Method for fitting dynamic constitutive model of geotechnical materials based on modified Ramberg-Osgood model

Abstract

The present 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. The method includes: obtaining empirical data on the relationship between the shear modulus ratio and shear strain and the relationship between the damping ratio constant and shear strain for different types of geotechnical materials; establishing the expressions of the modified Ramberg-Osgood model and its skeleton curve and hysteretic curve; determining the reference strain, and using the empirical data to calculate the fitting parameters and in the modified Ramberg-Osgood model; obtaining the fitted geotechnical dynamic constitutive model. By fitting the empirical data with the modified Ramberg-Osgood model, the present invention can relatively quickly and accurately construct a geotechnical dynamic constitutive model, thereby providing a more accurate geotechnical dynamic constitutive model for seismic dynamic analysis related to geotechnical engineering, improving the calculation accuracy, and saving research funds and time.

Description

Technical Field

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

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

[0003] However, currently, the dynamic constitutive model of geotechnical materials is usually obtained based on the dynamic constitutive model established by other tests such as dynamic triaxial tests, which requires a large amount of test funds and time, and there are difficulties in accurately fitting and constructing the dynamic constitutive model of geotechnical materials. Therefore, few ordinary geotechnical engineering projects conduct relevant research on the dynamic constitutive model of geotechnical materials, especially in the early stage of the project plan. For many geotechnical engineering projects, such as underground structures like subway tunnels and nuclear power plants, during the design stage, due to the lack of a dynamic constitutive model of geotechnical materials, other calculation schemes with lower accuracy are used to replace the seismic dynamic analysis, resulting in problems such as waste due to insufficient design accuracy and potential safety hazards in 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 dynamic constitutive model of geotechnical materials based on a modified Ramberg-Osgood model, aiming to provide a more accurate dynamic constitutive model of geotechnical materials for seismic dynamic analysis in geotechnical engineering.

[0005] The present invention provides a method for fitting a dynamic constitutive model of geotechnical materials based on a modified Ramberg-Osgood model, including the following steps:

[0006] S1. Obtain the corresponding relationship between the shear modulus ratio and the shear strain of different types of geotechnical materials, and the corresponding relationship between the damping ratio constant and the shear strain of multiple-point empirical data, mark them on a graph and connect the lines to form the curve of the empirical data and the curve; where is the initial shear modulus, and is the shear modulus;

[0007] S2. Establish a modified Ramberg-Osgood model; the skeleton curve of the modified Ramberg-Osgood model is expressed by Equation (1), and the hysteretic curve is expressed by Equation (2);

[0008] (1);

[0009] (2);

[0010] In Equation (1) - Equation (2), is the shear stress; is the shear strain and shear stress at the turning point of the hysteresis curve history; and are both fitting parameters to be solved;

[0011] S3. Solve the fitting parameters , which includes: expressing the damping ratio constant of the modified Ramberg - Osgood model as (3); when the shear modulus ratio in Equation (3) approaches 0, the damping ratio constant reaches the maximum value, denoted as , and calculating the fitting parameter according to Equation (4);

[0012] (3);

[0013] (4);

[0014] In Equation (3) - Equation (4), is the damping energy, is the damping energy change value; Take the value of the damping ratio constant corresponding to the shear modulus ratio approaching 0 on the curve of empirical data;

[0015] S4. Solve the fitting parameters , which includes: substituting Equation (4) into Equation (1) and Equation (2) to obtain Equation (5); determining the shear strain corresponding to the shear modulus ratio on the curve of empirical data as the reference strain , and calling the reference shear modulus ratio, and calculating the fitting parameter according to Equation (6);

[0016] (5);

[0017] (6);

[0018] The initial shear modulus Calculate according to Equation (7);

[0019] (7);

[0020] In Equation (7), is the unit weight of the foundation soil; is the acceleration due to gravity; is the soil layer number of the foundation;

[0021] is the shear elastic wave velocity of the soil layer of the foundation; when the soil layer of the foundation is sandy soil, ; when the soil layer of the foundation is clayey soil, ; is the standard penetration base number of the foundation soil; is the correction coefficient; when , ; when , ;

[0022] S5. Substitute the calculated fitting parameters , and the initial shear modulus into Equations (1)-(3) to obtain the fitted geotechnical dynamic constitutive model, and then obtain the curve and curve of the geotechnical dynamic constitutive model.

[0023] In some embodiments, in step S4, when determining the reference shear modulus ratio , the shear strain corresponding thereto is the reference strain , denoted as , and substitute it into Equation (6), so as to calculate the fitting parameter according to Equation (8);

[0024] (8).

