CN117371310B - Method for establishing wide highway pavement water film thickness prediction model - Google Patents
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Abstract
The invention relates to a method for establishing a wide highway pavement water film thickness prediction model. The method comprises the following steps: determining a water film thickness prediction basic model, wherein the basic model is as follows: step (2) selecting an SMA-13 road surface as a test material, carrying out an indoor rainfall simulation test to obtain actual measured values of the thickness of the water film under different test environments and rainfall intensities, carrying out regression fitting on the prediction model in the step (1) according to the actual measured values, and carrying out sensitivity analysis of four parameters of drainage length, rainfall intensity, gradient and construction depth on the thickness of the water film to obtain a regression formula of the thickness of the water film determined by the indoor rainfall simulation test; step (3) the water film thickness prediction model is subjected to outdoor test correction; and (4) adding additional accumulated water to the ruts except the construction depth of the road, so as to increase the thickness of the water film. The method ensures the accuracy of the acquired data in a mutual checking mode, and establishes the water film thickness prediction model so as to realize the accurate prediction of the water film thickness.
Description
Technical Field
The invention belongs to the field of roads, and particularly relates to a method for establishing a wide highway pavement water film thickness prediction model.
Background
The water-float phenomenon easily appears when the vehicle is in rainy day high-speed driving, and the water film thickness of ponding road surface has very big influence to tire water float, therefore, it is very necessary to monitor the water film thickness distribution on highway road surface in real time. The water film formed on the road surface by rainfall can obviously reduce the friction coefficient of the contact part of the tire and the road surface. The running on the wet road surface has a greater danger than that on the dry road surface, and the frictional resistance of the contact between the vehicle tire and the road surface is sharply reduced along with the increase of the speed of the vehicle and the increase of the depth of the water film on the road surface, so that the vehicle is watery and out of control. In addition, the water mist splashed by the vehicle during running on a wet road surface can reduce the visibility level during running, so that the road running safety is seriously affected. Therefore, in the road design stage and the operation and maintenance stage, it is necessary to grasp the relationship between the road geometry (flat, longitudinal, transverse), the surface characteristics of the road surface (construction depth, friction coefficient, flatness), the rainfall intensity and the road surface water film depth.
Regarding a model for predicting the water film depth of the pavement surface under the rainfall condition, students at home and abroad begin to work out from the 50 th century, a series of researches are sequentially carried out, and a plurality of water film depth prediction models are established and mainly comprise a regression model, a mathematical physical model and a neural network model. Although the method for predicting the water film thickness by adopting the neural network has high precision, the method requires that the input and the output are within the range of the value of the training sample due to the limitation of the algorithm, so that the method is not suitable for popularization, and larger access is possible to actually appear if the range of the training sample is exceeded. While the mathematical physical model can analyze the thickness of the water film theoretically, the slope flow during rainfall is complex, and a differential equation is difficult to solve, and if the mathematical physical model is simplified, the result often has a larger difference from the actual situation.
The regression model belongs to the category of an experience model, adopts a mathematical method to process the relation among various variables describing hydrologic phenomena, and obtains a mathematical expression of the model through regression by calibrating parameters in the model through a large amount of data, and then is applied to reality. However, the existing road surface water film thickness prediction model usually adopts a single simulation environment test as a main part, and lacks of mutual verification with the on-site actual measurement data of the road.
Disclosure of Invention
The invention aims to provide a method for establishing a wide highway pavement water film thickness prediction model. Firstly, a water film thickness prediction basic model is determined by briefly analyzing and comparing the regression formula of the existing more classical water film thickness prediction model, then, the parameters of the water film thickness prediction model are determined by an indoor simulation experiment and are compared and analyzed with the classical prediction model, and finally, all parameters of the model are corrected by an outdoor experiment.
