below water is obtained by combining equations (1) and (3): .

[0048] like Figure 3 As shown, a slope with a height AB = H fails under the action of water immersion. The water level at which the highest failure point E coincides with point A is called the limit water level. .

[0049] Therefore, the methods for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction also include: S201: Based on the principle of mass conservation, establish the equivalence between the mass of rock and soil lost above the water surface due to instability and the mass of rock and soil required below the water surface to form a new stable slope.

[0050] In this embodiment, the principle of mass conservation specifically refers to the following: under ideal conditions of no external material input and negligible lateral extrusion, after the reservoir impoundment causes the underwater slope angle to adjust from θ to a gentler α, the resulting additional wedge-shaped space (the area to be filled) must be completely compensated by the soil and rock mass provided by the near-shore slope collapse above water. Figure 3 As shown, when the fracture surface is damaged, a new slope EKO is formed, and the original natural slope EO no longer exists. At this time, a new area that needs to be filled is formed. That is, during the process of reservoir impoundment, when the above-water part collapses due to loss of support, the lost rock and soil must be used to fill the "gap" area created by the adjustment of the slope angle from θ to α in the underwater part.

[0051] For example, such as Figure 3As shown: the original slope is a straight line AC with an inclination angle of θ (natural slope angle above water); the water surface is located on the horizontal line OT, with a water depth of h; the underwater stable slope angle is α (red line OD), which is gentler than the original slope angle; the actual failure surface is EKJ, with an inclination angle of β, which is a potential sliding surface extending downward from point E; EKJ intersects the water surface at point O and the original slope at point E, with J being the foot of the perpendicular. It is the slope limit height corresponding to the slope inclination angle β of the failure surface.

[0052] according to Figure 3 As shown, when the water level rises to OT, the underwater portion needs to be adjusted from the original slope OC to a new stable slope OD, thus forming a wedge-shaped gap region OCD below the water surface (C is the intersection of the original slope and the extended line of the slope toe, and D is the intersection of the new slope and the slope toe). The volume of this region is the "underwater volume to be replenished".

[0053] Simultaneously, the above-water portion slid down from point E along the failure surface EKJ, forming a collapse body in the triangular region EJK. The volume of this region is the "above-water loss volume".

[0054] According to the law of conservation of mass, the two should be equal: .

[0055] S202: Using the equal relationship, combined with the current reservoir water level and depth, the natural slope angle above water, the stable slope angle underwater, and the inclination angle of the actual failure surface, calculate the critical instability range of the slope above water.

[0056] In this embodiment, the critical instability range refers to the distance from point O on the water surface upwards along the horizontal direction to the collapse starting point E, as shown in the figure. , or simplified to the horizontal projection length x.

[0057] Specifically, calculate the underwater filling volume. Let the current water depth of the reservoir be h (i.e., the vertical distance from point O to the horizontal reference plane). In right triangle OCT (T is the projection of the slope toe directly below point O), the horizontal projection length of segment OC is:

[0058] In the right triangle ODT, the horizontal projection length of segment OD is: .because ,have Therefore, the new slope OD is gentler than the original slope OC, and its horizontal projection is longer.

[0059] Therefore, the length of the base (horizontal direction) of triangle OCD is:

[0060] The height of triangle OCD is equal to the water depth h, therefore its area (volume per unit width) is:

[0061] Right now: .

[0062] Next: Calculate the volume of water loss. The water-borne collapse body is the soil that slides out along the actual failure surface at an angle β. Let its ultimate height be... That is, the vertical height difference from the damage front E to the water surface O, such as Figure 3 middle .

[0063] The projected length of the sliding body in the horizontal direction is The cross-section of the sliding body is a right triangle with an area of... Therefore, the volume of the slide per unit width is:

[0064] Solve the mass conservation equations simultaneously, let ,have to:

[0065] Summarized as follows: .

[0066] S203: Based on the trend of the critical instability range changing with the rise of water level, predict the location of the landslide failure front in the next stage to determine whether the risk of stepwise instability is triggered, and output the landslide instability prediction results.

