Roadbed allowable compressive strain calculation method considering annual temperature distribution probability

Abstract

The invention discloses a roadbed allowable compressive strain calculation method considering a temperature annual distribution probability. The roadbed allowable compressive strain calculation method comprises the following steps: S1, collecting the annual asphalt road surface temperature and forming a data set; s2, the annual asphalt road surface temperature is divided into a plurality of temperature subareas, and representative temperatures of the temperature subareas are obtained; s3, calculating the occurrence time corresponding to the temperature partition, and calculating the occurrence probability of the temperature partition; s4, calculating the vertical compressive strain of the top surface of the roadbed at the representative temperature of each temperature zone, and calculating a temperature conversion coefficient; s5, calculating a temperature adjustment coefficient; and S6, calculating the allowable compressive strain of the top surface of the roadbed according to the allowable compressive strain model of the top surface of the roadbed. According to the roadbed allowable compressive strain calculation method considering the annual temperature distribution probability, the annual temperature distribution rule of the road surface of each region can be accurately reflected, the calculation process is simple and convenient, the error of determining the temperature adjustment coefficient by a table look-up method is avoided, and the accurate calculation of the roadbed allowable compressive strain of each region is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic civil engineering application, and in particular to a method for calculating allowable compressive strain of a roadbed taking into account annual temperature distribution probability. Background Art

[0002] Full-thickness asphalt pavement is the predominant structural form of long-life asphalt pavements both domestically and internationally. The modulus of each structural layer of a full-thickness asphalt pavement varies significantly with temperature, making it more temperature-sensitive than semi-rigid base asphalt pavements. Existing pavement design methods in my country consider the vertical compressive strain of the subgrade top surface, mostly based on semi-rigid base asphalt pavements, and fail to reflect the significant impact of temperature on the modulus of full-thickness asphalt pavements. Secondly, the vertical compressive strain of the subgrade top surface represents the bearing capacity of the subgrade. Changes in the modulus of the surface layer will have a significant impact on the vertical compressive strain of the subgrade top surface, and this effect should be considered in pavement design. Therefore, to address the aforementioned issues, focusing on the impact of temperature on the vertical compressive strain of the subgrade of full-thickness asphalt pavements, it is necessary to propose a method for calculating the allowable compressive strain of the subgrade that considers the annual temperature distribution probability. Summary of the Invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for calculating the allowable compressive strain of a roadbed taking into account the annual temperature distribution probability.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A method for calculating the allowable compressive strain of a roadbed taking into account the annual temperature distribution probability is provided, comprising the following steps:

[0006] S1: Determine the collection time interval, collect the asphalt road surface temperature throughout the year according to the collection time interval and form a data set;

[0007] S2: Determine the temperature interval, divide the annual asphalt road surface temperature into several temperature zones according to the temperature interval, and use the median temperature of each temperature zone as the representative temperature of the temperature zone;

[0008] S3: Based on the frequency of occurrence of the temperature zone, calculate the corresponding occurrence time of the temperature zone according to the frequency and temperature interval, and calculate the occurrence probability of the temperature zone according to the corresponding occurrence time of the temperature zone and the total length of the year;

[0009] S4: Calculate the vertical compressive strain on the top surface of the roadbed at the representative temperature of each temperature zone, take the vertical compressive strain as the standard compressive strain, and calculate the temperature conversion coefficient based on the vertical compressive strain and the standard compressive strain;

[0010] S5. Obtaining a temperature adjustment coefficient based on the sum of the product of the occurrence probability of each temperature zone and the temperature conversion coefficient;

[0011] S6. Calculate the allowable compressive strain of the roadbed top surface based on the allowable compressive strain model of the roadbed top surface.

[0012] Furthermore, in step S3, the formula for calculating the appearance time corresponding to the temperature partition is as follows:

[0013] t i =N i ΔT;

[0014] Where, t i is the appearance time of the i-th temperature partition, N i is the frequency of occurrence of the i-th temperature partition, ΔT is the temperature interval;

[0015] The formula for calculating the occurrence probability of temperature zones is as follows:

[0016]

[0017] Where, P i is the occurrence probability of the i-th temperature partition, is the total duration of the year, t is the time of the year, and n is the number of all temperature zones.