The technical solution for realizing the purpose of the invention is as follows: a method for establishing a wide highway pavement water film thickness prediction model comprises the following steps:
step (1): determining a water film thickness prediction basic model, wherein the basic model is as follows:
wherein: d, water film thickness, mm; l-drainage length, m; s, road gradient,%; i-rainfall intensity, mm/min; t-construction depth, mm; k, K 1,k2,k3,k4 -regression coefficients;
Step (2): and (3) selecting an SMA-13 road surface as a test material, performing an indoor rainfall simulation test to obtain actual measurement values of the water film thickness under different test environments and rainfall intensities, performing regression fit on the prediction model in the step (1) according to the actual measurement values, and performing sensitivity analysis of four parameters of drainage length, rainfall intensity, gradient and construction depth on the water film thickness to obtain a water film thickness regression formula determined by the indoor rainfall simulation test, wherein the regression formula is as follows:
d＝0.401·I0.492·L0.356·S-0.276·T0.472；
Step (3): and (3) carrying out outdoor test correction on the water film thickness prediction model, wherein the corrected water film thickness prediction model is as follows:
d＝0.39·I0.515·L0.36·S-0.276·T0.445；
step (4): in addition to the depth of construction of the road itself, the increase in water film thickness resulting from the addition of additional water for ruts is formulated as follows:
d＝0.39·I0.515·L0.36·S-0.276·T0.445+r；
wherein: r-rut depth, mm.
Further, the basic model in the step (1) adopts a regression equation and a regression coefficient to carry out the significance test respectively, wherein the regression equation adopts F test, and the significance of the regression coefficient adopts t test.
Further, the test statistic F is:
Wherein: p-number of independent variables, wherein the independent variables are respectively rainfall intensity, construction depth, gradient and drainage length, so that p=4; n-sample size; s e, sum of squares of residual errors; s R, regression square sum; f statistics obey the F distribution with the degree of freedom of (n, n-p-1), and for a given significance level alpha, if F is less than or equal to F α (p, n-p-1), the regression effect of the model is not considered to be significant; if F > F α (p, n-p-1), the regression effect of the model is considered to be remarkable;
The test statistic t i is:
Wherein: -a least squares estimator of the parameter k i to be estimated; sigma-residual standard deviation; l xx -parameters of the ith influencing factor; the t statistic obeys the t distribution with the degree of freedom (n, n-p-1), for a given significance level α, if The ith influencing factor in the model can be considered to have no significant influence on the thickness of the water film; if the t-test corresponding to each influencing factor is obtainedIt is explained that the multiple regression equation thus found satisfies the significance requirement.
Further, the indoor rainfall simulation test in the step (2) has the following test conditions:
The rainfall intensity is measured in real time by an ABS-RS485 tipping bucket type rainfall sensor, the resolution is 0.2mm, and the maximum rainfall intensity is allowed to pass through for 8mm/min; the value range of the rainfall intensity is set to be 2.5-5 mm/min;
and a vernier caliper probe is used for reading the thickness of the water film.
Further, the arrangement of the indoor test scene of the indoor rainfall simulation test in the step (2) is specifically as follows:
The molding mixture type is that the standard rut board of 30cm multiplied by 30cm of SMA-13 is 4, 2 lines are drawn every 10cm in the transverse direction and the longitudinal direction, the intersection point of the transverse line and the longitudinal line is taken as a measured center point, and the average value of the constructional depth of the rut board is calculated by adopting a sand paving method and is taken as the actual measurement value of the constructional depth of the point.
Further, slope simulation of the indoor rainfall simulation test in the step (2) is divided into two scenarios:
aiming at a single gradient scene, each track plate is placed on a height-adjustable wedge iron, and five scenes of 0.5%, 1%, 1.5%, 2% and 2.5% are respectively determined according to the requirement of a test gradient;
Objects with different heights on four corner pads of each track plate are used for simulating the existence of a transverse slope and a longitudinal slope, the direction and the size of a composite gradient are calculated, and the test is carried out according to five scenes of 0.5%, 0.9%, 1.4%, 1.9% and 2.4% of the composite gradient.
Further, in the step (2), the influence degree of four parameters of drainage length, rainfall intensity, gradient and construction depth on the thickness of the water film is quantitatively analyzed through correlation calculation by using a gray correlation analysis method; the method comprises the following steps:
First, a reference sequence and a comparison sequence are designated, and a set of sequences is set as:
Wherein: x 0 (k) is a reference number column; x i (k) is a comparison array;
Normalizing the values by means of averaging, i.e
Calculating the association coefficient of the number sequence:
wherein: ζ i (k) is the correlation coefficient, i.e. the relative difference of the comparison curve y i (k) of the ith factor at the kth point and the reference curve y 0 (k); p is a resolution coefficient, and is selected from 0 to 1, wherein the smaller the value is, the more the difference between the coefficients can be improved;
Finally, gray correlation degree calculation is carried out:
Wherein: r i is the association of sequence y i to y 0.
