Roadbed top surface allowable vertical compressive strain calculation method considering principal stress axis rotation effect

Abstract

The invention discloses a roadbed top surface allowable vertical compressive strain calculation method considering a principal stress axis rotation effect. The method comprises the following steps: acquiring a three-dimensional stress state under a wheel load effect; quantifying a principal stress axis rotation effect; correcting permissible vertical compressive strain of the top surface of the roadbed; and calculating the vertical compressive strain of the top surface of the roadbed. According to the method, the influence of shear stress relative to principal stress is represented through # imgabs0 #, and (Rs) ave serves as an amplification factor of principal stress axis rotation on vertical compressive strain. The corrected permissible vertical compressive strain formula integrates the influence of the rotation of the principal stress axis, and more accurately reflects the vertical compressive strain bearing capacity of the top surface of the roadbed under the conditions of dynamic load and the rotation of the principal stress axis. By correcting a traditional standard formula, the calculation precision is improved, so that the roadbed design is optimized, and pavement diseases caused by accumulated permanent deformation are reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and relates to a method for calculating the allowable vertical compressive strain on the top surface of a roadbed, and specifically to a method for calculating the allowable vertical compressive strain on the top surface of a roadbed 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 needs to maintain structural stability and bearing capacity under load, avoid permanent deformation (such as irreversible settlement or deformation) caused by excessive deformation, and thus reduce the impact of rutting, cracking and other diseases on driving comfort and safety. In the design of highway asphalt pavement, the maximum allowable strain of the roadbed under load is usually determined by calculating the allowable vertical compressive strain on the top surface of the roadbed. If the vertical compressive strain on 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 the theory of elastic layered systems, tire loads are usually simplified as uniformly distributed circular loads, applied to the surface of the road surface, and assumed to be static or quasi-static. However, in actual engineering, the rapid movement of vehicles "far-near-far" will cause a complex three-dimensional stress state inside the roadbed, causing it to bear constantly changing dynamic loads, and the load distribution is not uniform and symmetrical, resulting in the rotation of the principal stress axis and the introduction of additional shear stress, thereby increasing the vertical strain and aggravating the accumulation of permanent deformation. Under the action of heavy traffic loads, the roadbed will bear greater dynamic loads, making the principal stress axis rotation effect more significant, further aggravating the decay of the roadbed service performance. The actual service life of the road is often difficult to reach the design life, precisely because the existing calculation method of the allowable compressive strain on the top surface of the roadbed may underestimate the accumulated plastic deformation in actual application. Under heavy load, dynamic and asymmetric load conditions, the rotation of the principal stress axis will have an amplifying effect on the vertical compressive strain. In order to more accurately consider this effect, the calculation method of the allowable vertical compressive strain on the top surface of the roadbed still needs to be further studied and improved. Summary of the invention

[0004] In order to solve the problem that the existing calculation method of the allowable vertical compressive strain of the top surface of the roadbed does not fully consider the influence of the rotation of the principal stress axis, resulting in underestimation of the cumulative plastic deformation under dynamic and asymmetric load conditions, the present invention provides a calculation method of the allowable vertical compressive strain of the top surface of the roadbed that considers the effect of the rotation of the principal stress axis. This method can more accurately reflect the influence of the rotation effect of the principal stress axis on the permanent deformation of the roadbed under dynamic and asymmetric load conditions.

[0005] The objective 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 comprises the following steps:

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

[0008] Three-dimensional stress tensor In the formula, 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, quantifying 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 of the stress state:

[0011]

[0012] In the formula, (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: Correct the allowable vertical compressive strain on the top surface of the roadbed:

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

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

[0018] Calculate the vertical compressive strain value of the top surface of the roadbed. The calculation result should satisfy the vertical compressive strain of the top surface of the roadbed 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 rotation of the principal stress axis on the vertical strain. To characterize the influence of shear stress on principal stress, substituting this ratio into the exponential formula, we get (R s ) ave As an amplification factor of the principal stress axis rotation on the vertical compressive strain. The revised allowable vertical compressive strain formula integrates the influence of the principal stress axis rotation and more accurately reflects the vertical compressive strain bearing capacity of the top surface of the roadbed under dynamic load and principal stress axis rotation conditions. By revising the traditional standard formula, the calculation accuracy is improved, thereby optimizing the roadbed design and reducing pavement diseases caused by accumulated permanent deformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The 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 implementation methods for obtaining 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 in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope 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 comprises the following steps:

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

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

[0028] Three-dimensional stress tensor In the formula, 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 tire load center and is the point of maximum vertical stress action; 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 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, quantifying the principal stress axis rotation effect:

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

[0037]

[0038] In the formula, (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 the principal stress axis rotation can be understood as an exponential function of the ratio of the maximum shear stress to the maximum principal stress, which represents the influence of the rotation effect on the internal stress state of the material. It is used to describe the degree of change of shear stress relative to principal stress caused by the rotation of principal stress axis. When it is larger, the influence of the rotation of the principal stress axis is significant. 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 rotation of the principal stress axis is smaller, (R s ) ave The low value of indicates that the effect of rotation on shear stress is limited.

[0040] Step S103, correcting the allowable 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 specification is revised to consider the amplification effect of the rotation of the principal stress axis 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 on the top surface of the roadbed after correction, 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 top surface of the roadbed 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 top surface of the roadbed that is 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 arranging a three-dimensional stress sensor at point A or establishing a three-dimensional finite element model, assuming that each layer of material is a linear elastic body, h, E, and μ represent the thickness, rebound modulus, and Poisson's ratio of each layer, and applying a static load of standard axle weight, each tire pressure is 0.7MPa, the single wheel ground contact equivalent circle diameter is 213mm, and the center distance between the two wheels is 319.5mm, in order to obtain the three-dimensional stress state under the wheel load. The structural parameters of each layer of the pavement are shown in Table 1:

[0049] Table 1 Pavement structure parameters

[0050] Horizon Structural 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 =13.682 kPa, maximum shear stress (τ yz ) max =4.047 kPa. 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 rotation of the principal stress axis 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 satisfy 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, obtaining the three-dimensional stress state under the wheel load: In the formula, σ xx , σ yy , σ zz is the vertical stress component, τ xy , τ xz , τ yz is the shear stress component; Step S102, quantifying 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 of the stress state: In the formula, (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, correcting the allowable vertical compressive strain on the top surface of the roadbed: The formula for the allowable vertical compressive strain on the top surface of the roadbed in the highway asphalt pavement design specification is revised. The corrected formula for the allowable vertical compressive strain on the top surface of the roadbed 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 factor; Step S104: Calculation of vertical compressive strain on the top surface of the roadbed: Calculate the vertical compressive strain value of the top surface of the roadbed. The calculation result should satisfy the vertical compressive strain of the top surface of the roadbed 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 on the top surface of the roadbed considering the rotation effect of the principal stress axis according to claim 1 is characterized in that In step S101, a three-dimensional stress state under the wheel load is obtained by arranging a three-dimensional stress sensor at the position of the mechanical response calculation point, or by establishing a three-dimensional finite element model based on the road surface structure.

3. The method for calculating the allowable vertical compressive strain on the top surface of the roadbed considering the rotation effect of the principal stress axis according to claim 2 is characterized in that In step S101, the method of using the three-dimensional stress sensor to obtain the three-dimensional stress state under the wheel load 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 action; points B, C, and D extend outward from point A in the horizontal direction to study the distribution and attenuation of stress and strain within the tire action range and 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) Static loading is used at the target location to obtain stress responses through multiple measuring points simultaneously 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 allowable vertical compressive strain on the top surface of the roadbed considering the rotation effect of the principal stress axis according to claim 1 is characterized in that In the step S104, the vertical compressive strain value of the top surface of the roadbed is calculated according to the elastic layered system theory or through numerical simulation.

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