WO2022083786A2 - Method for rapid prediction of dynamic modulus of resilience of graded crushed stone considering particle crushing - Google Patents

Abstract

A method for rapid prediction of the dynamic modulus of resilience of graded crushed stone considering particle crushing, the method specifically being: determining physical property parameters of a plurality of groups of graded crushed stone under different grade, different degree of compaction, and different water content conditions; on the basis of dynamic triaxial testing, respectively measuring the dynamic moduli of resilience of the plurality of groups of graded crushed stone, using a three-parameter model to perform prediction, and on the basis of the dynamic moduli of resilience of each group of graded crushed stone obtained in the dynamic triaxial testing, fitting the three-parameter model to obtain model fitting coefficients k1, k2 and k3; and determining contribution ratios of all physical property parameters of each group of graded crushed stone to the fitting parameters k1, k2 and k3 of the three-parameter model, and using a stepwise multiple regression analysis method to determine the correlation between the fitting parameters k1-k3 of the model and each physical property parameter, and thus obtain a rapid prediction formula. The present invention is able to conveniently and accurately obtain dynamic moduli of resilience of graded broken stone, allowing the design and construction of graded crushed stone in road surface structures to be scientifically guided, and guaranteeing engineering quality.

Description

A fast prediction method for dynamic elastic modulus of graded crushed stone considering particle crushing

This application claims the priority of the Chinese patent application filed on June 28, 2021 with the application number 202110718017.0 and the invention titled "Rapid Prediction Method of Dynamic Resilience Modulus of Gradient Crushed Stone Considering Particle Breaking", which The entire contents of this application are incorporated by reference.

technical field

The invention belongs to the technical field of road engineering, and relates to a rapid prediction method for the dynamic resilience modulus of graded crushed stone considering particle crushing.

Background technique

As the graded crushed stone material for the subgrade transition layer and cushion layer, due to the relatively uniform gradation and the relatively small contact area between particles, the particles are prone to crushing under the combined action of load stress and environmental factors, resulting in the deterioration of the crushed stone gradation and mechanical properties. The properties decay, and its resistance to deformation decreases. If the crushed stone material with unreasonable gradation, poor angularity and serious crushing is selected, it will lead to different degrees of settlement and deformation of the roadbed structure after overlaying, which will not only fail to improve the performance of the roadbed, but also greatly reduce the service life of the road structure. Endanger driving safety. Therefore, based on the strategic goals of road engineering stability and durability, it is of great significance to scientifically evaluate the rebound deformation properties of graded crushed stone materials.

At present, the latest editions of "Code for Design of Highway Subgrade" (JTG D30-2015) and "Code for Design of Highway Asphalt Pavement" (JTG D50-2017) both use dynamic resilience modulus as the design parameter for coarse-grained soil or gravel material. Due to the essential difference between the static calculation and the dynamic response of the structure, the early prediction results based on the static modulus, such as CBR conversion and table look-up method, are no longer applicable to the current road design, and it is impossible to accurately control the on-site construction control. guide. At the same time, the test method for the elastic modulus of granular materials proposed in the new version of the specification (Appendix D) requires the use of an expensive dynamic triaxial tester; in addition, the crushed stone material used for the test is loose, the specimen preparation is difficult, and the results are highly discrete. These factors limit the application of dynamic triaxial tester in road engineering. In the existing literature (such as the meso-thermodynamic mechanism of granular material crushing evolution path, Shen Chaomin et al., 2019.1), the research on the evolution law of the elastic modulus of graded crushed stone under different molding methods and moisture content conditions is not in-depth, and it is difficult to be accurate and fast. Prediction of dynamic elastic modulus of graded crushed stone.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a method for rapidly predicting the dynamic resilience modulus of graded crushed stone considering particle crushing, which can conveniently and accurately obtain the dynamic resilience modulus of graded crushed stone, and scientifically guide the graded crushed stone. The design and construction of the pavement structure ensures the quality of the project and solves the problems existing in the prior art.

