A construction method, numerical analysis method and device of a three-dimensional creep model

Abstract

The present application discloses a method for constructing a three-dimensional creep model, a numerical analysis method and a device, relating to the field of constitutive model research. The method includes: constructing a one-dimensional creep model of an elastic body, a one-dimensional creep model of a fractional-order viscous pot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative viscous pot according to the test data of the object creep test; the object is a geotechnical body, concrete or metal; constructing a three-dimensional creep model of the object according to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative viscous pot. The present application can provide a more concise three-dimensional creep model for characterizing the unstable characteristics of geotechnical bodies, concrete materials or metal materials.

Description

Technical Field

[0001] The present application relates to the field of constitutive model research, and particularly to a method for constructing a three-dimensional creep model, a numerical analysis method and a device therefor. Background Art

[0002] The designed service life of underground engineering usually spans several decades. During this period, surrounding rocks, linings and metal arches may experience time-related creep deformation and even structural failure under the action of continuous loads. Therefore, constructing an accurate mechanical model to predict the long-term creep behavior of surrounding rocks, linings and metal arches under constant loads and its relationship with service time, that is, the creep characteristics of rock and soil masses, concrete materials and metal materials, is a core topic in the field of underground engineering. Creep is a complex process in which the deformation of an object gradually accumulates over time under a constant stress state. Through systematic creep analysis, the creep constitutive relationship of rock and soil masses, concrete materials and metal materials can be deeply revealed, and then a mathematical model of stress, strain and time dependence can be established to provide theoretical support for the long-term stability assessment of underground engineering.

[0003] Currently, the basic framework of creep constitutive models is mainly composed of three basic creep elements - Hooke body (elastic body), Newton body and plastic body - combined in series, parallel or mixed connection ways, forming classic creep models such as Saint-Venant body, Maxwell body, Kelvin body, Bingham-Thomson body, etc. However, these models are constructed based on linear elements, which limits their application in describing the non-linear accelerating creep characteristics of rock and soil masses, concrete materials or metal materials. In order to more accurately characterize the unstable creep behavior of rock and soil masses, concrete materials or metal materials, it is necessary to non-linearly improve the constitutive relationship of the basic elements. Existing non-linear creep models are mostly improved on the basis of classic element models by introducing non-linear elements to characterize the unstable creep characteristics of rock and soil masses, concrete materials or metal materials. However, when describing the stress-strain behavior related to the loading strain rate, these models often involve complex mathematical expressions, making the models very complex and the physical meaning unclear. Therefore, there is an urgent need for a simple three-dimensional creep model to characterize the unstable characteristics of rock and soil masses, concrete materials or metal materials. Summary of the Invention

[0004] The purpose of the present application is to provide a method for constructing a three-dimensional creep model, a numerical analysis method and a device therefor, which can provide a more simple three-dimensional creep model for characterizing the unstable characteristics of rock and soil masses, concrete materials or metal materials.

[0005] To achieve the above object, the present application provides the following solutions: In the first aspect, the present application provides a method for constructing a three-dimensional creep model, including: constructing a one-dimensional creep model of an elastic body, a one-dimensional creep model of a fractional-order dashpot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative dashpot according to the test data of the object creep test; the object is a geotechnical body, concrete or metal.

[0006] Construct a three-dimensional creep model of the object according to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order dashpot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative dashpot.

[0007] In the second aspect, the present application provides a numerical analysis method for a three-dimensional creep model, including: determining the deviatoric strain rate expression of the three-dimensional creep model of the above-mentioned object.

[0008] Determine the three-dimensional increment expression according to the deviatoric strain rate expression.

[0009] Program the three-dimensional increment expression through the extended function interface of the numerical calculation software to obtain the user subroutine of the three-dimensional creep model of the object.

[0010] In the third aspect, the present application provides a device for constructing a three-dimensional creep model, including: a component one-dimensional creep model construction module for constructing a one-dimensional creep model of an elastic body, a one-dimensional creep model of a fractional-order dashpot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative dashpot according to the test data of the object creep test; the object is a geotechnical body, concrete or metal.

[0011] A three-dimensional creep model construction module of the object for constructing a three-dimensional creep model of the object according to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order dashpot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative dashpot.

[0012] In the fourth aspect, the present application provides a numerical analysis device for a three-dimensional creep model, including: a deviatoric strain rate expression determination module for determining the deviatoric strain rate expression of the three-dimensional creep model of the above-mentioned object.

[0013] A three-dimensional increment expression determination module for determining the three-dimensional increment expression according to the deviatoric strain rate expression.

[0014] A user subroutine determination module for programming the three-dimensional increment expression through the extended function interface of the numerical calculation software to obtain the user subroutine of the three-dimensional creep model of the object.

