A method for constructing a dynamic constitutive model of saturated sand considering fluctuation growth of pore pressure

Abstract

The application relates to a saturated sand dynamic constitutive model construction method considering pore pressure fluctuation growth, which comprises the following steps: determining total pore water pressure, which comprises a residual pore pressure component and a transient pore pressure component, and constructing a normalized stress ratio skeleton curve independent of the pore pressure state; correcting the total pore water pressure to obtain a corrected pore water pressure, and updating the average effective stress at the current time by using the corrected pore water pressure; coupling the normalized stress ratio skeleton curve and the updated average effective stress to obtain a maximum shear stress value; taking the maximum shear stress value as a target state point to construct a dynamic virtual hysteresis curve, which describes the stress-strain behavior of saturated sand, can effectively consider the cumulative damage and alternating shear shrinkage-dilation effect of the soil in the cyclic loading process, and can capture the pore pressure development curve and the cyclic shear stress-strain response which are more in line with the test law, thereby providing a valuable tool for evaluating the response and liquefaction strength of saturated sand under undrained cyclic loading conditions.

Description

Technical Field

[0001] This invention relates to the fields of geotechnical engineering and earthquake engineering, and specifically to a method for constructing a dynamic constitutive model of saturated sand soil that considers the growth of pore pressure fluctuations. Background Technology

[0002] Saturated sand exhibits significant nonlinearity and hysteresis under cyclic loading, with pore water pressure playing a crucial role in the cyclic deformation of the sand. The accumulation of pore water pressure can lead to a decrease in the stiffness of saturated sand and even liquefaction, thereby causing geological disasters and infrastructure damage. To accurately describe the nonlinearity and hysteresis of saturated sand, as well as its pore pressure response, various advanced soil constitutive models have been proposed in the prior art. Among them, the hysteretic nonlinear constitutive model is a widely used model in one-dimensional nonlinear site response analysis. It controls the unloading and reloading process according to predetermined rules and captures the stiffness reduction characteristics by weakly coupling with the pore water pressure model.

[0003] Currently, most experimental studies focus on the cyclic response of saturated sand under undrained cyclic loading after initial liquefaction. In recent years, significant deformation and lateral slippage following liquefaction of saturated sand layers caused by strong earthquakes have severely damaged structures; therefore, a deeper understanding of the post-liquefaction characteristics of liquefied soil layers has gained increasing attention. At high strain levels (above approximately 0.5%), the hysteresis curve exhibits an inverse S-shape, leading to a decrease in damping ratio with increasing shear strain. This contradicts the trend of increasing damping ratio with increasing shear strain at medium and low strain levels, making hysteretic nonlinear constitutive models unsuitable for application at high strain levels after liquefaction. Furthermore, the loading frequency also has a certain influence on the cyclic response of sand, but current methods for this are limited. Therefore, a method for constructing a dynamic constitutive model for saturated sand that considers the growth of pore pressure fluctuations is urgently needed to address these issues. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a dynamic constitutive model of saturated sand that considers the growth of pore pressure fluctuations, in order to solve the problems existing in the background art.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for constructing a dynamic constitutive model of saturated sand considering the growth of pore pressure fluctuations, comprising the following steps:

[0006] S1. Based on the strain state parameters of the obtained saturated sand, the residual pore pressure component and transient pore pressure component are calculated. The total pore water pressure is determined by superimposing the residual pore pressure component and the transient pore pressure component. ;

[0007] S2, Based on stress ratio Construct a normalized stress ratio skeleton curve independent of pore pressure state. ;

[0008] S3, the total pore water pressure Make corrections to obtain the corrected pore water pressure. To construct a pore pressure-shear strain curve that is monotonically varying within a single shear cycle and has an upper bound constraint, and to utilize the modified pore water pressure Update the mean effective stress at the current moment. ;

[0009] S4, Coupled Normalized Stress Ratio Skeleton Curve and the updated mean effective stress Obtain the maximum shear stress value ;

[0010] S5, based on the maximum shear stress value For the target state point, construct the second reversal point from the current cut. The initial dynamic virtual hysteresis curve serves as the current stress-strain path, describing the stress-strain behavior of saturated sand.

[0011] Preferably, based on uniform shear strain The shearing process is divided into transient shear contraction phase and transient shear dilatation phase, and the transient pore pressure component is calculated segment by segment. :

[0012] When in the transient shearing phase: ;

[0013] When in the transient shear dilatation phase: ;

[0014] in, It is a natural exponential function; and The transient pore pressure and uniform shear strain corresponding to the current monotonic shear sub-initial point; and For the transient pore pressure and uniform shear strain corresponding to the reference shear dilatation state point; and These are the physical parameters that control the rates of contraction and dilatation, respectively.

