CN111475876A - Method for obtaining dynamic resilience mechanical characteristic parameters of granules - Google Patents
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Abstract
The invention relates to the field of civil engineering, and discloses a method for obtaining dynamic resilience mechanical characteristic parameters of aggregates, which comprises the following steps: 1) deducing a stress increment constitutive equation of the granules, and determining a stress loading sequence according to the equation; 2) carrying out a dynamic triaxial test on the granules according to the stress loading sequence, recording the stress level, the stress increment, the corresponding horizontal deformation and the vertical deformation of the test, and calculating the horizontal strain increment and the vertical strain increment; 3) introducing a stress dependence model of dynamic resilience mechanical characteristic parameters; 4) and performing parameter regression analysis, and determining model parameters to obtain a nonlinear dynamic resilience mechanical characteristic parameter prediction model comprising dynamic resilience modulus, Poisson's ratio and orthotropic parameters. The method can establish a model for predicting the dynamic resilience mechanical characteristic parameters of the granules in different stress states, conveniently and accurately obtain the dynamic resilience mechanical characteristic parameters in various stress states, and meet the requirements of engineering construction.
Description
Technical Field
The invention relates to the field of civil engineering, in particular to a method for obtaining dynamic resilience mechanical characteristic parameters of granules.
Background
The aggregate is a common building material in civil engineering and is widely applied to road base layers, cushion layers and the like. The dynamic rebound mechanical properties of the granules have typical stress dependence and orthotropic anisotropy, namely the dynamic rebound modulus and the Poisson ratio of the granules change along with the change of the stress level, and the dynamic rebound modulus and the Poisson ratio are different in different stress directions (horizontal direction and vertical direction). The dynamic resilience mechanical property parameters of the granules directly influence the stress characteristics and structural strength of the base layer, and further influence the design of civil engineering structures and parameters. Therefore, the dynamic rebound mechanical property parameters of the granules under various stress states need to be acquired in civil engineering.
In current engineering applications, granular materials are often considered simply as linear elastic materials; or only the stress dependence of the dynamic modulus of resilience is considered, and the Poisson's ratio is regarded as a constant value; and the pellets were considered as isotropic material, ignoring the orthotropic. These measures, although simplifying the process of solving the mechanical parameters of the granules, inevitably reduce the accuracy thereof, and easily cause unreasonable structural response in the structural calculation. Some researches on stress dependence and orthotropic anisotropy of dynamic rebound mechanical properties of the granules are also carried out recently, but the researches are mainly carried out on the stress dependence and the orthotropic anisotropy of the dynamic rebound mechanical properties of the granules, and a quick and effective acquisition method is not carried out. The method of simulation experiment can only obtain the dynamic resilience mechanical property parameters under the set stress state, and the experiment process is complex and the obtaining speed is slow.
The current method for acquiring dynamic resilience mechanical property parameters is far from meeting the requirements of civil engineering design and acquisition of dynamic resilience mechanical property parameters in various stress states in the construction process, and has great influence on the stability or convenience of engineering construction.
Disclosure of Invention
The invention aims to provide a method for obtaining dynamic resilience mechanical characteristic parameters of granules, which can conveniently and accurately obtain the dynamic resilience mechanical characteristic parameters of the granules.
The method for obtaining the dynamic resilience mechanical characteristic parameters of the granules comprises the following steps: 1) deducing a stress increment constitutive equation of the granules, and determining a stress loading sequence comprising a stress level, a corresponding horizontal stress increment and a corresponding vertical stress increment according to the equation so as to improve a dynamic triaxial test scheme; 2) carrying out a dynamic triaxial test on the granular material test piece according to the stress loading sequence, recording the stress increment of each stress level in the stress loading sequence, measuring the corresponding horizontal deformation and vertical deformation, and calculating the horizontal strain increment and vertical strain increment; 3) introducing a stress dependence model of dynamic resilience mechanical characteristic parameters; 4) performing parameter regression analysis, determining model parameters, and obtaining a nonlinear dynamic resilience mechanical characteristic parameter prediction model; the dynamic resilience mechanical characteristic parameters comprise dynamic resilience modulus, Poisson ratio and orthotropic parameters, and the stress level comprises confining pressure and bias stress.