[0015] According to the specific embodiments provided by the present application, the present application has the following technical effects: The present application provides a method for constructing a three-dimensional creep model, a numerical analysis method and a device. The fractional-order dashpot and the memory-dependent derivative dashpot with strain trigger have fewer parameters. In the process of constructing the three-dimensional creep model of an object, the viscoelasticity of the object is characterized by using the fractional-order dashpot, and the non-linear accelerated creep characteristics of the object are characterized by using the memory-dependent derivative dashpot with strain trigger. By using the fractional-order dashpot and the memory-dependent derivative dashpot with strain trigger simultaneously, the complexity of the three-dimensional creep model of rock and soil, concrete materials or metal materials can be reduced, and simplicity can be achieved. Too many creep model parameters will lead to a reduction in the accuracy of the non-steady creep behavior during the creep process of the object calculated according to the model. The three-dimensional creep model provided by the present application is very simple, making the results of the non-steady creep behavior during the creep process of the object calculated through it more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0017] Figure 1 It is a flowchart of the method for constructing a three-dimensional creep model provided by an embodiment of the present application.

[0018] Figure 2 It is a general flowchart of the method for constructing a three-dimensional creep model provided by an embodiment of the present application.

[0019] Figure 3 It is a diagram for defining the starting point of the accelerated creep of an object in the triaxial compression creep test provided by an embodiment of the present application.

[0020] Figure 4 It is a one-dimensional creep model of an object provided by an embodiment of the present application.

[0021] Figure 5 It is a comparison diagram of the theoretical curve and the test result for the sandstone embodiment of the present application.

[0022] Figure 6 It is a comparison diagram of the theoretical curve and the test result for the concrete embodiment of the present application.

[0023] Figure 7 It is a comparison diagram of the theoretical curve and the test result for the alloy embodiment of the present application.

[0024] Figure 8 It is a general flowchart of the numerical analysis method of the three-dimensional creep model provided by an embodiment of the present application.

[0025] Figure 9 This is a comparison graph of the numerical simulation creep curve and the test results provided by an embodiment of the present application. Specific implementation manners

[0026] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts belong to the scope of protection of the present application.

[0027] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0028] In an exemplary embodiment, as Figure 1 shown, a method for constructing a three-dimensional creep model of an object is provided, including the following steps.

[0029] Step 201: According to the test data of the object creep test, construct a one-dimensional creep model of an elastic body, a one-dimensional creep model of a fractional-order dashpot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative dashpot; the object is a geotechnical body, concrete, or metal.

[0030] Step 202: According to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order dashpot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative dashpot, construct a three-dimensional creep model of the object.

[0031] By implementing the above steps 201 to 202, the three-dimensional creep model obtained by the present application, which characterizes the non-steady creep characteristics of the object, can calculate the non-steady creep behavior during the creep process of the object. The fractional-order dashpot and the strain-triggered memory-dependent derivative dashpot have fewer parameters. During the process of constructing the three-dimensional creep model of the object, the viscoelasticity of the object is characterized by using the fractional-order dashpot, and the non-linear accelerated creep characteristics of the object are characterized by using the strain-triggered memory-dependent derivative dashpot. By simultaneously using the fractional-order dashpot and the strain-triggered memory-dependent derivative dashpot, the complexity of the three-dimensional creep model of geotechnical bodies, concrete materials, or metal materials can be reduced, and simplicity can be achieved. Too many creep parameters will lead to a decrease in the accuracy of the non-steady creep behavior calculated according to the model during the creep process of the object. The three-dimensional creep model provided by the present application is very simple, making the results of the non-steady creep behavior calculated through it more accurate.

[0032] In another exemplary embodiment of the present application, based on the test data of the object creep test, a one-dimensional creep model of an elastomer, a one-dimensional creep model of a fractional-order viscous pot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative viscous pot are constructed. Specifically, it includes: plotting a creep curve based on the test data of the object creep test. Specifically: performing a triaxial compression creep test on the object at different stress levels to obtain the test data (strain values at each moment) at different stress levels, and plotting creep curves at different stress levels (complete creep curves during the process of the object creeping to failure) based on the test data at different stress levels. Based on the creep curves at different stress levels, the turning point at which the creep deformation rate of the object changes from stable to increasing is used as the starting point for entering the accelerated creep stage. As Figure 3 shown, the creep value corresponding to this point is defined as the strain threshold. When the strain value is lower than this threshold, the object is in the non-accelerated creep stage; once it exceeds this threshold, the object enters the accelerated creep stage, and its creep rate increases accordingly until the specimen fails.

[0033] Based on the creep curve, a one-dimensional creep model of an elastomer, a one-dimensional creep model of a fractional-order viscous pot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative viscous pot are constructed.

