A method for predicting mechanical response of sand based on state parameters

Abstract

The present invention discloses a method for predicting the mechanical response of sand based on state parameters, comprising: first establishing e–p' The traditional critical state line equation of the plane defines the state parameters of the sample and establishes the equation. The physical filling test method is used to measure the parameters and the relevant equation parameters are analyzed. Min-Max Normalization is performed to obtain a unified critical state line equation and the normalized state parameter equation for the specimen. Four sand specimens were selected for triaxial testing, and the critical state data were measured and normalized. Finally, the obtained normalized state parameters of the specimens were combined with critical state soil mechanics theory to establish a mechanical response prediction model under drained and undrained conditions. This invention incorporates the influence of particle shape into traditional state parameters and uses normalized state parameters to predict the mechanical properties of sands with different particle shapes, filling a gap in the existing technology.

Description

Technical Field

[0001] The present invention belongs to the technical field of monitoring and prediction of water conservancy projects and geotechnical projects, and in particular relates to a method for predicting the mechanical response of sand based on state parameters. Background Art

[0002] Sand, a common engineering foundation material, has mechanical properties that are directly related to the stability and safety of various engineering structures. Seismic activity is frequent in plate boundaries, and earthquake-induced disasters such as sand liquefaction pose a serious threat to infrastructure and the safety of people and property. In past earthquakes, abnormal mechanical response of sand has led to frequent incidents such as building tilts, road collapses, and bridge collapses. Therefore, in the field of geotechnical engineering, in-depth research on the mechanical response of sand is of great theoretical and practical significance for improving the seismic resistance of engineering projects and ensuring the safety of infrastructure.

[0003] At present, although some research has been carried out on the mechanical behavior of sand, covering sand strength, deformation characteristics and response laws under different load conditions, the existing research methods still have certain limitations. The traditional models for predicting the mechanical response of sand are too simplified and cannot accurately reflect the complex physical and mechanical properties of sand. For example, most models only consider conventional parameters such as particle grading and density of sand, but ignore factors such as sand particle shape and contact state between particles that have a significant impact on the mechanical response.

[0004] Therefore, developing a method that can comprehensively consider the various state parameters of sand and accurately predict the mechanical response of sand will not only help researchers deepen their understanding of the essence of sand mechanical behavior, but also provide more reliable theoretical basis and technical support for foundation design, stability assessment and disaster prevention in engineering construction. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting the mechanical response of sand based on state parameters, which solves the technical problem that the existing sand mechanical response prediction model has low prediction accuracy due to ignoring key factors such as particle shape and contact state.

[0006] To achieve the above object, the present invention provides a method for predicting the mechanical response of sand based on state parameters, comprising the following steps:

[0007] S1: Establishment e–p' Traditional critical state line equation in the plane;

[0008] S2: Define the sample state parameters and establish the sample state parameter equation. The sample state parameter equation is specifically shown in formula (1):

[0009] (1);

[0010] in: is the state parameter, is the initial state void ratio, is the critical state void ratio, The traditional critical state line is ep' The intercept void ratio on the plane, The traditional critical state line is ep' The slope of the plane, is the average effective stress at the critical state, is atmospheric pressure, The traditional critical state line is ep' calibration constants for the plane;

[0011] S3: Determine the first parameter using a physical filling test method;

[0012] S4: Use the parameters measured in S3 to calculate the second parameter in the traditional critical state line equation. Min-Max Normalize and get the first equation and the second equation in turn;

[0013] S5: Substitute the parameters measured in S3 and the equation obtained in S4 into the traditional critical state line equation established in S1 to obtain the unified critical state line equation;

[0014] S6: Use the parameters measured in S3 to perform the calculation on the parameters in the state parameter equation of the sample obtained in S2. Min-Max Normalization is performed to obtain the normalized initial state porosity equation and the normalized critical state porosity equation in sequence, and the obtained equations are substituted into the sample state parameter equation to obtain the normalized state parameter equation of the sample;

[0015] S7: Select a variety of sand samples for triaxial testing and measure the average effective stress of the various sand samples under critical conditions. Porosity ratio , respectively, the mean effective stress Porosity ratio The data is normalized to obtain the unified critical state line and normalized state parameters of the sample;

[0016] S8: Use the normalized state parameters of the specimen obtained in S7 and the critical state soil mechanics theory to establish a mechanical response prediction model under drainage conditions and a mechanical response prediction model under undrained conditions.