[0018] Furthermore, in step S4, the temperature conversion coefficient is calculated as follows:

[0019]

[0020] Where k εi is the temperature conversion coefficient; ε zi is the vertical compressive strain on the top surface of the roadbed in the ith temperature zone, and the elastic layered system or viscoelastic layered system is used to calculate the vertical compressive strain on the top surface of the roadbed at the representative temperature of each temperature zone; ε zs is the standard compressive strain of the vertical compressive strain on the top surface of the roadbed, which is calculated when the road surface temperature is 20℃.

[0021] Furthermore, in step S5, the temperature adjustment coefficient is calculated as follows:

[0022]

[0023] Where k T3 is the temperature adjustment coefficient k T3 .

[0024] Furthermore, in step S6, the formula for calculating the allowable compressive strain of the roadbed top surface is as follows:

[0025]

[0026] In the formula, [ε z ] is the allowable compressive strain of the top surface of the roadbed, β is the reliability coefficient, Ne4 The cumulative number of equivalent axle load actions during the service life is used to calculate the allowable compressive strain of the roadbed.

[0027] Furthermore, the time interval is less than or equal to 1 hour.

[0028] Furthermore, the temperature interval is less than or equal to 5°C.

[0029] The beneficial effects of the present invention are:

[0030] The allowable compressive strain of the full-thickness asphalt pavement subgrade calculated by the method of the present invention can accurately reflect the annual distribution pattern of the road surface temperature in various regions. The calculation process is simple, avoids the error of determining the temperature adjustment coefficient by the table lookup method, and realizes the accurate calculation of the allowable compressive strain of the subgrade in various regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a graph showing the relationship between road surface temperature and occurrence probability in Example 1;

[0032] Figure 2 This is a relationship diagram between road surface temperature and temperature conversion coefficient in Example 1;

[0033] Figure 3 This is a relationship diagram between road surface temperature and temperature adjustment coefficient in Example 1;

[0034] Figure 4 This is a graph showing the relationship between road surface temperature and occurrence probability in Example 2;

[0035] Figure 5 This is a relationship diagram between road surface temperature and temperature conversion coefficient in Example 2;

[0036] Figure 6 This is a relationship diagram between the road surface temperature and the temperature adjustment coefficient in Example 2; DETAILED DESCRIPTION

[0037] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0038] A method for calculating the allowable compressive strain of a roadbed considering the annual temperature distribution probability includes the following steps:

[0039] S1: Determine the collection time interval, collect the asphalt road surface temperature throughout the year according to the collection time interval and form a data set;

[0040] Specifically, the asphalt road surface temperature T is collected at a fixed time interval Δt (Δt≤1h) s , collect the time t and asphalt pavement surface temperature T throughout the year s The data forms a data set;

[0041] S2: Determine the temperature interval, divide the annual asphalt road surface temperature into several temperature zones according to the temperature interval, and use the median temperature of each temperature zone as the representative temperature of the temperature zone;

[0042] Specifically, the annual asphalt road surface temperature T is divided into fixed temperature intervals ΔT (ΔT≤5℃) s The annual temperature is divided into n temperature zones, the temperature range of the lowest temperature zone (i=1) is ≤0℃, the temperature range of the highest temperature zone (i=n) is ≥70℃, the median temperature of each temperature zone is taken as the representative temperature of the temperature zone, and the representative temperature of the i-th temperature zone is expressed as T si (2≤i≤n-1), lowest temperature partition T s1 =0℃, highest temperature zone T sn =70℃;

[0043] S3: Based on the frequency of occurrence of the temperature zone, calculate the corresponding occurrence time of the temperature zone according to the frequency and temperature interval, and calculate the occurrence probability of the temperature zone according to the corresponding occurrence time of the temperature zone and the total length of the year;

[0044] Specifically, the formula for calculating the appearance time corresponding to the temperature partition is as follows:

[0045] t i =N i ΔT;

[0046] Where N i is the frequency of occurrence of the ith temperature partition, t i is the appearance time of the i-th temperature partition;

[0047] The formula for calculating the occurrence probability of temperature zones is as follows:

[0048]

[0049] Where, P i is the occurrence probability of the i-th temperature partition, is the total length of the year, n is the number of all temperature zones;

[0050] S4: Calculate the vertical compressive strain of the top surface of the roadbed at the representative temperature of each temperature zone, take the vertical compressive strain of the top surface of the roadbed at the standard temperature as the standard compressive strain, and calculate the temperature conversion coefficient based on the vertical compressive strain of the top surface of the roadbed at the representative temperature and the standard compressive strain;

[0051] The formula for calculating the temperature conversion coefficient is as follows:

[0052]

[0053] Where k εi is the temperature conversion coefficient; ε zi is the vertical compressive strain on the top surface of the roadbed in the ith temperature zone, and the elastic layered system or viscoelastic layered system is used to calculate the vertical compressive strain on the top surface of the roadbed at the representative temperature of each temperature zone; ε zs The vertical compressive strain on the top surface of the roadbed is the standard compressive strain, which is calculated when the road surface temperature is 20℃;

[0054] S5. Obtaining a temperature adjustment coefficient based on the sum of the product of the occurrence probability of each temperature zone and the temperature conversion coefficient;

[0055] The formula for calculating the temperature adjustment coefficient is as follows:

[0056]

[0057] Where k T3 is the temperature adjustment coefficient k T3 ;

[0058] S6. Calculate the allowable compressive strain of the roadbed top surface according to the roadbed top surface allowable compressive strain model;

[0059] Specifically, the formula for calculating the allowable compressive strain on the top surface of the roadbed is as follows:

[0060]

[0061] In the formula, [ε z ] is the allowable compressive strain of the top surface of the roadbed, β is the reliability coefficient, N e4 The cumulative number of equivalent axle load actions during the service life is used to calculate the allowable compressive strain of the roadbed.

[0062] Example 1

[0063] According to the technical solution of the present invention, this embodiment takes a full-thickness asphalt pavement in area A as an example to calculate the allowable compressive strain of the roadbed top surface, specifically according to the following steps:

[0064] S1. Data collection. The asphalt road surface temperature T is collected at 15-minute intervals. s , collect the time t and asphalt pavement surface temperature T throughout the year s The data forms a data set.

[0065] S2. Temperature zoning. Divide the annual asphalt road surface temperature T into 5°C intervals. s, the annual temperature is divided into 16 temperature zones, and the specific temperature zones are shown in Table 1.

[0066] Table 1: Road surface temperature partition table 1

[0067] Temperature zone number 1 2 3 4 5 6 7 8 Temperature range (℃) ≤0 0～5 5～10 10～15 15～20 20～25 25～30 30～35 Temperature representative value (℃) 0 2.5 7.5 12.5 17.5 22.5 27.5 32.5 Temperature zone number 9 10 11 12 13 14 15 16 Temperature range (℃) 35～40 40～45 45～50 50～55 55～60 60～65 65～70 ≥70 Temperature representative value (℃) 37.5 42.5 47.5 52.5 57.5 62.5 67.5 70

[0068] S3. Temperature occurrence probability. Determine the frequency N of the occurrence of the i-th temperature partition i , N i The product of the frequency and the temperature interval ΔT is the occurrence time t of the i-th temperature partition i , the time t at which the i-th temperature partition appears i The ratio of the total duration of the year is recorded as the probability of occurrence of the i-th temperature zone P i , the probability of occurrence of temperature zones throughout the year is shown in Figure 1 , the calculation process is shown in Table 2.

[0069] Table 2: Occurrence probability of road surface temperature zones Table 1

[0070]

[0071]

[0072] S4, temperature conversion coefficient. The elastic layered system is used to calculate the vertical compressive strain of the roadbed top surface at the representative temperature of each temperature zone. The road surface temperature is 20℃ as the standard temperature. The vertical compressive strain of the roadbed top surface at the road surface temperature of 20℃ is calculated as the standard compressive strain ε zs , calculated to be 49.4 (10-6), the ratio of the vertical compressive strain on the top surface of the roadbed in the i-th temperature zone to the standard compressive strain is the temperature conversion coefficient k εi , the calculation results are shown in Figure 2 , the calculation process is shown in Table 3.

