A method for analyzing slope stability under rainfall conditions

Abstract

The application provides a kind of slope stability analysis method under rainfall condition, it is related to geotechnical slope analysis technical field, the application first calculates gravity-driven shear stress, and lays the static load benchmark for mechanical analysis;Secondly, the unsaturated infiltration model is used to solve the transient effective saturation, accurately reflects the pore water filling process caused by rainfall infiltration;Further, combined with the irreversible correction of cumulative damage factor and the reversible correction of water sensitivity softening, the real-time evolution of dynamic degradation shear modulus is obtained, which truly depicts the nonlinear attenuation of soil stiffness under the dual action of environment-time;Then, the logarithmic rheological time term is introduced to calculate the nonlinear cumulative dynamic displacement, effectively representing the creep effect of low stiffness soil, making up for the deficiency of traditional model in long-term deformation prediction;Finally, through real-time double-control early warning and damage updating mechanism of effective plastic deformation after rain, the state memory and management of slope full life cycle are realized, and safety misjudgment is avoided.

Description

Technical Field

[0001] This invention relates to the field of rock and soil slope analysis technology, specifically a method for slope stability analysis under rainfall conditions. Background Technology

[0002] In fields such as transportation subgrades, water conservancy projects, and mining, slope stability monitoring is a lifeline for ensuring safety. Soil and rock slopes exhibit significant porous media characteristics and water sensitivity; the impact of rainfall infiltration on them is a complex, time-varying process involving unsaturated seepage, material softening, and viscous rheology. Many instability incidents demonstrate significant cumulative and delayed effects. Slopes often remain in a sub-healthy state after repeated rainfall due to the hidden accumulation of internal structural damage, ultimately leading to sudden instability during regular rainfall or even after the rain stops. However, current monitoring methods widely used in the industry primarily focus on macroscopic observations of surface displacement, lacking quantitative tracking of real-time shear stiffness decay and historical damage memory within the soil and rock mass. This makes it difficult to accurately and proactively predict the gradual, qualitative deterioration process of slopes.

[0003] Among existing slope stability analysis techniques, publication number CN109063341A discloses a method for analyzing the stability of bedding slopes under rainfall conditions based on shoulder displacement. This technical solution primarily targets bedding rock slopes. By analyzing the variation of rainfall infiltration depth over time, a weakened model of the shear strength parameters of weak interlayers is established. Furthermore, based on limit equilibrium theory, a quantitative functional relationship between shoulder horizontal displacement and slope stability coefficient is constructed. This method attempts to establish the link between surface displacement and deep stability, providing a physical mechanism-based computational approach for slope safety assessment under single rainfall conditions.

[0004] However, the aforementioned existing technologies still have significant shortcomings in handling the refined analysis of complex rainfall conditions. First, existing models treat the effects of rainfall too statically, failing to consider the continuous process of pore flow based on unsaturated soil mechanics theory, and are unable to calculate the real-time changes in the transient effective saturation of the soil, making it difficult to distinguish the effects of different rainfall types. Second, existing methods have a step-like defect in assigning values ​​to mechanical parameters, typically assuming that the soil shear modulus is two fixed constants in dry and saturated states, ignoring the nonlinear characteristics of the continuous change of stiffness parameters with water content, and failing to achieve accurate mapping of dynamic stiffness. Finally, existing technologies lack effective fluid-structure interaction and damage accumulation mechanisms, often using simple linear superposition to calculate displacement, severing the physical connection between water-sensitive softening caused by the seepage field and cumulative damage caused by the stress field, failing to truly reproduce the resistance attenuation process of the soil skeleton due to the dual effects of water-sensitive softening and irreversible damage throughout the entire rainfall life cycle, thus affecting the accuracy of the analysis results.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for analyzing slope stability under rainfall conditions, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for slope stability analysis under rainfall conditions, comprising the following steps: In response to the onset of rainfall, rainfall intensity data is continuously collected. Based on the rainfall intensity data from the onset of rainfall to the current moment, a rainfall intensity curve is constructed. An unsaturated infiltration model is constructed based on the principle of mass conservation. By integrating the rainfall intensity curve over time and combining it with porosity constraints, the transient effective saturation of the soil in the slope at the current moment is calculated. Based on the geometric relationship between the soil saturation unit weight, potential sliding surface depth and slope angle of the slope, the gravity-driven shear stress acting on the sliding surface is calculated. Using the reference shear modulus of the slope as a benchmark, irreversible damage correction is performed using the cumulative damage factor, and reversible water-sensitive softening correction is performed using the transient effective saturation to obtain the dynamic deterioration shear modulus that evolves in real time. The ratio of gravity-driven shear stress to dynamic deterioration shear modulus is used as the elastic deformation term, and a logarithmic rheological time term is introduced to characterize the creep effect under low stiffness. The nonlinear cumulative dynamic displacement of the slope is then calculated. During rainfall, the nonlinear cumulative dynamic displacement at the current moment is monitored in real time, and the rate of change at the current moment within the preset monitoring time window is calculated. When the nonlinear cumulative dynamic displacement exceeds the preset critical cumulative dynamic displacement threshold, or the rate of change of the nonlinear cumulative dynamic displacement exceeds the preset critical acceleration threshold, a real-time landslide alarm is triggered. If a real-time landslide alarm is not triggered, after the rainfall ends, the effective plastic deformation exceeding the yield displacement threshold is calculated based on the plastic dissipation theory. The effective plastic deformation is converted into the damage increment of a single rainfall event and the cumulative damage factor is updated. If the updated cumulative damage factor exceeds the preset maintenance threshold, a maintenance notification is triggered.

