Evaluation method of liquefaction resistance of geotechnical granular materials under complex cyclic loading conditions
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-14
- Publication Date
- 2026-08-11
AI Technical Summary
该方法在单向加载以及双向等幅、等频条件下具有一定效果，但其推导主要基于单向加载和双向加载中CSRx= CSRy、fx= fy的试验数据，对于双向不等幅加载（如椭圆形应力路径）以及双向不等频加载（如八字形应力路径）等更一般的复杂应力路径的适用性仍然不足
本发明能够统一评价单向加载、双向等幅等频加载以及双向不等幅、不等频加载条件下岩土颗粒材料的液化抗力，解决传统CSR方法难以适用于复杂应力路径的问题；通过引入合循环剪应力比CSRR，解决了多向加载特别是CSRx≠ CSRy条件下循环应力比定义不明确的问题；同时，本发明能够更合理地反映不同应力路径在一个循环周期内对土体作用效应的差异，因此对椭圆形应力路径、八字形应力路径等复杂应力路径条件下的试验结果具有更好的归并效果和评价精度。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of mechanical response analysis technology for soil and rock media in extreme environments, and in particular to a method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions. Background Technology
[0002] Currently, the scale of construction of major infrastructure projects such as railways, highways, bridges, ports, and airports is continuously expanding, and the safety issues of geotechnical engineering under complex stress are becoming increasingly prominent. Particulate materials of soil and rock are widely distributed in roadbeds, slopes, embankments, and various foundation projects. Under cyclic loads such as earthquakes, waves, and traffic loads, they are prone to pore water pressure accumulation, stiffness degradation, deformation development, and even liquefaction instability, thus affecting the safety and service stability of major engineering structures. Therefore, establishing an evaluation method for the liquefaction resistance of particulate materials of soil and rock applicable to different cyclic load conditions is of great significance for ensuring the safe operation of major infrastructure and improving the disaster resistance and mitigation capabilities of engineering projects.
[0003] In existing technologies, Seed and Peacock proposed a method for determining dynamic strength based on cyclic stress ratio (CSR) in 1971. This method is widely used under simple loading conditions such as cyclic triaxial tests and unidirectional cyclic shear tests, and typically uses the relationship between CSR and failure number Nf to evaluate the cyclic resistance of soil. However, when the cyclic loading path is extended from unidirectional loading to bidirectional loading or more complex multidirectional loading, existing CSR-based evaluation methods have significant shortcomings. Existing research shows that under complex stress path conditions, there is usually no unique CSR-Nf relationship curve. This is because even if different loading paths have the same cyclic shear stress amplitude (i.e., the nominal CSR is the same), the cyclic effects on the soil within a cycle are not consistent due to differences in loading direction, amplitude combination, frequency combination, and loading path shape. This leads to significant differences in pore water pressure development, deformation accumulation, and liquefaction resistance. In other words, traditional CSR can only reflect partial stress amplitude information and is difficult to accurately characterize the actual cyclic load level borne by the soil under complex stress paths, thus making it unsuitable for a unified evaluation of cyclic resistance under unidirectional and multidirectional loading conditions.
[0004] To address the aforementioned issues, existing technologies have proposed a unified cyclic stress ratio (UCSR) based on the time-stress absolute time-history stress area (TSA) per unit cycle to characterize cyclic resistance under complex loading conditions. This method shows some effectiveness under unidirectional loading and bidirectional equal-amplitude, equal-frequency conditions, but its derivation is primarily based on the CSR under unidirectional and bidirectional loading. x = CSR y f x = f yThe experimental data are still insufficient to apply to more general and complex stress paths such as bidirectional unequal amplitude loading (e.g., elliptical stress path) and bidirectional unequal frequency loading (e.g., figure-eight stress path).
