Determining Travel Time Differentials for Multilane Highways With Zonal Pavement Distress

Transcription

1 Determining Travel Time Differentials for Multilane Highways With Zonal Pavement Distress Johnnie Ben-Edigbe Department of Civil Engineering, University of KwaZulu-Natal, Durban-4001, South Africa. Abstract In this paper travel time delaysassociated with pavement distress zone on multilane highways were investigated.the objective is to determine intermittent travel time differentials propagated atvarious pavement distress zone. Continous traffic volumes, speeds and vehicle types data were collected for six weeks at road sections with and without pavement distres zone. Travel timeand delay for road sections with and without pavement distress were computed and compared. Results show that for a multilane highway with pavement distress zone, aggregated travel time differentials range 29s to 43s irrespective of pothole and edge subsidence distribution. The paper concluded that potholes and edge subsidence are key contributors to substantial travel time differentials. Keywords: delay; travel time; travel speed; traffic volume; edge subsidence;potholes; INTRODUCTION Pavment functional distress is the gradual break-up of the bituminous pavement under the abrasive action of traffic and under the mechanical or chemical actions of weathering, typical examples of defects exhibiting this trend include are potholes and edge-break. Bituminous surfacing may crack for a variety of reasons that include lack of good bond between the surface layer and the course underneath, excessive pavement deflection, expansion and contraction of the sub grade, shrinkage and often, in early stages the crack patterns can indicate the cause. In any case when the cracks have developed over a large area and become sufficiently wide and numerous to allow the entry of surface water or disturbance of the surface by traffic, the road deteriorates. Defects associated with road deterioration are usually manifested in form of cracking, rutting, ravelling, potholes, roughness, edge break, and polished surface among others. Given that the justification for road construction is that they promote social development and economic growth, then the tests of optimising road use would call for road surfaces to be free from physical defects such as potholes, loose aggregates, and broken edges, rutting and cracking. Persistent pavement would induce travel time increase and facilitate delays.specifically, potholes are open cavity in road surface with at least 150mm diameter and at 25mm depth. UK Department of Transport 1997 road note advice 20/84 [10] suggest that for validity carriageway lane must not be less than 2.5m, therefore potholes, with transverse widths greater than 1000mm on a dual carriageway would have violated lane width tolerance level. Pavement distress develop over a period of time with potential to cause accidents. According to Ben-Edigbe [1] pothole with about 40mm in depth and 500mm across and central to the carriageway is deemed to be dangerous given that a typical tyre contact patch is about 125mm 2.If left unpatched, potholes get bigger as vehicles drive over them damaging the structure of the road overtime.potholes would often lead to carriageway width shrinkage. Once the road width tolerance level has been violated, traffic flowrate would become unstable. The paper presents the outcome of travel time diffentialsstudies on flexible roadways with significant pavement distress in Nigeria. PAVEMENT DISTRESS AND TRAVEL TIME Road pavement is made up different constituents (sub-base, road-base and surfacing). It can fail structurally and/or functionally. But it doesn t fail suddenly. It is generally considered to begin to deteriorate after entering service and then gradually, to get worse as time progresses until a failure condition is reached. The success and failure of the flexible road surfacing depends not only on the design, but also on the extent to which that design is realised in construction process.hypothetically, pavement distress and travel time relationship can be presented a non-linear function as shown below in figure 1. The relationship could be described by exponential function: f(p) = a (b p )can be re-written as f(p) = b p ± c.the exponential function in figure 1 has Maclaurin series according to Beyer, [11] and Zwillinger [12]. Since function. Then, (1) by uniqueness of the exponential 8340

