A method of coordinating the difference in stiffness between a pavement system and a substructure

Abstract

The application discloses a method for coordinating the stiffness difference between a pavement system and a lower bearing structure, which comprises the following steps: step S1, initially determining a target pavement structure combination: on the basis of an original reference pavement structure, a stiffness transition layer is additionally arranged between a surface pavement system and a lower bearing structure to construct a stiffness transition pavement structure; the stiffness transition pavement structure comprises the surface pavement system, the stiffness transition layer and the lower bearing structure from top to bottom; step S2, establishing a stiffness transition pavement structure mechanical model according to the target pavement structure combination; step S3, designing a response surface analysis test according to the stiffness transition pavement structure mechanical model to obtain a final response surface model; and step S4, determining target pavement structure parameters according to the final response surface model. The application can realize the stiffness transition between a surface pavement system and a lower bearing structure in a pavement structure, coordinate the stiffness difference between the surface pavement system and the lower bearing structure, and reduce the stress level of the pavement structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the coordination of the stiffness difference between the pavement system and the substructure, and in particular to a method for coordinating the stiffness difference between the pavement system and the substructure. BACKGROUND

[0002] The pavement structure is composed of the surface pavement system and the substructure, and is a common structure combination in engineering, such as the multi-layer flexible pavement, the airport pavement and the multi-layer foundation pavement. The surface pavement system includes one or two or three layers, and the most surface layer is the surface pavement layer. The substructure plays an important role in the pavement structure, and the stiffness of the substructure affects the mechanical behavior mode of the whole pavement structure.

[0003] According to the different materials used, the modulus of the substructure is very different: some are only a few hundred megapascals, and some can reach tens of thousands of megapascals. According to the layered elastic system mechanics theory, the overall stress mode of the pavement structure is very different under different pavement system-substructure stiffness combinations: when the modulus of the substructure is high and the stiffness is large, the substructure will bear most of the external load, and the surface pavement system is in a state of compression, and the stress level of the substructure is high; and when the modulus of the substructure is low and the stiffness is small, the pavement system mainly bears the bending and tensile action, and the load bearing requirement of the substructure will also be greatly improved.

[0004] On the other hand, the stiffness difference between the surface pavement system and the substructure also has a significant impact on the mechanical response characteristics of the individual structure layer: when the stiffness of the substructure is large, the increase of the stiffness difference between the surface pavement system and the substructure will increase the shear stress level of the surface pavement system; when the stiffness of the substructure is small, the stiffness difference between the surface pavement system and the substructure will have an adverse effect on the bending and tensile stress of the surface pavement system. It can be seen that the internal stiffness combination of the pavement structure has a very complex influence on the stress condition inside the structure, and the coordination of the stiffness combination plays a key role in reducing the excessive concentration of the stress in the pavement structure in a certain index and improving the durability of the pavement structure. SUMMARY

[0005] The technical problem to be solved by the present application is to overcome the shortcomings of the above background technology, and to provide a method for coordinating the stiffness difference between the pavement system and the substructure, which can realize the stiffness transition between the surface pavement system and the substructure in the pavement structure, coordinate the stiffness difference, and reduce the stress level of the pavement structure.

[0006] The technical solution adopted by the present application to solve the technical problem is a method for coordinating the stiffness difference between the pavement system and the substructure, comprising the following steps:

[0007] Step S1: preliminary target pavement structure combination: on the basis of the original reference pavement structure, a stiffness transition layer is added between the surface pavement system and the lower bearing structure to construct a stiffness transition pavement structure; the stiffness transition pavement structure includes the surface pavement system, the stiffness transition layer and the lower bearing structure from top to bottom;

[0008] Step S2, according to the target pavement structure combination, a stiffness transition pavement structure mechanical model is established;

[0009] Step S3: according to the stiffness transition pavement structure mechanical model, a response surface analysis test is designed to obtain the final response surface model;

[0010] Step S4: according to the final response surface model, the target pavement structure parameters are determined.

[0011] Further, in step S1, the original reference pavement structure is a semi-rigid base asphalt pavement structure.

[0012] Further, in step S1, the stiffness transition pavement structure includes the surface pavement system, the stiffness transition layer, the first lower bearing structure, the second lower bearing structure and the third lower bearing structure from top to bottom.