[0005] Furthermore, under multi-directional loads, especially when CSR x ≠ CSR y The definition of cyclic shear stress ratio is inherently ambiguous, and existing methods struggle to reasonably reflect the combined effects of loads under complex stress paths. This results in limited merging of relevant experimental results, failing to meet the engineering application requirements for a unified evaluation of the liquefaction resistance of soil and rock granular materials under complex stress paths. Therefore, it is necessary to propose a unified evaluation method for the liquefaction resistance of soil and rock granular materials that is applicable to unidirectional and multidirectional complex cyclic loading conditions, has a clear definition, broad applicability, and provides more reasonable evaluation results. Summary of the Invention
[0006] To address the aforementioned problems, this invention aims to provide a method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions. An evaluation model is established based on the results of unidirectional and multidirectional cyclic shear tests. This evaluation model can describe the liquefaction resistance of soil and rock granular materials under complex stress paths, achieving a unified characterization of liquefaction resistance under different loading paths. This provides a theoretical basis and technical support for liquefaction determination, dynamic stability analysis, and related engineering safety evaluation in geotechnical engineering.
[0007] The technical solution of the present invention is as follows: A method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions includes the following steps: S1: Simplify the complex working conditions in reality. The simplification includes the loading conditions and particle shape. For the aforementioned loading conditions, the cyclic stress path is summarized into four typical stress paths: linear stress path, circular stress path, elliptical stress path, and figure-eight stress path. Regarding the particle shape, various particle materials with different morphology characterization parameter values are prepared using round beads and broken beads; S2: For each type of particulate material, the four typical stress paths described above are applied under different cyclic stress ratios to conduct unidirectional and multidirectional cyclic shear tests and obtain test data; S3: Introduce the combined cyclic shear stress ratio as a characterization parameter for the intensity of multi-directional cyclic loads, and construct a unified cyclic stress ratio model by combining the influence coefficient of loading dimension and the influence coefficient of phase difference and frequency. S4: Establish a fitting relationship between the unified cyclic stress ratio and the number of cyclic failure cycles, and fit it with the unified cyclic stress ratio model to obtain a fitting relationship between the unified cyclic stress ratio and the number of cyclic failure cycles with determined parameters; S5: The fitting formula of the uniform cyclic stress ratio and cyclic failure number determined according to the parameters describes the liquefaction resistance of the material under different stress paths and different particle morphologies.
[0008] Preferably, in step S1, the linear stress path is used to characterize the unidirectional cyclic loading condition; The circular stress path is used to characterize a bidirectional loading condition with equal amplitude, equal frequency, and a phase difference of 90°. The elliptical stress path is used to characterize a loading condition with bidirectional unequal amplitude, equal frequency, and a phase difference of 90°. The figure-eight stress path is used to characterize a loading condition with bidirectional equal amplitude, different frequencies, and a phase difference of 0°.
[0009] Preferably, in step S1, the morphology characterization parameter value is calculated using the following formula: (1) In the formula: OR is the overall regularity; AR is the aspect ratio; S is the sphericity; C is the convexity; the subscript 50 indicates the cumulative value when the cumulative distribution reaches 50%.
[0010] Preferably, in step S2, during the test, the stress time histories of the two horizontal cyclic loads are calculated using the following formulas: (2) (3) In the formula: the subscripts x and y represent physical quantities along the x-axis and y-axis, respectively; τ is the shear stress; The initial vertical effective stress is given; CSR is the cyclic stress ratio; f is the loading frequency; and t is the time. This represents the phase difference between cyclic loads along the x-axis and y-axis. The combined strain under multi-directional cyclic loading is calculated using the following formula: (4) In the formula: To adapt to change; and These are the shear strains along the x-axis and y-axis, respectively.
[0011] Preferably, in step S2, when conducting the test, for uniaxial loading, the specimen is determined to have failed when the double shear strain is greater than the threshold; for multiaxial loading, the specimen is determined to have failed when the resultant strain is greater than the threshold.
[0012] Preferably, the threshold is 7.5%.