[0008] Furthermore, in response to the onset of rainfall, rainfall intensity data is continuously collected, and a rainfall intensity curve is constructed based on the rainfall intensity data from the onset of rainfall to the current time; An unsaturated infiltration model is constructed based on the principle of mass conservation. By utilizing the rainfall intensity curve, a numerical integration algorithm is used to calculate the cumulative infiltration of the slope on the rainfall time axis, and the cumulative infiltration is mapped to the transient effective saturation of the soil pores at the current moment. The principle of the unsaturated infiltration model is as follows: in, This represents the transient effective saturation at the current time t. This indicates the preset residual saturation of the soil. This represents the natural exponential function. On the rainfall intensity curve, Real-time rainfall intensity at any given moment This indicates the preset effective porosity. This indicates the preset characteristic infiltration depth.

[0009] Furthermore, based on the preset slope angle, the preset potential sliding surface depth, and the preset soil saturation unit weight, combined with the infinite slope stability theory, the gravity-driven shear stress generated by the gravity component and acting along the potential sliding surface is calculated. The principle of gravity-driven shear stress calculation is as follows: in, This represents gravity-driven shear stress. This indicates the preset saturated unit weight of the soil. Indicates the preset potential sliding surface depth. This indicates the preset slope angle.

[0010] Furthermore, based on the preset reference shear modulus of the slope, the preset cumulative damage factor is used to perform irreversible damage correction based on the concept of effective stress in damage mechanics. The transient effective saturation at the current moment is used to perform water-sensitive softening correction based on the unsaturated soil matrix suction theory. The dynamic deterioration shear modulus at the current moment is calculated by combining the irreversible damage correction and the water-sensitive softening correction. The principle for calculating the dynamic deterioration shear modulus at the current moment is as follows: in, This represents the dynamic degradation shear modulus at the current time t. This indicates the preset reference shear modulus. This represents the preset cumulative damage factor. This indicates the preset water-sensitive softening coefficient. This indicates the preset water sensitivity index.

[0011] Furthermore, based on gravity-driven shear stress as a constant load, the dynamic deterioration shear modulus at the current time t is used as a real-time changing resistance parameter. The characteristic length of the slope is calculated according to the slope angle and the potential sliding surface depth. Combined with the preset rheological model parameters, the nonlinear cumulative dynamic displacement generated by the slope along the sliding surface direction at the current time t is calculated using the nonlinear constitutive equation. The principle for calculating the nonlinear cumulative dynamic displacement of the slope along the sliding surface at the current time t is as follows: in, This represents the nonlinear cumulative dynamic displacement of the slope along the sliding surface at the current time t. This represents the preset rheological amplification factor. This represents the preset relaxation time constant. This represents the total duration from the start of rainfall detection to the current time t.

[0012] Furthermore, during the rainfall process, the nonlinear cumulative dynamic displacement at the current moment is monitored in real time, and the rate of change of the nonlinear cumulative dynamic displacement at the current moment within the preset monitoring time window is calculated according to the preset monitoring time window. Specifically, the preset monitoring time window is a preset time step forward based on the current moment.

[0013] Furthermore, if the nonlinear cumulative dynamic displacement at the current moment does not exceed the preset critical cumulative dynamic displacement threshold, and the nonlinear cumulative dynamic displacement change rate also does not exceed the preset critical acceleration threshold, then a real-time landslide alarm will not be triggered. If the nonlinear cumulative dynamic displacement exceeds the preset critical cumulative dynamic displacement threshold, or the nonlinear cumulative dynamic displacement change rate exceeds the preset critical acceleration threshold, then a real-time landslide alarm will be triggered. Vehicles and personnel within the slope's range will be identified through vehicle GPS and mobile phone positioning, and landslide alarm information will be sent to vehicles and personnel within the slope's range. Landslide early warning and maintenance notifications will also be sent to relevant personnel.

[0014] Furthermore, if a real-time landslide alarm is triggered during the rainfall, the maintenance phase will begin directly after the rainfall ends. If no real-time landslide alarm is triggered during the rainfall, the effective plastic deformation exceeding the yield displacement threshold will be calculated based on the plastic dissipation theory after the rainfall ends, and the effective plastic deformation will be converted into the damage increment of a single rainfall event. The principle for calculating the incremental damage from a single rainfall event is as follows: in, This indicates the incremental damage from a single rainfall event. This represents the nonlinear cumulative dynamic displacement at the end of this rainfall event. This indicates the preset yield displacement threshold. This indicates the preset ultimate failure displacement.

