A method for constructing a modified Davidenkov constitutive model

Abstract

The present invention discloses a method for constructing a modified Davidenkov constitutive model, comprising the following steps: S1: introducing the concept of "damping ratio degradation coefficient" into the Davidenkov constitutive model represented by a piecewise function; S2: deriving the dynamic stress-strain skeleton curve and hysteresis curve formula of the modified Davidenkov constitutive model; S3: deriving the damping ratio degradation coefficient, damping ratio and dynamic shear modulus formula of the modified Davidenkov constitutive model based on the modified Davidenkov stress-strain hysteresis curve. The present invention introduces the concept of "damping ratio degradation coefficient" on the basis of representing the Davidenkov constitutive model by a piecewise function, which not only inherits the advantages of the Davidenkov constitutive model represented by a piecewise function: the shear stress of the stress-strain skeleton curve no longer increases infinitely with the shear strain, but also improves the phenomenon that the damping ratio calculated by the Davidenkov stress-strain hysteresis curve is greater than the actual damping ratio of the soil, more realistically reflects the energy consumption of the soil, and provides a reasonable and feasible constitutive model for subsequent research.

Description

Technical Field

[0001] The invention relates to the field of geotechnical engineering, and in particular to a method for constructing a modified Davidenkov constitutive model. Background Art

[0002] Soil is a three-phase inhomogeneous medium composed of soil particles, water and air, with complex microstructure and mechanical properties. At present, scholars will establish the dynamic constitutive model of soil by selectively abandoning some minor factors and focusing on the main factors according to site conditions and engineering requirements. Among the hundreds of soil constitutive models that have been proposed, there is almost no model that can perfectly consider all the properties of soil and be applied to all types of soil. At this stage, soil constitutive models can be roughly divided into elastic models, viscoelastic models and elastoplastic models.

[0003] The viscoelastic model consists of a skeleton curve and a hysteresis curve, which reflects the entire process of the stress-strain relationship of the soil. The model is obtained by summarizing the experimental results. It has the advantages of simple and intuitive form and easy determination of parameters. It has been widely used in current practical engineering. Among them, the Davidenkov constitutive model is the mainstream for analyzing the nonlinear characteristics of soft soil. Hardin found that the dynamic shear modulus of soil under constant amplitude cyclic load is G / G max The relationship between the shear strain γ and the dynamic shear modulus ratio G / G is basically in accordance with the hyperbolic relationship. max and shear strain γ. Martin et al. then proposed a better fit for G / G max -γ curve Davidenkov constitutive model. Liu Qijian, Chen Guoxing, Rong Mianshui, Chen Bin and Ding Zude used Davidenkov constitutive model to study the dynamic characteristics of Shanghai soft soil, Nanjing soft soil, sea soft soil, Ningbo deep soft soil and Kunming peat soil. The results showed that Davidenkov constitutive model can better simulate the dynamic shear modulus ratio G / G of soft soil site. max And the relationship between the damping ratio D and the shear strain γ.

[0004] Although the Davidenkov constitutive model has been widely used in the field of geotechnical engineering, it still has certain shortcomings. In this regard, Chen Guoxing et al. solved the problem that the shear stress of the Davidenkov stress-strain skeleton curve will continue to increase with the increase of shear strain by using a piecewise function representation method without considering the softening characteristics of the soil.

[0005] So far, although some scholars have improved the Davidenkov constitutive model, none of them have taken into account the damping ratio D of the soil, which makes the calculated damping ratio greater than the damping ratio measured in the experiment, and the energy dissipation of the soil is also greater than the actual energy dissipation. When studying the nonlinearity of soil, the dynamic shear modulus G max and the damping ratio D are both basic parameters that reflect the dynamic characteristics of soil. Therefore, if the Davidenkov constitutive model is to truly reflect the dynamic characteristics of soil, it is necessary to consider not only the dynamic shear modulus G max In addition to the influence of the damping ratio D, the influence of the damping ratio D should also be considered. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention provides a method for constructing a modified Davidenkov constitutive model. The present invention introduces the "damping ratio degradation coefficient" into the Davidenkov constitutive model represented by a piecewise function, so that the shear stress change and energy consumption of the soil are closer to the soil condition under earthquake action, and the seismic dynamic characteristics of the soil are more realistically reflected.

