Investigating the Pavement Vibration Response for Roadway Investigating the Pavement Vibration Response for Roadway Service Condition Evaluation Service Condition Evaluation

. Dynamic response of pavement provides service condition information and helps with damage prediction, while limited research is available with the simulation of pavement vibration response for evaluating roadway service condition. This paper presents a numerical model for the analysis of the pavement vibration due to the dynamic load created by a passing vehicle. A quarter vehicle model was used for the determination of the vehicle moving load. Both random and spatial characteristics of the load were considered. The random nonuniform moving load was then introduced in a 3D ﬁnite element model for the determination of the traﬃc-induced pavement vibration. The validated numerical model was used to assess the eﬀects of dynamic load, material properties, and pavement structures on pavement vibration response. Numerical analyses showed that the vibration modes changed considerably for the diﬀerent roadway service conditions. The vibration signals reﬂect the level of road roughness, the stiﬀness of the pavement materials, and the integrity of pavement structure. The acceleration extrema, the time-domain signal waveform, the frequency distribution, and the sum of squares of Fourier amplitude can be potential indexes for evaluating roadway service condition. This provides recommendations for the application of pavement vibration response in early-warning and timely maintenance of road.


Introduction
Pavement, the important transportation infrastructure, provides a smooth riding surface and basic load-bearing capacity for vehicles to travel on.Pavement structure will deteriorate under cyclic traffic loading and environmental factors.Early repair and maintenance scheduling increase the safe operation and in-service performance of pavement.is can be achieved through an accurate and consistent monitoring of dynamic response of pavement.Because the signal pattern can be analyzed to distinguish between deteriorated or cracked pavement section from the intact ones [1].
Stress-strain, displacement, and acceleration are the important monitoring parameters for the dynamic response of pavement.Due to the substantial improvement of acceleration sensing technologies, the microelectromechanical system (MEMS)-based acceleration sensors have been used in the monitoring of pavement vibration.e acceleration signals caused by the moving vehicle load were processed to obtain traffic information including vehicle speed, axle, weight, and traffic volume [2][3][4][5].Moreover, by detecting the acceleration of pavement under specific wheel loadings and analyzing the vibration modes, it is possible to evaluate the pavement service condition.
Over the past several years, experimental studies have analyzed the pavement vibrations generated by vehicles to evaluate pavement service condition.Arraigada et al. [6] used accelerometers to measure pavement deflections due to traffic loads.Levenberg [7] inferred the pavement layer properties by using an integral electronic piezoelectric accelerometer.Yu and Yu [8] developed a cost-effective vibration-based system for preliminary evaluation of pavement conditions.Zhang et al. [9] analyzed time and frequency spectrums of vertical acceleration for the HMA slabs under different loading scenarios.However, the application of pavement vibration response in roadway service condition is still in the experimental stage.
On the contrary, theoretical and numerical studies have also been conducted.is can save large amount of laboratory efforts and time.e analyses considering the pavement vibration under dynamic vehicle load are widely adopted by many studies for various research purposes.Ju [10] developed a finite element (FE) model to investigate the characteristics of the building vibrations induced by adjacent moving trucks.Xu and Hong [11] investigated the effects of both a single heavy truck flow and a two-way traffic flow on building vibration.e results showed that traffic-induced ground vibrations disrupted high-tech facilities.Mhanna et al. [12] investigated the effect of the vehicle speed, the road unevenness, and the vehicle suspension system on the traffic-induced vibrations.Some recommendations were suggested for the reduction of these vibrations.Lak et al. [13] studied the relation between road unevenness, the dynamic vehicle response, and ground-borne vibrations.
e influence of road unevenness on the free field vibrations was investigated.Wang et al. [14] tested four trackbed materials for their relative vibration attenuation capacities and studied the effect of different speed and weight of the passing train on the performance of the paving materials.eir purpose is to reduce the adverse effects of pavement vibration on the surrounding structures and vehicles, rather than to analyze the pavement vibration signals for evaluating the pavement service condition.
However, there are few studies to evaluate the pavement service condition through vibration simulation analysis.
e assessment of roadway service condition is mainly reflected by the monitoring of stress, strain, and displacement.Saad et al. [15] examined the dynamic response of the fatigue strain at the bottom of the asphalt concrete layer and rutting strain at the top of the subgrade material by 3D FE analyses.Alavi et al. [16] compared the dynamic strain data of intact and damaged FE model under moving tire loading.Features extracted from the dynamic strain data were used to detect the damage progression.Xue et al. [17] simulated the loading process by using finite-element analysis.e ratio between vertical stress and longitudinal horizontal strain was demonstrated to be related to the strength of pavements and can be used for the backcalculation of pavement modulus.Wu et al. [18] investigated the dynamic responses of stress and deflection at the critical load position by changing thickness, modulus of isolating layer, and the combination between the isolating layer and concrete slab.Patil et al. [19] studied the effects of vehicle-pavement interaction, pavement thickness, and soil parameters on the dynamic response of pavement to reveal their influences on pavement dynamic performances, including the effects of subbase module on maximum deflection.
Due to the improved MEMS-accelerometer technology, pavement vibration response can be used not only for traffic information monitoring but also has the potential to be used for evaluating the roadway service condition.is paper presents a numerical model for the analyses in the timefrequency domain of the traffic-induced vibrations.e numerical modeling includes two stages.In the first stage, a quarter vehicle model is used for the determination in the time domain of the load due to road roughness.Both random and spatial characteristics of the load were considered.In the second stage, a 3D FE model of road is used to determine the pavement vibrations due to the load, which is calculated in the first stage.en, the validated road model is used to evaluate the effects of dynamic load, pavement materials, and structure on pavement vibration response, so as to determine the potential evaluation index of roadway service condition.