Preferably, the confining pressure is 10-150 kPa; the bias stress is 10-600 kPa. In the preferred technical scheme, the confining pressure range of 10-150kPa and the bias stress range of 10-600kPa cover the stress level which can be generated in the normal pavement structure, so that the dynamic resilience mechanical characteristic parameters of the aggregates obtained by the dynamic triaxial test can cover all reasonable stress ranges, and are more representative. Meanwhile, the test piece for the dynamic triaxial test cannot be damaged.
Preferably, the stress delta is no more than 10% of the stress level. By the preferred technical scheme, the disturbance amplitude of the stress level can be controlled, namely the stress increment borne by the granules is small, so that the generated strain is small, and the granules can be similar to linear elastic materials.
Preferably, under the action of said stress loading sequence, the pellets are in a state of compression, shear and tension, respectively. By the optimal technical scheme, the dynamic resilience mechanical characteristic parameters of the granules in various stress states can be detected, so that the finally obtained prediction result of the nonlinear dynamic resilience mechanical characteristic parameter prediction model can be close to the actual conditions of the granules in various stress states.
Preferably, in the step 1), the constitutive equation of the stress increment is:
in the formula (I), the compound is shown in the specification,
α is an orthotropic parameter satisfying α2＝Eh/EvAnd α ═ μhh/μvh；ΔσhIs the horizontal stress increment; delta sigmavIs a vertical stress increment; deltahIs the horizontal strain increment; deltavIs the vertical strain increment; mu.shhPoisson's ratio in the horizontal plane (horizontal stress causes strain in the horizontal direction); mu.svhPoisson's ratio in the vertical plane (strain in the horizontal direction due to vertical stress); ehThe dynamic resilience modulus is horizontal; evIs the vertical dynamic modulus of resilience. In the preferred technical scheme, the stress increment is constrained through a stress increment constitutive equation, so that the stress selection of the dynamic triaxial test is more reasonable and richer, and the obtained dynamic resilience mechanical property parameter prediction model is more accurate.
Preferably, in the step 1), the stress loading sequence includes 6 to 12 sets of stress values. In the preferred technical scheme, the stress dependence model of the dynamic rebound mechanics characteristic parameters can be well subjected to parameter regression analysis through dynamic triaxial tests of 6 to 12 groups of different stress values so as to determine model parameters, and the obtained parameters are verified. Meanwhile, the workload of the dynamic triaxial test is not too large.
Preferably, in the step 3), the stress-dependent model is a stress-dependent model based on body stress and shear stress; the bulk stress is a first invariant tensor of stress, and the shear stress is an octahedral shear stress. By the optimal technical scheme, the stress dependence model based on the body stress and the shear stress can more accurately reflect the actual dynamic resilience mechanical characteristic parameters of the granules; the first invariant tensor of stress and the shear stress of the octahedron can reflect the three-dimensional stress states of different points in the granules, and the method is simple to obtain and convenient to use.
Further preferably, the stress-dependent model is:
in the formula, Y is a dynamic resilience mechanical characteristic parameter of the granules; paIs at standard atmospheric pressure; i is1A first invariant tensor of stress; tau isoctOctahedral shear stress; k is a radical of1，k2，k3Are model parameters. Through the preferable technical scheme, the stress dependence characteristic of the dynamic resilience mechanical characteristic parameter of the granular material can be better reflected, so that the dynamic resilience mechanical characteristic parameter of the granular material can be better represented through the stress borne by the granular material.
Preferably, in the step 4), the method for analyzing the parameter regression is to perform nonlinear multi-parameter regression on the stress-dependent model according to results obtained from dynamic triaxial tests performed under different values in the stress loading sequence, so as to determine the model parameters. Through the optimal technical scheme, parameter regression analysis can be conveniently carried out, so that model parameters can be conveniently and accurately determined, and the determined nonlinear dynamic resilience mechanical characteristic parameter prediction model is obtained.