Further, the outdoor test in step (3) is specifically:
placing points on a selected test field by using a total station, wherein the transverse and longitudinal distances of the elevation measuring points are 1m, and simultaneously measuring the relative coordinates of each point; constructing a transverse-longitudinal distance of 1m between the depth measuring points, performing test according to relevant regulations of a sand paving method, testing three times around each measuring point, and averaging test results;
Detecting the water seepage coefficient of the road surface, and ensuring that accumulated water caused by rainfall is discharged through the road surface instead of being discharged through seepage;
after the road surface water film thickness monitoring system is ready, the rainfall simulation is started, the water film thickness monitoring is mainly performed by using a laser remote sensing type water film thickness detector, the conventional probe type measurement is performed by using an auxiliary means, the rainfall intensity is monitored and recorded by using a tipping bucket type rain gauge, and when the road surface is wet and saturated, the water film thickness of the road surface is started to be tested after the water flow of the road surface is stable.
Compared with the prior art, the invention has the remarkable advantages that:
The method combines indoor and outdoor modes, creates more abundant simulation conditions, enables the use scene to be more fit with the actual road, and improves the applicability of the water film thickness prediction model;
According to the invention, the water film thickness is measured by adopting a method of combining a remote sensing road surface condition sensor and a traditional vernier caliper method, the accuracy of collected data is ensured by a mutual calibration mode, and a water film thickness prediction model is established, so that the accurate prediction of the water film thickness is realized;
according to the invention, by developing the establishment of the wide highway water film thickness prediction model, the theoretical support for calculating the water film thickness and the drainage capacity is provided for the wide pavement drainage design.
Drawings
FIG. 1 is an indoor rut board test point arrangement of the present invention; wherein (a) is theory and (b) is practice.
FIG. 2 is a schematic drawing of the depth of a sanding process according to the present invention.
FIG. 3 is a schematic illustration of a test grade setting for a simulated longitudinal grade of the present invention.
FIG. 4 is a schematic illustration of a test grade setting of the present invention simulating the presence of both a lateral and a longitudinal grade.
FIG. 5 is a graph of drain length versus film thickness for the present invention.
FIG. 6 is a graph of rainfall intensity versus water film thickness for the present invention.
FIG. 7 is a graph of slope versus film thickness for the present invention.
FIG. 8 is a graph of depth of construction versus thickness of a water film in accordance with the present invention.
Fig. 9 shows the result of gray correlation calculation for each parameter.
FIG. 10 shows the results of regression equation analysis for the laboratory test.
FIG. 11 shows the regression coefficient analysis results of the indoor test.
FIG. 12 is a comparison of the calculation results of each predictive model.
FIG. 13 is a graph showing the average relative deviation of the calculation results of each prediction model.
Fig. 14 is a comparison of the calculation results after the Ji Tianjian model and Gallway model are modified.
FIG. 15 is a graph showing the average relative deviation of the calculation results of each prediction model.
Fig. 16 is an outdoor test site.
FIG. 17 is a graph comparing predicted data herein to measured water film thickness.
Fig. 18 is a regression coefficient analysis result of the outdoor test.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The method for establishing the water film thickness model is as follows;
Firstly, the model is assumed to be as follows:
wherein: d-film thickness (mm);
L-drainage length (m);
S-road surface gradient (%);
i-rainfall intensity (mm/min);
t-construction depth (mm).
K, K 1,k2,k3,k4 -regression coefficient.
After logarithmic transformation, a multiple linear regression equation is obtained:
lnd＝lnK+k1lnI+ k2lnL+k3lnS+k4lnT (2)
After the multiple linear regression equation is analyzed, the regression equation and the regression coefficient are subjected to the saliency test respectively, wherein the regression equation adopts F test, and the saliency of the regression coefficient adopts t test.
The test statistic F is:
Wherein: p—number of independent variables, herein, the independent variables are rainfall intensity, construction depth, gradient and drainage length, respectively, so p=4;
n-sample volume;
s e -sum of squares of residual errors;
s R -regression sum of squares.
F statistics obey the F distribution with the degree of freedom of (n, n-p-1), and for a given significance level alpha, if F is less than or equal to F α (p, n-p-1), the regression effect of the model is not considered to be significant; if F > F α (p, n-p-1), the regression effect of the model is considered significant.
