A method and apparatus for shallow foundation reliability analysis

Abstract

The application discloses a shallow foundation reliability analysis method and device. The method comprises the following steps: selecting a deterministic bearing capacity envelope surface equation of a shallow foundation according to requirements; obtaining a probability single-axis bearing capacity sample set; converting the deterministic bearing capacity envelope surface by using the probability single-axis bearing capacity sample to generate a large number of probability bearing capacity envelope surface samples; setting a load combination sample according to requirements, comparing the load combination sample with the bearing capacity envelope surface sample, and carrying out reliability analysis by combining a performance function and a Monte Carlo simulation. The core of the application is to solve the probability single-axis bearing capacity, combine the deterministic bearing capacity envelope surface equation, construct the probability bearing capacity envelope surface, and carry out the shallow foundation reliability analysis by using the Monte Carlo simulation. The method avoids numerical analysis for different load combinations respectively, greatly improves the calculation efficiency, and is simple in principle and convenient to use, thereby providing an efficient and practical tool for the shallow foundation reliability analysis under complex geological and load conditions.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering reliability analysis and electronic digital data processing technology, specifically to a method and apparatus for shallow foundation reliability analysis. Background Technology

[0002] In geotechnical engineering practice, shallow foundations are often subjected to vertical loads. V Horizontal load H and moment load M The combined effects of these factors, along with the spatial variability of soil parameters (such as cohesion and internal friction angle), constitute the main sources of uncertainty in shallow foundation reliability analysis. Solving for reliability under these complex conditions is crucial for quantifying engineering risks and achieving reliability-based design; this approach has been adopted by numerous design codes both domestically and internationally.

[0003] Existing methods for reliability analysis of shallow foundations under combined loading on spatially variable ground mainly fall into two categories: one is the direct method based on a one-time complete finite element model combined with Monte Carlo simulation, which has a huge computational load and extremely low efficiency; the other is the approximate method based on surrogate models (such as the Kriging model and polynomial chaotic expansion). However, the surrogate model method faces challenges when... VHM When performing composite loading, it is usually necessary to establish multiple surrogate models for different regions of the load space or different load combination paths. The process is cumbersome, the required training sample size is still considerable, and the theory is complex, making it inconvenient for engineers to understand and apply programmatically. Summary of the Invention

[0004] The present invention aims to overcome the above-mentioned defects of the prior art and provide a method and device for shallow foundation reliability analysis. Based on the probabilistic bearing capacity envelope and load combination samples, Monte Carlo simulation is performed to carry out the reliability analysis of shallow foundations under composite loading. This significantly improves the calculation efficiency of shallow foundation failure probability and reduces algorithm complexity, making it convenient for practical engineering applications.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A shallow foundation reliability analysis method based on the probabilistic bearing capacity envelope surface method includes the following steps:

[0007] Step S1: Select the deterministic bearing capacity envelope equation: Based on the design data of the target shallow foundation (foundation type, dimensions, depth, etc.), determine the normalizable bearing capacity envelope equation f( under deterministic foundation conditions) through theoretical derivation, finite element analysis, or experimental fitting. v , h , m )=0. This equation describes the fundamental... VHMThe ultimate bearing capacity boundary in space.

[0008] Step S2: Obtaining the probabilistic single-bearing load: Based on geological survey data, extract soil parameters (such as undrained shear strength). s u The spatial statistical characteristics of soil parameters (mean, standard deviation, autocorrelation length, and fluctuation range, etc.) are determined. Random field simulation techniques (such as the Karhunen-Loève expansion method and covariance matrix decomposition method) are used to generate a large number of random field samples of soil parameters that conform to these statistical characteristics. For these random field samples of soil parameters, finite element software (such as ABAQUS, PLAXIS) or simplified calculation methods are used to calculate the ultimate bearing capacity of the foundation under vertical, horizontal, and moment-only conditions, respectively, thus obtaining the probabilistic single-bearing capacity. V ult,i , H ult,i , M ult,i To reduce the number of numerical model calls, a global proxy model (such as Gaussian process regression) can be introduced at this step to approximate the random field characteristics to a single-axis probabilistic bearing capacity. It should be noted that steps S1 and S2 are used here only for ease of description and do not constitute a limitation on the order of these two steps.

