An asphalt pavement structure based on fabricated phosphogypsum-based layer and a design method thereof

Abstract

The application discloses an asphalt pavement structure based on an assembled phosphogypsum base layer and a design method thereof. The pavement structure design method firstly takes the phosphogypsum base material as a pavement base layer, and drafts an asphalt pavement structure; the thicknesses of various structural layers in the asphalt pavement structure are preliminarily determined according to the asphalt pavement design specification and highway traffic volume; the structural layers in the asphalt pavement structure and the thicknesses of the corresponding structural layers are selected as x factors and n levels for orthogonal experiment, and pavement structure design indexes are calculated; range analysis and variance analysis are carried out on the pavement structure design indexes, the main influencing factors of the mechanical properties of the pavement structure and the optimal combination of the structural layers with different thicknesses are determined, and the significance level of the main influencing factors is judged; finally, according to the range analysis and variance analysis results, the optimal thickness combination of the various structural layers meeting the pavement structure performance is selected, so that the best asphalt pavement structure based on the assembled phosphogypsum base layer is obtained, and the asphalt pavement structure has good popularization and application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of road engineering, and particularly relates to an asphalt pavement structure based on an assembled phosphogypsum base and a design method thereof. BACKGROUND

[0002] The asphalt pavement is a pavement formed by using asphalt material as a binder to bond mineral aggregate to build a surface layer and various base layers (sometimes containing functional layers). The asphalt pavement structure layer is composed of three parts: a surface layer, a base layer and a subbase layer. More than 90% of the asphalt pavement base layers and subbase layers of high-grade highways in China adopt semi-rigid materials, and the semi-rigid base asphalt pavement has become the main structure form of the asphalt pavement of high-grade highways in China.

[0003] Although the semi-rigid base asphalt pavement has been widely applied, it has some insurmountable deficiencies. For example, the traditional cement stabilized gravel base asphalt pavement will generate a large tensile stress in the running direction at the base layer bottom under the action of vehicle load and environmental load, and after the construction of the cement stabilized gravel base material is completed, the material will generate drying shrinkage and temperature shrinkage stress with the change of humidity and temperature, resulting in cracking, and then transmitting to the asphalt surface layer to form a reflection crack, causing damage to the local pavement structure.

[0004] Phosphogypsum is a solid waste produced by industrial wet-process production of phosphoric acid, and the degree of resource recycling of phosphogypsum is relatively low. The main disposal method of phosphogypsum in China is stacking, which occupies a large amount of land and pollutes the groundwater, soil and vegetation near the stacking site. The water-soluble pollutants such as phosphorus and fluorine in phosphogypsum can be greatly reduced after high-temperature calcination, achieving harmless treatment, and the calcined phosphogypsum has good mechanical properties. However, the initial setting time of phosphogypsum material is short, which is not conducive to on-site construction and quality control. The prefabrication of phosphogypsum into assembled base blocks can overcome the material defects of phosphogypsum itself, thereby having the potential to replace the existing pavement base materials.

[0005] At present, the annual consumption of aggregate is large, the mining of aggregate is destructive, and the economy is not good, so it is urgent to find a substitute resource. Therefore, the development of an asphalt pavement structure based on an assembled phosphogypsum base can not only avoid the problem of large damage of existing aggregate, but also realize the resource recycling of solid waste, thereby having good economic benefits. SUMMARY

[0006] In view of the deficiencies of the prior art, the present application aims to provide an asphalt pavement structure based on fabricated phosphogypsum base layer and a design method thereof. The fabricated base block prepared from phosphogypsum material is used to replace the existing cement stabilized graded gravel base layer for road base layer, which can reduce the cracks caused by temperature shrinkage of the pavement, and the influence of the thickness of the phosphogypsum base layer on the mechanical properties of the asphalt pavement is determined by range analysis and variance analysis, and the optimal thickness combination of each structural layer of the asphalt pavement structure based on the phosphogypsum base layer is designed.

