Method for fitting rock-soil dynamic constitutive model based on modified Ramberg-Osgood model

Abstract

The invention belongs to the technical field of geotechnical engineering, and particularly relates to a method for fitting a rock-soil dynamic constitutive model based on a modified Ramberg-Osgood model. The method comprises the following steps: acquiring empirical data of a corresponding relation between a shear modulus ratio and a shear strain and a corresponding relation between a damping ratio constant and the shear strain of different types of rock soil; establishing a corrected Ramberg-Osgood model and an expression of a skeleton curve and a hysteretic curve of the corrected Ramberg-Osgood model; the method comprises the following steps: determining reference strain, and calculating fitting parameters # imgabs0 # and # imgabs1 # in a corrected Ramberg-Osgood model by using empirical data, wherein the fitting parameters # imgabs0 # and # imgabs1 # in the Ramberg-Osgood model; and obtaining the fitted rock-soil dynamic constitutive model. According to the method, empirical data are fitted through the corrected Ramberg-Osgood model, and the rock-soil dynamic constitutive model can be quickly and accurately constructed, so that a more accurate rock-soil dynamic constitutive model is provided for seismic dynamic analysis related to geotechnical engineering, the calculation precision is improved, and the research expenditure and time are saved.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and particularly relates to a method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model. Background Art

[0002] The geotechnical dynamic constitutive model is the basis for understanding the dynamic characteristics of soil or soil structures under dynamic loads. Using the geotechnical dynamic constitutive model to conduct earthquake dynamic analysis related to geotechnical engineering is one of the most accurate analysis methods in computational research. In order to more accurately analyze and calculate problems in geotechnical engineering during earthquakes, it is first necessary to obtain a more accurate geotechnical dynamic constitutive model.

[0003] However, at present, the dynamic constitutive model of geotechnical materials is usually obtained based on the dynamic constitutive model established by other tests such as dynamic triaxial test, which requires a lot of experimental funds and time, and there is a problem of how to accurately fit and construct the dynamic constitutive model of geotechnical materials. Therefore, ordinary geotechnical engineering rarely conducts relevant research on the dynamic constitutive model of geotechnical materials, especially in the early stage of planning. Many geotechnical engineering projects, such as subway tunnels, nuclear power plants and other underground structures, do not have a dynamic constitutive model of geotechnical materials during the design stage, and use other less accurate calculation schemes instead for seismic dynamic analysis, resulting in waste due to insufficient design accuracy and safety hazards of engineering structures during earthquakes. Summary of the invention

[0004] In view of the deficiencies in the related art, the present invention provides a method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model, aiming to provide a more accurate geotechnical dynamic constitutive model for earthquake dynamic analysis related to geotechnical engineering.

[0005] The present invention provides a method for fitting a rock and soil dynamic constitutive model based on a modified Ramberg-Osgood model, comprising the following steps: S1. Obtain the shear modulus ratio of different types of rock and soil With shear strain Corresponding relationship, damping ratio constant With shear strain The corresponding relationship of multiple points of empirical data is marked in the chart and connected to form the empirical data Curves and curve; among them, is the initial shear modulus, is the shear modulus; S2. Establish a modified Ramberg-Osgood model; the skeleton curve of the modified Ramberg-Osgood model is expressed as formula (1), and the hysteresis curve is expressed as formula (2); (1); (2); In formula (1)-formula (2), is the shear stress; is the shear strain and shear stress at the turning point of the hysteresis curve; and are the fitting parameters to be solved; S3. Calculate fitting parameters , which includes: modifying the damping ratio constant of the Ramberg-Osgood model It is expressed as (3); when the shear modulus ratio in formula (3) When it approaches 0, the damping ratio constant Get the maximum value and record it as , according to formula (4) to calculate the fitting parameters ; (3); (4); In formula (3)-formula (4), is the damping energy, is the damping energy change value; Based on empirical data Shear modulus ratio on the curve The damping ratio constant approaches 0 To obtain the value; S4. Calculate fitting parameters , which includes: substituting formula (4) into formula (1) and formula (2) to obtain formula (5); determining the empirical data Shear modulus ratio on the curve The corresponding shear strain Base strain ,Will is called the benchmark shear modulus ratio, and the fitting parameters are calculated according to formula (6): ; (5); (6); The initial shear modulus in formula (6) is Calculate according to formula (7); (7); In formula (7), is the bulk density of foundation soil; is the acceleration due to gravity; is the soil layer number of the foundation; For the foundation The shear elastic wave velocity of the soil layer; When the soil layer is sandy, ; Local Kiti When the soil layer is clay soil, ; is the standard inertia basis of foundation soil; is the correction factor; when hour, ;when hour, ; S5. The calculated fitting parameters , and initial shear modulus Substitute it into equations (1) to (3) to obtain the fitted rock and soil dynamic constitutive model, and then obtain the rock and soil dynamic constitutive model Curve and curve.