2 (L) and free-flow speed (v f ). It can be written as: (6) As mentioned earlier, travel time delay is the difference between the actual travel times required to traverse a road section with potholes and the time corresponding to the average speed on road section without potholes. It includes acceleration and deceleration delay in addition to stopped delay. A vehicle approaching a pothole area would have gone through three driving sequence (free-flow, transition and pavement distress). After the free-flow section, vehicles enter the transition zone with reduced speed (v z ) so that the travel time is adjusted to transition travel time ( ) and estimated as: Figure : Exponential relationship between pavement distress (p) and travel time (t) In any case, when predicting travel time over length of roadway equation 2 can be used; Predicted travel time, (2) Where; T = predicted travel time over length of roadway; q = flow; Q = capacity; t f = travel time at free flow speed; a determines the ratio of free-flow speed to the speed at capacity and b determines how abruptly the curve drops from free-flow speed. A high value of b causes speed to be insensitive to v/c until v/c gets close to 1.0; then the speed drops abruptly. Dowling et al [4] adjusted equation1 such that a = 0.20, and b = 10. These updated curves generally involved the use of higher power functions that show relatively little sensitivity to volume changes until demand exceeds capacity, when the predicted speed drops abruptly to a very low value. Since the study is interested in predicting travel time where volume/capacity (v/c) < 0.90, then a = 0.20, and b = 10. If the coefficients are plugged into equation 1, then predictive travel time can be used.note that capacity in equation 2 can be computedby various methods that include, maximum volume, headway, speed/flow, flow/speed/density [5]. It has been shown in previous studies by Ben-Edigbe [2] that equation 3 can also be used to estimate capacity. Traffic flow, (3) for (7) Where delay is defined as an extra time spent by drivers against their expectation then the delay (d d ) due to deceleration (from v f to vz) is: (8) This delay is called deceleration delay because it occurs when vehicles decelerate before entering the pavement distress zone. Delay when vehicles travel through the pothole zone is the difference between the travel time needed to pass through the pothole area at reduced speed and the travel time needed to pass the same length of the roadway without pothole at free-flow speed. If the length of a pothole area is Lm, then the delay (d z ) of a vehicle travelling within the pothole area can be calculated as: (9) Delay in equation 9 is incurred from reduced speed through the pavement distress area. Upon exiting the pavement distress area at reduced speed vehicles accelerate and choose speed. Time needed to reach the free-flow speed is a delay tied to loss time. The distance (s) travelled due to speed change from v z to v f is (10) Where a denotes average acceleration, Time needed for a vehicle to accelerate from v z to v f is Capacity, (5) Travel time delay is the difference between the actual time required to traverse a section of roadway and the time corresponding to the average speed of traffic under normal condition. It includes acceleration and deceleration delay in addition to stopped delay. Delay is not always directly measurable in the field according to HCM [6]. However, freeflow travel time (t f ) in equation 2 is a function of road length (4) (11) Assuming no pavement distress zone, time needed for a vehicle to travel the same distance is (12) Therefore, the delay for a vehicle to accelerate to free-flow speed is the difference between time t 1 and t 2 : 8341

3 (13) Given the pavement distress scenario described so far in the paper, it may be necessary to know the distribution of vehicle arrivals into the distressed zone. Sometimes vehicle queue can occur during free-flow period because vehicle arrival is ransom and probabilistic. Nonetheless queuing is a delay function that can be analysed with the application of queuing theory, according to Ben-Edigbe and Astrid [3]. Where pavement distress zone is assumed to be a server with entry and exit points for vehicles in order of arrival, the average arrival rate of the vehicles is the traffic flowrate and the service rate of the system is the capacity of the distressed zone. Because of the randomness of road traffic, the queuing system can be represented as a system with Poisson arrivals, exponentially distributed service times, and one server. Queuing theory assumes that vehicle arrivals are independent, motorists do not leave or change queues, large queues do not discourage motorists and the mathematics of waiting lanes has exponential distributions, Ngoduy, D., [7]. Frankly these assumptions are slightly exaggerated; nevertheless, they can provide reasonable answers. The queuing systems are usually described by three values: arrival distribution, service distribution and number of servers. M/M/1 where the rate of arrival is exponentially distributed, hump service times are exponentially distributed and there is only one hump, Qiaoru, L., et al., [9]. Note that M denotes Markovian or exponentially distributed. Now if motorists are arriving at exponentially