Seasonal frozen soft soil layer foundation stability evaluation method and system and readable storage medium

Abstract

The application discloses a seasonal frozen soft soil layer foundation stability evaluation method, system and readable storage medium, belongs to the technical field of geotechnical engineering and cold region engineering, and comprises the following steps: S1, a foundation numerical model is established; S2, a deterministic temperature field control equation is established; S3, a random temperature field is modeled; S4, node temperature statistical characteristics are obtained; S5, a mapping relationship between temperature and shear strength parameters is established, and a strength field is obtained; S6, an integral extreme value method is used to determine a most unfavorable sliding surface, and corresponding safety factors and limit bearing capacities are calculated; S7, safety factor statistical results are obtained; S8, an instability probability is calculated, and an instability probability cloud map is obtained; and S9, a comprehensive evaluation report is output. The method comprehensively considers the influence of a random temperature field, realizes whole-process coupling of temperature-strength-stability, solves the most unfavorable sliding surface by using the integral extreme value method, improves calculation efficiency and accuracy, provides probabilistic stability evaluation results, and has strong practicability and can be integrated with an existing software platform.

Description

Technical Field

[0001] This invention relates to the fields of geotechnical engineering and cold-region engineering technology, and more specifically, to a method, system, and readable storage medium for evaluating the stability of seasonally frozen soft soil foundations. Background Technology

[0002] Seasonally frozen areas are widely distributed in Northeast, Northwest, and plateau regions of my country. Railway and highway subgrades and building foundations are directly or indirectly arranged on seasonally frozen soft soil layers. Soft soil has high strength and stiffness when frozen, but its strength decreases significantly after thawing. Furthermore, repeated freeze-thaw cycles can lead to structural damage and bearing capacity reduction in frozen soil, causing excessive settlement, tilting, or even overall slippage and instability of the foundation.

[0003] In existing engineering designs, the foundation stability evaluation usually adopts the following simplified methods: (1) the foundation soil is regarded as a homogeneous material with constant temperature, and only two sets of strength parameters are taken for limit equilibrium analysis under the two extreme conditions of "freezing" and "thawing"; (2) the temperature is regarded as a deterministic distribution, and only the soil above one isotherm is taken for strength reduction according to the design freezing depth; (3) finite element bearing capacity analysis is performed for winter and summer respectively, but the randomness and time-varying nature of temperature field and thermal parameters, strength parameters are not considered. The above methods ignore the spatial dispersion of thermal parameters (such as thermal conductivity, volumetric specific heat, latent heat, etc.) of seasonally frozen soft soil, the random fluctuation of atmospheric boundary temperature and geothermal gradient, and the evolution of soft soil strength parameters with temperature and the number of freeze-thaw cycles during the freeze-thaw process. The safety factor obtained is often conservative or optimistic, making it difficult to identify the "most unfavorable period" and "most dangerous slip surface" during the annual freeze-thaw cycle, and also unable to give a reliability evaluation based on the probability of instability.

[0004] Therefore, it is necessary to propose a new evaluation method for the stability analysis of seasonally frozen soft soil foundations, so as to achieve a refined and probabilistic evaluation of foundation stability throughout the freeze-thaw cycle. Summary of the Invention

[0005] The purpose of this invention is to provide a method, system, and readable storage medium for evaluating the stability of seasonally frozen soft soil foundations, in order to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for evaluating the stability of seasonally frozen soft soil foundations, comprising the following steps: S1: Establish a numerical model of the foundation of the seasonally frozen soft soil layer, and set boundary conditions and initial conditions; S2: Establish the deterministic temperature field control equations; S3: Modeling of stochastic temperature fields; S4: Based on the random temperature field in step S3, obtain the statistical characteristics of the node temperature; S5: Establish the mapping relationship between temperature and shear strength parameters, and obtain the strength field based on the nodal temperature statistical characteristics obtained in step S4; S6: Based on the strength parameter field obtained in step S5, the most unfavorable slip surface is determined using the integral extreme value method, and the corresponding safety factor and ultimate bearing capacity are calculated. S7: Calculate the safety factor in step S6 to obtain the safety factor statistical results; S8: Calculate the instability probability and obtain the instability probability cloud map; S9: Output a comprehensive evaluation report, which includes the temperature field, intensity field, most unfavorable slip surface morphology, safety factor statistics, and instability probability cloud map.

[0007] Furthermore, the specific process of step S1 includes: S11: Collect meteorological data, geothermal gradient, ground cover / structure type, and groundwater level information of the engineering area, and obtain the layered structure, soil mechanical parameters, and statistical characteristics of thermal parameters of the seasonally frozen soft soil layer. S12: Construct the foundation calculation domain according to the foundation type, determine the upper boundary as the ground or foundation bottom surface, determine the lower boundary as the isothermal surface, and determine the side boundaries as the adiabatic or symmetrical boundaries; S13: Discretize the foundation calculation domain using finite element method, divide the seasonally frozen soft soil layer area, and assign corresponding soil layer properties to each element; S14: The boundary conditions for determining the upper boundary are convective heat transfer boundaries based on atmospheric temperature changes over time; the boundary conditions for determining the lower boundary are geothermal gradient or constant heat flux boundaries; the boundary conditions for determining the lateral boundaries are adiabatic boundaries or given heat flux boundaries; and the initial conditions are measured or empirical geothermal profiles on a certain reference date.

[0008] Furthermore, the specific process of step S2 includes: In a rectangular coordinate system, the seasonally frozen soft soil is considered as a three-phase zone consisting of frozen soil, thawed soil, and phase transition zone, and the following are established respectively: Permafrost is a frozen zone, and its heat conduction equation is:

[0009] in, For time; The temperature of the soil in a frozen state; The thermal conductivity of frozen soil; The specific heat or equivalent heat capacity of frozen soil; The melting zone of the clay is represented by the following heat conduction equation:

[0010] in, The temperature of the frozen soil; The thermal conductivity of unfrozen soil; The volumetric specific heat or equivalent heat capacity of unfrozen soil; The phase transition zone is the phase transition region. The heat conduction equation is established using the equivalent thermal melting method. The equation is as follows:

[0011] in, Specific heat capacity; Based on volumetric specific heat; This refers to the soil density. Latent heat of phase transition; , These are the upper and lower limits of the phase transition temperature range. Indicates the freezing start temperature. This indicates the temperature at which freezing is complete.