[0013] Preferably, in step S3, the combined cyclic shear stress ratio is calculated using the following formula: (5) In the formula: CSR R The combined cyclic shear stress ratio; CSR x The cyclic stress ratio along the x-axis; CSR y The cyclic stress ratio is along the y-axis.
[0014] Preferably, in step S3, the loading dimension influence coefficient and the phase difference and frequency influence coefficient are calculated using the following formulas: (6) (7) (8) (9) (10) In the formula: U1 is the influence coefficient of the loading dimension; A p A is the sum of the areas of the absolute values of stress in the x-direction and the absolute values of stress in the y-direction per unit period; M U1 is the area of the absolute value of the stress in the x-direction per unit period; U2 is the phase difference and frequency influence coefficient; A q τ is the area of the absolute difference between the stress values in the x-direction and y-direction per unit period; T is the unit period; τ x (t) represents the stress-time history curve in the x-direction; t represents time; τ y (t) represents the stress-time history curve in the y-direction; The unified cyclic stress ratio model is as follows: (11) In the formula: UCSR is the uniform cyclic stress ratio; C1 and C2 are both fitting coefficients; CSR R The ratio of cyclic shear stress; In step S4, the fitting relationship is: (12) In the formula: a and b are both fitting coefficients; N f The number of cycles to be broken.
[0015] The beneficial effects of this invention are: This invention can uniformly evaluate the liquefaction resistance of soil and rock granular materials under uniaxial loading, biaxial equal amplitude and equal frequency loading, and biaxial unequal amplitude and unequal frequency loading conditions, solving the problem that traditional CSR methods are difficult to apply to complex stress paths; by introducing combined cyclic shear stress ratio CSR... R This solves the problem of multi-directional loading, especially CSR. x ≠ CSR yThis invention addresses the problem of unclear definition of cyclic stress ratio under certain conditions. Furthermore, it more reasonably reflects the differences in the effects of different stress paths on the soil within a single cycle, thus providing better merging and evaluation accuracy for test results under complex stress path conditions such as elliptical and figure-eight shaped stress paths.
[0016] Furthermore, the Unified Cyclic Stress Ratio (UCSR) model of this invention can automatically degenerate into the traditional CSR under unidirectional loading conditions, which facilitates integration with existing evaluation methods. It can be directly used for liquefaction resistance analysis, dynamic stability evaluation, and related engineering safety assessment of granular materials in complex dynamic environments, and can provide technical basis for geotechnical engineering design under active fault zones, slope engineering, and other complex load conditions. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0018] Figure 1 This is a flowchart illustrating the method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to the present invention. Figure 2 UCSR-N, a specific embodiment of experimental data on different particle morphologies. f Relationship diagram; Figure 3 This is a schematic diagram illustrating the application results of the uniform cyclic stress ratio (UCSR) in loose calcareous sand, loose siliceous sand, and soft clay in a specific embodiment. Figure 4 This is a schematic diagram illustrating the application results of a uniform cyclic stress ratio (UCSR) in medium-density fiber reinforced calcareous sand in a specific embodiment. Detailed Implementation
[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and technical features described in this application can be combined with each other. It should also be pointed out that, unless otherwise indicated, all technical and scientific terms used in this application have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "comprising" or "including" and similar words used in this invention refer to elements or objects preceding the word that encompass the elements or objects listed following the word and their equivalents, without excluding other elements or objects.
[0020] like Figure 1As shown, this invention provides a method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions, comprising the following steps: S1: Simplify the complex working conditions in reality. The simplification includes the loading conditions and particle shape. For the loading conditions, the cyclic stress path is summarized into four typical stress paths: linear stress path, circular stress path, elliptical stress path, and figure-eight stress path. For the particle shape, various particle materials with different morphology characterization parameter values are prepared by using round beads and broken beads.