[0009] Step S3: Generation of probabilistic bearing capacity envelope: For each probabilistic single bearing load sample obtained in step S2 ( V ult,i , H ult,i , M ult,i The normalized deterministic bearing capacity envelope equation f( v , h , m )=0 is converted to f( v i , h i , m i )=0, where v i = V / V ult,i , h i = H / H ult,i , m i = M / M ult,iThis equation represents the i-th probabilistic bearing capacity envelope sample. By traversing all samples, the probabilistic bearing capacity envelope sample set can be obtained.

[0010] Step S4: Reliability Analysis Results: Based on load specifications or measured data, determine the composite loads acting on the foundation. V s , H s , M s The probability distribution model of loads is used, and a corresponding load combination sample set is generated based on the statistical characteristics of loads acting on shallow foundations. Within the Monte Carlo simulation framework, the load combination samples ( V s,j , H s,j , M s,j The load point is compared with the corresponding i-th probabilistic bearing capacity envelope sample to determine whether it lies within the envelope. Define the function. g = R - S ,in R The bearing capacity represented by the envelope surface (here it is represented by the boundary of the envelope surface). S For load combinations. If g A value ≤0 is recorded as a single failure. The failure probability is obtained by counting the number of failures in a large number of simulations and dividing by the total number of simulations. P f The estimated value is obtained, and the reliability index is solved. β Complete the reliability analysis.

[0011] Further, step S1 includes,

[0012] The deterministic bearing capacity envelope is obtained based on analytical solutions, numerical analysis, or experimental data fitting, and is used to describe the shallow foundation under deterministic foundation conditions and vertical loads. V Horizontal load H and moment load M The mathematical expression for the ultimate bearing capacity envelope under combined action. The equation for the deterministic bearing capacity envelope can be normalized to f( v , h , m )=0, where v = V / V ult,det , h = H / H ult,det , m = M / Mult,det These are the normalized uniaxial ultimate bearing capacities, V ult,det , H ult,det , M ult,det These represent the uniaxial ultimate bearing capacity under deterministic foundation conditions.

[0013] Further, step S2 includes,

[0014] Step S2.1: Determine the spatial statistical characteristics of the foundation soil parameters based on the survey data, including mean, variance, autocorrelation length, and fluctuation range, etc.

[0015] Step S2.2: Based on the spatial statistical characteristics, a random field simulation algorithm is used to generate a random field sample of soil parameters that conforms to the statistical characteristics;

[0016] Step S2.3: For the random field sample of soil parameters, calculate the probabilistic uniaxial ultimate bearing capacity of the shallow foundation under only vertical, only horizontal, and only moment action by numerical analysis methods to obtain the probabilistic uniaxial bearing capacity sample set; the above numerical analysis method is the finite element method, finite difference method, or limit analysis method; and / or, when using the numerical analysis method, establish a proxy model to replace direct call to the numerical analysis software to reduce the calculation cost.

[0017] Further, step S3 includes,

[0018] For the i-th bearing force combination in the probability single bearing load sample set ( V ult,i , H ult,i , M ult,i ), which relates to the normalized deterministic bearing capacity envelope equation f( v , h , m The transformation method for f(=0) is: replace the equation with f( v i , h i , m i )=0, where v i = V / V ult,i , h i = H / H ult,i , m i = M / M ult,i This equation defines the i-th probability bearing capacity envelope sample.

[0019] Further, step S4 includes,

[0020] Step S4.1: Generate a load combination sample set based on the statistical characteristics of loads acting on shallow foundations. Each sample is ( V s , H s , M s )combination;

[0021] Step S4.2, for the j-th design load combination ( V s,j , H s,j , M s,j If the load combination point is located within the corresponding envelope surface of the i-th probability bearing capacity sample, it is determined to be in a safe state; otherwise, it is determined to be in a failure state.

