Method for predicting sand mechanical response based on state parameters

Abstract

The invention discloses a method for predicting sand mechanical response based on state parameters, which comprises the following steps: firstly, establishing an e-p'plane traditional critical state line equation, defining sample state parameters and establishing the equation, measuring parameters by adopting a physical filling test method, performing Min-Max normalization on related equation parameters, and calculating the sand mechanical response according to the Min-Max normalization. And obtaining a unified critical state line equation and a normalized state parameter equation of the sample. The method comprises the following steps: selecting four sandy soil samples to carry out a triaxial test, determining and normalizing critical state data, and finally, establishing a mechanical response prediction model under drainage and non-drainage conditions by utilizing normalized state parameters of the samples and combining a critical state soil mechanics theory. The mechanical properties of the sandy soil with different particle shapes are predicted by using normalized state parameters, and the defects in the prior art are overcome.

Description

Technical Field

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

[0002] As a common engineering foundation material, the mechanical properties of sand are directly related to the stability and safety of various engineering structures. In the plate boundary area, earthquake activities are frequent, and disasters such as sand liquefaction caused by earthquakes seriously threaten the safety of infrastructure and people's lives and property. In many earthquakes in the past, accidents such as building tilts, road collapses, and bridge collapses due to abnormal mechanical response of sand are common. Therefore, in the field of geotechnical engineering, in-depth research on the mechanical response characteristics of sand is of great theoretical and practical significance for improving the earthquake resistance of engineering and ensuring the safety of infrastructure.

[0003] At present, although some research has been carried out on the mechanical behavior of sand, covering the strength, deformation characteristics and response laws of sand 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 it is difficult to 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 the mechanical behavior of sand, but also provide a 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: S1: Establishment e–p' Traditional critical state line equation in the 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): (1); 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 porosity 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 the atmospheric pressure, The traditional critical state line is ep' calibration constant of the plane; S3: Determine the first parameter using a physical filling test method; 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; 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 a unified critical state line equation; S6: Use the parameters measured in S3 to respectively adjust the parameters in the sample state parameter equation obtained in S2. Min-Max Normalization is performed to obtain the normalized initial state porosity equation and the normalized critical state porosity equation in turn, and the obtained equations are substituted into the sample state parameter equation to obtain the normalized state parameter equation of the sample; S7: Select a variety of sand samples for triaxial tests and measure the average effective stress of the 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; 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.

[0007] Furthermore, the traditional critical state line equation in S1 is shown in formula (2): (2); in: is the critical state void ratio, The traditional critical state line is e- p' The intercept porosity 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 the atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0008] Furthermore, in S3, the parameters are determined by a physical filling test method, and the first parameter is specifically: the maximum void ratio Minimum porosity ratio .

[0009] Further, S4 is specifically: using the parameters measured in S3 to respectively calculate the second parameter in the traditional critical state line equation and conduct Min-Max Normalization.

[0010] Furthermore, the first equation in S4 is specifically the unified critical state line at 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; The unified critical state line is En-p' The intercept porosity equation on the plane is as shown in formula (3), En-p' The slope equation of the unified critical state line in the plane is shown in formula (4): (3); in: To unify the critical state line En-p' The intercept porosity 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; (4); 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.

[0011] Furthermore, the critical state line equation is unified in S5, as shown in formula (5): (5); in: E cs is the normalized critical state void ratio, To unify the critical state line En-p' The intercept porosity 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 the atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0012] Furthermore, the normalized state parameter equation of the sample in S6 is specifically shown in formula (6): (6); in: is the normalized initial state void ratio, To unify the critical state line En-p' The intercept porosity 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.

[0013] Furthermore, S7 is 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 of each sample. and porosity ratio e ; S7.2: Average the effective stress of the four specimens. and porosity ratio e Normalized processing is performed to obtain the normalized average effective stress and the normalized porosity ratio ; S7.3: The normalized mean effective stress and porosity ratio The data is 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.

[0014] Furthermore, the prediction models of 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, peak friction angle prediction model; 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): (7); (8); (9); 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; 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; 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), the instability index Iq prediction model is specifically shown in formula (13), the instability index Ip 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 the deviatoric stress state is specifically shown in formula (16), the maximum normalized excess pore water pressure prediction model is specifically shown in formula (17), and the critical state normalized excess pore water pressure prediction model is specifically shown in formula (18): (10); (11); (12); (13); (14); (15); (16); (17); (18); 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.