[0015] Furthermore, the incremental damage from a single rainfall event is summed with the cumulative damage factor in the current database to obtain the latest cumulative damage factor, and the database content is updated. The updated cumulative damage factor is compared with a preset maintenance threshold. If the updated cumulative damage factor does not exceed the preset maintenance threshold, no maintenance notification is triggered. If the updated cumulative damage factor exceeds the preset maintenance threshold, a maintenance notification is triggered and sent to relevant personnel. After maintaining the slope, the relevant personnel re-detect the slope's reference shear modulus, effective porosity, slope angle, and potential sliding surface depth. Based on the detected new reference shear modulus and effective porosity of the slope, the historical data in the database is analyzed, the cumulative damage factor of the slope after maintenance is reassessed, and the database is updated.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention, by performing time integration on the rainfall intensity curve and combining it with effective porosity constraints, can accurately invert the water filling process in soil pores, calculate the transient effective saturation that fluctuates continuously over time, and then construct a dynamic stiffness evolution model based on multi-field coupling. Compared with the crude approach of simplifying rainfall as a static variable and performing step-like parameter processing in existing technologies, this scheme uses transient effective saturation to continuously water-sensitively soften the reference shear modulus, achieving a refined mapping of the stiffness decay characteristics of soil under different rainfall durations. More importantly, this invention introduces a cumulative damage factor as a state variable to irreversibly damage the reference shear modulus of the slope, thereby incorporating the structural damage left by historical rainfall events throughout the slope's entire life cycle into the current stability evaluation system. This real-time evolving dynamic deterioration shear modulus, obtained based on dual correction of transient effective saturation and cumulative damage factor, truly depicts the resistance deterioration trajectory of the soil skeleton under the combined effects of environmental hydraulic softening and historical mechanical damage, greatly improving the applicability and accuracy of the model in complex hydrogeological environments.

[0017] This invention also introduces a logarithmic rheological time term to characterize the creep effect of soil under low stiffness, overcoming the theoretical deficiencies of existing technologies that either ignore soil viscous deformation or only use linear superposition calculations. This scheme uses the ratio of gravity-driven shear stress to the dynamically deteriorating shear modulus evolving in real time as the basic elastic deformation term. The nonlinear cumulative dynamic displacement calculated after coupling with the logarithmic rheological time term can cover both instantaneous elastic response and long-term rheological response, solving the problem of insufficient displacement estimation in traditional models during long-duration rainfall. Simultaneously, this invention establishes a damage update mechanism based on plastic dissipation theory. After rainfall, deformation exceeding the yield displacement threshold is converted into damage increments, iteratively updating the cumulative damage factor. This mechanism ensures that the model can remember the cumulative damage factor of the slope, making each stability analysis begin with the latest health state of the slope, avoiding safety misjudgments caused by ignoring historical plastic accumulation, and realizing quantitative tracking of the progressive damage of the slope from health to failure, providing relevant personnel with a more forward-looking basis for maintenance decisions. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram of the nonlinear cumulative dynamic displacement calculation process of the present invention; Figure 3 This is a data map of the slope soil. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0020] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] Example: Please see Figures 1 to 3 The present invention provides a technical solution: A method for slope stability analysis under rainfall conditions, comprising the following steps: Step 1: In response to the onset of rainfall, continuously collect rainfall intensity data. Based on the rainfall intensity data from the onset of rainfall to the current moment, construct a rainfall intensity curve. Based on the principle of mass conservation, construct an unsaturated infiltration model. By integrating the rainfall intensity curve over time and combining it with porosity constraints, calculate the transient effective saturation of the soil in the slope at the current moment. In this embodiment, in response to the start of rainfall, rainfall intensity data is continuously collected, and a rainfall intensity curve is constructed based on the rainfall intensity data from the start of rainfall to the current time. An unsaturated infiltration model is constructed based on the principle of mass conservation. By utilizing the rainfall intensity curve, a numerical integration algorithm is used to calculate the cumulative infiltration of the slope on the rainfall time axis, and the cumulative infiltration is mapped to the transient effective saturation of the soil pores at the current moment. The principle of the unsaturated infiltration model is as follows: in, This represents the transient effective saturation at the current time t. This represents the preset residual soil saturation, obtained by sampling the slope on-site and conducting soil-water tests in the laboratory. It represents the minimum water saturation level of the slope soil under natural drying conditions, which cannot be drained due to capillary binding. This represents the natural exponential function. On the rainfall intensity curve, The real-time rainfall intensity at a given moment, where φ represents the preset effective porosity, is obtained by measuring using a nuclear density meter, H inf The preset characteristic infiltration depth is obtained by conducting a double-ring infiltration experiment on the slope surface. The rainfall intensity curve serves as the time-dependent boundary condition for the unsaturated infiltration model, used in subsequent steps to invert the accumulation process of water in soil pores through time integration. Transient effective saturation combines several key factors, including the rainfall intensity curve, effective porosity, characteristic infiltration depth, and residual soil saturation. Its generated value dynamically changes over time, specifically reflecting the real-time state of soil pores being gradually filled with water during continuous rainfall. The physical meaning of transient effective saturation refers to the proportion of infiltrated rainfall water occupying the effective space of the soil capable of holding water at the current moment. This index transforms the originally discrete and fluctuating rainfall data into a continuously changing humidity state variable within the soil, thus distinguishing the different effects of short-duration heavy rainfall and long-duration weak rainfall on soil physical properties. Its technical advantage lies in providing real-time quantitative evidence for subsequent assessment of soil strength degradation due to increased water content. The cumulative effect of the rainfall intensity curve on the time axis directly determines the calculation result of transient effective saturation. As rainfall continues, the amount of water injected into the soil accumulates. According to the principle of mass conservation, the water content in the soil pores gradually approaches saturation from a dry state. Therefore, the greater the cumulative rainfall, the more water fills the soil pores, and the greater the corresponding transient effective saturation value. Effective porosity and characteristic infiltration depth together determine the physical limit capacity of the soil medium to hold water, and both play a volume constraint role in the calculation of transient effective saturation. Effective porosity characterizes the proportion of pore volume in the soil medium that can be used to store water, while characteristic infiltration depth defines the spatial scale of the soil column involved in infiltration calculation. The product of the two physically represents the total effective pore volume per unit area. According to the definition of saturation, which is the ratio of infiltrated water volume to total effective pore volume, under the premise of constant total rainfall infiltration, if the effective porosity of the soil is greater or the characteristic infiltration depth is deeper, it means that the total pore space used to distribute the infiltrated water volume is larger, resulting in a decrease in the proportion of water filling the pores.