The test statistic t i is:
Wherein: -a least squares estimator of the parameter k i to be estimated;
sigma-residual standard deviation;
L xx -parameters of the ith influencing factor.
The t statistic obeys the t distribution with the degree of freedom (n, n-p-1), for a given significance level α, ifThe ith influencing factor in the model can be considered to have no significant influence on the thickness of the water film; if the t-test corresponding to each influencing factor is obtainedIt is explained that the multiple regression equation thus found satisfies the significance requirement.
(II) Water film thickness model indoor test and model establishment
(1) Construction of indoor simulation environment
Since the macroscopic texture of the road surface is closely related to drainage, the tire increases the water pressure on the road surface, and the water is extruded and drained from the grooves provided by the texture, so that the SMA-13 road surface is selected as the indoor simulation test material. In addition, the gradient of the road surface also meets the requirements related to the expressway, so that the track boards are respectively placed according to five gradients of 0.5%, 1%, 1.5%, 2% and 2.5%.
The specific test conditions are as follows:
① Setting rainfall intensity. The rainfall intensity is measured in real time through an ABS-RS485 tipping bucket type rainfall sensor, the resolution is 0.2mm, the maximum rainfall intensity is allowed to be 8mm/min, and the tipping bucket type rainfall sensor records rainfall through a pulse signal technology and transmits the rainfall to a platform terminal.
As the invention researches the influence of short-time heavy rainfall on the ponding of the wide road surface of the expressway, the value range of the rainfall intensity is set to be 2.5-5 mm/min, namely 2.5mm/min, 3mm/min, 3.5mm/min, 4mm/min, 4.5mm/min and 5mm/min respectively.
② A traditional vernier caliper probe reads a water film thickness device. When the water film depth is measured, the water film thickness value is obtained by the method that the water film thickness value is obtained by smearing the water test paste on a vernier caliper probe with reading display, changing orange into purple when the water test paste contacts water, and recording the vernier caliper reading at the moment, wherein the color-changing boundary is the water film boundary.
③ The indoor test scenario is arranged as follows:
Firstly, forming 4 pieces of 30cm multiplied by 30cm standard rut boards with the mixture type of SMA-13 in a laboratory, drawing 2 lines every 10cm in the transverse and longitudinal directions, taking the intersection point of the transverse and longitudinal lines as a central point for measurement as shown in fig. 1, calculating the structural depth average value of the rut boards by adopting a sanding method (as shown in fig. 2), and taking the structural depth average value of the rut boards as a structural depth actual measurement value of the point (because the required area of the manual sanding method is not less than 30cm multiplied by 30cm, the structural depth test of each rut board can be considered for 3 times, and taking the average value as a uniform structural depth value of the rut boards). Table 1 is the construction depth measurement of four SMA13 rut plates.
TABLE 1SMA13 rut plate and AC-13 rut plate construction depth measurement
Secondly, aiming at gradient simulation, the test is arranged in two scenes, namely the following steps:
1) For single slope scenes, each track slab is placed on a height-adjustable wedge iron, and according to the test slope requirements, the height of the wedge is adjusted according to five scenes of longitudinal slopes of 0.5%, 1%, 1.5%, 2% and 2.5%, so that the gradient of the track slab meets the test requirements, as shown in fig. 3.
2) Objects with different heights on four corner pads of each track plate are used for simulating the conditions of transverse slopes and longitudinal slopes, the direction and the size of the composite gradient are calculated, and the test is carried out according to five scenes of 0.5%, 0.9%, 1.4%, 1.9% and 2.4% of the composite gradient, as shown in fig. 4.
(2) Test data summary and analysis
According to the test environment which is arranged in advance, the drainage length and the gradient of each measuring point are obtained, and then according to the construction depth of each track plate which is measured by a sand paving method, the water film thickness of each point which is measured under different rainfall intensities of 2.5mm/min, 3mm/min, 3.5mm/min, 4mm/min, 4.5mm/min, 5mm/min and the like is combined, so that regression fitting of the water film thickness prediction model is realized. Table 2 records the measured values of the water film thickness for each set at six rainfall intensities.
Table 2 indoor test data summary table
1) Firstly, the change condition of the water film thickness along with the parameters of drainage length, rainfall intensity, gradient, construction depth and the like is analyzed.
