Slope reliability prediction method coupled with extreme warm-wet and non-stationary random field of soil body

Abstract

The present application belongs to the technical field of highway engineering, and discloses a slope reliability prediction method coupled with extreme warm and wet and non-stationary random field of soil body, steps comprising: S1 obtaining soil body parameters of subgrade slope and relevant climate data of subgrade slope engineering; S2 calculating extreme warm and wet index based on relevant climate data of subgrade slope; S3 respectively constructing warm and wet driving mean function and standard deviation function of each soil body parameter; S4 constructing non-stationary correlation function driven by extreme warm and wet; S5 discretizing random field of soil body parameters of subgrade slope, and generating extreme warm and wet driving discrete random field of subgrade slope; S6 performing seepage-intensity coupling response analysis of subgrade slope under the action of extreme warm and wet environment, constructing limit state function, and calculating failure probability and reliability index at each time; S7 determining a dangerous time window, constructing a proxy model based on the dangerous time window, and correcting the failure probability and reliability index of the slope.

Description

Technical Field

[0001] This invention belongs to the field of highway engineering technology, and in particular relates to a method for predicting the reliability of slopes coupled with extreme warm and humid conditions and non-stationary random fields of soil. Background Technology

[0002] Against the backdrop of increasingly severe climate change, extreme warm and humid events (such as the alternation or superposition of high-temperature heat waves and heavy precipitation processes) occur frequently, posing a severe challenge to the stability of roadbed slopes. Extreme warm and humid events are a combination of high-temperature heat waves and heavy precipitation events. Unlike conventional single climate conditions, the impact of extreme warm and humid conditions on slope soil and rock exhibits significant nonlinear and time-varying characteristics: on the one hand, the hydraulic properties (such as soil moisture content and matrix suction) and mechanical properties (such as shear strength and permeability coefficient) of the soil respond to the combined changes in temperature and humidity in a nonlinear manner, exhibiting threshold effects and hysteresis effects; on the other hand, these parameters continue to evolve during the occurrence, development, and dissipation of extreme combined climate events, showing strong dynamic change patterns.

[0003] Existing slope risk assessment or early warning methods typically rely solely on cumulative rainfall, instantaneous moisture content, or static soil parameters, failing to comprehensively characterize the combined effects of high temperature, high humidity, and continuous rainfall on the thermo-hydrodynamic coupling of slope soil. This results in insufficient characterization of slope strength attenuation and permeability changes, leading to significant biases in instability probability assessments. Traditional models struggle to characterize the impact of such warm and humid events on soil properties, thus failing to meet the accuracy requirements of subsequent numerical simulations. Furthermore, they struggle to accurately identify critical periods of rapid slope risk increases, leading to delayed or premature early warnings. Traditional stationary random field models assume that soil parameters such as soil moisture content and permeability are constant in time and space. However, under extreme climatic conditions, soil wetting states, suction, and permeability parameters change over time.

[0004] Therefore, there is an urgent need to develop a method for predicting slope reliability that considers the coupling between extreme warm and humid conditions and non-stationary random fields in the soil. Summary of the Invention

[0005] The purpose of this invention is to provide a slope reliability prediction method coupled with extreme warm and humid conditions and non-stationary random fields of soil, so as to reduce the assessment bias of slope instability probability, improve the accuracy of early warning, and enable the model to reflect the time-varying deterioration of soil parameters and identify high-risk periods under complex meteorological conditions such as continuous high temperature and humidity, continuous rainfall and alternating wet and dry conditions.

[0006] The technical solution adopted in this invention is a slope reliability prediction method coupled with extreme warm and humid conditions and non-stationary random fields in soil. The steps include:

[0007] Step S1: Obtain the soil parameters of the roadbed slope and the relevant climate data of the roadbed slope engineering site;

[0008] Step S2: Calculate the extreme warm and humid index based on relevant climate data at the roadbed slope;

[0009] Step S3: Construct the extreme warm and humid driving mean function and standard deviation function for each soil parameter;

[0010] Step S4: Construct a non-stationary correlation function driven by extreme warm and humid conditions;

[0011] Step S5: Discretize the random field of soil parameters of the roadbed slope to generate an extreme warm and humid driven discrete random field of the roadbed slope.

[0012] Step S6: Perform seepage-strength coupled response analysis on the roadbed slope under extreme warm and humid environment, construct the limit state function, and calculate the failure probability and reliability index at each time point;

[0013] Step S7: Determine the critical time window, construct a surrogate model based on the critical time window, and correct the slope failure probability and reliability index.

[0014] Furthermore, the specific steps of S2 are as follows:

[0015] S21, calculate the rainfall humidity index and the high humidity persistence index, and then multiply the temperature and humidity excesses at the same time to obtain the high temperature and high humidity composite index. The calculation formula is as follows:

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, express The rainfall humidity index at any given time. express The high humidity index at any given time express The high temperature duration index at any given time. Indicates temperature. express The high temperature and high humidity composite index at any given time. express Rainfall at any given moment express Relative humidity at any given time Indicates the time lag steps. Indicates the target time. Indicates the length of the historical sliding time window. Indicates the rainfall attenuation coefficient. This indicates the effect of high humidity on the attenuation coefficient. This indicates that high temperature affects the attenuation coefficient. Indicates the high humidity threshold. Indicates the high temperature threshold. This represents the humidity cutoff function. Humidity at any time Above the high humidity threshold Only the excess portion is taken; otherwise, it is counted as 0. This represents the temperature cutoff function. Temperature of a moment Above the high temperature threshold Only the excess portion is taken; otherwise, it is counted as 0.

[0021] S22, the weighted summation of the rainfall humidity index, high humidity persistence index, high temperature persistence index, and high temperature and high humidity composite index yields the comprehensive warm and humid state intensity at time t, as shown in the following formula:

[0022]

[0023] In the formula, express The intensity of the combined extreme warm and humid conditions at any given time. , , , These represent the weights of the effects of rainfall and humidity, high humidity, high temperature, and the combined effects of high temperature and high humidity, respectively. Indicates the rainfall humidity index, Indicates the high humidity persistence index. This indicates the duration of high temperatures. This indicates the high temperature and high humidity composite index.

[0024] Furthermore, the specific steps of S3 are as follows:

[0025] S31, construct three soil parameters respectively. At all times in space The mean function driven by extreme warmth and humidity at a given location is used to calculate the variance of soil parameters, as shown in the following formula:

[0026]

[0027]

[0028]

[0029] In the formula, This indicates the soil cohesion at a point in space. The extreme warm and humid driving mean function at that location Indicates the internal friction angle of soil particles at a point in space. The extreme warm and humid driving mean function at that location This indicates the saturated permeability coefficient of soil at a spatial point. The extreme warm and humid driving mean function at that location Represents spatial location vector The mean initial cohesion field of the soil at that location, This represents the sensitivity coefficient of soil cohesion to extreme warm and humid conditions. Representing a spatial point The initial mean internal friction angle field of soil particles at the location. This represents the sensitivity coefficient of the internal friction angle of soil particles to extreme warm and humid conditions. Representing a spatial point Mean field of initial saturated permeability coefficient of soil at the location. This represents the sensitivity of the soil's saturated permeability coefficient to extreme warm and humid conditions. express The intensity of the overall extreme warm and humid conditions at any given moment;

[0030] S32, construct the corresponding extreme warm and humid driven nonstationary random fields respectively, as shown in the following formulas:

[0031]

[0032]

[0033] In the formula, Indicates the first The spatial location vector of soil parameters ,time Extreme warm and humid conditions drive nonstationary random fields; Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points The mean function at that point, Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points The standard deviation function at that location, Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points ,time Standardized random fields at that location, Indicates the first individual soil parameters at spatial points The base mean at that point Indicates the first individual soil parameters at spatial points The mean correction due to extreme warm and humid conditions. express The intensity of the overall extreme warm and humid conditions at any given moment.