The technical scheme adopted in the present invention is a method for rapidly predicting the dynamic elastic modulus of graded crushed stone considering particle crushing, which is specifically carried out according to the following steps:

Step S1: Determine the physical parameters of multiple groups of graded crushed stone under the conditions of different gradation, compaction and moisture content, that is, the thickness ratio G/S, the relative crushing potential B _r (w) under different moisture content, and the two-dimensional shape The shape feature parameter λ _F of the index, the shape feature parameter λ _G of the gradient edge index, the shape feature parameter λ _S of the sphericity index, the dry density γ _d , and the moisture content w;

Step S2: According to the dynamic triaxial test, the dynamic elastic modulus of multiple groups of graded crushed stones in step S1 are respectively measured, and the NCHRP 1-28A three-parameter model is used for prediction. The specific formula is as follows:

In the formula, E _y is the elastic modulus of the axial direction; θ _bs is the bulk stress, τ _oct is the octahedral shear stress, and _Pa is the reference atmospheric pressure. Elastic modulus, fitting the three-parameter model to obtain model fitting coefficients k ₁ , k ₂ and k ₃ ;

Step S3: Determine the contribution ratio of all the physical parameters of each group of graded crushed stone to the fitting parameters k ₁ , k ₂ and k ₃ of the three-parameter model, and use the stepwise multiple regression analysis method to determine the fitting parameters k ₁ to k of the model ₃ and the correlations with various physical parameters, respectively, to obtain a fast prediction formula.

The beneficial effects of the present invention are:

1. Using the method for rapidly predicting the dynamic elastic modulus of graded crushed stone obtained by the present invention, it is only necessary to test the basic physical properties of the graded crushed stone material, and then the graded crushed stone material under different working conditions can be more accurately predicted. The prediction of the elastic modulus greatly reduces the test time and difficulty of the test; it can replace the expensive, time-consuming and labor-intensive dynamic triaxial test, which greatly facilitates the design and construction inspection of graded crushed stone. The unit of triaxial test conditions provides obvious engineering convenience and has high market promotion value. Among them, the determination of dry density (γ _d ), moisture content (w), thickness ratio (G/S) and particle breakage are all conventional test methods, which can be tested in general production departments or construction sites, while for the collection In terms of the shape parameters of the material, the present invention adopts the statistical method to predict the overall aggregate, and does not need to carry out a large number of AIMS tests, but only needs to carry out regular sampling inspection of the crushed stone in the reclaiming field, so it does not affect the normal grading. Crushed stone construction and less expensive.

2. Compared with the existing standard method, the method for rapidly predicting the dynamic resilience modulus of graded crushed stone of the present invention can conveniently and accurately obtain the dynamic resilience modulus of graded crushed stone, and guides the grading more conveniently. The design and construction of crushed stone in the pavement structure, and the method can be extended to the design and detection of other granular materials, and has broad application value.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

Figure 1 is a schematic diagram of the shape parameter fitting results.

Figure 2 is a schematic diagram of the calculation of the relative crushing potential.

Figure 3 is a schematic diagram of the relationship between relative crushing potential and moisture content.

Figure 4 is a schematic diagram of the contribution rate of material parameters to model parameters.

FIG. 5 is a schematic diagram of the fitting result of the fast prediction model.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The embodiment of the present invention considers a method for rapidly predicting the dynamic elastic modulus of graded crushed stone with particle crushing, and is specifically carried out according to the following steps:

Step S1: Determine the physical parameters of multiple groups of graded crushed stone under the conditions of different gradation, compaction, and moisture content, that is, the thickness ratio G/S, the relative crushing potential B _r (w) under different moisture content, λ _F , λ _G , λ _S and dry density γ _d , moisture content w;

S1.1: Three kinds of continuously graded graded crushed stone specimens are prepared from limestone aggregates. The initial particle gradation of the specimens is shown in Table 1, and the thickness ratio G of the three grades is calculated by formula (1). /S, 1.22, 1.56, and 1.97, respectively. Then, the optimal water content (OMC) and maximum dry density (γ _dmax ) of the graded crushed stone were obtained through the indoor compaction test. The OMC and γ _dmax corresponding to the three graded crushed stones were: 4.96% and 2.261g, respectively. /cm ³ , 4.81% and 2.307 g/cm ³ , 4.61% and 2.331 g/cm ³ .

In the formula, p ₄ and p ₂₀₀ represent the passing percentage of No. 4 sieve (4.75 mm) and No. 200 sieve (0.075 mm), respectively.

Table 1 Percentage of particles passing through three continuous grades (%)

S1.2: Before preparing graded crushed stone specimens, use the AIMS II system produced by American Pine Company to test the shape parameters of crushed stone aggregates. A 2.0kg sample was randomly weighed in the sample, placed in a plastic tray, and the AIMS system was run to automatically calculate and obtain the two-dimensional shape index (Form2D), gradient angle value (GA) and sphericity index ( SP), and the calculation formula is shown in formulas (2) to (4).