[0017] Furthermore, the traditional critical state line equation in S1 is shown in formula (2):

[0018] (2);

[0019] in: is the critical state void ratio, The traditional critical state line is e- p' The intercept void ratio on the plane, The traditional critical state line is ep' The slope of the plane, is the average effective stress at the critical state, is atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0020] Furthermore, in S3, the physical filling test method is used to determine the parameters, and the first parameter is specifically: the maximum void ratio With minimum porosity ratio .

[0021] Furthermore, S4 is specifically as follows: using the parameters measured in S3 to respectively calculate the second parameter in the traditional critical state line equation and conduct Min-Max Normalization.

[0022] Furthermore, the first equation in S4 is specifically the unified critical state line in En-p' The intercept porosity equation on the plane, the second equation in S4 is specifically En-p' Unified critical state line slope equation in the plane;

[0023] The unified critical state line is En-p' The intercept porosity ratio equation on the plane is shown in formula (3). En-p' The slope equation of the unified critical state line in the plane is shown in formula (4):

[0024] (3);

[0025] in: To unify the critical state line En-p' The intercept void ratio on the plane, is the maximum void ratio, is the minimum void ratio, The traditional critical state line is ep' intercept porosity ratio on the plane;

[0026] (4);

[0027] in: The traditional critical state line is ep' The slope of the plane, for En-p 'The slope of the uniform critical state line in the plane.

[0028] Furthermore, the critical state line equation is unified in S5, as shown in formula (5):

[0029] (5);

[0030] in: E cs is the normalized critical state void ratio, To unify the critical state line En-p' The intercept void ratio on the plane, for En-p 'The slope of the uniform critical state line in the plane, is the average effective stress at the critical state, is atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0031] Furthermore, the normalized state parameter equation of the sample in S6 is shown in formula (6):

[0032] (6);

[0033] in: is the normalized initial state void ratio, To unify the critical state line En-p' The intercept void ratio on the plane, for En-p 'The slope of the uniform critical state line in the plane, is the normalized critical state void ratio, is the effective consolidation stress, is the normalized state parameter of the sample.

[0034] Furthermore, S7 is specifically:

[0035] S7.1: Select four sand samples: Pearl River sand, LBS sand, quartz sand A, and quartz sand B. Perform triaxial shear tests on each sample. When the sample reaches the critical state, record the average effective stress of each sample. and porosity ratio e ;

[0036] S7.2: Average the effective stress of the four specimens. and porosity ratio e Perform normalization to obtain the normalized average effective stress and the normalized porosity ratio ;

[0037] S7.3: Normalize the mean effective stress and porosity ratio The data are substituted into the unified critical state line equation for fitting to obtain the unified critical state line of the sample and the normalized state parameters of the sample.

[0038] Furthermore, the prediction models for the mechanical response of sand under drainage conditions in S8 include: volume strain prediction model under critical state, stress expansion friction angle prediction model, excess friction angle prediction model, normalized peak deviatoric stress prediction model, and peak friction angle prediction model;

[0039] The volume strain prediction model under the critical state is specifically shown in formula (7), the maximum friction angle prediction model of stress expansion is specifically shown in formula (8), and the excess friction angle prediction model is specifically shown in formula (9):

[0040] (7);

[0041] (8);

[0042] (9);

[0043] in: is the normalized state parameter of the sample, is the predicted volumetric strain, is the predicted maximum friction angle, is the predicted excess friction angle;

[0044] The prediction models of mechanical response of sand under undrained conditions in S8 include: normalized residual stress strength prediction model, normalized strength prediction model of UIS, normalized strength prediction model of QSS, instability index I q Prediction model, instability index I p Prediction model, flow potential index prediction model, excess pore water pressure prediction model under peak deviatoric stress state, maximum normalized excess pore pressure prediction model, critical normalized excess pore pressure prediction model;

[0045] Normalized residual stress strength prediction model, specifically shown in formula (10), normalized strength prediction model of UIS, specifically shown in formula (11), normalized strength prediction model of QSS, specifically shown in formula (12), instability index Iq prediction model, specifically shown in formula (13), instability index Ip prediction model, specifically shown in formula (14), flow potential index prediction model, specifically shown in formula (15), excess pore water pressure prediction model under deviatoric stress state, specifically shown in formula (16), maximum normalized excess pore water pressure prediction model, specifically shown in formula (17), critical state normalized excess pore water pressure prediction model, specifically shown in formula (18):