distributed rate λ, then the probability that there will be k driver after time t is; and straight to remove the effect of bendiness on travel speed. The road segment used for the study was not a bottleneck. This was needed to remove peak-hour effect from ensuing outcomes. Road segment was divided into three sections (A, B, C) with Section A as the upstream end (free-flow) and Section C the downstream end (potholes), while Section B was the transition section (no pothole). Each section was fitted with automatic traffic counters for a continuous period of six weeks. Traffic data were supplemented with pavement condition data. Generally, vehicles will traverse from freeflow to transition, then pavement distress area and finally exit the zone, subsections B and C are 100m in length for ease of computationas illustrated in Figure 2. Then defects and the extent of severity were recorded as shown in Table 1. Table 1: Survey pavement distress area Site A/W m 2 Potholes (Nos) Depth (mm) Length (m) Width (m) Note that A/W denotes pavement distress area (14) utilization = ρ = λs = faction of time the hump is busy. Based on Erlang s queuing theory the expected number of vehicles in the queue is: (15) The average waiting time that an arrival vehicle spends before entering the asphalt pavement distress area is: Q = average departure rate from the queue qλ = traffic flow arrival rate In sum total travel time delay is: V h =hourly flow of arrival vehicles at hour i; (16) (17) SETTING AND TRAFFIC DATA COLLECTION Within the purview of the study objectives and boundary, surveyed roadway must be flat to remove the effect of slope, -ATC denotes Automatic Traffic Counter -PD denotes Pavement Distress Figure 2: Typical Survey Site Layout Transition length was taken as a function of stopping sight distance (SSD) and computed using equation 18 below. (18) Where; v denotes vehicle speed; t denotes reaction time is 2.5s, and deceleration rate (a) is 3.4m/s 2 From observation at surveyed sites, trucks are less affected by potholes than passenger car, so it can be argued that the passenger car equivalent values of trucks or buses are either the same or somewhat lower than those of passenger cars on roadway stretch with potholes. In order to take into account the effects of pavement distress zone, passenger car equivalent (PCE) values were modified. PCEs can be defined as the ratio of the mean lagging headway of a subject vehicle divided by 8342

4 the mean lagging headway of the basic passenger car according to Seguin, [8]. Since this is not the focus of the study, a simple headway method was used to derive PCE values for the road sections. FINDINGS AND DISCUSSION Travel time and associated delays for section A and C were analysed. Travel time was computed for sections A and C using equation 2. The key parameters are free-flow speed, prevailing flow and capacity. Capacity was computed using equation 5 and results of computed model coefficients are summarized below in tables 2 and 3. Note thatestimated model coefficients for all sites have the expected signs and the coefficients of determinations (R 2 ) are much greater than 0.85 therefore, it can be suggested that a strong relationship between flows and densities exists and the model equations could be used to estimate capacity. Test statistics show that the F-observed statistics at 10 degree of freedom is much greater than F critical (4.94) suggesting that the relationship did not occur by chance. Also that the t-observed statistic at 10 degree of freedom tested at 5 % significance level is much greater than 2 thus suggesting that density is an important variable when estimating flow. From tables 2 and 3, note that travel speeds are almost halved, for example travel speed at sites 001 dropped from 127km/h to 50km/h. This trend is repeated at all surveyed sites Table 2: Summary of Model CoefficientsTable 3 Summary of Model Coefficients Site Section A (without PD) Flow- o Speed 1 k Density- 1 k 2 R Site Section C (with PD) Flow- o Speed 1 k Density- 1 k 2 R Estimation of travel time and discussion As shown below in table 4, traffic capacity was estimated from model equations in tables 2 and 3. For example at Site 001 along section without potholes; prevailing traffic flow is 624pcu/hour/lane and traffic flow model equation is: q =-2.02k k If q = uk, then, u =-4.04k Hence, free-flow speed, u f = 127.6km/hr, and density, k = 32veh/km dq/qk =-4.04k = 0 k = 127.6/4.04 = 31.4veh/km Capacity, Q =-2.02(31.4) (31.4) = 1846veh/hour/lane Travel time is then computed from equation 2; From table 4, volume/capacity ratios at all section without pavement distress are less than those at section with pavement distress mainly because of speed reduction. Travel times at section without potholes are less than those at section with potholes. Travel time differentials range from 43s to 29s and not influenced