In the formula, θ is the measurement angle; R _θ is the radius of the aggregate in the θ angle direction; Δθ is the measurement angle increment, which is 4°; n is the total number of edge points of the aggregate image; i is the edge of the aggregate image. ith point; d _L is the length of the minimum circumscribed cuboid of coarse aggregate; d _I is the width of the minimum circumscribed cuboid; d _S is the height of the minimum circumscribed cuboid, θ _i represents the measurement angle of the ith point, θ _i+3 Indicates the measurement angle of the i+3th point.

In order to quantitatively evaluate the distribution of aggregate shape parameters, the Weibull cumulative probability distribution was used to fit and analyze the AIMS results of the above three graded aggregates. The proportion parameter λ is related, and the fullness of the curve corresponding to the shape parameter a is mainly affected by the number of samples. Therefore, the proportion parameter λ is used as the shape characteristic quantity to evaluate the influence law of the shape parameter on the elastic modulus of graded crushed stone.

In the formula, F is the cumulative probability; x is the two-dimensional shape index, gradient edge index or sphericity; λ is the scale parameter; α is the shape parameter. x is a general expression, x is a statistical parameter to be solved, and represents any one of the two-dimensional shape index, gradient edge index, or sphericity index. When x is a two-dimensional shape index (Form2D), the fitting results are shown in Figure 1; when x is a gradient edge index or sphericity, the fitting results are basically consistent with Figure 1. According to the test results of the two-dimensional shape index, the gradient edge angle index or the sphericity, the proportional parameter λ and the shape parameter α can be obtained at the same time by fitting with the formula (5). If x represents the two-dimensional shape index, the scale parameter λ is the shape feature parameter of the two-dimensional shape index, denoted as λ _F , and the shape parameter α is the curve fullness parameter α _F ; if x represents the gradient edge index, the scale parameter λ is the gradient The shape feature parameter of the edge index is denoted as λ _G , the shape parameter α is the curve fullness parameter α _G ; if x represents the sphericity index, the proportional parameter λ is the shape feature parameter of the sphericity index, denoted as λ _S , the shape The parameter α is the curve fullness parameter α _S .

S1.3: According to the optimal moisture content (OMC) and maximum dry density (γ _dmax ) of graded crushed stone, for different compaction degrees (93%, 95% and 98%) and moisture content (OMC-1%) , OMC and OMC+1%) of each group of graded crushed stone were formed by static pressing method to form cylindrical standard specimens with a size of 100mm × 200mm. Using the water washing method screening test in the "Highway Engineering Aggregate Test Regulations" (JTG E42-2005), the particle gradation after molding of the test piece is counted, as shown in Figure 2; the corresponding test piece is calculated by formula (6). The relative breaking potential B _r of :

In the formula, B _t represents the total amount of crushing, and B _p represents the crushing potential; the total amount of crushing B _t is determined by the area enclosed by the initial particle gradation curve shown in Figure 2 and the particle gradation curve after molding, and the crushing potential B _p is determined by The initial particle gradation curve shown in Figure 2 and the area enclosed by the dashed line with the maximum particle size of 0.075 mm are determined.

According to the particle crushing conditions under different moisture content, as shown in Fig. 3, the relative crushing potential B _r changes linearly with the increase of moisture content w. Therefore, the influence of moisture content on particle breakage can be quickly predicted.

In the formula, k is the slope of the fitted straight line, and the value of k in this example is 0.042; B _r (w) represents the relative crushing potential under different moisture contents, and B _r (OMC) represents the relative crushing potential under OMC moisture content. , and quickly predict the effect of water content on particle breakage according to the particle breakage under different moisture contents.

Step S2: According to JTG D50-2017 "Specification for Design of Highway Asphalt Pavement" and dynamic triaxial test, 3 kinds of gradations (gradation A, B and C) and 3 kinds of compaction degrees (93%, 95% and 98%) and three moisture contents (OMC-1%, OMC and OMC+1%), and the dynamic resilience modulus of graded crushed stone was predicted by the American NCHRP 1-28A three-parameter model, see formula ( 8).

In the formula, E _y represents the elastic modulus in the axial direction (the loading direction of the specimen); θ _bs represents the bulk stress, or the first invariant of the stress tensor, which is the algebraic sum of the three principal stresses; τ _oct represents the eight Surface shear stress; _Pa is the reference atmospheric pressure; k ₁ , k ₂ and k ₃ are model fitting coefficients; based on the experimental data, k ₁ , k ₂ and k ₃ can be obtained by fitting formula (8) through excel.