[0006] In some embodiments, in step S4, a reference shear modulus ratio is determined. The corresponding shear strain Base strain , which is recorded as , substitute it into formula (6), and then calculate the fitting parameters according to formula (8): ; (8).

[0007] In some embodiments, in step S4, the reference strain is determined The following steps are also included: Using one-dimensional free field analysis software, according to the type of rock and soil to which each soil layer belongs, input the corresponding empirical data Curve, and input the calculated seismic wave parameters to directly calculate the equivalent shear modulus corresponding to each soil layer of the foundation ; Determining the Benchmark Shear Modulus Ratio The corresponding shear strain Base strain , which is recorded as , calculated according to formula (9) Substitute the value of into formula (6) to calculate the fitting parameters according to formula (10): ; (9); (10).

[0008] In some of the embodiments, in step S1, the empirical data comes from the data provided in Document No. 1788 of the Civil Engineering Research Institute of the Ministry of Construction of Japan, “Numerical Analysis Method for Earthquake Response Characteristics of Foundation”.

[0009] In some of the embodiments, the one-dimensional free-field analysis software is ArkQuake, shake or proshake analysis software.

[0010] Based on the above technical scheme, the method for fitting the geotechnical dynamic constitutive model based on the modified Ramberg-Osgood model in the embodiment of the present invention innovatively proposes to obtain the geotechnical dynamic constitutive model by fitting the empirical data by the modified Ramberg-Osgood model, thereby providing a more accurate geotechnical dynamic constitutive model for the seismic dynamic analysis related to geotechnical engineering, thereby improving the calculation accuracy of subsequent seismic dynamic analysis and saving research funds and time. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 Schematic diagram of the skeleton curve and hysteresis curve of the modified Ramberg-Osgood model in the present invention; Figure 2 Schematic diagram of the dependence between the shear modulus ratio, the damping ratio constant and the shear strain of the modified Ramberg-Osgood model in the present invention; Figure 3 This is an example diagram of the fitting results of the rock and soil dynamic constitutive model at the second soil layer (T-2) of the foundation according to the first embodiment of the present invention; Figure 4 This is an example diagram of the fitting results of the rock and soil dynamic constitutive model of the second embodiment of the present invention at the second soil layer (T-2) of the foundation; Figure 5 This is an example diagram of the fitting results of the rock and soil dynamic constitutive model at the third soil layer (T-3) of the foundation according to the first embodiment of the present invention; Figure 6 This is an example diagram of the fitting results of the rock and soil dynamic constitutive model at the third soil layer (T-3) of the foundation according to the second embodiment of the present invention; Figure 7 This is an example diagram of the fitting results of the rock and soil dynamic constitutive model at the 11th soil layer (T-11) of the foundation according to the first embodiment of the present invention; Figure 8 This is an example diagram of the fitting results of the rock and soil dynamic constitutive model of the second embodiment of the present invention at the 11th soil layer (T-11) of the foundation. DETAILED DESCRIPTION

[0012] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0013] In the description of the present invention, it should be understood that the terms "center", "lateral", "longitudinal", "up", "down", "top", "bottom", "inside", "outside", "left", "right", "front", "back", "vertical", "horizontal", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0014] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0015] refer to Figure 1-Figure 8 As shown, the present invention provides a method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model, which is used to provide a geotechnical dynamic constitutive model for earthquake dynamic analysis related to geotechnical engineering, and the geotechnical engineering includes but is not limited to underground structure engineering such as subway tunnels and nuclear power plants. The method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model includes the following steps: S1. Obtain the shear modulus ratio of different types of rock and soil With shear strain Corresponding relationship, damping ratio constant With shear strain The corresponding relationship of multiple points of empirical data is marked in the chart and connected to form the empirical data Curves and curve; among them, is the initial shear modulus, is the shear modulus; those skilled in the art will appreciate that, .

[0016] To further explain, the empirical data can come from the data provided in the Civil Engineering Research Institute of the Ministry of Construction of Japan's document No. 1788 "Numerical Analysis Method for Earthquake Response Characteristics of Foundations"; the empirical data can also come from the data provided in other documents such as the Technical Standard Method for Port Facilities, the Asuda Method, the Liquidal Manual or Yamade's Method, the Japanese Basic Building Law (No. 1457), etc.