Preferably, the granular material test piece is formed by compacting the granular material; the granular material test piece is a cylindrical test piece with the diameter more than 4 times of the maximum grain diameter of the granular material and the height diameter ratio of 1-3. In the preferred technical scheme, a test piece obtained by compacting the granules with a certain grading can be better subjected to a dynamic triaxial test, so that the body stress and the shear stress are conveniently applied to the granules, and the deformation detection of the granules is also convenient.
According to the method for obtaining the dynamic resilience mechanical characteristic parameters of the granules, the vertical dynamic resilience modulus, the horizontal dynamic resilience modulus, the Poisson ratio in the vertical plane, the Poisson ratio in the horizontal plane and the orthotropic parameters of the granules in different stress states are predicted by establishing the dynamic resilience mechanical characteristic parameter prediction model of the granules, the dynamic resilience mechanical characteristic parameters of the granules in different stress levels can be quickly obtained, the values of the dynamic resilience mechanical characteristic parameters of the granules are more reasonably taken, unreasonable simplification and approximation of the dynamic resilience mechanical characteristic parameters in the existing engineering structure design are improved, and the reasonability of the engineering structure design is improved. Compared with a commonly used two-parameter stress dependence model in the field, the three-parameter stress dependence model used in the invention considers the influence of confining pressure and bias stress simultaneously, so that the mechanical model is more reasonable and the result is more accurate. Compared with the method for acquiring the dynamic resilience mechanical characteristic parameters of the granules only considering the stress dependence of the dynamic resilience modulus in the field, the method for acquiring the dynamic resilience mechanical characteristic parameters of the granules can predict the vertical dynamic resilience modulus, the horizontal dynamic resilience characteristic, the poisson ratio in a vertical plane, the poisson ratio in a horizontal plane and the orthotropic degree of the granules at any stress level. Meanwhile, the problems of stress dependence and orthotropic of the granules are solved, the current granule material characteristic research method is improved and deepened, and the scientificity and reasonability of the value of the granule mechanical characteristic parameters in the civil engineering structural design are improved.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
FIG. 1 is a block diagram of one flow step of the method of the present invention;
FIG. 2 is a graph comparing predicted strain and measured strain in the method of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
In the present invention, the dynamic triaxial test is performed using a dynamic triaxial test system of the UMT-100 type manufactured by IPC of Australia. The linear displacement sensor is DONG-DO type pen type displacement sensor produced by Hangzhou oriental metrology technology company Limited. The used aggregate is limestone macadam. The test process is carried out according to a method of ' road asphalt pavement design Specification (JTG D50-2017) ' issued by the department of transportation of the people's republic of China.
As shown in fig. 1, one embodiment of the method for obtaining dynamic rebound mechanical characteristic parameters of granules of the present invention is performed by the following steps:
1) and deducing a stress increment constitutive equation of the granules, determining a stress loading sequence of the dynamic triaxial test according to the stress increment constitutive equation, and defining the stress loading sequence of the dynamic triaxial test to form an improved stress loading sequence. The stresses of the improved stress loading sequence include a stress loading sequence of stress levels, corresponding horizontal stress increments, and corresponding vertical stress increments capable of imparting a slight stress perturbation to the pellet at each stress level. Stress levels include confining pressure and bias stress. The confining pressure refers to a pressure applied to the pellet from the periphery of the pellet, and by which the pressure can be applied to the pellet from various directions of the pellet. The bias stress refers to an axial pressure that distorts the shape of the pellet. Body stress and shear stress can be obtained through confining pressure and bias stress. The combination of different stresses can reproduce various real stress states of the granules in the construction engineering.
2) And carrying out dynamic triaxial test on the granular material test pieces one by one according to the stress state determined in the improved stress loading sequence, recording various loaded stress states in the test process, and measuring the horizontal deformation delta b and the vertical deformation delta a of the granular material test pieces under the action of corresponding stress. Respectively calculating the horizontal strain of the granular material test piece according to the horizontal length b of the granular material test piece and the vertical length a of the granular material test piece
And vertical strain
Various data measured and calculated are recorded.
