JP7798688B2 - A method for predicting rutting depth taking into account the effect of temperature - Google Patents

Description

The present invention relates to a method for predicting the amount of rutting, and in particular to a method for predicting the amount of rutting in asphalt pavement under conditions that take into account the effects of temperature.

Rutting is a depth-wise displacement that occurs on the surface of asphalt pavement where wheels pass. If rutting becomes too large, rainwater and other liquids can accumulate in the depressions that have been displaced in the depth direction, causing tire slippage, water splashing, and hydroplaning, as well as encouraging water penetration into the pavement, making rutting an undesirable phenomenon.

Rutting is generally said to have two causes:
1) Deformation and lateral movement of the surface asphalt mixture due to repeated wheel passage (repeated loading).
2) Accumulation of residual deformation that occurs in each layer of asphalt pavement due to repeated wheel passage (repeated loading).

Regarding rutting caused by cause 1) above, countermeasures have been implemented in recent years thanks to the development of superior materials such as polymer-modified asphalt, and this has tended to be significantly reduced. On the other hand, for rutting caused by cause 2) above, measures must be taken for the entire asphalt pavement. However, at present, there is no practical method for accurately predicting the amount of rutting for the entire pavement, including the roadbed and subgrade, before the pavement is put into service. For example, Patent Documents 1 and 2 only propose technology for determining the amount of rutting that has already occurred after the fact by conducting a road surface property survey.

The difficulty in accurately predicting the amount of rutting, which is the cumulative residual deformation that occurs in each layer of asphalt pavement, is thought to be largely due to the structure of the asphalt pavement and the properties of the asphalt mixture. In other words, asphalt pavement is typically composed of a layer of asphalt mixture and the subgrade and roadbed layers underneath, and residual deformation due to repeated loading appears as the sum of the deformation amounts in the depth direction of each layer. Therefore, to predict the amount of rutting due to the cumulative residual deformation, it is necessary to make predictions that take into account not only the layer of asphalt mixture, but also the roadbed and roadbed.

Another major factor is that, because the physical properties of asphalt change significantly with temperature, the effects of temperature must be taken into account when predicting the amount of rutting caused by the accumulation of residual deformation. The surface layer of an asphalt pavement is directly affected by sunlight, wind, rain, etc., and heats up and cools down easily, whereas the layers below it take time for heat from the surface to be transmitted, making them slower to heat up and cool down. For this reason, even on a daily basis, a temperature gradient is thought to exist in the depth direction of the asphalt pavement, and when seasonal changes are taken into account, the temperature of the asphalt pavement is thought to change significantly and in complex ways throughout the year. To predict the amount of rutting taking the effects of temperature into account, it is necessary to take into account the effects of temperature, which changes in various ways throughout the year, across the entire asphalt pavement. However, while this is theoretically possible, it is extremely difficult in practice.

In the future, as regulations are relaxed, it is expected that the size and number of vehicles, as seen in the increase in large trailers, will increase, and as a result, the occurrence of rutting due to the accumulation of the above-mentioned residual deformation is likely to increase. Under these circumstances, in order to take effective measures against rutting, a practical method is needed that makes it possible to predict the amount of rutting caused by the accumulation of residual deformation in asphalt pavement at the pavement design stage.

Japanese Patent Application Laid-Open No. 2016-217084 Japanese Patent Application Laid-Open No. 2020-190438

The present invention was made in consideration of the above situation, and aims to provide a practical prediction method that makes it possible to predict the amount of rutting in asphalt pavement, taking into account the effects of temperature.

After extensive research and trial and error to solve the above problem, the inventors came up with the idea of dividing the design period into subperiods of appropriate length and predicting the amount of permanent deformation in the depth direction of the pavement for each subperiod and for each layer that makes up the asphalt pavement. Furthermore, by associating a pre-categorized and unified "deemed layer temperature" with the subperiod of the layer for which permanent deformation is to be predicted, they discovered that it is possible to predict permanent deformation for each layer and for each subperiod without undue burden, while taking into account the effects of temperature. To calculate the cumulative deformation of the entire asphalt pavement over the entire design period, the permanent deformation calculated for each subperiod and for each layer can be added together for all subperiods and all layers.

That is, the present invention provides a method for predicting the amount of rutting in an asphalt pavement, comprising:
(A) determining the amount of permanent deformation in the depth direction of the pavement that is predicted to occur during the design period due to the expected traffic load for each layer constituting the asphalt pavement and for each partial period constituting the design period; and
(a) adding up the determined permanent deformation amounts for all layers for which the permanent deformation amounts have been determined and for all partial periods for which the permanent deformation amounts have been determined, and setting the resulting value as a predicted value for the amount of rutting in the design period;
The step (a)
(c) among the layers for which the permanent deformation amount is to be calculated, for a layer for which the amount of permanent deformation to be calculated may be affected by temperature, a step of setting a predetermined representative temperature for a temperature range to which the average temperature of the layer in the partial period belongs as the deemed layer temperature of the layer in the partial period;
(e) The above problem is solved by providing a method for predicting the amount of rutting in asphalt pavement that takes into account the effects of temperature, which includes a step of using material constants and/or physical property values at the assumed layer temperature as the material constants and/or physical property values to be used when calculating the amount of permanent deformation of the layer in the relevant partial period.