[0034] In another exemplary embodiment of the present application, based on the creep curve, a one-dimensional creep model of an elastomer, a one-dimensional creep model of a fractional-order viscous pot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative viscous pot are constructed. Specifically, the creep curve is divided into three stages: decaying creep, constant-rate creep, and accelerated creep. In order to describe the characteristic that the creep rate of the object gradually decreases and tends to be stable with the increase of time in the decaying creep stage and the constant-rate creep stage, a fractional-order viscous pot with fewer parameters is introduced to characterize the viscoelasticity of the object. At the same time, considering that there is a specific strain threshold when the object transitions from the constant-rate creep stage to the accelerated creep stage, a strain-triggered memory-dependent derivative viscous pot with fewer parameters is introduced to describe the accelerated creep characteristics of the object. Therefore, the one-dimensional creep model of the elastomer (the stress-strain relationship of the elastomer) is:

[0035] (1)

[0036] In the formula: represents the stress of the elastomer, is the strain of the elastomer; is the elastic modulus of the elastomer.

[0037] The constitutive equation of the fractional-order viscous pot is:

[0038] (2)

[0039] Among them, represents the stress of the fractional-order viscous pot in the form of a time function, that is, the creep timet The stress of the lower fractional dashpot. Since the stress is constant during the creep process, let , and by using Laplace transform and inverse transform to process formula (2), the one-dimensional creep model of the fractional dashpot can be obtained as:

[0040] (3)

[0041] In the formula, represents the stress of the fractional dashpot, is the viscosity coefficient of the fractional dashpot, is the differential symbol, ( t ) represents the strain of the fractional dashpot in the form of a time function, that is, the strain of the fractional dashpot at the creep time t ; is the gamma function; is the fractional order.

[0042] The constitutive equation of the memory-dependent derivative dashpot with strain trigger is:

[0043] (4)

[0044] Among them, represents the stress of the memory-dependent derivative dashpot with strain trigger in the form of a time function, that is, the stress of the memory-dependent derivative dashpot with strain trigger at the time T corresponding to the accelerated creep stage. Since the stress is constant during the creep process, let , and by using Laplace transform and inverse transform to process formula (4), the one-dimensional creep model of the memory-dependent derivative dashpot with strain trigger can be obtained as:

[0045] (5)

[0046] In the formula, represents the stress of the memory-dependent derivative dashpot with strain trigger, is the viscosity coefficient of the memory-dependent derivative dashpot with strain trigger, is the second-order memory-dependent derivative symbol, (T) represents the strain of the memory-dependent derivative dashpot with strain trigger in the form of a time function, that is, the strain of the memory-dependent derivative dashpot with strain trigger at the time T corresponding to the accelerated creep stage; is the second-order memory-dependent derivative of strain with respect to time, represents creep, represents the strain threshold, is the time delay, e is the natural constant, T represents the time corresponding to the accelerated creep stage; T = t - ta , where t represents the creep time, t a represents the time corresponding to the strain threshold; the strain trigger threshold of the memory-dependent viscous pot with strain trigger is the strain threshold determined in the above test.

[0047] In another exemplary embodiment of the present application, according to the one-dimensional creep model of the elastomer, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, a three-dimensional creep model of the object is constructed, specifically including: according to the one-dimensional creep model of the elastomer, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, a one-dimensional creep model of the object is constructed.

[0048] According to the generalized plastic mechanics theory and the generalized Hooke's law, a three-dimensional creep model of the elastomer is obtained.

[0049] The one-dimensional creep models of the fractional-order viscous pot and the memory-dependent derivative viscous pot with strain trigger are processed by using the generalized plastic mechanics theory to obtain the three-dimensional creep models of the fractional-order viscous pot and the memory-dependent derivative viscous pot with strain trigger.

[0050] According to the one-dimensional creep model of the object, the three-dimensional creep model of the elastomer, the three-dimensional creep model of the fractional-order viscous pot, and the three-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, a three-dimensional creep model of the object is constructed.

[0051] In another exemplary embodiment of the present application, according to the one-dimensional creep model of the elastomer, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, a one-dimensional creep model of the object is constructed. Specifically: based on these three one-dimensional creep models, using the series criterion of the creep theory, a one-dimensional creep model of the object that characterizes the non-steady creep characteristics of the object and is composed of an elastomer, a fractional-order viscous pot, and a memory-dependent derivative viscous pot with strain trigger in series is constructed, as Figure 4 shown.

[0052] In another exemplary embodiment of the present application, the one-dimensional creep model of the object is:

[0053] (6)

[0054] where represents the one-dimensional creep strain of the object in the form of a time function, that is, the one-dimensional creep strain of the object at the creep time t.