[0013] Further, the surface pavement system is an asphalt surface layer, the first lower bearing structure is a first cement stabilized gravel base layer, the second lower bearing structure is a second cement stabilized gravel base layer, and the third lower bearing structure is a cement stabilized soil layer.

[0014] Further, in step S2, the standard lane width in the driving direction is taken as the length, the standard lane width perpendicular to the driving direction is taken as the width, and the depth direction is not less than the value of the roadbed working area to construct a cubic model, which is divided into the asphalt surface layer, the stiffness transition layer, the first cement stabilized gravel base layer, the second cement stabilized gravel base layer, the cement stabilized soil layer and the soil base layer from top to bottom; the thickness of each structure layer is: the thickness of the asphalt surface layer is x1, the thickness of the stiffness transition layer is x2, and the thickness of the remaining structure layers is consistent with the original semi-rigid base asphalt pavement structure.

[0015] Further, in the stiffness transition pavement structure mechanical model, the thickness of the surface pavement system is consistent with the original reference pavement structure, the thickness of the stiffness transition layer is consistent with the surface pavement system, and the thickness of the lower bearing structure layer is consistent with the original reference pavement structure; the initial material characteristics of each structure layer are: the material parameters of the surface pavement system are consistent with the original reference pavement structure, the material parameters of the stiffness transition layer are the same as those of the surface pavement system, and the material parameters of the lower bearing structure layer are the same as those of the original reference pavement structure.

[0016] Further, in the step S3, the designed response surface test takes the maximum shear stress y of the surface pavement system / stiffness transition layer as the output variable, and takes the thickness x1 of the surface pavement system, the thickness x2 of the stiffness transition layer and the modulus ratio x3 of the stiffness transition layer to the surface pavement system, i.e., the modulus ratio, as the input variables. Each input variable factor takes three levels of high, medium and low. The response surface analysis test adopts the Box-Behnken design method. According to the set response surface analysis test, the surface pavement system shear stress, the stiffness transition layer shear stress and the maximum shear stress are calculated, wherein the maximum shear stress = MAX (surface pavement system shear stress, stiffness transition layer shear stress), so as to reduce the shear stress level of the surface pavement system and the stiffness transition layer as the target, so that τ max = MAX (surface pavement system shear stress, stiffness transition layer shear stress) is minimum.

[0017] Suppose that y is the output variable τ max , and the input variables are the thickness x1 of the surface pavement system, the thickness x2 of the stiffness transition layer and the modulus ratio x3 of the stiffness transition layer to the surface pavement system. The following relationship exists:

[0018] y = f (x1, x2, x3) + ε (1)

[0019]

[0020] In the formula, ε is a random variable or a random error, β0is a constant; x i , x j are input variables, i = 1, 2, 3, j = 1, 2, 3, β i is a linear effect coefficient of x i ; β ij is a linear interaction coefficient between x i and x j ; β ii is a quadratic effect coefficient of x i .

[0021] When the test area is close to or in the optimal area, a nonlinear relationship exists between the response value and the factor. The maximum shear stress data is fitted to obtain the final response surface model.

[0022] Further, in the step S3, the response surface model is:

[0023] τ max = β0+ β1x1+ β2x2+ β3x3+ β 12 x1x2+ β 13 x1x3+ β 23 x2x3+ β 11 x1 2 + β 22 x2 2+ β 33 x3 2 (3)

[0024] wherein τ max is the maximum shear stress, β0, β1, β2, β 12 , β 13 , β 23 , β 11 , β 22 , β 33 are coefficients, x1 is the thickness of the surface pavement system, x2 is the thickness of the stiffness transition layer, and x3 is the modulus ratio.

[0025] Further, the β0=0.317103, β1=0.014573, β2=0.001061, β3=-0.006306, β 12 =0, β 13 =0.000508, β 23 =0, β 11 =-0.000475, β 22 =-0.000022, β 33 =0.