As described above, in the prediction method of the present invention, a single deemed layer temperature corresponding to the average temperature at each partial period of each layer making up the asphalt pavement is associated with each partial period. Then, when calculating the amount of permanent deformation for each layer and for each partial period, the material constants and/or physical properties at that deemed layer temperature are used. This eliminates the need to calculate the material constants and physical properties in detail for each temperature, nor the need for complex calculations that take into account the complex daily changes in temperature. The predicted amount of permanent deformation can be calculated while taking into account the effects of temperature.

The average temperature for each partial period of a layer whose permanent deformation may be affected by temperature can be determined by averaging actual measurements, or it can be determined from temperature data such as the average temperature for the partial period in question. When determining the temperature data, it is, of course, preferable to use temperature data for the area where the asphalt pavement being designed will be constructed.

In a preferred embodiment, the partial periods that make up the design period are periods measured in calendar months. The design period for asphalt pavement is typically measured in years, and often spans multiple years. When the design period spans multiple years, for example, January of the first year and January of the following year are considered equivalent partial periods, and the same is true for February, March, etc. Therefore, when the design period spans multiple years, January and February can be grouped together in monthly units to form a single partial period or group of partial periods.

In another preferred embodiment, the predicted permanent deformation is calculated for each layer and for each partial period based on the following formula (4):
In the above formula, the meanings of each symbol are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
m: Partial period number for which permanent deformation is to be calculated (m = 1, 2, 3, ...)
R _(i,m) : Amount of permanent deformation predicted for layer i in partial period m Tim: Deemed layer temperature for layer i in partial period m α _(i,Tim) , β _(i,Tim) : Material constants for layer i at deemed layer temperature Tim _Nm : Number of passing revolutions (times) expected in partial period m
ε _{e (i, m)} : Elastic strain occurring in layer i in partial period m hi : Layer thickness of layer i (mm).

As described above, R _{(i, m)} is the predicted value of the permanent deformation amount obtained for each layer i and for each partial period m, so by adding these values for all layers and all partial periods, the predicted value of the rutting amount can be obtained.

In another preferred embodiment, the prediction method of the present invention includes a step of determining the predicted amount of permanent deformation of the pavement in the depth direction for each layer constituting the asphalt pavement and for each partial period group, which is a group of one or more partial periods having the same assumed layer temperature, and a step of adding up the determined amounts of permanent deformation for all layers for which the amounts of permanent deformation have been determined and for all partial period groups for which the amounts of permanent deformation have been determined, to obtain a predicted value for the amount of rutting in the design period.

In the above aspect, the predicted permanent deformation amount for each layer constituting the asphalt pavement and for each partial period group is calculated based on the following formula (7):
In the above formula, the meanings of each symbol are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
r: Partial period group number for which permanent deformation is to be calculated (r = 1, 2, 3, ...)
R _(i,r) : Amount of permanent deformation predicted for layer i in partial period group r. Tir: Deemed layer temperature for layer i in partial period group r. α _(i,Tir) , β _(i,Tir) : Material constants for layer i at deemed layer temperature Tir. _Nr : Number of passing revolutions (times) expected in partial period group r.
ε _{e (i, r)} : Elastic strain occurring in layer i in sub-period group r hi: Layer thickness of layer i (mm).

In another preferred aspect, the prediction method of the present invention includes a step of determining the predicted amount of permanent deformation in the depth direction of the pavement for each layer constituting the asphalt pavement and for each temperature condition group, which is a group consisting of one or more partial periods in which the deemed layer temperature is the same for all corresponding layers, and a step of calculating the predicted amount of rutting by adding up the determined permanent deformation amounts for all layers for which the permanent deformation amounts were determined and for all temperature condition groups for which the permanent deformation amounts were determined.

In a preferred embodiment, the predicted permanent deformation amount is calculated for all layers for each temperature condition group based on the following formula (10):
In the above formula, the meanings of each symbol are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
n: total number of layers for which permanent deformation is to be calculated p: temperature condition group number (r = 1, 2, 3, ...)
Rp: The sum of the predicted permanent deformation amount for all layers in all partial periods belonging to temperature condition group p α _(i,p) , β _(i,p) : Material constants of layer i in all partial periods belonging to temperature condition group p N: Total number of passes (times) expected in the design period
γ _p : The time ratio (%) of all partial periods belonging to temperature condition group p to the design period
ε _{e (i, p)} : Elastic strain occurring in layer i in a partial period belonging to temperature condition group p. hi: Layer thickness of layer i (mm).

When the predicted permanent deformation amount is calculated for each temperature condition group for all layers, the predicted value of the rutting amount can be calculated by the following formula (11):
In the above formula, the meanings of each symbol are as follows:
R: Predicted permanent deformation amount s: Total number of temperature conditions.

The present invention has the advantage of being able to accurately predict the amount of rutting in asphalt pavement, taking into account the effects of temperature, without undue burden.

1 is a graph showing the relationship between the number of loadings and permanent set obtained in an FN test. 1 is a graph plotting the relationship between the ratio of permanent strain ε _p to elastic strain ε _e and the number of loadings.