[0022] A shallow foundation reliability analysis device:

[0023] The envelope surface equation selection module is used to select the deterministic bearing capacity envelope surface equation based on the design data of the target shallow foundation.

[0024] The probabilistic single-bearing load acquisition module is used to generate a probabilistic single-bearing load sample set based on soil parameters and a random field model. The probabilistic single-bearing load sample set includes multiple bearing capacity combinations, and each bearing capacity combination includes at least a vertical bearing capacity. V ult,i Horizontal bearing capacity H ult,i and moment bearing capacity M ult,i ;

[0025] The probability envelope surface generation module is used to transform the deterministic bearing capacity envelope surface using the probability single bearing load sample set to generate a probability bearing capacity envelope surface sample set.

[0026] The reliability analysis module is used to obtain a load combination sample set acting on the target shallow foundation, compare each sample in the load combination sample set with the corresponding sample in the probabilistic bearing capacity envelope sample set, and perform a function-based analysis. g = R - S Determine the failure status, where R For load-bearing capacity, SThe load is then used to solve the reliability analysis results of the target shallow foundation through Monte Carlo simulation.

[0027] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the aforementioned shallow-foundation reliability analysis method.

[0028] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned shallow-foundation reliability analysis method.

[0029] In summary, the present invention has the following advantages:

[0030] (1) The principle is simple and easy to implement: The core idea of ​​this invention is to construct the probabilistic bearing capacity envelope by solving the probabilistic single bearing capacity and combining it with the deterministic bearing capacity envelope equation. The Monte Carlo simulation is used to carry out the shallow foundation reliability analysis. The concept is intuitive and easy for engineers to understand and accept, and it is easy to implement by programming.

[0031] (2) High computational efficiency: This invention only requires one probabilistic analysis of the single bearing load (step S2) to obtain the probability envelope of all composite loading states through transformation. This avoids the need for traditional methods to obtain different... VHM The computational efficiency has been greatly improved in the process of performing massive finite element calculations or constructing multiple complex proxy models to meet the combined load-bearing capacity requirements.

[0032] (3) Accuracy and reliability: By comparing with high-precision benchmark examples (such as Monte Carlo simulation), the calculation results of this method have sufficient accuracy and can meet the requirements of engineering reliability analysis and design.

[0033] (4) Wide applicability: This method is applicable to various shallow foundation forms (such as strip foundation, square foundation, and circular foundation) and various foundation soil conditions. As long as the deterministic envelope equation and statistical characteristics of soil parameters can be obtained, it can be applied and has strong promotion. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the shallow foundation reliability analysis method provided in an embodiment of the present invention.

[0035] Figure 2 To determine the bearing capacity envelope in VHM A schematic diagram in space.

[0036] Figure 3 This is a schematic diagram illustrating the generation of probabilistic single-bearing load samples through random field simulation.

[0037] Figure 4This diagram illustrates the process of generating a probabilistic envelope surface sample set by transforming probabilistic single-bearing load samples into a deterministic load-bearing capacity envelope surface.

[0038] Figure 5 This is a schematic diagram for comparing load combination samples with probabilistic bearing capacity envelope samples to determine the failure state.

[0039] Figure 6 This is a structural block diagram of the shallow foundation reliability analysis device of the present invention.

[0040] Figure 7 This is a block diagram of the electronic device structure of the present invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0042] A shallow foundation reliability analysis method includes the following steps:

[0043] Step S1: Based on the design data of the target shallow foundation, select its deterministic bearing capacity envelope equation; wherein, the deterministic bearing capacity envelope is obtained based on analytical solutions, numerical analysis, or experimental data fitting, and is used to describe the shallow foundation under deterministic foundation conditions and vertical loads. V Horizontal load H and moment load M The mathematical expression for the ultimate bearing capacity envelope surface under combined action. All the deterministic bearing capacity envelope surface equations can be normalized to f( v , h , m )=0, where v = V / V ult,det , h = H / H ult,det , m = M / M ult,det These are the normalized uniaxial ultimate bearing capacities, V ult,det , H ult,det , M ult,det These represent the uniaxial ultimate bearing capacity under deterministic foundation conditions.