[0022] Step 2: Based on the geometric relationship between the soil saturation unit weight, potential sliding surface depth and slope angle of the slope, calculate the gravity-driven shear stress acting on the sliding surface. Using the reference shear modulus of the slope as a benchmark, perform irreversible damage correction using the cumulative damage factor, and perform reversible water-sensitive softening correction based on transient effective saturation to obtain the real-time evolving dynamic deterioration shear modulus. In this embodiment, based on the preset slope angle, the preset potential sliding surface depth and the preset soil saturation unit weight, and combined with the infinite slope stability theory, the gravity-driven shear stress generated by the gravity component and acting along the potential sliding surface is calculated. The principle of gravity-driven shear stress calculation is as follows: Where τ represents gravity-driven shear stress, γ represents the saturated unit weight of soil, obtained through field sampling and laboratory testing, and H slip The potential sliding surface depth is determined by geological survey and analysis, and the maximum depth of the weak interlayer within the target monitoring area is taken as the potential sliding surface depth. α represents the slope angle, which is determined by topographic mapping, and the average dip angle of the line connecting the top of the slope to the toe of the slope on the profile of the main sliding direction is taken.

[0023] Based on the mechanical model of infinite slope stability, the slope is assumed to be a homogeneous soil mass extending infinitely along the slope surface, with the potential sliding surface parallel to the slope surface. Under this model, the sliding force acting on the sliding surface mainly originates from the tangential component of the overlying soil column's self-weight along the slope surface. In the formula, the product of the saturated unit weight of the soil mass and the potential sliding surface depth represents the vertical self-weight of the soil column per unit area. The sine function of the slope angle decomposes the vertical self-weight into a driving force along the slope surface downwards, and the cosine function of the slope angle is used to convert the unit horizontal projected area into the unit sliding surface area. This gravity-driven shear stress is treated as a constant active load term in the single rainfall analysis process, and together with the dynamic resistance parameters that evolve over time in subsequent steps, it constitutes the mechanical criterion for slope stability.

[0024] Based on the preset reference shear modulus of the slope, the preset cumulative damage factor is used to perform irreversible damage correction based on the concept of effective stress in damage mechanics. The transient effective saturation at the current moment is used to perform water-sensitive softening correction based on the unsaturated soil matrix suction theory. The dynamic deterioration shear modulus at the current moment is calculated by combining the irreversible damage correction and the water-sensitive softening correction. The principle for calculating the dynamic deterioration shear modulus at the current moment is as follows: Among them, G1 t This represents the dynamic degradation shear modulus at the current time t. This represents the preset reference shear modulus, obtained through trans-hole seismic wave testing. The preset cumulative damage factor is obtained from the cumulative damage record updated at the end of the last monitoring cycle. Ω represents the preset water-sensitive softening coefficient, which is obtained by collecting undisturbed soil samples on site and preparing two sets of experimental samples in the laboratory. One set of experimental samples is dried to the residual saturation of the soil, and the other set is vacuum-saturated to the full saturation state. Dynamic triaxial tests are performed on the two sets of experimental samples respectively. n represents the preset water sensitivity index, which is obtained by setting multiple sets of experimental samples with different saturation according to the required data accuracy, measuring the shear modulus of each set of experimental samples and performing curve fitting. The dynamic deterioration shear modulus comprehensively considers the slope's reference shear modulus, cumulative damage factor, current transient effective saturation, and preset water-sensitive softening parameters. The generated dynamic deterioration shear modulus is a mechanical state quantity that fluctuates in real time with the environment and time, specifically reflecting the remaining true shear stiffness characteristics of the soil skeleton after enduring the dual effects of historically accumulated structural damage and current water-sensitive softening. The physical meaning of the dynamic deterioration shear modulus characterizes the actual ability of the soil to resist shear deformation at the current moment. The technical advantage of this parameter lies in breaking through the limitation of traditional methods that only treat stiffness as a static constant, realizing the restoration of shear resistance from an ideal state to a real state, and being able to distinguish and superimpose irreversible damage and reversible softening of the soil, thus providing a resistance index that conforms to physical facts for accurate calculation of nonlinear displacement. The slope's reference shear modulus, cumulative damage factor, and transient effective saturation are the core variables determining the magnitude of the dynamic deterioration shear modulus. The calculation logic fully considers the physical constraints between variables. Since the reference shear modulus defines the upper limit of the physical resistance of soil in its undamaged state, a larger value indicates a more robust soil skeleton, resulting in a larger calculated dynamic deterioration shear modulus. The cumulative damage factor and transient effective saturation weaken the resistance from the perspectives of structural integrity and environmental softening, respectively. As the cumulative damage factor increases, the cross-section within the soil capable of effectively transmitting stress shrinks due to the expansion of microcracks, leading to a decrease in overall stiffness. Simultaneously, with the increase in transient effective saturation, the lubrication effect of moisture at the particle contact surface is enhanced, reducing matrix suction and interlocking friction, thus exacerbating soil softening. Therefore, with an increase in either the cumulative damage factor or transient effective saturation, the corresponding dynamic deterioration shear modulus value will significantly decrease.