3) And introducing a stress-dependent model capable of representing dynamic resilience mechanical characteristic parameters. The dynamic resilience mechanical characteristic parameter can be vertical resilience modulus, horizontal resilience modulus, poisson's ratio in a vertical plane, poisson's ratio in a horizontal plane or orthotropic parameter.
4) According to the dynamic springback mechanical characteristic parameter values and the corresponding stress sequences obtained by the dynamic triaxial test, parameter regression analysis is carried out on the stress dependence model of the dynamic springback mechanical characteristic parameters, the parameters of the stress dependence model of the dynamic springback mechanical characteristic parameters are determined, the obtained parameters are substituted into the stress dependence model of the dynamic springback mechanical characteristic parameters, and the prediction model of the nonlinear dynamic springback mechanical characteristic parameters is obtained.
In some embodiments of the invention, the value of the confining pressure is set between 10kPa and 150kPa and the bias stress is set between 10kPa and 600 kPa. The stress range covers the stress level which possibly occurs in a normal pavement structure, so that the dynamic resilience mechanical characteristic parameters obtained through a dynamic triaxial test cover various different states in a reasonable stress range, the finally obtained dynamic resilience mechanical characteristic parameter prediction model can be better fitted in the normal pavement structure stress level range, and the obtained dynamic resilience mechanical characteristic parameter prediction result is more accurate.
In some embodiments of the invention, a certain stress increment is applied to the test piece at different stress levels during the application of the stress perturbation. The horizontal and vertical stress increments applied are no more than 10% of the corresponding directional stress values. In the tiny stress increment, the pellet can be approximately regarded as being in the linear elasticity category, the stress increment equation is satisfied, and the obtained pellet tangent modulus value is more scientific and reasonable.
In some embodiments of the present invention, in a stress sequence applied to a pellet, by setting a certain horizontal stress increment and a certain vertical stress increment on the basis of applying a certain stress level, three stress states of the pellet can be respectively obtained: a compressed state, a shear state and a tensile state. In particular by maintaining horizontal stress
Without change, applying a vertical stress increment
A compressed state is reached; by applying a negative horizontal stress increment (horizontal stress reduction)
Applying a vertical stress increment
And satisfy
Reaching a shearing state; by applying a horizontal stress increment
Applying a negative vertical stress increment (vertical stress reduction)
A stretched state is reached.
As an embodiment of the present invention, the constitutive equation of stress increment of the pellets is derived as follows:
for a linear elastic continuous medium, the stress-strain constitutive equation has the following general form:
σij＝Cijkl kl(1)
in the formula, σijIs the stress tensor;
Cijklis the elastic coefficient tensor;
klis the strain tensor.
Wherein, CijklThere are 81 independent elements. In the elastic range, the principle of the reciprocal theorem of shear stress and symmetry, CijklReduction to 9 independent elements, see formula (2):
the anisotropic properties of the granules are related to the geometrical properties of the granules, mainly caused by the arrangement difference of the granules under the action of vertical force (compaction and load), so that the difference of the resilience properties mainly exists in the vertical direction and the horizontal direction, namely, the anisotropy exists. Therefore, there are:
in the formula, EhThe dynamic resilience modulus is horizontal;
Evis the vertical dynamic modulus of resilience;
Gvshear modulus in the vertical plane;
μvhpoisson's ratio in the vertical plane (strain in the horizontal direction due to vertical stress);
μhvpoisson's ratio in the vertical plane (strain in the vertical direction due to horizontal stress);
μhhis the poisson's ratio in the horizontal plane (strain in the horizontal direction caused by horizontal stress).
Meanwhile, the symmetry shows that:
therefore, in the aggregate constitutive model considering anisotropy, 5 independent variables are required: eh，Ev，Gv，μvh，μhh。
In an indoor triaxial loading test, if the selected coordinate axis is consistent with the load acting direction, the vertical direction and the horizontal direction are both main stress acting directions, and sigma in the horizontal directionx＝σy. Therefore, equation (3) is further simplified as:
in the formula (I), the compound is shown in the specification,
as previously mentioned, the pellets are of a non-linear elastic material. However, when the stress level varies within a small range, the pellet can be considered approximately as a strand elastic material, and therefore, the following incremental equation is satisfied:
from the above analysis, the orthonormal constitutive model of the pellet is simplified, but all 5 unknowns cannot be obtained from 2 equations for this, the inventors introduced an orthonormal coefficient of α, satisfying α2＝Eh/EvAnd α ═ μhh/μvhSince the dynamic rebound behavior of the pellets is stress-dependent, α is no longer a constant value but also stress-dependent, and thus equation (6) is further reduced to 3 variables Ev，μvhAnd α.
