Disclosure of Invention
The invention provides a method for testing the comprehensive dynamic modulus of a roadbed and pavement structure, which is simple, convenient to operate, efficient and accurate and aims to overcome the technical problems that the evaluation result is inconsistent with the actual working condition and the on-site evaluation and design are disconnected when the modulus of the roadbed and pavement is evaluated at present.
In order to achieve the technical purpose, the technical scheme of the invention is that,
a method for testing the comprehensive dynamic modulus of a roadbed and pavement structure comprises the following steps:
firstly, carrying out rigid impact on the top surface of a road surface of a roadbed and a road surface to be detected, and recording a duration curve of the reaction force of the top surface of the road surface to the bottom surface of an excitation source generating the impact;
secondly, establishing a fitting model:
wherein tau is the preprocessing delay of the acquisition system, and t represents time; m (t) is a dimensionless value of the duration of the reaction force response of the road surface top surface to the bottom surface of the excitation source; f (t) duration of reaction force response (kN) of road surface top to excitation source bottom, F (t)maxIs the peak value; omega is the principal angular frequency of the counterforce time course of the road surface top surface to the bottom surface of the excitation source; h (·) is a unit jump function;
thirdly, fitting the reaction response duration of the road surface top surface to the bottom surface of the excitation source according to a fitting model to obtain a principal angular frequency omega, and further obtaining the comprehensive dynamic modulus E of the roadbed and road surface structure according to the following formula:
wherein E is the comprehensive dynamic modulus of the roadbed pavement structure; m is the mass of the excitation source, R is the bottom surface radius of the excitation source, and mu is the comprehensive Poisson's ratio of the roadbed pavement structure.
In the first step, when rigid impact is carried out on the top surface of the road surface of the roadbed and the road surface to be tested, the impact point selects the road surface position of a driving belt on the top surface of the roadbed and road surface structure, and the road surface position is a flat surface.
In the first step, when rigid impact is carried out on the top surface of the roadbed and the road surface to be tested, the deformation of the roadbed and the road surface structure caused by the impact is controlled within the elastic range of the roadbed and the road surface structure.
In the first step, when recording the duration curve of the counterforce of the road surface top surface to the bottom surface of the excitation source generating the impact, the test is continuously carried out for at least 2 times, and the arithmetic mean value is taken as the recording result.
In the second step, when the fitting model is established and the counterforce of the top surface of the road surface on the bottom surface of the excitation source generating impact is recorded, the pretreatment delay of the acquisition system, namely the duration tau of the refractory period is considered, and then the fitting model is as follows:
in the second step, the expression of the unit jump function H (-) is as follows:
in the third step, according to the difference of the road surface structure materials, the Poisson ratio mu is as follows: the mu value of the cement concrete pavement is 0.15-0.25; mu of the asphalt concrete pavement is 0.25-0.35; the mu value of the soil subgrade is 0.235 to 0.4.
Compared with the existing roadbed and pavement modulus testing method, the method has the technical effects that the comprehensive dynamic modulus of the roadbed and pavement structure can be obtained only according to the reaction force characteristics of the road surface to the excitation source, and the comprehensive dynamic modulus of the roadbed and pavement structure does not need to be obtained by simultaneously obtaining the reaction force and the displacement or deformation characteristics of the road surface like the existing method, so that the method is simpler and more efficient compared with the existing method.
The invention will be further explained with reference to the drawings.
Detailed Description
Referring to fig. 2, after a lot of previous studies and the results of road surface modulus tests of FWD specified in current road asphalt pavement design specification (JTG D50-2017), it is found that the time course curve of the reaction stress of the road surface on the bottom surface of the rigid drop hammer satisfies an approximate half-sine function after the rigid drop hammer freely falls on the road surface.
According to the half sine function model, assuming that the kinetic energy of the rigid drop hammer is completely converted into the deformation energy of the road surface in the mechanical behavior process of impacting the road surface by the rigid drop hammer according to the law of conservation of energy, and because the stress distribution characteristics of the bottom surface of the rigid drop hammer meet the Jerad model, the analytic relation between the principal angular frequency of the road surface responding to the reaction force of the bottom surface of the rigid drop hammer by the half sine duration and the comprehensive dynamic modulus of the roadbed and the road surface exists, as shown in the following formula (4)
(4) The formula is a theoretical analytic formula of the principal value ω (principal angular frequency, also referred to as angular frequency center value) of the angular frequency of the road surface of the roadbed impacted by the drop hammer. It can be seen that the principal angular frequency is directly proportional to the elastic modulus of the surface material and the root mean square of the radius of the bottom surface of the drop hammer, and inversely proportional to the root mean square of the mass of the drop hammer, while the principal angular frequency is independent of the drop height.