[0021] Under actual seismic loading, the load amplitude, loading frequency, and phase difference in the two horizontal directions are usually not the same, thus the actual stress path exhibits significant multidirectionality and complexity. To establish an implementable, comparable, and scalable method for evaluating liquefaction resistance, this invention reasonably simplifies complex actual working conditions, classifying them into four typical cyclic stress paths: linear stress path, circular stress path, elliptical stress path, and figure-eight stress path. These four typical paths can respectively reflect the influence of amplitude differences, frequency differences, and stress path shape differences on the cyclic resistance of soil-rock granular materials under bidirectional loading.
[0022] In one specific embodiment, the linear stress path is used to characterize a unidirectional cyclic loading condition; the circular stress path is used to characterize a bidirectional loading condition with equal amplitude, equal frequency, and a phase difference of 90°; the elliptical stress path is used to characterize a bidirectional loading condition with unequal amplitude, equal frequency, and a phase difference of 90°; and the figure-eight stress path is used to characterize a bidirectional loading condition with equal amplitude, different frequencies, and a phase difference of 0°.
[0023] In one specific embodiment, the morphological characterization parameter value is calculated using the following formula: (1) In the formula: OR is the overall regularity; AR is the aspect ratio; S is the sphericity; C is the convexity; the subscript 50 indicates the cumulative value when the cumulative distribution reaches 50%.
[0024] S2: For each type of particulate material, the four typical stress paths described above are applied under different cyclic stress ratios to conduct unidirectional and multidirectional cyclic shear tests and obtain test data.
[0025] In one specific embodiment, during the test, the stress time histories of the two horizontal cyclic loads are calculated using the following formulas: (2) (3) In the formula: the subscripts x and y represent physical quantities along the x-axis and y-axis, respectively; τ is the shear stress; The initial vertical effective stress is given; CSR is the cyclic stress ratio; f is the loading frequency; and t is the time. This represents the phase difference between cyclic loads along the x-axis and y-axis. The combined strain under multi-directional cyclic loading is calculated using the following formula: (4) In the formula: To adapt to change; and These are the shear strains along the x-axis and y-axis, respectively.
[0026] In one specific embodiment, during the test, for uniaxial loading, the specimen is determined to have failed when the combined shear strain exceeds a threshold; for multiaxial loading, the specimen is determined to have failed when the combined strain exceeds a threshold. Optionally, the threshold is 7.5%.
[0027] It should be noted that the threshold value is a manually set value; the larger the value, the greater the number of damage cycles. Besides the threshold used in the above embodiments, other threshold values can be selected according to actual needs.
[0028] S3: Introduce the combined cyclic shear stress ratio as a characterization parameter of multi-directional cyclic load strength, and construct a unified cyclic stress ratio model by combining the loading dimension influence coefficient and the phase difference and frequency influence coefficient.
[0029] In this invention, to accurately characterize the liquefaction resistance of granular materials in soil and rock under complex stress paths, a unified cyclic resistance evaluation index is constructed based on the concept of Time-Stress Absolute Time-History Stress Area (TSA) per unit cycle. Building upon existing unified cyclic stress ratio methods, this invention considers the ambiguity in the definition of cyclic shear stress ratio under multi-directional loads, especially in CSR. x ≠ CSR y Under certain conditions, traditional CSR is difficult to reasonably characterize the overall action level after the synthesis of bidirectional loads. Therefore, this invention introduces the combined cyclic shear stress ratio as a characterization parameter for the strength of multidirectional cyclic loads.
[0030] In one specific embodiment, the combined cyclic shear stress ratio is calculated using the following formula: (5) In the formula: CSR R The combined cyclic shear stress ratio; CSR x The cyclic stress ratio along the x-axis; CSR y The cyclic stress ratio is along the y-axis.