[0007] In order to solve the problems existing in the prior art, the technical solution adopted by the present invention is as follows:

[0008] A method for constructing a modified Davidenkov constitutive model, wherein the Davidenkov constitutive model is represented by a piecewise function, and the dynamic shear modulus of the Davidenkov constitutive model is G / G max The expression is as follows:

[0009] G / G max =1-H(γ) (1)

[0010]

[0011] Where G is the shear modulus; G max is the initial maximum shear modulus; γ is the shear strain; A, B and γ 0 is the fitting parameter related to soil properties;

[0012] The dynamic stress-strain skeleton curve of the Davidenkov constitutive model represented by a piecewise function is expressed as:

[0013]

[0014] Where τ(γ) is the shear stress; τ c is the shear stress corresponding to the turning point of the stress-strain hysteresis curve; τ ult To destroy shear stress;

[0015] The following steps are involved:

[0016] S1: The concept of “damping ratio degradation coefficient” is introduced into the Davidenkov constitutive model represented by piecewise function;

[0017] S2: Derive the dynamic stress-strain skeleton curve and hysteresis curve formula of the modified Davidenkov constitutive model;

[0018] S3: Based on the stress-strain hysteresis curve of the modified Davidenkov constitutive model, the damping ratio degradation coefficient, damping ratio and dynamic shear modulus formula of the modified Davidenkov constitutive model are derived.

[0019] Furthermore, the “damping ratio degradation coefficient” in step S1 refers to the ratio of the test damping ratio to the damping ratio calculated from the hysteresis curve: K(γ)=D T / D M (4)

[0020] Where K(γ) is the damping ratio degradation coefficient; D T is the damping ratio obtained through the experiment; D M is the damping ratio obtained from the hysteresis curve.

[0021] Furthermore, the dynamic stress-strain skeleton curve of the modified Davidenkov constitutive model in step S2 is

[0022] The line is represented as:

[0023]

[0024] In the formula, γ'=|±γ m -γ c | / 2,γ m is the maximum shear strain that can be reached in the stress-strain hysteresis curve.

[0025] Furthermore, the dynamic stress-strain hysteresis curve of the modified Davidenkov constitutive model in step S2 is expressed as:

[0026]

[0027] In the formula, τ m is the maximum shear stress that can be reached by the stress-strain hysteresis curve; τ c is the shear stress corresponding to the turning point of the stress-strain hysteresis curve under loading and unloading.

[0028] Furthermore, the damping ratio degradation coefficient of the modified Davidenkov constitutive model in step S3 is expressed as:

[0029]

[0030] Where D Dis the calculated damping ratio of the Davidenkov constitutive model represented by a piecewise function.

[0031] Furthermore, the damping ratio of the modified Davidenkov constitutive model described in step S3 is expressed as:

[0032]

[0033] Where D MD is the damping ratio of the modified Davidenkov constitutive model; S LOOP is the area of ​​a hysteresis loop; S E Represents the area of ​​a triangle.

[0034] Furthermore, the derivation of the dynamic shear modulus formula in step S3 includes the following steps:

[0035] (1): Taking the derivative of the shear strain γ in equation (5), we can obtain the calculation formula of the dynamic shear modulus in the initial loading section (|τ|≤τ ult ):

[0036]

[0037] (2): For (γ-γ in (6) c ) is derived to obtain the calculation formula of the dynamic shear modulus of the hysteresis curve:

[0038] When |τ|≤τ ult hour,

[0039]

[0040] When |τ|>τ ult When G t+Δt =0;

[0041] For the stability of numerical calculation, a minimum dynamic shear modulus G is given. min , when G <G min When G = G min =0.05G max .

