Saturated granular material liquefaction deformation calculation method based on state evolution model

Abstract

The invention relates to a saturated granular material liquefaction deformation calculation method based on a state evolution model, which comprises the following steps: establishing a saturated granular material liquefaction state evolution model, and setting a state parameter representing system fluidity in the state evolution model as a weighted average value of a historical strain rate function and an excess pore water pressure change rate function; analyzing and determining a shear strain time travel curve, a stress strain curve and a state parameter evolution curve according to the state evolution model; and carrying out saturation granular material liquefaction discrimination according to the state parameters. According to the saturated granular material liquefaction deformation calculation method based on the state evolution model, the Davidenkov model and the unified softening model are introduced to describe shear modulus softening, the liquefaction deformation calculation method is provided, and finally the accuracy of the calculation method is verified through a series of experimental data and simulation data.

Description

Technical Field

[0001] The present invention relates to the field of liquefaction model calculation of saturated granular materials, and more particularly to a method for calculating the liquefaction deformation of saturated granular materials based on a state evolution model. Background Art

[0002] Granular materials such as sand and soil can liquefy under dynamic loads, and large deformations during liquefaction are the primary cause of structural instability and failure. Analysis of the liquefaction resistance of saturated granular material systems has been limited to isotropic consolidation conditions, i.e., under symmetrical cyclic loading. Given that granular material systems in practical engineering problems are often subject to complex stress states, initial shear stress can lead to significant variations in liquefaction resistance. Furthermore, a more precise description of the deformation behavior of granular materials is lacking. Summary of the Invention

[0003] To address the above-mentioned shortcomings, the present invention provides a method for calculating the liquefaction deformation of saturated granular materials based on a state evolution model, comprising: establishing a state evolution model for the liquefaction of saturated granular materials, wherein the state parameters characterizing the fluidity of the system in the state evolution model are set to the weighted average of the historical strain rate function and the excess pore water pressure change rate function; according to the state evolution model, analyzing and determining the shear strain time history curve, the stress strain curve and the state parameter evolution curve; and using the state parameters to judge the liquefaction of the saturated granular material.

[0004] Optionally, the historical strain rate function and the excess pore water pressure change rate function have independent effects on the state parameters, and the weighted average value decays exponentially.

[0005] Optionally, the state evolution model includes a pore pressure evolution model.

[0006] Optionally, the state evolution model includes a unified softening model to characterize the softening upper limit of the system shear modulus in each cycle.

[0007] Optionally, the state evolution model includes a Davidenkov model, which is used to characterize the nonlinear softening and recovery characteristics of the system shear modulus with strain.

[0008] Optionally, the shear strain and state parameter calculation formulas satisfy the following formula:

[0009]

[0010] where σ is the deviatoric stress, is the rate of change of deviatoric stress, is the shear strain change rate, is the rate of change of excess pore water pressure, θ and is the state parameter of system liquidity and its rate of change;

[0011] G(t) is the time-dependent shear modulus, which satisfies the following formula:

[0012]

[0013] Among them, G max is the maximum shear modulus of the system, g a 、g c is a parameter;

[0014] According to the Davidenkov model, the following formula is satisfied:

[0015]

[0016] Among them, G max is the maximum shear modulus of the system, γ rev is the shear strain at the loading and unloading reversal point, and A, B and γ0 are the fitting parameters.

[0017] Optionally, according to the finite difference method, the shear strain and state parameter calculation formula further satisfies the following formula:

[0018]

[0019] Alternatively, A=1.294, B=0.794, γ0=0.00074, g a =0.455, g c =0.372, r uc =0.95,γ c =0.25, a1=35.5, b1=7.5.