[0031] In a specific embodiment, the loading dimension influence coefficient and the phase difference and frequency influence coefficient are calculated using the following formulas: (6) (7) (8) (9) (10) In the formula: U1 is the influence coefficient of the loading dimension; A p A is the sum of the areas of the absolute values of stress in the x-direction and the absolute values of stress in the y-direction per unit period; M U1 is the area of the absolute value of the stress in the x-direction per unit period; U2 is the phase difference and frequency influence coefficient; A q τ is the area of the absolute difference between the stress values in the x-direction and y-direction per unit period; T is the unit period; τ x (t) represents the stress-time history curve in the x-direction; t represents time; τ y (t) represents the stress-time history curve in the y-direction; The unified cyclic stress ratio model is as follows: (11) In the formula: UCSR is the uniform cyclic stress ratio; C1 and C2 are both fitting coefficients; CSR R The ratio of cyclic shear stress; In the above embodiments, U1 is used to measure the impact of the loading dimension; under unidirectional loading conditions, U1 = 1.0, and under bidirectional loading conditions, U1 > 1.0. U2 is used to measure the impact of the phase difference θ and loading frequency f under multidirectional loading conditions. In the indices used to calculate U1 and U2: under unidirectional loading conditions, A... M = A p = A q And U1 = U2 = 1.0, at this time UCS R = CSR R =CSR, i.e., the uniform cyclic stress ratio UCS R It can automatically degenerate into traditional CSR; under multi-directional loading conditions, this index can comprehensively reflect the dimensional effect, path shape effect and frequency phase effect of multi-directional loading, thereby realizing a unified evaluation of cyclic resistance under unidirectional and multi-directional loading conditions.
[0032] S4: Establish a fitting relationship between the unified cyclic stress ratio and the number of cyclic failure cycles, and fit it with the unified cyclic stress ratio model to obtain a fitting relationship between the unified cyclic stress ratio and the number of cyclic failure cycles with determined parameters.
[0033] In a specific embodiment, the fitting relationship is: (12) In the formula: a and b are both fitting coefficients; N fThe number of cycles to be broken.
[0034] In the above embodiments, the following formula is used for fitting: (13) In formula (13), all parameters except C1, C2, a, and b are known parameters. The above four unknown fitting parameters are obtained by fitting a four-parameter nonlinear model.
[0035] S5: The fitting formula of the uniform cyclic stress ratio and cyclic failure number determined according to the parameters describes the liquefaction resistance of the material under different stress paths and different particle morphologies.
[0036] In this embodiment, the formula (12) determined by a and b can describe the liquefaction resistance of the material under different stress paths and different particle morphologies by using a unified cyclic stress ratio.
[0037] In a specific embodiment, taking various soil and rock granular materials as examples, the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions described in this invention is evaluated using their liquefaction resistance assessment method. Specifically, the following steps are included: First, complex actual working conditions are summarized into the following four typical cyclic stress paths: linear stress path, circular stress path, elliptical stress path, and figure-eight stress path. The circular stress path is achieved as follows: the shear stress amplitudes in both horizontal directions are the same, the loading frequencies are the same, and the phase difference is 90°. The elliptical stress path is achieved as follows: the shear stress amplitudes in both horizontal directions are different, the loading frequencies are the same, and the phase difference is 90°. The figure-eight stress path is achieved as follows: the shear stress amplitudes in both horizontal directions are the same, the phase difference is 0°, and the loading frequency in one direction is twice that in the other direction. The linear stress path is achieved by applying cyclic loads only in a single direction.
[0038] Then, five types of particulate materials were prepared by mixing glass beads and glass shards with different contents, including A0R100 (overall regularity OR=0.977), A25R75 (overall regularity OR=0.948), A50R50 (overall regularity OR=0.919), A75R25 (overall regularity OR=0.889), and A100R0 (overall regularity OR=0.860) (the overall regularity is calculated by formula (1)).
[0039] For each type of particulate material, the above four typical stress paths were applied under different cyclic stress ratios to form a test scheme system covering unidirectional and multidirectional, regular and irregular loading paths. In the test, the stress time histories of the two horizontal cyclic loads were determined according to formulas (2) and (3), respectively, and the resultant strain under multidirectional cyclic loading was calculated according to formula (4).