[0067] In this embodiment, the position of the destruction front E on the horizontal plane can be determined by... Determined. Substituting equation (5) into the equation, we get: Equation (6) shows that the critical instability range x increases linearly with water depth h and is sensitive to α and β.

[0068] To illustrate further, let's continue with the Shuangjiangkou case mentioned above: Known h = 5.0m. Therefore... , , .but .

[0069] In other words, when the water depth is 5.0m, the horizontal range of approximately 2.59m above the water is in a critical instability state. If this range is close to the bridge abutment (30m from the toe of the slope), an early warning is required. As the water level rises, x continues to increase, and the fault front moves upward, forming a "gradual traction" pattern. When x reaches a certain threshold (e.g., 10% of the slope height), the system automatically triggers a yellow warning.

[0070] S3: Based on the refractive index value, qualitative or quantitative predictions are made on the instability risk and progressive damage range of the target reservoir bank slope during the reservoir impoundment process.

[0071] In this embodiment, qualitative prediction refers to quickly identifying the possibility of instability of the reservoir bank slope during reservoir impoundment by judging whether the refractive index n is greater than 1. The criterion is based on the physical nature of the "refractive effect": when the tangent value corresponding to the natural slope angle above water (or the actual slope angle of failure) is greater than the tangent value of the stable slope angle underwater, it indicates that the underwater part cannot maintain the original slope shape and must be compensated by the collapse of the above-water material, thereby triggering progressive failure.

[0072] Specifically, qualitative judgments include: Define refractive index: If initial terrain parameters are used, then If the slope has already deformed, the actual dip angle β of the failure surface should be used first, i.e. .

[0073] In this embodiment, the risk assessment rules are as follows: When n≤1, it indicates that the underwater stable slope angle α is not less than the natural slope angle above water (or the inclination angle of the failure surface), and the slope tends to be more stable or remains stable after water impoundment, and is judged as low risk; When n>1, it indicates that the above-water part is relatively steeper and the underwater part needs a gentler slope, which means there is a need for morphological reconstruction and is judged to be at risk of instability. When n≥1.2, it indicates a significant difference, which may trigger a large-scale collapse at a lower water level, and is judged as high risk.

[0074] Specifically, quantitative prediction refers to, based on qualitative judgment, further calculating the critical instability range, the location of the damage front, and whether it is approaching key structures corresponding to different water level stages, thereby outputting graded early warning signals.

[0075] Specifically, the refractive index n is linked to the mass conservation model in claim 4. It can be seen that cotα>cotβ, substituting into equation (6) yields the range of instability levels on the water: .

[0076] In another embodiment: n can be used as input to back-calculate β or check α, and then substituted into the volume balance equation.

[0077] The implementation process is as follows: Obtain the future reservoir scheduling curve and extract key water level nodes (e.g., 2500m, 2510m, 2520m). For each water level, calculate the corresponding water depth h; Calculate n based on the current soil and rock parameters (c, φ, γ, etc.) and the measured β; If n>1, then use equations (5) and (6) to calculate. With x; Superimpose x onto the original terrain to determine the elevation of the destruction front; determine whether the front enters the bridge abutment, tunnel entrance, or pipeline protection zone.

[0078] For example, taking the Shuangjiangkou project as an example, the bridge abutment foundation is located approximately 30m horizontally above the slope toe; the current water depth h=5.0m, and the calculated x≈2.59m, the failure front is only 2.6m from the slope toe, far from the bridge abutment, and the risk is controllable; if future rainfall causes... When the pressure is reduced to 5.0 kPa, α decreases to 34°, then cotα = 1.483, n = tan(38°) / tan(34°) ≈ 0.781 / 0.675 ≈ 1.16.

[0079] At this point, x = 5.0 × (1.483 − 1.143) × 1.280 ≈ 5.0 × 0.340 × 1.280 ≈ 5.0 × 0.660 ≈ 3.30 m; if the water level rises to 6.0 m, x ≈ 3.96 m, and the damage front continues to move upward; it is predicted that when the water level reaches 6.8 m and α ≤ 34°, x ≈ 4.5 m, although still much less than 30 m, but if superimposed with earthquakes or rainstorms, the evolution may be accelerated. Therefore, the system can output: "When n > 1.15 and water depth > 6.5 m, activate a yellow warning; when the damage front is < 10 m from critical facilities, activate a red warning."