[0046] (10);

[0047] (11);

[0048] (12);

[0049] (13);

[0050] (14);

[0051] (15);

[0052] (16);

[0053] (17);

[0054] (18);

[0055] in: is the normalized state parameter of the sample, is the predicted normalized residual stress intensity, is the normalized intensity of the predicted UIS, is the normalized intensity of the predicted QSS, is the predicted stability index Iq, is the predicted instability index Ip, is the predicted flow index, is the predicted excess pore water pressure under the deviatoric stress state, is the predicted maximum normalized excess pore water pressure, Normalized excess pore water pressure for the predicted critical state.

[0056] The beneficial effects of the present invention are as follows: the present invention measures the maximum and minimum porosity ratios of the sample through a physical filling test, normalizes the relevant parameters in the traditional critical state line equation and the state parameter equation, and obtains a unified critical state line equation and a normalized state parameter equation, which can unify the critical state lines of samples with different particle shapes and more accurately describe the characteristics of sand; the prediction model constructed by the present invention can accurately predict the mechanical response of sand based on the normalized state parameters, thereby providing quantitative theoretical guidance and technical support for key issues such as sand foundation stability analysis and soil deformation prediction in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 En– (p' / pa) Schematic diagram of normalized state parameters in the plane;

[0058] Figure 2Schematic diagram of the relationship between normalized state parameters and volume strain at critical state under drainage conditions;

[0059] Figure 3 Schematic diagram of the relationship between normalized state parameters and stress-swelling friction angle under drainage conditions;

[0060] Figure 4 Schematic diagram of the relationship between normalized state parameters and excess friction angle under drainage conditions;

[0061] Figure 5 Schematic diagram of the relationship between normalized state parameters and normalized peak deviatoric stress under drainage conditions;

[0062] Figure 6 Schematic diagram of the relationship between normalized state parameters and peak friction angle under drainage conditions;

[0063] Figure 7 Schematic diagram of the relationship between normalized state parameters and normalized residual stress intensity under undrained conditions;

[0064] Figure 8 Schematic diagram of the relationship between normalized state parameters and normalized intensity of UIS under undrained conditions;

[0065] Figure 9 Schematic diagram of the relationship between the normalized state parameter and the normalized intensity of QSS under undrained conditions;

[0066] Figure 10 Normalized state parameter and instability index I under undrained conditions q Relationship diagram;

[0067] Figure 11 Normalized state parameter and instability index I under undrained conditions p Relationship diagram;

[0068] Figure 12 Schematic diagram of the relationship between normalized state parameters and flow potential index under undrained conditions;

[0069] Figure 13 Schematic diagram of the relationship between the normalized state parameter and the excess pore water pressure at the peak deviatoric stress state under undrained conditions;

[0070] Figure 14 Schematic diagram of the relationship between normalized state parameters and maximum normalized excess pore water pressure under undrained conditions;

[0071] Figure 15 Schematic diagram of the relationship between the normalized state parameter and the critical state normalized excess pore water pressure under undrained conditions. DETAILED DESCRIPTION

[0072] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the two embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0073] The present invention proposes a method for predicting the mechanical response of sand based on state parameters, comprising the following steps:

[0074] S1: Establishment e– p' Traditional critical state line equation in the plane;

[0075] The traditional critical state line equation established in step S1 is specifically shown in formula (2):

[0076] (2);

[0077] in: is the critical state void ratio, The traditional critical state line is e- p' The intercept void ratio on the plane, The traditional critical state line is ep' The slope of the plane, is the average effective stress at the critical state, is atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0078] ep' The meaning of the plane is: the coordinate plane of the void ratio and effective stress of the specimen, ep' On a plane, by plotting test data points of soil under different conditions, the normal consolidation line and critical state curve of the soil can be obtained. It is an important tool for describing the deformation and stress state of the soil.

[0079] S2: Define the sample state parameters and establish the sample state parameter equation. The sample state parameter equation is shown in formula (1):

[0080] (1);

[0081] in: is the state parameter, is the initial state void ratio, is the critical state void ratio, The traditional critical state line is ep' The intercept void ratio on the plane, The traditional critical state line is ep' The slope of the plane, is the average effective stress at the critical state, is atmospheric pressure, The traditional critical state line is ep' calibration constants for the plane;

[0082] S3: The first parameter is determined by physical filling test method. The first parameter is specifically: maximum void ratio With minimum porosity ratio .