[0044] Step S2: Obtain a probabilistic single-bearing load sample set, which includes multiple load combinations, each load combination including at least a vertical load. Vult,i Horizontal bearing capacity H ult,i and moment bearing capacity M ult,i ;

[0045] Specifically, generating a probabilistic single-bearing load sample set includes:

[0046] S2.1 Determine the spatial statistical characteristics of the foundation soil parameters based on the survey data, including mean, variance, autocorrelation length, and fluctuation range;

[0047] S2.2, Based on the aforementioned spatial statistical characteristics, a random field simulation algorithm is used to generate random field samples of soil parameters that conform to the aforementioned spatial statistical characteristics;

[0048] S2.3, For the random field sample of soil parameters, the probabilistic uniaxial ultimate bearing capacity of shallow foundations under only vertical, only horizontal, and only moment action is calculated by numerical analysis methods to obtain the probabilistic uniaxial bearing capacity sample set; specifically, the numerical analysis method is the finite element method, finite difference method, or limit analysis method; and / or, when using the numerical analysis method, a proxy model is established to replace direct calling of numerical analysis software to reduce the calculation cost.

[0049] Step S3: The deterministic bearing capacity envelope equation is transformed using the probabilistic single-bearing load sample set to generate a probabilistic bearing capacity envelope sample set; wherein, the transformation is achieved through substitution, for the i-th bearing capacity combination in the probabilistic single-bearing load sample set ( V ult,i , H ult,i , M ult,i ), which relates to the normalized deterministic bearing capacity envelope equation f( v , h , m The transformation method for f(=0) is: replace the equation with f( v i , h i , m i )=0, where v i = V / V ult,i , h i = H / H ult,i , m i = M / M ult,iThis equation defines the i-th probability bearing capacity envelope sample.

[0050] Step S4: Obtain the load combination sample set acting on the target shallow foundation, compare each sample in the design load combination sample set with the corresponding sample in the probabilistic bearing capacity envelope sample set, and perform a function-based comparison. g = R - S Determine the failure status, where R For load-bearing capacity, S The load is then used to solve the reliability analysis results of the target shallow foundation through Monte Carlo simulation.

[0051] The load combination sample set is generated based on the statistical characteristics of loads acting on shallow foundations, and each sample is ( V s , H s , M s ) combination; the comparison process is as follows: for the j-th design load combination ( V s,j , H s,j , M s,j If the load combination point is located within the corresponding envelope surface of the i-th probability bearing capacity sample, it is determined to be in a safe state; otherwise, it is determined to be in a failure state.

[0052] Example 1: Taking a strip shallow foundation of an offshore platform as an example, the foundation width... B =2m. The foundation soil is saturated soft clay, with an undrained shear strength of... s u The spatial variability characteristics are: mean μ su =5kPa, standard deviation σ su =10kPa, soil strength non-uniformity index κ =6, autocorrelation length L v =5m, L h =1m, using an exponential correlation function. The vertical load borne by the foundation is ln... V s,j ~N (10kN, 1kN), horizontal load H s,j ~U(-1.5kN, 1.5kN), torque ln M s,j ~N(15kN·m, 4.5kN·m), the three are statistically independent.

[0053] Step S1: Obtain the soil strength non-uniformity index of the strip foundation through two-dimensional limit analysis. κ =6 Normalized deterministic bearing capacity envelope equation f( v , h , m = 0. To simplify the explanation, a widely used equation is used as an example:

[0054] Based on existing research, the normalized deterministic failure envelope of a strip foundation can be expressed by the following formula:

[0055] (1)

[0056] in, r m ( v , κ )and r h ( v , κ They are respectively about m and h The reduction factor is in the following form:

[0057] (2)

[0058] (3)

[0059] For the process parameters in Eq.(2) and Eq.(3) λ ( κ ), q ( v , h , κ )and a ( v , h , κ The following is represented:

[0060] (4)

[0061] (5)

[0062] (6)

[0063] Step S2: Generate a random field using the Karhunen-Loève expansion method, employing a cubic surrogate model with 300 training samples for each model, and obtain the probabilistic uniaxial ultimate bearing capacity. V ult,i , H ult,i and Mult,i The proxy model is used to output 100,000 load-bearing capacity combinations. V ult,i , H ult,i , M ult,i ).