[0020] The embodiment of the present invention proposes a method for calculating the liquefaction deformation of saturated granular materials based on a state evolution model, introduces the Davidenkov model and the unified softening model to describe the shear modulus softening, proposes a method for calculating the liquefaction deformation, and finally verifies the accuracy of the proposed calculation method through a series of experimental data and simulation data. Specifically, it includes establishing a state evolution model to describe the liquefaction deformation of saturated granular materials, and analyzing and obtaining the stress-strain curve, displacement time-history curve and flow state parameter curve of the saturated granular material sample, and using the flow state parameters to judge the liquefaction of the saturated granular material. The present invention fully considers the joint influence of the historical state of the granular material system and the pore water pressure on the liquefaction deformation, and provides a physical explanation for the intrinsic mechanism of the liquefaction triggering of saturated granular materials. Through data comparison, it is proved that this method can effectively describe the liquefaction deformation of saturated granular materials under arbitrary stress conditions, thereby providing a new method for the study of saturated granular materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The following drawings illustrate exemplary embodiments of the present invention by way of example, and the same or similar reference numerals are used in the drawings to represent the same or similar elements. In the drawings:

[0022] Figure 1 A flow chart of a method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to an exemplary embodiment of the present invention is shown.

[0023] Figure 2 A schematic diagram of a normalized time history curve of deviatoric stress according to an exemplary embodiment of the present invention is shown.

[0024] Figure 3 A schematic diagram of an excess pore water pressure ratio evolution curve according to an exemplary embodiment of the present invention is shown.

[0025] Figure 4 A graph of normalized shear modulus versus shear strain is shown for an exemplary embodiment of the present invention.

[0026] Figure 5 A graph of normalized shear modulus versus normalized time is shown for an exemplary embodiment of the present invention.

[0027] Figure 6 A schematic diagram of a shear strain time history curve of an exemplary embodiment of the present invention is shown.

[0028] Figure 7 A schematic diagram of a stress-strain curve of an exemplary embodiment of the present invention is shown.

[0029] Figure 8 FIG. 4 is a schematic diagram showing a state parameter evolution curve of an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0030] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation methods in conjunction with the accompanying drawings.

[0031] In the present invention, the term "and / or" is intended to cover all possible combinations and subcombinations of the listed elements, including any one, any subcombination, or all of the elements listed individually, without necessarily excluding other elements. Unless otherwise specified, the terms "first," "second," and the like are used to describe various elements without intending to limit the positional relationship, temporal relationship, or importance relationship of these elements. Such terms are only used to distinguish one element from another. Unless otherwise specified, the directions or positional relationships indicated by the terms "front, back, up, down, left, right," and the like are generally based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience and simplification of description, and should not be understood as limiting the scope of protection of the present invention.

[0032] Figure 1A flow chart of a method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to an exemplary embodiment of the present invention is shown.

[0033] S102: Establishing a state evolution model for liquefaction of saturated granular materials, wherein a state parameter characterizing system fluidity in the state evolution model is set to a weighted average of a historical strain rate function and an excess pore water pressure change rate function.

[0034] For saturated granular materials, it is easy to understand that the state parameters that characterize the fluidity of the system are affected by historical strain and pore water pressure. Therefore, a state evolution model of the saturated granular material system is established, which satisfies the following formula:

[0035]

[0036] Where σ is the deviatoric stress, and are the rate of change of deviatoric stress, shear strain and excess pore water pressure, θ and It is the state parameter that characterizes the fluidity of the system and its rate of change, and G(t) is the time-dependent shear modulus.

[0037] The state parameter is defined as the weighted average of the historical strain rate function and the excess pore water pressure change rate function. The influence of the two on the state parameter is assumed to be independent of each other to further simplify the state evolution model:

[0038]

[0039] Assuming that the weighting function decays exponentially, we get:

[0040]

[0041] Among them, γ c and r uc are the characteristic strain and characteristic pore pressure ratio, respectively.