① Fig. 5 is a graph showing the relationship between the drainage length and the water film thickness at a rainfall intensity of 2.5mm/min, a gradient of 0.5% and a construction depth of 0.87mm, and it can be seen from the graph that the water film thickness of the road surface tends to increase nonlinearly with the increase of the drainage length in the case where the rainfall intensity, the gradient and the construction depth are constant. When the drainage length is small, the water film thickness increases relatively rapidly along with the increase of the drainage length, and when the drainage length is long, the increase speed of the water film thickness tends to be gentle.
② FIG. 6 is a graph showing the relationship between the rainfall intensity and the water film thickness at a drainage length of 1m, a gradient of 1% and a construction depth of 0.87 mm.
As can be seen from the figure, the thickness of the water film shows a gradually increasing trend along with the increase of the rainfall intensity, and basically shows a straight line form, which is possibly related to the minimum rainfall intensity of 2.5mm/min simulated in the test. It can be found from the figure that for the thickness of the pavement water film at the same position, the larger increase occurs along with the increase of rainfall intensity, which is also an important reason that traffic accidents are more likely to occur in heavy rain or stormwater weather than in smaller rainfall weather. Therefore, the influence of rainfall intensity on the road surface water film thickness is not negligible.
③ FIG. 7 is a graph showing the relationship between the gradient and the thickness of a water film at a rainfall intensity of 2.5mm/min, a drainage length of 1m and a construction depth of 0.87mm, and it can be seen from the graph that the thickness of the water film shows a gradual decrease trend with increasing gradient under the conditions of constant rainfall intensity, drainage length and construction depth, and the curve decreases faster when the gradient is less than 2.0%; when the gradient is greater than 2.0%, the speed at which the water film thickness decreases with increasing gradient gradually becomes gentle. The water film thickness and the gradient show such opposite increasing and decreasing relation, mainly because when the gradient is increased, the drainage speed of the slope runoff is increased, so that the rainwater falling on the road surface can be quickly discharged, and the water film thickness of the road surface is reduced. In this sense, an appropriate increase in the gradient of the road surface lateral slope is advantageous for reducing the road surface water film thickness and accelerating the road surface drainage, within the allowable range. The method is also a factor for comprehensively considering the gradient of the road surface by highway design workers, and can rapidly drain the accumulated water on the road surface in rainy days by properly increasing the gradient of the road surface, and meanwhile, the probability of traffic accidents in rainy days is reduced.
④ Fig. 8 is a graph of the relationship between the construction depth and the water film thickness at a rainfall intensity of 2.5mm/min, a drainage length of 1m and a gradient of 1%, and it can be seen from the graph that the construction depths of SMA rutting plates formed in a laboratory are respectively 0.87mm, 0.88mm, 0.91mm and 0.93mm, and the construction depth values are relatively close, so that the corresponding water film thickness values are relatively close, but the graph shows a trend of curve change, and the water film thickness value increases with the increase of the construction depth.
In summary, it is known that the water film thickness value increases with an increase in drainage length, rainfall intensity, and construction depth, but decreases with an increase in gradient. In addition, four parameters of drainage length, rainfall intensity, gradient and depth of formation will be analyzed herein for sensitivity to water film thickness.
2) Sensitivity analysis of drainage length, rainfall intensity, gradient and depth of formation to water film thickness
In order to further analyze the influence degree of the drainage length, rainfall intensity, gradient and construction depth on the water film thickness, the influence degree of the four parameters on the water film thickness data is quantitatively analyzed through correlation calculation by using a gray correlation analysis method.
The gray correlation analysis method is used for measuring the correlation degree between factors according to the similarity or the dissimilarity degree of development situations between the factors. The method has no high requirement on the size of the sample, does not need a typical distribution rule during analysis, can extract the main factors affecting the system, the main characteristics and the differences of the system influence among the factors from a plurality of factors, and has wide practicability. The gray correlation analysis is a quantitative comparison analysis of development situations, and a main factor affecting a target value is sought by calculating the degree of correlation and the order of the degree of correlation of the target value (reference series) and the influencing factor (comparison series). The gray correlation is calculated as follows.
First, a reference sequence and a comparison sequence are designated, and a set of sequences is set as:
Wherein: x 0 (k) is a reference number column; x i (k) is a comparison array.