[0012] Furthermore, the specific process of step S3 includes: S31: Treat the thermal parameters of soft soil as a spatial random field, set the mean and standard deviation, and construct the spatial correlation function and covariance matrix; S32: Treat the atmospheric boundary temperature parameters as a random field, set the mean and standard deviation, and construct the spatial correlation function and covariance matrix; S33: Perform spectral decomposition on the random fields of steps S31 and S32 using Neumann expansion or Karhunen–Loève expansion to obtain a linear combination of several independent standard normal random variables; S34: Use the Monte Carlo method to sample the random variables in step S33 to generate multiple sets of thermal parameters and boundary condition samples; S35: For each sample group, based on the foundation numerical model of step S1 and the deterministic temperature field control equation of step S2, the heat conduction equation is discretized using the weighted residual method to obtain the discrete equation:

[0013] in, Represents the heat conduction matrix; Indicates time Temperature vector at any given time; Represents the heat capacity matrix; Indicates time The load vector at time; S36: The stochastic temperature field during multi-year freeze-thaw cycles is obtained by using backward difference or Crank–Nicolson time integration scheme methods.

[0014] Furthermore, the specific process of step S5 includes: S51: Based on indoor frozen soil tests or literature experience, establish the mapping relationship between the shear strength parameters of seasonally frozen soft soil and temperature. The mapping relationship is as follows: ,

[0015] in, This represents the soil temperature, which can be negative or positive. This is the absolute value of the temperature, representing the temperature range from 0℃. For temperature Cohesion at that time; For temperature The internal friction angle at that time; Cohesion at a reference temperature (usually 0°C or a certain reference temperature); The internal friction angle at the reference temperature; This is the coefficient representing the change in cohesion as a function of the absolute value of temperature. This is the coefficient that represents the change of the internal friction angle with the absolute value of temperature. S52: Based on the node temperature statistical characteristics of step S4, obtain temperature data, substitute the corresponding temperatures into the mapping relationship of step S51, and generate several sets of intensity fields.

[0016] Furthermore, the specific process of step S6 includes: S61: Define the family of slip surfaces based on the basic form and potential instability modes; S62: Treat the foundation as a heterogeneous body, in a plane Inside, using the coordinates of the center of the circle. With radius The slip surface is represented by the slip surface formula: , The slip surface intersects the ground surface at two points. , The corresponding arc function is: , , S63: The foundation sliding body is... The upper boundary of the sliding body is discretized by vertical strips. The lower boundary of the sliding body is The strip width is Then the strip height for: , strip area for:

[0017] strip weight for:

[0018] in, This represents the severity of the band at the corresponding location. Tangent angle of slip surface The formula is obtained from the derivative of the slip surface, as follows:

[0019]

[0020] Differential of arc length of slip surface for:

[0021] S64: The infinitesimal tangential force element of the strip along the slip surface direction without introducing inter-strip forces. for:

[0022] Normal force element for:

[0023] Considering pore water pressure The reduction in effective normal force results in the pore pressure per unit width of the slip surface being: Effective normal force element Represented as:

[0024] The shear strength at any point on the slip surface is expressed using the Mohr-Coulomb effective stress, as shown in the formula:

[0025] in, Indicates the location Shear strength of the soil at the location; For in position The cohesion of the soil; For in position The internal friction angle of the soil at that location; Effective normal stress; Effective normal stress The formula is:

[0026] Total resistance of the slip surface The integral over the arc length is given by the formula:

[0027] Sliding force The formula for the tangential integral over the slip surface is:

[0028] The parameters of the slip surface family are Safety factor at time Defined as:

[0029] S65: The slip surface that minimizes the safety factor is defined as the most unfavorable slip surface, i.e.:

[0030] in, For the feasible region of the parameters; This is the optimal solution; like exist If an element is interiorly differentiable, then the interior extrema satisfy a necessary first-order condition:

[0031]

[0032] The equivalent extreme value condition is obtained as follows:

[0033] in , , , Solve by applying the chain rule to the upper and lower limits of integration and the integrand; S66: Approximation using numerical difference method , The formula is:

[0034]

[0035] S67: For each set of intensity field samples, the most unfavorable slip surface and corresponding safety factor are solved at each key date using grid search and local optimization methods. S68: For each set of strength field samples, the ultimate bearing capacity of the foundation is obtained by the strength reduction finite element method.

[0036] Furthermore, the specific process of step S7 includes: S71: For the safety factor of all samples, calculate the mean, standard deviation, coefficient of variation, and distribution function of the safety factor. The mean safety factor is: ,

[0037] in, Indicates the number of key dates; Indicates the number of samples; It is an index variable, from 1 to... This is used to iterate through all key dates; It is an index variable, from 1 to... This is used to iterate through all samples; Indicates key dates; Indicates the key date The average safety factor at the location; Indicates the first Key Dates in Group Intensity Field Samples Safety factor at the location; The standard deviation of the safety factor is:

[0038] in, Indicates the key date The standard deviation of the safety factor at the location; The coefficient of variation of the safety factor is:

[0039] in, Indicates the key date The safety factor and coefficient of variation at the location; The empirical distribution function of the safety factor is:

[0040] in, The representation function takes the value 1 if the condition is true, and 0 otherwise; For a given threshold; S72: The minimum safety factor among all samples in the multi-year freeze-thaw cycle. for:

[0041] Corresponding most dangerous date index for:

[0042] Statistics of all samples The occurrence of the minimum safety factor is used to obtain the critical date and freezing depth corresponding to the minimum safety factor. The minimum safety factor is then represented by time series as "minimum safety factor - critical date - corresponding freezing depth". S73: Obtain the statistical results of the safety factor.