[0083] S4: Use the parameters measured in S3 to analyze the parameters in the traditional critical state line equation and conduct Min-Max Normalize and get the first equation and the second equation in turn;

[0084] The first equation is specifically the unified critical state line in En–p' The intercept porosity equation on the plane, the second equation is specifically En-p' Unified critical state line slope equation in the plane;

[0085] The unified critical state line is En-p' The intercept porosity ratio equation on the plane is shown in formula (3): En-p' The slope equation of the unified critical state line in the plane is shown in formula (4):

[0086] (3);

[0087] in: To unify the critical state line En-p' The intercept void ratio on the plane, is the maximum void ratio, is the minimum void ratio, The traditional critical state line is ep' intercept porosity ratio on the plane;

[0088] (4);

[0089] in: The traditional critical state line is ep' The slope of the plane, for En-p 'The slope of the uniform critical state line in the plane.

[0090] En– p' The plane is the coordinate plane of the normalized void ratio and effective stress of the sample. En– p' On a plane, by plotting test data points of soil under different conditions, the normal consolidation line and critical state curve of the soil can be obtained. It is an important tool for describing the deformation and stress state of the soil.

[0091] S5: Substitute the parameters measured in S3 and the equation obtained in S4 into the traditional critical state line equation established in S1 to obtain the unified critical state line equation. The unified critical state line equation is shown in formula (5):

[0092] (5);

[0093] in: E cs is the normalized critical state void ratio, To unify the critical state line En-p' The intercept void ratio on the plane, for En-p 'The slope of the uniform critical state line in the plane, is the average effective stress at the critical state, is atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0094] S6: Use the parameters measured in S3 to perform the calculation on the parameters in the state parameter equation of the sample obtained in S2. Min-Max Normalization is performed to obtain the normalized initial state porosity equation and the normalized critical state porosity equation in sequence, and the obtained equations are substituted into the sample state parameter equation to obtain the normalized state parameter equation of the sample;

[0095] The normalized state parameter equation of the sample is shown in formula (6):

[0096] (6);

[0097] in: is the normalized initial state void ratio, To unify the critical state line En-p' The intercept void ratio on the plane, for En-p 'The slope of the uniform critical state line in the plane, is the normalized critical state void ratio, is the effective consolidation stress, is the normalized state parameter of the sample.

[0098] What needs to be explained is: Figure 1 As shown, the Normalized Status Parameter (NSP) is defined as the initial shear state （E c ，p' c ） and En –p' The corresponding point on the unified critical state line in space ( E cs , p'c ), in the present invention, the state parameter in the initial shear state ψ n (0) is represented by ψ n .

[0099] Figure 1 middle En– (p' / pa) A plane is a coordinate plane used to analyze the mechanical properties of soil.

[0100] The NSP is a physical parameter in the plane of the unified critical state line with reference to the corresponding critical state. The mechanical properties of sand are predicted and quantified by controlling the mechanical properties of triaxial shear tests under undrained conditions with the NSP, combined with the effects of normalized void ratio and mean effective stress level.

[0101] S7: Four different sand samples were selected for triaxial testing to determine the average effective stress of the four sand samples at the critical state. Porosity ratio e, , respectively, the mean effective stress Porosity ratio e, The data is normalized to obtain the unified critical state line and normalized state parameters of the sample;

[0102] S7 specifically involves selecting four sand samples: Pearl River Sand (ZRS), Leighton Buzzard Sand (LBS), Quartz Sand A, and Quartz Sand B. Triaxial shear tests are performed on each sample. When the sample reaches the critical state, the average effective stress of each sample is recorded. and porosity ratio e ; The average effective stress of the four samples and porosity ratio e Perform normalization to obtain the normalized average effective stress and the normalized porosity ratio ; The normalized mean effective stress and porosity ratio The data are substituted into the unified critical state line equation for fitting to obtain the unified critical state line of the sample and the normalized state parameters of the sample.

