Construction method of polyurethane grouting constitutive model considering damage and compaction coupling effect

Abstract

The application discloses a kind of polyurethane grouting constitutive model construction method considering damage and compaction coupling effect, step 1: the material macroscopic stress response is decomposed into the damage term caused by cell wall rupture and the compaction term caused by pore compaction;Step 2: based on Weibull distribution, establish damage evolution equation, combined with initial secant modulus to establish damage term mathematical expression;Step 3: draw lessons from the thought of Avalle model to build compaction strengthening function;Step 4: the damage term and compaction term are superimposed to form coupled constitutive model;Step 5: through uniaxial compression test data, model parameters are jointly calibrated using least squares method.The model parameters of the application have clear physical meaning, and the calibration method is simple and efficient, which can quickly predict the stress-strain relationship of polyurethane grouting material at different loading stages in engineering site, and is suitable for road repair, tunnel reinforcement and other fields.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of road and railway engineering materials, and in particular to a method for constructing a polyurethane grouting constitutive model considering the coupling effect of damage and compaction. BACKGROUND

[0002] Polyurethane grouting materials are widely used in pavement structure layer repair, tunnel reinforcement and other engineering fields due to their controllable curing rate, high mechanical strength, good adaptability and foamable forming characteristics. During service, polyurethane grouting materials exhibit significant nonlinear mechanical response under different strain rates and loading modes, including an initial elastic stage, a damage accumulation stage, and a compaction strengthening stage at high strain.

[0003] Currently, researchers have established a large number of constitutive models to describe the stress-strain behavior of polyurethane grouting materials. For example, the Gibson model takes into account the damage effect and can better describe the stress-strain behavior of polyurethane foam materials, but the model parameters must be obtained through microstructure analysis, which limits its practicality. Although the Avalle model overcomes the above shortcomings, it is relatively complex and only considers the compaction effect, and the parameters lack physical significance. Empirical models are relatively simple to establish and are usually obtained by directly fitting the stress-strain curves of experiments using polynomials, multi-segment functions or power functions, but they also have the shortcomings of lacking physical significance and poor generalizability. Under external load, the mechanical response of polyurethane materials can be considered as a coupling process between the damage effect caused by bubble wall damage and the strengthening effect caused by pore compaction, as shown in the coupling diagram Figure 1 However, the coupling effect of the two effects has not been considered in existing constitutive models. In summary, it is of great significance to establish an accurate constitutive model for predicting the mechanical response of materials under different working conditions, optimizing engineering design parameters and guiding construction control. SUMMARY

[0004] In view of the deficiencies in the prior art, a polyurethane grouting material constitutive model considering the coupling effect of damage and compaction is provided, which can accurately predict the stress-strain behavior of the material throughout the loading process and is of great significance for optimizing engineering design parameters and guiding construction control.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] A method for constructing a polyurethane grouting material constitutive model considering the coupling effect of damage and compaction, comprising:

[0007] Step 1: decompose the macroscopic stress response of the material into a damage term caused by bubble wall rupture and a compaction term caused by pore compaction;

[0008] Step 2: Construct the damage evolution equation based on the Weibull distribution, and establish the mathematical expression of the damage term combined with the initial secant modulus;

[0009] Step 3: Construct the pressure densification function by referring to the Avalle model idea;

[0010] Step 4: Superimpose the damage term and the pressure term to form the coupled constitutive model;

[0011] Step 5: Through the uniaxial compression test data, the least square method is used to jointly calibrate the model parameters.

[0012] Further, the initial secant modulus is obtained by linear fitting of the initial segment of the stress-strain curve.

[0013] Further, the step 1 specifically includes the damage term caused by the rupture of the cell wall And the pressure term caused by the pore pressure is , obtaining

[0014] .

[0015] Further, the step 2 specifically includes that according to the measured stress-strain curve, the damage factor , so the damage term is:

[0016] ;

[0017] Assume that the damage development satisfies the Weibull distribution:

[0018] ;

[0019] Integrate equation (3) to obtain the damage factor D is:

[0020] ;

[0021] Substitute equation (4) into equation (1) to obtain the damage term:

[0022] ;

[0023] In the formula is the Weibull distribution parameter.

[0024] Further, the step 3 specifically includes that by means of the Avalle model idea, the pressure densification function is described by the following formula:

[0025] .

