A calculation method for the allowable vertical compressive strain on the roadbed top surface considering the rotation effect of the principal stress axis

Abstract

The present invention discloses a method for calculating the permissible vertical compressive strain of the roadbed top surface taking into account the effect of principal stress axis rotation. The method comprises the following steps: obtaining the three-dimensional stress state under wheel load; quantifying the effect of principal stress axis rotation; correcting the permissible vertical compressive strain of the roadbed top surface; and calculating the vertical compressive strain of the roadbed top surface. The present invention uses #imgabs0# to characterize the influence of shear stress on principal stress, and converts (R s ) ave As an amplification factor for the vertical compressive strain caused by principal stress axis rotation, the revised allowable vertical compressive strain formula incorporates the effects of principal stress axis rotation and more accurately reflects the vertical compressive strain bearing capacity of the subgrade top surface under dynamic loads and principal stress axis rotation. By revising the traditional standard formula, calculation accuracy is improved, thereby optimizing subgrade design and reducing pavement damage caused by accumulated permanent deformation.

Description

Technical Field

[0001] The present invention belongs to the field of geotechnical engineering technology, and relates to a method for calculating the allowable vertical compressive strain of a roadbed top surface, and specifically relates to a method for calculating the allowable vertical compressive strain of a roadbed top surface taking into account the rotation effect of the principal stress axis. Background Art

[0002] In highway design, the stability and durability of the roadbed are one of the key factors that determine the service life of the road. As the supporting structure of the pavement, the roadbed must maintain structural stability and bearing capacity under load, avoid permanent deformation caused by excessive deformation (such as irreversible settlement or deformation), and thus reduce the impact of defects such as rutting and cracking on driving comfort and safety. In the design of asphalt pavements, the allowable vertical compressive strain of the top surface of the roadbed is usually calculated to determine the maximum allowable strain of the roadbed under load. If the vertical compressive strain of the top surface of the roadbed exceeds the allowable value, the roadbed material will gradually accumulate plastic deformation, resulting in increasing permanent deformation. Therefore, a reasonable setting of the allowable vertical compressive strain can ensure that the cumulative deformation of the roadbed under actual use conditions does not exceed the design requirements, thereby controlling the permanent deformation within an acceptable range and extending the service life of the pavement.

[0003] In elastic layered system theory, tire loads are often simplified as uniformly distributed circular loads applied to the pavement surface, assuming a static or quasi-static load. However, in practical applications, the rapid "far-to-near-to-far" movement of vehicles induces a complex three-dimensional stress state within the roadbed, subjecting it to constantly changing dynamic loads. The non-uniform and symmetrical load distribution causes rotation of the principal stress axes and introduces additional shear stresses, which increases vertical strain and exacerbates the accumulation of permanent deformation. Under heavy traffic loads, the roadbed is subjected to even greater dynamic loads, making the principal stress axis rotation even more pronounced, further exacerbating the degradation of the roadbed's service performance. The actual service life of roads often fails to reach their design life because existing methods for calculating the allowable compressive strain on the roadbed top surface may underestimate the accumulated plastic deformation in practice. Under heavy, dynamic, and asymmetric loading conditions, principal stress axis rotation can amplify vertical compressive strain. To more accurately account for this effect, the calculation method for the allowable vertical compressive strain on the roadbed top surface requires further research and improvement. Summary of the Invention

[0004] To address the problem that existing methods for calculating the permissible vertical compressive strain on the top surface of a roadbed fail to fully consider the effects of principal stress axis rotation, leading to underestimation of cumulative plastic deformation under dynamic and asymmetric loading conditions, this paper provides a method for calculating the permissible vertical compressive strain on the top surface of a roadbed that considers the effects of principal stress axis rotation. This method can more accurately reflect the impact of principal stress axis rotation on the permanent deformation of the roadbed under dynamic and asymmetric loading conditions.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for calculating the allowable vertical compressive strain on the top surface of a roadbed considering the rotation effect of the principal stress axis includes the following steps:

[0007] Step S101: Obtain the three-dimensional stress state under the wheel load:

[0008] Three-dimensional stress tensor Where, σ xx , σ yy , σ zz is the vertical stress component, τ xy , τ xz , τ yz is the shear stress component;

[0009] Step S102: quantify the principal stress axis rotation effect:

[0010] Based on the three-dimensional stress tensor, the maximum vertical stress and maximum shear stress are obtained, and the ratio of the maximum shear stress to the maximum vertical stress is introduced to measure the degree of change in the stress state:

[0011]

[0012] Where, (R s ) ave is the amplification factor, (σ z ) max is the maximum principal stress, (τ yz ) max is the maximum principal stress, A is the material parameter;

[0013] Step 103: Modify the allowable vertical compressive strain on the top surface of the roadbed:

[0014] The formula for the allowable vertical compressive strain of the roadbed top surface in the highway asphalt pavement design specification is revised. The revised formula for the allowable vertical compressive strain of the roadbed top surface is:

[0015] [ε z ] 修正 =1.25×10 4-0.1β (k T3 N e4 ) -0.21 / (R s ) ave

[0016] In the formula, [ε z ] 修正 is the corrected allowable vertical compressive strain on the top surface of the roadbed, β is the target reliability index, N e4 k is the cumulative number of equivalent design axle load actions on the design lane within the design service life, T3is the temperature adjustment coefficient;

[0017] Step S104: Calculation of vertical compressive strain on the top surface of the roadbed:

[0018] Calculate the vertical compressive strain value of the roadbed top surface. The calculation result should satisfy the vertical compressive strain of the roadbed top surface is less than the allowable compressive strain value, that is, ε z <[ε z ] 修正 Otherwise, adjust the pavement structure plan and recalculate until it meets the requirements.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] In order to more accurately reflect the strain under actual working conditions, the present invention takes into account the amplification effect of the principal stress axis rotation on the vertical strain. To characterize the influence of shear stress on principal stress, the ratio is substituted into the exponential formula to obtain (R s ) ave As an amplification factor for the vertical compressive strain caused by principal stress axis rotation, the revised allowable vertical compressive strain formula incorporates the effects of principal stress axis rotation and more accurately reflects the vertical compressive strain bearing capacity of the subgrade top surface under dynamic loads and principal stress axis rotation. By revising the traditional standard formula, calculation accuracy is improved, thereby optimizing subgrade design and reducing pavement damage caused by accumulated permanent deformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Flow chart of the calculation method of the allowable vertical compressive strain on the top surface of the roadbed considering the rotation of the principal stress axis;

[0022] Figure 2 Illustration of two ways to obtain the three-dimensional stress state under the wheel load at the mechanical response calculation point;

[0023] Figure 3 This is a diagram showing the locations of the mechanical response calculation points. DETAILED DESCRIPTION

[0024] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0025] The present invention provides a method for calculating the allowable vertical compressive strain on the top surface of the roadbed taking into account the rotation effect of the principal stress axis. Figure 1 As shown, the method includes the following steps:

[0026] Step S101: Obtain the three-dimensional stress state under the wheel load:

[0027] according to Figure 3 As shown in the figure, a 3D stress sensor is placed at the mechanical response calculation point, or a 3D finite element model is established based on the pavement structure (assuming that each layer of material is a linear elastic body). The 3D stress state under the wheel load is obtained through the above two methods:

[0028] Three-dimensional stress tensor Where, σ xx , σ yy , σ zz is the vertical stress component, τ xy , τ xz , τ yz is the shear stress component.

[0029] In this step, the method of using the three-dimensional stress sensor to obtain the three-dimensional stress state under the wheel load is as follows:

[0030] The three-dimensional stress sensor can measure the vertical stress components and shear stress components in all directions under dynamic and asymmetric loads, thereby obtaining a complete three-dimensional stress tensor.

[0031] Among the mechanical response calculation points, point A is located at the center of the tire load and is the point of maximum vertical stress; points B, C, and D extend outward from point A in the horizontal direction and are used to study the distribution and attenuation of stress and strain within the tire's range of action and its edge areas.

[0032] like Figure 2 As shown in the figure, taking point A as an example, there are two ways to obtain the three-dimensional stress state under the wheel load at the mechanical response calculation point:

[0033] (1) Static loading is used at the target location, and stress responses are obtained simultaneously through multiple measuring points to obtain the vertical stress and shear stress of the roadbed under the action of wheel load.

[0034] (2) Under dynamic loading conditions, stress data is obtained through only a single measuring point during the movement of the wheel to obtain the vertical stress and shear stress of the roadbed under the action of the wheel load.

