Saturated sand dynamic constitutive model construction method considering pore pressure fluctuation increase

Abstract

The invention 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 including residual pore pressure component and transient pore pressure component, and constructing a normalized stress ratio skeleton curve independent of a pore pressure state; correcting the total pore water pressure to obtain corrected pore water pressure, and updating the average effective stress at the current moment 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; the maximum shear stress value is used as a target state point, a dynamic virtual hysteretic curve is constructed, the stress-strain behavior of saturated sandy soil is described, accumulated damage and alternate shear shrinkage-shear expansion effects of a soil body in the cyclic loading process can be effectively considered, a pore pressure development curve and cyclic shear stress-strain response which better conform to the test rule are captured, and the test accuracy is improved. And a valuable tool is provided for evaluating the response and liquefaction strength of the saturated sand under the undrained cyclic loading condition.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of geotechnical engineering and earthquake engineering, and particularly relates to a saturated sand dynamic constitutive model construction method considering pore pressure fluctuation growth. BACKGROUND

[0002] Saturated sand shows obvious nonlinearity and hysteresis under cyclic loading, wherein the generation of pore water pressure plays a key role in the cyclic deformation of sand; the accumulation of pore water pressure can lead to the reduction of the stiffness of saturated sand, and even liquefaction, thereby causing geological disasters and infrastructure damage; in order to accurately describe the nonlinearity and hysteresis of saturated sand and the pore pressure response, various advanced soil constitutive models are proposed in the prior art; among them, the hysteretic nonlinear constitutive model is a model widely used in one-dimensional nonlinear site response analysis, which controls the unloading and reloading process according to predetermined rules and captures the stiffness reduction characteristics through weak coupling with the pore water pressure model.

[0003] At present, most experimental researches mainly focus on the cyclic response of saturated sand under undrained cyclic loading causing initial liquefaction. In recent years, the deformation and lateral slip of saturated sand layer after large-scale liquefaction caused by strong earthquakes have caused serious damage to structures; therefore, in-depth understanding of the post-liquefaction characteristics of liquefied soil layer has also been increasingly concerned; at a large strain level (more than about 0.5%), the hysteretic curve shows an inverse S shape, resulting in a decrease in the damping ratio with the increase of shear strain; this is contrary to the trend of the increase of the damping ratio with the increase of shear strain at a small and medium strain level, so that the hysteretic nonlinear constitutive model is not suitable for use at a large strain level after liquefaction. In addition, the loading frequency also has a certain influence on the cyclic response of sand, but there are limitations at present, so there is an urgent need for a saturated sand dynamic constitutive model construction method considering pore pressure fluctuation growth to solve the above problems. SUMMARY

[0004] The purpose of the present application is to provide a saturated sand dynamic constitutive model construction method considering pore pressure fluctuation growth to solve the problems in the background art.

[0005] To solve the above technical problems, the application adopts the following technical scheme: a saturated sand dynamic constitutive model construction method considering pore pressure fluctuation growth, comprising the following steps: S1, based on the obtained strain state parameters of saturated sand, calculating the residual pore pressure component and the transient pore pressure component, and superimposing the residual pore pressure component and the transient pore pressure component to determine the total pore water pressure ; S2, constructing a normalized stress ratio skeleton curve independent of the pore pressure state based on the stress ratio ; ; S3, to the total pore water pressure corrected pore water pressure , to construct a monotonic pore pressure-shear strain curve within each shear cycle and with an upper bound constraint, and to utilize the corrected pore water pressure update the current average effective stress ; S4, coupling the normalized stress ratio skeleton curve and the updated average effective stress obtain the maximum shear stress value ; S5, taking the maximum shear stress value as the target state point, construct a dynamic virtual hysteresis curve starting from the current shear cycle reversal point as the current stress-strain path to describe the stress-strain behavior of saturated sand.

[0006] Preferably, based on the unified shear strain , the shear process is divided into a transient shear contraction phase and a transient shear dilation phase, and the transient pore pressure component is calculated in segments : When in the transient shear contraction phase: ; When in the transient shear dilation phase: ; wherein is a natural exponential function; and are the transient pore pressure and the unified shear strain corresponding to the current monotonic shear cycle starting point; and are the transient pore pressure and the unified shear strain corresponding to the reference shear dilation state point; and are physical parameters that control the shear contraction and shear dilation rates, respectively.

[0007] Preferably, for the shear strain in each monotonic shear process, a coordinate transformation is performed so that the deformation process of each monotonic shear cycle is uniformly mapped in a consistent direction: ; wherein is the sign of the shear strain increment; and the region of corresponds to the shear contraction phase with rising pore pressure, which is determined as the transient shear contraction phase, the region of corresponds to the shear dilation phase with falling pore pressure, which is determined as the transient shear dilation phase.

[0008] Preferably, the total pore water pressure is corrected to obtain the corrected pore water pressure , specifically: determining the current soil body is in transient shear contraction phase or transient shear dilation phase by the positive and negative signs of the unified shear strain ; when the soil body is in transient shear contraction phase, the pore water pressure value corresponding to the zero strain point in the current monotonic shear curve or the TPT is taken as the corrected pore water pressure ; when the soil body is in transient shear dilation phase, the total pore water pressure and the pore water pressure value are compared, and the smaller one is taken as the corrected pore water pressure .