[0017] This embodiment takes the empirical data provided by the Civil Engineering Research Institute of the Ministry of Construction of Japan, document No. 1788, "Numerical Analysis Method for Earthquake Response Characteristics of Foundations" as an example; the Civil Engineering Research Institute of the Ministry of Construction of Japan has studied and summarized the empirical data on the relationship between shear modulus and shear strain of various rock and soils (such as alluvial sandy soil, alluvial sandy soil, alluvial clay soil, and alluvial clay soil), and also gave the corresponding damping ratio coefficient, which is shown below.

[0018] ① Shear modulus ratio of alluvial sandy soil and flood sandy soil , shear strain The representative values ​​of are shown in Table 1. The damping ratio constant Calculate according to formula (14).

[0019] The curve is expressed as formula (11): (11); In formula (11), The maximum shear modulus (kg / cm 2 ); P is the average effective main pressure (kg / cm 2 ), calculated according to equations (12) and (13); is the strain function index; (12); (13); In formula (12), is the static principal pressure coefficient; is the effective load acting on the center of the target soil layer (kg / cm 2 ); The soil layer above the center of the target soil layer ( i ) effective unit volume weight (g / m 3 ,t / m 3 ); For the i Thickness of soil layer (m).

[0020] Table 1 Alluvial sandy soil and flood sandy soil , , Representative value of

[0021] (14).

[0022] ② Shear modulus ratio of alluvial clay , shear strain The representative values ​​of are shown in Table 2, where is the average effective principal stress (kg / cm 2 ); Shear strain of alluvial clay , damping ratio constant The representative values ​​of are shown in Table 3.

[0023] Table 2 Considerations Alluvial clay soil , Representative value of

[0024] Table 3 Alluvial clay soil , Representative value of

[0025] ③ Shear modulus ratio of alluvial clay , shear strain , damping ratio constant The representative values ​​of are shown in Table 4.

[0026] Table 4 Alluvial clay soil , , Representative value of

[0027] S2. Establish a modified Ramberg-Osgood model; the skeleton curve of the modified Ramberg-Osgood model is expressed as formula (1), and the hysteresis curve of the modified Ramberg-Osgood model is expressed as formula (2). It can be understood by those skilled in the art that the hysteresis curve of the modified Ramberg-Osgood model is obtained according to the Masing criterion.

[0028] (1); (2); In formula (1)-formula (2), is the shear strain; is the shear stress; is the shear strain and shear stress at the turning point of the hysteresis curve history; and are the fitting parameters to be solved.

[0029] S3. Calculate fitting parameters , which includes: modifying the damping ratio constant of the Ramberg-Osgood model Expressed as (3); The shear modulus ratio of the modified Ramberg-Osgood model is plotted graphically , damping ratio constant With shear strain The dependencies between Figure 2 As shown in the dependence diagram, it can be seen that when the shear strain As it approaches infinity, the shear modulus ratio The closer it is to 0, the damping ratio constant The closer it is to the maximum value; when the shear modulus ratio in formula (3) When it approaches 0, the damping ratio constant Get the maximum value and record it as , according to formula (4) to calculate the fitting parameters ; (3); (4); In formula (3)-formula (4), is the damping energy, is the damping energy change value; Based on empirical data Shear modulus ratio on the curve The damping ratio constant approaches 0 Get the value.

[0030] S4. Calculate fitting parameters , which includes: substituting formula (4) into formula (1) and formula (2) to obtain formula (5); determining the empirical data Shear modulus ratio on the curve The corresponding shear strain Base strain ,like Figure 2 As shown, is called the benchmark shear modulus ratio, and the fitting parameters are calculated according to formula (6): ; (5); (6); The initial shear modulus in formula (6) is Calculate according to formula (7); (7); In formula (7), is the bulk density of foundation soil; is the acceleration due to gravity; is the soil layer number of the foundation; For the foundation The shear elastic wave velocity of the soil layer; When the soil layer is sandy, ; Local Kiti When the soil layer is clay soil, ; is the standard inertia basis of foundation soil; is the correction factor; when hour, ;when hour, Therefore, according to the rock and soil type and bulk density of each soil layer of the foundation , Standard inertia basis of foundation soil , the initial shear modulus can be obtained , and then obtain the fitting parameters .

[0031] S5. The calculated fitting parameters , and initial shear modulus Substitute it into equations (1) to (3) to obtain the fitted rock and soil dynamic constitutive model, and then obtain the rock and soil dynamic constitutive model Curve and curve.