[0064] Step S3: For the i-th probabilistic single bearing load sample, its corresponding probabilistic bearing capacity envelope equation is: F( V / V ult,i , H / H ult,i , M / M ult,i )=0.

[0065] Step S4: Randomly generate 100,000 load combination samples from the load distribution. V s,j , H s,j , M s,j Substitute the j-th load sample into the equation of the j-th probability envelope surface to calculate the function value. g i,j =-f( V s,j / V ult,i , H s,j / H ult,i , M s,j / M ult,i ).like g i,j If the value is ≤0, then record a failure. This is based on statistics from 100,000 simulations. g i,j The number of times ≤0 N f Then the failure probability estimate is... P f = N f / 100000. Calculated, in this example... P f ≈7.06×10 -2 Reliability index β =1.471.

[0066] To verify the computational accuracy and reliability of the method proposed in this invention, a comparative verification analysis was conducted on the same engineering case. The verification example used a complete Monte Carlo finite element simulation as a high-precision benchmark method. The specific process is as follows: The sample set of identical load combinations generated in step S4 of this invention (…) V s,j , H s,j , M s,j The bearing capacity is calculated by directly inputting the corresponding soil random field model into the same high-precision finite element numerical analysis platform for the bearing capacity calculation. By determining whether the mechanical response of the foundation under each load sample reaches the limit state (i.e., whether it fails) and counting the total number of failures, the baseline failure probability is calculated.

[0067] Considering computational costs, this verification involved 10,000 complete finite element simulations. The baseline calculation results are as follows: failure probability. P f,基准 ≈7.05×10 -2 Corresponding reliability index β 基准 =1.472, fluctuation of failure probability COV Pf,基准 The value of 0.0363 indicates that the results have good statistical stability and can be used as a reliable benchmark.

[0068] The calculation results of the method of the present invention (as described in the embodiments) are compared with the above-mentioned benchmark results: the relative error between the failure probability calculated by the present invention and the benchmark value is less than 0.2%, and the relative error of the reliability index is less than 0.1%. The two results are highly consistent and the error is extremely small.

[0069] This comparative verification fully demonstrates that, under the same random loads and spatially variable foundation conditions, the calculation method based on the probabilistic bearing capacity envelope method proposed in this invention yields results almost identical to those of the computationally intensive and time-consuming full Monte Carlo finite element benchmark method. This strongly proves that the method of this invention, while ensuring extremely high computational efficiency, possesses excellent computational accuracy and reliability, fully meeting the needs of engineering reliability analysis and design.

[0070] This embodiment verifies the complete process and feasibility of the proposed method. By employing a surrogate model, the entire calculation process can be completed within hours on a regular workstation, while the traditional full Monte Carlo finite element method may take up to a week. Furthermore, the principle of this method is clearer and easier to integrate into reliability design software.

[0071] Example 2: Figure 6 As shown, a shallow foundation reliability analysis device includes:

[0072] The envelope surface equation determination module 501 is used to select the deterministic bearing capacity envelope surface equation based on the design data of the target shallow foundation.

[0073] The probabilistic single bearing load acquisition module 502 is used to generate a probabilistic single bearing load sample set based on soil parameters and a random field model. The probabilistic single bearing load sample set includes multiple bearing capacity combinations, and each bearing capacity combination includes at least vertical bearing capacity, horizontal bearing capacity, and moment bearing capacity.

[0074] The probability envelope surface generation module 503 is used to transform the deterministic bearing capacity envelope surface using the probability single bearing load sample set to generate a probability bearing capacity envelope surface sample set.

[0075] The reliability analysis module 504 is used to obtain a sample set of design load combinations acting on the target shallow foundation, compare each sample in the load combination sample set with the corresponding sample in the probabilistic bearing capacity envelope sample set, and perform a function-based analysis. g = R - S Determine the failure status, where R For load-bearing capacity, S The load is then used to solve the reliability analysis results of the target shallow foundation through Monte Carlo simulation.