Numerical Model
In the case of vehicle-road interaction, the prediction of the dynamic axle loads can be uncoupled from the solution of the road-pavement interaction problem due to the high stiffness of the road compared to the vehicle's suspension system or tire [20][21][22][23].erefore, the numerical modeling includes two stages: Firstly, the dynamic axle load resulting from pavement roughness was calculated by establishing a moving vehicle model composed of springs, dampers, and lumped mass.en, the resulting axle dynamic load is used in a 3D numerical modeling for the determination of the pavement vibrations.Advances in Civil Engineering [24].Although the quarter vehicle model does not allow to model pitch and roll effect on tire forces, the stochastic load can be simulated efficiently by using the quarter vehicle model when vehicle moves straight at a constant speed.

Random Nonuniform
Figure 1 shows the quarter vehicle model [25].
In this model, the suspension and nonsuspension masses corresponding to the one corner of the vehicle are denoted by m 1 and m 2 , respectively.e suspension system is represented by a linear spring of stiffness k 1 and a linear damper of damping rate c 1 .e tire is modeled by a linear spring of stiffness k 2 and a linear damper of damping rate c 2 .e vertical displacements of suspension mass and nonsuspension mass are x 1 and x 2 , respectively.e parameter values chosen for this study are shown in Table 1 [26].
According to the D'Alembert's principle, the motion differential equations of this vibration system are written as where M, C, K, X, and P are mass matrix, damping matrix, stiffness matrix, displacement matrix, and excitement matrix, respectively.ey are written as where q is the displacement excitated by road roughness, which can be calculated as [27] _ where w(t) is the time domain signal of Gaussian white noise with mean zero; G q is the road roughness coefficient; v is the vehicle speed (m/s); and n 0 is the reference space frequency and n 0 � 0.1 m −1 .According to (1)-( 7), the vehicle random dynamic load forcing on the pavement can be calculated as where F t is the vehicle random dynamic load; G is the vehicle static load; g is the acceleration of gravity; and F d is the dynamic load applied by tires on pavement.e quarter vehicle model was established in Matlab/Simulink.e speed was set to 10 m/s.According to the ISO 8608, the classes A, B, and C of road were obtained by adjusting the geometric mean of road roughness coefficient.e geometric mean of road roughness coefficient was set as 16 (i.e., G q � 16) when the road was a class A road [28].Class A road represents high grade road, such as the highway, indicating that the surface of road is smoothness.
e sampling frequency of stochastic load was set as 1000 Hz. Figure 2 shows the random dynamic load when the vehicle speed is 10 m/s and road is class A road.
When the vehicle travels on the class A road, the value of vehicle dynamic load is not constant due to the effect of road roughness, vehicle suspension system, vehicle speed, weight, and other factors.
e value of vehicle dynamic load is random and fluctuates around 48 kN.