[0042] The advantages and beneficial effects of the present invention are:

[0043] The invention discloses a method for constructing a modified Davidenkov constitutive model, which introduces a "damping ratio degradation coefficient" into the Davidenkov constitutive model represented by a piecewise function, so that the shear stress change and energy consumption of the soil are closer to the soil condition under earthquake action, and the seismic dynamic characteristics of the soil are more realistically reflected, thereby solving the problem that the damping ratio calculated by the Davidenkov constitutive model is greater than the actual damping ratio and the calculated soil energy consumption is too large.

[0044] The present invention introduces the concept of "damping ratio degradation coefficient" in the Davidenkov constitutive model represented by a piecewise function with the failure shear strain as the demarcation point, and derives the dynamic stress-strain skeleton curve, hysteresis curve, damping ratio degradation coefficient, damping ratio and dynamic shear modulus formula of the modified Davidenkov constitutive model. Compared with the uncorrected Davidenkov constitutive model, the modified Davidenkov constitutive model of the present invention corrects the dynamic stress-strain hysteresis curve of the Davidenkov constitutive model, so that the calculated damping ratio is reduced, the overall energy consumption of the soil is reduced, and it is more consistent with the actual situation. By comparing the numerical simulation with the test results, it is proved that the difference between the acceleration magnification coefficient of the soil using the modified Davidenkov constitutive model and the test acceleration magnification coefficient is less than 5%, which is closer to the test result than the simulation result of the soil using the Davidenkov constitutive model.

[0045] The seismic dynamic characteristics of the soft site using the modified Davidenkov constitutive model of the present invention are consistent with the changing law of the seismic dynamic characteristics of the soft site in the actual project. Taking the typical soft soil as the research object, the dynamic characteristics of different soil samples under the action of different intensities of earthquake motion are analyzed, and compared with the test results and the calculation results of the unmodified Davidenkov constitutive model, the rationality and feasibility of the modified Davidenkov constitutive model of the present invention are verified. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be further described below in conjunction with the accompanying drawings:

[0047] Figure 1 The stress-strain skeleton curve and hysteresis curve of Davidenkov constitutive model expressed by piecewise function;

[0048] Figure 2 This is a comparison diagram of the hysteresis curves before and after the introduction of the damping ratio degradation coefficient;

[0049] Figure 3 This is a schematic diagram of bidirectional equal-amplitude cosine loading;

[0050] Figure 4 This is a schematic diagram of bidirectional damped cosine loading;

[0051] Figure 5 This is a schematic diagram of bidirectional amplified cosine loading;

[0052] Figure 6 It is the acceleration time history curve of EL-Centro wave;

[0053] Figure 7 It is the acceleration time history curve of Kobe wave;

[0054] Figure 8 It is the acceleration response spectrum curve of EL-Centro wave and Kobe wave;

[0055] Fig. 9 The hysteresis curves of Davidenkov constitutive model and modified Davidenkov constitutive model under bidirectional equal-amplitude cosine loading;

[0056] Fig.10 The hysteresis curves of Davidenkov constitutive model and modified Davidenkov constitutive model under bidirectional damped cosine loading;

[0057] Fig.11 The hysteresis curves of Davidenkov constitutive model and modified Davidenkov constitutive model under bidirectional amplified cosine loading;

[0058] Fig.12 The hysteresis curves of Davidenkov constitutive model and modified Davidenkov constitutive model under EL-Centro wave loading;

[0059] Fig.13 G / G of soil sample 1 fitted by test, Davidenkov constitutive model and modified Davidenkov constitutive model max—γ Graphs;

[0060] Fig.14 D is the D of soil sample 1 fitted according to the test, Davidenkov constitutive model and modified Davidenkov constitutive model —γ Graphs;

[0061] Fig.15 G / G of soil sample 2 fitted by test, Davidenkov constitutive model and modified Davidenkov constitutive model max—γ Graphs;

[0062] Fig.16 D is the D of soil sample 2 fitted according to the test, Davidenkov constitutive model and modified Davidenkov constitutive model —γ Graphs;