[0007] The technical scheme of the present application is implemented in the following manner: the present application provides an asphalt pavement structure design method based on fabricated phosphogypsum base layer, comprising the following steps:

[0008] S1, using phosphogypsum base material as pavement base layer, preparing asphalt pavement structure;

[0009] S2, according to the asphalt pavement design specification and highway traffic volume, preliminarily determining the thickness of each structural layer in the asphalt pavement structure;

[0010] S3, selecting the structural layers in the asphalt pavement structure and the thickness of the corresponding structural layers as x factors and n levels for orthogonal experiment, and calculating the pavement structure design index;

[0011] S4, performing range analysis and variance analysis on the pavement structure design index respectively, determining the main influencing factors of the mechanical properties of the pavement structure and the optimal combination of structural layers with different thicknesses;

[0012] S5, according to the results of range analysis and variance analysis, selecting the optimal thickness combination of each structural layer that meets the performance of the pavement structure, and obtaining the best asphalt pavement structure based on fabricated phosphogypsum base layer.

[0013] Preferably, in step S1, the asphalt pavement structure comprises, from top to bottom, a first asphalt layer, a second asphalt layer, a third asphalt layer, a first phosphogypsum base layer, a second phosphogypsum base layer, a graded gravel bottom base layer and a soil base layer.

[0014] Preferably, the thickness of the first asphalt layer is 30-50mm, the thickness of the second asphalt layer is 50-70mm, the thickness of the third asphalt layer is 70-90mm, and the total thickness of the first phosphogypsum base layer and the second phosphogypsum base layer is 300-500mm.

[0015] Preferably, the phosphogypsum base material comprises phosphogypsum and ceramsite; the phosphogypsum is calcined phosphogypsum with a particle size of 150-300μm, and the density of the ceramsite is 700-800kg / m 3 .

[0016] Preferably, in step S3, the asphalt layer, the phosphogypsum base layer in the asphalt pavement structure and the thickness of the asphalt layer and the thickness of the phosphogypsum base layer are selected as the x factors and n levels for orthogonal experiment.

[0017] Preferably, in step S3, the pavement structure design indexes include the vertical compressive strain of the top surface of the subgrade, the tensile strain at the bottom of the asphalt layer and the tensile stress at the bottom of the phosphogypsum base layer.

[0018] Preferably, in step S4, the range analysis includes calculation and judgment; the calculation includes calculation of K jm , k jm and R j values, and the judgment includes factor levels, optimal levels and optimal combinations; wherein: K jm is the test index corresponding to the m level of the jth column factor, k jm is the average value of K jm , and R j is the range of the jth column factor.

[0019] Preferably, in step S4, the variance analysis includes calculation of F value and comparison with the standard F α value under different confidence intervals for significance analysis.

[0020] The application also provides an asphalt pavement structure designed by the asphalt pavement structure design method based on the assembled phosphogypsum base layer.

[0021] The application also provides an application of the asphalt pavement structure design method based on the assembled phosphogypsum base layer in the construction of the asphalt pavement structure.

[0022] The application has the following beneficial effects:

[0023] 1. The application adopts orthogonal experiment design, and the influence of the thickness of the phosphogypsum base layer on the mechanical properties of the asphalt pavement is determined through range analysis and variance analysis, and the optimal thickness combination of each structure layer in the asphalt pavement structure based on the assembled phosphogypsum base layer is determined; and in the asphalt pavement structure, the phosphogypsum base layer reduces the tensile stress at the bottom of the base layer compared with the cement stabilized graded gravel base layer, thereby prolonging the service life of the asphalt pavement.

[0024] 2. The application uses phosphogypsum as the base layer material of the asphalt pavement, which replaces the existing cement stabilized graded gravel base layer for road base, solves the problems of large amount of aggregate, large environmental damage and high price, and realizes the resource utilization of a large amount of stored phosphogypsum. Moreover, the phosphogypsum material itself has small density and low thermal conductivity, and the temperature sensitivity is smaller than that of the cement stabilized gravel base layer, thereby reducing the cracks caused by temperature shrinkage. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1A flow chart of an asphalt pavement structure design method based on an assembled phosphogypsum base layer of the present application;

[0026] Figure 2 An asphalt pavement structure based on an assembled phosphogypsum base layer of the present application;

[0027] In the figure: 1, first asphalt layer; 2, second asphalt layer; 3, third asphalt layer; 4, first phosphogypsum base layer; 5, second phosphogypsum base layer; 6, graded gravel subbase; 7, soil base layer. DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to 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 of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts fall within the scope of the present application.