[0073] Table 3: Road surface temperature zone temperature conversion coefficient table 1

[0074] Temperature zone number 1 2 3 4 5 6 7 8 <![CDATA[Subgrade compressive strain (10 -6 )]]> 28.2 30.1 35.1 41.0 47.4 55.3 64.2 74.6 <![CDATA[Standard compressive strain (10 -6 )]]> 49.4 49.4 49.4 49.4 49.4 49.4 49.4 49.4 Temperature conversion coefficient 0.57 0.61 0.71 0.83 0.96 1.12 1.30 1.51 Temperature zone number 9 10 11 12 13 14 15 16 <![CDATA[Subgrade compressive strain (10 -6 )]]> 86.9 100.8 117.1 135.9 158.1 183.8 213.4 229.7 <![CDATA[Standard compressive strain (10 -6 )]]> 49.4 49.4 49.4 49.4 49.4 49.4 49.4 49.4 Temperature conversion coefficient 1.76 2.04 2.37 2.75 3.20 3.72 4.32 4.65

[0075] S5. Temperature adjustment coefficient. The sum of the product of the probability of occurrence of each temperature zone and the temperature conversion coefficient is the temperature adjustment coefficient k T3 ,See Figure 3 , the adjustment coefficient in Example 1 is 1.55.

[0076] S6, allowable compressive strain on the top surface of the roadbed. β=1.28,N e4 =1E+9, then [ε z ]=103.4(10-6).

[0077] Example 2

[0078] According to the technical solution of the present invention, this implementation takes a full-thickness asphalt pavement in area B as an example to calculate the allowable compressive strain of the roadbed top surface, specifically following the steps below:

[0079] S1. Data collection. The asphalt road surface temperature T is collected at 15-minute intervals. s , collect the time t and asphalt pavement surface temperature T throughout the year s The data forms a data set.

[0080] S2. Temperature zoning. Divide the annual asphalt road surface temperature T into 5°C intervals. s , the annual temperature is divided into 16 temperature zones, and the specific temperature zones are shown in Table 4.

[0081] Table 4: Road surface temperature partition table 2

[0082] Temperature zone number 1 2 3 4 5 6 7 8 Temperature range (℃) ≤0 0～5 5～10 10～15 15～20 20～25 25～30 30～35 Temperature representative value (℃) 0 2.5 7.5 12.5 17.5 22.5 27.5 32.5 Temperature zone number 9 10 11 12 13 14 15 16 Temperature range (℃) 35～40 40～45 45～50 50～55 55～60 60～65 65～70 ≥70 Temperature representative value (℃) 37.5 42.5 47.5 52.5 57.5 62.5 67.5 70

[0083] S3. Temperature occurrence probability. Determine the frequency N of the occurrence of the i-th temperature partition i , N i The product of the frequency and the temperature interval ΔT is the occurrence time t of the i-th temperature partition i , the time t at which the i-th temperature partition appears i The ratio of the total duration of the year is recorded as the probability of occurrence of the i-th temperature zone P i , the probability of occurrence of temperature zones throughout the year is shown in Figure 4 , the calculation process is shown in Table 5.

[0084] Table 5: Occurrence probability of road surface temperature zones Table 2

[0085] Temperature zone number 1 2 3 4 5 6 7 8 Frequency (times) 1051 2271 4205 3490 3833 4222 4044 3854 Occurrence duration (h) 262.8 567.6 1051.2 872.5 958.3 1055.6 1010.9 963.6 Probability of occurrence (%) 3.0 6.48 12.0 9.96 10.94 12.05 11.54 11.0 Temperature zone number 9 10 11 12 13 14 15 16 Frequency (times) 2894 1780 1191 771 701 420 308 4 Occurrence duration (h) 723.6 445.0 297.8 192.7 175.2 105.1 77.1 0.9 Probability of occurrence (%) 8.26 5.08 3.4 2.2 2.0 1.2 0.88 0.01

[0086] S4, temperature conversion coefficient. The elastic layered system is used to calculate the vertical compressive strain of the roadbed top surface at the representative temperature of each temperature zone. The road surface temperature is 20℃ as the standard temperature. The vertical compressive strain of the roadbed top surface at the road surface temperature of 20℃ is calculated as the standard compressive strain ε zs , calculated to be 49.4 (10-6), the ratio of the vertical compressive strain on the top surface of the roadbed in the i-th temperature zone to the standard compressive strain is the temperature conversion coefficient k εi , the calculation results are shown in Figure 5 , the calculation process is shown in Table 6.