[0025] Step 3: Using the ratio of gravity-driven shear stress to dynamic deterioration shear modulus as the elastic deformation term, a logarithmic rheological time term is introduced to characterize the creep effect under low stiffness, and the nonlinear cumulative dynamic displacement of the slope is calculated. In this embodiment, based on gravity-driven shear stress as a constant load, the dynamic deterioration shear modulus at the current time t is used as the real-time changing resistance parameter. The characteristic length of the slope is calculated according to the slope angle and the potential sliding surface depth, and combined with the preset rheological model parameters, the nonlinear cumulative dynamic displacement generated by the slope along the sliding surface direction at the current time t is calculated using the nonlinear constitutive equation. The principle for calculating the nonlinear cumulative dynamic displacement of the slope along the sliding surface at the current time t is as follows: in, This represents the nonlinear cumulative dynamic displacement of the slope along the sliding surface at the current time t. This represents the preset rheological amplification factor, obtained by collecting undisturbed soil samples in the field and conducting indoor triaxial creep tests in the laboratory, and then fitting the result to a logarithmic displacement-time curve. This represents the preset relaxation time constant, a characteristic time constant obtained through regression analysis of the shift-time logarithmic curves from indoor triaxial creep tests. This represents the total duration from the start of rainfall detection to the current time t; The nonlinear cumulative dynamic displacement comprehensively considers several key factors, including the potential sliding surface depth, slope angle, gravity-driven shear stress, dynamic degradation shear modulus, rheological amplification factor, relaxation time constant, and total rainfall duration. The generated nonlinear cumulative dynamic displacement is a monotonically increasing cumulative quantity over time, specifically reflecting the total deformation distance along the sliding surface caused by the combined effects of continuous gravity driving, real-time stiffness decay, and material viscous rheology. Physically, it refers to the actual displacement of the slope mass relative to the stable bedrock at the current moment. The technical advantage of this parameter lies in overcoming the limitation of traditional elastic models that can only calculate instantaneous deformation. By introducing a time-dependent rheological mechanism, it can accurately describe the creep phenomenon of soft soil due to viscous characteristics during and after rainfall, thus explaining the hysteresis characteristic of the slope displacement continuing to increase after rainfall stops. The computational logic fully considers the physical constraints between variables. Specifically, there is a positive geometric integral relationship between the nonlinear cumulative dynamic displacement and the geometric scale of the sliding body. The sine of the potential sliding surface depth divided by the slope angle physically represents the actual length of the sliding surface. This is analogous to an integral effect: under the same strain conditions, the longer the original length of the sliding surface, the greater its total elongation. This means that at a fixed depth, a gentler slope angle corresponds to a longer sliding path and a larger cumulative displacement. Simultaneously, there is a positive mechanical response relationship between the nonlinear cumulative dynamic displacement and the basic elastic deformation term. Gravity-driven shear stress, as the active driving force causing deformation, counteracts the dynamic degradation shear modulus, which acts as a resistance to deformation. A larger gravity-driven shear stress or a reduced dynamic degradation shear modulus due to water-sensitive softening directly leads to a larger shear strain per unit length in the sliding body, thus increasing the final calculated displacement value. Furthermore, there is a positive growth relationship between the nonlinear cumulative dynamic displacement and the rheological time term based on the material viscosity. Given that saturated soft soil has creep characteristics similar to high-viscosity fluids, even under constant stress, the deformation will develop slowly over time. Longer rainfall duration or larger rheological amplification factor characterizes more viscous deformation accumulated by time effects, resulting in a monotonically increasing trend in the value of nonlinear cumulative dynamic displacement.