[0103] It should be noted that: Pearl River Sand is an angular silica sand from the Pearl River (Zhujiang) in southern Guangdong Province, China, and its nature is angular sand. Leighton Buzzard Sand is a widely studied quartz sand composed of 3 strong, regular, highly spherical particles from the UK, and its nature is round sand. Quartz Sand A (QSA) is an angular quartz sand, and Quartz Sand B (QSB) is a quartz sand with significantly varied particle shape from Zhuhai in southern Guangdong Province, China.

[0104] S8: Use the normalized state parameters of the specimen obtained in S7 to establish a mechanical response prediction model under drainage conditions and a mechanical response prediction model under undrained conditions.

[0105] The prediction models of sand mechanical response under drainage conditions include: volume strain prediction model under critical state, stress expansion friction angle prediction model, excess friction angle prediction model, normalized peak deviatoric stress prediction model, and peak friction angle prediction model;

[0106] The volume strain prediction model under the critical state is specifically shown in formula (7), the maximum friction angle prediction model of stress expansion is specifically shown in formula (8), and the excess friction angle prediction model is specifically shown in formula (9):

[0107] (7);

[0108] (8);

[0109] (9);

[0110] in: is the normalized state parameter of the sample, is the predicted volumetric strain, is the predicted maximum friction angle, is the predicted excess friction angle;

[0111] The prediction models of sand mechanical response under undrained conditions include: normalized residual stress strength prediction model, UIS (Quasi Steady State) normalized strength prediction model, QSS (Undrained Instable State) normalized strength prediction model, instability index Iq prediction model, instability index I p Prediction model, flow potential index prediction model, excess pore water pressure prediction model under peak deviatoric stress state, maximum normalized excess pore water pressure relationship prediction model, critical state normalized excess pore water pressure relationship prediction model;

[0112] Normalized residual stress strength prediction model, specifically as shown in formula (10), normalized strength prediction model of UIS, specifically as shown in formula (11), normalized strength prediction model of QSS, specifically as shown in formula (12), instability index I q The prediction model is shown in formula (13), and the instability index I p The prediction model is specifically shown in formula (14), the flow potential index prediction model is specifically shown in formula (15), the excess pore water pressure prediction model under peak deviatoric stress state is specifically shown in formula (16), the maximum normalized excess pore water pressure relationship prediction model is specifically shown in formula (17), and the critical state normalized excess pore water pressure relationship prediction model is specifically shown in formula (18):

[0113] (10);

[0114] (11);

[0115] (12);

[0116] (13);

[0117] (14);

[0118] (15);

[0119] (16);

[0120] (17);

[0121] (18);

[0122] in: is the normalized state parameter of the sample, is the predicted normalized residual stress intensity, is the normalized intensity of the predicted UIS, is the normalized intensity of the predicted QSS, is the predicted stability index Iq, is the predicted instability index Ip, is the predicted flow index, is the predicted excess pore water pressure under the deviatoric stress state, is the predicted maximum normalized excess pore water pressure, Normalized excess pore water pressure for the predicted critical state.

[0123] In the first step, drained and undrained triaxial shear tests were conducted on four different sandy soils (ZRS, LBS, QSA, and QSB). All samples were 38 mm in diameter and 76 mm in height and were prepared using wet ramming and undercompaction techniques. This method resulted in a wider range of initial void ratios and a more uniform spatial distribution of particles of varying sizes within the samples.

[0124] All specimens were subjected to carbon dioxide flushing and degassed water flushing, followed by a back pressure of 250–350 kPa, to obtain a B value (soil sample saturation) greater than 0.98. During triaxial shear, the shear strain rate for each specimen was 0.5% height / min.

[0125] In the second step, four different sand samples were selected for triaxial testing. When the samples reached the critical state, the average effective stress of each sample was recorded. and porosity ratio e , the average effective stress of the four samples and porosity ratio e Perform normalization to obtain the normalized average effective stress and the normalized porosity ratio , the normalized mean effective stress and porosity ratio The data are substituted into the unified critical state line equation for fitting to obtain the unified critical state line of the sample and the normalized state parameters of the sample.

[0126] The third step is to use the normalized state parameters of the specimen to establish a mechanical response prediction model under drainage conditions and a mechanical response prediction model under undrained conditions.