[0087] Table 6: Road surface temperature zone temperature conversion coefficient table 2

[0088]

[0089]

[0090] S5. Temperature adjustment coefficient. The sum of the product of the probability of occurrence of each temperature zone and the temperature conversion coefficient is the temperature adjustment coefficient k T3 ,See Figure 6 , the temperature adjustment coefficient in Example 2 is 1.32.

[0091] S6, allowable compressive strain on the top surface of the roadbed. β=1.56,N e4 =1E+9, then [ε z ]=106.1(10-6).

Claims

1. A method for calculating the allowable compressive strain of a roadbed considering the annual temperature distribution probability, characterized in that: The steps include: S1: Determine the collection time interval, collect the asphalt road surface temperature throughout the year according to the collection time interval and form a data set; S2: Determine the temperature interval, divide the annual asphalt road surface temperature into several temperature zones according to the temperature interval, and use the median temperature of each temperature zone as the representative temperature of the temperature zone; S3: Based on the frequency of occurrence of the temperature zone, calculate the corresponding occurrence time of the temperature zone according to the frequency and temperature interval, and calculate the occurrence probability of the temperature zone according to the corresponding occurrence time of the temperature zone and the total length of the year; S4: Calculate the vertical compressive strain on the top surface of the roadbed at the representative temperature of each temperature zone, take the vertical compressive strain as the standard compressive strain, and calculate the temperature conversion coefficient based on the vertical compressive strain and the standard compressive strain; S5. Obtaining a temperature adjustment coefficient based on the sum of the product of the occurrence probability of each temperature zone and the temperature conversion coefficient; S6. Calculate the allowable compressive strain of the roadbed top surface based on the allowable compressive strain model of the roadbed top surface.

2. The method for calculating the allowable compressive strain of the roadbed considering the annual temperature distribution probability according to claim 1 is characterized in that: In step S3, the formula for calculating the appearance time corresponding to the temperature partition is as follows: t i =N i ΔT; Where, t i is the appearance time of the i-th temperature partition, N i is the frequency of occurrence of the i-th temperature partition, ΔT is the temperature interval; The formula for calculating the occurrence probability of temperature zones is as follows: Where, P i is the occurrence probability of the i-th temperature partition, is the total duration of the year, t is the time of the year, and n is the number of all temperature zones.

3. The method for calculating the allowable compressive strain of the roadbed considering the annual temperature distribution probability according to claim 2 is characterized in that: In step S4, the temperature conversion coefficient is calculated as follows: Where k εi is the temperature conversion coefficient; ε zi is the vertical compressive strain on the top surface of the roadbed in the ith temperature zone; ε zs is the standard compressive strain of the vertical compressive strain on the top surface of the roadbed.

4. The method for calculating the allowable compressive strain of the roadbed considering the annual temperature distribution probability according to claim 3 is characterized in that: In step S5, the temperature adjustment coefficient is calculated as follows: Where k T3 is the temperature adjustment factor.

5. The method for calculating the allowable compressive strain of the roadbed considering the annual temperature distribution probability according to claim 4 is characterized in that: In step S6, the formula for calculating the allowable compressive strain of the roadbed top surface is as follows: In the formula, [ε z ] is the allowable compressive strain of the top surface of the roadbed, β is the reliability coefficient, N e4 The cumulative number of equivalent axle load actions during the service life is used to calculate the allowable compressive strain of the roadbed.

6. The method for calculating the allowable compressive strain of the roadbed considering the annual temperature distribution probability according to claim 1 is characterized in that: The time interval is less than or equal to 1 hour.

7. The method for calculating the allowable compressive strain of roadbed considering the annual temperature distribution probability according to claim 1, characterized in that: The temperature interval is less than or equal to 5°C.

Images