[0080] Finally, the above analysis results were integrated into a standardized prediction report, including: refractive index n and its variation trend, critical instability range x and failure front coordinates at each water level, risk level (low / medium / high), and recommended measures. The risk levels are categorized as low, medium, and high. Recommended measures include enhanced monitoring, limiting the impoundment rate, and pre-reinforcement.

[0081] In one embodiment, such as Figure 3 As shown, a slope with height AB = H fails under the action of water immersion. The water level at which the highest failure point E coincides with point A is called the ultimate water level, where H is the total height of the target reservoir bank slope, the current water surface is at point O, and the water depth is h. When the failure front E moves up to the top of the slope A, the corresponding water depth is h. The method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction also includes: calculating the ultimate water level depth. The critical water level depth refers to the depth at which the landslide damage extends to the top of the slope. in, Calculate using the following steps: Obtain the total height H, the natural slope angle θ above water, and the stable slope angle underwater of the target reservoir bank slope. and the actual dip angle of the damaged surface. ; (b) Based on the limit equilibrium condition, calculate the slope limit height corresponding to the actual failure surface dip angle β. ,satisfy: or

[0082] make Solving using geometric compatibility relations The geometric compatibility relation is: .

[0083] In this embodiment, the maximum slope height This refers to the maximum vertical height at which a slope can maintain its limit equilibrium under given soil and rock parameters and a failure surface dip angle β. Its physical essence is that the height of the soil column reaches a critical value when the sliding force equals the resisting force.

[0084] Considering unit width and height as The soil column slides along a plane with an inclination angle β, and its weight is W = γ. According to the principle of limit equilibrium: Sliding force = Anti-slip force. That is... γh max sinβ=c+γh max cosβtanφ (Formula 2), rearranged, we get the first expression: Using trigonometric identities This yields the second commonly used form: Equation 9 approaches from above as β→ϕ, which conforms to the physical law that cohesive soil (c=0) cannot form a steep slope. Equation (8) is based on the limit equilibrium state of the detached body of the slope in Equation (2), that is, the safety factor of the detached body Fs=1 at this time, from which the limit height of the slope when the slope angle β is constant is derived. Equation 6 can be used to calculate the maximum height that a soil mass can maintain without support and gravity when the shear plane dip angle is assumed to be constant. Conversely, if the slope height is constant, the maximum slope angle β that the slope will not fail without support and gravity is shown in Equation 7.

[0085] For example, taking the Shuangjiangkou case as an example: Given c = 12.5 kPa, ϕ = 32°, The actual failure surface inclination angle β = 38°, substituting into equation (8):

[0086] That is, under the current soil and rock conditions, the failure surface can support a slope of up to about 5.45m in height.

[0087] From equation (8), we can obtain the slope height that can be maintained for a slope with a certain angle β≤φ. When the slope height is greater than At that time, failure will inevitably occur on the inclined plane with an angle of β. Conversely, according to (9) with a height of The slope angle of the stable failure surface that can be maintained is less than or equal to β. When the slope angle θ is greater than β, failure will inevitably occur on the failure surface with an inclination angle of θ, and the inclination angle of the failure surface will not be less than β.

[0088] (9) When c=0, β=φ, which is consistent with Coulomb's theory; for example, the stable limit slope angle of dry sand or sandy soil underwater is consistent with the stable slope angle above or below water.

[0089] When c>0, β>φ, which is consistent with common phenomena in the natural environment. The presence of cohesion provides an additional stability margin to the slope, enabling it to maintain a stable slope angle steeper than the internal friction angle. For example, water spraying is often used in sand pits to improve the stability of sand piles.

[0090] like Figure 3 As shown, the geometric compatibility relationship can be verified by the horizontal compensation distance OR at the water surface, where OR represents the horizontal projection offset formed by the intersection of the original slope, the actual failure surface, and the underwater stable slope under extreme water level conditions: Where OR is the horizontal distance from the intersection point O of the water surface and the original slope to the projection point R of the new sliding surface on the water surface under extreme water level conditions.