[0055] In another exemplary embodiment of the present application, according to the generalized plastic mechanics theory and the generalized Hooke's law, a three-dimensional creep model of the elastic body is obtained. Specifically: According to the generalized plastic mechanics theory, the stress tensor at any point inside the object under a three-dimensional stress state is determined and the deviatoric stress tensor and the spherical stress tensor The relationship expressions between them, as well as the strain tensor and the deviatoric strain tensor and the spherical strain tensor The relationship expressions between them are:

[0056] (7)

[0057] (8)

[0058] (9)

[0059] (10)

[0060] In the formula, is the Kronecker symbol. When i = j , ; i ≠ j When, ; , , respectively represent the first, second, and third principal stresses at any point inside the object; , , respectively represent the strains generated in the directions of the first, second, and third principal stresses at any point inside the object. Using the generalized Hooke's law, the spherical stress tensor and the deviatoric stress tensor of any point inside the object are determined:

[0061] (11)

[0062] (12)

[0063] In the formula, represents the spherical strain tensor at any point inside the object, represents the deviatoric strain tensor at any point inside the object, K , G are the bulk modulus and the shear modulus respectively.

[0064] Substituting formula (11) and formula (12) into formula (8), the three-dimensional creep model of the elastic body is obtained as:

[0065] (13)

[0066] In the formula, represents the strain tensor generated by the elastic body under three-dimensional stress, K and G are the bulk modulus and the shear modulus, respectively.

[0067] In another exemplary embodiment of the present application, the one-dimensional creep models of the fractional-order dashpot and the memory-dependent derivative dashpot with strain trigger are processed by using the generalized plastic mechanics theory to obtain the three-dimensional creep models of the fractional-order dashpot and the memory-dependent derivative dashpot with strain trigger. Specifically, existing research has shown that the deviatoric stress tensor plays a major role in the creep process, and the spherical stress tensor has little effect on the creep of the object. Ignoring the influence of the spherical stress tensor, accordingly, formulas (7) and (8) are processed to obtain , . By analogy with formula (3) according to formula (12), the stress and strain (t) in formula 3 are replaced to obtain and . Furthermore, the replaced formula (3) is as follows:

[0068] = (14)

[0069] Replace the strain tensor and the deviatoric strain tensor in with the strain tensor and generated by the fractional-order dashpot under three-dimensional stress in the form of a time function, and the following formula is obtained:

[0070] (15)

[0071] Substitute formula (14) into formula (15) to obtain the three-dimensional creep model of the fractional-order dashpot:

[0072] (16)

[0073] Among them, represents the deviatoric strain tensor generated by the fractional-order dashpot under three-dimensional stress in the form of a time function, that is, the deviatoric strain tensor generated by the fractional-order dashpot under three-dimensional stress at creep time t, represents the strain tensor generated by the fractional-order dashpot under three-dimensional stress in the form of a time function, that is, the strain tensor generated by the fractional-order dashpot under three-dimensional stress at creep time t.

[0074] Processing formulas (7) and (8) gives , , analogizing formula (5) according to formula (12) and replacing the in formula (5) with , replacing with , and then the replaced formula (5) is:[[]]END]]

[0075] (17)

[0076] Replacing the strain tensor and the deviatoric strain tensor in with the strain tensors and generated by a strain-triggered memory-dependent derivative dashpot under three-dimensional stress in the form of a time function, the following formula is obtained:

[0077] (18)

[0078] Substituting formula (17) into formula (18) gives the three-dimensional creep model of the strain-triggered memory-dependent derivative dashpot:

[0079] (19)

[0080] where represents the deviatoric strain tensor generated by a strain-triggered memory-dependent derivative dashpot under three-dimensional stress in the form of a time function, i.e., the deviatoric strain tensor generated by a strain-triggered memory-dependent derivative dashpot under three-dimensional stress at creep time t, represents the strain tensor generated by a strain-triggered memory-dependent derivative dashpot under three-dimensional stress in the form of a time function, i.e., the strain tensor generated by a strain-triggered memory-dependent derivative dashpot under three-dimensional stress at time T corresponding to the accelerated creep stage.

[0081] In another exemplary embodiment of the present application, constructing the three-dimensional creep model of an object according to the one-dimensional creep model of the object, the three-dimensional creep model of an elastomer, the three-dimensional creep model of a fractional-order dashpot, and the three-dimensional creep model of a strain-triggered memory-dependent derivative dashpot specifically includes: substituting the three-dimensional creep model of the elastomer, the three-dimensional creep model of the fractional-order dashpot, and the three-dimensional creep model of the strain-triggered memory-dependent derivative dashpot into the one-dimensional creep model of the object to obtain the three-dimensional creep model of the object.