[0032] The above-mentioned schematic embodiment innovatively proposes to obtain a geotechnical dynamic constitutive model by fitting empirical data through a modified Ramberg-Osgood model, thereby solving the problem of difficulty in constructing a geotechnical dynamic constitutive model when performing seismic dynamic analysis on geotechnical engineering projects such as underground structures, thereby improving the calculation accuracy of subsequent seismic dynamic analysis and saving research funds and time.

[0033] Determine the base strain Embodiment 1: In step S4, the reference shear modulus ratio is determined The corresponding shear strain Base strain , which is recorded as , substitute it into formula (6), and then calculate the fitting parameters according to formula (8): ; (8).

[0034] The fitting parameters calculated in this embodiment are , the fitting parameters calculated by the above embodiment and initial shear modulus Substitute it into equations (1) to (3) to obtain the fitted rock and soil dynamic constitutive model, and then obtain the rock and soil dynamic constitutive model Curve and curve.

[0035] Table 5 shows the characteristic parameters of each soil layer in the foundation from the empirical data provided by the Civil Engineering Research Institute of the Ministry of Construction of Japan, document No. 1788.

[0036] Table 5 Characteristics parameters of each stratum of the foundation

[0037] Taking the second, third and eleventh soil layers of the foundation as an example, the base strain is The fitting of the dynamic constitutive model of rock and soil at the time of Figure 3 , Figure 5 , Figure 7 ;Depend on Figure 3 , Figure 5 , Figure 7 It can be seen that the reference strain is determined as When , the dynamic constitutive model of rock and soil has a good fit with the empirical data.

[0038] The above exemplary embodiments are based on the empirical data. Shear modulus ratio on the curve The corresponding shear strain Determined as the baseline strain , realizing the rapid fitting of the dynamic constitutive model of rock and soil.

[0039] Determine the base strain Embodiment 2 of the present invention: Based on the first embodiment, the reference strain Do further research. Figure 3 , Figure 5 , Figure 7 It is known that The fitting method of the dynamic constitutive model determined as the reference strain is simple and convenient, and the fitting effect is good, but empirical data show that in the initial stage, as the shear stress Increase, shear modulus ratio The decrease is slow at first, when the shear modulus of the foundation soil is Larger shear strain When the reference strain is small, the curve fitting deviation of the rock and soil dynamic constitutive model obtained according to the first embodiment is large, that is, it cannot fit all the strain level points well; and if the soil does not produce large strain during the earthquake, more attention should be paid to the fitting effect of the small strain segment in the rock and soil dynamic constitutive model. In view of this, the first embodiment is improved to explore the reference strain A more appropriate determination method improves the fitting effect.

[0040] In step S4, the reference strain is determined The following steps are also included: One-dimensional free-field analysis is performed on the soil layer where the underground structure is located. The one-dimensional free-field analysis software is used to input the corresponding empirical data into the analysis software according to the rock and soil type of each soil layer of the foundation. Curve, and input calculation seismic wave parameters, can use one-dimensional free field analysis software to directly calculate the equivalent shear modulus corresponding to each soil layer of the foundation , through the equivalent shear modulus The strain amplitude of each soil layer of the foundation during an earthquake can be determined; further, the one-dimensional free field analysis software is analysis software such as ArkQuake, shake or proshake, but is not limited thereto.

[0041] Determining the Benchmark Shear Modulus Ratio The corresponding shear strain Base strain , which is recorded as , calculated according to formula (9) Substitute the value of into formula (6) to calculate the fitting parameters according to formula (10): ; (9); (10).

[0042] The fitting parameters calculated in this embodiment are , the fitting parameters calculated by the above embodiment and initial shear modulus Substitute it into equations (1) to (3) to obtain the fitted rock and soil dynamic constitutive model, and then obtain the rock and soil dynamic constitutive model Curve and curve.

[0043] Table 6 shows the calculated benchmark shear modulus ratio based on the empirical data provided by the Civil Engineering Research Institute of the Ministry of Construction of Japan, document No. 1788. .

[0044] Table 6 Base shear modulus ratio of each soil layer in the foundation The calculation results

[0045] Taking the second, third and eleventh soil layers of the foundation as an example, the reference shear modulus ratios shown in Table 6 are Calculated value to determine the base strain The dynamic constitutive model of rock and soil is fitted. The comparison between the fitting results and empirical data can be found in Figure 4 , Figure 6 , Figure 8 ;Depend on Figure 3-Figure 8 It can be seen that when the base strain Based on the equivalent shear modulus When determining, the geotechnical dynamic constitutive model has a better fit with the empirical data, especially the fit in the small strain section, which makes up for the unfavorable characteristic of the large shear modulus ratio in small strain, thereby improving the fitting effect of all strain level points and improving the accuracy of the geotechnical dynamic constitutive model.