[0091] In this embodiment, geometric compatibility refers to the height of the water-based collapse when the failure front reaches the top of the slope. The total slope height H, the natural slope angle θ above water, the stable slope angle α underwater, and the dip angle β of the failure surface must satisfy the spatial geometric closure condition.

[0092] Specifically, such as Figure 3 As shown, draw a vertical line from the top of the slope A down to the water surface O, and then extend it along the new underwater slope surface OD to the foot of the slope. The entire slope is divided into three sections: Above water: Height Inclination angle β; Transition section at the water surface; Underwater section: Height , Inclination angle α.

[0093] Through geometric projection analysis, we can obtain: Equation (11) is derived from the limit height The difference between the total height H and the total height is derived through a trigonometric relationship to ensure that the failure surface extends from the top of the slope to the underwater stable toe.

[0094] In this embodiment, based on geometric compatibility, due to The value (5.45m) has been determined by equation (8), and the vertical difference between the top of the slope and the water surface is... The length of this segment along the failure surface β is Its horizontal projection is .

[0095] On the other hand, the horizontal projection is also equal to the horizontal distance from the top of the slope to point O minus OR:

[0096] Substituting equation (10) into the equation and rearranging, we get:

[0097] In another embodiment, a more direct approach can be adopted: that is, the height of the water-borne collapse is equal to the height difference between the top of the slope and the water surface, i.e.: This is the simplest and most physically clear approximation (suitable for situations where the slope angle does not change significantly). (The situation is as follows).

[0098] therefore: =32.0−5.45=26.55m. That is, when the reservoir water depth reaches approximately 26.6m, the failure front will extend to the top of the slope, triggering overall instability. This result is reasonable: water depth 26.6m < total height 32m, which conforms to common engineering sense.

[0099] Verify using OR: cotθ=1.143, cotβ=1.280, cotα=1.352. .

[0100] The negative sign indicates that point R is upstream of point O (closer to the top of the slope), which is consistent with... Figure 3 The trend and the numerical values ​​are reasonable.

[0101] Ultimately, Convert the water level to reservoir elevation (e.g., if the dam bottom elevation is 2500m, then the warning water level is 2500 + 26.55 = 2526.55m). It is recommended to set the following thresholds: yellow warning at water level ≥ 2520m (h = 20m), red warning at water level ≥ 2525m (h = 25m), and prohibiting water storage at water level ≥ 2526m. These thresholds can be directly written into the reservoir operation regulations to achieve mechanism-driven safety control.

[0102] In one embodiment, the method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction further includes: verifying and calibrating the refractive index calculation model through physical model tests. The physical model tests employ immersion-control operation to simulate the dynamic change process of soil and rock cohesion. S601: First, completely immerse the artificially prepared loose slope model in still water to saturate the loose slope model and form a stable underwater slope angle α.

[0103] In this embodiment, as Figure 4 As shown, two sets of intuitive experiments were first used to verify the physical fact that "water energy can significantly improve the stable slope angle of granular slopes", providing mechanistic support for subsequent modeling of refraction effects.

[0104] Experiment 1 (Sand Column Stacking Test): 120-mesh dry quartz sand, under anhydrous conditions, naturally stabilized at a slope angle of only 15°~19°. Subsequently, using a method of spray humidification and layered sand application, a nearly vertical sand cone approximately 10cm high was successfully stacked on a horizontal surface similar to a 2.5cm diameter one-yuan coin. Measurements showed that the average slope angle in the central area was close to 83°. This phenomenon indicates that moisture, through capillary meandering, creates tension between particles (i.e., the water meniscus effect), generating significant apparent cohesion, thus temporarily stabilizing the loose material that would otherwise be unable to maintain a steep slope.

[0105] Experiment 2 (Steel Ball Adhesion Test): A 1mm diameter steel ball was placed on a painted, tilted biscuit tin lid (30° angle). Under dry conditions, the steel ball immediately rolled off; however, after a small amount of water was added between the steel ball and the inclined surface, the steel ball remained stable and stationary. This further demonstrates that even on smooth surfaces, the adhesive force of water can provide an equivalent cohesive effect.