[0025] In some embodiments, in step S4, when determining the reference strain further includes the following steps:

[0026] Use one-dimensional free-field analysis software, according to the types of geotechnical materials of each soil layer of the foundation, input the curve corresponding to the empirical data thereof, and input the calculated seismic wave parameters, and directly calculate the equivalent shear modulus corresponding to each soil layer of the foundation;

[0027] Determine the reference shear modulus ratio The shear strain corresponding thereto is the reference strain which is denoted as and the value of is calculated according to Equation (9) and substituted into Equation (6), so that the fitting parameter is calculated according to Equation (10);

[0028] (9);

[0029] (10).

[0030] In some embodiments, in step S1, the empirical data comes from the data provided in Document No. 1788 of the Geotechnical Research Institute of the Ministry of Construction of Japan, "Numerical Analysis Method for Seismic Response Characteristics of Foundation Soils".

[0031] In some embodiments, the one-dimensional free-field analysis software is ArkQuake, shake or proshake analysis software.

[0032] Based on the above technical solutions, the method for fitting the dynamic constitutive model of rock and soil based on the modified Ramberg-Osgood model in the embodiments of the present invention innovatively proposes to obtain the dynamic constitutive model of rock and soil by fitting the empirical data through the modified Ramberg-Osgood model, providing a more accurate dynamic constitutive model of rock and soil for seismic dynamic analysis related to geotechnical engineering, thereby improving the calculation accuracy in subsequent seismic dynamic analysis and saving research funds and time. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings described herein are used to provide a further understanding of the present invention and form a part of this application. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0034] Figure 1 is a schematic diagram of the backbone curve and hysteresis curve of the modified Ramberg-Osgood model in the present invention;

[0035] Figure 2 is a schematic diagram of the dependence relationship between the shear modulus ratio, damping ratio constant and shear strain of the modified Ramberg-Osgood model in the present invention;

[0036] Figure 3 is an example diagram of the fitting result of the dynamic constitutive model of rock and soil in the first embodiment of the present invention at the second soil layer (T-2) of the foundation;

[0037] Figure 4An example diagram of the fitting result of the geotechnical dynamic constitutive model of the second embodiment of the present invention at the second soil layer (T-2) of the foundation;

[0038] Figure 5 An example diagram of the fitting result of the geotechnical dynamic constitutive model of the first embodiment of the present invention at the third soil layer (T-3) of the foundation;

[0039] Figure 6 An example diagram of the fitting result of the geotechnical dynamic constitutive model of the second embodiment of the present invention at the third soil layer (T-3) of the foundation;

[0040] Figure 7 An example diagram of the fitting result of the geotechnical dynamic constitutive model of the first embodiment of the present invention at the eleventh soil layer (T-11) of the foundation;

[0041] Figure 8 An example diagram of the fitting result of the geotechnical dynamic constitutive model of the second embodiment of the present invention at the eleventh soil layer (T-11) of the foundation. Detailed implementation manners

[0042] Next, the technical solutions in the embodiments will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0043] In the description of the present invention, it should be understood that the terms "center", "horizontal", "longitudinal", "upper", "lower", "top", "bottom", "inner", "outer", "left", "right", "front", "rear", "vertical", "horizontal", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention.

[0044] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installation", "connection", and "connection" 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 directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0045] Reference Figures 1 - 8As shown in the figure, the present invention provides a method for fitting a dynamic constitutive model of geotechnical materials based on the modified Ramberg-Osgood model, which is used to provide a dynamic constitutive model of geotechnical materials for seismic dynamic analysis related to geotechnical engineering. Geotechnical engineering includes, but is not limited to, underground structure engineering such as subway tunnels and nuclear power plants. The method for fitting a dynamic constitutive model of geotechnical materials based on the modified Ramberg-Osgood model includes the following steps:

[0046] S1. Obtain the shear modulus ratio of different types of geotechnical materials and the shear strain corresponding relationship, and the damping ratio constant and the shear strain corresponding relationship of multi-point empirical data, mark them in a chart and connect them to form the curve of the empirical data and curve; where is the initial shear modulus, is the shear modulus; those skilled in the art can understand that .

[0047] Further explanation, the empirical data can be from the data provided in the 1788th document of the Civil Engineering Research Institute of the Ministry of Construction of Japan, "Numerical Analysis Method for Seismic Response Characteristics of Foundation"; the empirical data can also be from other data such as the Technical Standard Method for Port Facilities, Asuda Method, Liquidal Manual or Yamade's Method, and the Basic Law of Japanese Architecture (No. 1457).