The method for predicting the amount of rutting according to the present invention includes the steps of (a) determining the amount of permanent deformation in the depth direction of the pavement that is predicted to occur during a design period due to anticipated traffic loads for each layer that constitutes the asphalt pavement and for each partial period that constitutes the design period, and (b) adding up the determined amounts of permanent deformation for all layers and for all partial periods for which the amounts of permanent deformation were determined, and calculating the resulting amount as the predicted amount of rutting for the design period.

<Layer structure of asphalt pavement>
An example of the layer structure of an asphalt pavement targeted by the prediction method according to the present invention is shown in Table 1 below.

As shown in Table 1, the example asphalt pavement is composed of five layers, starting from the pavement surface: surface layer, intermediate layer, base layer, roadbed, and subgrade. The roadbed is further divided into three layers depending on the materials used: asphalt stabilized layer, graded crushed stone layer (upper roadbed), and crushed run layer (lower roadbed), for a total of seven layers that make up the asphalt pavement.

The method of dividing the multiple layers that make up an asphalt pavement is not limited to that described in Table 1, but because permanent deformation is calculated for each layer, it is best to classify layers made of materials that are predicted to have a different response to the expected wheel load as separate layers. Furthermore, when calculating permanent deformation for each layer and for each partial period, the effect of the temperature of that layer during that partial period is taken into account. Therefore, even if layers are made of the same material, it is best to classify parts that are at different depths from the surface and where the average temperature during the partial period is predicted to be significantly different as separate layers.

<Partial period>
On the other hand, partial periods constituting a design period include, for example, partial periods obtained by dividing the design period by the length of each calendar month. If the partial periods are calendar months, then if the design period is one year, the design period will be composed of 12 partial periods from January to December. If the design period is less than one year or longer than one year, the design period will be composed of partial periods equal to the number of months that make up the design period. If the design period spans multiple years, it is considered that one year will be repeated under the same conditions. Therefore, for example, January of each year is considered to be an equivalent partial period, and the same is true for February, March, etc. Therefore, as described above, January and February may be grouped together as a single partial period or group of partial periods, with each month being January and February, respectively.

However, partial periods are not limited to calendar months. Instead of dividing partial periods from January to December based on the length of each calendar month, a year can be divided into 12 equal parts, with each partial period being 365 days/12, or any number of partial periods of any length can be set.

However, if the length of the partial period is too short, the effort required to calculate the amount of permanent deformation will be excessive, which may make it impractical, and is therefore undesirable. Conversely, if the length of the partial period is too long, this is also undesirable, as it may result in large errors when considering the effects of temperature, making accurate predictions impossible. The length of each partial period should preferably be at least one week, and at most three months, but it is most convenient and most preferable to use calendar months as partial periods.

<Predicted permanent deformation>
There are no particular limitations on the method for calculating the predicted permanent deformation for each layer and for each partial period based on the layer structure of the asphalt pavement in question, the design period, and the partial periods that make up the design period. Any method may be used as long as it is possible to calculate the predicted permanent deformation for each layer and for each partial period. However, it is preferable to use, for example, the following formula (1) described in "Pavement Engineering Library 7: Fundamentals of Pavement Engineering," Japan Society of Civil Engineers, March 2012, page 76.
In the above formula (1), ε _p is the permanent strain, N is the number of passing wheels, ε _e is the elastic strain, and α and β are material constants.

The permanent deformation Ri of layer i can be calculated by multiplying the permanent deformation ε _p by the thickness hi of layer i. Since the permanent deformation ε _p is expressed by the above formula (1), the permanent deformation Ri of layer i can be calculated by the following formula (2).
In the above formula (2), αi and βi are material constants of the material constituting layer i, and can be calculated based on the relationship between the number of loadings and permanent strain obtained from material tests such as cyclic triaxial tests. However, since the material constants αi and βi usually depend on temperature, in order to calculate the permanent deformation Ri while taking into account the effect of temperature, it is necessary to use the values of αi and βi corresponding to the temperature of layer i. _εei is the elastic strain of layer i.

<Deemed layer temperature>
As mentioned above, the material constants αi and βi of layer i are temperature-dependent material constants. However, the temperature of each layer that makes up the asphalt pavement varies from layer to layer, changes daily, and is usually different between day and night even on a daily basis. Therefore, it is not realistic to determine the material constants αi and βi of layer i taking into account the complex changes in the temperature of each layer. Therefore, in this invention, the assumed layer temperature Tim is used as the temperature of layer i.

In other words, the deemed layer temperature Tim is a temperature determined based on the average temperature of layer i during partial period m for which the amount of permanent deformation is being calculated, and a predetermined representative temperature for the temperature range to which the average temperature belongs is used as the deemed layer temperature Tim for that partial period. The relationship between the predetermined temperature range and the similarly predetermined representative temperature is, for example, as shown in Table 2.

For example, if the average temperature in subperiod m of layer i is 22.0°C, the temperature range to which that average temperature belongs is the first temperature range, which is set to "up to 25.0°C," so the representative temperature of 20°C, which is preset for the first temperature range, is the deemed layer temperature Tim for subperiod m of layer i. Similarly, if the average temperature in subperiod m of layer i is 27.0°C, the temperature range to which that average temperature belongs is the second temperature range, which defines a temperature range of "greater than 25.0°C to 35.0°C," so the representative temperature of 30°C, which is preset for the second temperature range, is the deemed layer temperature Tim for subperiod m of layer i. Similarly, for a layer and subperiod whose average temperature belongs to the third temperature range, which defines a temperature range of "greater than 35.0°C to 45.0°C," the deemed layer temperature Tim is 40°C.