[0076] The specific implementation of each module in this embodiment can be found in Embodiment 1 above, and will not be repeated here. It should be noted that the device provided in this embodiment is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0077] Example 3: As Figure 7 As shown, this embodiment provides an electronic device, including a processor 602, a memory, an input device 603, a display 604, and a network interface 605 connected via a system bus 601. The processor 602 provides computing and control capabilities. The memory includes a non-volatile storage medium 606 and internal memory 607. The non-volatile storage medium 606 stores an operating system, computer programs, and a database. The internal memory 607 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium 606. When the computer programs are executed by the processor 602, they implement the aforementioned shallow-based reliability analysis method.

[0078] Example 4: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the shallow-foundation reliability analysis method described above.

[0079] The storage medium described in this embodiment can be a disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), USB flash drive, portable hard drive, etc.

[0080] The core technical features of this invention exhibit significant synergistic effects. Around the core technical concept of the probabilistic bearing capacity envelope, it organically integrates the deterministic bearing capacity envelope, probabilistic single-bearing load, envelope transformation, and Monte Carlo simulation, jointly achieving the goal of efficient, accurate, and universal shallow foundation failure probability calculation. Its synergistic effect is mainly reflected in the following four dimensions:

[0081] I. Collaborative Integration of Core Steps: Solving Complex Analytical Problems

[0082] The core innovation of this invention is the integration of spatially variable foundations with... VHM The complex problem of composite loading is transformed into two independent steps: probabilistic single-bearing load analysis and deterministic envelope surface transformation. The realization of these two steps depends on the deep linkage of multiple technical features:

[0083] The deterministic bearing capacity envelope provides the boundary form of the ultimate bearing capacity under composite loading: based on analytical solutions, numerical analysis, or fitting of experimental data, it accurately describes the shallow foundations in deterministic foundations under [various conditions]. VHM The bearing capacity constraint relationship under the combined action provides a stable template framework for subsequent probabilistic expansion.

[0084] The probabilistic single-axis bearing capacity sample set provides a probabilistic quantitative basis for the spatial variability of the foundation: by simulating the spatial statistical characteristics of soil parameters through random field simulation, and combining numerical analysis / surrogate model to calculate the ultimate bearing capacity of the single axis, the uncertainty of the foundation is accurately captured.

[0085] The probabilistic envelope surface transformation is the key bridge for this linkage: using probabilistic single-axis bearing capacity samples as transformation elements, a large number of probabilistic bearing capacity envelope surface samples are generated. This step not only reuses the composite loading boundary form of the deterministic envelope surface, but also incorporates the foundation uncertainty information of the probabilistic single-axis samples, achieving an organic combination of composite loading form and foundation probabilistic characteristics.

[0086] The core effect of the synergy of these three methods is to avoid the drawbacks of repeatedly constructing proxy models or incurring large amounts of numerical analysis costs for different load combinations in traditional methods. By sorting out the sources of uncertainty, the uncertainty of soil and the uncertainty of load are organically combined to achieve a simplification effect.

[0087] II. Two-way synergy for efficiency optimization: significantly reducing computing costs

[0088] The two efficiency optimization features of this invention (introduction of proxy model and scaling to avoid repetitive modeling) work synergistically to further amplify the efficiency advantage:

[0089] Proxy model: When generating probabilistic single bearing load samples, a proxy model is used to replace direct finite element method calls, reducing the cost of single bearing load calculation per operation and solving the problem of time-consuming single-axis calculation caused by the large sample size of random fields.

[0090] Transformation steps: Transform the deterministic envelope using uniaxial probability samples; no additional steps are required. VHM By constructing multiple proxy models in different regions / paths of composite loading, the problem of cumbersome proxy model construction caused by composite loading adjustments is solved.