[0015] The beneficial effects of the present invention are as follows: the present invention measures the maximum and minimum void ratios of a sample through a physical filling test, normalizes relevant parameters in a traditional critical state line equation and a 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

[0016] Figure 1 En– (p' / pa) Schematic diagram of normalized state parameters in the plane; Figure 2 Schematic diagram of the relationship between normalized state parameters and volume strain at critical state under drainage conditions; Figure 3 Schematic diagram of the relationship between normalized state parameters and stress expansion friction angle under drainage conditions; Figure 4 Schematic diagram of the relationship between normalized state parameters and excess friction angle under drainage conditions; Figure 5 Schematic diagram of the relationship between normalized state parameters and normalized peak deviatoric stress under drainage conditions; Figure 6 Schematic diagram of the relationship between normalized state parameters and peak friction angle under drainage conditions; Figure 7 Schematic diagram of the relationship between normalized state parameters and normalized residual stress intensity under undrained conditions; Figure 8 Schematic diagram of the relationship between normalized state parameter and normalized intensity of UIS under undrained conditions; Fig. 9 Schematic diagram of the relationship between the normalized state parameter and the normalized intensity of QSS under undrained conditions; Fig.10 Normalized state parameter and instability index I under undrained conditions q Relationship diagram; Fig.11 Normalized state parameter and instability index I under undrained conditions p Relationship diagram; Fig.12 Schematic diagram of the relationship between normalized state parameters and flow potential index under undrained conditions; Fig.13 Schematic diagram of the relationship between normalized state parameters and excess pore water pressure under peak deviatoric stress state under undrained conditions; Fig.14 Schematic diagram of the relationship between normalized state parameters and maximum normalized excess pore water pressure under undrained conditions; Fig.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

[0017] 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 described embodiments 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 creative work are within the scope of protection of the present invention.

[0018] The present invention proposes a method for predicting the mechanical response of sand based on state parameters, comprising the following steps: S1: Establishment e–p' Traditional critical state line equation in the plane; The traditional critical state line equation established in step S1 is specifically shown in formula (2): (2); in: is the critical state void ratio, The traditional critical state line is e- p' The intercept porosity 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 the atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0019] ep' The plane means: 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. This is an important tool for describing the deformation and stress state of the soil.

[0020] S2: Define the sample state parameters and establish the sample state parameter equation. The sample state parameter equation is shown in formula (1): (1); 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 porosity 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 the atmospheric pressure, The traditional critical state line is ep' calibration constant of the plane; S3: The first parameter is determined by a physical filling test method. The first parameter is specifically: maximum void ratio Minimum porosity ratio .

[0021] S4: The parameters measured in S3 are used to calculate 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; 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; The unified critical state line is En-p' The intercept porosity equation on the plane is as shown in formula (3): En-p' The slope equation of the unified critical state line in the plane is shown in formula (4): (3);

[0022] in: To unify the critical state line En-p' The intercept porosity 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; (4); 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.

[0023] 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. This is an important tool for describing the deformation and stress state of the soil.

[0024] S5: Substitute the parameters measured by S3 and the equation obtained by S4 into the traditional critical state line equation established by S1 to obtain the unified critical state line equation. The unified critical state line equation is specifically shown in formula (5): (5); in: E cs is the normalized critical state void ratio, To unify the critical state line En-p' The intercept porosity 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 the atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

[0025] S6: Use the parameters measured in S3 to respectively adjust the parameters in the sample state parameter equation obtained in S2. Min-Max Normalization is performed to obtain the normalized initial state porosity equation and the normalized critical state porosity equation in turn, and the obtained equations are substituted into the sample state parameter equation to obtain the normalized state parameter equation of the sample; The normalized state parameter equation of the sample is shown in formula (6): (6); in: is the normalized initial state void ratio, To unify the critical state line En-p' The intercept porosity 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.

[0026] 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 .

[0027] Figure 1 middle En– (p' / pa) A plane is a coordinate plane used to analyze the mechanical properties of soil.

[0028] 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 combining the influence of normalized void ratio and mean effective stress level through the control of the mechanical properties of triaxial shear test by NSP and the control of the mechanical properties of triaxial shear test under undrained conditions.