By transforming the formula (4), a calculation formula of the comprehensive dynamic modulus E of the roadbed pavement structure can be further obtained, and the calculation formula is shown as the following formula:
from the above formula, it can be seen that when the mass of the drop hammer and the radius of the bottom surface are fixed, the comprehensive dynamic modulus E of the roadbed and the road surface is proportional to the square of the principal angular frequency ω, and therefore. And combining the mass m of the drop hammer and the radius R of the bottom surface, and obtaining omega through actually measuring a reaction force waveform curve on the drop hammer impact road surface, so that the comprehensive dynamic modulus E of the roadbed and road surface structure can be quickly solved. And the principal angular frequency omega of the ground with the falling weight can be obtained by comparing and analyzing the actually measured wave curve of the ground with the falling weight according to nonlinear fitting. Wherein the non-linear mathematical model is as
The non-linear method is carried out according to the Guass-Newton method.
In the embodiment, a metal cylinder is used as an excitation source of rigid impact load, the metal cylinder is lifted to a height at which a free impact road surface structure does not generate plastic deformation, the excitation source is used for generating the rigid impact load by falling on the top surface of the road surface, an acceleration pressure sensor arranged in the excitation source is used for recording a duration curve of the counter force of the top surface of the road surface to the bottom surface of the excitation source, and fitting is performed according to a half sine wave mathematical model according to the form of the duration curve and the limit condition of the duration curve, so that the principal angular frequency omega (rad/s) of the counter force duration of the top surface of the road surface to the bottom surface of the excitation source is obtained. And establishing an analytic relation between the principal angular frequency omega of the reaction time course of the top surface of the road surface to the bottom surface of the excitation source and the comprehensive modulus E of the roadbed pavement structure based on the mechanical energy conservation in the impact process, so as to realize the rapid test of the comprehensive modulus of the roadbed pavement structure.
In specific implementation, this embodiment includes the following steps:
the first step is as follows: site selection of test point location
The measuring points are selected from the positions of the driving belt road surface on the top surface of the roadbed road surface structure, the top surface of the road surface at the testing positions is ensured to be smooth, the floating soil and dust on the road surface are removed, in order to ensure that the testing results have better stability and representativeness, the testing is continuously carried out for 4 times on the measuring points, and the arithmetic mean value is taken as the testing result of the point.
The second step is that: acquisition of road surface top surface counter force time domain characteristics under action of rigid impact load
The metal cylinder is used as an excitation source of the rigid impact load, and is lifted to a certain height, the height is preferably not to enable the road surface structure to generate plastic deformation, namely the deformation of the roadbed and road surface structure under the excitation action of the rigid load is controlled within an elastic range, the excitation source falls on the top surface of the road surface to generate the rigid impact load, and an acceleration pressure sensor arranged in the excitation source is used for recording a duration curve of the counter force of the top surface of the road surface to the bottom surface of the excitation source, as shown in fig. 1.
Because the acquisition system has a certain reaction time, which is shown in fig. 1, that is, τ is the preprocessing delay (refractory period) of the acquisition system, a corresponding fitting model is proposed according to the time course curve form and the limit condition, as shown in formula (1):
wherein t represents time(s); m (t) is a dimensionless value of the duration of the reaction force response of the road surface top surface to the bottom surface of the excitation source; f (t) duration of reaction force response (kN) of road surface top to excitation source bottom, F (t)maxIs the peak value; omega is the main angular frequency (rad/s) of the reaction time course of the top surface of the road surface to the bottom surface of the excitation source; τ is the period of the preprocessing delay of the acquisition system, also called refractory period(s), and H (·) is a unit jump function (also called heaviside function), as shown in equation (2).