[0034] Furthermore, the specific steps of S4 are as follows:

[0035] S41, design extreme warm and humid driving functions for the transverse and longitudinal directions of the roadbed slope, taking one of the following: linear function, saturated function, or logarithmic function;

[0036] S42, determine the variation of the transverse and longitudinal correlation length models of the roadbed slope with warm and humid conditions, construct a spatial correlation length model driven by extreme warm and humid conditions, and perform local corrections using the wetting front correction function, as shown in the following formula:

[0037]

[0038]

[0039]

[0040] In the formula, express Depth of the wetting front on the roadbed slope at any given time. This indicates that the moist front affects bandwidth. Indicates the correction strength. , Roadbed slopes under extreme warm and humid conditions The horizontal and vertical correlation lengths at any given moment , These represent the initial relevant lengths in the horizontal and vertical directions of the roadbed slope, respectively. , These represent the influence coefficients of extreme warm and humid conditions on the horizontal and vertical correlation lengths, respectively. , Let represent the extreme warm and humid driving functions in the horizontal and vertical directions, respectively. Representing a spatial point The vertical coordinate, Representing a spatial point The vertical coordinate, This represents the correction function for the wetting front. express The intensity of the combined extreme warm and humid conditions at any given time. Indicates taking the absolute value;

[0041] S43, construct a non-stationary spatial correlation function driven by extreme warm and humid conditions, calculate the correlation coefficient of the parameter field at different locations, and first discretize the slope calculation area into spatial points. Then calculate the first Any two spatial points of soil parameters , exist The non-stationary spatial correlation coefficient at time t, The formula is as follows:

[0042]

[0043] In the formula, Indicates the first Any two spatial points in the parameter field of a soil parameter , exist Correlation coefficient at time, , Representing spatial points , Horizontal coordinates , Representing spatial points , The vertical coordinates, Indicating the first under extreme warm and humid conditions The correlation length of the parametric field of each soil parameter in the horizontal direction. Indicating the first under extreme warm and humid conditions The vertical correlation length of the parameter field for each soil parameter. This represents the correction function for the wetting front. express The intensity of the combined extreme warm and humid conditions at any given time. Indicates soil cohesion, Indicates the internal friction angle of soil particles, Indicates the saturated permeability coefficient of the soil. This indicates taking the absolute value.

[0044] Furthermore, the specific steps of S5 are as follows:

[0045] S51, this constructs a parameter cross-correlation model driven by extreme warm and humid conditions, and calculates the correlation coefficients between soil parameters under the combined extreme warm and humid conditions, as shown in the following formula:

[0046]

[0047] In the formula, express Under the combined intensity of extreme warm and humid conditions, the first and Correlation coefficients between soil parameters Indicates the first and The initial correlation coefficients between the soil parameters This indicates that the first [condition] caused by extreme warm and humid conditions and The magnitude of the correlation increment between individual soil parameters Indicates the sensitivity coefficient driven by extreme warmth and humidity. express The intensity of the combined extreme warm and humid conditions at any given time. Represents a constant function;

[0048] S52, Construct soil parameters at spatial points , The cross-covariance function between the soil parameters and the joint covariance matrix containing the three soil parameters. The formula is as follows:

[0049]

[0050]

[0051]

[0052] In the formula, express Time of the first and individual soil parameters at spatial points , The cross-variance between them Indicates the first under extreme warm and humid conditions and Cross-correlation coefficients between soil parameters express Time of the first and Spatial correlation correction terms between soil parameters Indicates the first Any two spatial points in the parameter field of a soil parameter , exist Correlation coefficient at time, express Time of the first and individual soil parameters at spatial points , Cross-correlation coefficients between them , These represent the first under extreme warm and humid conditions. and individual soil parameters at spatial points , The standard deviation function at that location, express The joint covariance matrix at time t, for The elements in express The covariance of soil cohesion at any given time. express The covariance of soil cohesion and soil particle internal friction angle at time t is given by the following element, which is the same for all other elements. Each element represents the covariance between the two soil parameters represented by its lower angle. Indicates soil cohesion. Indicates the internal friction angle of soil particles. This represents the saturated permeability coefficient of the soil.

[0053] S53, using the KL expansion method to obtain the discrete random field driven by extreme warm and humid conditions corresponding to the soil parameters, firstly, the joint covariance matrix... Perform eigenvalue decomposition to obtain eigenvalues. With characteristic function Then, sort the feature values ​​from largest to smallest and select the top ones. The eigenvalues ​​and their corresponding eigenvectors are truncated and expanded using KL expansion to generate joint random field samples. For each random sample... All of these yielded a time-varying random field of coupled soil parameters.

[0054] Finally, the joint random field samples will be used. Split according to parameter type to get the first A random sample in Discrete random field of soil parameters driven by extreme warm and humid conditions at any given time: ,in, Indicates transpose. Indicates the first A random sample in The cohesive coupled random field vector at time t, Indicates the first A random sample in The internal friction angle coupled random field vector at time t. Indicates the first A random sample in The saturation permeability coefficient at time t is coupled to the random field vector.

[0055] Furthermore, the first A random sample in Cohesive Coupled Random Field Vector at Time Extremely warm and humid driven discrete random fields are ;

[0056] The first A random sample in Internal friction angle coupled random field vector at time t Extremely warm and humid driven discrete random fields are ;

[0057] The first A random sample in Saturation permeability coefficient coupled random field vector at time step Extremely warm and humid driven discrete random fields are ;

[0058] in, Represents the cohesive coupled random field vector At the moment spatial points Extremely warm and humid conditions drive discrete random fields. Represents the vector of the coupled random field with the internal friction angle. At the moment spatial points Extremely warm and humid conditions drive discrete random fields. Represents the saturated permeability coefficient coupled random field vector At the moment spatial points Extremely warm and humid conditions drive discrete random fields.

[0059] Furthermore, the specific steps of S6 are as follows:

[0060] S61, for the first A random sample, and its any point in space at any time The cohesion, internal friction angle, and saturated permeability of the extreme warm and humid driven discrete random fields are denoted as follows: , , ;

[0061] S62, construct the unsaturated seepage response and shear strength model under rainfall infiltration, generate soil cohesion, internal friction angle and saturated permeability coefficient at different locations of the roadbed slope through extreme warm and humid driving discrete random field, write the saturated permeability coefficient into the seepage equation, write the cohesion and internal friction angle into the shear strength formula, and calculate the roadbed slope safety factor FS.

[0062] S63, construct the limiting state function considering extreme warm and humid conditions, according to the first... A random sample at time... Based on the safety factor, pore water pressure, and displacement response, limit state functions for the roadbed slope safety factor, pore water pressure, and displacement are constructed to quantitatively evaluate the slope stability and classify the risk level. The formula is as follows:

[0063] ,

[0064] ,

[0065] ,

[0066]

[0067] In the formula, express The comprehensive limit state function for slope safety at time t. express Time of the first The safety coefficient limit state function for a random sample express Time of the first The pore water pressure limit state function for a random sample. express Time of the first The displacement limit state function of a random sample. Indicates the first under extreme warm and humid conditions A random sample in Safety factor at all times, This represents the critical value of the safety factor affected by extreme warm and humid conditions. This indicates the upper limit of the permissible pore pressure under extreme warm and humid conditions. Indicates the first A random sample at time... Maximum pore water pressure, This indicates the upper limit of permissible displacement under extreme warm and humid conditions; Indicates the first A random sample at time... The maximum slope displacement, This represents the critical value of the baseline safety factor. This represents the correction factor for the critical value of the safety factor under extreme warm and humid conditions. Indicates the upper limit of the allowable orifice pressure. This represents a correction factor for the upper limit of permissible pore pressure under extreme warm and humid conditions. Indicates the upper limit of the allowable displacement of the reference. This represents the correction factor for the upper limit of permissible displacement under extreme warm and humid conditions;

[0068] Iterate through all random samples and calculate the comprehensive safety limit value of the slope for each random sample;

[0069] S64, count the number of samples in the slope failure state to obtain the time-varying failure probability. Then, the failure probabilities at each time point are used to construct a full-time failure probability curve, and the time-varying reliability index driven by extreme warm and humid conditions is calculated. The formula is as follows:

[0070]

[0071]

[0072] in, for The total number of random field samples at time 1. for The number of samples that are constantly in a slope failure state. It is the inverse function of the standard normal distribution. for Time-varying reliability index driven by extreme warm and humid conditions.

[0073] Furthermore, the specific steps of S62 are as follows:

[0074] S62a, will the first Saturation permeability coefficient of a random sample random field The pressure head, pore water pressure, water content, and wetting front location are calculated using an unsaturated seepage model under extreme warm and humid conditions and rainfall infiltration. The formulas are as follows:

[0075]

[0076]

[0077]

[0078] By solving the above seepage equation, we obtain the first... A random sample in Pore ​​pressure field at time:

[0079]

[0080] In the formula, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time Pressure head, Indicates specific water capacity. Indicates the first A random sample at spatial point ,time Total head Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time Pressure head is Temperature is The unsaturated permeability coefficient generated by the time-stochastic field Indicates the location elevation. Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time The saturation permeability coefficient generated by the random field Indicates pressure head The relative permeability coefficient, This represents the temperature correction function for the seepage process. Indicates the boundary of rainfall infiltration. Indicates the specific gravity of water, or Indicates the first A random sample at spatial point ,time Pressure head;

[0081] S62b, will the first Cohesion of a random sample under extreme warm and humid conditions driven by random fields Internal friction angle extreme warm and humid driven random field and pore water pressure extreme warm and humid driven random fields Write it into the unsaturated soil shear model, that is:

[0082]

[0083]

[0084] In the formula, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time shear strength, Indicates the total normal pressure. Indicates pore gas pressure. Indicates the first Pore ​​water pressure of a random sample This represents the parameter of the internal friction angle of suction. This represents the tangent function.