by the number of potholes and edge subsidence. For example at site 002 and site 006, number of potholes is 13 but travel time differentials are about 43s and 36s respectively; at site 001 and 004, number of potholes is 15 but travel time differentials are about 43s and 40s respectively. Even though the difference in the number of potholes at site 003 and 005 is one, travel time differentials are about 29s and 42s respectively Table 4: Estimated travel time for sections with and without potholes Site P prevailing Section A without PD Section C with PD T nos flow (q) t f Q f Q p t f (s) pcu/h/ln km/h pcu/hr/ln T f (s) T p (s) pcu/hr/ln km/h ,34 28,25 71, , ,31 29,05 71, , ,45 31,78 60, , ,42 32,03 72, , ,48 33,33 75, , ,37 31,78 65, , Note: D-pavement distress; P-potholes; t f -free-flow speed; T- travel time; Q-capacity; q-traffic flow; T-differential travel time Estimation of travel time delay and discussion Average travel time delay per 100m stretch of road length with pavement distress is about 18s. If travel time delays are read in conjunction with pavement distress measurements, it can be seen from tables 5 and 6 that travel time delay does not depend entirely on the size of the pavement distress area. For example site 001 has the highest pavement distress area (265m 2 ) with total delay of 18.42s per 100m length; compared to site 004 (125m 2 ) with total delay of 18.07s per 100m length. Site 003 has the least number of potholes (9) spread over the entire 100m length. Site 003 has 30.95s total travel time delay suggesting that extent of pothole disperse has effect on travel time. Table 5: Travel time delay parameters Table 6. Total travel time delay Site V f (s) t f (s) V z (s) qλ

5 Site V h d d d z d a (d w ) d T However, the highest travel time delay occurred from average waiting time that an arrival vehicle spends before entering the asphalt pavement distress area. Site 005 with 10 number of potholes has second highest travel time delay of 19.31s and the average waiting time that an arrival vehicle spends before entering the distress area is 13.03s. Pavement distresses at site 005 cover the whole road width probably explaining why travel time delay is second highest. If an assumption of 5m road space per vehicle is applied, the maximum queue length would be 20 vehicles per 100m pavement distress road lane of a two-lane highway. CONCLUSION The paper presents the outcome of travel time and delay study on flexible road with potholes. Travel time was taken as the actual time required by a motorist to traverse a road section under prevailing condition. Pavement distress was taken as physical constraints on roadway significant enough to act as vehicles speed reduction impediments to an otherwise free traffic flow. The paper concluded that: There is a significant change in travel time due to pavement distress zone. Significant delay will result from pavement distress zone. Passenger car equivalent values must be modified for roadways with pavement distress Potholes and edge subsidence are significant pavement distress contributor to delays Travel time delays are not solely dependent exponentially on the size and depth of pavement distress zone, once the allowable size and depth have been reached delay increases irrespective of further increase in size and depth of pavement distress. [3] Ben-Edigbe J and Astrid K.Y 2013 Determining Road Lighting Impact on Traffic Stream Characteristics. American Journal of Applied Sciences 10 (7): [4] Dowling, R., Kittelson, W., Zegeer, J. and Skabardonis, A. (1997) Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications, NCHRP Report 387, Transportation Research Board. [5] Greenshields. B.D (1935) A Study of Traffic Capacity, Proceedings of the Highway Research Board. HRB 1935 Vol. 14, pp [6] Highway Capacity Manual (2010) Transportation Research Board Washington DC [7] Ngoduy, D., (2011), Multiclass First-order Traffic Model Using Stochastic Fundamental Diagrams. Transportmetrica 7(2), [8] Seguin, E.L. Crowley, K.W., and Zweig, W.D (1998) Passenger Car Equivalents on Urban Freeways. Interim Report, Contract DTFH61-C00100, Institute for Research (IR), State College, Pennsylvania. [9] Qiaoru, L., et al., (2011), Influence of the Moving Bottleneck on the Traffic Flow on Expressway. Applied Mechanics and Materials, 97-98, [10] UK Department of Transport,(1997) Advice Note TA 20/84,TRRL Report LR 774 [11] Beyer, W. H. (1987) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 217 [12] Zwillinger, D. (1995.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press REFERENCES [1] Ben-Edigbe, J Determining Flow-Density Asymmetric Curve using Direct Empirical Approach. Caspian Journal of Applied Sciences Research [2] Ben-Edigbe, J Assessment of speed-flowdensity functions under adverse pavement condition. International Journal of Sustainable Development and Planning 3(5):