[0026] Further, in step S4, the method for formulating the target pavement structure parameters is as follows:

[0027] Equation (3) can be expressed in the form of a matrix as follows:

[0028] Y = β0+ Xb T + XBX T (4)

[0029]

[0030] wherein β0is a constant; X=(x1, x2, x3); b=(β1, β2, β3), β i is a linear effect coefficient of x i , i=1, 2, 3; B is a k-order symmetric matrix, β ij is a linear interaction coefficient between x i and x j , β ii is a quadratic effect coefficient of x i ;

[0031] First-order derivatives are respectively taken for the variables x1, x2, and x3 in equation (4), and if the response can reach an optimal point, then the response value has an extreme point in the variable interval, satisfying:

[0032]

[0033] Formula (6) is a 3-term linear equation group containing x1, x2, x3, and the solution of formula (6) is a stable point X0, which is expressed as:

[0034]

[0035] Finally, the target pavement structure parameters under the optimal key mechanical response level are obtained through formula (4)-(7); when the stable point X0 does not exist, that is, the solution of formula (6) is not in the variable value range, then the minimum point of the key mechanical response in the variable value range is calculated, and the solution of the independent variable x1, x2, x3 corresponding to the minimum point is the target pavement structure parameter under the minimum key mechanical response level.

[0036] Compared with the prior art, the advantages of the present application are as follows:

[0037] (1) The present application sets up a stiffness transition layer in the pavement structure, which can realize the stiffness transition of the surface pavement system in the pavement structure and the underlying structure, coordinate the stiffness difference, and reduce the stress level of the pavement structure.

[0038] (2) The present application uses the response surface method to solve the problem of nonlinear mechanical response data processing, considers the interaction of multiple variables on the mechanical response data in the case that the mechanical response data is affected by multiple variables, fits the complex unknown function relationship in a small area with a polynomial model, reduces the test cost, improves the test quality, and finally finds the optimal target pavement structure parameters. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a schematic diagram of the existing semi-rigid base asphalt pavement structure.

[0040] Figure 2 is a schematic diagram of the stiffness transition pavement structure of the embodiment of the present application.

[0041] Figure 3 is a schematic diagram of the mechanical model of the stiffness transition pavement structure of the embodiment of the present application.

[0042] Figure 4 is a flowchart of the embodiment of the present application.

[0043] In the figure, 1 is an asphalt surface layer, 2 is a first cement stabilized macadam base, 3 is a second cement stabilized macadam base, 4 is a cement stabilized soil layer, and 5 is a stiffness transition layer. DETAILED DESCRIPTION

[0044] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0045] In this embodiment, a method for coordinating the stiffness difference between the pavement system and the underlying structure is described. The reference pavement structure selected is the semi-rigid base asphalt pavement structure widely used in my country, such as Figure 1 The semi-rigid base asphalt pavement structure includes, from top to bottom, an asphalt surface layer 1, a first cement-stabilized crushed stone base 2, a second cement-stabilized crushed stone base 3, and a cement-stabilized soil layer 4. The first cement-stabilized crushed stone base 2, the second cement-stabilized crushed stone base 3, and the cement-stabilized soil layer 4 constitute the semi-rigid base. The asphalt surface layer of a semi-rigid base asphalt pavement is considered the surface paving system, and the semi-rigid base is the underlying structure.

[0046] A method proposed in the present invention to coordinate the stiffness difference between the pavement system and the underlying structure is used to construct a semi-rigid base asphalt pavement structure with a transition in stiffness. The aim is to solve the stiffness mutation problem between the flexible surface layer and the semi-rigid base layer in the semi-rigid base asphalt pavement and improve the stress of the pavement structure.

[0047] The method of coordinating the stiffness difference between the pavement system and the underlying support structure in this embodiment includes the following steps:

[0048] Step S1: Initially designing a target pavement structure combination: Based on the original baseline pavement structure, a stiffness transition layer is added between the surface pavement system and the underlying support structure to construct a stiffness transition pavement structure. The stiffness transition pavement structure includes, from top to bottom, the surface pavement system, the stiffness transition layer, and the underlying support structure. This constructed stiffness transition pavement structure is called the target pavement structure.