[0085] S62c, calculate the... A random sample at time... The slope safety factor is calculated using the following formula:

[0086]

[0087] In the formula, Indicates the first A random sample at time... The safety factor, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time shear strength, express At all times in space The sliding force or actual shear stress is generated by the combined effects of the soil's own weight, external loads, and seepage force. Indicates the first on the sliding surface The length of each discrete segment This represents the total number of discrete segments of the sliding surface.

[0088] Furthermore, in S63, the comprehensive limit state function value of slope safety A value greater than 0 indicates that the slope is in a safe state. This indicates that the slope is in a critical state. This indicates that the slope is in a state of failure.

[0089] Furthermore, the specific steps of S7 are as follows:

[0090] S71, based on time interval Extreme warm and humid driving time-varying reliability indicators for all moments within the time frame were selected to meet the requirements. The continuous time interval is the danger window;

[0091] In the formula, for Time-varying reliability indicators driven by extreme warm and humid conditions This represents the minimum value among all random samples driven by extreme warm and humid time-varying reliability indices. This indicates the permissible threshold for a dangerous time window. Total duration;

[0092] S72. Based on the safety factor corresponding to each moment within the critical time window, a Gaussian process regression surrogate model is established. The soil parameters and corresponding time and extreme temperature and humidity index within the critical time window are used as inputs, and the limit state function value and safety factor obtained through numerical simulation are used as outputs to train the surrogate model.

[0093] S73, a time-window weighted active learning function is designed. The safety coefficient, calculated using refined numerical values ​​from the surrogate model, is used as the sample points. The function selects these sample points for real numerical simulation calculations, and the results are added to the training sample set to update the surrogate model. This process is repeated iteratively until the convergence condition is met. The formula for the active learning function is as follows:

[0094]

[0095]

[0096]

[0097] In the formula, This represents an active learning function. This represents the mean of the surrogate model's predictions for the limit state function. This represents the standard deviation of the surrogate model's prediction of the limit state function. This represents the limit state function predicted by the surrogate model. This represents the vector of standard normal random variables in the KL expansion of a random field. This represents the safety factor to prevent the denominator from being zero. Indicates time risk, As a hydraulically sensitive indicator, Indicates pore water pressure, Indicates soil saturation. express Depth of the wetting front on the roadbed slope at any given time; , , These represent the weighting coefficients for approximating the limit state surface within the active learning function, the time risk weighting coefficient, and the hydraulic sensitivity weighting coefficient, respectively. Indicates the total duration. Indicates taking the absolute value;

[0098] S74, based on the updated surrogate model of S73, performs refined reliability calculations on non-stationary random field samples within the critical time window. For each moment within the critical time window, it calculates the... The comprehensive limit state function value predicted by the updated surrogate model for a random sample. Determine random samples To determine whether a failure has occurred, the number of samples in a failed state at each moment within the critical time window is counted again to obtain a finely corrected time-varying failure probability and reliability index, as shown in the following formula:

[0099]

[0100]

[0101]

[0102] in, Indicates fine-tuning Probability of failure at any given time Indicates fine-tuning Real-time reliability metrics It is the inverse function of the standard normal distribution. Indicates the most dangerous moment. This represents the value of the independent variable that minimizes the objective function.

[0103] The beneficial effects of this invention are:

[0104] 1. This invention transforms extreme warm and humid environmental factors such as rainfall, temperature, and relative humidity into comprehensive warm and humid indices, and drives the spatiotemporal evolution of soil cohesion, internal friction angle, and saturated permeability coefficient of roadbed slopes. It can reflect the real deterioration process of roadbed slopes under the influence of extreme warm and humid weather, rather than just making static evaluations based on fixed soil parameters, thus achieving a more accurate description of actual working conditions.

[0105] 2. By updating the warm and humid index, wetting front depth, pore water pressure field and safety factor field according to time steps, this invention can obtain the results of the change of roadbed slope failure probability and reliability index over time, thereby identifying dangerous time windows such as delayed instability after extreme rainfall and strength decay after continuous high humidity, providing quantitative basis for road maintenance, traffic control and emergency patrol.

[0106] 3. This invention can be directly connected with the actual monitoring and maintenance data of roadbed slopes. The output time-varying failure probability, time-varying reliability index and identification results of dangerous time windows can provide maintenance management departments with clear priority handling time points and key sections, thereby transforming passive emergency repairs into proactive preventive reinforcement, which greatly reduces traffic interruption losses and emergency rescue costs caused by roadbed slope collapses. Attached Figure Description

[0107] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0108] Figure 1 This is a flowchart of the present invention.

[0109] Figure 2 This is a distribution map of extreme warm and humid environment indicators of the present invention, wherein (a) is a distribution map of rainfall indicators, (b) is a distribution map of temperature indicators, (c) is a distribution map of relative humidity indicators, (d) is a distribution map of the intensity of the four indicators, and (e) is a distribution map of comprehensive warm and humid environment indicators.

[0110] Figure 3 This is a graph showing the time-varying safety factor of the present invention.

[0111] Figure 4 This is a graph showing the time-varying safety factor variation using traditional methods.

[0112] Figure 5 This is a graph showing the changes in the time-varying failure probability and reliability index of the method of this invention.

[0113] Figure 6This is a graph showing the changes in time-varying failure probability and reliability index using traditional methods. Detailed Implementation

[0114] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0115] Embodiments of the present invention provide a slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in the soil. The flowchart is shown below. Figure 1 As shown, the steps include:

[0116] Step S1: Obtain soil parameters that control the stability of the roadbed slope, as well as relevant climate data at the roadbed slope engineering site. The soil parameters include cohesion, internal friction angle, and saturated permeability coefficient, and the relevant climate data includes rainfall, relative humidity, and temperature.

[0117] Step S2: Calculate the extreme warmth and humidity index based on relevant climate data at the roadbed slope. The specific steps are as follows:

[0118] S21. A rainfall humidity index is calculated based on historical rainfall data, and a high humidity persistence index is calculated based on the excess relative humidity. These indices are used to determine whether temperature and humidity have reached extreme warm and humid levels. Then, the excess temperature and humidity at the same time (the portion exceeding the high temperature and high humidity thresholds) are multiplied to obtain a high temperature and high humidity composite index, reflecting the combined effect of simultaneous high temperature and high humidity on the deterioration of roadbed slope soil. The high temperature and high humidity thresholds are the 90th percentiles of the local historical temperature and relative humidity for the same period, respectively. The calculation formula is as follows:

[0119]

[0120]

[0121]

[0122]

[0123] In the formula, express The rainfall humidity index at any given time. express The high humidity index at any given time express The high temperature duration index at any given time. Indicates temperature. express The high temperature and high humidity composite index at any given time. express Rainfall at any given moment express Relative humidity at any given time Indicates the time lag steps. Indicates the target time. This represents the length of the historical sliding time window. In this invention, for each target time... Using a length of Historical sliding time window, backtracking calculation forward The cumulative lag effects of rainfall, humidity and temperature within a time step; This represents the rainfall attenuation coefficient; the larger the coefficient, the faster the rainfall attenuates. Indicates the high humidity attenuation coefficient. This indicates that high temperature affects the attenuation coefficient. Indicates the high humidity threshold. Indicates the high temperature threshold. This represents the humidity cutoff function. The humidity at any given time is higher than the high humidity threshold. Only the excess portion is taken; otherwise, it is counted as 0. This represents the temperature cutoff function. The temperature at that moment was higher than the high temperature threshold. Only the excess portion is taken; otherwise, it is counted as 0.

[0124] If both temperature and humidity complete the transition from normal / low to extreme states within 3 days (<3 days) (reaching the high temperature and high humidity thresholds), it is considered to have reached an extreme warm and humid level, and enters an extreme warm and humid composite state, initiating the high temperature and high humidity composite index; if only the temperature reaches the high temperature threshold, it enters a high temperature driven state; if only the rainfall reaches the 90th percentile of the local historical average or the humidity reaches the high humidity threshold, it enters a humid driven state.