[0040] Before cyclic shear loading, the specimens underwent CO2 saturation, water head saturation, back pressure saturation, B-value testing, and consolidation stages sequentially. When the specimen's B-value reached 0.95 or higher, it was considered to have reached complete saturation; consolidation was considered complete when the specimen's axial displacement remained essentially constant. After consolidation, cyclic loading was applied according to the predetermined test plan, and response data such as shear stress, shear strain, and pore water pressure under different working conditions were recorded in real time.
[0041] To standardize the determination of specimen failure states under different stress paths, this embodiment employs the following criteria for uniaxial and multiaxial loading: For uniaxial loading (linear stress path), specimen failure is determined when the double-amplitude shear strain exceeds 7.5%; for multiaxial loading (circular, elliptical, and figure-eight stress paths), specimen failure is determined when the resultant strain exceeds 7.5%. Based on these failure criteria, the number of cycles N required for the specimen to reach failure under each test condition is determined. f This will enable the establishment of the foundational database required for the subsequent unified cyclic stress ratio model.
[0042] Based on the aforementioned basic database, the best fitting values of fitting parameters a, b, C1, and C2 in formulas (11)-(12) are obtained through regression analysis of experimental data. Thus, the UCSR and the number of cycle failures N shown in formula (12) for determining the fitting parameters are established. f The functional relationship between them can be used to uniformly describe the cyclic resistance of materials under different stress paths and different particle morphologies.
[0043] Figure 2 The UCSR-N, which shows experimental data of different particle morphologies in this embodiment, is illustrated. f Relationship, from Figure 2 It can be seen that the data points under the same particle morphology parameters are roughly concentrated on the same relationship curve, indicating that the unified cyclic stress ratio (UCSR) index proposed in this invention can effectively describe the liquefaction resistance of particulate materials under unidirectional and multidirectional cyclic shearing.
[0044] To further verify the effectiveness and applicability of the evaluation method proposed in this invention, experimental data published by other researchers were selected for comparative verification. The verification objects included different material types such as loose calcareous sand, loose siliceous sand, soft clay, and medium-dense fiber reinforced calcareous sand, covering different relative densities, different confining pressure conditions, and different material compositions.
[0045] Substituting the aforementioned independent experimental data into the unified cyclic stress ratio (UCSR) model proposed in this invention for analysis, it was found that for experimental results obtained under different material types and different experimental conditions, the unified cyclic stress ratio (UCSR) is related to the number of failure cycles (N). f Approximately unique correspondences can be established between them, demonstrating good merging effect and high correlation. Figure 3 and Figure 4 The analysis results of the Unified Cyclic Stress Ratio (UCSR) for other materials are shown. The verification results indicate that the unified cyclic resistance evaluation method proposed in this invention is not only applicable to the glass particle material in this embodiment, but also to various geotechnical materials such as calcareous sand, siliceous sand, soft clay, and fiber-reinforced calcareous sand, demonstrating strong applicability and promotional value.
[0046] In summary, this invention summarizes complex cyclic loading paths into typical loading paths, establishes unified test and failure criteria, and constructs a system based on TSA and CSR. R A unified cyclic stress ratio (UCSR) index was developed, and parameter fitting and external verification were performed using multiple sets of experimental data to achieve a unified evaluation of the liquefaction resistance of soil granular materials under unidirectional and multidirectional complex cyclic loading conditions. This method can be used for the analysis and evaluation of the liquefaction resistance, cyclic strength, and dynamic stability of soil granular materials under complex seismic loads, wave loads, and traffic cyclic loads.
[0047] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.