[0042] The rate of change of state parameters can be further expressed as:

[0043]

[0044] For unknown functions Performing Taylor expansion, we get:

[0045]

[0046] when When it is 0, the saturated granular material system should be in the initial state, that is, Therefore, a0=0, ignoring the higher-order terms and combining with formula (1), we can obtain:

[0047]

[0048] Furthermore, the pore pressure evolution model is introduced:

[0049]

[0050] Where t0 is the time when the system reaches initial liquefaction, u a ,u b and u c are the fitting coefficients.

[0051] Furthermore, a unified softening model is introduced to describe the softening upper limit of the system shear modulus in each cycle:

[0052]

[0053] Among them, G max is the maximum shear modulus of the system, C1 and C2 are constants determined by the initial conditions, and a is the Taylor expansion constant. When t = 0, the system shear modulus is not softened by cyclic load, so G(t) / G0 = 1, that is, C2 / G0-ln(C1G0) / a = 1, and 1 / a = g a , C1G0=g c , then the unified softening model can be simplified as:

[0054]

[0055] The Davidenkov model is introduced to characterize the nonlinear softening and recovery characteristics of the system shear modulus with strain.

[0056]

[0057] G max is the maximum shear modulus of the system, γ rev is the shear strain at the loading and unloading reversal point, A, B and γ0 are fitting parameters, which can be obtained from G / G max -γ curve is obtained. When the shear strain is not reversed during initial loading, the shear modulus is corrected using formula (9); after the shear strain is reversed for the first time, the shear modulus is corrected using formula (10) during subsequent loading and unloading.

[0058] Using the finite difference method to solve equation (6), the calculation formulas for shear strain and state parameters can be further expressed as:

[0059]

[0060] S104: Analyze and determine the shear strain time history curve, the stress strain curve, and the state parameter evolution curve according to the state evolution model.

[0061] S106: Using the state parameters to determine whether the saturated granular material is liquefied.

[0062] Combine Figures 1-8 As shown, in order to make the purpose, technical solutions and advantages of this application more clear, the embodiments of the present invention are further described in detail.

[0063] Spherical glass beads were selected as the test material and prepared into a standard triaxial specimen with a diameter of 50 mm and a height of 100 mm. The specific operation steps are as follows:

[0064] The sample was prepared by the wet ramming method. A certain mass of glass beads was weighed and prepared into a wet sample with a moisture content of 5% for later use. The sample was evenly divided into 5 layers, poured into the mold layer by layer, and compacted to the corresponding height. The prepared sample was placed in the pressure chamber of the triaxial apparatus and a confining pressure of 20 kPa was applied. The valve was opened, CO2 and airless water were introduced, and the sample was saturated with back pressure. When the B value reached 0.98 or above, the sample was considered to be fully saturated. A confining pressure was applied to the sample to reach the target average effective confining pressure of 100 kPa and consolidated.

[0065] After the isotropic consolidation is completed, the specimen is first subjected to 10 -6 Strain, calculate the small strain shear stiffness through the stress-strain curve as the maximum shear modulus G of the specimen max .

[0066] The saturated specimens were subjected to cyclic dynamic loading with a cyclic stress ratio (CSR) of 0.25 and a loading frequency of 0.05 Hz. The dynamic response curves of the saturated specimens under cyclic loading were obtained. The time required for the specimen to reach initial liquefaction was recorded as t0, and the stress, strain, and excess pore water pressure ratio time history curves were normalized.

[0067] The maximum shear modulus and loading conditions, including initial deviatoric stress, cyclic stress ratio, and average effective confining pressure, were input into the calculation program.

[0068] like Figure 2 As shown in FIG, according to the loading conditions, the deviatoric stress loading path is set in the calculation program, and the experimental deviatoric stress loading path is compared with the input deviatoric stress loading path. When the deviatoric stress loading paths match, the input deviatoric stress loading path is used as the calculated deviatoric stress path.

[0069] like Figure 3 As shown in the figure, based on the normalized time history curve of excess pore water pressure ratio fitted by formula (7), the fitting parameter value is determined, that is, u a =0.751,u b =1.632,u c =0.302,.