[0082] In another exemplary embodiment of the present application, the three-dimensional creep model of the object is specifically:[[]]END]]

[0083] (20)

[0084] Among them, represents the strain tensor generated by the model under three-dimensional stress in the form of a time function, that is, the strain tensor generated by the model under three-dimensional stress at creep time t.

[0085] This application also provides an embodiment. As Figure 2 shown, after constructing the three-dimensional creep model of an object based on the one-dimensional creep model of an elastomer, the one-dimensional creep model of a fractional-order viscous pot, and the one-dimensional creep model of a strain-triggered memory-dependent derivative viscous pot, it further includes: conducting triaxial compression creep tests on sandstone specimens at different stress levels to verify the accuracy and rationality of the three-dimensional creep model of the object when the object is a geotechnical body. The specific steps are as follows.

[0086] Step C1: Conduct triaxial compression creep tests on sandstone specimens at different stress levels, and obtain the creep-time curve, creep rate-time curve, and the starting point of accelerating creep.

[0087] Step C2: Based on the test data (creep-time curve, creep rate-time curve, and the starting point of accelerating creep) obtained in Step C1 and the three-dimensional creep model of the object, use the Levenberg-Marquardt algorithm and the general global optimization algorithm in Origin software to perform parameter identification to obtain the corresponding creep model parameters under each stress state. The specific parameters are shown in Table 1.

[0088] Step C3: Substitute the creep model parameters obtained in Step C2 into the three-dimensional creep model of the object to obtain the specific equation of the three-dimensional creep model of the object.

[0089] Step C4: Based on the specific equation of the three-dimensional creep model of the object obtained in Step C3, generate a theoretical curve characterizing the unstable creep characteristics of sandstone, and compare it with the test results (creep values at each moment) in Step C1. The results are as Figure 5 shown.

[0090] Through Figure 5 it can be concluded that when the object is a geotechnical body, the three-dimensional creep model of the object obtained in this application can accurately describe the three-stage creep characteristics of sandstone under triaxial compression conditions. Especially for the characteristics of the unstable creep stage of sandstone (including the constant-rate creep stage and the accelerating creep stage), the model shows a good fitting effect.

[0091] Table 1 Sandstone creep parameters under triaxial compression

[0092]

[0093] This application also provides an embodiment. A triaxial compression creep test is carried out on concrete specimens under different stress levels to verify the accuracy and rationality of the three-dimensional creep model of the object when the object is made of concrete material. The specific steps are the same as those of the embodiment for processing sandstone above. During the processing, the concrete creep parameters are shown in Table 2. The theoretical curve characterizing the unstable creep characteristics of concrete is compared with the test results (creep values at each moment), and the results are as Figure 6 shown.

[0094] Through Figure 6 it can be concluded that when the object is made of concrete material, the three-dimensional creep model of the object obtained in this application can accurately describe the three-stage creep characteristics of concrete under triaxial compression conditions. Especially for the characteristics of the unstable creep stage of concrete (including the constant-rate creep stage and the accelerating creep stage), the model shows a good fitting effect.

[0095] Table 2 Concrete creep parameters under triaxial compression

[0096]

[0097] This application also provides an embodiment. A uniaxial tensile creep test is carried out on alloy specimens under different stress levels to verify the accuracy and rationality of the three-dimensional creep model of the object when the object is made of metal material. The specific steps are as follows.

[0098] Step C1': Carry out a uniaxial tensile creep test on alloy specimens under different stress levels, and obtain the creep-time curve, creep rate-time curve, and the starting point of accelerating creep.

[0099] Step C2': Based on the test data (creep-time curve, creep rate-time curve, and the starting point of accelerating creep) obtained in Step C1' and the three-dimensional creep model of the object, use the Levenberg-Marquardt algorithm and the general global optimization algorithm in Origin software to perform parameter identification to obtain the corresponding creep model parameters under each stress state. The specific parameters are shown in Table 3 for details.

[0100] Step C3': Substitute the creep model parameters obtained in Step C2' into the three-dimensional creep model of the object to obtain the specific equation of the three-dimensional creep model of the object.

[0101] Step C4': Based on the specific equation of the three-dimensional creep model of the object obtained in Step C3', generate a theoretical curve characterizing the unstable creep characteristics of the alloy, and compare it with the test results (creep values at each moment) in Step C1'. The results are as Figure 7 shown.

[0102] Through Figure 7It can be concluded that when the object is made of a metal material, the three-dimensional creep model of the object obtained in this application can accurately describe the three-stage characteristics of the creep of the alloy under uniaxial tension conditions. In particular, for the characteristics of the unstable creep stage of the alloy (including the constant-rate creep stage and the accelerating creep stage), the model shows a good fitting effect.