Normalizing the values, herein by means of a averaging method, i.e
Calculating the association coefficient of the number sequence:
Wherein: ζ i (k) is the correlation coefficient, i.e. the relative difference of the comparison curve y i (k) of the ith factor at the kth point and the reference curve y 0 (k); p is a resolution coefficient, and is selected from 0 to 1, and the smaller the value is, the more the difference between the coefficients can be improved.
Finally, gray correlation degree calculation is carried out:
Wherein: r i is the association of sequence y i to y 0.
The drainage length, rainfall intensity, gradient and construction depth are taken as comparison series, the actually measured water film thickness is taken as reference series, the correlation calculation is carried out according to the test result, and the calculation result is shown in fig. 9.
As can be seen from the gray correlation calculation result in fig. 9, the gray correlation value of the rainfall intensity is 0.6693, the gray correlation value of the drainage length is 0.6555, the gray correlation value of the construction depth is 0.6414, the gray correlation value of the gradient is 0.5817, and the gray correlation value of each parameter is: r Intensity of rainfall >r Length of drain >r Depth of construction >r Gradient of slope . It is known that among the four factors affecting the thickness of the water film on the asphalt pavement, the rainfall intensity and the drainage length are the main influencing factors, and the construction depth is the second, and finally the gradient is the gradient, wherein the minimum gradient association degree is probably caused by the association of the gradient with the drainage path.
(3) Establishment of water film thickness prediction model
Fig. 10 and 11 are results obtained by analysis of the test data in table 2, p=4, n=336, the F statistic obeys the F distribution of degrees of freedom (336, 331), F 0.01 (336,331) =3.38 is known by table look-up for a given level of significance of 1%, and the regression equation F statistic obtained by spss analysis is 227.245, much greater than F 0.01 (336,331), indicating that the linear correlation described by the regression equation is more pronounced. Similarly, it is known from looking up the t distribution table that the degree of freedom is 336, the significance level is 5% of the double-sided test threshold value t α/2 =1.967, but the absolute values of the t statistics corresponding to the regression coefficients K, K 1,k2,k3,k4 obtained by spss analysis are 11.584, 14.535, 16.543, 20.146 and 34.453 respectively, which are all much larger than t α/2, which means that the influence of these parameters on the thickness of the water film is significant.
Through the analysis, a regression formula of the water film thickness determined by the indoor rainfall simulation test of the subject can be preliminarily obtained as follows:
d＝0.401·I0.492·L0.356·S-0.276·T0.472 (9)
wherein: d-film thickness (mm);
L-drainage length (m);
S-road surface gradient (%);
i-rainfall intensity (mm/min);
t-construction depth (mm).
(4) Comparison analysis with classical predictive model
The predictive models herein were compared to classical models, including Luo Jing model, ji Tianjian model, and Gallway model, each of which is shown in table 3.
TABLE 3 Water film thickness prediction model
The above 4 models were verified by randomly selecting 20 sets of data from the test, and the calculation results of the obtained models are shown in table 4. And carrying out verification analysis on the classical model by the data acquired by the indoor simulation test, wherein the calculation results of the obtained models are shown in the following table.
Table 4 comparison results of the prediction models (Unit: mm)
As can be seen from fig. 12 and 13, the model herein and the rogin model are close to the actual measurement value curve, while the model Ji Tianjian and the model Gallway have larger deviation from the actual measurement value, and the average relative deviation of the model predicted herein is 2.09%, the average relative deviation of the model Luo Jing is 8.17% and the average relative deviation of the model Ji Tianjian and the model Gallway from the actual measurement value is 56.37% and 52.89%, respectively, and the calculation results are shown in table 5, fig. 14 and fig. 15 if the calculated water film thickness calculated by the model Ji Tianjian and the model Gallway is added to the corresponding average construction depth value, since the construction depth of the road surface itself is excluded from the calculation formula only by considering the road surface water film thickness in the model Ji Tianjian and the model Gallway.
Table 5 Ji Tianjian model and Gallway model modified Water film thickness comparison results (unit: mm)
From the above figures, it can be seen that by comparing the Ji Tianjian model and Gallway model which increase the construction depth, the average relative deviation values of the predictive models, luo Jing model, ji Tianjian model and Gallway model and the predictive values thereof are 2.09%, 8.17% and 11.77% and 8.18%, respectively, further explaining the influence of the construction depth which must be considered when building the water film thickness predictive model.