Step S3: According to Step S1, obtain the material parameters related to the elastic modulus performance of graded crushed stone, such as thickness ratio (G/S), relative crushing potential (B _r ), AIMS aggregate shape Weibull fitting result, and pass The dry density (γ _d ) and water content (w) obtained from the physical property test were obtained through the Bootstrap forest model in the JMP statistical software to obtain the three fitting parameters k ₁ , k ₂ and the NCHRP 1-28A model. The contribution ratio of k ₃ is shown in Figure 4; the stepwise multiple regression analysis method is used to detect the correlation between the model parameters (k ₁ , k ₂ and k ₃ ) and the physical parameters of various materials, and finally the gradation crushing considering the particle crushing is obtained. The quick prediction formulas for the dynamic elastic modulus of rock are shown in equations (9) to (11):

k ₁ =-1.296+3.082ln(γ _d )-0.434ln(w)+0.238ln(G/S)+0.811λ _S (9)

k ₂ =1.175-0.069ln(G/S)+0.400ln(λ _F )-0.172ln(λ _G )-0.210λ _S (10)

k ₃ =-1.348+0.453B _r (w)+0.024ln(G/S)+0.159ln(λ _G )-0.071λ _S (11)

Among them, the values of the parameters that are not between 0 and 1.0 are in the form of natural logarithms.

Table 3 Aggregate physical property index and three-parameter fitting results (gradation A)

Table 4 Aggregate physical property index and three-parameter fitting results (gradation B)

Table 5 Aggregate physical properties index and three-parameter fitting results (gradation C)

Consistency test is carried out on formulas (9) to (11), as shown in Figure 5, the determination coefficient R ² is all greater than 85%, and the fitting effect can meet the needs of general engineering.

The method for rapidly predicting the resilience modulus adopted in the present invention can comprehensively consider the variation of resilience modulus of graded crushed stone under different gradation, moisture content, particle crushing and aggregate shape, and has clear physical meaning to Describe the effect of material parameters on the behavior of the elastic modulus of graded crushed stone. Combined with the quick prediction formulas (9) to (11), it can be seen that the elastic modulus of graded crushed stone is positively correlated with the maximum dry density and negatively correlated with the moisture content, which is consistent with the actual test results and engineering experience. And within a certain gradation range, increasing the content of coarse particles (G/S) can improve the skeletal properties of the graded crushed stone, thereby improving the resilience performance of the specimen; improving the two-dimensional shape index From2D of the aggregate can significantly improve the gradation. The sensitivity of crushed stone to bulk stress; the shear strain of graded crushed stone is closely related to material gradation and particle breakage. These conclusions can further guide the grading design and quality optimization of the field graded crushed stone, so that the graded crushed stone can obtain a higher dynamic elastic modulus.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims (7)

1. A method for rapidly predicting the dynamic elastic modulus of graded crushed stone considering particle crushing, which is characterized in that the specific steps are as follows:

   Step S1: Determine the physical parameters of multiple groups of graded crushed stone under the conditions of different gradations, different degrees of compaction, and different moisture contents, that is, the thickness ratio G/S, the relative crushing potential B _r (w) under different moisture contents, the second The shape feature parameter λ _F of the dimensional shape index, the shape feature parameter λ _G of the gradient edge index, the shape feature parameter λ _S of the sphericity index, the dry density γ _d , and the moisture content w;

   Step S2: According to the dynamic triaxial test, the dynamic elastic modulus of multiple groups of graded crushed stone in step S1 is measured respectively, and the NCHRP 1-28A three-parameter model is used to predict, as shown in formula (1-1);

   

   In the formula, E _y is the elastic modulus of the axial direction; θ _bs is the bulk stress, τ _oct is the octahedral shear stress, and _Pa is the reference atmospheric pressure. Elastic modulus, fitting the three-parameter model to obtain model fitting coefficients k ₁ , k ₂ and k ₃ ;

   Step S3: Determine the contribution ratio of all the physical parameters of each group of graded crushed stone to the fitting parameters k ₁ , k ₂ and k ₃ of the three-parameter model, and use the stepwise multiple regression analysis method to determine the fitting parameters k ₁ to k of the model ₃ and the correlations with various physical parameters, respectively, to obtain a fast prediction formula.
2. The method according to claim 1, wherein, in the step S3, the fast prediction formula is shown in formulas (1-2) to (1-4):

   k ₁ =-1.296+3.082ln(γ _d )-0.434ln(w)+0.238ln(G/S)+0.811λ _S (1-2)

   k ₂ =1.175-0.069ln(G/S)+0.400ln(λ _F )-0.172ln(λ _G )-0.210λ _S (1-3)

   k ₃ =-1.348+0.453B _r (w)+0.024ln(G/S)+0.159ln(λ _G )-0.071λ _S (1-4)