Spatial Distribution.
In order to obtain the more actual pavement dynamic response, it is necessary to consider both random and spatial characteristics of the load.e actual tireto-pavement contact is surface to surface contact.Once the total tire force is known, the actual or more rational contact pressure distribution can be used by considering the actual configurations of the tires [29].e actual tire-to-pavement contact is simplified as a rectangular area [30].e rectangular area is affected by the tire pattern and the load value which varies with the space.Figure 3 shows a common style of tire pattern.e size of the rectangular area is 20 cm × 18 cm.ere are five rib areas caused by the tire pattern [31].When the vehicle moves straight at a constant speed, the ratio of load amplitude is about 1 : 0.9 : 0.5 in center rib (R3), intermediate rib (R2, R4), and edge rib (R1, R5).Moreover, the spatial distribution of the vertical load can be simplified as a half-sine function in each rib area along the traffic direction [31,32].

Moving Load.
In order to simulate the movement of vehicle load, the secondary development of DLOAD subroutine was carried out based on FE software, ABAQUS, to simulate the random nonuniform moving load.A specified coordinate function COORDS( * ) and a time function TIME (1) were used to define the loading area and implement the moving load.Equation ( 9) means the loading area moves at a constant velocity along the X axis which is defined as traffic direction.
Advances in Civil Engineering where COORDS( 1) is an array containing the X coordinates of the load integration point; X 0 is initial coordinate X value of load; V is the vehicle speed; and TIME(1) is the current value of step time.erefore, X is an array containing the X coordinates of the load integration point corresponding to the moving coordinate system.en the load in each rib by considering random and spatial characteristics was defined.Equation (11) means the spatial distribution of load at time t.
where COORDS( 2) is an array containing the Y coordinates of the load integration point; the direction of Y axis is perpendicular to the traffic direction; Y 0 is initial coordinate Y value of load; abs(X) ≤ (b/2) defines the length of the loading area; abs(Y) ≤ (c/2) defines the width of the loading area; a is the ratio of load amplitude, which is set as 1 for R3, 0.9 for R2 and R4, and 0.5 for R1 and R5; b is the length of the load distribution along the traffic direction, which is set as 18 cm for R3, 16 cm for R1, R2, R4, and R5; c is the width of the load distribution perpendicular to the traffic direction, which is set as 3 cm for each rib; S is the actual contact area that is the sum of the areas from R1 to R5; P(t) is the set of the surface pressure on the load integration point at TIME(1); and F(t) is the random load produced by the quarter vehicle model at TIME (1).e random nonuniform moving load is achieved by ( 9) and (11).e vehicle speed was set as 10 m/s, and the length of loading area was set as 3 m.erefore, the total time period was 0.3 s. e increment time was set as 0.001 s, which was consistent with the sampling frequency (1000 Hz) of stochastic load.
us, the applied load can be assumed a continuous moving load if loading time is short enough.

Finite Element Model of Road.
With the increased computational capabilities, the dynamic FE analysis of a pavement structure is a technique of considerable reduction in computation cost than before.A 3D FE model was developed to analyze the dynamic response of pavement under a moving truck tire loading.

Calculation Parameters.
A model geometry of 9.0 m × 6.5 m × 4 m block was created to represent a typical four-layer roadway structure that referred to the structure of  4 Advances in Civil Engineering Beijing 6th ring road.e information of this structure came from Dong's research [31].Figure 4 shows the road model.e surface layer includes SMA, AC25, and AC30.e axes of X, Y, and Z were set align with the longitudinal, transverse, and vertical direction, respectively.e driving direction was along the positive direction of X axis.
Material parameters of each structure layer were determined by reference to the Specifications for Design of Highway Asphalt Pavement (Appendix E) [33], as shown in Table 2. e material parameters of AC30 were estimated by referring to the lower limit value of material parameters of AC25.e material viscosity was considered using Rayleigh damping for the energy dissipation through the medium.
e damping ratio of pavement structure is generally between 0.02 and 0.2 and is set as 0.05 [34].

Constrain Condition and Mesh Generation.
e three direction movements and rotations were restrained at the bottom of the subgrade on the model.e normal directions were restrained corresponding to the four sides of the model.In order to decrease the number of elements and reduce the cost of computation, the interface between subbase and subgrade was set as Tie constraint because of the small deformation on the subgrade.A Tie constraint ties two separate surfaces together so that there is no relative motion between them.e central area of the model surface was set as the loading area, so as to reduce the effect of boundary constraint on the simulation results.
Finer meshes were used in the loading area.e coarser meshes were used for the area far away from the loading area not only to ensure accuracy but also to improve calculation efficiency, as shown in Figure 5.
e road model was idealized with linear hexahedral element of type (C3D8R).e length and width of elements were 2 cm × 2 cm in the loading area.e heights of elements were 2 cm, 2.5 cm, and 3.5 cm for SMA, AC25, and AC30 layers, respectively.