[0043] Furthermore, the specific process of step S8 includes: S81: For key dates Define two types of limit state functions: Limit state function based on safety factor :

[0044] in, The target safety factor; The corresponding instability event is:

[0045] Limit state function based on bearing capacity :

[0046] in, Indicates the first Key Dates in Group Intensity Field Samples Ultimate bearing capacity at the location; Indicates demand carrying capacity; The corresponding instability event is:

[0047] S82: Probability of instability based on safety factor criterion for:

[0048] Instability probability based on bearing capacity criterion for:

[0049] Joint failure If we adopt the principle that "satisfying any instability probability is considered a failure," then the instability probability is:

[0050] If we adopt the principle that "satisfying both conditions simultaneously constitutes a failure", then the instability probability is:

[0051] S83: Set the instability probability threshold ,satisfy The set of dates constitutes the risk period; S84: Merge consecutive dates into a range And according to the maximum instability probability within the interval Risk classification is performed using the following formula:

[0052] in, These are the lower and upper time limits of the interval, respectively. S85: Based on the foundation numerical model of step S1, for each finite element element... unit shear strength for:

[0053] in, This represents the finite element. In the Key Dates in Group Intensity Field Samples Cohesion at the point; This represents the finite element. In the Key Dates in Group Intensity Field Samples Effective normal stress at the location; This represents the finite element. In the Key Dates in Group Intensity Field Samples The internal friction angle at the location; Unit safety margin function for:

[0054] in, Indicates the required shear stress of the element; The unit instability event is:

[0055] Then the probability of unit instability for:

[0056] All units Map back to the grid to get the key date The probability cloud of instability.

[0057] This invention provides a system for evaluating the stability of seasonally frozen soft soil foundations, comprising: The input module is used to input foundation geometric information, soil layer division, statistical characteristics of soil mechanical and thermal parameters, and meteorological and geothermal data; The foundation numerical modeling module is used to establish a foundation numerical model for seasonally frozen soft soil layers. The random temperature field modeling module is used to construct random fields of thermal parameters and boundary conditions, perform spectral decomposition and sample sampling, solve equations for each set of samples, and obtain the random temperature field during multi-year freeze-thaw cycles. The parameter mapping module is used to convert the temperature field into an intensity field; The stability analysis module is used to determine the most unfavorable slip surface and calculate the safety factor; The reliability evaluation and visualization module is used to perform statistical analysis on the safety factor, calculate the instability probability, and output a comprehensive evaluation report on foundation stability.

[0058] Furthermore, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0059] Compared with the prior art, the present invention has the following technical effects: In this invention, the stability evaluation method for terrestrial soft soil layers provided by this invention treats thermal parameters and atmospheric boundary temperature parameters as random fields, and uses stochastic finite element analysis to calculate the temperature evolution during the multi-year freeze-thaw process. This truly reflects the uncertainty and time-varying nature of the temperature field of the terrestrial soft soil foundation, and comprehensively considers the influence of the random temperature field. By establishing a mapping relationship between soft soil strength parameters and temperature, a strength field is formed in space and an evolution sequence is formed in time, expanding the foundation stability evaluation from the traditional "static two-condition" to "full-process time-varying analysis," realizing the full-process coupling of temperature, strength, and stability. Based on integral poles... The value method for solving the most unfavorable slip surface eliminates the need for extensive trial calculations, improving computational efficiency and accuracy. It is also applicable to integrated foundation-subgrade conditions. Through Monte Carlo simulation and statistical analysis of safety factors, a comprehensive evaluation report is provided, offering quantitative basis for selecting design safety factors, comparing reinforcement schemes, and managing operational risks. It also provides probabilistic stability evaluation results, which have practical guiding significance for engineering design. Based on a finite element / finite difference platform, it is easy to interface with existing geotechnical analysis software and monitoring systems, and can be widely applied in railway, highway, municipal, and building foundation engineering. It has strong applicability and is conducive to integration with existing software platforms. Attached Figure Description

[0060] Figure 1 This is a flowchart of the method for evaluating the stability of seasonally frozen soft soil foundations according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the foundation calculation domain and boundary conditions according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the random temperature field of the seasonally frozen soft soil layer and the location of the 0°C isotherm in an embodiment of the present invention. Figure 4 This is a schematic diagram of the parameterization of the slip surface and the geometric quantities of the stripe in an embodiment of the present invention; Figure 5 This is a schematic diagram of the strip under stress according to an embodiment of the present invention; Figure 6 This is a flowchart illustrating the integral extremum method for determining the most unfavorable slip surface and safety factor according to an embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the evolution of the most unfavorable slip surface location under different freeze-thaw stages in an embodiment of the present invention; Figure 8 This is a schematic diagram of the structure of the seasonally frozen soft soil foundation stability evaluation system according to an embodiment of the present invention. Detailed Implementation

[0061] 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 a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0062] In this article, terms such as "left," "right," "up," "down," "front," and "back" are established based on the positional relationships shown in the attached drawings. Depending on the attached drawings, the corresponding positional relationships may also change. Therefore, they should not be interpreted as an absolute limitation on the scope of protection.

[0063] Please see Figures 1 to 8 This embodiment provides a method for evaluating the stability of seasonally frozen soft soil foundations, including the following steps: S1: Establish a numerical model of the foundation of the seasonally frozen soft soil layer, and set boundary conditions and initial conditions.

[0064] Specifically, the process of step S1 includes: S11: Collect meteorological data (such as multi-year average daily temperature, annual temperature range, and warming trend), geothermal gradient, surface cover / structure type, and groundwater level information for the project area; obtain the layered structure, soil mechanical parameters, and statistical characteristics of thermal parameters of the seasonally frozen soft soil layer. The statistical characteristics of soil mechanical and thermal parameters include natural unit weight, water content, void ratio, thermal conductivity, specific heat, latent heat, and freezing temperature range.

[0065] S12: Construct a two-dimensional or three-dimensional foundation calculation domain based on the foundation type (such as strip foundation, isolated foundation, raft foundation or roadbed-subgrade integrated structure, etc.), determine the upper boundary as the ground or foundation bottom surface, determine the lower boundary (fixed boundary) as an isothermal surface at a certain depth, and determine the side boundary (non-drained boundary) as an adiabatic or symmetrical boundary.