[0049] like Figure 2 The original reference pavement structure of this embodiment is a semi-rigid base asphalt pavement structure, which includes, from top to bottom, a surface paving system (asphalt surface layer 1), a first supporting structure (first cement-stabilized gravel base 2), a second supporting structure (second cement-stabilized gravel base 3), and a third supporting structure (cement-stabilized soil layer 4). A stiffness transition layer 5 is added between the asphalt surface layer 1 and the first cement-stabilized gravel base 2 of the semi-rigid base asphalt pavement structure to construct a stiffness transition pavement structure. The stiffness transition pavement structure includes, from top to bottom, a surface paving system (asphalt surface layer 1), a stiffness transition layer 5, a first supporting structure (first cement-stabilized gravel base 2), a second supporting structure (second cement-stabilized gravel base 3), and a third supporting structure (cement-stabilized soil layer 4).

[0050] Step S2, establishing a stiffness transition pavement structure mechanical model according to the target pavement structure combination;

[0051] According to the preliminary target pavement structure combination, the stiffness transition pavement structure mechanical model is established based on the finite element method, such as Figure 3As shown in the figure, a cubic model is constructed with the standard lane width in the driving direction as the length, the standard lane width perpendicular to the driving direction as the width, and the value not less than the subgrade working area in the depth direction as the height. The driving load of the cubic model is valued according to the actual situation, and is generally taken as a single-axle double-wheel load of 0.707 MPa. In the embodiment, the length of the cubic model is taken as the standard lane width of 3.75 m along the driving direction, the width is taken as the standard lane width of 3.75 m perpendicular to the driving direction, the height is not less than the subgrade working area along the depth direction, and is generally taken as 3 m. The driving load parameter is valued according to the traffic condition, and is taken as a single-axle double-wheel load of 0.707 MPa in the embodiment.

[0052] The cubic model is divided into an asphalt surface layer from top to bottom, a stiffness transition layer, a first cement stabilized macadam base, a second cement stabilized macadam base, a cement stabilized soil layer, and a soil base. The thicknesses of the respective structure layers are as follows: the thickness x1 of the asphalt surface layer to be determined, the thickness x2 of the stiffness transition layer to be determined, and the thicknesses of the remaining structure layers are consistent with the reference structure layer. In the embodiment, the thickness of the asphalt surface layer is x1, the initial value of the thickness of the asphalt surface layer is 18 cm, the thickness of the stiffness transition layer is x2, the initial value of the thickness of the stiffness transition layer is 18 cm, the thickness of the soil base is 2.08 m, the cement stabilized soil layer is 20 cm, the first cement stabilized macadam base is 18 cm, and the second cement stabilized macadam base is 18 cm. The modulus of the stiffness transition layer is to be determined, and the material parameters of the remaining pavement structure layers are consistent with the reference structure. The initial value of the modulus of the stiffness transition layer is 1400 MPa, as shown in Table 1.

[0053] Table 1: Material parameters of the mechanical model

[0054]

[0055]

[0056] In the mechanical model, the initial thickness characteristics of the respective structure layers are as follows: the thickness of the surface paving system is consistent with the reference structure, the thickness of the stiffness transition layer is consistent with the surface paving system, and the thickness of the lower bearing structure layer is consistent with the reference structure.

[0057] In the mechanical model, the initial material characteristics of the respective structure layers are as follows: the material parameters of the surface paving system are consistent with the reference structure, the material parameters of the stiffness transition layer are the same as those of the surface paving system, and the material parameters of the lower bearing structure layer are the same as those of the reference structure.

[0058] Step S3: According to the mechanical model of the stiffness transition paving structure, a response surface analysis test is designed to obtain a final response surface model.

[0059] According to the stress characteristics and failure mode of the original pavement structure (reference structure), the key mechanical response thereof is taken as a design index of the method for coordinating the stiffness difference between the pavement system and the lower bearing structure. The key mechanical response is the most unfavorable mechanical response for controlling the failure of the pavement structure. In this embodiment, the maximum shear stress of the selected semi-rigid base asphalt pavement is taken as the key mechanical response.