[0125] S22, weighted summation of rainfall wetting index, high humidity persistence index, high temperature persistence index, and high temperature and high humidity composite index, yields the comprehensive warm and humid state intensity at time t. This intensity characterizes the impact of rainfall infiltration, high humidity retention, and the coupling effect of high temperature and high humidity on the mechanical (hydraulic) properties of the roadbed slope, providing driving variables for subsequent non-stationary evolution modeling of soil parameters and slope reliability analysis. The formula is as follows:

[0126]

[0127] In the formula, express The intensity of the combined extreme warm and humid conditions at any given time. , , , These represent the weights of the effects of rainfall and humidity, high humidity, high temperature, and the combined effects of high temperature and high humidity, respectively. ; Indicates the rainfall humidity index, Indicates the high humidity persistence index. This indicates the duration of high temperatures. This indicates the high temperature and high humidity composite index.

[0128] Step S3: The soil parameters obtained in S1, such as cohesion, internal friction angle, and saturated permeability coefficient, are used as random field variables, and the strength under extreme warm and humid conditions is considered. As driving variables, the mean function and standard deviation function of each soil parameter under extreme warm and humid environment were constructed to characterize the spatiotemporal evolution characteristics of soil parameters. The specific steps are as follows:

[0129] S31, construct three soil parameters respectively. At all times in space The extreme warmth and humidity at a given location drive the mean function, and the variance of the soil parameters is calculated (variance calculation is an existing technique). The mean function describes the average variation trend of soil parameters at different spatial locations and under different extreme warmth and humidity conditions, while the variance describes the fluctuation range and uncertainty level of the soil parameters, thereby simulating the non-homogeneity of soil in actual engineering. The formula is as follows:

[0130]

[0131]

[0132]

[0133] In the formula, This indicates the soil cohesion at a point in space. The extreme warm and humid driving mean function at that location Indicates the internal friction angle of soil particles at a point in space. The extreme warm and humid driving mean function at that location This indicates the saturated permeability coefficient of soil at a spatial point. The extreme warm and humid driving mean function at that location Represents spatial location vector The mean initial cohesion field of the soil at that location, This represents the sensitivity coefficient of soil cohesion to extreme warm and humid conditions. Representing a spatial point The initial mean internal friction angle field of soil particles at the location. This represents the sensitivity coefficient of the internal friction angle of soil particles to extreme warm and humid conditions. Representing a spatial point Mean field of initial saturated permeability coefficient of soil at the location. This represents the sensitivity of the soil's saturated permeability coefficient to extreme warm and humid conditions. express The intensity of the overall extreme warm and humid conditions at any given moment.

[0134] S32, based on the mean function of the extreme warm and humid driving forces of three soil parameters, construct the corresponding extreme warm and humid driving non-stationary random fields (the expressions for the extreme warm and humid driving non-stationary random fields corresponding to the three soil parameters are consistent), as shown in the following formula:

[0135]

[0136]

[0137] In the formula, Indicates the first The spatial location vector of soil parameters ,time A warm and humid environment drives a nonstationary random field. Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points The mean function at a given location is used to represent the average level of the parameter at that location and under those warm and humid conditions. Indicates the first under warm and humid driving force individual soil parameters at spatial points The standard deviation function at a given point is used to represent the fluctuation range of the parameter. Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points ,time The standardized random field at a given location has a mean of 0 and a variance of 1, and is used to represent random fluctuation states. Indicates the first individual soil parameters at spatial points The baseline mean at each location is obtained from indoor test or geological survey data; Indicates the first individual soil parameters at spatial points The mean correction amount due to extreme warm and humid conditions is determined based on historical climate data of the project site and experience with similar slope projects. , respectively representing soil cohesion Internal friction angle of soil particles Soil saturated permeability coefficient ; express The intensity of the overall extreme warm and humid conditions at any given moment.

[0138] S4. Based on the mean and variance of soil parameters, a non-stationary correlation function driven by extreme warm and humid conditions is constructed to reflect the spatial continuity of soil parameters of the roadbed slope and their variation with extreme warm and humid conditions. The specific steps are as follows:

[0139] S41. Based on the actual climate characteristics and parameter sensitivity of the roadbed slope area, extreme warm and humid driving functions are designed along the slope surface and depth directions (i.e., transverse and longitudinal directions) to describe the impact of extreme warm and humid conditions on the spatial structure of the roadbed slope. Linear, saturated, and logarithmic functions are typically used, and the optimal function is selected based on the fitting effect of climate data from different regions. Specifically:

[0140] When the extreme warmth and humidity index is relatively small and the parameter deterioration increases linearly, a linear function is chosen, and the formula is as follows:

[0141] ,

[0142] When there is an upper limit to the effects of extreme warmth and humidity, a saturated function is chosen, as shown in the following formula:

[0143] ,

[0144] In cases where the initial response is sensitive and the later growth is logarithmic, a logarithmic function is chosen, as shown in the following formula:

[0145] ,

[0146] In the formula, , These represent the undetermined coefficients for the horizontal and vertical linear relationships, respectively. , These represent the undetermined coefficients for the horizontal and vertical indices, respectively. , These represent the undetermined logarithmic coefficients for the horizontal and vertical directions, respectively, which were obtained by fitting the data based on the climatic conditions of different regions. express The intensity of the combined extreme warm and humid conditions at any given time. This represents a constant function.

[0147] S42, determine the variation of the transverse and longitudinal correlation length models of the roadbed slope with warm and humid conditions, construct a spatial correlation length model driven by extreme warm and humid conditions to describe the soil softening and crack development process caused by enhanced warm and humid conditions, and consider the process of wetting front advancement caused by rainfall infiltration. The correlation structure is locally corrected by the wetting front correction function, as shown in the following formula:

[0148]

[0149]

[0150]

[0151] In the formula, express Depth of the wetting front on the roadbed slope at any given time. This indicates that the moist front affects bandwidth; The correction intensity is determined based on inversion of field monitoring data, indoor tests, or engineering experience. , Roadbed slopes under extreme warm and humid conditions The horizontal and vertical correlation lengths at any given moment , These represent the initial relevant lengths in the horizontal and vertical directions of the roadbed slope, respectively. , These represent the influence coefficients of extreme warm and humid conditions on the horizontal and vertical correlation lengths, respectively. , Let represent the extreme warm and humid driving functions in the horizontal and vertical directions, respectively. Representing a spatial point The vertical coordinate, Representing a spatial point The vertical coordinate, This represents the correction function for the wetting front. express The intensity of the combined extreme warm and humid conditions at any given time. This indicates taking the absolute value.

[0152] S43. Construct a non-stationary spatial correlation function driven by extreme warm and humid conditions to calculate the correlation coefficient of the parameter field at different locations, so as to characterize the spatial correlation of the soil parameters of the roadbed slope and its variation with extreme warm and humid conditions. First, the slope calculation area is discretized into spatial points. Then calculate the first Any two spatial points of soil parameters , exist The non-stationary spatial correlation coefficient at time t, The formula is as follows:

[0153]

[0154] In the formula, Indicates the first Any two spatial points in the parameter field of a soil parameter , exist The correlation coefficient at time is used to measure the similarity between two location parameters; , Representing spatial points , Horizontal coordinates , Representing spatial points , The vertical coordinates, Indicating the first under extreme warm and humid conditions The correlation length of the parametric field of each soil parameter in the horizontal direction. Indicating the first under extreme warm and humid conditions The vertical correlation length of the parameter field for each soil parameter. This represents the correction function for the wetting front. express The intensity of the combined extreme warm and humid conditions at any given time. Indicates soil cohesion, Indicates the internal friction angle of soil particles, Indicates the saturated permeability coefficient of the soil. This indicates taking the absolute value.

[0155] Step S5: Based on the spatially non-stationary correlation function driven by extreme warm and humid conditions, the random field of soil parameters of the roadbed slope is discretized to generate the spatial parameter field of the roadbed slope. The specific steps are as follows:

[0156] S51. Since the cohesion, internal friction angle of particles, and saturated permeability coefficient of the subgrade slope soil are not independent of each other, and their correlation changes with extreme warm and humid conditions, a cross-correlation model of parameters driven by extreme warm and humid conditions is constructed to calculate the correlation coefficient between soil parameters under the comprehensive extreme warm and humid conditions. The formula is as follows:

[0157]

[0158] In the formula, express Under the combined intensity of extreme warm and humid conditions, the first and Correlation coefficients between individual soil parameters ( ), Indicates the first and The initial correlation coefficients between the soil parameters This indicates that the first [condition] caused by extreme warm and humid conditions and The magnitude of the correlation increment between individual soil parameters Indicates the sensitivity coefficient driven by extreme warmth and humidity. express The intensity of the combined extreme warm and humid conditions at any given time. This represents a constant function.