Equation 6 is the stress increment constitutive equation of the granules derived by the present invention, in which,
α is an orthogonality parameter and satisfies α2＝Eh/EvAnd α ═ μhh/μvhThe stress increment constitutive equation applies certain stress disturbance under different stress levels to respectively reach a compression state, a shearing state and a stretching state, so that stress paths are enriched, the stress state is closer to an actual state, certain stress increment is applied to a test piece under different stress levels in the stress disturbance process, in small stress increment, granules are in a linear elasticity category, the stress increment equation is satisfied, the tangent modulus value of the granules is obtained, the stress increment constitutive equation is more scientific and reasonable, and the orthotropic parameter α introduced by the stress increment constitutive equation satisfies α2＝Eh/EvAnd α ═ μhh/μvh. The method can not only characterize the orthotropic of the material, but also reduce the unknown number in the stress increment constitutive equation.
In some embodiments of the invention, the dynamic triaxial test stress loading sequence selected according to the stress increment constitutive equation of the pellet includes 6 to 12 sets of stress values. The vertical dynamic resilience modulus, the horizontal dynamic resilience modulus, the poisson ratio in the vertical plane, the poisson ratio in the horizontal plane and the orthotropic degree value of the granules under 6 to 12 groups of different stress levels can be calculated through 6 to 12 groups of stress values. And (3) carrying out parameter regression analysis on the stress dependence model of the dynamic resilience mechanical characteristic parameters by using 6-12 groups of vertical dynamic resilience modulus, horizontal dynamic resilience modulus, Poisson ratio in the vertical plane, Poisson ratio in the horizontal plane, orthogonal anisotropy degree values and corresponding stress sequence values of the granules under different stress levels, obtaining parameter values in the stress dependence model, and obtaining the prediction model capable of calculating the nonlinear dynamic resilience mechanical characteristic parameters of the granules. The number of dynamic triaxial tests may be any value in the range of 6 to 12, such as 7, 8, 9, 10 or 11. Of course, the number of dynamic triaxial tests may also be selected to be outside the range of 6 to 12, such as 5, 14 or 20, etc., or any other value in between. Although the number of dynamic triaxial tests outside the range of 6-12 times or the fitting accuracy is slightly poor or the test workload is large, the test process and the result are within an acceptable range.
In some embodiments of the invention, when introducing a stress-dependent model of the dynamic rebound mechanics characteristic parameter, the introduced stress-dependent model is a stress-dependent model based on body stress and shear stress. That is, the dynamic rebound mechanics characteristic parameter of the pellet in the model is a function of the bulk stress and the shear stress. The bulk stress uses a first invariant tensor of stress that does not change with changes in the coordinates of the pellets, and the shear stress uses an octahedral shear stress that facilitates simplified calculations.
Specifically, the stress-dependent model of the introduced dynamic resilience mechanical characteristic parameters of the granules is as follows:
in this model, Y is the dynamic rebound mechanics characteristic parameter of the pellet, which can be the vertical dynamic rebound modulus EvHorizontal dynamic modulus of resilience EhPoisson's ratio mu in vertical planevhPoisson's ratio mu in the horizontal planehhOr parameter a. PaIs at standard atmospheric pressure; i is1A first invariant tensor of stress; tau isoctOctahedral shear stress; k is a radical of1，k2，k3Are model parameters. On the basis of the constitutive equation (6) of stress increment of the granules, the inventor selects the vertical dynamic rebound modulus E for convenient calculationvPoisson ratio mu in vertical planevhAnd the reciprocal 1/A of the parameter A as a variable, where A ═ 1-. mu.hh)/Eh＝(1-αμvh)/(α2Ev) The anisotropy variable α is contained in parameter A. obviously, Ev，μvhAnd 1/A both have stress dependence, for which the stress dependence is characterized using a stress-dependent model:
in the formula K1To K9For different model parameters, the meaning of the other parameters is as described above.
