Modern Transportation March 2014, Volume 3, Issue 1, PP.1-7
Sensitivity Analysis of Guardrail Impact Parameters Based on Deflection Index Shuming Yan#, Ning Jia, Yaping Liang, Xin Wang Beijing Zhongluan Traffic Technology Co., Ltd, Beijing 100071, China Email: shumingyan@sina.com
Abstract Based on a high impact worthiness level combined bridge barrier, finite element simulation model was set up and proved correct by impact test and energy analysis method, and quantitative analyses of sensitivity degree of maximum dynamic deflection of guardrail to impact parameter were done by single parameter sensitivity analysis method. The research results indicate that the simulation method is reliable for the simulation results, meets the impact test results and the energy curves are reasonable. The sensitivity coefficients of guardrail maximum dynamic deflection to vehicle mass, to impact velocity and to impact angle are 0.625, 1.64 and 1.635; impact speed and impact angle are the most sensitive factors to guardrail maximum dynamic deflection. The research results have guiding significance to set out error range of impact test in formulating standard for safety performance evaluation of highway barriers. Keywords: Traffic Facility; Safety Evaluation; Impact Test; Sensitivity Analysis; Computer Simulation; Finite Element Method; Error
1 INTRODUCTION If safety performances of guardrail meet the requirements on roads, it would reduce traffic fatality rate effectively [1]. Through the real vehicle full-scale impact tests to evaluate the safety performance of the guardrail, the guardrail maximum dynamic deformation index is the concrete embodiment of the guardrail structural protection performance [2] . The real vehicle full-scale impact test conditions include three parameters: vehicle mass (m), impact speed (v) and impact angle (θ) [2-4]. During the setting up of impact test, the impact parameters errors are inevitable. In order to provide evidence for formulating reasonable impact parameters error range, it is necessary to analyze the sensitivity of impact parameters relative to the guardrail maximum dynamic deformation index [5]. In this paper, the finite element simulation model was built and the impact test was set up to prove the correctness of the finite element model. Then analyze the sensitivity of impact parameters relative to the guardrail maximum dynamic deformation index.
2 SINGLE PARAMETER SENSITIVITY ANALYSIS Sensitivity analysis is a kind of uncertainty analysis method, which study the influence grade on one, or a set of key indexes from the quantitative view of analysis when relevant factors have some changes. Its essence is to explain the law how much the key index influenced these parameters by the method of changing the correlated variables numerical. Employ single parameter sensitivity analysis method to analyze the sensitivity of impact parameter relative to the guardrail maximum dynamic deformation index [5-7]. Sensitivity coefficient is the percentage ratio of the guardrail maximum dynamic deformation index to the change of impact parameter. The sensitivity coefficient, which indicates a high degree of sensitivity of the guardrail maximum dynamic deformation index to the impact parameter when it is large, is calculated as: E
A / A I / I
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(1)
Where: E-guardrail maximum dynamic deformation index; A-sensitivity coefficient related to impact parameter I; ΔI/I-Impact parameter change rate of I; ΔA/A-the change rate of A when impact parameter I has changed ΔI. E>0 means guardrail maximum dynamic deformation index and impact parameter change in the same direction while E<0 means the maximum dynamic deformation index and impact parameter change opposite. Absolute value of the larger E shows that the guardrail maximum dynamic deformation index to the impact parameter is more sensitive. Single parameter sensitivity analysis to identify sensitive parameter by calculating sensitivity coefficient laid a foundation for reasonably determining the impact parameter error range.
3 IMPACT PARAMETERS AND DYNAMIC DEFORMATION INDEX 3.1 Impact Parameters. Figure 1 shows the sketch of impact condition. In the real vehicle full scale impact tests, to control several major impact condition parameters of the vehicle mass, impact speed and impact angle effectively are the most important work for the test set up, and also to determine whether the test set up success or not, so the vehicle mass, impact speed and impact angle are treated as the indexes of the impact parameters, which influence the guardrail maximum dynamic deformation.