[0026] Combined with the trend of slope soil changes with rainfall time and cumulative infiltration Figure 3As the duration of rainfall increases, the cumulative infiltration increases, leading to a gradual increase in transient effective saturation and a gradual decrease in dynamic deterioration shear modulus. The nonlinear cumulative dynamic displacement of the slope begins to increase as the dynamic deterioration shear modulus decreases. The specific trends are shown in Table 1.

[0027] Table 1: Schematic diagram of the variation trend of slope soil with rainfall time and cumulative infiltration. Step 4: During the rainfall process, monitor the nonlinear cumulative dynamic displacement at the current moment in real time, and calculate the rate of change of the current moment within the preset monitoring time window. When the nonlinear cumulative dynamic displacement exceeds the preset critical cumulative dynamic displacement threshold, or the rate of change of the nonlinear cumulative dynamic displacement exceeds the preset critical acceleration threshold, trigger a real-time landslide alarm. In this embodiment, during rainfall, the nonlinear cumulative dynamic displacement at the current moment is monitored in real time, and the rate of change of the nonlinear cumulative dynamic displacement at the current moment within the preset monitoring time window is calculated according to the preset monitoring time window. Specifically, the preset monitoring time window is a preset time step forward based on the current moment. If the current nonlinear cumulative dynamic displacement does not exceed the preset critical cumulative dynamic displacement threshold, and the nonlinear cumulative dynamic displacement change rate does not exceed the preset critical acceleration threshold, then a real-time landslide alarm will not be triggered. If the nonlinear cumulative dynamic displacement exceeds the preset critical cumulative dynamic displacement threshold, or the nonlinear cumulative dynamic displacement change rate exceeds the preset critical acceleration threshold, then a real-time landslide alarm will be triggered. Vehicles and personnel within the slope's range will be identified through vehicle GPS and mobile phone positioning, and landslide alarm information will be sent to vehicles and personnel within the slope's range. A landslide early warning and maintenance notification will also be sent to relevant personnel.

[0028] Step 5: If the real-time landslide alarm is not triggered, after the rainfall ends, the effective plastic deformation exceeding the yield displacement threshold is calculated based on the plastic dissipation theory. The effective plastic deformation is converted into the damage increment of a single rainfall and the cumulative damage factor is updated. If the updated cumulative damage factor exceeds the preset maintenance threshold, a maintenance notification is triggered.

[0029] In this embodiment, if a real-time landslide alarm is triggered during the continuous rainfall, the maintenance phase will begin directly after the rainfall ends. If no real-time landslide alarm is triggered during the continuous rainfall, the effective plastic deformation exceeding the yield displacement threshold will be calculated based on the plastic dissipation theory after the rainfall ends, and the effective plastic deformation will be converted into the damage increment of a single rainfall event. The principle for calculating the incremental damage from a single rainfall event is as follows: in, This indicates the incremental damage from a single rainfall event. This represents the nonlinear cumulative dynamic displacement at the end of this rainfall event. This represents the preset yield displacement threshold, obtained through large-scale indoor direct shear tests conducted on undisturbed soil samples from the slope sliding zone. The preset ultimate failure displacement is obtained through empirical calculation based on slope geometry according to the "Code for Investigation of Landslide Prevention Engineering". The single-event damage increment comprehensively considers several key factors, including the nonlinear cumulative dynamic displacement at the end of the rainfall event, the preset yield displacement threshold, and the ultimate failure displacement. The generated single-event damage increment is a physical quantity characterizing the degree of structural deterioration. Specifically, it reflects the proportion of irreversible structural damage to the slope soil caused by plastic deformation exceeding the elastic limit during this rainfall event. Physically, it refers to the share of the slope's total disaster resistance capacity consumed by this rainfall. The technical advantage of this parameter is that it enables the state memory of the slope throughout its entire life cycle, quantifying and accumulating the structural damage left by each rainfall event, thus avoiding the risk of misjudging aging slopes as healthy slopes. The nonlinear cumulative dynamic displacement, yield displacement threshold, and ultimate failure displacement at the end of the rainfall event directly determine the calculated damage increment. The calculation logic fully considers the mutual constraints between variables based on the theory of plastic dissipation. First, there is a positive driving relationship between the damage increment of a single rainfall and the nonlinear cumulative dynamic displacement at the end of the rainfall, based on plastic flow. When the displacement exceeds the yield point, the particle skeleton inside the soil begins to undergo irreversible displacement and slippage. The larger the displacement, the greater the cumulative amount of plastic strain and the more severe the damage to the soil structure. Therefore, under the premise of a fixed yield threshold, the larger the displacement value at the end, the larger the calculated damage increment. Secondly, there is a negative buffer relationship between the incremental damage from a single rainfall event and the plastic-ductile range formed by the yield displacement threshold and the ultimate failure displacement, based on the failure capacity. The yield displacement threshold defines the threshold for damage to occur, while the ultimate failure displacement defines the endpoint of complete slope failure. The difference between the two constitutes the total capacity that the slope can withstand plastic deformation. The higher the yield threshold, the wider the elastic range, and the less likely it is to enter the damage stage. Similarly, the larger the ultimate failure displacement, the better the material ductility, and the more deformation it can accommodate without collapsing. Therefore, under the condition of producing the same amount of displacement, if the yield threshold of the slope is higher or the ultimate failure displacement is larger, the proportion of damage occupied by this deformation is smaller, and the calculated incremental damage from a single rainfall event is also smaller. The incremental damage from a single rainfall event is added to the cumulative damage factor in the current database to obtain the latest cumulative damage factor, and the database content is updated. The updated cumulative damage factor is compared with the preset maintenance threshold. If the updated cumulative damage factor does not exceed the preset maintenance threshold, no maintenance notification is triggered. If the updated cumulative damage factor exceeds the preset maintenance threshold, a maintenance notification is triggered and sent to the relevant staff. After the relevant staff maintain the slope, they re-detect the slope's reference shear modulus, effective porosity, slope angle, and potential sliding surface depth. Based on the detected new reference shear modulus and effective porosity of the slope, the historical data in the database is analyzed, the cumulative damage factor of the slope after maintenance is reassessed, and the database is updated. Updating the reference shear modulus is to determine the initial baseline stiffness of the soil skeleton in the restored slope, serving as the physical basis for subsequent stiffness reduction calculations. Updating the effective porosity is to quantify the seepage channel characteristics of the restored slope soil medium. This parameter determines the potential space the soil can hold water, directly affecting the sensitivity of transient saturation to rainfall infiltration. Updating the potential sliding surface depth is to requantify the volumetric size of the landslide mass on the restored slope. The potential sliding surface depth defines the height of the overburden column acting on a unit area of ​​the sliding surface, directly determining the magnitude of the total vertical stress generated by the overburden. The deeper the depth, the greater the hydrostatic and earth pressure acting at the bottom; it is a size factor connecting microscopic stress and macroscopic geological structure. Updating the slope angle is to achieve the geometric decomposition of the gravity vector of the restored slope. Gravity is vertically downward, while the force causing slope instability is the tangential component along the sliding surface. The slope angle determines the proportion of gravity converted into the sliding driving force; the steeper the slope, the greater the component of gravity along the slope surface, and the higher the shear stress. It is a key geometric transformation parameter that maps the vertical gravitational field onto the inclined sliding surface. The updated cumulative damage factor is introduced to characterize the irreversible plastic damage state of the slope at the end of the previous monitoring period. It is used as an initial state variable in the calculation to ensure that the stability analysis is based on the current true physical state of the slope.