The temperature ranges and representative temperatures shown in Table 2 are examples, and the number of temperature ranges, respective temperature ranges, and representative temperatures are not limited to those shown in Table 2. The temperature range of 25.0°C or less may be divided into two or more temperature ranges, or a temperature range above 45.0°C may be set. For example, five temperature ranges may be set from 0°C to 50°C in increments of 10°C. A different representative temperature may also be set for each temperature range from those listed in Table 2, but it is preferable to set approximately the midpoint of the set temperature range as the representative temperature.

Note that while the deemed layer temperature may be calculated for all layers that make up the asphalt pavement in question, it is more reasonable to calculate it only for those layers for which the amount of permanent deformation is being calculated and for which the amount of permanent deformation may be affected by temperature. For example, in the layer structure shown in Table 1, the amount of permanent deformation that is being calculated for the surface layer, intermediate layer, base layer, and asphalt stabilized layer may be affected by temperature, so it is best to calculate the deemed layer temperature for at least these layers for each partial period.

On the other hand, the average temperature of layer i during partial period m can be determined by any appropriate method. For example, if there is already average temperature data obtained by actual measurements for asphalt pavement with a similar layer structure that already exists in an area where the same or similar weather conditions are expected, or if it is possible to obtain average temperature data by actual measurements, then the measured average temperature can be used.

If there is no actual measured average temperature data or it is difficult to obtain it by actual measurement, the average pavement temperature Mp for each layer in each partial period may be obtained from the temperature data for the relevant region using the following formula (5.3.3) described in "5-3-2 Structural Design Conditions" in the "Pavement Design Handbook," compiled by the Japan Road Association, February 2006, pp. 113-118.
In the above formula,
Mp: Monthly average pavement temperature (℃)
Ma: Monthly average temperature (℃)
z: Depth (cm) from the surface of the point at which the temperature is to be estimated.

Incidentally, in the above-mentioned section of the Pavement Design Handbook, after explaining the symbols used in formula (5.3.3), it states, "The average temperature of a certain layer is the temperature at a position h'/3 from the top surface of that layer (thickness = h'). Therefore, the average temperature of a certain layer is defined as the depth from the road surface to the top of that layer plus h'/3, which is z."

Based on this, the average temperatures for each layer during each subperiod were calculated for the case in which an asphalt pavement with the layer configuration shown in Table 1 was constructed in a certain hypothetical area. The subperiods were 12 subperiods, measured in calendar months from January to December, and the monthly mean temperature Ma was calculated from the published monthly mean temperatures for the target area over the past five years. The value z was calculated by adding one-third of the layer thickness to the depth from the pavement surface of the top surface of each layer. Note that the temperature data used to calculate the monthly mean temperature Ma is not limited to the past five years. It is also possible to use monthly mean temperatures Ma calculated from monthly mean temperatures over periods shorter or longer than five years. Of the layer configurations shown in Table 1, the fine-grained crushed stone layer, crushed ore layer, and subgrade were not included in the layers for which the average temperature was calculated, as it was determined that the permanent deformation of these layers was unlikely to be affected by temperature. The results are shown in Table 3.

By applying the average temperatures for each partial period of each layer listed in Table 3 to the relationship between the temperature range and representative temperature in Table 2, the assumed layer temperatures are calculated as shown in Table 4 below.

<Material constants α, β>
Once the assumed layer temperature Tim for each layer in each partial period is determined, the material constants α and β for each layer at each assumed layer temperature can be determined based on the relationship between the elastic modulus of each pavement material determined by the DM test (Dynamic Modulus test) and the number of loadings determined by the FN test (Flow Number test) (permanent strain ε _p / elastic strain ε _e ).

The DM test is a triaxial cyclic compression test, as described in "Study on the relationship between the dynamic modulus of elasticity E ^* and plastic deformation resistance of asphalt mixtures using AMPT," 72nd Annual Academic Conference of the Japan Society of Civil Engineers, September 2017, presentation number V-008. A load is applied to a cylindrical specimen with displacement meters attached to three points on its side to generate a certain strain, and the dynamic modulus of elasticity E ^* is calculated from the stress and strain. The FN test is a stress-controlled cyclic compression test, as described in "Study on the relationship between the dynamic modulus of elasticity E ^* and plastic deformation resistance of asphalt mixtures using AMPT," 72nd Annual Academic Conference of the Japan Society of Civil Engineers, September 2017, presentation number V-008. A creep curve is obtained by measuring the plastic strain generated during repeated loading, and the number of loadings FN until the rate of change of plastic strain changes from a decrease to an increase is calculated.

Table 5 shows the conditions for the DM test, and Table 6 shows the conditions for the FN test.

In Tables 5 and 6, the test temperatures of 20°C, 30°C, and 40°C correspond to the assumed layer temperatures of each layer shown in Table 4, and the loading pressure of 0.70 MPa in Table 6 corresponds to a wheel load of 5.75 tons, a loading pressure that takes into account the expected increase in vehicle size in the future.

The DM test described above was used to determine the elastic modulus at each temperature for the asphalt mixture (Material A) primarily used for the intermediate or base layer, the asphalt mixture (Material B) primarily used for the surface layer, and the asphalt stabilized layer. The results are shown in Table 7.