[0029] As shown in the figure, the embodiments of the present application provide an asphalt pavement structure design method based on an assembled phosphogypsum base layer, comprising the following steps: Figure 1

[0030] S1, using a phosphogypsum base material as a pavement base layer, and preparing an asphalt pavement structure;

[0031] S2, preliminarily determining the thicknesses of the structural layers in the asphalt pavement structure according to the asphalt pavement design specification and the highway traffic volume;

[0032] S3, selecting the structural layers in the asphalt pavement structure and the thicknesses of the corresponding structural layers as x factors and n levels for orthogonal experiment, and calculating to obtain pavement structure design indexes;

[0033] S4, respectively performing range analysis and variance analysis on the pavement structure design indexes, and determining the main influencing factors of the pavement structure mechanical properties and the optimal combination of the structural layers with different thicknesses;

[0034] S5, according to the results of the range analysis and the variance analysis, selecting the optimal thickness combination of the structural layers that meet the pavement structure performance, and obtaining the best asphalt pavement structure based on the assembled phosphogypsum base layer.

[0035] To make the purpose, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings of the present application.

[0036] Embodiment 1

[0037] An asphalt pavement structure design method based on an assembled phosphogypsum base layer, comprising the following steps:

[0038] ​(1) Design the asphalt pavement structure; as shown in the figure, the asphalt pavement structure includes first asphalt layer 1, second asphalt layer 2, third asphalt layer 3, first phosphogypsum base layer 4, second phosphogypsum base layer 5, graded gravel bottom base layer 6 and soil base layer 7 from top to bottom. Figure 2

[0039] The phosphogypsum base layer is obtained by pressure forming phosphogypsum and ceramsite in a mass ratio of 9:1. The phosphogypsum is calcined phosphogypsum after high-temperature calcination at 1000°C, with a particle diameter of 150-300μm. High-temperature calcination can convert calcium sulfate dihydrate (CaSO4·2H2O) in phosphogypsum into calcium sulfate hemihydrate (CaSO4·1 / 2H2O), and the content of phosphorus pentoxide and fluoride is also greatly reduced, achieving harmlessness. The ceramsite is produced by Hubei Juhai Environmental Technology Co., Ltd. and is prepared from municipal sludge by high-temperature calcination, with a density of 700-800kg / m 3 The soil base (subgrade) layer is an improved subgrade soil layer, which is formed by mixing cement or lime into the subgrade soil layer.

[0040] The maximum dry density, optimum moisture content, unconfined compressive strength, flexural tensile strength, elastic modulus and Poisson's ratio of the phosphogypsum base layer material are tested, and the specimen size is 100mm×100mm×200mm. The elastic modulus of the phosphogypsum base layer material is 6800MPa (adjusted to 3400MPa after adjustment of the structural layer modulus adjustment coefficient), and the Poisson's ratio is 0.27. Compared with the cement stabilized gravel base layer material, the results are shown in Table 1.

[0041] Table 1 Performance test results of phosphogypsum base layer material

[0042]

[0043] As can be seen from Table 1, compared with the cement stabilized gravel base layer material, the phosphogypsum base layer material has small density and high compressive strength, which meets the technical requirements of highway pavement base layer, but the difference in elastic modulus between the two is large, so the thickness of the pavement structure needs to be designed.

[0044] (2) Use the asphalt pavement structure design method in "Highway Asphalt Pavement Design Specification" (JTG D50-2017), and refer to the traffic volume of a certain highway in Hubei Province to preliminarily determine the thickness range of each structure layer and the thickness range of each surface layer and phosphogypsum base layer of the asphalt pavement, as shown in Table 2.

[0045] Table 2 Related parameters of each structure layer of asphalt pavement

[0046]

[0047] ​

[0048] (3) The thicknesses of each structural layer of the asphalt pavement and the thickness of the assembled phosphogypsum base layer are combined according to the orthogonal experimental design of four factors and three levels, and an L9(3 4 ) orthogonal table is selected, as shown in Table 3 below. The interaction between factors is not considered, and the thickness of the graded gravel bottom base layer is fixed at 200 mm. The assembled phosphogypsum base layer is divided into two layers, which can reduce the self-weight of the phosphogypsum base block, thereby facilitating transportation, construction and paving, and post-pavement maintenance. Based on the previous indoor forming test pieces, the uniformity of small-sized test pieces is better, and the quality is more stable. Assuming that the assembled phosphogypsum base layer is completely continuous between layers, only the total thickness of the phosphogypsum base layer is shown in the table below.