[0106] The above experimental results show that the moisture state (dry, unsaturated, saturated) in natural rock and soil directly affects its effective cohesion c, thereby controlling the ultimate stable slope angle.

[0107] Specifically, to simulate the mechanical behavior of real reservoir bank rock and soil (such as weathered residual soil of Shuangjiangkou granite), artificial granules were prepared according to specific proportions: Use 4-16 mesh and 120 mesh quartz sand, mixed at a dry mass ratio of 3:1; The measured natural slope angle above water is 40°~45°, and the stable slope angle underwater is 38°~42°. The dry density is 1.53 g / cm³, the bulk density after saturation with water and removal of free water is 16.6 kN / m³, and the moisture content is 8.9%~9.5%.

[0108] The experiment was conducted in a transparent acrylic water tank (39.5cm long × 30cm wide × 22cm deep). To prepare initial slopes at high angles (e.g., 50°, 60°, 70°), the "inclined trough method" was used: one end of the water tank was first raised to the target inclination angle, and sand was filled and shaped while the tank was tilted; then the water tank was slowly leveled, and gravity was used to create a steep slope. This method requires no external support and can accurately reflect the stability of granular materials without structural constraints.

[0109] To reproduce the dynamic evolution of soil and rock cohesion during reservoir impoundment and drawdown, controlled water level fluctuations can be implemented: Immersion stage: Water is slowly poured into the tank (rate ≤1cm / min) until the slope is completely submerged and left to stand for 24 hours. During this process, capillary water is replaced by free water, the water-moon bay disappears, and the apparent cohesion approaches zero. The slope gradually collapses, eventually forming a stable underwater slope shape, and the underwater stable slope angle α is measured to be 39.2°.

[0110] Water control phase: The bottom drain valve is opened, and water is drained at a uniform rate of 0.5 cm / h to simulate the slow receding of a reservoir. As the surface water is drained and the surface moisture evaporates, capillary negative pressure is reformed between the particles, and the apparent cohesion gradually recovers. After the slope deformation stabilizes (usually requiring 48 hours), the natural slope angle θ above the water is measured to be 42.5°. The criteria for determining the completion of the water control operation are: no visible free water in the water tank and no flowing water on the sample surface.

[0111] S602: Subsequently, the drainage rate is controlled to slowly lower the water level, allowing the surface moisture of the granular slope model to evaporate or be discharged, restoring the apparent cohesion generated by capillary negative pressure, so as to form a natural slope angle θ on the water.

[0112] S603: By comparing the slope evolution parameters and collapse variation range at different water level stages, the actual failure surface dip angle β is inverted and used to correct the calculation parameters of refractive index n.

[0113] In this embodiment, during water control, when the water level drops to a certain critical depth, localized traction-induced collapses often occur in the near-shore section above water. High-speed photography and image difference technology are used to record the geometry of the collapsed structure. A typical collapse is used as an example: Collapse volume: 0.012 m³ (unit width); Sliding surface fitting tilt angle: β = 40.8°.

[0114] The β value is between θ and α, which conforms to the refraction law of "steeper above water, gentler below water, and the failure surface in the middle".

[0115] For example, the theoretical refractive index can be expressed as: or ,

[0116] Substitute the experimental values:

[0117] Simultaneously, verification was performed through mass conservation: Measured collapse volume The water depth is h = 8cm = 0.08m. The discovery of volume mismatch indicates that the static slope angle cannot fully reflect the dynamic process. Further analysis shows that the underwater stable slope angle still retains some capillary force in the initial stage of drainage, and the actual... .

[0118] Revised version:

[0119] This value is closer to the critical state (n≈1), which is consistent with the phenomenon that only small-scale local damage occurred in the experiment.

[0120] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0121] In one embodiment, a reservoir impoundment-induced landslide prediction system based on the principle of refraction is provided, which corresponds to the reservoir impoundment-induced landslide prediction method based on the principle of refraction described in the above embodiment.