[0026] Furthermore, step 4 specifically includes substituting formulas (5) and (6) into (1) to obtain the final expression of the material constitutive model:

[0027] ;

[0028] In the formula, B and n are model parameters.

[0029] Furthermore, the material constitutive model is simplified into a two-stage model, namely:

[0030] Ignoring the influence of the compaction effect before loading, equation (7) can be considered as a two-stage model, that is, when hour

[0031] ;

[0032] when hour

[0033] ;

[0034] in, Peak intensity The corresponding strain, at the peak stress point, The following relationship exists:

[0035] ;

[0036] .

[0037] Furthermore, in step 5, the least squares objective function for the model predictions and experimental values ​​is:

[0038] ;

[0039] in, E Characterizes the overall stiffness of the material in the initial stage of loading; The average critical strain level required to characterize the rupture of the bubble wall; It reflects the discreteness of damage; B characterizes the extent of stress recovery after the pores are compacted in the high strain stage; n represents the growth rate of the compaction effect with increasing strain.

[0040] Furthermore, the parameters are calibrated using a global optimization algorithm for coarse search, followed by a nonlinear least squares algorithm for local fine optimization.

[0041] Furthermore, the convergence criterion of the optimization algorithm is: the relative rate of change of the parameters is less than... And the change in the objective function is less than .

[0042] The present invention has the following technical effects:

[0043] The application fully describes the mechanical behavior of the polyurethane grouting material in the whole loading process by coupling the damage development and the compaction effect. The model parameters have clear physical meanings, the calibration method is simple and efficient, the prediction precision is high, and the method is suitable for rapid evaluation of material performance in engineering field. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 A schematic diagram for considering the coupling effect of damage and compaction effect of the application;

[0045] Figure 2 A comparison chart of the polyurethane grouting material mechanical constitutive model involved in the polyurethane grouting material method considering the coupling effect of damage and compaction effect of the application and the test results. DETAILED DESCRIPTION

[0046] In order to make the purpose, advantages and characteristics of the application more obvious, the application will be further described in detail below in combination with the drawings and specific embodiments.

[0047] The constitutive model construction method of the polyurethane grouting material considering the coupling effect of damage and compaction provided by the embodiment includes the following steps:

[0048] 1) The macroscopic stress response of the material is decomposed into two parts: a damage term caused by the rupture of the bubble wall and a compaction term caused by the compaction of the pore , to obtain

[0049] ;

[0050] 2) The mathematical construction of the damage term is carried out, and the specific process is as follows.

[0051] ① According to the measured stress-strain curve, the material is approximately linear elastic in the initial stage, and the initial stiffness is represented by the secant modulus E . With the progress of loading, the damage factor is introduced due to the continuous development of material damage, so the damage term is:

[0052] ;

[0053] ② It is assumed that the damage development satisfies the Weibull distribution:

[0054] ;

[0055] Integrating equation (3), the damage factor D is obtained as:

[0056] ;

[0057] ③Put (4) back into (1) to get the damage term:

[0058] ;

[0059] where m , f are the Weibull distribution parameters.

[0060] 3) Develop the compaction term Mathematical construction, the specific process is as follows.

[0061] With the loading, the material is constantly compacted, the strength and stiffness are constantly restored, the specimen mainly shows damage when the deformation is small, and when the deformation is large, the compaction effect is dominant. Introduce the compaction strengthening function, help Avalle model idea, use the following formula for description:

[0062] ;

[0063] 4) Put formula (5), (6) into (1) to get the final expression of the material constitutive model:

[0064] ;

[0065] where B, n is the model parameter.

[0066] Further: if the influence of compaction effect before loading is ignored, formula (7) can be considered as a two-stage model, that is

[0067] When ,

[0068] ;

[0069] When ,

[0070] ;

[0071] where, is the peak strength corresponding to the strain, and at the peak stress point, there should be the following relationship:

[0072] ;

[0073] ;

[0074] The following are the parameter calibration steps:

[0075] 1) Obtain the stress-strain data set through uniaxial compression test , covering the whole process from initial loading to high strain stage.

[0076] 2) The coupling constitutive model proposed in the application is adopted:

[0077] ;

[0078] Wherein :

[0079] ;

[0080] E The initial secant modulus is obtained by fitting the initial section of the stress-strain curve obtained by experiment, is a parameter to be calibrated.