[0049] Table 3 Factor Level Table

[0050] Factor Level 1 Level 2 Level 3 A First asphalt layer thickness / mm 30 40 50 B Second asphalt layer thickness / mm 50 60 70 C Third asphalt layer thickness / mm 70 80 90 D Total thickness of phosphogypsum upper and lower base layers / mm 300 400 500

[0051] A three-dimensional solid model with a length of 6 m, a width of 6 m, and a thickness of 5 m is selected for modeling using ABAQUS finite element software. The boundary conditions are completely fixed on all four sides, and the interlayer contact is completely continuous between the structural layers of the asphalt pavement. A single axle-double wheel group axle load with an axle load of 100 kN is used as the design axle load, and the tire ground pressure is 0.7 MPa. The double circular uniform load is converted to a rectangular load, and the converted tire size is 0.23 m x 0.16 m. The asphalt pavement model is relatively regular in shape, so the mesh division uses eight-node hexahedral linear reduced integration elements (C3D8R). The calculation results of the vertical compressive strain on the top surface of the subgrade, the tensile strain at the bottom of the asphalt mixture layer, and the tensile stress at the bottom of the assembled phosphogypsum base layer obtained by ABAQUS finite element are shown in Table 4 below.

[0052] Table 4 Finite Element Calculation Results

[0053]

[0054]

[0055] (4) The results obtained by the above ABAQUS finite element software are analyzed by range analysis using SPSSAU data analysis software. Range analysis can determine the order of the effects of each factor and determine the optimal level combination. Range analysis, abbreviated as R method, includes two steps of calculation and judgment, as follows:

[0056]

[0057] wherein: K jm is the test index and of the jth column factor m level, and k jm is the K jmThe average value, the size can determine the j column factor optimal level and optimal combination. R j The range is the range of the j column factor, which reflects the fluctuation of the level of the j column factor. The range analysis results are shown in Tables 5-7 below.

[0058] Table 5 Roadbed top vertical compressive strain range analysis results

[0059]

[0060]

[0061] Table 6 Asphalt mixture layer bottom tensile strain range analysis results

[0062]

[0063] Table 7 Phosphogypsum base layer bottom tensile stress range analysis results

[0064]

[0065]

[0066] The above Tables 5-7 range analysis results are arranged in Table 8 below.

[0067] Table 8 Primary and secondary order and optimal combination

[0068] Design index Primary and secondary order Optimal combination Vertical compressive strain of subgrade top surface D>A>B>C [A1 B1 C1 D1] Tensile strain at the bottom of the asphalt mixture layer B>A>C>D [A3B3C2D1] Tensile stress at the bottom of the phosphogypsum base layer D>A>B>C [A1 B1 C1 D1]

[0069] From the above table, the first asphalt layer thickness A, the second asphalt layer thickness B and the phosphogypsum base layer thickness D have a greater impact on the mechanical response of the asphalt pavement. Therefore, based on the analysis results, the main factors to consider are the first asphalt layer thickness A, the second asphalt layer thickness B and the phosphogypsum base layer thickness D, especially the first asphalt layer thickness A and the assembled phosphogypsum base layer thickness D.

[0070] (5) The results obtained by the finite element software in step (3) are analyzed using SPSS AU data analysis software. Since the experimental amount in the variance analysis needs to meet the requirement of 10 pavement combinations, A2B2C2D2 assembled phosphogypsum base layer thickness combination is supplemented. The inter-group degrees of freedom are 2 and the intra-group degrees of freedom are 7. The F α values under different confidence intervals are obtained by looking up the upper side quantile table of F distribution, as shown in Table 9 below.