[0009] Preferably, the average effective stress at the current time is updated by using the corrected pore water pressure , which is expressed as: ; wherein is the initial average effective stress.

[0010] Preferably, the maximum shear stress value is expressed as: , is the maximum shear strain in history.

[0011] Preferably, the virtual hysteretic curve is a set of virtual hyperbolic hysteretic curves, and the initial tangent modulus of the virtual hysteretic curve is obtained by attenuating the pore water pressure at the reversal point : ; wherein is the maximum shear modulus of the soil body, and is a material parameter.

[0012] Preferably, a dynamic shape parameter is introduced into the virtual hysteretic curve, so that the virtual hysteretic curve is directed towards the maximum strain point; the dynamic shape parameter is expressed as: ; wherein is the corrected shear stress at the reversal point of the loading direction, which is expressed as .

[0013] Preferably, based on the constructed virtual hysteretic curve, the shear stress value corresponding to the shear strain at the current time is obtained, which is expressed as: .

[0014] ​​Beneficial effects: can effectively consider the cumulative damage of soil in the process of cyclic loading and the alternating shear shrinkage-dilation effect, and capture the pore pressure development curve and cyclic shear stress-strain response more in line with the test law; the method can simulate the flow sliding and cyclic active liquefaction failure mode of saturated sand; and provides a valuable tool for evaluating the response and liquefaction strength of saturated sand under undrained cyclic loading conditions. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 For the curve calculation schematic diagram; Figure 2 The τ*-γ* curve calculation example of the large deformation stage after liquefaction calculated based on the modified ū-γ* relationship; Figure 3 For the comparison chart of the test results and the simulation results of the verification group of the present application; Figure 4 For the comparison chart of the calculated and measured N Cf of the model group and the verification group under the working conditions of the present application; Figure 5 For the CSR-N Cf curve chart under different and f. DETAILED DESCRIPTION

[0016] In order to make the purpose and advantages of the present application more clear and explicit, the present application will be specifically described below in combination with embodiments. It should be understood that the following text is only used to describe one kind of saturated sand dynamic constitutive model construction method considering the fluctuation growth of pore pressure or several specific embodiments of the present application, and does not strictly limit the specific protection scope requested by the present application.

[0017] Embodiment: a saturated sand dynamic constitutive model construction method considering the fluctuation growth of pore pressure, comprising: S1, based on the obtained strain state parameters of saturated sand, calculating to obtain the residual pore pressure component and the transient pore pressure component, superimposing the residual pore pressure component and the transient pore pressure component to determine the total pore water pressure ; Residual pore pressure component formula: ; ; Wherein, t is time, is shear strain, is shear shrinkage threshold shear strain; is the reference cumulative shear strain, C1 and C2 are curvature parameters; C1 and C2 are material parameters independent of sand density and loading conditions, and in this example, for Fujian sand, C1 = 0.17 and C2 = 3.24. For the transient pore pressure component based on the unified shear strain , the shear process is divided into transient shear shrinkage phase and transient shear expansion phase, and the transient pore pressure component is calculated by segment: When in the transient shear shrinkage phase: ; When in the transient shear expansion phase: ; wherein is a natural exponential function; and are the transient pore pressure and the unified shear strain corresponding to the current starting point of the monotonic shear; and are the transient pore pressure and the unified shear strain corresponding to the reference shear expansion state point; and are physical parameters for controlling the shear shrinkage and shear expansion rates, respectively; In this example, the shear strain in each monotonic shear process is subjected to coordinate transformation, so that the deformation process of each monotonic shear is uniformly mapped in the same direction: ; wherein is the sign of the shear strain increment; and the area of corresponds to the shear shrinkage phase with rising pore pressure, which is determined as the transient shear shrinkage phase, the area of

[0018] corresponds to the shear expansion phase with falling pore pressure, which is determined as the transient shear expansion phase. The total pore water pressure is:

[0019] The pore pressure fluctuation caused by the alternating shear shrinkage-expansion characteristics of sand is captured, which is closer to the observed phenomena in the test; S2, based on the stress ratio (the ratio of shear stress τ to average effective stress p' at any time), a normalized stress ratio skeleton curve independent of pore pressure state is constructed ; as a benchmark for describing the inherent nonlinear characteristics of soil; the normalized stress ratio skeleton curve is expressed as: ; wherein is the normalized small-strain shear modulus, is the reference shear strain when G' / G'0 = 0.5.

[0020] S3, the total pore water pressure is corrected to obtain the corrected pore water pressure to construct a pore pressure-shear strain curve that is monotonically changing within a single shear step and has an upper bound constraint, so as to eliminate abnormal fluctuations of effective stress in the large deformation shear shrinkage stage, specifically: the positive and negative signs of the unified shear strain are used to determine whether the current soil body is in a transient shear shrinkage phase or a transient shear expansion phase; when the soil body is in the transient shear shrinkage phase, the pore water pressure value corresponding to the zero strain point in the current monotonous shear step or the TPT is taken as the corrected pore water pressure ; when the soil body is in the transient shear expansion phase, the total pore water pressure and the pore water pressure value are compared, and the smaller one is taken as the corrected pore water pressure .