[0015] Preferably, for the shear strain in each monotonic shear process Perform a coordinate transformation so that the deformation process of each monotonic shearing iteration is uniformly mapped to a consistent direction:

[0016] ;

[0017] in, The sign of the shear strain increment; and The region corresponds to the shearing stage of pore pressure rise and is identified as a transient shearing phase. The region corresponds to the shear dilatation stage of pore pressure decrease and is identified as the transient shear dilatation phase.

[0018] Preferably, the total pore water pressure Make corrections to obtain the corrected pore water pressure. Specifically:

[0019] Using uniform shear strain The sign of the soil particle determines whether it is in a transient shear contraction phase or a transient shear dilatation phase.

[0020] When the soil is in the transient shear-shrinkage phase, the pore pressure value corresponding to the zero strain point or TPT in the current monotonic shear cycle is used. As a correction of pore water pressure ;

[0021] When the soil is in the transient shear dilatation phase, compare the total pore water pressure. and pore pressure value The smaller of the two values ​​was used as the corrected pore water pressure. .

[0022] Preferably, by utilizing modified pore water pressure Update the mean effective stress at the current moment. , is represented as:

[0023] ;

[0024] in, This represents the initial average effective stress.

[0025] Preferably, the maximum shear stress value Represented as: , This represents the largest shear strain in history.

[0026] Preferably, the virtual hysteresis curve is a set of virtual hyperbolic hysteresis curves, and is determined according to the reversal point. Pore ​​water pressure at time Attenuation correction is performed to obtain the initial tangent modulus of the virtual hysteresis curve. :

[0027] ;

[0028] in, This is the maximum shear modulus of the soil. These are material parameters.

[0029] Preferably, a dynamic shape parameter is introduced into the virtual hysteresis curve. This causes the virtual hysteresis curve to align with the direction of the maximum strain point; the dynamic shape parameters Represented as:

[0030] ;

[0031] in, To correct the shear stress at the point where the loading direction reverses, it is expressed as: .

[0032] Preferably, the shear strain at the current moment is obtained based on the constructed virtual hysteresis curve. Corresponding shear stress value , is represented as: .

[0033] Beneficial effects: It can effectively consider the cumulative damage and alternating shear contraction-dilatation effect of soil during cyclic loading, and capture pore pressure development curves and cyclic shear stress-strain responses that are more consistent with experimental data; the method can simulate the flow slip and cyclic active liquefaction failure modes of saturated sand; and it provides a valuable tool for evaluating the response and liquefaction strength of saturated sand under undrained cyclic loading conditions. Attached Figure Description

[0034] Figure 1 For the present invention Schematic diagram of curve calculation;

[0035] Figure 2 Example of τ*-γ* curve calculation for the large deformation stage after liquefaction, obtained based on the modified ū-γ* relationship;

[0036] Figure 3 This is a comparison chart of the experimental results and simulation results of the verification group of this invention;

[0037] Figure 4 N is calculated and measured under the operating conditions of the model group and the verification group of this invention. Cf Comparison chart;

[0038] Figure 5 For different CSR-N under f Cf Line graph. Detailed Implementation

[0039] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe a method for constructing a dynamic constitutive model of saturated sand soil considering the growth of pore pressure fluctuations, or several specific implementation methods, and does not strictly limit the scope of protection specifically claimed by this invention.

[0040] Example: A method for constructing a dynamic constitutive model for saturated sand soil considering the growth of pore pressure fluctuations, comprising:

[0041] S1. Based on the strain state parameters of the obtained saturated sand, the residual pore pressure component and transient pore pressure component are calculated. The total pore water pressure is determined by superimposing the residual pore pressure component and the transient pore pressure component. ;

[0042] Residual pore pressure component formula:

[0043] ;

[0044] ;

[0045] Where t is time, For shear strain, For shear strain at the shear threshold; C1 and C2 are the reference cumulative shear strain and curvature parameters. C1 and C2 are material parameters that are independent of the compaction of the sand and the loading conditions. In this embodiment, for Fujian sand, the values ​​are: C1 = 0.17, C2 = 3.24;

[0046] For transient pore pressure components Based on unified shear strain The shearing process is divided into transient shear contraction phase and transient shear dilatation phase, and the transient pore pressure component is calculated segment by segment. :

[0047] When in the transient shearing phase: ;

[0048] When in the transient shear dilatation phase: ;

[0049] in, It is a natural exponential function; and The transient pore pressure and uniform shear strain corresponding to the current monotonic shear sub-initial point; and For the transient pore pressure and uniform shear strain corresponding to the reference shear dilatation state point; and These are the physical parameters that control the rates of contraction and dilatation, respectively.