[0103] Table 3 Creep parameters of the alloy under uniaxial tension

[0104]

[0105] Taking the creep tests of three materials, namely sandstone, concrete, and alloy, as examples, this application verifies that the three-dimensional creep model of the object can well describe the instantaneous deformation and decelerating creep characteristics of the object in a low-stress state, the instantaneous deformation, decelerating creep, and constant-rate creep characteristics of the object in a medium-stress state, and the instantaneous deformation, decelerating creep, constant-rate creep, and accelerating creep characteristics of the object in a high-stress state. It can more accurately characterize the non-linear characteristics of each creep stage of the object, not only reflecting the creep deformation law of the object but also describing the memory effect of the creep deformation of the object.

[0106] Based on the same inventive concept, the embodiment of this application also provides a rock three-dimensional creep model construction device for implementing the above-mentioned object three-dimensional creep model construction method. The solution provided by this device to solve the problem is similar to the solution described in the above method. Therefore, the specific limitations in one or more of the following embodiments of the three-dimensional creep model construction device can refer to the limitations on the three-dimensional creep model construction method in the above text and will not be elaborated here.

[0107] In an exemplary embodiment, a three-dimensional creep model construction device is provided, including: a one-dimensional creep model construction module for elements, which is used to construct a one-dimensional creep model of an elastic body, a one-dimensional creep model of a fractional-order viscous pot, and a one-dimensional creep model of a strain-triggered memory-dependent derivative viscous pot according to the test data of the object creep test; the object is a geotechnical body, concrete, or metal.

[0108] A three-dimensional creep model construction module for the object, which is used to construct a three-dimensional creep model of the object according to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative viscous pot.

[0109] In an exemplary embodiment, as Figure 8 shown, this application provides a numerical analysis method for a three-dimensional creep model, including: determining the deviatoric strain rate expression of the three-dimensional creep model of the object provided in the above embodiment.

[0110] Determining the three-dimensional increment expression according to the deviatoric strain rate expression.

[0111] Program the three-dimensional incremental expression through the extended function interface of numerical calculation software to obtain the user subroutine of the three-dimensional creep model of the object (creep model numerical program).

[0112] In an exemplary embodiment, the deviatoric strain rate expression of the three-dimensional creep model of the object is specifically:

[0113] (21)

[0114] In the formula, is the total deviatoric strain rate; is the deviatoric strain rate of the elastic body; is the deviatoric strain rate of the fractional-order viscous pot; is the deviatoric strain rate of the strain-triggered memory-dependent viscous pot.

[0115] In an exemplary embodiment, determine the three-dimensional incremental expression according to the deviatoric strain rate expression, and program the three-dimensional incremental expression through the extended function interface of numerical calculation software to obtain the user subroutine of the three-dimensional creep model of the object. Specifically: Based on the central difference theory, determine the three-dimensional incremental expression according to the deviatoric strain rate expression. The incremental form of the specific three-dimensional creep model is:

[0116] (22)

[0117] In the formula, is the total deviatoric strain increment; is the deviatoric strain increment of the elastic body; is the deviatoric strain increment of the fractional-order viscous pot; is the deviatoric strain increment of the strain-triggered memory-dependent viscous pot.

[0118] Under the three-dimensional deviatoric stress state, the form of the deviatoric strain increment of the elastic body is:

[0119] (23)

[0120] In the formula, is a time step within the deviatoric stress increment.

[0121] Under the three-dimensional deviatoric stress state, the form of the deviatoric strain increment of the fractional-order viscous pot is:

[0122] (24)

[0123] Under the three-dimensional deviatoric stress state, the form of the deviatoric strain increment of the strain-triggered memory-dependent viscous pot is:

[0124] (25)

[0125] Combining the partial strain increment form of the creep equations of an elastic body, a fractional-order viscous pot, and a memory-dependent viscous pot with strain trigger under a comprehensive three-dimensional deviatoric stress state, the specific expression of the increment form of the three-dimensional creep model of an object under a three-dimensional stress state is obtained as follows:

[0126] (26)

[0127] According to the central difference principle, the deviatoric stress increment and the partial strain increment can be expressed as:

[0128] (27)

[0129] (28)

[0130] where is the new deviatoric stress increment within a time step ; is the old deviatoric stress increment within a time step ; is the new partial strain increment within a time step ; is the old partial strain increment within a time step .

[0131] Combining equations (26), (27), and (28), and solving for the new deviatoric stress within a time step yields equation (29):

[0132] (29)

[0133] where C and D are intermediate variables.

[0134] (30)

[0135] (31)

[0136] where represents a time step.

[0137] Through the extended function interface (application programming interface) of numerical calculation software, C++ programming is performed on equations (26) to (31) to obtain a user subroutine, and the user subroutine can be called using numerical calculation software.