[0048] In this embodiment, the empirical data provided in the 1788th document of the Civil Engineering Research Institute of the Ministry of Construction of Japan, "Numerical Analysis Method for Seismic Response Characteristics of Foundation", is taken as an example; the Civil Engineering Research Institute of the Ministry of Construction of Japan has summarized the empirical data of the shear modulus and shear strain relationship of various geotechnical materials (such as alluvial sandy soil, diluvial sandy soil, alluvial clay, diluvial clay), and at the same time gives the corresponding damping ratio coefficient, which is shown as follows.

[0049] ① The representative values of the shear modulus ratio and the shear strain of alluvial sandy soil and diluvial sandy soil are shown in Table 1, and the damping ratio constant is calculated according to Equation (14).

[0050] The curve is expressed as Equation (11):

[0051] (11);

[0052] In Equation (11), is the maximum shear modulus of (kg / cm 2 ); Pis the average effective principal pressure (kg / cm 2 ), calculated according to Equations (12) and (13); is the strain function exponent;

[0053] (12);

[0054] (13);

[0055] In Equation (12), is the coefficient of the static principal pressure; is the effective load (kg / cm 2 ) acting on the center of the target soil layer; is the effective unit volume weight (g / m i ) of the soil layer above the center of the target soil layer ( 3 , t / m 3 ); is the thickness (m) of the i soil layer.

[0056] Table 1 Representative values of alluvial sandy soil, diluvial sandy soil , ,

[0057]

[0058] (14).

[0059] ② The representative values of the shear modulus ratio and the shear strain of alluvial cohesive soil are shown in Table 2, where is the average effective principal stress (kg / cm 2 ); the representative values of the shear strain and the damping ratio constant of alluvial cohesive soil are shown in Table 3.

[0060] Table 2 Representative values considering alluvial cohesive soil ,

[0061]

[0062] Table 3 Representative values of alluvial cohesive soil ,

[0063]

[0064] ③ The shear modulus ratio and the shear strain​​​ , the representative value of the damping ratio constant is shown in Table 4

[0065] Table 4 Diluvial cohesive soil , , representative value

[0066]

[0067] S2. Establish a modified Ramberg - Osgood model; the skeleton curve of the modified Ramberg - Osgood model is expressed as Equation (1), and the hysteretic curve of the modified Ramberg - Osgood model is expressed as Equation (2). Those skilled in the art can understand that the hysteretic curve of the modified Ramberg - Osgood model is obtained according to the Masing criterion

[0068] (1);

[0069] (2);

[0070] In Equations (1) - (2), is the shear strain; is the shear stress; are the shear strain and shear stress at the turning point of the hysteretic curve resume; and are both fitting parameters to be solved

[0071] S3. Solve the fitting parameters , which includes: expressing the damping ratio constant of the modified Ramberg - Osgood model as (3); plotting the dependence relationship between the shear modulus ratio , the damping ratio constant and the shear strain of the modified Ramberg - Osgood model, as shown in Figure 2 . According to this dependence relationship diagram, it can be seen that when the shear strain tends to infinity, the shear modulus ratio tends to 0, while the damping ratio constant tends to the maximum value; when the shear modulus ratio in Equation (3) tends to 0, the damping ratio constant obtains the maximum value, denoted as , and calculate the fitting parameter according to Equation (4);

[0072] (3);

[0073] (4);

[0074] In Equation (3) - Equation (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 when approaching 0 Is taken.

[0075] S4. Solve the fitting parameters , which includes: Substituting Equation (4) into Equation (1) and Equation (2) to obtain Equation (5); Determining the empirical data Shear modulus ratio on the curve The corresponding shear strain when Is the reference strain , as Figure 2 Shown, call The reference shear modulus ratio, and calculate the fitting parameter According to Equation (6);

[0076] (5);

[0077] (6);

[0078] The initial shear modulus in Equation (6) Is calculated according to Equation (7);

[0079] (7);

[0080] In Equation (7), Is the unit weight of the foundation soil; Is the acceleration due to gravity; Is the soil layer number of the foundation;

[0081] Is the Shear elastic wave velocity of the soil layer of the foundation; When the Soil layer of the foundation is sandy soil, ; When the Soil layer of the foundation is cohesive soil, ; Is the standard penetration base number of the foundation soil; Is the correction coefficient; When , ; When , ; Therefore, according to the types of rock and soil to which each soil layer of the foundation belongs, the unit weight , the standard penetration base number of the foundation soil , the initial shear modulus can be obtained , and then the fitting parameters can be obtained .

[0082] S5. Substitute the calculated fitting parameters , and the initial shear modulus into equations (1)-(3) to obtain the fitted dynamic constitutive model of rock and soil, and then obtain the curve and curve of the dynamic constitutive model of rock and soil.