[0091] The combined effect of the two is that the proxy model reduces the computational cost of a single axis, the scaling step avoids the repeated construction of the proxy model during compound loading, and the bidirectional support significantly improves computational efficiency, far exceeding the optimization effect of a single efficiency feature.

[0092] III. Multi-layered verification collaboration to ensure accuracy: balancing reliability and accuracy

[0093] Multiple technical features ensure computational accuracy from different levels, forming a complete chain of accuracy synergy from source to process to result:

[0094] Accuracy of the deterministic envelope: Based on analytical solutions, numerical analysis, or fitting of experimental data, ensure the formal accuracy of the composite loading bearing capacity boundary, providing a reliable basis for subsequent probabilistic expansion.

[0095] Statistical reliability of probabilistic uniaxial samples: By strictly following the spatial statistical characteristics of soil parameters through random field simulation, the accuracy of the probability distribution of uniaxial bearing load samples is ensured, reflecting the uncertainty of the real foundation.

[0096] Functionality and Failure Detection: Definition g = RS Clear failure criteria and unified comparison standards between load combinations and probability envelope surfaces are needed to ensure the consistency and accuracy of failure state judgment and avoid statistical errors caused by ambiguous judgment standards.

[0097] The combined effect of the three methods is that the relative error between the final calculation result and the complete Monte Carlo finite element method (high-precision benchmark) is less than 0.2%, achieving a balance between efficient calculation and accurate results.

[0098] IV. Flexible Adaptation and Collaboration for Expanded Applicability: Enlarging the Scope of Engineering Applications

[0099] The multiple features of this invention work synergistically to achieve broad adaptability to different foundation types and ground conditions:

[0100] Universality of deterministic envelope: It supports obtaining the envelope through various methods such as finite element method, theory, and experimentation, and can be adapted to various shallow foundation forms such as strip foundation, square foundation, and circular foundation, providing flexible foundation form adaptability.

[0101] The flexibility of probabilistic uniaxial samples: Random field simulations can adjust parameters based on survey data of different foundation soils (such as statistical characteristics of cohesion and internal friction angle), adapting to various foundation conditions such as saturated soft clay and sand, and providing flexible foundation type adaptability.

[0102] Load sample compatibility: The design load combination sample set can be generated based on load specifications or measured data, supporting different distribution types (normal distribution, uniform distribution, etc.). VHM Load combinations provide flexible adaptability to load conditions.

[0103] The combined effect of the three is that as long as the deterministic envelope surface equation and statistical characteristics of soil parameters can be obtained, they can be applied to various shallow foundations and complex geological / load conditions, with applicability far exceeding the adaptability of a single feature.

[0104] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A shallow foundation reliability analysis method, characterized in that: Includes the following steps, Based on the design data of the target shallow foundation, select the appropriate deterministic bearing capacity envelope equation; The probabilistic single-bearing capacity of soil is solved by experimental fitting or numerical analysis methods, and a sample set of probabilistic single-bearing capacity is obtained. The sample set of probabilistic single-bearing capacity includes multiple bearing capacity combinations, and each bearing capacity combination includes at least a vertical bearing capacity. V ult,i Horizontal bearing capacity H ult,i and moment bearing capacity M ult,i ; The deterministic bearing capacity envelope equation is transformed using the probabilistic single bearing load sample set to generate a probabilistic bearing capacity envelope sample set. Based on the requirements, a load combination sample set is set to act on the target shallow foundation. Each sample in the load combination sample set is compared with the corresponding sample in the probabilistic bearing capacity envelope sample set, based on the function. g = R - S Determine the failure status, where R For load-bearing capacity, S The load is then used to solve the reliability analysis results of the target shallow foundation through Monte Carlo simulation; The specific components of obtaining the probabilistic single bearing load sample set include: Determine the spatial statistical characteristics of the foundation soil parameters, including mean, variance, autocorrelation length, and fluctuation range; Based on the aforementioned spatial statistical characteristics, a random field algorithm is used to generate random field samples of soil parameters that conform to the aforementioned spatial statistical characteristics. For the random field sample of soil parameters, the probabilistic single bearing load of shallow foundation under vertical, horizontal and moment-only action is calculated by numerical analysis method, and the probabilistic single bearing load sample set is obtained.