[0063] Fig.17 It is the acceleration amplification factor diagram of soil when the input acceleration peak is 0.1g seismic wave;

[0064] Fig.18 This is the acceleration amplification factor diagram of the soil when the input acceleration peak is 0.2g seismic wave;

[0065] Fig.19 This is the acceleration amplification factor diagram of the soil when the input acceleration peak is 0.4g seismic wave;

[0066] Fig. 20 It is the acceleration time history curve of the soil surface of soil sample 1 when the EL-Centro wave with the peak acceleration of 0.2g is input;

[0067] Fig.21 It is the acceleration time history curve of the soil surface of soil sample 1 when the EL-Centro wave with the peak acceleration of 0.2g is input;

[0068] Fig. 22 It is the acceleration time history curve of the soil surface of soil sample 2 when the EL-Centro wave with the peak acceleration of 0.2g is input;

[0069] Fig.23 This is the acceleration time history curve of the soil surface of soil sample 2 when the EL-Centro wave with an acceleration peak of 0.2g is input. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below in conjunction with specific embodiments, but the protection scope of the present invention is not limited by the specific embodiments, but is subject to the claims. In addition, under the premise of not violating the technical solution of the present invention, any modification or change made to the present invention that is easily realized by a person of ordinary skill in the art will fall within the scope of the claims of the present invention.

[0071] A method for constructing a modified Davidenkov constitutive model comprises the following steps:

[0072] Among them, the Davidenkov constitutive model was proposed by Martin et al. to better fit the dynamic shear modulus ratio G / G of various soils. max—γ The curve proposed.

[0073] Dynamic shear modulus ratio G / G max The expression is as follows:

[0074] G / G max =1-H(γ) (1)

[0075]

[0076] Where G is the shear modulus; G max is the initial maximum shear modulus; γ is the shear strain; A, B and γ 0 are fitting parameters related to soil properties.

[0077] It can be seen from formulas (1) and (2) that the Davidenkov constitutive model only considers the influence of the dynamic shear modulus, and does not consider the influence of the soil damping ratio D. As a result, the damping ratio calculated according to the Davidenkov constitutive model is greater than the actual damping ratio of the soil, and the energy dissipation of the soil is inconsistent with the actual situation.

[0078] like Figure 1 As shown in Figure 1, the skeleton curve of the Davidenkov constitutive model is represented by a piecewise function with the upper limit shear strain as the dividing point.

[0079] The expression is as follows:

[0080]

[0081] Where τ(γ) is the shear stress; τ c is the shear stress corresponding to the turning point of the stress-strain hysteresis curve; τ ult To break shear stress.

[0082] like Figure 2 As shown in the figure, the “damping ratio degradation coefficient” refers to the difference between the test damping ratio and the damping ratio calculated from the hysteresis curve.

[0083] Ratio: K(γ)=D T / D M (4)

[0084] Where K(γ) is the damping ratio degradation coefficient; D T is the damping ratio obtained through the experiment; D M is the damping ratio obtained from the hysteresis curve.

[0085] S1: Considering that the soil energy dissipation calculated by the hysteresis loop area is greater than the actual energy dissipation of the soil, that is, the calculated damping ratio is greater than the actual damping ratio, the present invention introduces the concept of "damping ratio degradation coefficient" in the Davidenkov constitutive model expressed by a piecewise function.

[0086] S2: The dynamic stress-strain skeleton curve of the modified Davidenkov constitutive model is derived as follows:

[0087]

[0088] In the formula, γ'=|±γ m -γ c | / 2,γ m is the maximum shear strain that can be reached in the stress-strain hysteresis curve.

[0089] The dynamic stress-strain hysteresis curve of the modified Davidenkov constitutive model is derived as follows:

[0090]

[0091] In the formula, τ m is the maximum shear stress that can be reached by the stress-strain hysteresis curve; τ c is the shear stress corresponding to the turning point of the stress-strain hysteresis curve under loading and unloading.