[0083] In the above-mentioned exemplary embodiment, an innovative method is proposed to obtain the dynamic constitutive model of rock and soil by fitting empirical data through modifying the Ramberg-Osgood model, which solves the problem of difficult construction of the dynamic constitutive model of rock and soil in geotechnical engineering projects such as underground structures during seismic dynamic analysis. Furthermore, it can improve the calculation accuracy during subsequent seismic dynamic analysis, saving research funds and time.

[0084] Example 1 for determining the reference strain :

[0085] In step S4, when determining the reference shear modulus ratio , the shear strain corresponding to it is taken as the reference strain , denoted as , and it is substituted into equation (6), so as to calculate the fitting parameter according to equation (8);

[0086] (8).

[0087] Substitute the fitting parameters calculated in this embodiment, the fitting parameters calculated in the previous embodiment and the initial shear modulus into equations (1)-(3) to obtain the fitted dynamic constitutive model of rock and soil, and then obtain the curve and curve of the dynamic constitutive model of rock and soil.

[0088] Table 5 shows the characteristic parameters of each soil layer of the foundation in the empirical data provided by the 1788th document of the Civil Engineering Research Institute of the Ministry of Construction of Japan.

[0089] Table 5 Characteristic parameters of each soil layer of the foundation

[0090]

[0091] Taking the 2nd soil layer, 3rd soil layer, and 11th soil layer of the foundation as examples, when the reference strain is Fitting of the dynamic constitutive model of rock and soil at a certain time. For the comparison between the fitting results and the empirical data, see Figure 3 , Figure 5 , Figure 7 ; It can be seen from Figure 3 , Figure 5 , Figure 7 that when the reference strain is determined to be , the fitting degree between the dynamic constitutive model of rock and soil and the empirical data is relatively good.

[0092] In the above-mentioned schematic embodiment, by using the curve of the empirical data, the shear strain corresponding to the shear modulus ratio is determined as the reference strain , realizing the rapid fitting of the dynamic constitutive model of rock and soil.

[0093] Example two for determining the reference strain :

[0094] On the basis of Example one, further research is carried out on the reference strain . By observing Figure 3 , Figure 5 , Figure 7 it can be seen that although the fitting method of determining the reference strain as is simple and convenient and has a good fitting effect, the empirical data shows that in the initial stage, as the shear stress increases, the shear modulus ratio initially decreases slowly. When the shear modulus ratio of the foundation soil layer is relatively large and the shear strain is relatively small, the curve fitting deviation of the dynamic constitutive model of rock and soil obtained according to Example one is relatively large, that is, it cannot fit well at all strain level points; 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 section in the dynamic constitutive model of rock and soil. In view of this, Example one is improved to explore a more appropriate determination method of the reference strain to improve the fitting effect.

[0095] In step S4, when determining the reference strain , the following steps are further included:

[0096] Conduct a one-dimensional free field analysis on the soil layer where the underground structure is located. Using the one-dimensional free field analysis software, according to the types of rock and soil to which each soil layer of the foundation belongs, input the curve of the empirical data corresponding to it in the analysis software, and input the calculated seismic wave parameters. It is possible to directly calculate the equivalent shear modulus corresponding to each soil layer of the foundation by using the one-dimensional free field analysis software. Through the equivalent shear modulus The strain amplitudes of each soil layer in 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.

[0097] Determine the reference shear modulus ratio The corresponding shear strain is the reference strain , denoted as , calculate the value of according to Equation (9), substitute it into Equation (6), and thus calculate the fitting parameter ;

[0098] (9);

[0099] (10).

[0100] Substitute the fitting parameter solved in this embodiment, the fitting parameter solved in the foregoing embodiment, and the initial shear modulus into Equations (1)-(3) to obtain the fitted dynamic constitutive model of geotechnical materials, and then obtain the curve and curve of the dynamic constitutive model of geotechnical materials.

[0101] Table 6 shows the calculated reference shear modulus ratio taking the empirical data provided in the 1788th document of the Civil Engineering Research Institute of the Ministry of Construction of Japan as an example.

[0102] Table 6 Reference shear modulus ratio of each soil layer in the foundation Calculation results of

[0103]

[0104] Taking the 2nd, 3rd, and 11th soil layers of the foundation as examples, the reference strain is determined according to the calculated value of the reference shear modulus ratio shown in Table 6 for fitting the dynamic constitutive model of geotechnical materials. For the comparison of the fitting results and the empirical data, see Figure 4 , Figure 6 , Figure 8 ; It can be seen from Figures 3 - 8 that when the reference strain is determined based on the equivalent shear modulus , the fitting degree of the dynamic constitutive model of geotechnical materials and the empirical data is better, especially improving the fitting degree in the small strain section, making up for the disadvantage of the relatively large shear modulus ratio in small strains, and then improving the fitting effect for all strain level points and improving the accuracy of the dynamic constitutive model of geotechnical materials.