In Table 7, the elastic modulus of graded crushed stone and crusher run is a transcription of the values listed in "Pavement Design Handbook," compiled by the Japan Road Association, February 2006, pages 113-118, and in "5-3-2 Structural Design Conditions," page 117, Table 5.3.1. Regarding the subgrade, page 114 of the Pavement Design Handbook states, "When the CBR value is known, the elastic modulus is usually estimated from equation (5.3.1)," and lists the formula elastic modulus E = 10CBR. Based on this, and since the design CBR of the assumed subgrade is 12, we set the elastic modulus to 120, which is 10 times that. Furthermore, because these graded crushed stone, crusher run, and subgrade are pavement materials that do not contain asphalt, their elastic modulus was assumed to be constant regardless of temperature.

The results of the FN test conducted on Material A at a test temperature of 40°C are shown in Figure 1. As shown in Figure 1, the FN test determines the relationship between the number of loading cycles N at a loading pressure of 0.70 MPa and the permanent strain _εp that occurs at that time.

On the other hand, the elastic strain _εe can be calculated as _εe = σ/E from the loading pressure σ (0.7 MPa) applied during the FN test and the elastic modulus E of each material calculated in the DM test. Therefore, the material constants α and β of the materials used in the DM test and FN test can be calculated based on the relationship between _εp , N, and _εe and the formula (1) shown above.

That is, equation (1) is as follows:
This can be transformed into the following equation (3).
When ε _p /ε _e is plotted on the vertical axis and N on the horizontal axis, both on a logarithmic scale, and the approximate curve equation is calculated, the approximate curve equation y = 2.5663 ^{x 0.1692} is obtained, for example, as shown in Figure 2. This approximate curve equation corresponds to ε _p /ε _e = αN ^β , and therefore the material constants in this example, i.e., the material constants α and β of Material A at 40°C, can be calculated as α = 2.5663 and β = 0.1692, respectively.

As described above, DM tests and FN tests were performed at different temperatures and with different materials, and the material constants α and β determined for each material at each temperature were shown in Table 8 below.

For the material constants α and β, if literature values are available, those values can also be used. For roadbeds and subgrades, where temperature is not thought to have a significant effect, there is a particular advantage to using literature values, as there is no need to be concerned about the temperature at which the material constants are used. For example, for granular materials such as sized crushed stone and crusher run, which are used in roadbeds, the material constants α and β for granular materials listed in "Pavement Engineering Library 7: Fundamentals of Pavement Engineering," Japan Society of Civil Engineers, March 2012, page 77, Example 3.13 may be used. For roadbeds, the material constants α and β for gravelly soil listed in "Pavement Engineering Library 7: Fundamentals of Pavement Engineering," Japan Society of Civil Engineers, March 2012, page 77, Table 3.7 may be used.

<Elastic strain ε _e >
The elastic strain _εe generated in each layer of asphalt pavement can be determined using the pavement structure analysis program "GAMES," which is based on the multilayer elastic theory and is introduced, along with its operating method, in "Pavement Engineering Library 3: Introduction to Pavement Structural Analysis Using Multilayer Elastic Theory," Japan Society of Civil Engineers, April 2005, pp. 69-94. In other words, the elastic strain εe generated in each layer of asphalt pavement can be determined by setting the required analysis conditions, such as temperature, elastic _modulus of each layer, Poisson's ratio, subgrade thickness, interlayer slippage, and loading conditions, and then running the program according to the operating method of "GAMES."

The temperature can be, for example, the assumed layer temperature of 20°C, 30°C, or 40°C. The modulus of elasticity can be the value shown in Table 7. The subgrade thickness can be, for example, a standard 100 cm. The interlayer slip ratio can be "0" because the asphalt mixture is bonded with a tack coat, and "0.99" because the asphalt mixture and the subbase, the subbase and the subbase, and the subbase and the subgrade are all unbonded. The loading condition can be set to, for example, 56.35 kN, taking into account the expected increase in vehicle size. The Poisson's ratio for each material can be the value listed in the "Pavement Design Handbook," compiled by the Japan Road Association, February 2006, pp. 113-118, or in "5-3-2 Structural Design Conditions," page 117, Table 5.3.1.

<Length of partial period>
On the other hand, the length of a partial period is reflected in the number of passing wheels N, i.e., the number of times the wheel load acts. For example, if the design period is composed of 12 partial periods, the length of the partial period is reflected by setting the number of passing wheels in the partial period to 1/12 of the total number of passing wheels expected in the design period.

<Permanent deformation for each story in partial periods>
As described above, when the material constants α and β of each layer and the elastic strain ε _e of each layer at each assumed layer temperature are known, the permanent deformation amount of layer i in partial period m can be calculated by the following equation (4).
In the above formula, the meanings of each symbol are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
m: Partial period number for which permanent deformation is to be calculated (m = 1, 2, 3, ...)
R _(i,m) : Amount of permanent deformation predicted for layer i in partial period m Tim: Deemed layer temperature for layer i in partial period m α _(i,Tim) , β _(i,Tim) : Material constants for layer i at deemed layer temperature Tim _Nm : Number of passing revolutions (times) expected in partial period m
ε _{e (i, m)} : Elastic strain occurring in layer i in partial period m hi : Layer thickness of layer i (mm).