[0092] S3: Based on the stress-strain skeleton curve and hysteresis curve formula of the modified Davidenkov constitutive model, the damping ratio degradation coefficient of the modified Davidenkov constitutive model is derived:

[0093]

[0094] Where D D is the calculated damping ratio of the Davidenkov constitutive model represented by a piecewise function;

[0095] The damping ratio of the modified Davidenkov constitutive model is expressed as:

[0096]

[0097] Where D MD is the damping ratio of the modified Davidenkov constitutive model; S LOOP is the area of ​​a hysteresis loop. E Represents the area of ​​a triangle.

[0098] It not only inherits the advantages of the Davidenkov constitutive model represented by a piecewise function: the shear stress of the stress-strain skeleton curve no longer increases infinitely with the shear strain, but also improves the phenomenon that the damping ratio calculated by the Davidenkov stress-strain hysteresis curve is greater than the actual damping ratio of the soil, and more realistically reflects the energy consumption of the soil.

[0099] Dynamic shear modulus formula:

[0100] (1): Taking the derivative of the shear strain γ in equation (5), we can obtain the calculation formula of the dynamic shear modulus in the initial loading section (|τ|≤τ ult ):

[0101]

[0102] (2): For (γ-γ in (6) c ) is derived to obtain the calculation formula of the dynamic shear modulus of the hysteresis curve:

[0103] When |τ|≤τ ult hour,

[0104]

[0105] When |τ|>τ ult When G t+Δt =0;

[0106] For the stability of numerical calculation, a minimum dynamic shear modulus G is given. min , when G <G min hour,

[0107] G=G min =0.05G max .

[0108] This lays the foundation for the implementation of the modified Davidenkov constitutive model in ABAQUS software.

[0109] The present invention introduces the concept of "damping ratio degradation coefficient" on the basis of using the upper limit shear strain as the demarcation point and using piecewise functions to represent the Davidenkov constitutive model, and derives the stress-strain skeleton curve, hysteresis curve, damping ratio degradation coefficient, damping ratio and dynamic shear modulus formulas of the modified Davidenkov constitutive model. It not only inherits the advantages of the Davidenkov constitutive model represented by piecewise functions: the shear stress of the stress-strain skeleton curve no longer increases infinitely with the shear strain, but also improves the phenomenon that the damping ratio calculated by the Davidenkov stress-strain hysteresis curve is greater than the actual damping ratio of the soil, more realistically reflects the energy consumption of the soil, and provides a reasonable and feasible constitutive model for subsequent research on the dynamic characteristics of the soil and soil-structure interaction.

[0110] Embodiment 1:

[0111] (1) Composition:

[0112] Taking two soft soil samples as the research objects, the hysteresis curves, dynamic shear modulus ratio curves, damping ratio curves, acceleration amplification factors and surface acceleration of the soils using the Davidenkov constitutive model and the modified Davidenkov constitutive model were compared and analyzed. The rationality and feasibility of the modified Davidenkov constitutive model in this paper were verified by comparing the finite element simulation results with the test results. The parameters of the soft soil samples are shown in Table 1. Figure 3 , 4 , 5, the application of ground motion is shown in Table 2, and the acceleration time history curves of EL-Centro wave and Kobe wave are shown in Figure 6 , 7 As shown in Figure 2, the acceleration response spectrum curve is as follows: Figure 8 shown.

[0113] Table 1 Soil sample parameters

[0114]

[0115] Table 2 Conditions of applied seismic waves

[0116]

[0117]

[0118]

[0119] (2) Effects:

[0120] The hysteresis curves of soil sample 2 under different loading and unloading paths when the Davidenkov constitutive model and the modified Davidenkov constitutive model are applied are shown in Figure 2. Fig. 9 , 10 , 11, and 12. The maximum damping ratio calculated by the hysteresis curve of the Davidenkov constitutive model and the maximum damping ratio calculated by the modified Davidenkov constitutive model are shown in Table 3.