[0066] S13: Discretize the foundation calculation domain using finite element methods, divide the seasonally frozen soft soil layer area using triangular or quadrilateral meshes, and assign corresponding soil layer properties to each element.

[0067] S14: The boundary conditions for the upper boundary are determined using a convective heat transfer boundary where atmospheric temperature varies over time. This temperature variation can be expressed as a superposition of multi-year averages, periodic terms, and long-term warming trends. The boundary conditions for the lower boundary are determined using a geothermal gradient or a constant heat flux boundary. The boundary conditions for the lateral boundaries are determined using an adiabatic boundary or a given heat flux boundary. Initial conditions are based on measured or empirical geothermal profiles from a reference date.

[0068] S2: Establish the deterministic temperature field control equations.

[0069] Specifically, the process of step S2 includes: In a rectangular coordinate system, the seasonally frozen soft soil is considered as a three-phase region consisting of frozen soil, thawed soil, and phase transition zone, and the following are established respectively: Permafrost is a frozen zone, and its heat conduction equation is:

[0070] in, For time; The temperature of the soil in a frozen state ( (meaning frozen); The thermal conductivity of frozen soil; This refers to the volumetric specific heat or equivalent heat capacity of frozen soil.

[0071] The melting zone of the clay is represented by the following heat conduction equation:

[0072] in, The temperature of the frozen soil ( (meaning unfrozen); The thermal conductivity of unfrozen soil; This refers to the volumetric specific heat or equivalent heat capacity of unfrozen soil.

[0073] The phase transition zone is the phase transition region. The heat conduction equation is established using the equivalent thermal melting method. The equation is as follows:

[0074] in, Specific heat capacity; Reference volumetric specific heat (can be taken as) Or a weighted average of the volumetric specific heat of freezing / thawing). This refers to the soil density. Latent heat of phase change (units can be taken as follows) ); , These are the upper and lower limits of the phase change temperature range (freeze-thaw temperature range). Indicates the freezing start temperature. Indicates the temperature at which freezing is complete, generally .

[0075] S3: Modeling of stochastic temperature fields.

[0076] Specifically, the process of step S3 includes: S31: Treating the thermal conductivity, specific heat, and latent heat of soft soil as spatial random fields, and setting the mean and standard deviation, a spatial correlation function and a covariance matrix are constructed. The covariance matrix is ​​constructed using the local averaging method. The spatial correlation length can be obtained from the spatial correlation function, and the spatial correlation length is taken as 2~10m, preferably 3~6m.

[0077] S32: Treat atmospheric boundary temperature parameters (such as annual average temperature, annual amplitude, long-term warming rate, etc.) as random fields, set the mean and standard deviation, and construct the spatial correlation function and covariance matrix. The covariance matrix is ​​constructed using the local averaging method, and the spatial correlation length can be obtained from the spatial correlation function. The spatial correlation length is 2~10m, preferably 3~6m.

[0078] S33: Perform spectral decomposition on the random field in steps S31 and S32 using Neumann expansion or Karhunen–Loève expansion, approximating the random field as a linear combination of several (preferably 5 to 20) independent standard normal random variables in this embodiment.

[0079] S34: Use the Monte Carlo method to sample the random variables in step S33 to generate N sets of thermal parameters and boundary condition samples (N≥200, preferably 500~1000).

[0080] S35: For each sample group, based on the foundation numerical model of step S1 and the deterministic temperature field control equation of step S2, the heat conduction equation is discretized by finite element method using the weighted residual method (specifically Galerkin method in this embodiment) to obtain the discrete equation:

[0081] in, Represents the heat conduction matrix; Indicates time Temperature vector at any given time; Represents the heat capacity matrix; Indicates time The load vector at time t.

[0082] S36: Using the backward difference or Crank–Nicolson time integration scheme, with a time step of day or hour (the time step can be 0.5 to 24 hours), the temperature field in the multi-year freeze-thaw cycle process is calculated step by step, and finally the stochastic temperature field in the multi-year freeze-thaw cycle process is obtained.

[0083] S4: Based on the random temperature field obtained in step S3, obtain the nodal temperature statistical characteristics for each key date (such as the initial freezing point, the maximum freezing depth, the initial thawing point, and the complete thawing point) within a given evaluation year. The temperature statistical characteristics include the mean temperature field, variance field, coefficient of variation field, and the location of the 0℃ isotherm.

[0084] S5: Establish the mapping relationship between temperature and shear strength parameters. Based on the nodal temperature statistical characteristics of step S4, obtain the strength field (i.e., random strength parameter samples).

[0085] Specifically, the process of step S5 includes: S51: Based on indoor frozen soil tests or literature experience, establish the mapping relationship between the shear strength parameters of seasonally frozen soft soil and temperature. The mapping relationship is as follows: ,

[0086] in, The soil temperature (°C) can be negative (frozen) or positive (unfrozen). This is the absolute value of the temperature, representing the temperature range from 0℃. For temperature Cohesion at time ； For temperature The internal friction angle at that time; Cohesion at a reference temperature (usually 0°C or a certain reference temperature); The internal friction angle at the reference temperature; It is the coefficient of cohesion as a function of the absolute value of temperature, reflecting "how much cohesion increases for every 1°C increase (or decrease); This is the coefficient by which the internal friction angle changes with the absolute value of temperature.

[0087] S52: For each unit, based on the node temperature statistical characteristics obtained in step S4, temperature data samples are obtained. The corresponding temperatures are then substituted into the mapping relationship in step S51 to generate random intensity parameter samples for that unit on each key date. , .in, For the first The finite element element in the first... The nth random temperature field sample (the nth Sample values ​​of cohesion (effective cohesion) at a specified key date (or specified time) under sub-Monte Carlo / random field realizations, typically in kPa; For the first The finite element element in the first... Sample values ​​of internal friction angle (effective internal friction angle) at a specified key date (or specified time) under a random temperature field sample; subscript Indicates "element number / element index"; superscript Indicates "the The random sample / the first The random implementation / the "Group of temperature field samples".