[0159] S52, based on the cross-correlation coefficients between different soil parameters of the roadbed slope and the non-stationary spatial correlation coefficients obtained in S4, constructs the spatial points of soil parameters. , The cross-covariance functions between the soil parameters are used to calculate the cross-covariances, which form a joint covariance matrix containing the three soil parameters. This is used to generate a nonstationary random field sample that couples cohesion, internal friction angle, and saturated permeability coefficient. The formula is as follows:

[0160]

[0161]

[0162]

[0163] In the formula, express Time of the first and individual soil parameters at spatial points , The cross-variance between them Indicates the first under extreme warm and humid conditions and Cross-correlation coefficients of individual soil parameters express Time of the first and Spatial correlation correction terms between soil parameters Indicates the first Any two spatial points in the parameter field of a soil parameter , exist Correlation coefficient at time, express Time of the first and individual soil parameters at spatial points , Cross-correlation coefficients between them , These represent the first under extreme warm and humid conditions. and individual soil parameters at spatial points , The standard deviation function at that location, express The joint covariance matrix at time t, for The elements in express The covariance of soil cohesion at any given time. express The covariance of soil cohesion and soil particle internal friction angle at time t is given by the following element, which is the same for all other elements. Each element represents the covariance between the two soil parameters represented by its lower angle. Indicates soil cohesion. Indicates the internal friction angle of soil particles. This represents the saturated permeability coefficient of the soil.

[0164] S53, using the KL (Karhunen-Loève) expansion method, obtains the discrete random field driven by extreme warm and humid conditions corresponding to the soil parameters. First, the joint covariance matrix is... Perform eigenvalue decomposition to obtain eigenvalues. With characteristic function Then, sort the feature values ​​from largest to smallest and select the top ones. eigenvalues ​​and their corresponding eigenvectors (i.e., the first eigenvalues) The KL expansion of each modality is truncated to generate a joint random field sample (i.e., a coupled soil parameter random field vector driven by extreme warmth and humidity). The formula for truncating the KL expansion of the eigenvalues ​​and their corresponding eigenvectors is as follows:

[0165]

[0166] In the formula, Indicates the first A random sample at time... The coupled soil parameter random field vector driven by extreme warmth and humidity. This represents the joint mean vector consisting of the mean values ​​of cohesion, internal friction angle, and saturated permeability coefficient at all spatial nodes. This represents mutually independent standard normal random variables, i.e. ; Indicates the first One modality.

[0167] For each random sample All of these yielded a time-varying random field of coupled soil parameters.

[0168] Finally, the joint random field samples will be used. Split according to parameter type to get the first A random sample in Discrete random field of soil parameters driven by extreme warm and humid conditions at any given time: , This indicates the transpose. Wherein, the cohesive coupled random field vector... Extremely warm and humid driven discrete random fields are Internal friction angle coupled random field vector Extremely warm and humid driven discrete random fields are ; Saturated permeability coefficient coupled random field vector Extremely warm and humid driven discrete random fields are . Represents the cohesive coupled random field vector At the moment spatial points Extremely warm and humid conditions drive discrete random fields. Represents the vector of the coupled random field with the internal friction angle. At the moment spatial points Extremely warm and humid conditions drive discrete random fields. Represents the saturated permeability coefficient coupled random field vector At the moment spatial points Extremely warm and humid conditions drive discrete random fields.

[0169] The three discrete random fields mentioned above are not generated independently of each other, but are coupled random field samples generated under the same joint covariance matrix. Therefore, they can simultaneously reflect the spatial nonstationarity of each soil parameter and the correlation between different soil parameters.

[0170] Step S6: Based on the extreme warm and humid driven discrete random field generated in S5, perform seepage-strength coupled response analysis on the roadbed slope under the action of extreme warm and humid environment, and construct the limit state function according to the safety factor, pore water pressure and displacement response to calculate the failure probability and reliability index at each time point, thereby realizing the determination of slope instability state. The specific steps are as follows:

[0171] S61, for the first A random sample, and its any point in space at any time The extreme warm and humid driven discrete random fields of the three soil parameters (cohesion, internal friction angle, and saturated permeability coefficient) are denoted as follows: , , .

[0172] S62. Construct an unsaturated seepage response and shear strength model under rainfall infiltration. Using an extreme warm and humid environment, generate soil cohesion, internal friction angle, and saturated permeability coefficient at different locations on the roadbed slope using a discrete random field. Incorporate the saturated permeability coefficient into the seepage equation, and the cohesion and internal friction angle into the shear strength formula. Calculate the roadbed slope safety factor FS. The specific steps are as follows:

[0173] S62a, will the first Saturation permeability coefficient of a random sample random field The pressure head, pore water pressure, water content, and wetting front location are calculated using an unsaturated seepage model under extreme warm and humid conditions and rainfall infiltration. The formulas are as follows:

[0174]

[0175]

[0176]

[0177] By solving the above seepage equation, we obtain the first... A random sample in Pore ​​pressure field at time:

[0178]

[0179] In the formula, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time Pressure head, Indicates specific water capacity. Indicates the first A random sample at spatial point ,time Total head Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time Pressure head is Temperature is The unsaturated permeability coefficient generated by the time-stochastic field Indicates the location elevation. Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time The saturation permeability coefficient generated by the random field Indicates pressure head The relative permeability coefficient can be obtained by fitting the van Genuchten-Mualem model, Brooks-Corey model, or soil-water characteristic curve test. The function representing the temperature correction for the seepage process is obtained through empirical fitting. This indicates the rainfall infiltration boundary, which is determined based on the rainfall amount and the infiltration capacity of the slope soil. This indicates the specific gravity of water, approximately 9.8 kN / m³. 3 or 10 kN / m 3 ; Indicates the first A random sample at spatial point ,time Pressure head.

[0180] S62b, will the first Cohesion of a random sample under extreme warm and humid conditions driven by random fields Internal friction angle extreme warm and humid driven random field and pore water pressure extreme warm and humid driven random fields Write it into the unsaturated soil shear model, that is:

[0181]

[0182]

[0183] In the formula, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time shear strength, Indicates the total normal pressure. Indicates pore gas pressure. Indicates the first Pore ​​water pressure of a random sample This represents the parameter of the internal friction angle of suction. This represents the tangent function.

[0184] Therefore, the influence of extreme temperature and humidity on slope strength is incorporated into the shear strength calculation through two paths:

[0185] The first path (S62a). Change the random field of cohesion and the random field of internal friction angle;

[0186] The second path (S62b). Changing the permeability coefficient random field affects the pore water pressure.

[0187] S62c, based on shear strength and sliding force, calculate the first... A random sample at time... The slope safety factor is calculated using the following formula:

[0188]

[0189] In the formula, Indicates the first A random sample at time... The safety factor, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time shear strength, express At all times in space The sliding force or actual shear stress is generated by the combined effects of the soil's own weight, external loads, and seepage force. Indicates the first on the sliding surface The length of each discrete segment This represents the total number of discrete segments of the sliding surface. The length and number of these discrete segments are obtained through numerical simulation based on actual working conditions.

[0190] S63, construct the limiting state function considering extreme warm and humid conditions, according to the first... A random sample at time... Based on the safety factor, pore water pressure, and displacement response, limit state functions for the roadbed slope safety factor, pore water pressure, and displacement are constructed. These comprehensive limit state functions are used to determine whether the roadbed slope has become unstable, thereby achieving a quantitative evaluation of slope stability and risk level classification. The formula is as follows:

[0191] ,

[0192] ,

[0193] ,

[0194]

[0195] In the formula, express The comprehensive limit state function for slope safety at time t. A value greater than 0 indicates that the slope is in a safe state. This indicates that the slope is in a critical state. This indicates that the slope is in a state of failure; express Time of the first The safety coefficient limit state function for a random sample express Time of the first The pore water pressure limit state function for a random sample. express Time of the first The displacement limit state function of a random sample. Indicates the first under extreme warm and humid conditions A random sample in Safety factor at all times, This represents the critical value of the safety factor affected by extreme warm and humid conditions. This indicates the upper limit of the permissible pore pressure under extreme warm and humid conditions. Indicates the first A random sample at time... Maximum pore water pressure, This indicates the upper limit of permissible displacement under extreme warm and humid conditions; Indicates the first A random sample at time... The maximum slope displacement can be calculated using a seepage-stress coupled numerical model; This represents the critical value of the baseline safety factor, which is usually taken as 1. This represents the correction factor for the critical value of the safety factor under extreme warm and humid conditions, and is generally taken as 0~0.15; The upper limit of the allowable pore pressure is indicated by the relevant construction specifications. This represents a correction factor for the upper limit of permissible pore pressure under extreme warm and humid conditions, typically ranging from 0 to 0.3. The upper limit of the allowable displacement of the reference datum is determined by the relevant construction specifications. This represents the correction factor for the upper limit of allowable displacement under extreme warm and humid conditions, and is generally taken as 0 to 0.3.