3.2 Dynamic Deformation Index. The maximum dynamic deformation of guardrail is an important index of the guardrail safety performance [8]. If the maximum dynamic deformation is too large for the roadside guardrail, the vehicle probably crossed the embankment edge line and driven outside or impacted roadside obstacles; for central reserve guardrail, the vehicle is likely to endanger the safety of the pier, lampposts and other structures in the central reserve. Set the maximum dynamic deformation of the guardrail as the key index and study how the changes of impact parameters affect the key index. Angle
Barrier Velocity Vehicle
FIG.1 SKETCH OF IMPACT CONDITION
(A) WHOLE STRUCTURE
(B) COLUMN AND ANCHOR BOLTS FIG.2 A COMBINED BRIDGE GUARDRAIL
FIG.3 TEST VEHICLE
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(C) BEAM SPLICE
4 TEST AND THE MODEL 4.1 Test Guardrail. The design containment level of a bridge guardrail is SH 640 kJ, using combined guardrail structure that the concrete wall for lower part and metal beam-column for upper. Total guardrail height is 1.4 m. Height of dual beams of the upper metal beam-column structure is 0.55 m and the height of concrete wall is 0.85 m at the lower part. For the upper, including oblique H-type column with the flanges and webs whose thickness are both 10 mm, the spacing between column is 2 m, the size of rectangular steel beams are 160 mm×120 mm×10 mm and the thickness of brackets is 10 mm. Beams are connected in sleeve splice way. For the lower, the concrete wall used F-shaped slope surface. II-class vertical reinforcement of Φ18 mm and longitudinal reinforcement of Φ12 mm are used for the wall. II-class vertical reinforcement of Φ20 mm is used to connect the flange plate and the concrete wall. Using anchor bolts to connect metal beam-column and concrete wall. Five anchor bolts are arranged forward and four behind. Figure 2 shows the combined bridge guardrail for test. For the lower, the concrete wall used F-shaped slope surface. II-class vertical reinforcement of Φ18 mm and longitudinal reinforcement of Φ12 mm are used for the wall. II-class vertical reinforcement of Φ20 mm is used to connect the flange plate and the concrete wall. Using anchor bolts to connect metal beam-column and concrete wall. Five anchor bolts are arranged forward and four behind. Figure 2 shows the combined bridge guardrail for test.
4.2 Test Vehicle. For the guardrail impact test, there are two types of vehicles, small vehicle and large vehicle. Due to the mass of the large vehicle, it brings bigger destructive force and larger dynamic deformation. So mainly large vehicle is adopted impacting on the guardrail and the maximum guardrail dynamic deformation index is detected To analyze the guardrail maximum dynamic deformation index of the combined bridge guardrail, a four-axis truck was used to impact the guardrail. The impact parameters are v=65 km/s, m=33 t and θ=20º. Figure 3 shows the test vehicle.
4.3 Simulation Model. In previous study,finite element simulation models of guardrail and vehicle were based on the test condition. The results are compared between simulation and test. The reliability of the simulation model is verified from the point view of deformation [9-10]. Figure 4 shows the finite element simulation model of guardrail and vehicle. Figure 5 shows the energy transferring curves that are extracted from the simulation results. During the impact, the system kinetic energy decreases gradually, deformation energy and frictional energy increase gradually. Because the roll motion and climbing of the vehicle bring the work of gravity, so there is a little change in total energy, the results conform to the law of conservation of energy; the false deformation energy of single point integral is 10% less than the total energy. So the simulation results can meet the required precision very well. According to the impact results analysis, the simulation energy curves are reasonable. Deformation and acceleration results can meet the test results very well. The reliability of the simulation model has been proved. This study laid a foundation for analyzing the sensitivity parameters of guardrail maximum dynamic deformation index by simulation method.
5 SENSITIVITY ANALYSIS 5.1 Sensitivity Analysis Parameter Set up the unit truck simulation model based on the following parameters: v=60 km/h, m=40 t and θ=20º. The truck mass, impact speed and impact angle are changed to inspect the sensitiveness of guardrail maximum dynamic deformation index. The adjustment range of impact parameters is 10% of standard value. The impact parameters are shown in table 1. -3www.ivypub.org/mt
(A) GUARDRAIL SIMULATION MODEL (B) TEST DEFORMATION (C) VEHICLE SIMULATION MODEL (D) SIMULATION DEFORMATION FIG.4 MODELS AND RESULTS
FIG.5 ENERGY TRANSFERRING CURVE TAB.1 IMPACT PARAMETER TABLE
Standard value
Vehicle mass (t) 40
Angle (ยบ) 20
Vehicle speed (km/h) 60
Value increase 10% Value reduce 10%
44 36
22 18
66 54
Impact parameter
FIG.6 DISPLACEMENT VS. TIME CURVE OF THE MAXIMUM DEFLECTION POINT ON GUARDRAIL UNDER DIFFERENT VEHICLE QUALITY TAB.2 MAXIMUM DYNAMIC DEFORMATION SENSITIVITY TABLE FOR DIFFERENT MASS CONDITIONS
Impact parameter (I) Rate of Angle Change (ยบ) (%) 40 ----44 10 36 -10