[0088] Specifically, the mapping relationship can be transformed into a more general piecewise linear or nonlinear extended form, and a freeze-thaw cycle coefficient can be further introduced. The influence of temperature, strength, and pore pressure can be further investigated for highly saturated soft soils. For these soils, a multivariate relationship between cohesion, internal friction angle, ice content, and pore water pressure can be established to achieve a coupled mapping of temperature, strength, and pore pressure.

[0089] S6: Based on the strength parameter field obtained in step S5, the most unfavorable slip surface is determined using the integral extreme value method, and the corresponding safety factor is calculated.

[0090] Specifically, the process of step S6 includes: S61: Define a family of slip surfaces based on the basic form and potential instability modes, including slip surfaces with the base surface as the main slip surface, circular-fold slip surfaces passing through weak interlayers, and overall tilting slip surfaces, etc.

[0091] S62: Treat the foundation as a heterogeneous body, in a plane Inside, using the coordinates of the center of the circle. With radius The slip surface is represented by the slip surface formula:

[0092] The slip surface intersects the ground surface (or slope) at two endpoints. , The corresponding circular arc function (taking the branch located at the lower boundary of the sliding body) is: ,

[0093] Among them, the two endpoints , From the slip surface and the surface line Intersection equations To obtain.

[0094] S63: The foundation sliding body is... The upper boundary of the sliding body is discretized by vertical strips. The lower boundary (slip surface) of the sliding body is The strip width is Then the strip height for: , strip area (Plane strain per unit thickness) is:

[0095] strip weight for:

[0096] in, This represents the density of the corresponding position of the strip (which can vary with stratification).

[0097] Tangent angle of slip surface The formula is obtained from the derivative of the slip surface, as follows:

[0098]

[0099] Differential of arc length of slip surface for:

[0100] S64: The infinitesimal tangential force element of the strip along the slip surface direction without introducing interstrip forces (which can be regarded as a simplified Bishop / Ordinary method in the sense of global integration). for:

[0101] Normal force element (When inter-strength correction is neglected) is:

[0102] Considering pore water pressure The reduction in effective normal force results in the pore pressure per unit width of the slip surface being: Effective normal force element Represented as:

[0103] The shear strength at any point on the slip surface is expressed using the Mohr-Coulomb effective stress, as shown in the formula:

[0104] in, Indicates the location Shear strength of the soil at the location; For in position The cohesion of the soil can vary with space (layers); For in position The internal friction angle of the soil can vary with space (layers); This is the effective normal stress.

[0105] Effective normal stress The formula is:

[0106] Total resistance of the slip surface (per unit thickness) The integral over the arc length is given by the formula:

[0107] Sliding force The formula for the tangential integral over the slip surface is:

[0108] The parameters of the slip surface family are Safety factor at time Defined as: .

[0109] S65: The slip surface that minimizes the safety factor is defined as the most unfavorable slip surface, i.e.:

[0110] in, The feasible region for parameters (ensuring that the slip surface has two intersections with the ground surface, the area of ​​the slip body is positive, and the slip surface does not penetrate the bottom edge of the computational domain, etc.). The optimal solution (that is, the objective function) (Parameter value that reaches the minimum value).

[0111] like exist If an element is interiorly differentiable, then the interior extrema satisfy a necessary first-order condition:

[0112]

[0113] The equivalent extreme value condition is obtained as follows:

[0114] in , , , The solution is found by applying the chain rule to the upper and lower limits of integration and the integrand.

[0115] S66: In the project, , , , Since it is difficult to solve analytically, the numerical difference method is used for approximation. , The formula is:

[0116]

[0117] S67: For each set of intensity field samples, the most unfavorable slip surface and corresponding safety factor are solved at each critical date using grid search and local optimization methods. The local optimization method can be the gradient method or the quasi-Newton method.

[0118] S68: For each set of strength field samples, the ultimate bearing capacity of the foundation is obtained by the strength reduction finite element method.

[0119] S7: Statistically analyze the safety factor in step S6 to obtain the safety factor statistical results.

[0120] Specifically, the process of step S7 includes: S71: For the safety factor of all samples, calculate the mean, standard deviation, coefficient of variation, and distribution function of the safety factor. The mean safety factor is: ,

[0121] in, Indicates the number of key dates; Indicates the number of samples; It is an index variable, from 1 to... This is used to iterate through all key dates; It is an index variable, from 1 to... This is used to iterate through all samples; Indicates key dates; Indicates the key date The average safety factor at the location; Indicates the first Key Dates in Group Intensity Field Samples Safety factor at the location.

[0122] The standard deviation of the safety factor is:

[0123] in, Indicates the key date The standard deviation of the safety factor at the location.

[0124] The coefficient of variation of the safety factor is:

[0125] in, Indicates the key date The safety factor and coefficient of variation at the location.

[0126] The empirical distribution function of the safety factor is:

[0127] in, The representation function takes the value 1 if the condition is true, and 0 otherwise; For a given threshold.

[0128] S72: The minimum safety factor among all samples in the multi-year freeze-thaw cycle. for:

[0129] Corresponding most dangerous date index for:

[0130] Statistics of all samples The occurrence of the minimum safety factor is used to obtain the critical date and freezing depth corresponding to the minimum safety factor. The minimum safety factor is then represented by time series as "minimum safety factor - critical date - corresponding freezing depth".

[0131] S73: Obtain the statistical results of the safety factor.

[0132] S8: Calculate the instability probability and obtain the instability probability cloud map; Specifically, the process of step S8 includes: S81: For key dates Define two types of limit state functions: Limit state function based on safety factor :

[0133] in, The target safety factor.

[0134] The corresponding instability event is:

[0135] Limit state function based on bearing capacity :

[0136] in, Indicates the first Key Dates in Group Intensity Field Samples Ultimate bearing capacity at the location; This represents the required bearing capacity, which can be taken as the average pressure of the design foundation or the required value calculated based on the load combination.