[0070] like Figure 4As shown, based on the formula (10) in the Davidenkov model, the nonlinear softening of the shear modulus is fitted, and the fitting parameter values are obtained, namely A = 1.294, B = 0.794, and γ0 = 0.00074.

[0071] like Figure 5 As shown in the figure, based on the unified softening model, the upper limit of the shear modulus recovery is fitted to obtain the fitting parameter value, i.e. g a =0.455, g c =0.372.

[0072] Enter other parameters, r uc =0.95,γ c =0.25, a1=35.5, b1=7.5, set the calculation step size to 0.001 in the calculation program, and stop running after 1000 steps.

[0073] Finally, combine Figure 6-8 As shown in Figure 3, the shear strain time history curve, stress-strain relationship and state parameter evolution of this calculation method are obtained. Comparison shows that this calculation method has higher accuracy.

[0074] The embodiments of the present invention link the internal state of the system with the pore water pressure, while also considering the nonlinear softening and recovery of the shear modulus, enabling a more accurate description of the liquefaction deformation behavior of a saturated granular material system. Specifically, the embodiments of the present invention are based on a calculation method for a state evolution model, taking into account the nonlinear evolution of the shear modulus. The Davidenkov model and the unified softening model are introduced to characterize the nonlinear softening of the shear modulus and its upper limit of recovery. A state evolution model for saturated granular materials is established, and iterative calculations are performed using MATLAB. This method is simple and highly accurate. Based on this, different pore pressure models can be replaced based on previous research to describe the liquefaction deformation of different granular material types, greatly reducing the experimental difficulty and significantly promoting the study of the liquefaction of saturated granular materials.

[0075] It will be understood that the present invention is described by way of some embodiments, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be protected by the present invention.

Claims

1. A method for calculating the liquefaction deformation of saturated granular materials based on a state evolution model, characterized in that: include: Establishing a state evolution model for liquefaction of saturated granular materials, wherein a state parameter representing the fluidity of the system in the state evolution model is set to a weighted average of a historical strain rate function and an excess pore water pressure change rate function; Analyzing and determining a shear strain time history curve, a stress-strain curve, and a state parameter evolution curve according to the state evolution model; The liquefaction of the saturated granular material is determined based on the state parameters.

2. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 1, characterized in that: The influences of the historical strain rate function and the excess pore water pressure change rate function on the state parameters are independent of each other, and the weighted average value decays exponentially.

3. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 2, wherein: The state evolution model includes a pore pressure evolution model.

4. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 3, wherein: The state evolution model includes a unified softening model, which is used to characterize the upper limit of the recovery of the system shear modulus after softening in each cycle.

5. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 4, characterized in that: The state evolution model includes a Davidenkov model, which is used to characterize the nonlinear softening characteristics of the system shear modulus with strain.

6. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 5, characterized in that: The calculation formula of shear strain and state parameters satisfies the following formula: where σ is the deviatoric stress, is the rate of change of deviatoric stress, is the shear strain change rate, is the rate of change of excess pore water pressure, θ and is the state parameter of system liquidity and its rate of change; G(t) is the time-dependent shear modulus, which satisfies the following formula: Among them, G max is the maximum shear modulus of the system, g a 、g c is a parameter; According to the Davidenkov model, the following formula is satisfied: Among them, G max is the maximum shear modulus of the system, γ rev is the shear strain at the loading and unloading reversal point, and A, B and γ0 are the fitting parameters.

7. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 6, characterized in that: According to the finite difference method, the shear strain and state parameter calculation formula further satisfies the following formula:

8. The method for calculating liquefaction deformation of saturated granular materials based on a state evolution model according to claim 6, wherein: A=1.294,B=0.794,γ0=0.00074,g a =0.455,g c =0.372,r uc =0.95,c c =0.25,a1=35.5,b1=7.5。

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