[0121] Table 3 Maximum damping ratio of soil sample 2 calculated using different constitutive models

[0122]

[0123] Note: D D is the maximum damping ratio calculated from the hysteresis curve of the Davidenkov constitutive model; D MD Maximum damping ratio calculated using the modified Davidenkov constitutive model.

[0124] from Fig. 9 , 10 , 11, 12 show that: ① Under different loading and unloading conditions, the modified Davidenkov constitutive model can describe the same dynamic stress-strain hysteresis curve of the soil as the Davidenkov constitutive model, indicating that the loading and unloading criteria of the modified Davidenkov constitutive model are still reasonable. ② When a large strain is generated, the hysteresis curve simulated by the Davidenkov constitutive model is fuller, and the calculated hysteresis damping ratio is significantly greater than the experimental damping ratio, but the modified Davidenkov constitutive model can obtain a more reasonable hysteresis curve, and the calculated damping ratio is also closer to the experimental damping ratio.

[0125] The damping ratio of soil sample 2 measured by the experiment is 0.28. It can be clearly seen from Table 3 that the maximum damping ratio calculated by the hysteresis curve of the Davidenkov constitutive model is significantly larger than the measured maximum damping ratio, but the maximum damping ratio calculated by the modified Davidenkov constitutive model is very close to the measured maximum damping ratio.

[0126] It can be clearly seen from the hysteresis curve of soil sample 2 and the calculated maximum damping ratio that the modified Davidenkov constitutive model has a very obvious correction effect on the damping ratio, which can better reflect the damping ratio characteristics and energy consumption of the soil.

[0127] The Davidenkov constitutive model and the modified Davidenkov constitutive model are applied to two soft soil samples respectively. The dynamic shear modulus ratio and shear strain G / G max -γ curve and the damping ratio and shear strain D-γ curve, such as Fig.13 , 14 , 15, and 16. When the shear strain γ amplitude is 10 -1 When the dynamic shear modulus of soil sample 1 measured by the test, calculated by the Davidenkov constitutive model and calculated by the modified Davidenkov constitutive model is G / G max The dynamic shear modulus ratio G / G of soil sample 2 obtained by experimental measurement, calculation using the Davidenkov constitutive model, and calculation using the modified Davidenkov constitutive model when the shear strain γ amplitude is 10 is shown in Figure 2. max The difference between the damping ratio D and the damping ratio D is shown in Table 4.

[0128] Table 4 Differences of G / Gmax and D between two soil samples

[0129]

[0130] Note: D is the Davidenkov constitutive model; MD is the modified Davidenkov constitutive model. Difference = (theoretical damping ratio - experimental damping ratio) / experimental damping ratio.

[0131] from Fig.13 and Fig.15 It can be seen that with the increase of dynamic shear strain γ, the dynamic shear modulus ratio G / G max When the shear strain is small, the difference between the curves fitted by the Davidenkov constitutive model and the modified Davidenkov constitutive model and the experimental fitting curve is not obvious; when the shear strain is large, although the difference between the curves fitted by the Davidenkov constitutive model and the modified Davidenkov constitutive model and the experimental fitting curve is small, the curve fitted by the modified Davidenkov constitutive model is obviously closer to the experimental fitting curve. Fig.14 and Fig.16It can be seen that with the increase of dynamic shear strain γ, the damping ratio D increases slowly at first and then increases rapidly. When the shear strain is small, the curves fitted by the Davidenkov constitutive model and the modified Davidenkov constitutive model are smaller than the experimental fitting curve; when the shear strain is large, the theoretical fitting curves in both soil samples are significantly larger than the experimental fitting curve, but the curve fitted by the modified Davidenkov constitutive model is closer to the experimental fitting curve, and the difference between the two is small.

[0132] from Fig.13 , 14 , 15, 16 and Table 4 show that the modified Davidenkov constitutive model can accurately describe the dynamic shear modulus ratio G / G of various soft soils. max The relationship between shear strain γ, damping ratio D and shear strain γ solves the deficiency that the original Davidenkov constitutive model cannot truly reflect the damping ratio characteristics of soil.