<Predicted amount of rutting>
The predicted permanent deformation R _{(i, m)} in the partial period m of the layer i is added together for all layers and all partial periods to obtain the predicted rutting amount R. That is, the predicted rutting amount R can be obtained by the following formula (5) or (6).
In the above formulas (5) and (6), n is the total number of layers i, and u is the total number of partial periods m.

As described above, the prediction method of the present invention determines the deemed layer temperature for each layer for each of the multiple sub-periods that make up the design period, and uses physical properties such as the material constants α and β of each material at the deemed layer temperature Tim in each sub-period for each layer, and the elastic modulus E of each material at the deemed layer temperature Tim in each sub-period for each layer, to determine the predicted amount of permanent deformation for each layer and for each sub-period. This has the advantage of allowing the predicted amount of rutting to be determined while taking into account the effects of temperature, within the normally expected range of effort and time, without requiring excessive time and effort or extensive calculations.

In the above example, the predicted amount of permanent deformation was calculated for each layer and for each partial period. However, it is also possible to set up a partial period group consisting of one or more partial periods with the same assumed layer temperature, and calculate the predicted amount of permanent deformation for each layer and for each partial period group.

In this case, the amount of permanent deformation predicted for each layer and for each partial period group is calculated for each layer and for each partial period group based on the following formula (7).
In the above formula, the meanings of each symbol are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
r: Partial period group number for which permanent deformation is to be calculated (r = 1, 2, 3, ...)
R _(i,r) : Amount of permanent deformation predicted for layer i in partial period group r. Tir: Deemed layer temperature for layer i in partial period group r. α _(i,Tir) , β _(i,Tir) : Material constants for layer i at deemed layer temperature Tir. _Nr : Number of passing revolutions (times) expected in partial period group r.
ε _{e (i, r)} : Elastic strain occurring in layer i in sub-period group r hi: Layer thickness of layer i (mm).

To calculate the predicted amount of rutting, the permanent deformation amounts calculated for each layer and for each sub-period group are added together for all layers and for all sub-period groups.
That is, the predicted value R of the amount of rutting can be calculated by the following formula (8) or (9).
In the above formulas (8) and (9), n is the total number of layers i, and v is the total number of partial period groups r (however, the total number v of partial period groups r differs depending on the layer).

As described above, when the amount of permanent deformation is calculated for each group of partial periods, which are groups of one or more partial periods with the same assumed layer temperature, the advantage is that the predicted amount of rutting can be calculated with less work than when the amount of permanent deformation is calculated for each layer and for each partial period.

Furthermore, in the above example, the predicted amount of permanent deformation was calculated for each layer and for each partial period or group of partial periods. However, it is also possible to set a group of temperature conditions, each group consisting of one or more partial periods in which the deemed layer temperature is the same for all corresponding layers, and calculate the predicted amount of permanent deformation for each layer and for each group of temperature conditions.

The temperature conditions are explained below using the assumed layer temperatures shown in Table 4 as an example.

As mentioned above, in the example shown in Table 9, during the seven-month partial periods from January to April and October to December, the deemed layer temperatures of the surface layer, middle layer, base layer, and AS stabilization layer are all 20°C, and since the deemed layer temperatures are the same for all corresponding layers, this is considered to be one temperature condition group A.

However, when comparing April and May, the deemed layer temperatures for the base layer and AS stabilized layer are both the same at 20°C, but for the surface and intermediate layers, the deemed layer temperature in April is 20°C, but in May it is 30°C, so it cannot be said that the deemed layer temperatures are the same for all corresponding layers. Therefore, May is classified as temperature condition group B, which is different from temperature condition group A. As there is no other month in which the deemed layer temperature is the same as May for all corresponding layers, May alone constitutes temperature condition group B.

In June, July, and September, the deemed layer temperature was 30°C in all of the surface, middle, base, and AS stabilization layers, and the deemed layer temperature was the same for all corresponding layers, so these were grouped into one temperature condition group C. August differs from all other months in that the deemed layer temperature in the surface layer was 40°C, so it is grouped into temperature condition group D by itself.

The assumed layer temperature for each layer in each temperature condition group and the percentage of the period each temperature condition group occupies in 12 months are shown in Table 10 below.

When using the temperature condition groups described above, the expected number of passing wheels for each temperature condition group can be determined by multiplying the total expected number of passing wheels during the design period by the proportion of the period that each temperature condition group occupies during the design period.

When the above temperature condition groups are used, the predicted permanent deformation amount can be calculated for each temperature condition group by the following formula (10).
In the above formula, the meanings of the symbols are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
n: total number of layers for which permanent deformation is to be calculated p: temperature condition group number (r = 1, 2, 3, ...)
Rp: The sum of the predicted permanent deformation amount for all layers in all partial periods belonging to temperature condition group p α _(i,p) , β _(i,p) : Material constants of layer i in all partial periods belonging to temperature condition group p N: Total number of passes (times) expected in the design period
γ _p : The time ratio (%) of all partial periods belonging to temperature condition group p to the design period
ε _{e (i, p)} : Elastic strain occurring in layer i in a partial period belonging to temperature condition group p. hi: Layer thickness of layer i (mm).