Model Validation.
In order to verify the road model, the simulation results were compared with the experimental data.
e measured strain data came from Dong's research [31].Dong et al. embedded the fiber Bragg grating (FBG) sensors on the Beijing Liuhuan Expressway.e FBG sensors were used to measure the vertical, transversal, and longitudinal strains of the pavement under the vehicle moving load.e measured vibration data came from our field test.e selfdeveloped acceleration sensing nodes were embedded on G320 road at Kunming to acquire the pavement vibration signal generated by vehicle moving load.e medium truck with a total weight of 25t passed the monitoring area at a speed of 35 km/h.e depth of the accelerometer from the surface of road is 8 cm.e pavement vibration signal excited by the front axle of this truck was chosen to compare with the simulated data, as shown in Figure 6.
Figure 7 shows the monitoring points.e point #A was selected for strain and vibration response analysis.e point  Advances in Civil Engineering #B was selected for strain response analysis.Figure 8 shows the comparison between simulated data and measured data.
In Figures 8(a)-8(c), the strain curves of simulation rebounded rapidly and did not have hysteresis after loading because the viscoelasticity of the asphalt pavement was not considered.However, the difference of maximum values between the simulated and measured data is just around 15%.And the trend of strain curves matches well.e reasons for the deviations of strain curves were attributed to difference in the material parameters and random vehicle load adopted in real situation.However, the comparison still exhibits consistency between simulated and measured data and verifies that the numerical model used for FE simulation is coherent.
Figure 8(d) shows only one peak for the vibration because of one-wheel loading.e waveform initially falls and rises rapidly to form a significant peak and then falls again.Finally, it levels off.ese characteristics are consistent with the measured data trend.However, the magnitude of simulated data is 10 times larger than the experimental data.
is is because the simulated acceleration data can only be extracted from nodes of element by using ABAQUS program, and the nodes have a mass close to zero.However, the sensor node for pavement vibration monitoring has real mass.According to Newton's second law, the magnitude of the acceleration of an object is inversely proportional to the mass of the object.erefore, the measured data were used as a reference, and the mass scaling factor was set to 10. e mass-scaled simulation data match well with measured data.
is model can be used to analyze road vibration response qualitatively under multiple conditions.

Results and Discussions
e validated FE model was adopted for various simulations to provide additional information on dynamic pavement performance, which might prove costly via laboratory tests only.
e factors that would influence the dynamic responses of pavement under moving vehicle load are typically related with the external excitation from vehicle load, material properties, and geometric properties of pavement.
3.1.Influence of Dynamic Load.Vehicle parameters, speed, weight, and road roughness have influence on dynamic load of tire to pavement [25,29,35].erefore, the dynamic load coefficient (DLC) was used to represent the variation of the dynamic load, which can be calculated as where F i is the vehicle random dynamic load at the ith time step; F s is the static load produced by vehicles; and N is the total time step.e time step is 0.001 s and the total time is 0.3 s. e random dynamic load corresponding to different DLC was obtained by the quarter vehicle model, as shown in Figure 9.A larger value of DLC indicates the load fluctuates more dramatically.
By considering the actual tire-to-pavement contact, the random nonuniform load was applied to the road model to acquire pavement vibration response.e monitoring area was the surface of SMA layer below the tire center line, as shown in Figure 10.
Figure 11 shows the acceleration extrema of each node in the monitoring area.e acceleration extrema are the difference value between the maximum and the minimum acceleration in a loading time period.
In Figure 11, the variation of the acceleration extrema is random.e distribution range of acceleration extrema is larger when DLC is higher.e median values significantly increase with an increase in DLC, which is from 0.8 g to 1.33 g, indicating that the number of larger acceleration extrema will grow if the dynamic load fluctuates more dramatically.
DLC increases when the surface condition of pavement declines.DLC increases with the increase of vehicle speed and the decrease of vehicle weight [29,35].When the experimental vehicle passes the test road at the same speed, the vehicle weight and speed can remain the same.e distribution range of acceleration extrema is larger when DLC is higher.
erefore, the wider distribution range of acceleration extrema indicates the worst condition of road surface.