[0122] A reservoir impoundment-induced landslide prediction system based on the principle of refraction includes a data acquisition module, a refractive index calculation module, and a risk prediction module. Detailed descriptions of each functional module are as follows: The data acquisition module is used to acquire the natural slope angle and soil parameters of the target reservoir bank slope in its natural state, and the relationship between the underwater stable slope angle and soil parameters in the saturated state. The refractive index calculation module is used to introduce and calculate the refractive index, which characterizes the degree of difference between the natural slope angle above water and the stable slope angle below water, based on the difference between the two. The introduction of refractive index is based on the following understanding of slope mechanism: During the reservoir impoundment process, the water surface serves as the interface for abrupt changes in the physical and mechanical properties of the rock and soil, resulting in a discontinuous reconstruction of the slope stability mode with the water surface as the boundary. The above-water and underwater parts tend to the limit equilibrium slope angle controlled by their respective effective strength parameters. The reservoir impoundment process follows the principle of mass conservation, and the actual failure surface inclination angle can better reflect the mechanical state of slope instability than the natural slope angle above the water. The risk prediction module is used to qualitatively or quantitatively predict the instability risk and progressive damage range of the target reservoir bank slope during the reservoir impoundment process, based on the refractive index value.

[0123] For specific limitations regarding the reservoir impoundment-induced landslide prediction system based on the principle of refraction, please refer to the limitations of the reservoir impoundment-induced landslide prediction method based on the principle of refraction mentioned above, which will not be repeated here. Each module in the above-mentioned reservoir impoundment-induced landslide prediction system based on the principle of refraction can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in the processor of the computer device in hardware form or independent of the processor, or it can be stored in the memory of the computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0124] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 5 As shown, the computer device includes a processor, memory, network interface, and database connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores numerical values ​​of the refractive index and various calculation expressions. The network interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction.

[0125] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements steps such as a method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction.

[0126] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the above-described method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction.

[0127] Those skilled in the art will understand that all or part of the processes in the methods of 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 of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0128] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0129] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, characterized in that, include: Obtain the natural slope angle and soil parameters of the target reservoir bank slope in its natural state, and the relationship between the stable slope angle and soil parameters in the underwater state under saturated water conditions. Based on the above-water natural slope angle and the underwater stable slope angle The difference is used to introduce and calculate the refractive index that characterizes the degree of difference; The introduction of the refractive index is based on the following understanding of the slope mechanism: During the reservoir impoundment process, the water surface serves as the interface for the abrupt change in the physical and mechanical properties of the soil and rock, resulting in a discontinuous reconstruction of the slope stability mode with the water surface as the boundary. The above-water and underwater parts tend to the limit equilibrium slope angle controlled by their respective effective strength parameters. The reservoir impoundment process follows the principle of mass conservation, and the actual failure surface inclination angle, instead of the natural slope angle above the water, can better reflect the mechanical state when the slope is unstable. Based on the value of the refractive index, the instability risk and progressive damage range of the target reservoir bank slope during the reservoir impoundment process can be qualitatively or quantitatively predicted.

2. The method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, as described in claim 1, is characterized in that... The refractive index is calculated using the following formula: Alternatively, when the actual failure surface dip angle β is known, the expression used is: The natural slope angle θ above water and the stable slope angle α underwater are determined through the following steps: Samples were taken from the target reservoir bank soil and rock mass, and the shear strength parameters of the target reservoir bank soil and rock mass under natural water content and saturated conditions were tested respectively. The cohesion c and internal friction angle under natural conditions were obtained. γ, unit weight, and effective cohesion under saturation. Effective internal friction angle buoyancy ; (b) Determine the representative height h and pore water pressure of the potential sliding body based on the plane sliding assumption. The maximum slope angles of the target reservoir bank rock and soil mass that reach the limit equilibrium state under the natural water content state and the saturated state are obtained by using the limit equilibrium conditions, and are respectively taken as θ and α. Based on the ultimate height of the soil column above the shear surface with an actual failure angle of β, the potential sliding body is analyzed using limit equilibrium conditions. The value of the most unfavorable shear surface angle β is calculated through the characteristics of the soil and rock mass. The expression for calculating angle β is: 。 3. The method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, as described in claim 1 or 2, is characterized in that... The above-water natural slope angle and the underwater stable slope angle are determined by the strength parameters of the soil and rock mass under the corresponding states through limit equilibrium conditions. For a given actual failure surface dip angle β, the corresponding slope limit height satisfy: in, These represent the unit weight, cohesion, and angle of internal friction in their natural state; when used underwater, they are replaced with buoyant unit weight. Effective cohesion and effective internal friction angle .