[0029] S7: Four different sand samples were selected for triaxial tests, and the average effective stress of the four sand samples under critical conditions was measured. 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; S7 is as follows: four sand samples, namely, Pearl River Sand (ZRS), Leighton Buzzard Sand (LBS), quartz sand A and quartz sand B, are selected, and 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 Normalized processing is performed to obtain the normalized average effective stress and the normalized porosity ratio ; The normalized average effective stress and porosity ratio The data is 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.

[0030] 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 and regular highly spherical particles from the United Kingdom, 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 a significantly changed particle shape from Zhuhai in southern Guangdong Province, China.

[0031] S8: Use the normalized state parameters of the sample obtained in S7 to establish a mechanical response prediction model under drainage conditions and a mechanical response prediction model under undrained conditions.

[0032] The prediction models of mechanical response of sand 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, peak friction angle prediction model; 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): (7); (8); (9); 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; The prediction models of mechanical response of sand under undrained conditions include: normalized residual stress strength prediction model, normalized strength prediction model of UIS (Quasi Steady State), normalized strength prediction model of QSS (Undrained Instable State after Undrained Instable State), 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; The normalized residual stress strength prediction model is shown in formula (10), the normalized strength prediction model of UIS is shown in formula (11), the normalized strength prediction model of QSS is shown in formula (12), and the instability index I qThe prediction model is shown in formula (13), 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): (10); (11); (12); (13); (14); (15); (16); (17); (18); 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.

[0033] In the first step, drained and undrained triaxial shear tests were performed on four different sand samples (ZRS, LBS, QSA, QSB). All samples were 38 mm in diameter and 76 mm in height, and were prepared using wet ramming and undercompaction techniques. Using this method, the initial porosity range of the samples will be wider, and the spatial distribution of particles of different particle sizes in the samples will be more uniform.

[0034] All specimens were subjected to a B value (degree of saturation) greater than 0.98 by flushing with carbon dioxide and degassed water, followed by a back pressure of 250–350 kPa. During triaxial shear, the shear strain rate for each specimen was 0.5% height / min.

[0035] 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 Normalized processing is performed to obtain the normalized average effective stress and the normalized porosity ratio , the normalized mean effective stress and porosity ratio The data is 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.

[0036] 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.

[0037] 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; Figure 2 It shows the relationship between the normalized state parameter under drainage condition 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 has a good fit. Therefore, when the NSP of the specimen under drained shear conditions is known, the volume strain at the critical state can be predicted, and the prediction equation is: .

[0038] Figure 3 It shows the relationship between the normalized state parameter and the stress expansion friction angle under drainage conditions. Figure 3 It 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 maximum friction angle changes with Figure 3 The linear function in has a good fit. Therefore, when the NSP of the specimen under drained shear conditions is known, the maximum friction angle of stress expansion can be predicted, and the prediction equation is: .

[0039] Figure 4 It shows the relationship between the normalized state parameter and the excess friction angle under drainage conditions. Figure 4It 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 is well fitted. Therefore, when the NSP of the specimen sheared under drained shear conditions is known, the excess friction angle can be predicted, and the prediction equation is: .

[0040] 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.

[0041] Figure 6 It shows the relationship between the normalized state parameter 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 during shearing gradually decreases. At the same NSP level, under drained shear conditions, the peak friction angle of shear resistance of the Pearl River sand sample lags behind that of the British sand sample (LBS).

[0042] 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 with the increase of NSP before shearing, the undrained strength of UIS gradually decreases during shearing. And the change of undrained strength of UIS fits well with the linear function in the figure. Therefore, when the NSP of the sample is known, the undrained strength of UIS under undrained shearing conditions can be predicted, and the prediction equation is: .

[0043] Figure 8 It shows the relationship between the normalized state parameter and the normalized strength 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 has a good fit. Therefore, when the NSP of the sample is known, the undrained strength of UIS under undrained shear conditions can be predicted, and the prediction equation is: .

[0044] Fig. 9 It shows the relationship between the normalized state parameter and the normalized intensity of QSS under undrained conditions. Fig. 9It can be seen that with the increase of NSP before shearing, the undrained strength at QSS gradually decreases during shearing. And the change of undrained strength at QSS fits well with the linear function in the figure. Therefore, when the NSP of the sample is known, the undrained strength at QSS under undrained shearing conditions can be predicted, and the prediction equation is: .