[0060] With reference to Figure 4 The response surface test designed in this embodiment takes the maximum shear stress y of the asphalt surface layer / stiffness transition layer as the output variable, and takes the thickness x1 of the asphalt surface layer, the thickness x2 of the stiffness transition layer, and the modulus ratio x3 (referred to as modulus ratio) of the stiffness transition layer to the asphalt surface layer as the input variables. Each input variable factor takes three levels of high, medium, and low, as shown in Table 2. In Table 2, 1 represents the high level, 0 represents the medium level, and -1 represents the low level. In the high level group, the thickness x1 of the asphalt surface layer is 12 cm, the thickness x2 of the stiffness transition layer is 12 cm, and the modulus ratio x3 is 6. In the medium level group, the thickness x1 of the asphalt surface layer is 9 cm, the thickness x2 of the stiffness transition layer is 9 cm, and the modulus ratio x3 is 4. In the low level group, the thickness x1 of the asphalt surface layer is 6 cm, the thickness x2 of the stiffness transition layer is 6 cm, and the modulus ratio x3 is 2. The response surface analysis test of this embodiment adopts the Box-Behnken (referred to as BBD) design method, and the design values of the response surface test factors are shown in Table 3.

[0061] Table 2 Design factors and level factors

[0062]

[0063] Table 3 Design values of response surface test factors

[0064]

[0065] According to the set response surface analysis test, the shear stress of the asphalt surface layer, the shear stress of the stiffness transition layer, and the maximum shear stress are calculated, wherein the maximum shear stress = MAX (shear stress of the asphalt surface layer, shear stress of the stiffness transition layer). The shear stress data of the response surface analysis test are shown in Table 4.

[0066] Table 4 Shear stress data of response surface test

[0067]

[0068] The target is to reduce the shear stress level of the asphalt surface layer and the stiffness transition layer, that is, to comprehensively consider the asphalt surface layer and the stiffness transition layer, so that τ max = MAX (shear stress of the asphalt surface layer, shear stress of the stiffness transition layer) is minimum.

[0069] Suppose y is the output variable τ maxThe following relationships exist between the input variables asphalt surface thickness x1, stiffness transition layer thickness x2, and modulus ratio of the stiffness transition layer to the asphalt surface x3:

[0070] y = f(x1, x2, x3) + ε (1)

[0071]

[0072] In the formula, ε is a random variable or random error, β0 is a constant; x i , x j are input variables, i = 1, 2, 3, j = 1, 2, 3, β i is a linear effect coefficient of x i ; β ij is a linear interaction coefficient between x i and x j ; and β ii is a quadratic effect coefficient of x i .

[0073] When the test area is close to or in the optimal area, a nonlinear relationship exists between the response value and the factors. The maximum shear stress data is fitted to obtain a final response surface model, which is formula (3),

[0074] τ max = β0+ β1x1+ β2x2+ β3x3+ β 12 x1x2+ β 13 x1x3+ β 23 x2x3+ β 11 x1 2 + β 22 x2 2 + β 33 x3 2 (3)

[0075] In the formula, τ max is the maximum shear stress, β0, β1, β2, β3, β 12 , β 13 , β 23 , β 11 , β 22 , β 33 are coefficients, wherein β0 = 0.317103, β1 = 0.014573, β2 = 0.001061, β3 = -0.006306, β 12 = 0, β 13 = 0.000508, β 23 = 0, β 11 = -0.000475, β 22 = -0.000022, and β 33= 0, x1 is the thickness of the asphalt surface layer, x2 is the thickness of the stiffness transition layer, and x3 is the modulus ratio.

[0076] The specific process is as follows: initial response surface model is obtained by fitting the maximum shear stress data; significant influencing factors of the initial response surface model are found through variance analysis; non-significant influencing factors are eliminated; and the initial response surface model is adjusted to obtain the final response surface model.

[0077] The variance analysis result is shown in Table 5.

[0078] Table 5: Variance analysis table

[0079]

[0080] As can be seen from the variance analysis in Table 5, the F value of the fitted model is 614.73, and the P value is less than 0.05, indicating that the model is significant. x1, x2, x3, x1x3, x1 2 , x2 2 are all significant model terms, so the thickness of the asphalt surface layer, the thickness of the stiffness transition layer, the modulus ratio of the stiffness transition layer to the asphalt surface layer and their interactions are all significant influencing factors of the maximum shear stress τ max of the asphalt surface layer.

[0081] Step S4: According to the final response surface model, the target pavement structure parameters are determined.