[0138] In an exemplary embodiment, after obtaining the user subroutine, a triaxial compression numerical simulation test can also be carried out on the sandstone specimen to perform numerical simulation and verify the accuracy and rationality of the user subroutine. The steps are as follows: Triaxial compression numerical simulation tests on sandstone were carried out under different stress levels, and the model parameters were those in Table 1. These parameters were input into the user subroutine for numerical simulation, thereby obtaining the corresponding numerical simulation creep curves, and the results are as Figure 9 shown.

[0139] It can be known through Figure 9 that the creep model numerical program proposed in this application can accurately simulate the three stages of creep of sandstone under triaxial compression, especially the unstable creep stage of sandstone.

[0140] The creep constitutive models built into existing numerical calculation and simulation software often fail to fully consider the accelerating creep characteristics of objects, resulting in limitations when simulating complex underground engineering problems. Since the three-dimensional creep model provided in the above embodiment of this application considers the accelerating creep characteristics of objects, in this embodiment, the three-dimensional increment expression of the above three-dimensional creep model is derived according to the central difference principle. Then, the three-dimensional increment expression is redeveloped using C++ programming to obtain the corresponding application program. The numerical calculation software is used to call the application program to numerically implement the constitutive model built in the commercial numerical calculation software, solve the above limitation problems, and can provide a theoretical basis and implementation means for the analysis of the unstable creep deformation of objects, provide a more accurate tool for the long-term stability analysis of underground engineering structures, and provide a theoretical basis and application method for the long-term performance analysis of underground engineering.

[0141] Based on the same inventive concept, the embodiment of this application also provides a three-dimensional creep model numerical analysis device for implementing the three-dimensional creep model numerical analysis method involved above. The solution provided by this device to solve the problem is similar to the solution described in the above method. Therefore, the specific limitations in one or more of the following embodiments of the three-dimensional creep model numerical analysis device can refer to the limitations on the three-dimensional creep model numerical analysis method in the above text, and will not be repeated here.

[0142] In an exemplary embodiment, a three-dimensional creep model numerical analysis device is provided, including: a deviatoric strain rate expression determination module for determining the deviatoric strain rate expression of the three-dimensional creep model of the object provided in the above embodiment.

[0143] A three-dimensional increment expression determination module for determining the three-dimensional increment expression according to the deviatoric strain rate expression.

[0144] A user subroutine determination module is used to program a three-dimensional incremental expression through an extended function interface of numerical calculation software to obtain a user subroutine of a three-dimensional creep model of an object.

[0145] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0146] Specific examples are used in this article to elaborate on the principles and implementation manners of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A method for constructing a three-dimensional creep model, characterized in that The construction method of the three-dimensional creep model includes: According to the test data of the object creep test, construct the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger; the object is a geotechnical body, concrete or metal; According to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, construct the three-dimensional creep model of the object. Specifically, according to the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, construct the one-dimensional creep model of the object; According to the generalized plastic mechanics theory and the generalized Hooke's law, obtain the three-dimensional creep model of the elastic body; Use the generalized plastic mechanics theory to process the one-dimensional creep model of the fractional-order viscous pot and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger to obtain the three-dimensional creep model of the fractional-order viscous pot and the three-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger; According to the one-dimensional creep model of the object, the three-dimensional creep model of the elastic body, the three-dimensional creep model of the fractional-order viscous pot, and the three-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, construct the three-dimensional creep model of the object; The one-dimensional creep model of the object is: , where represents the one-dimensional creep strain of an object in the form of a time function, represents the stress of an elastomer, represents the elastic modulus of an elastomer, represents the stress of a fractional-order viscous pot, represents the viscosity coefficient of a fractional-order viscous pot, represents the creep time, represents the gamma function, represents the fractional-order, represents creep, represents the strain threshold, represents the stress of a memory-dependent derivative viscous pot with strain trigger, represents the viscosity coefficient of a memory-dependent derivative viscous pot with strain trigger, represents the time delay, represents the time corresponding to the accelerated creep stage, e represents the natural constant; The three-dimensional creep model of the object is: , where represents the strain tensor generated by the model under three-dimensional stress in the form of a time function, represents the deviatoric stress tensor at any arbitrary point inside the object, represents the shear modulus of the object, represents the spherical stress tensor at any arbitrary point inside the object, represents the bulk modulus of the object, represents the Kronecker symbol, represents the viscosity coefficient of the fractional-order dashpot, represents the creep time, represents the fractional order, represents creep, represents the strain threshold, () represents the gamma function, represents the viscosity coefficient of the memory-dependent derivative dashpot with strain trigger, represents the time delay, represents the time corresponding to the accelerated creep stage, e represents the natural constant.