[0035] Step S102: quantify the principal stress axis rotation effect:

[0036] Based on the three-dimensional stress tensor, the maximum vertical stress and maximum shear stress are obtained. Rotation of the principal stress axes usually introduces additional shear stress components within the material, thereby changing the original stress distribution and affecting the accumulation of permanent deformation. To quantify the amplification effect of this rotation effect on vertical strain, the ratio of maximum shear stress to maximum vertical stress is introduced to measure the degree of change in the stress state:

[0037]

[0038] Where, (R s ) ave is the amplification factor, (σ z ) max is the maximum principal stress, (τ yz ) max is the maximum principal stress, and A is the material parameter.

[0039] In this step, the definition of principal stress axis rotation can be understood as an exponential function of the ratio of maximum shear stress to maximum principal stress, which represents the influence of the rotation effect on the internal stress state of the material. Used to describe the degree of change in shear stress relative to the principal stress caused by the rotation of the principal stress axis. When it is larger, the influence of the principal stress axis rotation is significant, (R s ) ave The value of will also increase accordingly, indicating that the rotation of the principal stress axis brings about a larger shear stress accumulation. When it is smaller, the influence of the principal stress axis rotation is smaller, (R s ) ave The low value of indicates that the effect of rotation on shear stress is limited.

[0040] Step S103: Correct the permissible vertical compressive strain on the top surface of the roadbed:

[0041] The formula for the allowable vertical compressive strain on the top surface of the roadbed in the highway asphalt pavement design specifications is revised to take into account the amplification effect of the principal stress axis rotation on the vertical strain. The revised formula for the allowable vertical compressive strain on the top surface of the roadbed is:

[0042] [ε z ] 修正 =1.25×10 4-0.1β (k T3 N e4 ) -0.21 / (R s ) ave

[0043] In the formula, [ε z ] 修正 is the permissible vertical compressive strain of the modified roadbed top surface, β is the target reliability index, which is determined according to the highway grade, and N e4 k is the cumulative number of equivalent design axle load actions on the design lane within the design service life, T3 is the temperature adjustment factor.

[0044] In this step, under dynamic and asymmetric loads, the principal stress axes of the roadbed will rotate, which will induce additional shear stress in the soil and lead to an increase in vertical strain. s ) ave, the amplification effect of the principal stress axis rotation on the vertical strain can be quantified.

[0045] Step S104: Calculation of vertical compressive strain on the top surface of the roadbed:

[0046] The vertical compressive strain value of the roadbed top surface is calculated based on the elastic layered system theory or through numerical simulation. The calculation result should satisfy the vertical compressive strain value of the roadbed top surface less than the allowable compressive strain value, that is, ε z <[ε z ] 修正 Otherwise, the pavement structure plan should be adjusted and recalculated until the requirements are met.

[0047] Example:

[0048] (1) Take the tire load center point A as an example. Figure 3 As shown, by placing a 3D stress sensor at point A or establishing a 3D finite element model, assuming that each layer is a linear elastic body, with h, E, and μ representing the thickness, rebound modulus, and Poisson's ratio of each layer, respectively, and applying a static load with a standard axle load, a tire pressure of 0.7 MPa, a single wheel contact equivalent circle diameter of 213 mm, and a wheel center distance of 319.5 mm, the 3D stress state under wheel load is obtained. The structural parameters of each pavement layer are shown in Table 1:

[0049] Table 1 Pavement structure parameters

[0050] Stratum Structural layer material category Thickness / m Dynamic rebound modulus / Mpa Poisson's ratio Surface asphalt concrete 0.14 9000 0.25 grassroots Graded gravel 0.20 600 0.35 Subbase Graded gravel 0.20 250 0.35 roadbed roadbed soil - 40 0.4

[0051] (2) The following formula is used to quantify the amplification effect of the principal stress axis rotation on the vertical strain by combining the ratio of the maximum shear stress to the maximum principal stress. Taking the finite element model as an example, the maximum vertical stress at point A is (σ z ) max =13.682kPa, maximum shear stress (τ yz ) max =4.047kPa. Material parameter A=2.57.