2. The shallow foundation reliability analysis method according to claim 1, characterized in that, The deterministic bearing capacity envelope is obtained based on analytical solutions, numerical analysis, or experimental data fitting methods, and is used to describe the shallow foundation under deterministic foundation conditions and vertical loads. V Horizontal load H and moment load M Mathematical expression for the envelope of ultimate bearing capacity under combined action.

3. The shallow foundation reliability analysis method according to claim 2, characterized in that, The deterministic bearing capacity envelope equations can all be normalized and expressed as f( v , h , m )=0, where v = V / V ult,det , h = H / H ult,det , m = M / M ult,det These are the normalized uniaxial ultimate bearing capacities, V ult,det , H ult,det , M ult,det These represent the uniaxial ultimate bearing capacity under deterministic foundation conditions.

4. The shallow foundation reliability analysis method according to claim 1, characterized in that, The numerical analysis method is the finite element method, the finite difference method, or the limit analysis method; and / or, when using a numerical analysis method, a proxy model is established to replace direct calling of numerical analysis software to reduce computational costs.

5. The shallow foundation reliability analysis method according to claim 2, characterized in that, The transformation is achieved through substitution, for the i-th bearing force combination in the probability single bearing load sample set ( V ult,i , H ult,i , M ult,i ), which relates to the normalized deterministic bearing capacity envelope equation f( v , h , m The transformation method for f( ) = 0 is: replace the equation with f( v i , h i , m i )=0, where v i = V / V ult,i , h i = H / H ult,i , m i = M / M ult,i This equation defines the i-th probability bearing capacity envelope sample.

6. The shallow foundation reliability analysis method according to claim 1, characterized in that, The load combination sample set is generated based on the statistical characteristics of loads acting on shallow foundations, and each sample is ( V s , H s , M s ) combination; comparing each sample in the load combination sample set with the corresponding sample in the probabilistic bearing capacity envelope sample set specifically involves: for the j-th design load combination ( V s,j , H s,j , M s,j If the load combination is located within the corresponding envelope surface of the i-th probability bearing capacity sample, it is determined to be in a safe state; otherwise, it is determined to be in a failure state.

7. A shallow foundation reliability analysis device, characterized in that, include: The envelope surface equation selection module is used to select the deterministic bearing capacity envelope surface equation based on the design data of the target shallow foundation. The probabilistic single-bearing capacity acquisition module is used to solve the probabilistic single-bearing capacity of soil through experimental fitting or numerical analysis methods, and to obtain a probabilistic single-bearing capacity sample set. The probabilistic single-bearing capacity sample set includes multiple bearing capacity combinations, and each bearing capacity combination includes at least a vertical bearing capacity. V ult,i Horizontal bearing capacity H ult,i and moment bearing capacity M ult,i ; Specifically, the probabilistic single-bearing load sample set includes: Determine the spatial statistical characteristics of the foundation soil parameters, including mean, variance, autocorrelation length, and fluctuation range; Based on the aforementioned spatial statistical characteristics, a random field algorithm is used to generate random field samples of soil parameters that conform to the aforementioned spatial statistical characteristics. For the random field sample of soil parameters, the probabilistic single bearing load of shallow foundation under vertical, horizontal and moment-only action is calculated by numerical analysis method, and the probabilistic single bearing load sample set is obtained. The probability envelope surface generation module is used to transform the deterministic bearing capacity envelope surface using the probability single bearing load sample set to generate a probability bearing capacity envelope surface sample set. The reliability analysis module is used to set a load combination sample set acting on the target shallow foundation according to requirements, compare each sample in the load combination sample set with the corresponding sample in the probabilistic bearing capacity envelope sample set, and perform a function-based analysis. g = R - S Determine the failure status, where R For load-bearing capacity, S The load is then used to solve the reliability analysis results of the target shallow foundation through Monte Carlo simulation.

8. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the shallow-foundation reliability analysis method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the shallow-foundation reliability analysis method as described in any one of claims 1 to 6.

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