To obtain a predicted value of the amount of rutting, the permanent deformation Rp obtained for each temperature condition group may be added together for all temperature condition groups, as shown in the following formula (11).
In the above formula, the meanings of the symbols are as follows:
R: Predicted permanent deformation amount s: Total number of temperature conditions.

By introducing the concept of temperature condition groups, the relationship between partial periods and assumed temperatures can be organized by dividing partial periods into temperature condition groups. This not only significantly simplifies calculations and work compared to calculating permanent deformation for each layer and for each partial period, but it is also expected to result in greater labor savings compared to calculating permanent deformation for each layer and for each partial period group with the same assumed layer temperature.

<Example 1 of rutting prediction>
For the asphalt pavement having the layer configuration shown in Table 11 below, the amount of permanent deformation was determined for each layer and for each temperature condition group, thereby determining the predicted amount of rutting.

The construction location was the same as the location where the average temperatures for the past five years were shown in Table 3, and the temperature range and representative temperature were also set the same as in Table 2, so the temperature condition groups and their proportions are as shown in Table 10 above.

The elastic modulus of each material at each temperature was determined using the values shown in Table 7, while the material constants α and β for Material A, Material B, and the asphalt stabilization layer were determined using the values shown in Table 8 above. The material constants α and β for the grading crushed stone, crusher run, and subgrade were determined using the values shown in Table 12 below, based on values found in literature, and were assumed to be constant regardless of temperature.

Using the pavement structure analysis program "GAMES" mentioned above and setting the same analysis conditions as above, the amount of elastic strain in the depth direction of the road for each layer was determined for each temperature condition group. The results are shown in Table 13.

The design period is set at 25 years, and the load pressure is set at 0.70 MPa, taking into account future increases in vehicle size. The number of passing vehicles over the 25-year design period is based on the fatigue failure number for traffic volume category N7, which is listed in Table 3.2.2 on page 30 of the "Pavement Design Handbook," published by the Japan Road Association (a public interest incorporated association) in February 2006, at 35,000,000 passes/10 years, and is multiplied by 2.5 to arrive at 87,500,000 passes/25 years.

Using the above values, the predicted amount of rutting was calculated based on equations (10) and (11). The results are shown in Table 14.

<Example 2 of rutting prediction>
For an asphalt pavement that had been constructed 9 years and 4 months earlier and had rutting of up to 17 mm measured, the predicted rutting volume was calculated based on the above formulas (10) and (11) and compared with the measured value. The material constants α, β, and elastic modulus E of the materials that make up the asphalt pavement were calculated using the same materials as those used during construction. The layer structure of the asphalt pavement in question is shown in Table 15.

The construction site was the same as the location where the average temperatures for the past five years were shown in Table 3, so the monthly average temperatures for each layer were set to the same values as those shown in Table 3. The temperature ranges and representative temperatures were also set to the same values as in Table 2, so the temperature condition groups and their proportions are as shown in Table 10 above.

The elastic modulus E and material constants α and β at each deemed layer temperature for the polymer-modified Type II asphalt mixture and straight asphalt mixture were determined using DM tests and FN tests, as described above. The loading pressure in the FN test was 0.63 MPa, equivalent to a normal design wheel load of 5 tons. The determined elastic modulus E and material constants α and β are shown in Tables 16 and 17, respectively, below. The elastic moduli of the asphalt stabilized layer, grading-adjusted crushed stone, crusher run, and subgrade listed in Table 16 were the same as those listed in Table 7. As shown in Table 9 above, the deemed layer temperature of the asphalt stabilized layer at the target construction site never reached 40°C, so the material constants α and β at 40°C for the asphalt stabilized layer were not determined.

The material constants for the graded crushed stone, crusher run, and roadbed are shown in Table 12 and are assumed to be constant regardless of temperature.

Using the pavement structure analysis program "GAMES" mentioned above, the analysis conditions were changed to correspond to the layer structure of the asphalt pavement under consideration, and the amount of elastic strain in the depth direction of the road for each layer was determined for each temperature condition group. The results are shown in Table 18.

The design period was set at 9 years and 4 months, the period that has already elapsed on site, and the load pressure was set at 0.63 MPa, the current design value. The number of passing vehicles over the 9-year and 4-month design period was calculated based on the fatigue failure number for traffic volume category N7 (35,000,000 passes/10 years) listed in Table 3.2.2 on page 30 of the "Pavement Design Handbook," published by the Japan Road Association (February 2006), multiplied by 9 years and 4 months/10 years to arrive at 32,666,667 passes/9 years and 4 months.

Using the above values, the predicted amount of rutting was calculated based on equations (10) and (11). The results are shown in Table 19.

As described above, the predicted rutting depth obtained using the prediction method of the present invention was 19.8 mm, which was in excellent agreement with the maximum rutting depth of 17 mm actually measured at the site 9 years and 4 months after construction.

In the above prediction example, the percentage of each temperature condition group in the 12 months was multiplied by the total number of wheels passing through the 9-year, 4-month design period to determine the number of wheels passing through each temperature condition group. However, the percentage of each temperature condition group can be adjusted depending on the month and year in which the 4-month portion exceeding the full 9 years falls. For example, if the 4-month excess is the 4 months from January to April, all of these belong to temperature condition group A, so the percentage of temperature condition group A is (7 months x 9 years + 4 months) / (12 months x 9 years + 4 months) x 100 = 67 months / 112 months x 100 = 59.8%, and the percentages of the other temperature condition groups will also change accordingly.