The expressions (7) to (9) respectively represent the vertical dynamic modulus of resilience EvPoisson ratio mu in vertical planevhAnd the stress dependence model of parameter A, while the horizontal dynamic modulus of resilience EhAnd Poisson's ratio μ in the horizontal planehhThen the data can be passed through formula α respectively2＝Eh/EvAnd α ═ μhh/μvhAnd (4) calculating.
By repeatedly loading the triaxial test, model parameter K in (9) to (11) is corrected1～K9By performing nonlinear fitting, E can be solvedv，μvhAnd 1/a. α can be represented by a ═ 1- μhh)/Eh＝(1-αμvh)/(α2Ev) Solving is carried out, and E is further solvedh，μhh。
Compared with the stress dependence of the dynamic rebound modulus in the field, the stress dependence of the dynamic rebound modulus and the dependence of the Poisson ratio and the orthotropic are considered in the stress dependence model of the dynamic rebound mechanical characteristic parameters of the granules, and the introduced three-parameter stress dependence model not only represents the dynamic rebound modulus, but also can be used for representing the Poisson ratio and the orthotropic parameters. The obtained non-linear prediction model of the granules can predict the vertical dynamic resilience modulus, the horizontal dynamic resilience characteristic, the poisson ratio in a vertical plane, the poisson ratio in a horizontal plane and the degree of orthotropic of the granules at any stress level. Meanwhile, the stress dependence and the orthotropic problem of the granules are solved, the currently common granule characteristic research method is improved and deepened, and the scientificity and the rationality of the value of the mechanical characteristic parameters of the granules are improved.
In some embodiments of the present invention, in performing the parametric regression analysis, the adopted parametric regression analysis method is to perform nonlinear multi-parameter regression analysis on the stress-dependent model according to the results obtained from the dynamic triaxial tests performed under different stress values in the stress loading sequence and the corresponding stress values, and determine the parameter values of the stress-dependent model. And replacing parameters in the stress dependence model with the obtained parameter values to obtain a prediction model of the nonlinear dynamic resilience mechanical characteristic parameters. The fitted correlation coefficient R can also be calculated in the nonlinear multi-parameter regression analysis process2And performing correlation verification on the prediction result of the obtained prediction model to verify the accuracy of the prediction result.
In some embodiments of the present invention, a granular material having a certain gradation (distribution of particle sizes) is selected, compacted and formed into a cylindrical test piece having a diameter of 4 times or more the maximum diameter of the granular material and a height-to-diameter ratio of 1 to 3 at a specific water content, and a dynamic triaxial test is performed using the test piece.
The following is a specific example illustrating a specific operation procedure of the method for obtaining the dynamic rebound mechanical characteristic parameter of the pellet of the present invention.
Selecting granules with the maximum nominal grain diameter of 19mm, and compacting and molding under the optimal water content of 7.5%. Specifically, the pellets may be compacted using a 4.54kg drop weight falling from a 457mm high free fall. In order to ensure the compaction effect, the test piece is compacted by layering, the thickness of each layer is 50mm, and the test piece is hammered for 50 times. Finally, the mixture is compacted and formed into a cylindrical pellet test piece with the diameter of 100mm and the height of 200 mm.
The stress loading sequence shown in the table 1 is selected according to the material characteristics and engineering requirements to carry out the repeated loading dynamic triaxial test of the multi-stage stress level. Vertical stress σ applied during the testvAnd horizontal stress σhSee columns 2 and 3, respectively, of table 1; and maintaining the vertical stress sigmavAnd horizontal stress σhApplying stress disturbance to the test piece under the condition of no change, wherein the applied disturbance stress is respectively maintaining horizontal stress
Invariably (
0), applying a vertical stress increment
Forming a compressive stress state; applying a negative horizontal stress increment
By simultaneous application of a vertical stress increment
And satisfy
Forming a shear stress state; applying a horizontal stress increment
While applying a negative vertical stress increment
A tensile stress state is formed. The applied stress increments are shown in columns 4 through 9, respectively, of table 1. And (3) lubricating two ends of the test piece by adopting a plastic film and lubricant method during the dynamic triaxial test so as to eliminate the influence of end effects on the test result in the test process.