[0050] In this embodiment, the shear strain during each monotonic shear process is... Perform a coordinate transformation so that the deformation process of each monotonic shearing iteration is uniformly mapped to a consistent direction:

[0051] ;

[0052] in, The sign of the shear strain increment; and The region corresponds to the shearing stage of pore pressure rise and is identified as a transient shearing phase. The region corresponds to the shear dilatation stage of pore pressure decrease and is identified as the transient shear dilatation phase.

[0053] Total pore water pressure for:

[0054]

[0055] It can capture the pore pressure fluctuations caused by the alternating shear contraction-dilatation characteristics of sand, which is closer to the phenomena observed in experiments;

[0056] S2, Based on stress ratio (The ratio of shear stress τ to average effective stress p' at any given time) constructs a normalized stress ratio skeleton curve independent of the pore pressure state. ; as a benchmark for describing the inherent nonlinear properties of soil; normalized stress ratio skeleton curve Represented as:

[0057] ;

[0058] in, It is the normalized small strain shear modulus. It is the reference shear strain when G' / G'0 = 0.5.

[0059] S3, Total pore water pressure Make corrections to obtain the corrected pore water pressure. To construct a pore pressure-shear strain curve that is monotonically varying within a single shear cycle and has an upper bound constraint, thereby eliminating abnormal fluctuations in effective stress during the large deformation shearing stage, specifically:

[0060] Using uniform shear strain The sign of the soil particle determines whether it is in a transient shear contraction phase or a transient shear dilatation phase.

[0061] When the soil is in the transient shear-shrinkage phase, the pore pressure value corresponding to the zero strain point or TPT in the current monotonic shear cycle is used. As a correction of pore water pressure ;

[0062] When the soil is in the transient shear dilatation phase, compare the total pore water pressure. and pore pressure value The smaller of the two values ​​was used as the corrected pore water pressure. .

[0063] Using modified pore water pressure Update the mean effective stress at the current moment. In this embodiment, it is represented as:

[0064] ;

[0065] in, This represents the initial average effective stress.

[0066] S4, Coupled Normalized Stress Ratio Skeleton Curve and the updated mean effective stress Obtain the maximum shear stress value : , This represents the largest shear strain in history.

[0067] S5, based on the maximum shear stress value For the target state point, construct the second reversal point from the current cut. The initial virtual hysteresis curve, as the current stress-strain path, describes the stress-strain behavior of saturated sand.

[0068] In this embodiment, the virtual hysteresis curve is a set of virtual hyperbolic hysteresis curves, and is determined according to the reversal point. Pore ​​water pressure at time Attenuation correction is performed to obtain the initial tangent modulus of the virtual hysteresis curve. :

[0069] ;

[0070] in, This is the maximum shear modulus of the soil. These are material parameters.

[0071] Dynamic shape parameters are introduced into the virtual hysteresis curve. This causes the virtual hysteresis curve to align with the direction of the maximum strain point; the dynamic shape parameters Represented as:

[0072] ;

[0073] in, To correct the shear stress at the point where the loading direction reverses, it is expressed as: .

[0074] Based on the constructed virtual hysteresis curve, the shear strain at the current moment is obtained. Corresponding shear stress value , is represented as:

[0075] .

[0076] refer to Figure 1 As shown, The schematic diagram of the curve calculation illustrates the process of determining the stress-strain curve based on the pore pressure-strain relationship; in the TC stage from point P0 to P2, u follows... Increase with the increase, such as Figure 1 As shown in (a); according to the skeleton curve rule, the corresponding skeleton curve decreases from curve B0 to B2, as shown in (a). Figure 1 As shown in (b), therefore, at the point of maximum strain The virtual hysteresis curve connecting the strain reversal point and the maximum strain point is determined from point MP0 to MP2, and the curve is lowered from H0 to H2; therefore, points P0, P1, and P2... The values ​​are determined based on curves H0, H1, and H2, respectively; similarly, as... Figure 1 As shown in (a), during the transient shear dilatation (TD) stage, and Below As u decreases from point P2 to P4, the skeleton curve, the maximum strain point, and the virtual hysteresis curve change accordingly. The increase is due to the increase, such as Figure 1 As shown in (c), points P2, P3, and P4 The values ​​are also determined based on the virtual hysteresis curves H2, H3, and H4; when It continues to increase during the transient shear dilatation (TD) phase and exceeds... As u further decreases, the skeleton curve rises from curve B4 to B6. At this point, the stress-strain points are located on the skeleton curve, specifically points P4, P5, and P6. The values ​​are determined based on the skeleton curves B4, B5, and B6, respectively.