[0127] The models established under drainage conditions include volume strain prediction model under critical state, stress expansion friction angle prediction model, excess friction angle prediction model, normalized peak deviatoric stress prediction model, and peak friction angle prediction model;

[0128] Figure 2 It shows the relationship between the normalized state parameters under drainage conditions and the volume strain under critical state. Figure 2 It can be seen that with the increase of NSP (the sample changes from dense to loose before shearing), the volume strain in the critical state gradually increases (the shear sample changes from expansion to contraction), and the volume strain change is related to Figure 2 The linear function in the equation fits well. Therefore, when the NSP of the specimen under drained shear conditions is known, the volume strain at the critical state can be predicted using the following equation: .

[0129] Figure 3 It shows the relationship between normalized state parameters and stress expansion friction angle under drainage conditions. Figure 3It can be seen that the present invention conducts triaxial shear tests on sands of four different particle shapes under drainage conditions. As the NSP of the dense sample before shearing increases, the maximum friction angle of stress expansion during shearing gradually decreases. And the change of the maximum friction angle is related to Figure 3 The linear function in the equation is well fitted. Therefore, when the NSP of the specimen under drained shear conditions is known, the maximum friction angle of stress expansion can be predicted using the following equation: .

[0130] Figure 4 It shows the relationship between normalized state parameters and excess friction angle under drainage conditions. Figure 4 It can be seen that the NSP of the dense sample increases before shearing, and the excess friction angle gradually decreases during the shearing process. Figure 4 The linear function in the equation is well fitted. Therefore, when the NSP of the specimen sheared under drained shear conditions is known, the excess friction angle can be predicted using the following equation: .

[0131] Figure 5 It shows the relationship between normalized state parameters and normalized peak deviatoric stress under drainage conditions. Figure 5 It can be seen that with the increase of NSP, the normalized peak deviatoric stress during shear gradually decreases. At the same NSP level, under drained shear conditions, the normalized peak deviatoric stress of the Pearl River sand sample lags behind that of the British sand sample.

[0132] Figure 6 It shows the relationship between the normalized state parameters and the peak friction angle under drainage conditions. Figure 6 It can be seen that as the NSP of the dense sample before shearing increases, the peak friction angle of shear resistance gradually decreases during shearing. At the same NSP level, under drained shear conditions, the peak friction angle of the Pearl River sand sample lags behind that of the British sand sample (LBS).

[0133] Figure 7 It shows the relationship between normalized state parameters and normalized residual stress intensity under undrained conditions. Figure 7 It can be seen that as the NSP before shear increases, the undrained strength of the UIS gradually decreases during the shear process. The change in the undrained strength of the UIS is well fitted with the linear function in the figure. Therefore, when the NSP of the sample is known, the undrained strength of the UIS under undrained shear conditions can be predicted using the following equation:

[0134] .

[0135] Figure 8It shows the relationship between normalized state parameters and normalized intensity of UIS under undrained conditions. Figure 8 It can be seen that with the increase of NSP before shearing, the undrained strength of UIS gradually decreases during shearing. Figure 8 The linear function in the equation is well fitted. Therefore, when the NSP of the specimen is known, the undrained strength of the UIS under undrained shear conditions can be predicted using the following equation: .

[0136] Figure 9 It shows the relationship between the normalized state parameter and the normalized intensity of QSS under undrained conditions. Figure 9 It can be seen that as the NSP before shear increases, the undrained strength at the QSS gradually decreases during the shear process. The change in the undrained strength at the QSS fits well with the linear function in the figure. Therefore, when the NSP of the specimen is known, the undrained strength at the QSS under undrained shear conditions can be predicted using the following equation:

[0137] .

[0138] Figure 10 It represents the normalized state parameter and instability index I under undrained conditions. q Relationship diagram, Figure 11 It represents the normalized state parameter and instability index I under undrained conditions. p Relationship diagram, comprehensive Figure 10 , Figure 11 It can be seen that when the specimen exhibits stable behavior under the undrained test, the instability index is zero. When the specimen exhibits true liquefaction behavior under the undrained test, the instability index is 1. When the instability index is between 0 and 1, as the instability index value increases, the liquefaction sensitivity and instability degree of the specimen will increase. Therefore, the normalized state parameters can be used to analyze the instability index of the undrained triaxial shear test, and the prediction equations are: , .

[0139] Figure 12 It shows the relationship between normalized state parameters and flow potential index under undrained conditions. Figure 12 It can be seen that as the NSP before shearing increases, the flow potential index during shearing gradually increases, and the change in the flow potential index fits well with the linear function in the figure. Therefore, when the NSP of the sample is known, the flow potential index under undrained shearing conditions can be predicted, and the prediction equation is: .