[0052]

[0053] (3) The road grade is a secondary road, the target reliability index β is 1.04, and the temperature adjustment coefficient k T3 is 0.88, and the cumulative number of equivalent design axle load actions on the design lane within the design service life is N e4 =1.27154×10 7 The allowable vertical compressive strain on the top surface of the roadbed can be calculated as follows:

[0054] ε z =1.25×10 4-0.1β (k T3 Ne4 ) -0.21 =1.25×10 4-0.1×1.28 ×(0.88×10 7 ) -0.21

[0055] =325.58×10 -6

[0056] Considering the amplification effect of the principal stress axis rotation on the vertical strain, the corrected allowable vertical compressive strain on the top surface of the roadbed is:

[0057] [ε z ] 修正 =ε z / (R s ) ave =325.58×10 -6 / 2.139=152.21×10 -6

[0058] (4) The vertical compressive strain on the top surface of the roadbed is obtained based on the elastic layered system theory or through numerical simulation, ε z =325.58×10 -6 , the calculation result does not meet the requirement that the vertical compressive strain on the top surface of the roadbed is less than the allowable compressive strain value, that is, ε z <[ε z ] 修正 The pavement structure plan should be adjusted and recalculated until it meets the requirements.

Claims

1. A method for calculating the allowable vertical compressive strain on the top surface of a roadbed considering the rotation effect of the principal stress axis, characterized in that The method comprises the following steps: Step S101: Obtain the three-dimensional stress state under the wheel load: Where, σ xx , σ yy , σ zz is the vertical stress component, τ xy , τ xz , τ yz is the shear stress component; Step S102: quantify the principal stress axis rotation effect: Based on the three-dimensional stress tensor, the maximum vertical stress and maximum shear stress are obtained, and the ratio of the maximum shear stress to the maximum vertical stress is introduced to measure the degree of change in the stress state: Where, (R s ) ave is the amplification factor, (σ z ) max is the maximum principal stress, (τ yz ) max is the maximum principal stress, A is the material parameter; Step S103: Correct the permissible vertical compressive strain on the top surface of the roadbed: The formula for the allowable vertical compressive strain of the roadbed top surface in the highway asphalt pavement design specification is revised. The revised formula for the allowable vertical compressive strain of the roadbed top surface is: [e z ] 修正 =1.25×10 4-0.1β (k T3 N e4 ) -0.21 / (R s ) ave In the formula, [ε z ] 修正 is the corrected allowable vertical compressive strain on the top surface of the roadbed, β is the target reliability index, N e4 k is the cumulative number of equivalent design axle load actions on the design lane within the design service life, T3 is the temperature adjustment coefficient; Step S104: Calculation of vertical compressive strain on the top surface of the roadbed: Calculate the vertical compressive strain value of the roadbed top surface. The calculation result should satisfy the vertical compressive strain of the roadbed top surface is less than the allowable compressive strain value, that is, ε z <[ε z ] 修正 Otherwise, adjust the pavement structure plan and recalculate until it meets the requirements.

2. The method for calculating the allowable vertical compressive strain of the roadbed top surface considering the principal stress axis rotation effect according to claim 1 is characterized in that In step S101, a three-dimensional stress state under the wheel load is obtained by arranging three-dimensional stress sensors at the mechanical response calculation points or by establishing a three-dimensional finite element model based on the road surface structure.

3. The method for calculating the permissible vertical compressive strain of the roadbed top surface considering the principal stress axis rotation effect according to claim 2 is characterized in that In step S101, the method for obtaining the three-dimensional stress state under the wheel load using the three-dimensional stress sensor is as follows: Among the mechanical response calculation points, point A is located at the tire load center and is the point of maximum vertical stress. Points B, C, and D extend horizontally outward from point A to study the distribution and attenuation of stress and strain within the tire's operating range and at its edge areas. There are two ways to obtain the three-dimensional stress state under the wheel load at the mechanical response calculation point: (1) Using static loading at the target location, the stress response is obtained simultaneously through multiple measuring points to obtain the vertical stress and shear stress of the roadbed under the wheel load; (2) Under dynamic loading conditions, stress data is obtained through only a single measuring point during the movement of the wheel to obtain the vertical stress and shear stress of the roadbed under the action of the wheel load.

4. The method for calculating the permissible vertical compressive strain of the roadbed top surface considering the rotation effect of the principal stress axis according to claim 1 is characterized in that In step S104, the vertical compressive strain value of the top surface of the roadbed is calculated based on the elastic layered system theory or through numerical simulation.

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