[0030] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0031] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0032] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0033] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for analyzing slope stability under rainfall conditions, characterized in that, The specific steps include: In response to the onset of rainfall, rainfall intensity data is continuously collected. Based on the rainfall intensity data from the onset of rainfall to the current moment, a rainfall intensity curve is constructed. An unsaturated infiltration model is constructed based on the principle of mass conservation. By integrating the rainfall intensity curve over time and combining it with porosity constraints, the transient effective saturation of the soil in the slope at the current moment is calculated. Based on the geometric relationship between the soil saturation unit weight, potential sliding surface depth and slope angle of the slope, the gravity-driven shear stress acting on the sliding surface is calculated. Using the reference shear modulus of the slope as a benchmark, irreversible damage correction is performed using the cumulative damage factor, and reversible water-sensitive softening correction is performed using the transient effective saturation to obtain the dynamic deterioration shear modulus that evolves in real time. The ratio of gravity-driven shear stress to dynamic deterioration shear modulus is used as the elastic deformation term, and a logarithmic rheological time term is introduced to characterize the creep effect under low stiffness. The nonlinear cumulative dynamic displacement of the slope is then calculated. During rainfall, the nonlinear cumulative dynamic displacement at the current moment is monitored in real time, and the rate of change at the current moment within the preset monitoring time window is calculated. When the nonlinear cumulative dynamic displacement exceeds the preset critical cumulative dynamic displacement threshold, or the rate of change of the nonlinear cumulative dynamic displacement exceeds the preset critical acceleration threshold, a real-time landslide alarm is triggered. If a real-time landslide alarm is not triggered, after the rainfall ends, the effective plastic deformation exceeding the yield displacement threshold is calculated based on the plastic dissipation theory. The effective plastic deformation is converted into the damage increment of a single rainfall event and the cumulative damage factor is updated. If the updated cumulative damage factor exceeds the preset maintenance threshold, a maintenance notification is triggered.

2. The slope stability analysis method under rainfall conditions according to claim 1, characterized in that: In response to the onset of rainfall, rainfall intensity data is continuously collected, and a rainfall intensity curve is constructed based on the rainfall intensity data from the onset of rainfall to the current time. An unsaturated infiltration model is constructed based on the principle of mass conservation. By utilizing the rainfall intensity curve, a numerical integration algorithm is used to calculate the cumulative infiltration of the slope on the rainfall time axis, and the cumulative infiltration is mapped to the transient effective saturation of the soil pores at the current moment. The principle of the unsaturated infiltration model is as follows: in, This represents the transient effective saturation at the current time t. This indicates the preset residual saturation of the soil. This represents the natural exponential function. On the rainfall intensity curve, Real-time rainfall intensity at any given moment This indicates the preset effective porosity. This indicates the preset characteristic infiltration depth.