TABLE 1 Multi-stage stress level repeated loading triaxial test recording table
Recording the horizontal displacement and the vertical displacement of the test piece under different stress levels in the test process, and calculating the horizontal strainbAnd vertical straina。
Stress-dependent model for dynamic resilience mechanical property parameters of introduced aggregates
Using this model to characterize the vertical dynamic modulus of restitution EvPoisson's ratio mu in the vertical planevhAnd the stress dependence of parameter A, as shown in the following formulas:
using non-linearitiesRegression was performed on the above equation by multiparameter fitting (specifically, non-linear fitting was performed using the Solver program in Excel), and the error between the calculated strain and the measured strain calculated by equation 6 was minimized to obtain the dynamic modulus of restitution EvPoisson ratio muvhAnd parameter a the parameters of the stress model are shown in table 2.
TABLE 2 dynamic rebound mechanics Properties parameters
The model parameters in Table 2 are used to replace the parameters k in the above formula1To k is9Obtaining the following nonlinear dynamic resilience mechanical characteristic parameter prediction models:
the comparison between the predicted strain and the measured strain obtained by using the above prediction model is shown in fig. 2, and it can be seen from fig. 2 that the predicted strain and the measured strain are well matched. Coefficient of correlation R2The dynamic characteristic parameter prediction model is more than 99%, and the obtained nonlinear dynamic resilience mechanical characteristic parameter prediction model has high accuracy and reliability. The prediction model is adopted to predict the nonlinear dynamic resilience mechanical characteristic parameters, and the prediction result is accurate and reasonable.
In conclusion, the invention provides a method for conveniently and quickly acquiring dynamic resilience mechanical characteristic parameters of granules. According to the method for obtaining the dynamic resilience mechanical characteristic parameters of the granules, a certain stress disturbance is applied under different stress levels through the stress increment constitutive equation to respectively reach a compression state, a shearing state and a stretching state, so that the stress is enrichedIn the stress disturbance process, a certain stress increment is applied to the test piece under different stress levels, and in the tiny stress increment, the granules are in the linear elasticity category, so that the stress increment equation is satisfied, the tangent modulus value of the granules is obtained, and the method is more scientific and reasonable2＝Eh/EvAnd α ═ μhh/μvh. The method can not only characterize the orthotropic of the material, but also reduce the unknown number in the stress increment constitutive equation. The method can not only characterize the orthotropic of the material, but also reduce the unknown number in the stress increment constitutive equation. The three-parameter stress dependence model used in the invention not only represents the dynamic resilience modulus, but also can be used for representing Poisson's ratio and orthotropic parameters. The obtained nonlinear dynamic resilience mechanical characteristic parameter prediction model can predict the dynamic resilience modulus, the Poisson ratio and the degree of orthotropic under various stress levels. Meanwhile, the problems of stress dependence and orthotropic of the granules are solved, the current granule material characteristic research method is improved and deepened, and the scientificity and reasonability of the value of the granule mechanical characteristic parameters in the civil engineering structural design are improved.
In the description herein, references to the description of the term "one embodiment," "some embodiments," or "an implementation" or the like are intended to mean that a particular feature in connection with the embodiment or implementation is included in at least one embodiment or implementation of the present invention. The above-described schematic representations of terms are not necessarily intended to be the same embodiment or implementation. Furthermore, the particular features described may be combined in any suitable manner in any one or more of the embodiments or implementations. Furthermore, those of skill in the art may combine and combine features of different embodiments or implementations and features of different embodiments or implementations in this specification without contradiction.
The preferred embodiments of the present invention have been described above in detail, but the present invention is not limited thereto. Within the scope of the technical idea of the invention, many simple modifications can be made to the technical solution of the invention, including combinations of various technical features in any other suitable way, and these simple modifications and combinations should also be regarded as the disclosure of the invention, and all fall within the scope of the invention.