   Among them, k ₁ , k ₂ , and k ₃ are all fitting parameters of the NCHRP _1-28A model, γd represents the dry density of the corresponding graded crushed stone, w represents the moisture content of the corresponding graded crushed stone, and G/S represents the corresponding The thickness ratio of graded crushed stone, λ _S represents the shape feature parameter corresponding to the sphericity index of the graded crushed stone, λ _F represents the shape feature parameter corresponding to the two-dimensional shape index of the graded crushed stone, and λ _G represents the corresponding grade The shape characteristic parameter of the gradient edge and angle index of the graded crushed stone, B _r (w) represents the relative crushing potential of the graded crushed stone corresponding to different moisture contents.
3. The method according to claim 1, is characterized in that, in described step S1, the thickness ratio G/S of each group of graded crushed stone is obtained according to formula (1-5),

   

   In the formula, p ₄ and p ₂₀₀ represent the passing percentage of the sieve with an aperture of 4.75 mm and a sieve with an aperture of 0.075 mm, respectively.
4. The method according to claim 1, characterized in that, in the step S1, the relative crushing potential B _r (w) under different moisture contents of each group of graded crushed stone is obtained according to the following steps:

   According to the optimum water content OMC and the maximum dry density γ _dmax of the corresponding graded crushed stone, for the compaction degree of 93%, 95% and 98%, the water content is OMC-1%, OMC and OMC+1% respectively. Each group of graded crushed stone is formed by static pressure method to form cylindrical standard specimens, and the sieving test by water washing method is used to calculate the particle gradation after the specimens are formed, and the relative crushing of the corresponding specimens is calculated by formula (1-6). Potential B _r :

   

   In the formula, B _t represents the total amount of crushing, and B _p represents the crushing potential; the total amount of crushing B _t is determined by the area enclosed by the initial particle gradation curve and the particle gradation curve after molding, and the crushing potential B _p is determined by the initial particle gradation curve. and the area enclosed by the dotted line with the maximum particle size of 0.075mm; the relative crushing potential B _r of the specimen changes linearly with the increase of the moisture content w, and the slope of the fitted straight line is k; according to formula (1-7) Quickly determine the relative breakage potential B _r (w) at different moisture contents:

   

   In the formula, B _r (OMC) represents the relative crushing potential under the optimum moisture content OMC.
5. The method according to claim 1, characterized in that, in the step S1, the two-dimensional shape index, gradient edge value and sphericity index of each group of graded crushed stones are obtained through calculation by the AIMS system.
6. method according to claim 5, is characterized in that, the calculation of described two-dimensional shape index, gradient edge angle value and sphericity index see formula (1-9), (1-10), (1-11) respectively:

   

   

   

   In the formula, θ is the measurement angle; R _θ is the radius of the aggregate in the θ angle direction; Δθ is the measurement angle increment; n is the total number of edge points in the aggregate image; i is the ith point on the edge of the aggregate image ; d _L is the length of the smallest circumscribed cuboid of coarse aggregate; d _I is the width of the smallest circumscribed cuboid; d _S is the height of the smallest circumscribed cuboid, θ _i represents the measurement angle of the ith point, θ _i+3 represents the i+th Measured angle at 3 points.
7. The method according to claim 1, characterized in that, in the step S1, the AIMS results of the multiple groups of graded crushed stones described in the step S1 are fitted through the Weibull cumulative probability distribution, and a model is established, as shown in the formula (1- 8):

   

   In the formula, F is the cumulative probability; x is the statistical parameter of AIMS, representing any one of the two-dimensional shape index, gradient edge index or sphericity index; λ is the scale parameter; α is the shape parameter; according to the two-dimensional shape index, gradient The test results of the angularity index or sphericity can be fitted by formula (1-8), and the proportional parameter λ and the shape parameter α can be obtained at the same time; if x represents the two-dimensional shape index, the proportional parameter λ is the two-dimensional shape index. The shape feature parameter, denoted as λ _F , if x represents the gradient edge index, the proportional parameter λ is the shape feature parameter of the gradient edge index, denoted as λ _G ; if x represents the sphericity index, the proportional parameter λ is the sphericity index. Shape feature parameter, denoted as λ _S .

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