[0137] The corresponding instability event is:

[0138] S82: Probability of instability based on safety factor criterion for:

[0139] Instability probability based on bearing capacity criterion for:

[0140] Joint failure If we adopt the principle that "satisfying any instability probability is considered a failure," then the instability probability is:

[0141] If we adopt the principle that "satisfying both conditions simultaneously constitutes a failure", then the instability probability is:

[0142] S83: Set the instability probability threshold (e.g., 5%, 10%, etc., can be set according to project management requirements), to meet The set of dates constitutes the risk period.

[0143] S84: Merge consecutive dates into a range And according to the maximum instability probability within the interval Risk classification is performed using the following formula:

[0144] in, These represent the lower and upper time limits of the interval, respectively.

[0145] S85: Based on the foundation numerical model of step S1, for each finite element element... unit shear strength for:

[0146] in, This represents the finite element. In the Key Dates in Group Intensity Field Samples Cohesion at the point; This represents the finite element. In the Key Dates in Group Intensity Field Samples Effective normal stress at the location; This represents the finite element. In the Key Dates in Group Intensity Field Samples The internal friction angle at the location; Unit safety margin function for:

[0147] in, This represents the unit's required shear stress, derived from numerical calculations (such as shear stress output or equivalent shear stress under the influence of self-weight / frost heave).

[0148] The unit instability event is:

[0149] Then the probability of unit instability for:

[0150] All units Map back to the grid to get the key date The instability probability cloud (colors indicate the magnitude of the probability).

[0151] S9: Output a comprehensive evaluation report, which includes the temperature field, intensity field, most unfavorable slip surface morphology, safety factor statistics, and instability probability cloud map.

[0152] Please see Figure 5 This embodiment provides a stability evaluation system for seasonally frozen soft soil foundations, including: The input module is used to input foundation geometric information, soil layer division, statistical characteristics of soil mechanical and thermal parameters, and meteorological and geothermal data; The foundation numerical modeling module is used to establish a foundation numerical model for seasonally frozen soft soil layers. The random temperature field modeling module is used to construct random fields of thermal parameters and boundary conditions, perform spectral decomposition and sample sampling, solve equations for each set of samples, and obtain the random temperature field during multi-year freeze-thaw cycles. The parameter mapping module is used to convert the temperature field into an intensity field; The stability analysis module is used to determine the most unfavorable slip surface and calculate the safety factor; The reliability evaluation and visualization module is used to perform statistical analysis on the safety factor, calculate the instability probability, and output a comprehensive evaluation report on foundation stability.

[0153] This embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the stability evaluation method for seasonally frozen soft soil foundations as described above.

[0154] Specifically, the stability evaluation method for seasonally frozen soft soil layers provided by this invention treats thermal parameters and atmospheric boundary temperature parameters as random fields and uses stochastic finite element analysis to calculate temperature evolution during multi-year freeze-thaw cycles. This realistically reflects the uncertainty and time-varying nature of the temperature field in the foundation of seasonally frozen soft soil layers, comprehensively considering the influence of the random temperature field. By establishing a mapping relationship between soft soil strength parameters and temperature, a strength field is formed spatially and an evolution sequence is formed temporally, expanding the foundation stability evaluation from the traditional "static two-condition" to "full-process time-varying analysis," realizing the full-process coupling of temperature, strength, and stability. Based on integral extreme values... The method for solving the most unfavorable slip surface eliminates the need for extensive trial calculations, improving computational efficiency and accuracy. It is applicable to integrated foundation-subgrade conditions. Through Monte Carlo simulation and statistical analysis of safety factors, a comprehensive evaluation report is provided, offering quantitative basis for selecting design safety factors, comparing reinforcement schemes, and managing operational risks. It also provides probabilistic stability evaluation results, which have practical guiding significance for engineering design. Based on a finite element / finite difference platform, it is easy to interface with existing geotechnical analysis software and monitoring systems, and can be widely applied in railway, highway, municipal, and building foundation engineering. It has strong applicability and is easy to integrate with existing software platforms.

[0155] To further elaborate on the method for evaluating the stability of foundations in seasonally frozen soft soil layers, the following section takes a seasonally frozen region as the research object and provides a more detailed explanation of the invention.

[0156] I. Project Overview A railway is located in a seasonally frozen region with a maximum frost depth of approximately 1.8 meters, an embankment height of 4 meters, and a soft soil layer of approximately 6 meters thick, underlying a medium-dense sand layer. The design speed is relatively high, placing strict requirements on roadbed deformation and stability.

[0157] II. Establishment of Foundation Numerical Model Based on the survey data, the soil layers were divided into three layers from top to bottom: embankment fill, seasonally frozen soft clay, and medium-graveled sand. A two-dimensional plane strain model was used to simulate the embankment-foundation system. The computational domain length was taken as at least three times the embankment height on both sides of the embankment width, and the depth was 15m. The upper boundary was the embankment slope and pavement, the lower boundary was the isothermal surface, and the side boundaries were adiabatic boundaries. An unstructured triangular mesh was used to partition the seasonally frozen soft soil layer, with the mesh size finer at the embankment toe and weak interlayers. Boundary conditions for the upper, lower, and side boundaries, as well as initial conditions, were set.

[0158] III. Modeling of Stochastic Temperature Fields Based on 30 years of local meteorological data, atmospheric boundary temperature parameters such as annual average temperature, annual temperature range, and warming trend were obtained. These parameters were treated as random fields, and their mean and coefficient of variation were calculated. The thermal conductivity, volumetric specific heat, and latent heat of each soil layer were also treated as spatial random fields, and the probability distributions of these parameters were determined based on indoor measurements. Using a spatial length of 5 m, the Karhunen–Loève expansion was employed to reduce the dimensionality of each random field to 10 independent standard normal variables. N=500 samples were generated using the Monte Carlo method. By calculating the temperature field on several key dates each year during a 10-year freeze-thaw cycle, the nodal temperature statistical characteristics were obtained for each key date (e.g., initial freezing point, maximum freezing depth, initial thawing point, and complete thawing point) within a given evaluation year.