[0196] Iterate through all random samples and calculate the comprehensive slope safety limit value for each random sample.

[0197] S64, count the number of samples in the slope failure state to obtain the time-varying failure probability. Then, the failure probabilities at each time point are used to construct a full-time failure probability curve to identify critical time windows and the most critical moment, and to calculate the time-varying reliability index driven by extreme warm and humid conditions. The formula is as follows:

[0198]

[0199]

[0200] in, for The total number of random field samples at time 1. for The number of samples that are constantly in a slope failure state. It is the inverse function of the standard normal distribution. for Time-varying reliability index driven by extreme warm and humid conditions.

[0201] Step S7: Determine the critical time window, construct a proxy model based on the critical time window, and perform a detailed time-varying reliability assessment. The specific steps are as follows:

[0202] S71, based on time interval Extreme warm and humid driving time-varying reliability indicators for all moments within the time frame were selected to meet the requirements. The continuous time interval is the danger window.

[0203] In the formula, for Time-varying reliability indicators driven by extreme warm and humid conditions This represents the minimum value among all random samples driven by extreme warm and humid time-varying reliability indices. This represents the permissible threshold for a dangerous time window. It is an empirical parameter, with an optimal range of 0.1 to 0.5. The specific value should be adjusted according to the engineering accuracy requirements. Total duration (time interval) (Set according to actual needs).

[0204] S72. Based on the safety factors corresponding to each moment within the critical time window, a Gaussian process regression surrogate model is established. The soil parameters and corresponding time and extreme temperature and humidity index within the critical time window are used as inputs, and the limit state function value and safety factor obtained through numerical simulation are used as outputs to train the surrogate model. In subsequent steps, the trained surrogate model is used to quickly predict the safety factor or limit state function value of uncalculated random samples within the critical time window, thereby improving the efficiency of reliability assessment.

[0205] S73, a time-window weighted active learning function is designed. The safety factor calculated by the surrogate model using refined numerical calculations is used as the sample point. It comprehensively considers the uncertainty of the surrogate model's prediction of the limit state function, the time risk weight within the critical time window, and the sensitivity of the seepage response to the limit state function. A larger active learning function value indicates higher uncertainty in the surrogate model's prediction at the corresponding sample point, a slope state closer to the failure boundary, and a higher risk period or greater sensitivity to hydraulic factors. This sample point is preferentially selected for real numerical simulation calculations, and the calculation results are added to the training sample set to update the surrogate model. This iteration is repeated until the convergence condition is met. Through this process, the accuracy of slope failure probability and reliability index calculations within the critical time window can be improved while reducing the large amount of repetitive numerical calculations throughout the entire time period. The formula for the active learning function is as follows:

[0206]

[0207]

[0208]

[0209] In the formula, This represents the active learning function, used to determine the next most worthwhile sample point to compute; This represents the mean of the surrogate model's predictions for the limit state function. This represents the standard deviation of the surrogate model's prediction of the limit state function. This represents the limit state function predicted by the surrogate model. This represents the standard normal random variable vector in the KL expansion of the random field, used as the input of random samples; This represents the safety factor to prevent the denominator from being zero, and is usually taken as 1e. -6 ; Indicates time risk, It is a hydraulically sensitive index, indicating the degree of sensitivity of the limiting state to pore pressure, saturation, and the location of the wetting front; Indicates pore water pressure, Indicates soil saturation. express Depth of the wetting front on the roadbed slope at any given time; , , These represent the weighting coefficients for approximating the limit state surface within the active learning function, the time risk weighting coefficient, and the hydraulic sensitivity weighting coefficient, respectively. Indicates the total duration. This indicates taking the absolute value.

[0210] In this invention, uncertainty-driven terms Used to identify the areas most likely to fail. The greater the weight of a value, the higher the probability of a landslide occurring at that moment. The model will shift its learning focus to accurately calculate the probability of a landslide occurring near these high-weight, high-risk moments. (Hydraulic sensitivity index) The larger the value, the more sensitive the limit state function is to changes in hydraulic conditions. By actively learning the function to guide the update of sample points, invalid sampling by the surrogate model during stable periods or low-risk areas can be avoided. This allows computational resources to be concentrated on critical periods and spatial areas where slope stability is rapidly reduced due to heavy rainfall, high humidity, and the advance of moist fronts, thereby achieving the rapid and reliable assessment required for risk early warning of roadbed slopes during operation.

[0211] S74, based on the updated surrogate model of S73, performs refined reliability calculations on non-stationary random field samples within the critical time window. For each moment within the critical time window, it calculates the... The comprehensive limit state function value predicted by the updated surrogate model for a random sample. Determine random samples To determine whether the slope has failed, the number of samples in a failed state at each time point within the danger window is counted again to obtain a finely corrected time-varying failure probability and reliability index. This index is used to determine whether the slope at time t requires an early warning and whether there is a significant landslide risk. The formula is as follows:

[0212]

[0213]

[0214]

[0215] in, Indicates fine-tuning Probability of failure at any given time Indicates fine-tuning Real-time reliability metrics It is the inverse function of the standard normal distribution. Indicates the most dangerous moment, The moment corresponding to the minimum; This represents the value of the independent variable that minimizes the objective function.

[0216] Based on the preliminary reliability assessment of the entire time period in step S6, this invention can concentrate computational resources on the dangerous time window during which the stability of the slope rapidly decreases under extreme warm and humid conditions. This reduces repetitive numerical calculations during stable periods and improves the calculation accuracy of failure probability and reliability indicators during dangerous periods, thereby providing quantitative basis for risk warning, traffic control, inspection and maintenance, and preventive reinforcement of highway subgrade slopes.

[0217] This invention can be used for dynamic risk identification, early warning timing determination, and maintenance and reinforcement priority ranking of highway subgrade slopes under extreme warm and humid weather conditions. It can avoid the problems of delayed identification of dangerous time windows or biased estimation of failure probability in traditional static parameter methods.

[0218] Experimental verification

[0219] A comparison of the present invention with conventional methods yields the following results: Figures 2-6 As shown, Figure 2 (a) is a distribution map of rainfall, (b) is a distribution map of temperature, (c) is a distribution map of relative humidity, (d) is a distribution map of the intensity of the four indicators, and (e) is a distribution map of the comprehensive warm and humid index. Figure 2 It can be seen that rainfall, high temperature, and relative humidity do not change synchronously over time, but rather exhibit superposition and lag effects over several time periods. Therefore, a comprehensive extreme warm and humid index can more accurately reflect the combined meteorological effects on slope soil. Figure 2 (d) High Temperature Duration Index Composite index with high temperature and high humidity Both of these indicators include temperature exceeding a threshold, so they are both set to zero when the temperature does not exceed the threshold. Therefore, they appear to overlap in certain time periods. In this experiment, the high-temperature and high-humidity processes mainly occurred within similar timeframes, resulting in similar fluctuation sequences for the two indicators, thus appearing visually overlapping in the graph. In reality... Used to describe the cumulative and decay effects of high temperatures. It is used to describe the combined effect of high temperature and high humidity, and the two have different calculation methods and physical meanings.

[0220] Then Figure 2 The extreme warm and humid environment index distribution map shown is used to calculate the slope sample safety factor at each time point driven by extreme warm and humid conditions, based on environmental parameters. The final result is as follows: Figure 3 The time-varying safety factor shown, and Figure 5 The time-varying failure probability and reliability index are shown, and the most dangerous moment t*=14 is calculated. Figure 3 The results show that, after adopting the method of this invention, the slope safety factor exhibits significant time-varying fluctuations with changes in extreme warm and humid conditions, reaching its lowest value near t=14. This indicates that the invention can capture the dangerous moment when slope stability rapidly declines under extreme warm and humid conditions. In contrast, Figure 4 The traditional method shown does not incorporate a non-stationary random field driven by extreme warm and humid conditions, resulting in a small variation in the safety factor and failing to accurately reflect the impact of sudden meteorological changes on slope stability. Figure 5 and Figure 6 Further comparison shows that the present invention enables the failure probability and reliability index to respond synchronously to extreme warm and humid processes, thereby identifying the danger window earlier and avoiding the warning delay caused by the lag in the identification of danger moments in traditional methods.

[0221] Compared with traditional methods Figure 4 , Figure 6 The comparison reveals that the safety factors of the slope samples calculated at various times without considering the extreme warm and humid conditions are significantly underestimated. The failure probability and reliability indicators fail to respond to sudden extreme warm and humid conditions, leading to an artificially high failure probability and affecting the accurate prediction of slope landslides in practical engineering. Furthermore, the traditional method calculates the most dangerous time as t*=17, proving that the traditional method cannot accurately respond to the time-varying deterioration process caused by extreme warm and humid conditions. This may cause bias in identifying dangerous times, and overestimation or underestimation of failure probability, thus affecting the accuracy of early warning. If slope early warning is conducted using the traditional method, economic or loss of life may result due to untimely warnings.