[0082] Formula (3) can be expressed in the form of a matrix as follows:

[0083] Y = β0 + Xb T + XBX T (4)

[0084]

[0085] In the formula: β0 is a constant; X = (x1, x2, x3); b = (β1, β2, β3), β i is the linear effect coefficient of x i , i = 1, 2, 3; B is a k-order symmetric matrix, β ij is the linear interaction coefficient between x i and x j , and β ii is the quadratic effect coefficient of x i .

[0086] First-order derivatives of the variables x1, x2 and x3 in formula (4) are taken respectively, and if the response can reach the optimal point, there is an extreme point of the response value in the variable interval, satisfying:

[0087]

[0088] Formula (6) is a 3-term linear equation system containing x1, x2, x3, and the solution of formula (6) is a stable point X0, which is expressed as:

[0089]

[0090] Finally, the target pavement structure parameters under the optimal key mechanical response level can be obtained through formula (4)-(7). When there is no stable point X0, i.e., the solution of formula (6) is not within the variable value range, the minimum point of the key mechanical response within the variable value range is calculated, and the solution of the independent variables x1, x2, x3 corresponding to the minimum point is the target pavement structure parameter under the minimum key mechanical response level.

[0091] In this embodiment, the target pavement structure parameters obtained are: the asphalt surface layer thickness is 6 cm, the stiffness transition layer thickness is 6.8 cm, the stiffness transition layer modulus is 6 times the modulus of the asphalt surface layer, i.e., 8400 MPa, the cement stabilized soil layer is set to 20 cm, the first cement stabilized macadam base is set to 18 cm, and the second cement stabilized macadam base is set to 18 cm. According to calculation, the asphalt surface layer shear stress at this time is 0.37 MPa, and the stiffness transition layer shear stress is 0.36 MPa. As a comparison, when the asphalt surface layer of the semi-rigid base asphalt pavement structure without the stiffness transition layer is 12.8 cm thick, the maximum shear stress of the asphalt surface layer is 0.43 MPa. The shear stress level of the modulus transition semi-rigid base asphalt pavement structure obtained by the method of the present application is greatly reduced.

[0092] The present application sets a stiffness transition layer in the pavement structure, which can realize the stiffness transition of the surface pavement system in the pavement structure and the underlying structure, coordinate the stiffness difference, and reduce the stress level of the pavement structure. The present application adopts the response surface method to solve the problem of nonlinear mechanical response data processing. In the case that the mechanical response data is affected by multiple variables, the interaction of multiple variables on the mechanical response data is considered, the complex unknown function relationship is fitted with a polynomial model in a small area, the test cost is reduced, the test quality is improved, and finally the optimal target pavement structure parameters are found.

[0093] The proposed pavement structure thickness parameters do not limit the present application, and the specific target pavement structure layer parameters and material parameters can be adjusted according to the structure combination, material parameters and other influencing factors in the actual reference structure by using the method described in the present application.

[0094] Those skilled in the art can make various modifications and variations to the present application, and if these modifications and variations are within the scope of the claims of the present application and the equivalent technology, they are also within the protection scope of the present application.

[0095] The description herein of any aspects of examples of the technology disclosed herein can be considered as presented in the general context of computer-executable instructions, such as program modules. Generally, program modules include routines, programs, objects,