[0133] The simulation results of the acceleration amplification factor of soil sample 1 are as follows: Fig.17 , 18 , as shown in 19.

[0134] Among them: EL-E is the experimental result under the action of EL waves; EL-MD is the calculation result of the Davidenkov constitutive model modified in this paper under the action of EL waves; EL-D is the calculation result of the Davidenkov constitutive model under the action of EL waves; KB-E is the experimental result under the action of Kobe waves; KB-MD is the calculation result of the Davidenkov constitutive model modified in this paper under the action of Kobe waves; KB-D is the calculation result of the Davidenkov constitutive model under the action of Kobe waves.

[0135] The test results of the surface acceleration amplification coefficient of soil sample 2 are shown in Table 5.

[0136] Table 5 Surface acceleration amplification factor

[0137]

[0138] Depend on Fig.17 , 18, 19 and Table 5 show that in different soils, under different intensities of earthquake motion, the simulation results of the acceleration magnification coefficient using the modified Davidenkov constitutive model are closer to the experimental value than the simulation results of the acceleration magnification coefficient using the Davidenkov constitutive model, and the difference in acceleration magnification coefficient is within 5%. This proves that compared with the Davidenkov constitutive model, the modified Davidenkov constitutive model corrects the shape of the dynamic stress-strain hysteresis curve, thereby reducing the calculated damping ratio of the soil and reducing the overall energy consumption of the soil, which is more consistent with the actual situation.

[0139] Depend on Fig.17 , 18 , 19 It can be seen that when the EL-Centro wave with an acceleration peak of 0.10g acts, the soil has the most significant amplification effect on the seismic response, and the soil surface acceleration amplification factor is 1.77. The greater the earthquake motion input to the bedrock, the smaller the surface acceleration amplification factor, indicating that as the earthquake motion increases, the soil has a certain shock absorption effect, which is consistent with the actual situation. As the soil depth decreases, the Kobe wave acceleration amplification factor decreases first and then increases. Due to the influence of the input seismic wave spectrum component on acceleration, the change law of the acceleration amplification factor of the soil at different burial depths when the EL-Centro wave acts is different from that of the Kobe wave: when the input acceleration peak is 0.10g earthquake motion, it tends to increase all the time; when the input acceleration peak is 0.20g and 0.40g earthquake motion, it tends to decrease first and then increase.

[0140] The Davidenkov constitutive model and the modified Davidenkov constitutive model were used in soil samples 1 and 2 to simulate the seismic dynamic response of the soil surface after the EL-Centro wave with a peak velocity of 0.20g was input to the bedrock. The acceleration time history curves and response spectrum curves are shown in Figure 2. Fig. 20 , 21 , 22, and 23.

[0141] from Fig. 20 and Fig. 22 It can be seen that even in different soft soil samples, the acceleration results calculated by the modified Davidenkov constitutive model are smaller than those calculated by the Davidenkov constitutive model. Specifically, the peak value of the surface acceleration calculated by the Davidenkov constitutive model in soil sample 1 is 0.26g, and the peak value of the surface acceleration calculated by the modified Davidenkov constitutive model is 0.25g; the peak value of the surface acceleration calculated by the Davidenkov constitutive model in soil sample 2 is 0.22g, and the peak value of the surface acceleration calculated by the modified Davidenkov constitutive model is 0.20g. Fig.21 and Fig.23 It can be seen that when the structural damping is 5%, in different soft soil samples, affected by the characteristics of the soil itself, the peak values ​​of the surface acceleration response spectra calculated by the two constitutive models are different, but the shapes of the response spectrum curves are relatively similar. Specifically, the acceleration response spectrum curve of soil sample 1 generally shows an amplification trend in the period range of T = 0 to 0.92s, and shows an attenuation trend after the period T = 0.92s. The peak value of the acceleration response spectrum calculated by the modified Davidenkov constitutive model is 0.72g; the acceleration response spectrum curve of soil sample 2 generally shows an amplification trend in the period range of T = 0 to 0.84s, and shows an attenuation trend after the period T = 0.84s. The peak value of the acceleration response spectrum calculated by the modified Davidenkov constitutive model is 0.70g. The period of high-frequency components of surface seismic waves in soil sample 1 is slightly larger than that of soil sample 2, indicating that different soil samples show different seismic characteristics due to the influence of seismic wave frequency.