The third step: calculating comprehensive modulus of resilience of roadbed and pavement
Fitting the reaction response duration of the top surface of the road surface to the bottom surface of the excitation source according to a formula (1) and a formula (2) to obtain the main angular frequency omega, and substituting the main angular frequency omega into a formula (3) derived according to the law of conservation of mechanical energy to quickly obtain the comprehensive dynamic modulus E of the roadbed and road surface structure.
Wherein E is the comprehensive dynamic modulus (pa) of the roadbed pavement structure; m is the mass (kg) of the rigid metal column, namely the excitation source, R is the bottom surface radius (m) of the excitation source, and mu is the comprehensive Poisson's ratio of the roadbed pavement structure.
In this embodiment, the poisson ratio μ should be appropriately adjusted according to the difference of the road surface structural materials. Wherein, the mu of the cement concrete pavement is preferably 0.15 to 0.25; the mu of the asphalt concrete pavement is preferably 0.25-0.35; the thickness of the soil subgrade is preferably 0.235 to 0.4.
In this embodiment, the comprehensive modulus E of the roadbed and the road surface is a dynamic elastic modulus, and is calculated based on the principal angular frequency ω of the time course of the reaction force of the top surface of the road surface to the bottom surface of the excitation source and the formula (3) derived from the law of conservation of mechanical energy, and is different from a static elastic modulus calculated according to the conventional half-space Boussinesq solution. Compared with the existing roadbed and pavement modulus testing method, the comprehensive dynamic modulus of the roadbed and pavement structure can be obtained only according to the reaction force characteristics of the road surface to the excitation source, and the roadbed and pavement structure comprehensive dynamic modulus does not need to be obtained by simultaneously obtaining the reaction force and the displacement or deformation characteristics of the road surface like the existing method, so that the method is simpler and more efficient compared with the existing method.
Example 1:
stiffness evaluation engineering example for old cement road of Changsha dam in Hunan province
Engineering for improving old cement road of Changsha dam in Hunan provinceThe early stage on-site rigidity evaluation engineering is based on, the load transfer and bearing capacity of the joint of the old cement road panel is tested and evaluated on site by using the method of the invention, the old cement road is a municipal road, and the structure form of the old cement road is as follows: 15cm concrete panel +25cm cement stabilized macadam base, the panel size is 4 x 5 m. The modulus result E tested by the method of the invention is compared by point-to-point testing the plate edge and the plate corner of the cement paneldAnd a test result E of the FWD method specified in the Highway subgrade and pavement site test Specification (JTG E60-2008)FWD. The time course of the reaction force generated by the rigid metal drop hammer free falling impact road table and a half sine wave model obtained by Guass-Newton fitting are shown in figure 3, and the correlation analysis of the test result is shown in figure 4.
EFWD=0.2947Ed 1.1157(n=101,R2=0.9372) (5)
The image result shows that the application of the invention to the implementation of rigid impact load on the cement road surface can well fit the reaction time course by the half sine wave function shown in the formula (1). Through comparison tests, the modulus result E tested by the method of the inventiondFWD test result E increasing from 359.2MPa to 5045.2MPaFWDThe pressure is increased from 224.8MPa to 4643.6MPa, the pressure and the temperature are positively correlated, and the correlation coefficient R is2Reaching 0.9732, a good power function is presented, as shown in equation (5). Wherein, the modulus result E of the method of the present embodimentdAverage ratio EFWDThe height is that the test result of the embodiment can better reflect the characteristic that the roadbed and pavement structure is impacted by power in the elastic deformation stage because the FWD acts on the rubber cushion block in the impact action process of the falling hammer and then transmits the load to the earth surface, and the rubber cushion block plays a role in damping and absorbs a large amount of kinetic energy of the falling hammer, so that the deformation of the road surface is seriously delayed.
Example 2:
research example of construction monitoring technology of asphalt concrete pavement of Lungui road in Changde district in Fushan City
Based on the research of the construction monitoring technology of the Lungui road asphalt concrete pavement in the Shunde district of Fushan City, the dynamic modulus of the top surface of the K0+ 180-K1 +470 section of the Lungui road asphalt pavement is compared and tested by applying the method. The main test means is a Portable Falling Weight Deflectometer (PFWD for short) and the method of the invention. The time course of the reaction force generated by adopting the rigid metal drop hammer free falling impact road table and a half sine wave model obtained by Guass-Newton fitting are shown in figure 5, and the correlation analysis of the test result is shown in figure 6.