4. The method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, as described in claim 1, is characterized in that... The prediction method further includes: Based on the principle of mass conservation, an equivalence relationship is established between the mass of rock and soil lost above the water surface due to instability and the mass of rock and soil required below the water surface to form a new stable slope. Using the aforementioned quantitative relationships, combined with the current reservoir water level and depth, the natural slope angle above water, the stable slope angle underwater, and the actual inclination angle of the failure surface, the critical instability range of the above-water slope is calculated. Based on the changing trend of the critical instability range with the rise of water level, the location of the landslide failure front in the next stage is predicted to determine whether the risk of stepwise instability is triggered, and the landslide instability prediction result is output.

5. The method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, as described in claim 3, is characterized in that... The method further includes: calculating the extreme water level depth. The extreme water level depth refers to the critical water depth corresponding to the extent that the landslide damage extends to the top of the slope; Among them, the Calculate using the following steps: Obtain the total height H, the natural slope angle θ above water, and the stable slope angle underwater of the target reservoir bank slope. and the actual dip angle of the damaged surface. ; (b) Based on the limit equilibrium condition, calculate the slope limit height corresponding to the actual failure surface dip angle β. ,satisfy: or ， make Solving using geometric compatibility relations The geometric compatibility relationship is as follows: ， The geometric compatibility relationship can be verified by the horizontal compensation distance OR at the water surface, where OR represents the horizontal projection offset formed by the intersection of the original slope, the actual failure surface, and the underwater stable slope under extreme water level conditions: 。 6. The method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction, as described in claim 1, is characterized in that... The method also includes verifying and calibrating the refractive index calculation model through physical model experiments. The physical model experiments use immersion-controlled water operation to simulate the dynamic change process of cohesion in soil and rock masses. First, the artificially prepared loose slope model is completely submerged in still water to saturate the loose slope model and form a stable underwater slope angle α. Subsequently, the drainage rate is controlled to slowly lower the water level, allowing the surface moisture of the loose slope model to evaporate or be discharged, restoring the apparent cohesion generated by capillary negative pressure, so as to form a natural slope angle θ on the water. By comparing the slope evolution parameters and collapse variation range at different water level stages, the actual failure surface dip angle β is inverted and used to correct the calculation parameters of refractive index n.

7. A reservoir impoundment-induced landslide prediction system based on the principle of refraction, characterized in that, The system includes: The data acquisition module is used to acquire the natural slope angle and soil parameters of the target reservoir bank slope in its natural state, and the relationship between the underwater stable slope angle and soil parameters in the saturated state. The refractive index calculation module is used to introduce and calculate the refractive index that characterizes the degree of difference between the natural slope angle above water and the stable slope angle below water, based on the difference between the natural slope angle above water and the stable slope angle below water. The introduction of the refractive index is based on the following understanding of the slope mechanism: During the reservoir impoundment process, the water surface serves as the interface for the abrupt change in the physical and mechanical properties of the soil and rock, resulting in a discontinuous reconstruction of the slope stability mode with the water surface as the boundary. The above-water and underwater parts tend to the limit equilibrium slope angle controlled by their respective effective strength parameters. The reservoir impoundment process follows the principle of mass conservation, and the actual failure surface inclination angle, instead of the natural slope angle above the water, can better reflect the mechanical state when the slope is unstable. The risk prediction module is used to qualitatively or quantitatively predict the instability risk and progressive damage range of the target reservoir bank slope during the reservoir impoundment process, based on the value of the refractive index.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for predicting reservoir bank landslides induced by reservoir impoundment based on the principle of refraction as described in any one of claims 1 to 6.

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