[0045] Fig.10 It represents the normalized state parameter and instability index I under undrained conditions. q Relationship diagram, Fig.11 It represents the normalized state parameter and the instability index I under undrained conditions. p Relationship diagram, comprehensive Fig.10 , Fig.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 instability index of the undrained triaxial shear test can be analyzed using the normalized state parameters, and the prediction equations are: , .

[0046] Fig.12 It shows the relationship between normalized state parameters and flow potential index under undrained conditions. Fig.12 It can be seen that with the increase of NSP before shearing, the flow potential index during shearing gradually increases, and the change of 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: .

[0047] Fig.13 It shows the relationship between the normalized state parameter under undrained conditions and the excess pore water pressure under the peak deviatoric stress state. Fig.14 It shows the relationship between the normalized state parameter and the maximum normalized excess pore water pressure under undrained conditions. Fig.15 Schematic diagram of the relationship between normalized state parameters and critical state normalized excess pore water pressure under undrained conditions. Fig.13 , Fig.14 , Fig.15 It can be seen that with the increase of NSP before shearing, the normalized excess pore water pressure under three different stress states during shearing gradually increases, and the changes of their normalized excess pore water pressure are respectively Fig.12The linear function in has a good fitting degree. Therefore, when the NSP of the sample is known, the normalized excess pore water pressure of three different stress states under undrained shear conditions can be predicted, and the prediction equation is: , , .

[0048] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0049] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope 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: Establishment e–p' Traditional critical state line equation in the 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): （1）； 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 porosity 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 the atmospheric pressure, The traditional critical state line is ep' calibration constant of the plane; S3: Determine the first parameter using a physical filling test method; 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; 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 a unified critical state line equation; S6: Use the parameters measured in S3 to respectively adjust 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 turn, and the obtained equations are substituted into the sample state parameter equation to obtain the normalized state parameter equation of the sample; S7: Select a variety of sand samples for triaxial tests and measure the average effective stress of the 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; 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): （2）； in: is the critical state void ratio, The traditional critical state line is e- p' The intercept porosity 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 the atmospheric pressure, The traditional critical state line is ep' Calibration constant for the plane.

3. The method for predicting the mechanical response of sand based on state parameters according to claim 1 is characterized in that: S3 uses a physical filling test method to determine the parameters. The first parameter is specifically: the maximum void ratio Minimum porosity ratio .

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

5. The method for predicting the mechanical response of sand based on state parameters according to claim 1 is characterized in that: The first equation in S4 is specifically the unified critical state line at En-p' The intercept porosity ratio equation on the plane, the second equation in S4 is specifically: En-p' Unified critical state line slope equation in the plane; The unified critical state line is En-p' The intercept porosity equation on the plane is as shown in formula (3), En-p' The slope equation of the unified critical state line in the plane is shown in formula (4): （3）； in: To unify the critical state line En-p' The intercept porosity 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; （4）； 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.

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): （5）； in: E cs is the normalized critical state void ratio, To unify the critical state line En-p' The intercept porosity 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 the atmospheric pressure, The traditional critical state line is ep' Calibration constant for the 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 described in S6 is specifically shown in formula (6): （6）； in: is the normalized initial state void ratio, To unify the critical state line En-p' The intercept porosity 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.

8. The method for predicting the mechanical response of sand based on state parameters according to claim 1, characterized in that: S7 is 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 of each sample. and porosity ratio e ; S7.2: Average the effective stress of the four specimens. and porosity ratio e Normalized processing is performed to obtain the normalized average effective stress and the normalized porosity ratio ; S7.3: The normalized mean effective stress and porosity ratio The data is 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 mechanical response of sand under drainage conditions described in S8 includes: volume strain prediction model under critical state, stress expansion friction angle prediction model, excess friction angle prediction model, normalized peak deviatoric stress prediction model, peak friction angle prediction model; 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): （7）； （8）； （9）； 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; The prediction models for mechanical response of sand under undrained conditions described in S8 include: normalized residual stress strength prediction model, normalized strength prediction model of UIS, normalized strength prediction model of QSS, instability index Iq prediction model, instability index Ip 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, and 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), the instability index Iq prediction model is specifically shown in formula (13), the instability index Ip 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 the deviatoric stress state is specifically shown in formula (16), the maximum normalized excess pore water pressure prediction model is specifically shown in formula (17), and the critical state normalized excess pore water pressure prediction model is specifically shown in formula (18): （10）； （11）； （12）； （13）； （14）； （15）； （16）； （17）； （18）； 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.

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