[0142] The above conclusions prove the rationality of introducing the damping ratio degradation coefficient into the Davidenkov constitutive model and its practicability in actual engineering.

Claims

1. A method for constructing a modified Davidenkov constitutive model, characterized in that: The following steps are involved: S1: The concept of "damping ratio degradation coefficient" is introduced into the Davidenkov constitutive model represented by a piecewise function. The "damping ratio degradation coefficient" refers to the ratio of the experimental damping ratio to the damping ratio calculated from the hysteresis curve, and is defined as: K(γ)=D T / D M (1) Where, K(γ) is the damping ratio degradation coefficient, D T is the damping ratio obtained through experiments, D M is the damping ratio obtained from the hysteresis curve; S2: The dynamic stress-strain skeleton curve and hysteresis curve formula of the modified Davidenkov constitutive model are derived: The dynamic stress-strain skeleton curve of the modified Davidenkov constitutive model is expressed as: In the formula, γ'=|±γ m -γ c | / 2,γ m is the maximum shear strain that can be reached by the dynamic stress-strain hysteresis curve; The dynamic stress-strain hysteresis curve of the modified Davidenkov constitutive model is expressed as: In the formula, τ m is the maximum shear stress that can be reached by the dynamic stress-strain hysteresis curve; τ c is the shear stress corresponding to the turning point of the stress-strain hysteresis curve at loading and unloading; S3: Based on the stress-strain hysteresis curve of the modified Davidenkov constitutive model, the damping ratio degradation coefficient, damping ratio and dynamic shear modulus formula of the modified Davidenkov constitutive model are derived: The damping ratio degradation coefficient of the modified Davidenkov constitutive model is expressed as: K(γ')=D T / D D (4) Among them, D D is the calculated damping ratio of the Davidenkov constitutive model represented by a piecewise function; The specific calculation expression is: The damping ratio of the modified Davidenkov constitutive model is expressed as: Where D MD To modify the damping ratio of the Davidenkov constitutive model, S LOOP is the area of ​​a hysteresis loop, S E represents the area of ​​a triangle; The specific calculation formula is: The method for constructing the modified Davidenkov constitutive model is characterized in that the derivation of the dynamic shear modulus formula includes the following steps: (1) The shear strain γ in the dynamic stress-strain skeleton curve (2) of the modified Davidenkov constitutive model is differentiated to obtain the calculation formula of the dynamic shear modulus in the initial loading section. When |τ|≤τ ult When , the calculation formula of the dynamic shear modulus is: (2) The dynamic stress-strain hysteresis curve of the Davidenkov constitutive model (3) (γ-γ c ) is derived to obtain the calculation formula of the dynamic shear modulus of the hysteresis curve: When |τ|≤τ ult hour: When |τ|>τ ult When G t+Δt = 0, for the stability of numerical calculation, a minimum dynamic shear modulus G is given min , when G <G min hour: G=G min =0.05G max (10) The Davidenkov constitutive model is represented by a piecewise function. The dynamic shear modulus ratio of the Davidenkov constitutive model is G / G max The expression is as follows: G / G max =1-H(γ) (11) Where G is the shear modulus; G max is the initial maximum shear modulus; γ is the shear strain; A, B and γ0 are fitting parameters related to soil properties; The dynamic stress-strain skeleton curve of the Davidenkov constitutive model represented by a piecewise function is expressed as: Where τ(γ) is the shear stress; τ c is the shear stress corresponding to the turning point of the stress-strain hysteresis curve at loading and unloading; τ ult To break shear stress.

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