(III) correction of water film thickness prediction model outdoor test
The test selects a certain park road as a test site. Placing points on a selected test field by using a total station, wherein the transverse and longitudinal distances of the elevation measuring points are 1m, and simultaneously measuring the relative coordinates of each point; the transverse and longitudinal spacing of the depth measuring points is 1m, the test is carried out according to the relevant regulation of the sand laying method, the test is carried out three times around each measuring point, and the test result is averaged. In addition, the water seepage coefficient of the road surface is detected, so that the accumulated water caused by rainfall is mainly discharged through the road surface instead of being discharged through seepage. After the road surface water film thickness monitoring system is ready, the rainfall simulation is started, the water film thickness monitoring is mainly performed by using a laser remote sensing type water film thickness detector, the conventional probe type measurement is performed by using a secondary means, the rainfall intensity is still recorded by using a tipping bucket type rain gauge, when the road surface is wet and saturated, the water film thickness of the road surface can be started to be tested after the water flow of the road surface is stable, and the test result is shown in the following table.
Table 6 data summary table collected by outdoor test
The measured data is taken into the predictive model herein and compared to the measured values for analysis, as shown in fig. 17.
As can be seen from fig. 17, the data predicted by the water film thickness model herein are not completely consistent with the measured data, and have a certain difference, but by analyzing the relative deviation value between the two, the relative deviation percentage of the measured value relative to the model predicted value is distributed within the range of [ -6.78%,8.42% ], the relative deviation value is within the range of 10%, and the average relative deviation percentage is only 4.28%, which indicates that the prediction model herein has a certain reliability.
Thus, the regression analysis was performed comprehensively by integrating the indoor test and the outdoor road surface measured data, and the results are shown in fig. 18 below.
Therefore, the corrected water film thickness prediction model is:
d＝0.39·I0.515·L0.36·S-0.276·T0.445 (10)
wherein: d-film thickness (mm);
L-drainage length (m);
S-road surface gradient (%);
i-rainfall intensity (mm/min);
t-construction depth (mm).
In addition, considering that the conditions of ruts and pit slots are common in the actual operation process of the highway, when the highway is rainy, besides the construction depth of the road, the thickness of a water film caused by adding extra ponding of the ruts and the pit slots is recommended to be increased, and the formula is as follows:
d＝0.39·I0.515·L0.36·S-0.276·T0.445+r (11)
Wherein: r-rut depth (mm).
Claims (4)
1. The method for establishing the wide highway pavement water film thickness prediction model is characterized by comprising the following steps of:
step (1): determining a water film thickness prediction basic model, wherein the basic model is as follows:
d＝K·Ik1·Lk2·Sk3·Tk4
wherein: d, water film thickness, mm; l-drainage length, m; s, road gradient,%; i-rainfall intensity, mm/min; t-construction depth, mm; k, K 1,k2,k3,k4 -regression coefficients;
After logarithmic transformation of the basic model, a multiple linear regression equation is obtained:
lnd＝lnK+k1lnI+ k2lnL+k3lnS+k4lnT (2)
After the multiple linear regression equation is analyzed, performing the significance test on the regression equation and the regression coefficient respectively, wherein the regression equation adopts F test, and the significance of the regression coefficient adopts t test;
the test statistic F is:
Wherein: p—number of independent variables, herein, the independent variables are rainfall intensity, construction depth, gradient and drainage length, respectively, so p=4;
n-sample volume;
s e -sum of squares of residual errors;
S R -regression sum of squares;
F statistics obey the F distribution with the degree of freedom of (n, n-p-1), and for a given significance level alpha, if F is less than or equal to F α (p, n-p-1), the regression effect of the model is not considered to be significant; if F > F α (p, n-p-1), the regression effect of the model is considered to be remarkable;
The test statistic t i is:
Wherein: -a least squares estimator of the parameter k i to be estimated;
sigma-residual standard deviation;
l xx -parameters of the ith influencing factor;
the t statistic obeys the t distribution with the degree of freedom (n, n-p-1), for a given significance level α, if The ith influencing factor in the model is considered to have no significant influence on the thickness of the water film; if the t-test corresponding to each influencing factor is obtainedThen the multiple regression equation obtained is described as meeting the significance requirement;