[0071] Table 9 F distribution confidence interval table

[0072] Confidence interval F α ]]> 90% confidence interval F 0.1 (2,7) = 3.26 95% confidence interval F 0.05 (2,7) = 4.74 99% confidence interval F 0.01 (2,7) = 9.55

[0073] If the calculated F value is greater than F αIf the factor has a significant influence, the variance of each factor is calculated and a significance analysis is performed, and the results are shown in Table 10 below.

[0074] Table 10 Variance analysis results

[0075] Design index A B C D Vertical compressive strain of subgrade top surface 0.121 0.092 0.096 40.140 Tensile strain at the bottom of the asphalt mixture layer 1.407 4.828 0.163 0.093 Tensile stress at the bottom of the phosphogypsum base layer 0.103 0.079 0.082 46.901

[0076] From the above table, it can be seen that the tensile strain at the bottom of the asphalt mixture layer is greatly affected by the thickness of the second asphalt layer B, and the vertical compressive strain at the top of the subgrade and the tensile stress at the bottom of the phosphogypsum base layer are greatly affected by the thickness of the phosphogypsum base layer D.

[0077] Based on the results of range analysis and variance analysis, it can be seen that the thickness of the first asphalt layer A, the thickness of the second asphalt layer B, and the thickness of the phosphogypsum base layer D have a greater impact on the mechanical response of the asphalt pavement, among which the second asphalt layer B has a greater impact on the tensile strain at the bottom of the asphalt mixture layer, and the vertical compressive strain at the top of the subgrade and the tensile stress at the bottom of the phosphogypsum base layer are greatly affected by the thickness of the phosphogypsum base layer D. Therefore, in actual construction, the optimal combination of asphalt pavement structure performance can be selected according to the above analysis results.

[0078] Based on the results of range analysis and variance analysis, combined with the requirements of the "Highway Asphalt Pavement Design Specification" for asphalt mixture surface layer, and considering the molding process and cost of the assembled phosphogypsum base layer, the optimal combination of the thickness of the asphalt pavement structure based on the assembled phosphogypsum base layer is selected as A3B2C1D2, i.e. the first asphalt layer is 50mm, the second asphalt layer is 60mm, the third asphalt layer is 70mm, the assembled phosphogypsum base layer is 400mm (200mm for the upper and lower base layers), and the graded gravel bottom base layer is 200mm.

[0079] According to the "Highway Asphalt Pavement Design Specification" (JTG D50-2017), the permanent deformation of the asphalt mixture layer of the pavement structure designed by the optimal combination selected in this embodiment and the cumulative equivalent axle number corresponding to the fatigue cracking of the phosphogypsum base layer are checked, and the results are shown in Table 11 below.

[0080] Table 11 Checking results

[0081] Index Calculated value Comparison value Permanent deformation of the asphalt mixture layer 14.4 mm 15 mm Fatigue cracking life of the phosphogypsum base layer (axle times) 1757433332 1117619749

[0082] From the above table results, it can be seen that the calculated values of the permanent deformation of the asphalt mixture layer and the cumulative equivalent axle number corresponding to the fatigue cracking of the phosphogypsum base layer are less than the comparison values, which meet the specification requirements.

[0083] Finally, the phosphogypsum-based layer pavement under the optimal combination is selected, cement stabilized graded gravel base asphalt pavement with the same thickness of each structural layer, and the existing common highway asphalt pavement structure (top layer 40mm, middle layer 60mm, bottom layer 80mm, cement stabilized graded gravel base 400mm and graded gravel bottom base 200mm) are compared, the same elastic parameters of each structural layer are maintained, and the results are shown in Table 12 by ABAQUS finite element calculation.

[0084] Table 12 Comparison results of base layer bottom tensile stress of three pavement structures

[0085]

[0086] Among them, serial number 1 represents the assembled phosphogypsum-based layer asphalt pavement structure of the embodiment of the application, serial number 2 represents the cement stabilized graded gravel base asphalt pavement structure, and serial number 3 represents the common highway asphalt pavement structure. As shown in the above table data, for the base layer bottom tensile stress, the assembled phosphogypsum-based layer asphalt pavement structure designed by the application is reduced by about 40% in the numerical value compared with the two cement stabilized graded gravel base asphalt pavement structures, which shows that the asphalt pavement structure based on the assembled phosphogypsum-based layer designed by the design method provided by the application has a significantly reduced base layer bottom tensile stress, and can prolong the service life of the asphalt pavement.