2. The construction method of the three-dimensional creep model according to claim 1, characterized in that According to the test data of the object creep test, construct the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, specifically including: Draw the creep curve according to the test data of the object creep test; Based on the creep curve, construct the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger.

3. The construction method of the three-dimensional creep model according to claim 1, characterized in that According to the one-dimensional creep model of the object, the three-dimensional creep model of the elastic body, the three-dimensional creep model of the fractional-order viscous pot, and the three-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger, construct the three-dimensional creep model of the object, specifically including: Substitute the three-dimensional creep model of the elastic body, the three-dimensional creep model of the fractional-order viscous pot, and the three-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger into the one-dimensional creep model of the object to obtain the three-dimensional creep model of the object.

4. A numerical analysis method for a three-dimensional creep model, characterized in that, The numerical analysis method of the three-dimensional creep model includes: Determine the deviatoric strain rate expression of the three-dimensional creep model of the object in claim 1 above; Determine the three-dimensional increment expression according to the deviatoric strain rate expression; Program the three-dimensional increment expression through the extended function interface of the numerical calculation software to obtain the user subroutine of the three-dimensional creep model of the object.

5. The numerical analysis method of the three-dimensional creep model according to claim 4, characterized in that Determine the three-dimensional increment expression according to the deviatoric strain rate expression, specifically: Based on the central difference theory, determine the three-dimensional increment expression according to the deviatoric strain rate expression.

6. A device for constructing a three-dimensional creep model, characterized in that The construction device of the three-dimensional creep model includes: The one-dimensional creep model construction module of the component is used to construct the one-dimensional creep model of the elastic body, the one-dimensional creep model of the fractional-order viscous pot, and the one-dimensional creep model of the memory-dependent derivative viscous pot with strain trigger according to the test data of the object creep test; the object is a geotechnical body, concrete or metal; The three-dimensional creep model construction module of the object is used to construct the three-dimensional creep model of the object according to the one-dimensional creep model of the elastomer, the one-dimensional creep model of the fractional-order dashpot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative dashpot. Specifically, according to the one-dimensional creep model of the elastomer, the one-dimensional creep model of the fractional-order dashpot, and the one-dimensional creep model of the strain-triggered memory-dependent derivative dashpot, construct the one-dimensional creep model of the object; According to the generalized plastic mechanics theory and the generalized Hooke's law, obtain the three-dimensional creep model of the elastomer; Use the generalized plastic mechanics theory to process the one-dimensional creep model of the fractional-order dashpot and the one-dimensional creep model of the strain-triggered memory-dependent derivative dashpot to obtain the three-dimensional creep model of the fractional-order dashpot and the three-dimensional creep model of the strain-triggered memory-dependent derivative dashpot; According to the one-dimensional creep model of the object, the three-dimensional creep model of the elastomer, the three-dimensional creep model of the fractional-order dashpot, and the three-dimensional creep model of the strain-triggered memory-dependent derivative dashpot, construct the three-dimensional creep model of the object; The one-dimensional creep model of the object is: , where represents the one-dimensional creep strain of an object in the form of a time function, represents the stress of an elastomer, represents the elastic modulus of an elastomer, represents the stress of a fractional-order viscous pot, represents the viscosity coefficient of a fractional-order viscous pot, represents the creep time, represents the gamma function, represents the fractional order, represents creep, represents the strain threshold, represents the stress of a strain-triggered memory-dependent derivative viscous pot, represents the viscosity coefficient of a strain-triggered memory-dependent derivative viscous pot, represents the time delay, represents the time corresponding to the accelerated creep stage, e represents the natural constant; The three-dimensional creep model of the object is: , where represents the strain tensor generated by the model under three-dimensional stress in the form of a time function, represents the deviatoric stress tensor at any point inside the object, represents the shear modulus of the object, represents the spherical stress tensor at any point inside the object, represents the bulk modulus of the object, represents the Kronecker symbol, represents the viscosity coefficient of the fractional-order viscous pot, represents the creep time, represents the fractional order, represents creep, represents the strain threshold, ( ) represents the gamma function, represents the viscosity coefficient of the memory-dependent derivative viscous pot with strain trigger, represents the time delay, represents the time corresponding to the accelerated creep stage, e represents the natural constant.

7. A numerical analysis device for a three-dimensional creep model, characterized in that, The numerical analysis device of the three-dimensional creep model includes: The partial strain rate expression determination module is used to determine the partial strain rate expression of the three-dimensional creep model of the object in claim 1 above; The three-dimensional increment expression determination module is used to determine the three-dimensional increment expression according to the partial strain rate expression; The user subroutine determination module is used to program the three-dimensional increment expression through the extended function interface of the numerical calculation software to obtain the user subroutine of the three-dimensional creep model of the object.

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