Claims
1. A method for evaluating the liquefaction resistance of granular materials in soil and rock under complex cyclic loading conditions, characterized in that, Includes the following steps: S1: Simplify the complex working conditions in reality. The simplification includes the loading conditions and particle shape. For the aforementioned loading conditions, the cyclic stress path is summarized into four typical stress paths: linear stress path, circular stress path, elliptical stress path, and figure-eight stress path. Regarding the particle shape, various particle materials with different morphology characterization parameter values are prepared using round beads and broken beads; S2: For each type of particulate material, the four typical stress paths described above are applied under different cyclic stress ratios to conduct unidirectional and multidirectional cyclic shear tests and obtain test data; S3: Introduce the combined cyclic shear stress ratio as a characterization parameter for the intensity of multi-directional cyclic loads, and construct a unified cyclic stress ratio model by combining the influence coefficient of loading dimension and the influence coefficient of phase difference and frequency. S4: Establish a fitting relationship between the unified cyclic stress ratio and the number of cyclic failure cycles, and fit it with the unified cyclic stress ratio model to obtain a fitting relationship between the unified cyclic stress ratio and the number of cyclic failure cycles with determined parameters; S5: The fitting formula of the uniform cyclic stress ratio and cyclic failure number determined according to the parameters describes the liquefaction resistance of the material under different stress paths and different particle morphologies.
2. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to claim 1, characterized in that, In step S1, the linear stress path is used to characterize the unidirectional cyclic loading condition; The circular stress path is used to characterize a bidirectional loading condition with equal amplitude, equal frequency, and a phase difference of 90°. The elliptical stress path is used to characterize a loading condition with bidirectional unequal amplitude, equal frequency, and a phase difference of 90°. The figure-eight stress path is used to characterize a loading condition with bidirectional equal amplitude, different frequencies, and a phase difference of 0°.
3. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to claim 1, characterized in that, In step S1, the morphological characterization parameter values are calculated using the following formula: （1） In the formula: OR is the overall regularity; AR is the aspect ratio; S is the sphericity; C is the convexity; the subscript 50 indicates the cumulative value when the cumulative distribution reaches 50%.
4. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to claim 1, characterized in that, In step S2, during the test, the stress time histories of the two horizontal cyclic loads are calculated using the following formulas: （2） （3） In the formula: the subscripts x and y represent physical quantities along the x-axis and y-axis, respectively; τ is the shear stress; The initial vertical effective stress is given; CSR is the cyclic stress ratio; f is the loading frequency; and t is the time. This represents the phase difference between cyclic loads along the x-axis and y-axis. The combined strain under multi-directional cyclic loading is calculated using the following formula: （4） In the formula: To adapt to change; and These are the shear strains along the x-axis and y-axis, respectively.
5. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to claim 1, characterized in that, In step S2, during the test, for uniaxial loading, the specimen is determined to have failed when the double shear strain exceeds the threshold; for multiaxial loading, the specimen is determined to have failed when the resultant strain exceeds the threshold.
6. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to claim 5, characterized in that, The threshold is 7.5%.
7. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to claim 1, characterized in that, In step S3, the combined cyclic shear stress ratio is calculated using the following formula: （5） In the formula: CSR R The combined cyclic shear stress ratio; CSR x The cyclic stress ratio along the x-axis; CSR y The cyclic stress ratio is along the y-axis.
8. The method for evaluating the liquefaction resistance of soil and rock granular materials under complex cyclic loading conditions according to any one of claims 1-7, characterized in that, In step S3, the loading dimension influence coefficient and the phase difference and frequency influence coefficient are calculated using the following formulas: （6） （7） （8） （9） （10） In the formula: U1 is the influence coefficient of the loading dimension; A p A is the sum of the areas of the absolute values of stress in the x-direction and the absolute values of stress in the y-direction per unit period; M U1 is the area of the absolute value of the stress in the x-direction per unit period; U2 is the phase difference and frequency influence coefficient; A q τ is the area of the absolute difference between the stress values in the x-direction and y-direction per unit period; T is the unit period; τ x (t) represents the stress-time history curve in the x-direction; t represents time; τ y (t) represents the stress-time history curve in the y-direction; The unified cyclic stress ratio model is as follows: （11） In the formula: UCSR is the uniform cyclic stress ratio; C1 and C2 are both fitting coefficients; CSR R The ratio of cyclic shear stress; In step S4, the fitting relationship is: （12） In the formula: a and b are both fitting coefficients; N f The number of cycles to be broken.