Step (2): and (3) selecting an SMA-13 road surface as a test material, performing an indoor rainfall simulation test to obtain actual measurement values of the water film thickness under different test environments and rainfall intensities, performing regression fit on the prediction model in the step (1) according to the actual measurement values, and performing sensitivity analysis of four parameters of drainage length, rainfall intensity, gradient and construction depth on the water film thickness to obtain a water film thickness regression formula determined by the indoor rainfall simulation test, wherein the regression formula is as follows:
d＝0.401·I0.492·L0.356·S-0.276·T0.472；
Step (3): and (3) carrying out outdoor test correction on the water film thickness prediction model, wherein the corrected water film thickness prediction model is as follows:
d＝0.39·I0.515·L0.36·S-0.276·T0.445；
step (4): in addition to the depth of construction of the road itself, the increase in water film thickness resulting from the addition of additional water for ruts is formulated as follows:
d＝0.39·I0.515·L0.36·S-0.276·T0.445+r；
wherein: r-rut depth, mm;
the arrangement of the indoor test scene of the indoor rainfall simulation test in the step (2) is specifically as follows:
Forming 4 standard rut plates with 30cm multiplied by 30cm of the type of the mixture of SMA-13, drawing 2 lines every 10cm in the transverse direction and the longitudinal direction, taking the intersection point of the transverse line and the longitudinal line as a measured center point, and calculating the structural depth average value of the rut plates by adopting a sand paving method to obtain a structural depth actual measurement value of the point;
Slope simulation of the indoor rainfall simulation test in the step (2) is divided into two scenes:
aiming at a single gradient scene, each track plate is placed on a height-adjustable wedge iron, and five scenes of 0.5%, 1%, 1.5%, 2% and 2.5% are respectively determined according to the requirement of a test gradient;
Objects with different heights on four corner pads of each track plate are used for simulating the existence of a transverse slope and a longitudinal slope, the direction and the size of a composite gradient are calculated, and the test is carried out according to five scenes of 0.5%, 0.9%, 1.4%, 1.9% and 2.4% of the composite gradient.
2. The method of claim 1, wherein the indoor simulated rainfall test in step (2) is performed under the following test conditions:
The rainfall intensity is measured in real time by an ABS-RS485 tipping bucket type rainfall sensor, the resolution is 0.2mm, and the maximum rainfall intensity is allowed to pass through for 8mm/min; the value range of the rainfall intensity is set to be 2.5-5 mm/min;
and a vernier caliper probe is used for reading the thickness of the water film.
3. The method according to claim 2, wherein the influence degree of four parameters of drainage length, rainfall intensity, gradient and construction depth on the thickness of the water film is quantitatively analyzed through correlation calculation by using a gray correlation analysis method in the step (2); the method comprises the following steps:
First, a reference sequence and a comparison sequence are designated, and a set of sequences is set as:
Wherein: x 0 (k) is a reference number column; x i (k) is a comparison array;
Normalizing the values by means of averaging, i.e
Calculating the association coefficient of the number sequence:
Wherein: x i (k) is the correlation coefficient, i.e., the relative difference between the comparison curve y i (k) at the kth point and the reference curve y 0 (k) for the ith factor; p is a resolution coefficient, and is selected from 0 to 1, wherein the smaller the value is, the more the difference between the coefficients can be improved;
Finally, gray correlation degree calculation is carried out:
Wherein: r i is the association of sequence y i to y 0.
4. A method according to claim 3, wherein the outdoor test in step (3) is specifically:
placing points on a selected test field by using a total station, wherein the transverse and longitudinal distances of the elevation measuring points are 1m, and simultaneously measuring the relative coordinates of each point; constructing a transverse-longitudinal distance of 1m between the depth measuring points, performing test according to relevant regulations of a sand paving method, testing three times around each measuring point, and averaging test results;
Detecting the water seepage coefficient of the road surface, and ensuring that accumulated water caused by rainfall is discharged through the road surface instead of being discharged through seepage;
after the road surface water film thickness monitoring system is ready, the rainfall simulation is started, the water film thickness monitoring is mainly performed by using a laser remote sensing type water film thickness detector, the conventional probe type measurement is performed by using an auxiliary means, the rainfall intensity is monitored and recorded by using a tipping bucket type rain gauge, and when the road surface is wet and saturated, the water film thickness of the road surface is started to be tested after the water flow of the road surface is stable.
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