[0046] In the above exemplary embodiment, the equivalent shear modulus The solution can determine the strain amplitude of each soil layer in the foundation during an earthquake, thereby guiding the key fitting interval of the rock and soil dynamic constitutive model and making the parameter setting in the model more reasonable; Determine the base strain The reference strain No longer fixed The position of the reference strain point can be determined more reasonably, thereby achieving a better fitting effect and further improving the calculation accuracy of the seismic dynamic analysis of underground structures.

[0047] In summary, the method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model of the present invention innovatively proposes to obtain a geotechnical dynamic constitutive model by fitting empirical data through a modified Ramberg-Osgood model, which solves the problem that it is difficult to construct a geotechnical dynamic constitutive model when performing seismic dynamic analysis on geotechnical engineering projects such as underground structures, and provides a more accurate geotechnical dynamic constitutive model for seismic dynamic analysis related to geotechnical engineering, thereby improving the calculation accuracy of subsequent seismic dynamic analysis, thereby improving the accuracy and efficiency of seismic design of underground structures, saving research funds and time, and having very high practical value.

[0048] Finally, it should be noted that: the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0049] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or some technical features can be replaced by equivalents without departing from the spirit of the technical solution of the present invention, which should be included in the scope of the technical solution for protection of the present invention.

Claims

1. A method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model, characterized in that: The following steps are involved: S1. Obtain the shear modulus ratio of different types of rock and soil With shear strain Corresponding relationship, damping ratio constant With shear strain The corresponding relationship of multiple points of empirical data is marked in the chart and connected to form the empirical data Curves and curve; among them, is the initial shear modulus, is the shear modulus; S2. Establishing a modified Ramberg-Osgood model; the skeleton curve of the modified Ramberg-Osgood model is expressed as formula (1), and the hysteresis curve is expressed as formula (2); （1）； （2）； In formula (1)-formula (2), is the shear stress; are the shear strain and shear stress at the turning point of the hysteresis curve history; and are the fitting parameters to be solved; S3, calculating the fitting parameters , which includes: changing the damping ratio constant of the modified Ramberg-Osgood model It is expressed as (3); when the shear modulus ratio in formula (3) When it approaches 0, the damping ratio constant Get the maximum value and record it as , the fitting parameters are calculated according to formula (4) ; （3）； （4）； In formula (3)-formula (4), is the damping energy, is the damping energy change value; According to the empirical data Shear modulus ratio on the curve The damping ratio constant approaches 0 To obtain the value; S4, calculating the fitting parameters , which includes: substituting formula (4) into formula (1) and formula (2) to obtain formula (5); determining the empirical data Shear modulus ratio on the curve The corresponding shear strain Base strain ,Will is called the benchmark shear modulus ratio, and the fitting parameters are calculated according to formula (6): ; （5）； （6）； The initial shear modulus in formula (6) is Calculate according to formula (7); （7）； In formula (7), is the bulk density of foundation soil; is the acceleration due to gravity; is the soil layer number of the foundation; For the foundation The shear elastic wave velocity of the soil layer; When the soil layer is sandy, ; Local Kiti When the soil layer is clay soil, ; is the standard inertia basis of foundation soil; is the correction factor; when hour, ;when hour, ; S5, the calculated fitting parameters , and initial shear modulus Substitute it into equations (1) to (3) to obtain the fitted rock and soil dynamic constitutive model, and then obtain the rock and soil dynamic constitutive model Curve and curve.

2. The method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model according to claim 1, characterized in that: In step S4, the reference shear modulus ratio is determined The corresponding shear strain Base strain , which is recorded as , and substitute it into formula (6), so as to calculate the fitting parameters according to formula (8): ; （8）。 3. The method for fitting a geotechnical dynamic constitutive model based on a modified Ramberg-Osgood model according to claim 1, characterized in that: In step S4, the reference strain is determined The following steps are also included: Using one-dimensional free field analysis software, according to the rock and soil type of each soil layer of the foundation, input the corresponding empirical data Curve, and input the calculated seismic wave parameters to directly calculate the equivalent shear modulus corresponding to each soil layer of the foundation ; Determining the Benchmark Shear Modulus Ratio The corresponding shear strain Base strain , which is recorded as , calculated according to formula (9) The value of is substituted into formula (6), and then the fitting parameters are calculated according to formula (10): ; （9）； （10）。 4. The method for fitting a rock and soil dynamic constitutive model based on a modified Ramberg-Osgood model according to claim 3, characterized in that: The one-dimensional free field analysis software is ArkQuake, shake or proshake analysis software.

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