Evaluation standard (A)
Sensitivity coefficients (E)
Maximum dynamic deformation (mm)
Angle (ยบ)
Rate of change (%)
311.8 328.0 287.7
-----5.20 -7.29
-----0.520 0.729
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FIG.7 DISPLACEMENT VS. TIME CURVE OF THE MAXIMUM DEFLECTION POINT ON GUARDRAIL UNDER DIFFERENT VEHICLE IMPACT SPEED CONDITIONS TAB.3 MAXIMUM DYNAMIC DEFORMATION SENSITIVITY ANALYSIS TABLE FOR DIFFERENT VELOCITY CONDITIONS
Impact
Evaluation
parameters (I)
standards (A)
Rate of change (%) ----10 -10
Angle (ยบ) 60 66 54
Sensitivity coefficients (E)
Maximum dynamic deformation (mm)
Angle (ยบ)
Rate of change (%)
311.8 338.4 236.0
-----8.5 -24.3
-----0.85 2.43
FIG.8 DISPLACEMENT VS. TIME CURVE OF THE MAXIMUM DEFLECTION POINT ON GUARDRAIL UNDER DIFFERENT IMPACT ANGLE CONDITIONS TAB.4 MAXIMUM DYNAMIC DEFORMATION SENSITIVITY ANALYSIS TABLE FOR DIFFERENT IMPACT ANGLE CONDITIONS
Impact
Evaluation
Sensitivity
parameter (I)
standard (A)
coefficients (E)
Angle (ยบ) 20 22 18
Rate of change (%) ----10 -10
Maximum dynamic deformation (mm)
Angle (ยบ)
311.8 346.7 244.8
-----11.2 -21.5
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Rate of change (%) -----0.867 0.847
5.2 Sensitivity Analysis. For the guardrail from which the vehicle can exit smoothly, there always have two peaks of dynamic deformation displacement time-histories curves, the first one comes out at the time of guardrail was impacted by the truck head, and the second comes out at the time of guardrail was impacted by the truck trail, and then we analyze the sensitivity of the bigger one. Figure 6 shows the displacement time-histories curves during the impact process of vehicle with different mass at the maximum dynamic deformation point. From the figure we can get that the mass of vehicle is 36 t、40 t or 44 t, the maximum dynamic deformation of guardrail is 287.7 mm、311.8 mm or 328.0 mm, it means during the impact process the bigger vehicle mass can bring the more serious guardrail maximum dynamic deformation. Table 2 shows the sensitivity analysis of guardrail maximum dynamic deformation under different mass conditions. It shows when the vehicle mass rose by 10%, guardrail maximum dynamic deformation increased by 5.2%. The sensitivity parameter is 0.52; the vehicle quality fell by 10%, guardrail maximum dynamic deformation reduced by 7.29%, the sensitivity parameter is 0.729. The average value of guardrail maximum dynamic deformation to the vehicle mass is 0.625. Figure 7 shows the displacement time-histories curves during the impact process of vehicle with different speeds at the maximum dynamic deformation point. From the figure we can get when the speeds of vehicle are 4 km/h、60 km/h or 66 km/h, the maximum dynamic deformations of guardrail are 236.0 mm, 311.8 mm or 332.4 mm, it means during the impact process bigger vehicle speed can bring the more serious guardrail maximum dynamic deformation. Table 3 shows the sensitivity analysis of guardrail maximum dynamic deformation under different impact velocity. It shows when the velocity rose by 10%, the maximum dynamic deformation increased by 8.5%, the sensitivity parameter is 0.85; the speed fell by 10%, the maximum dynamic deformation reduced by 24.3%, the sensitivity parameter is 2.43. The average value of guardrail maximum dynamic deformation to the impact speed is 1.64. Figure 8 shows the displacement time-histories curves during the impact process of vehicle with different impact angles at the maximum dynamic deformation point. From the figure we can get when the impact angle is 18º、20º or 22º, the maximum dynamic deformation of guardrail is 265.5 mm,244.3 mm or 223.6 mm, it means during the impact process bigger impact angle can bring more serious guardrail maximum dynamic deformation. Table 4 shows the sensitivity analysis of guardrail maximum dynamic deformation under different impact angles. It shows when the angle rose by 10%, the maximum dynamic deformation increased by 11.2%, the sensitivity parameter is 1.12; the angle fell by 10%, the maximum dynamic deformation reduced by 21.5%, the sensitivity parameter is 2.15. The average value of guardrail maximum dynamic deformation to the impact angle is 1.635.
6 CONCLUSIONS Through the computer simulation, this paper analyzed the sensitivity of the guardrail maximum dynamic to the change of vehicle mass, impact angle and impact speed. The results showed that the error of vehicle quality, impact angle and impact speed brought great influence on guardrail maximum dynamic deformation index. According to the sensitive grade, impact speed, impact angle and vehicle mass are in order. Using the simulation model that has been verified by impact test to analyze the impact acceleration sensitivity can get the reliable and scientific results. The research results have certain guiding significance for determining the error range of real vehicle impact test.
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AUTHOR Shuming Yan (1976- ), male, China, Graduated from Northeastern University, Master degree, now he is the chief engineer and deputy general manager of BEIJING Zhongluan Traffic Technology Co., Ltd, Senior engineer of traffic engineering. Email: shumingyan@sina.com.
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