[0081] 3) The least square objective function is constructed:

[0082] ;

[0083] 4) Initial value setting and constraint condition: The peak strain is taken, m The initial value is 2-5, B The initial value is an approximate value of the stress level in the high strain stage, n The initial value is 1-3; the constraint condition is .

[0084] 5) Global iterative optimization:

[0085] The global optimization algorithm is used for coarse search to obtain the global optimal region; the global optimal solution is taken as the initial value, and the nonlinear least square algorithm is used for local fine optimization; in each iteration, the model calculation and the test data are compared point by point, and the cumulative error is taken as the evaluation index.

[0086] 6) Convergence criterion: when the relative change rate of parameters is less than and the change amount of the objective function is less than , it is considered that the optimization converges.

[0087] 7) Result verification: output fitting value, and draw a comparison diagram of the fitting curve and the experimental curve. Figure 1 The black line in the figure is the stress-strain data of the polyurethane grouting material measured by the uniaxial compression test, and the blue line is the predicted value by the constitutive model. It can be seen that the constitutive model proposed in the application can well describe the stress-strain development law of the polyurethane grouting material under uniaxial compression state.

[0088] The model is suitable for predicting the mechanical properties and construction control of polyurethane grouting materials in the fields of pavement repair, tunnel reinforcement and the like.

[0089] The above embodiments are only used to illustrate the patent of the application, but not to limit the patent of the application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the patent of the application. Therefore, all equivalent technical solutions belong to the patent of the application. The patent protection scope of the patent of the application should be defined by the claims. The contents not described in detail in the specification belong to the prior art known by those skilled in the art.

Claims

1. A method for constructing a polyurethane grouting constitutive model considering damage and compaction coupling effects, characterized in that, The application relates to a material constitutive model for a porous material. Step 1: decomposing the material macro stress response into a damage term caused by cell wall rupture and a compaction term caused by pore compaction; Step 2: constructing a damage evolution equation based on a Weibull distribution and combining an initial secant modulus to establish a mathematical expression of the damage term; Step 3: constructing a compaction strengthening function by referring to the Avalle model thought; Step 4: superimposing the damage term and the compaction term to form a coupled constitutive model; Step 5: jointly calibrating model parameters by adopting a least square method through uniaxial compression test data; The step 4 specifically comprises substituting formulas (5) and (6) into (1) to obtain a final expression of the material constitutive model: ; In the formula, B represents the stress recovery amplitude of pores after compaction in a high strain stage; and n represents the growth rate of the compaction effect with the increase of strain; The material constitutive model is simplified into a two-stage model, namely: Neglecting the effect of preloading compaction, equation (7) can be considered as a two-stage model, i.e., when time ; When time ; wherein is the peak intensity corresponding strain, at the peak stress point, there is a relationship: ; ; The step 5 is a least square objective function of a model prediction value and a test value: ; wherein, E B characterizes the overall stiffness of the material at the beginning of loading; B characterizes the average critical strain level required for cell wall rupture; reflects the damage dispersion; B characterizes the amplitude of stress recovery after the pores are compacted at high strain stage; n indicates the growth rate of the compaction effect with strain increase.

2. The method of claim 1, wherein, The initial secant modulus is obtained by linear fitting of an initial section of a stress-strain curve.

3. The method of claim 1, wherein, The step 1 specifically includes a damage term caused by cell wall rupture and a compaction term caused by pore compaction , to obtain 。 4. The method of claim 1, wherein, The step 2 specifically comprises, according to the measured stress-strain curve, calculating the damage factor Therefore, the damage term is: ; It is assumed that damage development satisfies a Weibull distribution: ; Integrating equation (3) gives the damage factor D is: ; Substituting formula (4) into formula (1) to obtain a damage term: ; In the formula is a Weibull distribution parameter.

5. The method of claim 1, wherein, The step 3 specifically comprises adopting the following formula to describe the compaction strengthening function by means of the Avalle model thought: 。 6. The method of claim 1, wherein, The calibration of the parameters adopts a global optimization algorithm for coarse search and then adopts a nonlinear least square algorithm for local fine optimization.

7. The method of claim 6, wherein, The convergence criterion of the optimization algorithm is that the relative change rate of the parameters is less than 10 -6 and the change amount of the objective function is less than 10 -8 .

Images