Claims (10)
1. A method for obtaining dynamic resilience mechanical characteristic parameters of granules is characterized by comprising the following steps:
1) deducing a stress increment constitutive equation of the granules, and determining a stress loading sequence comprising a stress level, a corresponding horizontal stress increment and a corresponding vertical stress increment according to the equation so as to improve a dynamic triaxial test scheme;
2) carrying out a dynamic triaxial test on the granular material test piece according to the stress loading sequence, recording the stress increment of each stress level in the stress loading sequence, measuring the corresponding horizontal deformation and vertical deformation, and calculating the horizontal strain increment and vertical strain increment;
3) introducing a stress dependence model of dynamic resilience mechanical characteristic parameters;
4) performing parameter regression analysis, determining model parameters, and obtaining a nonlinear dynamic resilience mechanical characteristic parameter prediction model;
the dynamic resilience mechanical characteristic parameters comprise dynamic resilience modulus, Poisson ratio and orthotropic parameters, and the stress level comprises confining pressure and bias stress.
2. The method of claim 1, wherein the confining pressure is 10-150 kPa; the bias stress is 10-600 kPa.
3. The method of claim 1, wherein the stress delta is no more than 10% of the stress level.
4. The method of claim 1, wherein under the stress loading sequence, the pellets are in a compressed state, a shear state, and a tensile state, respectively.
5. The method according to claim 1, wherein in step 1), the stress increment constitutive equation is:
in the formula (I), the compound is shown in the specification,
α is an orthotropic parameter satisfying α2＝Eh/EvAnd α ═ μhh/μvh；
ΔσhIs the horizontal stress increment;
Δσvis a vertical stress increment;
Δhis the horizontal strain increment;
Δvis the vertical strain increment;
μhhpoisson's ratio in the horizontal plane (horizontal stress causes strain in the horizontal direction);
μvhpoisson's ratio in the vertical plane (strain in the horizontal direction due to vertical stress);
Ehthe dynamic resilience modulus is horizontal;
Evis the vertical dynamic modulus of resilience.
6. The method of claim 1, wherein in step 1), the stress loading sequence includes 6-12 sets of stress values.
7. The method according to claim 1, wherein in step 3), the stress-dependent model is a stress-dependent model based on bulk stress and shear stress; the bulk stress is a first invariant tensor of stress, and the shear stress is an octahedral shear stress.
8. The method of claim 7, wherein the stress-dependent model is:
in the formula, Y is a dynamic resilience mechanical characteristic parameter of the granules;
Pais at standard atmospheric pressure;
I1a first invariant tensor of stress;
τoctoctahedral shear stress;
k1，k2，k3are model parameters.
9. The method according to claim 1, wherein in the step 4), the method of parametric regression analysis is to perform nonlinear multi-parameter regression on the stress-dependent model according to the results of dynamic triaxial tests performed under different stress states in the stress loading sequence to determine the model parameters.
10. The method of any one of claims 1 to 9, wherein the pellet specimen is compacted from the pellets; the granular material test piece is a cylindrical test piece with the diameter more than 4 times of the maximum grain diameter of the granular material and the height diameter ratio of 1-3.
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| CN112182716A (en) * | 2020-10-10 | 2021-01-05 | 长沙理工大学 | Method for obtaining response modulus of granular material layer structure |
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| CN112765825A (en) * | 2021-01-27 | 2021-05-07 | 长沙理工大学 | Roadbed surface displacement response determination method considering transverse isotropy and modulus nonlinear distribution, application, equipment and storage medium |
| CN112765825B (en) * | 2021-01-27 | 2022-07-08 | 长沙理工大学 | Roadbed surface displacement response determination method considering modulus nonlinear distribution |
| CN113075027A (en) * | 2021-04-27 | 2021-07-06 | 长沙理工大学 | Test device and method for measuring dynamic elastic modulus of soil body model |
| CN113075027B (en) * | 2021-04-27 | 2022-05-31 | 长沙理工大学 | Test device and method for measuring dynamic elastic modulus of soil body model |
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