[0222] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0223] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for predicting slope reliability coupled with extreme warm and humid conditions and non-stationary random fields in soil, characterized by the following steps: include: Step S1: Obtain the soil parameters of the roadbed slope and the relevant climate data of the roadbed slope engineering site. The soil parameters include cohesion, internal friction angle and saturated permeability coefficient. Step S2: Calculate the extreme warm and humid index based on relevant climate data at the roadbed slope; Step S3: Construct the extreme warm and humid driving mean function and standard deviation function for each soil parameter; Step S4: Construct a non-stationary correlation function driven by extreme warm and humid conditions; Step S5: Discretize the random field of soil parameters of the roadbed slope to generate an extreme warm and humid driven discrete random field of the roadbed slope. Step S6: Perform seepage-strength coupled response analysis on the roadbed slope under extreme warm and humid environment, construct the limit state function, and calculate the failure probability and reliability index at each time point; Step S7: Determine the critical time window, construct a surrogate model based on the critical time window, and correct the slope failure probability and reliability index; The specific steps of S3 are as follows: S31, construct three soil parameters respectively. At all times in space The mean function driven by extreme warmth and humidity at a given location is used to calculate the variance of soil parameters, as shown in the following formula: ； ； ； In the formula, This indicates the soil cohesion at a point in space. The extreme warm and humid driving mean function at that location Indicates the internal friction angle of soil particles at a point in space. The extreme warm and humid driving mean function at that location This indicates the saturated permeability coefficient of soil at a spatial point. The extreme warm and humid driving mean function at that location Represents spatial location vector The mean initial cohesion field of the soil at that location, This represents the sensitivity coefficient of soil cohesion to warm and humid conditions. Representing a spatial point The initial mean internal friction angle field of soil particles at the location. This represents the sensitivity coefficient of the internal friction angle of soil particles to warm and humid conditions. Representing a spatial point Mean field of initial saturated permeability coefficient of soil at the location. This represents the sensitivity of the soil's saturated permeability coefficient to warm and humid conditions. express The intensity of the combined extreme warm and humid conditions at any given moment; S32, construct the corresponding extreme warm and humid driven nonstationary random fields respectively, as shown in the following formulas: ； ； In the formula, Indicates the first The spatial location vector of soil parameters ,time Extreme warm and humid conditions drive nonstationary random fields; Indicating the first under extreme warm and humid conditions Soil parameters at spatial points The mean function at that point, Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points The standard deviation function at that location, Indicating the first under extreme warm and humid conditions individual soil parameters at spatial points ,time Standardized random fields at that location, Indicates the first individual soil parameters at spatial points The base mean at that point Indicates the first individual soil parameters at spatial points The mean correction due to extreme warm and humid conditions. express The intensity of the combined extreme warm and humid conditions at any given moment; The specific steps of S4 are as follows: S41, design extreme warm and humid driving functions for the transverse and longitudinal directions of the roadbed slope, taking one of the following: linear function, saturated function, or logarithmic function; S42, determine the variation of the transverse and longitudinal correlation length models of the roadbed slope with warm and humid conditions, construct a spatial correlation length model driven by extreme warm and humid conditions, and perform local corrections using the wetting front correction function, as shown in the following formula: ； ； ； In the formula, express Depth of the wetting front on the roadbed slope at any given time. This indicates that the moist front affects bandwidth. Indicates the correction strength. , Roadbed slopes under extreme warm and humid conditions The horizontal and vertical correlation lengths at any given moment , These represent the initial relevant lengths in the horizontal and vertical directions of the roadbed slope, respectively. , These represent the influence coefficients of extreme warm and humid conditions on the horizontal and vertical correlation lengths, respectively. , Let represent the extreme warm and humid driving functions in the lateral and longitudinal directions, respectively. Representing a spatial point The vertical coordinate, Representing a spatial point The vertical coordinate, This represents the correction function for the wetting front. express The intensity of the combined extreme warm and humid conditions at any given time. Indicates taking the absolute value; S43, construct a non-stationary spatial correlation function driven by extreme warm and humid conditions, calculate the correlation coefficient of the parameter field at different locations, and first discretize the slope calculation area into spatial points. Then calculate the first Any two spatial points of soil parameters , exist The non-stationary spatial correlation coefficient at time t, The formula is as follows: ； In the formula, Indicates the first Any two spatial points in the parameter field of a soil parameter , exist Correlation coefficient at time, , Representing spatial points , Horizontal coordinates , Representing spatial points , The vertical coordinates, Indicating the first under extreme warm and humid conditions The correlation length of the parametric field of each soil parameter in the horizontal direction. Indicating the first under extreme warm and humid conditions The vertical correlation length of the parameter field for each soil parameter. This represents the correction function for the wetting front. express The intensity of the combined extreme warm and humid conditions at any given time. Indicates soil cohesion, Indicates the internal friction angle of soil particles, Indicates the saturated permeability coefficient of the soil. This indicates taking the absolute value.

2. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 1, is characterized in that... The specific steps of S2 are as follows: S21, calculate the rainfall humidity index and the high humidity persistence index, and then multiply the temperature and humidity excesses at the same time to obtain the high temperature and high humidity composite index. The calculation formula is as follows: ； ； ； ； In the formula, express The rainfall humidity index at any given time. express The high humidity index at any given time express The high temperature duration index at any given time. Indicates temperature. express The high temperature and high humidity composite index at any given time. express Rainfall at any given moment express Relative humidity at any given time Indicates the time lag steps. Indicates the target time. Indicates the length of the historical sliding time window. Indicates the rainfall attenuation coefficient. This indicates the effect of high humidity on the attenuation coefficient. This indicates that high temperature affects the attenuation coefficient. Indicates the high humidity threshold. Indicates the high temperature threshold. This represents the humidity cutoff function. Humidity at any time Above the high humidity threshold Only the excess portion is taken; otherwise, it is counted as 0. This represents the temperature cutoff function. Temperature of a moment Above the high temperature threshold Only the excess portion is taken; otherwise, it is counted as 0. S22, the weighted summation of the rainfall humidity index, high humidity persistence index, high temperature persistence index, and high temperature and high humidity composite index yields the comprehensive warm and humid state intensity at time t, as shown in the following formula: ； In the formula, express The intensity of the combined extreme warm and humid conditions at any given time. , , , These represent the weights of the effects of rainfall and humidity, high humidity, high temperature, and the combined effects of high temperature and high humidity, respectively. Indicates the rainfall humidity index, Indicates the high humidity persistence index. express The high temperature duration index at any given time. This indicates the high temperature and high humidity composite index.

3. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 1, is characterized in that... The specific steps of S5 are as follows: S51, this constructs a parameter cross-correlation model driven by extreme warm and humid conditions, and calculates the correlation coefficients between soil parameters under the combined extreme warm and humid conditions, as shown in the following formula: ； In the formula, express Under the combined intensity of extreme warm and humid conditions, the first and Correlation coefficients between soil parameters Indicates the first and Initial correlation coefficients between soil parameters This indicates that the first [condition] caused by extreme warm and humid conditions and The magnitude of the correlation increment between individual soil parameters Indicates the sensitivity coefficient driven by extreme warmth and humidity. express The intensity of the combined extreme warm and humid conditions at any given time. Represents a constant function; S52, Construct soil parameters at spatial points , The cross-covariance function between the soil parameters and the joint covariance matrix containing the three soil parameters. The formula is as follows: ； ； ； In the formula, express Time of the first and individual soil parameters at spatial points , The cross-variance between them Indicates the first under extreme warm and humid conditions and Correlation coefficients between soil parameters express Time of the first and Spatial correlation correction terms between soil parameters Indicates the first Any two spatial points in the parameter field of a soil parameter , exist Correlation coefficient at time, express Time of the first and individual soil parameters at spatial points , Cross-correlation coefficients between them , These represent the first under extreme warm and humid conditions. and individual soil parameters at spatial points , The standard deviation function at that location, express The joint covariance matrix at time t, for The elements in express The covariance of soil cohesion at any given time. express The covariance of soil cohesion and soil particle internal friction angle at time t is given by the following element, which is the same for all other elements. Each element represents the covariance between the two soil parameters represented by its lower angle. Indicates soil cohesion. Indicates the internal friction angle of soil particles. Indicates the saturated permeability coefficient of the soil; S53, using the KL expansion method to obtain the discrete random field driven by extreme warm and humid conditions corresponding to the soil parameters, firstly, the joint covariance matrix... Perform eigenvalue decomposition to obtain eigenvalues. With characteristic function Then, sort the feature values ​​from largest to smallest and select the top ones. The eigenvalues ​​and their corresponding eigenvectors are truncated and expanded using KL expansion to generate joint random field samples. For each random sample... All of these yielded a time-varying random field of coupled soil parameters; Finally, the joint random field samples will be used. Split according to parameter type to get the first A random sample in Discrete random field of soil parameters driven by extreme warm and humid conditions at any given time: ,in, Indicates transpose. Indicates the first A random sample in The cohesive coupled random field vector at time t, Indicates the first A random sample in The internal friction angle coupled random field vector at time t. Indicates the first A random sample in The saturation permeability coefficient at time t is coupled to the random field vector.

4. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 3, is characterized in that... The first A random sample in Cohesive Coupled Random Field Vector at Time Extremely warm and humid driven discrete random fields are ; The first A random sample in Internal friction angle coupled random field vector at time t Extremely warm and humid driven discrete random fields are ; The first A random sample in Saturation permeability coefficient coupled random field vector at time step Extremely warm and humid driven discrete random fields are ; in, Represents the cohesive coupling random field vector At the moment spatial points Extremely warm and humid conditions drive discrete random fields. Represents the vector of the coupled random field with the internal friction angle. At the time of spatial points Extremely warm and humid conditions drive discrete random fields. Represents the saturated permeability coefficient coupled random field vector At the time of spatial points Extremely warm and humid conditions drive discrete random fields.

5. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 1, is characterized in that... The specific steps of S6 are as follows: S61, for the first A random sample, and its any point in space at any time The cohesion, internal friction angle, and saturated permeability of the extreme warm and humid driven discrete random fields are denoted as follows: , , ; S62, construct the unsaturated seepage response and shear strength model under rainfall infiltration, generate soil cohesion, internal friction angle and saturated permeability coefficient at different locations of the roadbed slope through extreme warm and humid driving discrete random field, write the saturated permeability coefficient into the seepage equation, write the cohesion and internal friction angle into the shear strength formula, and calculate the roadbed slope safety factor FS. S63, construct the limiting state function considering extreme warm and humid conditions, according to the first... A random sample at time... Based on the safety factor, pore water pressure, and displacement response, limit state functions for the roadbed slope safety factor, pore water pressure, and displacement are constructed to quantitatively evaluate the slope stability and classify the risk level. The formula is as follows: ； ； ； ； In the formula, express The comprehensive limit state function for slope safety at time t. express Time of the first The safety coefficient limit state function for a random sample express Time of the first The pore water pressure limit state function for a random sample. express Time of the first The displacement limit state function of a random sample. Indicates the first under extreme warm and humid conditions A random sample in Safety factor at all times, This represents the critical value of the safety factor affected by extreme warm and humid conditions. This indicates the upper limit of the permissible pore pressure under extreme warm and humid conditions. Indicates the first A random sample at time... Maximum pore water pressure, This indicates the upper limit of permissible displacement under extreme warm and humid conditions; Indicates the first A random sample at time... The maximum slope displacement, This represents the critical value of the baseline safety factor. This represents the correction factor for the critical value of the safety factor under extreme warm and humid conditions. Indicates the upper limit of the allowable orifice pressure. This represents a correction factor for the upper limit of permissible pore pressure under extreme warm and humid conditions. Indicates the upper limit of the allowable displacement of the reference. This represents the correction factor for the upper limit of permissible displacement under extreme warm and humid conditions; Iterate through all random samples and calculate the comprehensive safety limit value of the slope for each random sample; S64, count the number of samples in the slope failure state to obtain the time-varying failure probability. Then, the failure probabilities at each time point are used to construct a full-time failure probability curve, and the time-varying reliability index driven by extreme warm and humid conditions is calculated. The formula is as follows: ； ； in, for The total number of random field samples at time 1. for The number of samples that are constantly in a slope failure state. It is the inverse function of the standard normal distribution. for Time-varying reliability index driven by extreme warm and humid conditions.

6. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 5, is characterized in that... The specific steps of S62 are as follows: S62a, will the first Saturation permeability coefficient of a random sample random field The pressure head, pore water pressure, water content, and wetting front location are calculated using an unsaturated seepage model under extreme warm and humid conditions and rainfall infiltration. The formulas are as follows: ； ； ； By solving the above seepage equation, we obtain the first... A random sample in Pore ​​pressure field at time: ； In the formula, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time Pressure head, Indicates specific water capacity. Indicates the first A random sample at spatial point ,time Total head Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time Pressure head is Temperature is The unsaturated permeability coefficient generated by the time-stochastic field Indicates the location elevation. Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time The saturation permeability coefficient generated by a random field. Indicates pressure head The relative permeability coefficient, This represents the temperature correction function for the seepage process. Indicates the boundary of rainfall infiltration. Indicates the specific gravity of water, or Indicates the first A random sample at spatial point ,time Pressure head; S62b, will the first Cohesion of a random sample under extreme warm and humid conditions driven by random fields Internal friction angle extreme warm and humid driven random field and pore water pressure extreme warm and humid driven random fields Write it into the unsaturated soil shear model, that is: ； ； In the formula, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time shear strength, Indicates the total normal pressure. Indicates pore gas pressure. Indicates the first Pore ​​water pressure of a random sample This represents the parameter of the internal friction angle of suction. Represents the tangent function; S62c, calculate the... A random sample at time... The slope safety factor is calculated using the following formula: ； In the formula, Indicates the first A random sample at time... The safety factor, Indicating the first under extreme warm and humid conditions A random sample at spatial point ,time shear strength, express At all times in space The sliding force or actual shear stress is generated by the combined effects of the soil's own weight, external loads, and seepage force. Indicates the first on the sliding surface The length of each discrete segment This represents the total number of discrete segments of the sliding surface.

7. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 5, is characterized in that... In S63, the comprehensive limit state function value of slope safety A value greater than 0 indicates that the slope is in a safe state. This indicates that the slope is in a critical state. This indicates that the slope is in a state of failure.

8. The slope reliability prediction method coupled with extreme warm and humid conditions and a non-stationary random field in soil, as described in claim 1, is characterized in that... The specific steps of S7 are as follows: S71, based on time interval Extreme warm and humid driving time-varying reliability indicators for all moments within the time frame were selected to meet the requirements. The continuous time interval is the danger window; In the formula, for Time-varying reliability indicators driven by extreme warm and humid conditions This represents the minimum value among all random samples driven by extreme warm and humid time-varying reliability indices. This indicates the permissible threshold for a dangerous time window. Total duration; S72. Based on the safety factor corresponding to each moment within the critical time window, a Gaussian process regression surrogate model is established. The soil parameters and corresponding time and extreme temperature and humidity index within the critical time window are used as inputs, and the limit state function value and safety factor obtained through numerical simulation are used as outputs to train the surrogate model. S73, a time-window weighted active learning function is designed. The safety coefficient, calculated using refined numerical values ​​from the surrogate model, is used as the sample points. The function selects these sample points for real numerical simulation calculations, and the results are added to the training sample set to update the surrogate model. This process is repeated iteratively until the convergence condition is met. The formula for the active learning function is as follows: ； ； ； In the formula, This represents an active learning function. This represents the mean of the surrogate model's predictions for the limit state function. This represents the standard deviation of the surrogate model's prediction of the limit state function. This represents the limit state function predicted by the surrogate model. This represents the vector of standard normal random variables in the KL expansion of a random field. This represents the safety factor to prevent the denominator from being zero. Indicates time risk, As a hydraulically sensitive indicator, Indicates pore water pressure, Indicates soil saturation. express Depth of the wetting front on the roadbed slope at any given time; , , These represent the weighting coefficients for approximating the limit state surface within the active learning function, the time risk weighting coefficient, and the hydraulic sensitivity weighting coefficient, respectively. Indicates the total duration. Indicates taking the absolute value; S74, based on the updated surrogate model of S73, performs refined reliability calculations on non-stationary random field samples within the critical time window. For each time step within the critical time window, it calculates the... The comprehensive limit state function value predicted by the updated surrogate model for a random sample. Determine random samples To determine whether a failure has occurred, the number of samples in a failed state at each moment within the critical time window is counted again to obtain a finely corrected time-varying failure probability and reliability index, as shown in the following formula: ； ； ； in, Indicates fine-tuning Probability of failure at any given time Indicates fine-tuning Real-time reliability metrics It is the inverse function of the standard normal distribution. Indicates the most dangerous moment. This represents the value of the independent variable that minimizes the objective function.

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