[0077] refer to Figure 2 As shown, based on the corrected The experiment of relation calculation with MD-0.05 Curve examples, (a) the 3rd monotonically sheared order; (b) the 17th monotonically sheared order; from Figure 2 As can be seen from the calculation, There is good agreement between the relationship and the test results; this agreement greatly enhances confidence in the ability of the proposed hysteretic nonlinear constitutive model to predict the stress-strain response of materials under undrained cyclic loading at strain levels from small to large.

[0078] This application also provides a specific experimental analysis of the above-mentioned method for constructing a dynamic constitutive model for saturated sand considering the growth of pore pressure fluctuations, as detailed below:

[0079] The reliability of the model was verified through six validation tests. The test specimens covered three states: loose, medium-dense, and dense, and stress-controlled undrained cyclic shear was performed at frequencies of 0.1 Hz and 1 Hz. The stress applied in the actual test was used as the input for the calculation. The shear strain and pore pressure response of the sand dynamic constitutive model constructed using the method of this invention were calculated during the entire cyclic loading process. A total of 11 parameters were included, and Table 1 lists the model parameter values ​​used for calculation under each simulation condition.

[0080] Table 1. Model parameter values ​​for the validation group experiment.

[0081]

[0082] refer to Figure 3 As shown, the comparison diagrams of the test results and simulation results of the validation group are as follows: (a) Test VL-0.1; (b) Test VL-1; (c) Test VM-0.1; (d) Test VM-1; (e) Test VD-0.1; (f) Test VD-1. The strain and pore pressure time histories, stress-strain hysteresis curves, and effective stress paths in the test and calculation results are shown. There is good consistency between the test and calculated shear responses, which indicates that the proposed model can effectively capture the influence of relative density and loading frequency on the undrained cyclic response. In addition, the model accurately simulates two typical liquefaction failure modes: flow slip (suitable for tests on loose sand or under high-frequency loading) and cyclic flow (suitable for tests on dense sand or under low-frequency loading).

[0083] refer to Figure 4 As shown, the number of cycles N required to cause liquefaction failure in the simulation results is... Cf This was verified, meaning the pore pressure reached [a certain value] for the first time. The number of times initial liquefaction was triggered was calculated; the operating conditions in the model group and the validation group were calculated, and N was performed. Cf Comparison and evaluation; such as Figure 4 As shown, the calculated N Cf N obtained from the experiment Cf The good consistency between the model predictions and the actual experimental results indicates a high degree of similarity between them; this provides strong evidence for the accuracy and reliability of the dynamic constitutive model of sand constructed by the method of this invention in capturing the failure behavior of saturated sand under undrained cyclic loading conditions.

[0084] refer to Figure 5 As shown, the dynamic constitutive model of sand constructed using the method of this invention simulates the CSR-N of saturated Fujian sand under different relative densities and loading frequencies under a confining pressure of 100 kPa. Cf Anti-liquefaction curve; Figure 5 Showing CSR-N values ​​of 40%, 55%, and 60% sand were simulated at loading frequencies of 0.1 Hz, 0.5 Hz, and 2 Hz. Cf The simulation results of curve l show that, The reaction with f has a significant effect on the resistance to liquefaction strength; CSR-N Cf The curve follows The decrease in the value indicates that loose, saturated sand is more prone to liquefaction; this can be attributed to two main factors: firstly, Lower-density sandy soils have more porosity, increasing the migration and retention of pore water and promoting pore pressure accumulation. Secondly, the looser structure of sandy soils reduces interparticle friction and increases particle fluidity, making soil particles more prone to rearrangement under cyclic loading, thus leading to faster pore pressure growth. On the other hand, CSR-N... Cf The curve decreases as f decreases, indicating that lower frequency loading makes saturated sand more susceptible to liquefaction. This is because low-frequency loading prolongs the duration of each loading cycle, subjecting the soil to more and longer cyclic stresses. Consequently, the soil undergoes deformation and stress transfer processes more fully under these loading conditions. Under these conditions, soil particles have ample time to rearrange and reorganize, leading to faster pore pressure increases and thus increased liquefaction susceptibility. Therefore, both experimental and simulation results consistently demonstrate that lower frequency loading increases the potential risk of liquefaction and reduces the soil's resistance to liquefaction. Figure 5 CSR-N for Fuzhou sand was also provided. Cf A comparison of the curve distribution ranges shows that the shape of the distribution ranges in the simulation results is similar to that of experimental results in existing literature. The simulation results also demonstrate that the model proposed in this invention can reliably capture… The influence of f on the liquefaction resistance of saturated sand.