As explained above, the present invention makes it possible to very accurately predict the amount of rutting in asphalt pavement under conditions that take into account the effects of temperature. The rutting prediction values provided by the present invention provide enormous convenience to road managers and road builders, and have great industrial applicability.

Claims (9)

A method for predicting the amount of rutting in an asphalt pavement, comprising:
(A) determining the amount of permanent deformation in the depth direction of the pavement that is predicted to occur during the design period due to the expected traffic load for each layer constituting the asphalt pavement and for each partial period constituting the design period; and
(a) adding up the determined permanent deformation amounts for all layers for which the permanent deformation amounts have been determined and for all partial periods for which the permanent deformation amounts have been determined, and setting the resulting value as a predicted value for the amount of rutting in the design period;
The step (a)
(c) among the layers for which the permanent deformation amount is to be calculated, for a layer for which the amount of permanent deformation to be calculated may be affected by temperature, a step of setting a predetermined representative temperature for a temperature range to which the average temperature of the layer in the partial period belongs as the deemed layer temperature of the layer in the partial period;
(D) A step of using material constants and/or physical property values at the deemed layer temperature as material constants and/or physical property values to be used when calculating the amount of permanent deformation of the layer in the partial period.
A method for predicting the amount of rutting in asphalt pavement taking into account the effects of temperature. 2. The method according to claim 1, wherein in the step (a), the predicted permanent deformation is calculated for each layer and for each partial period based on the following formula (4):
In the above formula, the meanings of the symbols are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
m: Partial period number for which permanent deformation is to be calculated (m = 1, 2, 3, ...)
R _(i,m) : Amount of permanent deformation predicted for layer i in partial period m Tim: Deemed layer temperature for layer i in partial period m α _(i,Tim) , β _(i,Tim) : Material constants for layer i at deemed layer temperature Tim _Nm : Number of passing revolutions (times) expected in partial period m
ε _{e (i, m)} : Elastic strain occurring in layer i in partial period m hi : Layer thickness of layer i (mm). A forecasting method according to claim 1 or 2, wherein the partial periods constituting the design period are periods measured in calendar months. The prediction method of claim 1 or 2, further comprising a step of determining, by actual measurement or from air temperature data, the average temperature of a layer during a partial period during which the amount of permanent deformation to be determined may be affected by temperature. The step (a) is a step of determining the predicted amount of permanent deformation of the pavement in the depth direction for each layer constituting the asphalt pavement and for each partial period group, which is a group of one or more partial periods having the same assumed layer temperature;
2. The prediction method according to claim 1, wherein the step (i) is a step of adding up the determined permanent deformation amounts for all layers for which the permanent deformation amounts have been determined and for all partial period groups for which the permanent deformation amounts have been determined, and setting the sum as a predicted value for the amount of rutting in the design period. 6. The prediction method according to claim 5, wherein in the step (a), the predicted permanent deformation amount is calculated for each layer and for each partial period group based on the following formula (7):
In the above formula, the meanings of each symbol are as follows:
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
r: Partial period group number for which permanent deformation is to be calculated (r = 1, 2, 3, ...)
R _(i,r) : Amount of permanent deformation predicted for layer i in partial period group r. Tir: Deemed layer temperature for layer i in partial period group r. α _(i,Tir) , β _(i,Tir) : Material constants for layer i at deemed layer temperature Tir. _Nr : Number of passing revolutions (times) expected in partial period group r.
ε _{e (i, r)} : Elastic strain occurring in layer i in sub-period group r hi: Layer thickness of layer i (mm). The step (a) is a step of calculating the predicted permanent deformation of the pavement in the depth direction for each layer constituting the asphalt pavement and for each temperature condition group, which is a group of one or more partial periods in which the assumed layer temperature is the same for all corresponding layers;
2. The prediction method according to claim 1, wherein the step (i) is a step of adding up the determined permanent deformation amounts for all layers for which the permanent deformation amounts have been determined and for all temperature condition groups for which the permanent deformation amounts have been determined, and setting the sum as a predicted value for the amount of rutting during the design period. 8. The method according to claim 7, wherein the predicted permanent deformation is calculated for each temperature condition group for all layers for which the permanent deformation is calculated, based on the following formula (10):
In the above formula,
i: Layer number for which permanent deformation is to be calculated (i = 1, 2, 3, etc.)
n: total number of layers for which permanent deformation is to be calculated p: temperature condition group number (r = 1, 2, 3, ...)
Rp: The sum of the predicted permanent deformation amount for all layers in all partial periods belonging to temperature condition group p α _(i,p) , β _(i,p) : Material constants of layer i in all partial periods belonging to temperature condition group p N: Total number of passes (times) expected in the design period
γ _p : The time ratio (%) of all partial periods belonging to temperature condition group p to the design period
ε _{e (i, p)} : Elastic strain occurring in layer i in a partial period belonging to temperature condition group p. hi: Layer thickness of layer i (mm). 9. The method according to claim 8, wherein the predicted permanent deformation amount is calculated based on the following formula (11):
In the above formula,
R: Predicted permanent deformation amount s: Total number of temperature conditions.