EPFWD=0.2022Ed 1.1511(n=42,R2=0.8460) (6)
The results in the figure show that the application of the invention to the implementation of rigid impact load on the asphalt road surface can well fit the counter force time course by the half sine wave function shown in the formula (1). Through comparison tests, the modulus result E tested by the method of the inventiondPFWD test result E increasing from 932.7MPa to 2822.7MPaPFWDIncreasing from 505.4MPa to 2177.7MPa, and positively correlating the two, wherein the correlation coefficient R2Reaching 0.8460, a good power function is presented, as shown in equation (6). Wherein, the modulus result E of the test of the method of the inventiondAverage ratio EFWDThe test result of the invention can reflect the characteristic that the roadbed and pavement structure is impacted by power in the elastic deformation stage.
Example 3:
on-site bearing capacity evaluation example of new high-speed roadbed widening and expanding project in Hunan Lou
Based on the evaluation of the road condition in the early stage of the new high-speed roadbed widening and extension project of the New high-speed roadbed in Hunan province, the splicing positions of the new and old roadbeds at sections K3+ 410-K3 +510 and K3+ 780-K3 +860 of the New high-speed roadbed in the Hunan province are selected as test sections on site, the method and the PFWD are applied to carry out test and comparison, a pile number is selected at each 5m of the test section, a measuring point is selected in each of the new and old roadbeds at the parallel position of the pile number, and the PFWD dynamic modulus and the method are sequentially carried out at each measuring pointAnd (5) carrying out comparative testing. Wherein the roadbed filling soil is low liquid limit cohesive soil CL, the compactness requirement is 96 percent, and the liquid limit w isL40.7% of plastic limit wP28.4% and a plasticity index IPAt 12.2%, the optimum water content wo18.7% maximum dry density pdmaxIs 1.73 g.cm-3. The reaction time course of impacting the top surface of the roadbed by the free falling of the rigid metal drop hammer and the half sine wave form obtained by Guass-Newton fitting by applying the method are shown in figure 7, and the correlation of the test results of the two comparison methods is shown in figure 8.
EPFWD=1.7341Ed 0.846(n=76,R2=0.8151) (7)
The graph results show that the application of the invention to the rigid impact load of the top surface of the roadbed can well fit the reaction time course by the half sine wave function shown in the formula (1). Through comparison tests, the modulus result E tested by the method of the inventiondPFWD test result E increasing from 26.6MPa to 383.4MPaPFWDThe pressure is increased from 34.0MPa to 389.5MPa, the pressure and the temperature are positively correlated, and the correlation coefficient R is2Reaching 0.8151, a good power function is presented, as shown in equation (7).
Example 4:
engineering example of filling deformation control technology for Guangdong Guangfhao expressway
Based on the roadbed filling deformation control technical project of the Guangfhao expressway in Guangdong province, the typical completely weathered granite forming fill roadbed from Zhaoqingwang to K116+ 980-K117 +180 sections is selected, and the method and the PFWD are applied for testing and comparison. Wherein the engineering name of the road subgrade filler is clay sand, the compactness requirement is 94 percent, and the liquid limit w isL42.0% of plastic limit wP22.9% and a plasticity index IPAt 19.1%, the optimum water content wo10.5% maximum dry density pdmaxIs 1.91 g.cm-3. The counter force time course of impacting the top surface of the roadbed by the free falling of the rigid metal drop hammer and the half sine wave form obtained by Guass-Newton fitting are shown in the figure, and the correlation of the test results of the two comparison methods is shown in the figure 10.
EPFWD=1.186Ed 0.9391(n=58,R2=0.8193) (8)
The graph results show that the application of the invention to the rigid impact load of the top surface of the roadbed can well fit the reaction time course by the half sine wave function shown in the formula (1). Through comparison tests, the modulus result E tested by the method of the inventiondPFWD test result E increasing from 57.0MPa to 142.9MPaPFWDThe pressure is increased from 49.1MPa to 131.9MPa, the two are positively correlated, and the correlation coefficient R2Reaching 0.8193, a good power function relationship is presented, as shown in formula (8).