Claims

1. A method for coordinating the stiffness differences between the pavement system and the underlying support structure, characterized by: The following steps are involved: Step S1: Preliminary target pavement structure combination: Based on the original reference pavement structure, a stiffness transition layer is added between the surface pavement system and the underlying support structure to construct a stiffness transition pavement structure; the stiffness transition pavement structure includes the surface pavement system, stiffness transition layer and underlying support structure from top to bottom; In step S1, the stiffness transition pavement structure includes, from top to bottom, a surface pavement system, a stiffness transition layer, a first support structure, a second support structure, and a third support structure; Step S2, establishing a stiffness transition pavement structure mechanical model according to the target pavement structure combination; Step S3: Based on the stiffness transition pavement structural mechanics model, a response surface analysis experiment is designed to obtain the final response surface model; In step S3, the designed response surface experiment takes the maximum shear stress y of the surface pavement system / stiffness transition layer as the output variable, and the input variables are the thickness of the surface pavement system , thickness of stiffness transition layer Ratio of the modulus of the transition layer and the modulus of the surface paving system , referred to as modulus ratio, each input variable factor takes three levels: high, medium and low. The response surface analysis test adopts the Box-Behnken design method. According to the set response surface analysis test, the shear stress of the surface pavement system, the shear stress of the stiffness transition layer and the maximum shear stress are calculated, where the maximum shear stress = MAX (surface pavement system shear stress, stiffness transition layer shear stress). The goal is to reduce the shear stress level of the surface pavement system and the stiffness transition layer, so that = MAX(surface paving system shear stress, stiffness transition layer shear stress) minimum; Assume y is the output variable , and the input variable surface pavement system thickness , thickness of stiffness transition layer , modulus ratio of stiffness transition layer to surface paving system The following relationship exists: （1） （2） Where: is a random variable or random error, is a constant; 、 are input variables, i=1,2,3, j=1,2,3, for The linear effect coefficient of for and The linear interaction coefficient between for The quadratic effect coefficient of When the test region is close to or within the optimal region, the response value and the factors show a nonlinear relationship, and the maximum shear stress data are fitted to obtain the final response surface model; Step S4: According to the final response surface model, the target pavement structure parameters are formulated.

2. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 1, characterized in that: In step S1, the original reference pavement structure is a semi-rigid base asphalt pavement structure.

3. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 1, characterized in that: The surface paving system is an asphalt surface layer, the first supporting structure is a first cement-stabilized gravel base layer, the second supporting structure is a second cement-stabilized gravel base layer, and the third supporting structure is a cement-stabilized soil layer.

4. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 3, characterized in that: In step S2, a cube model is constructed with the standard lane width in the driving direction as the length, the standard lane width perpendicular to the driving direction as the width, and the value in the depth direction not less than the roadbed working area as the height. The cube model is divided into an asphalt surface layer, a rigidity transition layer, a first cement-stabilized gravel base layer, a second cement-stabilized gravel base layer, a cement-stabilized soil layer, and a soil base layer from top to bottom; the thickness of each structural layer is: thickness to be determined Asphalt surface layer, thickness to be determined The stiffness transition layer is used, and the thickness of the remaining structural layers is consistent with the original semi-rigid base asphalt pavement structure.

5. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 4, characterized in that: In the mechanical model of the stiffness transition pavement structure, the thickness of the surface pavement system is consistent with that of the original reference pavement structure, the thickness of the stiffness transition layer is consistent with that of the surface pavement system, and the thickness of the underlying structure layer is consistent with that of the original reference pavement structure; The initial material characteristics of each structural layer are as follows: the material parameters of the surface paving system are consistent with the original reference paving structure, the material parameters of the stiffness transition layer are the same as the surface paving system, and the material parameters of the underlying structural layer are the same as the original reference paving structure.

6. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 3, characterized in that: In step S3, the response surface model is: （3） Where: is the maximum shear stress, 、 、 、 、 、 、 、 、 、 is the coefficient, is the thickness of the surface paving system, is the thickness of the stiffness transition layer, is the modulus ratio.

7. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 6, characterized in that: described =0.317103, =0.014573, =0.001061, =-0.006306, =0, =0.000508, =0, =-0.000475, =-0.000022, =0.

8. The method for coordinating the stiffness difference between the pavement system and the underlying support structure according to claim 6, characterized in that: In step S4, the method for formulating the target pavement structure parameters is as follows: Formula (3) can be expressed in matrix form as: （4） （5） Where: is a constant; X=( , , );b=( , , ), for The linear effect coefficient, i=1,2,3; B is a k-order symmetric matrix, for and The linear interaction coefficient between for The quadratic effect coefficient of The variables in formula (4) are , , Perform first-order derivative. If the response can reach the optimal point, then the response value has an extreme point in the variable interval, satisfying: （6） Formula (6) contains , , The solution of the three-term linear equation system, X0, is a stable point, and the stable point X0 is expressed as: （7） Finally, the target pavement structure parameters under the optimal key mechanical response level are obtained through equations (4) to (7); when there is no stable point X0, that is, when the solution of equation (6) is not within the variable value range, the minimum point of the key mechanical response within the variable value range is calculated, and the independent variable corresponding to the minimum point is , , The solution is the target pavement structure parameter under the minimum critical mechanical response level.

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