[0087] In summary, the vertical compressive strain of the roadbed top surface, the asphalt mixture layer bottom tensile strain and the phosphogypsum base layer bottom tensile stress are used as design indexes. The orthogonal experiment design is adopted to perform finite element numerical simulation analysis on the thickness of the phosphogypsum base layer asphalt pavement structure, the optimal design combination is selected in various structural combinations through range analysis and variance analysis, the permanent deformation of the asphalt mixture layer and the cumulative equivalent axle times corresponding to the base layer fatigue cracking are checked, and the optimal combination is compared with the existing semi-rigid base to prove the rationality and feasibility.

[0088] It should be noted that each of the above embodiments belongs to the same inventive concept, and the description of each embodiment has its own emphasis. If the description is not exhaustive in some embodiments, the description in other embodiments can be referred to.

[0089] The above-described embodiments only express the implementation of the application, and the description is more specific and detailed, but it should not be construed as limiting the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the inventive concept, a number of modifications and improvements can be made, which are within the scope of the application. Therefore, the protection scope of the patent of the application should be subject to the appended claims.

Claims

1. A design method for an asphalt pavement structure based on a fabricated phosphogypsum-based layer, characterized in that, The method comprises the following steps: S1, taking phosphogypsum base material as a road surface base layer, and designing an asphalt pavement structure; the asphalt pavement structure comprises, from top to bottom, a first asphalt layer, a second asphalt layer, a third asphalt layer, a first phosphogypsum base layer, a second phosphogypsum base layer, a graded gravel bottom base layer, and a soil base layer; S2, according to the asphalt pavement design specification and the highway traffic volume, the thicknesses of the structure layers in the asphalt pavement structure are preliminarily determined; S3, the structure layers in the asphalt pavement structure and the thicknesses of the corresponding structure layers are selected as x factors and n levels for orthogonal experiment, pavement structure design indexes are selected, the pavement structure design indexes are a vertical compressive strain of a roadbed top surface, a tensile strain of a bottom of an asphalt layer, and a tensile stress of a bottom of a phosphogypsum base layer, and the specific values of the pavement structure design indexes are calculated by using ABAQUS software; S4, the specific values of the pavement structure design indexes are respectively subjected to range analysis and variance analysis, the main influencing factors of the pavement structure design indexes and the optimal combination of the structure layers with different thicknesses are determined; S5, according to the results of the range analysis and the variance analysis, the optimal thickness combination of the structure layers meeting the pavement structure performance is selected, and the best asphalt pavement structure based on the assembled phosphogypsum base layer is obtained; The thickness of the first asphalt layer is 30-50 mm, the thickness of the second asphalt layer is 50-70 mm, the thickness of the third asphalt layer is 70-90 mm, and the total thickness of the first phosphogypsum base layer and the second phosphogypsum base layer is 300-500 mm. In step S1, the phosphogypsum base material comprises phosphogypsum and ceramsite; the phosphogypsum is calcined phosphogypsum, the particle size is 150-300 μm, and the density of the ceramsite is 700-800 kg / m 3 .

2. The design method of the fabricated phosphogypsum-based layer-based asphalt pavement structure according to claim 1, characterized in that, In step S3, the asphalt layer and the phosphogypsum base layer in the asphalt pavement structure, and the thicknesses of the asphalt layer and the phosphogypsum base layer are selected as x factors and n levels for orthogonal experiment.

3. The design method of the fabricated phosphogypsum-based layer-based asphalt pavement structure according to claim 1, characterized in that, In step S4, the range analysis includes calculation and judgment; the calculation includes calculation of K jm , k jm and R j values, and the judgment includes judgment of factor levels, optimal levels and optimal combination; wherein: K jm is the test index sum corresponding to the jth column factor m level, k jm is the average value of K jm , and R j is the range of the jth column factor.

4. The design method of the fabricated phosphogypsum-based layer-based asphalt pavement structure according to claim 1, characterized in that, In step S4, the variance analysis includes calculating F values and comparing them with standard F values at different confidence intervals to perform significance analysis. α values are compared to perform significance analysis.

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