[0159] IV. Temperature-Intensity Mapping Based on the indoor freeze-thaw cycle triaxial test, the functional relationship between cohesion and internal friction angle with temperature during freezing and thawing was obtained by fitting, and strength parameter samples were calculated for each unit and each time point.

[0160] V. Stability Analysis Under a given embankment load, the integral extreme value method was used to search for overall slip and deep slip surfaces. For each set of strength field samples, the most unfavorable slip surface and safety factor were calculated at the critical date. Statistical results showed that: the safety factor slightly increased in the early stage of freezing; the safety factor reached its maximum when the maximum frost depth approached the design frost depth; in the early stage of spring thaw, due to the partial melting of soft soil and the increase in pore water pressure, the safety factor rapidly decreased, and the probability of instability increased significantly; after multiple freeze-thaw cycles, the minimum safety factor gradually decreased and moved closer to the ground surface within the year.

[0161] VI. Evaluation and Reinforcement Recommendations Based on the target safety factor and the instability probability limit, it was determined that the roadbed-foundation section has a high risk of slippage during the spring thaw. Measures such as adding an insulation layer at the toe of the embankment, setting up drainage ditches, and local pile foundation reinforcement were proposed.

[0162] The above embodiments merely illustrate the basic principles and characteristics of the present invention, but are not limited to the above implementation schemes. It should be understood that those skilled in the art can make various changes and modifications to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the stability of foundations in seasonally frozen soft soil layers, characterized in that, Includes the following steps: S1: Establish a numerical model of the foundation of the seasonally frozen soft soil layer, and set boundary conditions and initial conditions; S2: Establish the deterministic temperature field control equations; S3: Modeling of stochastic temperature fields; S4: Based on the random temperature field in step S3, obtain the statistical characteristics of the node temperature; S5: Establish the mapping relationship between temperature and shear strength parameters, and obtain the strength field based on the nodal temperature statistical characteristics obtained in step S4; S6: Based on the strength parameter field obtained in step S5, the most unfavorable slip surface is determined using the integral extreme value method, and the corresponding safety factor and ultimate bearing capacity are calculated. S7: Calculate the safety factor in step S6 to obtain the safety factor statistical results; S8: Calculate the instability probability and obtain the instability probability cloud map; S9: Output a comprehensive evaluation report, which includes the temperature field, intensity field, most unfavorable slip surface morphology, safety factor statistics, and instability probability cloud map.

2. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 1, characterized in that, The specific process of step S1 includes: S11: Collect meteorological data, geothermal gradient, ground cover / structure type, and groundwater level information of the engineering area, and obtain the layered structure, soil mechanical parameters, and statistical characteristics of thermal parameters of the seasonally frozen soft soil layer. S12: Construct the foundation calculation domain according to the foundation type, determine the upper boundary as the ground or foundation bottom surface, determine the lower boundary as the isothermal surface, and determine the side boundaries as the adiabatic or symmetrical boundaries; S13: Discretize the foundation calculation domain using finite element method, divide the seasonally frozen soft soil layer area, and assign corresponding soil layer properties to each element; S14: The boundary conditions for determining the upper boundary are convective heat transfer boundaries based on atmospheric temperature changes over time; the boundary conditions for determining the lower boundary are geothermal gradient or constant heat flux boundaries; the boundary conditions for determining the lateral boundaries are adiabatic boundaries or given heat flux boundaries; and the initial conditions are measured or empirical geothermal profiles on a certain reference date.

3. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 1, characterized in that, The specific process of step S2 includes: In a rectangular coordinate system, the seasonally frozen soft soil is considered as a three-phase zone consisting of frozen soil, thawed soil, and phase transition zone, and the following are established respectively: Permafrost is a frozen zone, and its heat conduction equation is: in, For time; The temperature of the soil in a frozen state; The thermal conductivity of frozen soil; The specific heat or equivalent heat capacity of frozen soil; The melting zone of the clay is represented by the following heat conduction equation: in, The temperature of the frozen soil; The thermal conductivity of unfrozen soil; The volumetric specific heat or equivalent heat capacity of unfrozen soil; The phase transition zone is the phase transition region. The heat conduction equation is established using the equivalent thermal melting method. The equation is as follows: in, Specific heat capacity; Based on volumetric specific heat; This refers to the soil density. Latent heat of phase transition; , These are the upper and lower limits of the phase transition temperature range. Indicates the freezing start temperature. This indicates the temperature at which freezing is complete.

4. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 1, characterized in that, The specific process of step S3 includes: S31: Treat the thermal parameters of soft soil as a spatial random field, set the mean and standard deviation, and construct the spatial correlation function and covariance matrix; S32: Treat the atmospheric boundary temperature parameters as a random field, set the mean and standard deviation, and construct the spatial correlation function and covariance matrix; S33: Perform spectral decomposition on the random fields of steps S31 and S32 using Neumann expansion or Karhunen–Loève expansion to obtain a linear combination of several independent standard normal random variables; S34: Use the Monte Carlo method to sample the random variables in step S33 to generate multiple sets of thermal parameters and boundary condition samples; S35: For each sample group, based on the foundation numerical model of step S1 and the deterministic temperature field control equation of step S2, the heat conduction equation is discretized using the weighted residual method to obtain the discrete equation: in, Represents the heat conduction matrix; Indicates time Temperature vector at any given time; Represents the heat capacity matrix; Indicates time The load vector at time t; S36: The stochastic temperature field during multi-year freeze-thaw cycles is obtained by using backward difference or Crank–Nicolson time integration scheme methods.

5. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 1, characterized in that, The specific process of step S5 includes: S51: Based on indoor frozen soil tests or literature experience, establish the mapping relationship between the shear strength parameters of seasonally frozen soft soil and temperature. The mapping relationship is as follows: ， in, This represents the soil temperature, which can be negative or positive. This is the absolute value of the temperature, representing the temperature range from 0℃. The temperature is Cohesion at that time; The temperature is The internal friction angle at that time; Cohesion at a reference temperature (usually 0°C or a certain reference temperature); The internal friction angle is at the reference temperature; This is the coefficient representing the change in cohesion as a function of the absolute value of temperature. This is the coefficient that represents the change of the internal friction angle with the absolute value of temperature. S52: Based on the node temperature statistical characteristics of step S4, obtain temperature data, substitute the corresponding temperatures into the mapping relationship of step S51, and generate several sets of intensity fields.

6. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 1, characterized in that, The specific process of step S6 includes: S61: Define the family of slip surfaces based on the basic form and potential instability modes; S62: Treat the foundation as a heterogeneous body, in a plane Inside, using the coordinates of the center of the circle. With radius The slip surface is represented by the slip surface formula: ， The slip surface intersects the ground surface at two points. , The corresponding arc function is: ， ， S63: The foundation sliding body is... The upper boundary of the sliding body is discretized by vertical strips. The lower boundary of the sliding body is The strip width is Then the strip height for: ， strip area for: strip weight for: in, This represents the severity of the band at the corresponding location. Tangent angle of slip surface The formula is derived from the derivative of the slip surface, as follows: Differential of arc length of slip surface for: S64: The infinitesimal tangential force element of the strip along the slip surface direction without introducing inter-strip forces. for: Normal force element for: Considering pore water pressure The reduction in effective normal force results in the pore pressure per unit width of the slip surface being: Effective normal force element Represented as: The shear strength at any point on the slip surface is expressed using the Mohr-Coulomb effective stress, as shown in the formula: in, Indicates the location Shear strength of the soil at the location; For in position The cohesion of the soil; For in position The internal friction angle of the soil at the location; Effective normal stress; Effective normal stress The formula is: Total resistance of the slip surface The integral over the arc length is given by the formula: Sliding force The formula for the tangential integral over the slip surface is: The parameters of the slip surface family are Safety factor at time Defined as: S65: The slip surface that minimizes the safety factor is defined as the most unfavorable slip surface, i.e.: in, For the feasible region of the parameters; This is the optimal solution; like exist If an element is interiorly differentiable, then the interior extrema satisfy a necessary first-order condition: The equivalent extreme value condition is obtained as follows: in , , , Solve by applying the chain rule to the upper and lower limits of integration and the integrand; S66: Approximation using numerical difference method , The formula is: S67: For each set of intensity field samples, the most unfavorable slip surface and corresponding safety factor are solved at each key date using grid search and local optimization methods. S68: For each set of strength field samples, the ultimate bearing capacity of the foundation is obtained by the strength reduction finite element method.

7. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 6, characterized in that, The specific process of step S7 includes: S71: For the safety factor of all samples, calculate the mean, standard deviation, coefficient of variation, and distribution function of the safety factor. The mean safety factor is: ， in, Indicates the number of key dates; Indicates the number of samples; It is an index variable, from 1 to... This is used to iterate through all key dates; It is an index variable, from 1 to... This is used to iterate through all samples; Indicates key dates; Indicates the key date The average safety factor at the location; Indicates the first Key Dates in Group Intensity Field Samples Safety factor at the location; The standard deviation of the safety factor is: in, Indicates the key date The standard deviation of the safety factor at the location; The coefficient of variation of the safety factor is: in, Indicates the key date The safety factor and coefficient of variation at the location; The empirical distribution function of the safety factor is: in, An expression function that takes the value 1 if the condition is true, and 0 otherwise; For a given threshold; S72: The minimum safety factor among all samples in the multi-year freeze-thaw cycle. for: Corresponding most dangerous date index for: Statistics of all samples The occurrence of the minimum safety factor is used to obtain the critical date and freezing depth corresponding to the minimum safety factor. The minimum safety factor is then represented by time series as "minimum safety factor - critical date - corresponding freezing depth". S73: Obtain the statistical results of the safety factor.

8. The method for evaluating the stability of seasonally frozen soft soil foundations according to claim 7, characterized in that, The specific process of step S8 includes: S81: For key dates Define two types of limit state functions: Limit state function based on safety factor : in, The target safety factor; The corresponding instability event is: Limit state function based on bearing capacity : in, Indicates the first Key Dates in Group Intensity Field Samples Ultimate bearing capacity at the location; Indicates demand carrying capacity; The corresponding instability event is: S82: Probability of instability based on safety factor criterion for: Instability probability based on bearing capacity criterion for: Joint failure If we adopt the principle that "satisfying any instability probability is considered a failure," then the instability probability is: If we adopt the principle that "satisfying both conditions simultaneously constitutes a failure," then the instability probability is: S83: Set the instability probability threshold ,satisfy The set of dates constitutes the risk period; S84: Merge consecutive dates into intervals And according to the maximum instability probability within the interval Risk classification is performed using the following formula: in, These are the lower and upper time limits of the interval, respectively. S85: Based on the foundation numerical model of step S1, for each finite element element... unit shear strength for: in, This represents the finite element. In the Key Dates in Group Intensity Field Samples Cohesion at the point; This represents the finite element. In the Key Dates in Group Intensity Field Samples Effective normal stress at the location; This represents the finite element. In the Key Dates in Group Intensity Field Samples The internal friction angle at the location; Unit safety margin function for: in, This represents the required shear stress of the element; The unit instability event is: Then the probability of unit instability for: All units Map back to the grid to get the key date The probability cloud map of instability.

9. A stability evaluation system for seasonally frozen soft soil foundations, characterized in that, include: The input module is used to input foundation geometric information, soil layer division, statistical characteristics of soil mechanical and thermal parameters, and meteorological and geothermal data; The foundation numerical modeling module is used to establish a foundation numerical model for seasonally frozen soft soil layers. The random temperature field modeling module is used to construct random fields of thermal parameters and boundary conditions, perform spectral decomposition and sample sampling, solve equations for each set of samples, and obtain the random temperature field during the multi-year freeze-thaw cycle. The parameter mapping module is used to convert the temperature field into an intensity field; The stability analysis module is used to determine the most unfavorable slip surface and calculate the safety factor; The reliability evaluation and visualization module is used to perform statistical analysis on the safety factor, calculate the instability probability, and output a comprehensive evaluation report on foundation stability.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

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