3. The slope stability analysis method under rainfall conditions according to claim 2, characterized in that: Based on the preset slope angle, preset potential sliding surface depth and preset soil saturation unit weight, combined with the infinite slope stability theory, the gravity-driven shear stress generated by the gravity component and acting along the potential sliding surface is calculated. The principle of gravity-driven shear stress calculation is as follows: in, This represents gravity-driven shear stress. This indicates the preset saturated unit weight of the soil. Indicates the preset potential sliding surface depth. This indicates the preset slope angle.

4. The slope stability analysis method under rainfall conditions according to claim 3, characterized in that: Based on the preset reference shear modulus of the slope, the preset cumulative damage factor is used to perform irreversible damage correction based on the concept of effective stress in damage mechanics. The transient effective saturation at the current moment is used to perform water-sensitive softening correction based on the unsaturated soil matrix suction theory. The dynamic deterioration shear modulus at the current moment is calculated by combining the irreversible damage correction and the water-sensitive softening correction. The principle for calculating the dynamic deterioration shear modulus at the current moment is as follows: in, This represents the dynamic degradation shear modulus at the current time t. This indicates the preset reference shear modulus. This represents the preset cumulative damage factor. This indicates the preset water-sensitive softening coefficient. This indicates the preset water sensitivity index.

5. The slope stability analysis method under rainfall conditions according to claim 4, characterized in that: Based on gravity-driven shear stress as a constant load, the dynamic deterioration shear modulus at the current time t is used as the real-time changing resistance parameter. The characteristic length of the slope is calculated according to the slope angle and potential sliding surface depth. Combined with the preset rheological model parameters, the nonlinear cumulative dynamic displacement generated by the slope along the sliding surface direction at the current time t is calculated using the nonlinear constitutive equation. The principle for calculating the nonlinear cumulative dynamic displacement of the slope along the sliding surface at the current time t is as follows: in, This represents the nonlinear cumulative dynamic displacement of the slope along the sliding surface at the current time t. This represents the preset rheological amplification factor. This represents the preset relaxation time constant. This represents the total duration from the start of rainfall detection to the current time t.

6. The slope stability analysis method under rainfall conditions according to claim 1, characterized in that: During rainfall, the nonlinear cumulative dynamic displacement at the current moment is monitored in real time, and the rate of change of the nonlinear cumulative dynamic displacement at the current moment within the preset monitoring time window is calculated according to the preset monitoring time window. Specifically, the preset monitoring time window is a preset time step forward based on the current moment.

7. The slope stability analysis method under rainfall conditions according to claim 6, characterized in that: If the current nonlinear cumulative dynamic displacement does not exceed the preset critical cumulative dynamic displacement threshold, and the nonlinear cumulative dynamic displacement change rate does not exceed the preset critical acceleration threshold, then a real-time landslide alarm will not be triggered. If the nonlinear cumulative dynamic displacement exceeds the preset critical cumulative dynamic displacement threshold, or the nonlinear cumulative dynamic displacement change rate exceeds the preset critical acceleration threshold, then a real-time landslide alarm will be triggered. Vehicles and personnel within the slope's range will be identified through vehicle GPS and mobile phone positioning, and landslide alarm information will be sent to vehicles and personnel within the slope's range. A landslide early warning and maintenance notification will also be sent to relevant personnel.

8. The slope stability analysis method under rainfall conditions according to claim 1, characterized in that: If a real-time landslide alarm is triggered during the rainfall, the maintenance phase will begin immediately after the rainfall ends. If no real-time landslide alarm is triggered during the rainfall, the effective plastic deformation exceeding the yield displacement threshold will be calculated based on the plastic dissipation theory after the rainfall ends, and the effective plastic deformation will be converted into the damage increment of a single rainfall event. The principle for calculating the incremental damage from a single rainfall event is as follows: in, This indicates the incremental damage from a single rainfall event. This represents the nonlinear cumulative dynamic displacement at the end of this rainfall event. This indicates the preset yield displacement threshold. This indicates the preset ultimate failure displacement.

9. The slope stability analysis method under rainfall conditions according to claim 8, characterized in that: The incremental damage from a single rainfall event is added to the cumulative damage factor in the current database to obtain the latest cumulative damage factor, and the database content is updated. The updated cumulative damage factor is compared with the preset maintenance threshold. If the updated cumulative damage factor does not exceed the preset maintenance threshold, no maintenance notification is triggered. If the updated cumulative damage factor exceeds the preset maintenance threshold, a maintenance notification is triggered and sent to relevant personnel. After the relevant personnel maintain the slope, they re-detect the slope's reference shear modulus, effective porosity, slope angle, and potential sliding surface depth. Based on the detected new reference shear modulus and effective porosity of the slope, the historical data in the database is analyzed, the cumulative damage factor of the slope after maintenance is reassessed, and the database is updated.

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