[0085] The embodiments of the present invention have been described in detail above with reference to the examples. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for constructing a dynamic constitutive model for saturated sand soil considering the growth of pore pressure fluctuations, characterized in that: Includes the following steps: S1. Based on the strain state parameters of the obtained saturated sand, the residual pore pressure component and transient pore pressure component are calculated. The total pore water pressure is determined by superimposing the residual pore pressure component and the transient pore pressure component. ; S2, Based on stress ratio stress ratio To define the ratio of shear stress τ to average effective stress p' at any given time, a normalized stress ratio skeleton curve independent of the pore pressure state is constructed. ; S3, the total pore water pressure Make corrections to obtain the corrected pore water pressure. To construct a pore pressure-shear strain curve that is monotonically varying within a single shear cycle and has an upper bound constraint, and to utilize the modified pore water pressure Update the mean effective stress at the current moment. ; S4, Coupled Normalized Stress Ratio Skeleton Curve and the updated mean effective stress Obtain the maximum shear stress value ; S5, based on the maximum shear stress value For the target state point, construct the second reversal point from the current cut. The initial dynamic virtual hysteresis curve serves as the current stress-strain path, describing the stress-strain behavior of saturated sand. Based on unified shear strain The shearing process is divided into transient shear contraction phase and transient shear dilatation phase, and the transient pore pressure component is calculated segment by segment. : When in the transient shearing phase: ; When in the transient shear dilatation phase: ; in, It is a natural exponential function; and The transient pore pressure and uniform shear strain corresponding to the current monotonic shear sub-initial point; and For the transient pore pressure and uniform shear strain corresponding to the reference shear dilatation state point; and These are the physical parameters that control the rates of contraction and dilatation, respectively. Shear strain for each monotonic shear process Perform a coordinate transformation so that the deformation process of each monotonic shearing iteration is uniformly mapped to a consistent direction: ； in, The sign of the shear strain increment; and The region corresponds to the shearing stage of pore pressure rise and is identified as a transient shearing phase. The region corresponds to the shear dilatation stage of pore pressure decrease and is identified as the transient shear dilatation phase; The total pore water pressure Make corrections to obtain the corrected pore water pressure. Specifically: Using uniform shear strain The sign of the soil particle determines whether it is in a transient shear contraction phase or a transient shear dilatation phase. When the soil is in the transient shear-shrinkage phase, the pore pressure value corresponding to the zero strain point or TPT in the current monotonic shear cycle is used. As a correction of pore water pressure ; When the soil is in the transient shear dilatation phase, compare the total pore water pressure. and pore pressure value The smaller of the two values ​​was used as the corrected pore water pressure. ; Using modified pore water pressure Update the mean effective stress at the current moment. , is represented as: ； in, The initial average effective stress; The maximum shear stress value Represented as: , This represents the largest shear strain in history.

2. The method for constructing a dynamic constitutive model of saturated sand soil considering the growth of pore pressure fluctuations according to claim 1, characterized in that: The virtual hysteresis curves are a set of virtual hyperbolic hysteresis curves, and are determined based on the reversal point. Pore ​​water pressure at time Attenuation correction is performed to obtain the initial tangent modulus of the virtual hysteresis curve. : ； in, This is the maximum shear modulus of the soil. These are material parameters.

3. The method for constructing a dynamic constitutive model of saturated sand soil considering the growth of pore pressure fluctuations according to claim 2, characterized in that: Introducing dynamic shape parameters into virtual hysteresis curves This causes the virtual hysteresis curve to align with the direction of the maximum strain point; the dynamic shape parameters Represented as: ； in, To correct the shear stress at the point where the loading direction reverses, it is expressed as: .

4. The method for constructing a dynamic constitutive model of saturated sand soil considering the growth of pore pressure fluctuations according to claim 3, characterized in that: Based on the constructed virtual hysteresis curve, the shear strain at the current moment is obtained. Corresponding shear stress value , is represented as: .

Images