[0140] Figure 13It shows the relationship between the normalized state parameter under undrained conditions and the excess pore water pressure under peak deviatoric stress state. Figure 14 It shows the relationship between the normalized state parameter and the maximum normalized excess pore water pressure under undrained conditions. Figure 15 Schematic diagram of the relationship between normalized state parameters and critical state normalized excess pore water pressure under undrained conditions, Figure 13 , Figure 14 , Figure 15 It can be seen that with the increase of NSP before shearing, the normalized excess pore water pressure under three different stress states gradually increases during the shearing process, and the changes in the normalized excess pore water pressure are respectively Figure 12 The linear function in the equation is well fitted. Therefore, when the NSP of the specimen is known, the normalized excess pore water pressure of three different stress states under undrained shear conditions can be predicted using the following equation: , , .

[0141] Each embodiment in this specification is described in a related manner. Similar parts between the various embodiments can be referred to in conjunction with each other. Each embodiment focuses on the differences between the other embodiments. In particular, the system embodiment is generally similar to the method embodiment, so the description is relatively simple. For related parts, refer to the description of the method embodiment.

[0142] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A method for predicting the mechanical response of sand based on state parameters, characterized in that: The specific steps are as follows: S1: Establish the traditional critical state line equation in the e–p' plane; S2: Define the sample state parameters and establish the sample state parameter equation. The sample state parameter equation is specifically shown in formula (1): Where: ψ is the state parameter, e c is the initial porosity ratio, e cs is the critical state porosity ratio, e Γ is the intercept porosity ratio of the traditional critical state line on the e-p' plane, λ e is the slope of the traditional critical state line in the e-p' plane, p' cs is the average effective stress at the critical state, p a is the atmospheric pressure, α is the calibration constant of the traditional critical state line in the e-p' plane; S3: Determine the first parameter using a physical filling test method; S4: Use the parameters measured in S3 to perform Min-Max normalization on the second parameter in the traditional critical state line equation, and obtain the first equation and the second equation respectively; S5: Substitute the parameters measured in S3 and the equation obtained in S4 into the traditional critical state line equation established in S1 to obtain the unified critical state line equation; S6: Use the parameters measured in S3 to perform Min-Max normalization on the parameters in the state parameter equation of the sample obtained in S2, and obtain the normalized initial state porosity equation and the normalized critical state porosity equation in turn. Substitute the obtained equations into the state parameter equation of the sample to obtain the normalized state parameter equation of the sample; S7: Select a variety of sand samples for triaxial testing, measure the average effective stress p' and porosity e of the sand samples under the critical state, normalize the average effective stress p' and porosity e data, and obtain the unified critical state line and normalized state parameters of the samples; S8: Use the normalized state parameters of the specimen obtained in S7 and the critical state soil mechanics theory to establish a mechanical response prediction model under drainage conditions and a mechanical response prediction model under undrained conditions.

2. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: The traditional critical state line equation described in S1 is specifically shown in formula (2): Among them: e cs is the critical state porosity ratio, e Γ is the intercept porosity ratio of the traditional critical state line on the e-p' plane, λ e is the slope of the traditional critical state line in the e-p' plane, p' cs is the average effective stress at the critical state, p a is the atmospheric pressure, and α is the calibration constant of the traditional critical state line in the e-p' plane.

3. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: In S3, the parameters were determined by the physical filling test method. The first parameter was specifically: the maximum void ratio e max With the minimum porosity ratio e min .

4. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: S4 is specifically as follows: using the parameters measured in S3 to calculate the second parameter e in the traditional critical state line equation Γ and λ e Perform Min-Max normalization.

5. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: The first equation in S4 is specifically the porosity equation of the intercept of the unified critical state line on the En-p' plane, and the second equation in S4 is specifically the slope equation of the unified critical state line on the En-p' plane; The intercept porosity equation of the unified critical state line on the En-p' plane is specifically shown in formula (3), and the slope equation of the unified critical state line in the En-p' plane is specifically shown in formula (4): Where: E Γ is the intercept porosity ratio of the unified critical state line on the En-p' plane, e max is the maximum porosity ratio, e min is the minimum porosity ratio, e Γ is the porosity ratio of the intercept of the traditional critical state line on the e-p' plane; Where: e is the slope of the traditional critical state line in the e-p' plane, λ E is the slope of the unified critical state line in the En-p' plane.

6. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: The unified critical state line equation described in S5 is specifically shown in formula (5): Where: E cs is the normalized critical state void ratio, E Γ is the intercept porosity ratio of the unified critical state line on the En-p' plane, λ E is the slope of the unified critical state line in the En-p' plane, p' cs is the average effective stress at the critical state, p a is the atmospheric pressure, and α is the calibration constant of the traditional critical state line in the e-p' plane.

7. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: The normalized state parameter equation of the sample in S6 is specifically shown in formula (6): Where: E c is the normalized initial state void ratio, E Γ is the intercept porosity ratio of the unified critical state line on the En-p' plane, λ E is the slope of the unified critical state line in the En-p' plane, E cs is the normalized critical state porosity ratio, p′ c is the effective consolidation stress, ψ n is the normalized state parameter of the sample.

8. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: S7 specifically: S7.1: Select four sand samples: Pearl River sand, LBS sand, quartz sand A, and quartz sand B. Perform triaxial shear tests on each sample. When the sample reaches the critical state, record the average effective stress p′ and porosity e of each sample. S7.2: Normalize the average effective stress p′ and porosity e of the four samples to obtain the normalized average effective stress p * and the normalized porosity ratio e * ; S7.3: The normalized mean effective stress p * and porosity ratio e * The data are substituted into the unified critical state line equation for fitting to obtain the unified critical state line of the sample and the normalized state parameters of the sample.

9. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: The prediction model of sand mechanical response under drainage conditions described in S8 includes: a volume strain prediction model under critical state, a stress expansion friction angle prediction model, an excess friction angle prediction model, a normalized peak deviatoric stress prediction model, and a peak friction angle prediction model; The volume strain prediction model under the critical state is specifically shown in formula (7), the stress expansion friction angle prediction model is specifically shown in formula (8), and the excess friction angle prediction model is specifically shown in formula (9): y1=12.66x+0.57 (7) y2=-24.96x+1.51 (8) y3=-10.86x+2.41 (9) Where: x is the normalized state parameter of the specimen, y1 is the volume strain prediction model under the critical state, y2 is the stress expansion friction angle prediction model, and y3 is the excess friction angle prediction model; The prediction models for the mechanical response of sand under undrained conditions in S8 include: normalized residual stress strength prediction model, normalized strength prediction model of UIS, normalized strength prediction model of QSS, instability index I q Prediction model, instability index I p Prediction model, flow potential index prediction model, excess pore water pressure prediction model under peak deviatoric stress state, maximum normalized excess pore pressure prediction model, critical normalized excess pore pressure prediction model; The normalized residual stress strength prediction model is specifically shown in formula (10), the normalized strength prediction model of UIS is specifically shown in formula (11), the normalized strength prediction model of QSS is specifically shown in formula (12), and the instability index I q The prediction model is shown in formula (13), and the instability index I p The prediction model is specifically shown in formula (14), the flow potential index prediction model is specifically shown in formula (15), the excess pore water pressure prediction model under peak deviatoric stress state is specifically shown in formula (16), the maximum normalized excess pore pressure prediction model is shown in formula (17), and the critical normalized excess pore pressure prediction model is shown in formula (18): y4=66.10x 2 -6.55x+0.2 (10) y5=1.13x 2 -1.21x+0.47 (11) <h2 style=";text-align:left;direction:ltr">y6 = 1.94x<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> -1.66x+0.32 (12) y7=2.22x+0.35 (13) y8=2.21x+0.4 (14) y9=1.98x+0.49 (15) y 10 =23x+2.8 (16) and 11 =1.29x+0.67 (17) y 12 =-57.93x 2 +6.13x+0.75 (18); Where: x is the normalized state parameter of the specimen, y4 is the normalized residual stress strength prediction model, y5 is the normalized strength prediction model of UIS, y6 is the normalized strength prediction model of QSS, and y7 is the instability index I q Prediction model, y8 is the instability index I p Prediction model, y9 is the flow index prediction model, y 10 is the prediction model of excess pore water pressure under peak deviatoric stress state, y 11 is the maximum normalized excess pore pressure prediction model, y 12 It is a critical normalized excess pore pressure prediction model.

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