Influence of Surface Materials.
Asphalt and cement concrete are the common materials of the pavement surface layer, and their material properties are different.Asphalt concrete is a flexible material while cement concrete is a rigid one.erefore, the influence of material properties on the pavement vibration was analyzed by comparing asphalt and cement concrete.Table 3 shows the material parameters of the cement concrete [18]: e vibration response was compared between asphalt and cement concrete pavements.e monitoring points #1, #2, and #3 of asphalt concrete pavement were placed below Advances in Civil Engineering the tire, at the top of the SMA layer, the AC25 layer, and the AC30 layer, respectively.e coordinate of monitoring points in the model of cement concrete pavement was kept the same, as shown in Figure 12.
e dynamic load was applied to the road model when the road was class A road and the vehicle speed was 10 m/s.e vertical acceleration signals of different materials were compared at each monitoring point, as shown in Figure 13.
In Figures 13(a) and 13(b), the time-domain signal waveform can reflect information about the properties of the pavement materials, such as the degrees of flexibility and rigidness.For the asphalt concrete pavement, the vertical acceleration amplitude decreases significantly with an increase in the depth.e waveform tends to vibrate upward, which is due to the flexibility and integrality of the asphalt concrete pavement.e energy of downward vibration is absorbed by the flexible structures.On the contrary, for the cement concrete pavement, the waveform is almost symmetric, and the vertical acceleration amplitude has no obvious change at each point.is is due to a high strength of     Advances in Civil Engineering According to the Parseval's theorem, the energy of vibration can be identified as the sum of squares of Fourier amplitude.e energy of vibration becomes smaller with an increase in the depth.e energy is 15.83 mW at point #1, while it is only 1.58 mW at point #3.On the contrary, the vibration frequency of the cement concrete pavement distributes normally.e energy of vibration is 0.42 mW at point #1′ and 0.20 mW at point #2, which is far less than that of asphalt concrete pavement.e energy becomes smaller with an increase in the depth, but the decrease of energy is small.is is due to the good integer property of the surface layer of the cement concrete pavement.According to the law of conservation of energy, when the vehicle drives on the cement concrete pavement, the vehicle suspension system absorbs more energy, which results in the bumpiness of vehicle.But, the driving experience is good when the vehicle drives on the asphalt concrete pavement.However, the asphalt concrete pavement is susceptible to damage as it absorbs more energy.

Influence of the Structure Integrity.
e pavement vibration response was compared between two cases: one with a road model that has no crack and the other with 3 m-long and 10 cm-wide by 15.2 cm-deep crack located in the base layer, as shown in Figure 14. e crack area of the base layer was hollowed out according to the set size. e crack area was no need to mesh and define material parameter.
e vertical acceleration signals of different structure integrity were compared at each monitoring point, as shown in Figure 15.
In Figures 15(a

Figure 2 :
Figure 2: e random dynamic load when the vehicle speed is 10 m/s and road is class A road.

Figure 7 :
Figure 7: e monitoring points on the transverse section of the model center.

Figure 8 :
Figure 8: e comparison between simulated data and measured data (blue curves are simulated data and red curves are measured data).(a) e comparison of vertical strain.(b) e comparison of longitudinal strain.(c) e comparison of transverse strain.(d) e comparison of vertical acceleration.

Figure 9 :
Figure 9: e random dynamic load corresponding to different DLC.

Figure 11
Figure 11: e distribution of acceleration extrema under different dynamic load.(a) e acceleration extrema of each node in the monitoring area.(b) e distribution box of acceleration extrema.

Figure 13 :
Figure 13: Comparison of vertical acceleration signals between asphalt and cement concrete pavements.(a) Time-domain vertical acceleration signals of asphalt concrete pavement.(b) Time-domain vertical acceleration signals of cement concrete pavement.(c) Frequencydomain vertical acceleration signals of asphalt concrete pavement.(d) Frequency-domain vertical acceleration signals of cement concrete pavement.

10
) and 15(b), the vertical acceleration amplitude decreases as the depth increases for the noncracked model.However, for the cracked model, the vertical acceleration amplitude first decreases and then increases as the depth increases.e vertical acceleration amplitude of cracked model is maximum at point #3′.Moreover, the vertical acceleration signals of cracked model have more prominent fluctuation characteristics under moving load, which is especially evident at point #3′ near the crack zone. is is because the crack decreases the bearing capacity and stability of pavement structure.

Table 1 :
e parameters of medium truck.

Table 2 :
e material parameters of asphalt concrete pavement.