[0105] In the above-described exemplary embodiment, by solving the equivalent shear modulus , the strain amplitude of each soil layer of the foundation during an earthquake can be judged, thereby guiding the key fitting interval of the geotechnical dynamic constitutive model and making the parameter setting in the model more reasonable; by determining the reference strain based on the equivalent shear modulus , the reference strain is no longer fixed at the position of . Thus, a more reasonable reference strain point position can be determined, and further, a better fitting effect can be obtained, and the calculation accuracy of the seismic dynamic analysis of the underground structure can be further improved.

[0106] In summary, the method for fitting the geotechnical dynamic constitutive model based on the modified Ramberg-Osgood model of the present invention innovatively proposes to obtain the geotechnical dynamic constitutive model by fitting the empirical data through the modified Ramberg-Osgood model, solves the problem of difficult construction of the geotechnical dynamic constitutive model in seismic dynamic analysis of geotechnical engineering projects such as underground structures, provides a more accurate geotechnical dynamic constitutive model for seismic dynamic analysis related to geotechnical engineering, and further can improve the calculation accuracy in subsequent seismic dynamic analysis, thereby improving the accuracy and efficiency of the seismic design of underground structures, saving research funds and time, and having very high practical value.

[0107] Finally, it should be noted that: the various embodiments in this specification are described in a progressive manner, and the key point of each embodiment is to describe the differences from other embodiments. The same and similar parts between the various embodiments can be referred to each other.

[0108] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or some technical features can be equivalently replaced without departing from the spirit of the technical solutions of the present invention, and they should all be covered within the scope of the technical solutions claimed by the present invention.

Claims

1. A method for fitting a dynamic constitutive model of geotechnical materials based on the modified Ramberg-Osgood model, characterized in that, It includes the following steps: S1. Obtain the shear modulus ratios of different types of rock and soil and the shear strain corresponding relationship, damping ratio constant and the shear strain corresponding relationship of multi-point empirical data, mark them in a chart and connect the lines to form the curve of the empirical data and the curve; where 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 Equation (1), and the hysteretic curve is expressed as Equation (2); （1）； （2）； In Formula (1) - Formula (2), is the shear stress; are the shear strain and shear stress at the inflection point of the hysteresis curve history; and are both fitting parameters to be solved; S3. Solve the fitting parameters , which includes: expressing the damping ratio constant of the modified Ramberg-Osgood model as (3); when the shear modulus ratio in equation (3) approaches 0, the damping ratio constant reaches the maximum value, denoted as , and calculating the fitting parameter according to equation (4); （3）； （4）； In Equation (3) - Equation (4), is the damping energy, is the damping energy change value; According to the shear modulus ratio on the curve of the damping ratio constant when approaching 0 is taken; S4. Solve the fitting parameters , which includes: Using a one-dimensional free-field analysis software, according to the types of rock and soil of each soil layer in the foundation, input the curve corresponding thereto, and input the calculated seismic wave parameters to directly calculate the equivalent shear modulus corresponding to each soil layer in the foundation ; Substitute Equation (4) into Equation (1) and Equation (2) to obtain Equation (5); （5）； Determine the shear modulus ratio on the curve of the empirical data, and the shear strain corresponding thereto is taken as the reference strain , and is called the reference shear modulus ratio; determine the shear strain corresponding to the reference shear modulus ratio as the reference strain , which is denoted as , and calculate the value of according to Equation (9); calculate the fitting parameter according to Equation (10); （9）； （10）； The initial shear modulus in Equation (10) is calculated according to Equation (7); （7）； In formula (7), is the unit weight of foundation soil; is the acceleration of gravity; is the soil layer number of the foundation; is the shear elastic wave velocity of the soil layer of the foundation; when the soil layer of the foundation is sandy soil, ; when the soil layer of the foundation is cohesive soil, ; is the standard penetration base number of the foundation soil; is the correction coefficient; when , ; when , ; S5. Substitute the calculated fitting parameters , and the initial shear modulus into equations (1) - (3) to obtain the fitted dynamic constitutive model of rock and soil, and further obtain the curve and curve of the dynamic constitutive model of rock and soil.

2. The method for fitting a dynamic constitutive model of rock and soil based on the modified Ramberg-Osgood model according to claim 1, characterized in that, The one-dimensional free-field analysis software is ArkQuake, shake or proshake analysis software.

Images