[0021] the average effective stress at the current time is updated using the corrected pore water pressure ; in this embodiment, it is represented as: ; wherein is the initial average effective stress.

[0022] S4, coupling the normalized stress ratio skeleton curve and the updated average effective stress to obtain the maximum shear stress value : , is the historical maximum shear strain; S5, taking the maximum shear stress value as the target state point, a virtual hysteretic curve starting from the current shear step reversal point is constructed as the current stress-strain path to describe the stress-strain behavior of saturated sand.

[0023] wherein, in this embodiment, the virtual hysteretic curve is a set of virtual hyperbolic hysteretic curves, and the initial tangent modulus of the virtual hysteretic curve is obtained by performing attenuation correction on the pore water pressure at the time of the reversal point : ; wherein is the maximum shear modulus of the soil body, ​​These are material parameters.

[0024] 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: ; in, To correct the shear stress at the point where the loading direction reverses, it is expressed as: .

[0025] Based on the constructed virtual hysteresis curve, the shear strain at the current moment is obtained. Corresponding shear stress value , represented as: .

[0026] 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.

[0027] refer to Figure 2 As shown, based on the corrected The test M-D-0.05 of the relationship calculation The curve examples, (a) the 3rd monotonic shear stage; (b) the 17th monotonic shear stage; from Figure 2 It can be seen from the above that the calculated relationship is in good agreement with the test results; such agreement greatly enhances the confidence in the proposed hysteretic nonlinear constitutive model in predicting the stress-strain response of the material from small strain to large strain level under undrained cyclic loading.

[0028] The application also provides a specific test for comprehensively analyzing the construction method of the saturated sand dynamic constitutive model considering the pore pressure fluctuation growth provided above, and the specific construction method is as follows: The reliability of the model is verified through six verification tests; the test samples cover three states of loose, medium dense and dense, and undrained cyclic shear under stress control is carried out at frequencies of 0.1 Hz and 1 Hz; the stress applied in the actual test is used as the input for calculation, the sand dynamic constitutive model constructed by the method of the application is used to calculate the shear strain and pore pressure response in the whole cyclic loading process; a total of 11 parameters are included, and the model parameter values used for calculation under each simulation condition are listed in Table 1: Table 1 Model parameter values of the verification group test

[0029] Referring to Figure 3 Fig. 2, which is a comparison diagram of the test results and the simulation results of the verification group test, (a) test V-L-0.1; (b) test V-L-1; (c) test V-M-0.1; (d) test V-M-1; (e) test V-D-0.1; (f) test V-D-1, which shows the strain and pore pressure time history, stress-strain hysteresis curve and effective stress path in the test results and the calculation results; there is good consistency between the test and the calculation shear response, which shows that the proposed model can effectively capture the influence of the relative density and the loading frequency on the undrained cyclic response; in addition, the model accurately simulates two typical liquefaction failure modes, i.e., flow sliding (applicable to loose sand or high-frequency loading test) and cyclic flowability (applicable to dense sand or low-frequency loading test).

[0030] Referring to Figure 4 Fig. 3, the number of cycles N Cf required to cause liquefaction failure in the simulation results is verified, that is, the number of times when the pore pressure first reaches and causes initial liquefaction; the conditions in the model group and the verification group are calculated, and the N Cf is compared and evaluated; as shown in Figure 4 Fig. 4, the calculated N Cf is in good agreement with the N CfThe 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.

[0031] 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.

[0032] The embodiments of the present application are described in detail above with reference to the embodiments, but the present application is not limited to the above-described embodiments, and for those skilled in the art, after learning the contents described in the present application, some equivalent transformations and substitutions can be made without departing from the principles of the present application, and these equivalent transformations and substitutions should also be considered as belonging to the protection scope of the present application.

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 Construct a normalized stress ratio skeleton curve independent of pore pressure state. ; 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.

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: 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.

3. 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: 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.

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: 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, the total pore water pressure is compared to... and pore pressure value The smaller of the two values ​​was used as the corrected pore water pressure. .

5. 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: Using modified pore water pressure Update the mean effective stress at the current moment. , is represented as: ； in, This represents the initial average effective stress.

6. The method for constructing a dynamic constitutive model of saturated sand considering the growth of pore pressure fluctuations according to claim 5, characterized in that: The maximum shear stress value Represented as: , This represents the largest shear strain in history.

7. The method for constructing a dynamic constitutive model of saturated sand considering the growth of pore pressure fluctuations according to claim 6, 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.

8. The method for constructing a dynamic constitutive model of saturated sand soil considering the growth of pore pressure fluctuations according to claim 7, 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: .

9. A method for constructing a dynamic constitutive model of saturated sand soil considering the growth of pore pressure fluctuations according to claim 8, 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: .

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