60 Ellison: Quantified Tree Risk Assessment in Management of Amenity Trees fallen or falling tree is the ratio of the hours a point in the road is occupied by a vehicle—including safe stopping distance—to the hours in a day. Pedestrians The probability of pedestrians occupying a target (Table 2) is calculated on the basis that an individual will spend, on average, 5 seconds occupying the target area, unless a longer occupation is likely, as with a habitable structure or park bench. For example, ten pedestrians per day each occupying the target area for 5 seconds is a daily occupa- tion of 50 seconds, by which the total seconds in a day are divided to give a probability of target occupation. When evaluating pedestrian and vehicular frequency (events) during daylight hours, we must consider whether fre- quency will be significantly reduced during hours of darkness. The calculation of frequency must in all cases be the total hours in a year divided by the number of events in a year. Although a tree failing during the day might be more likely to strike a mobile target than the same tree at night, it is the frequency of the targets and not the failure of the tree that is most significantly influenced by the time of day. The sum of the higher daytime occupation and the lower nighttime occupation is the daily occupation. Similarly, a single annual event attracting large numbers of visitors could significantly increase the target value and should be included in the assessment. Structures When evaluating a target structure, it is necessary to consider the approximate value of repairs or replacement that might be required if the tree should fail. The values in Table 3 represent cost of repair or replacement. The ranges of repair value for structures used in Table 3 are derived from a value of “hypothetical life” of £1,000,000 (US$1,850,000). For example, target range 2 represents a probability of pedestrian occupation up to 1/20; £1,000,000 ÷ 20 = £50,000. Thus, structures likely to incur a repair cost of £50,000, which is one-twentieth the value of a hypotheti- cal life, are apportioned a ratio of 1/20. Individual trees should be selected on the basis that they are within striking distance of a significant target or that their failure could result in neighboring trees striking a target. Example 1 (see section titled Calculating Risk of Harm) illustrates that an individual tree cannot represent an unacceptable risk of significant harm if within striking distance of only a target within range 6 (assuming that the tree manager is operating to an acceptable level of risk of 1/10,000). Having established that a tree requires assessment, the inspector should assess it according to current practice. Tree inspection procedure is well documented elsewhere (Matheny and Clark 1994; Mattheck and Breloer 1994; Lonsdale 1999) and is not discussed here. Impact Potential Table 2. Pedestrian frequency. Occupation of the target area calculated from an average occupation of 5 seconds, other than constant and 50% occupied. Pedestrian frequency Constant 50% occupied 100 per hour 50 per hour 10 per hour 5 per hour 1 per hour 1 per day 1 per week Total occupation per day (seconds) 86,400 43,200 12,000 6,000 1,200 600 120 5 0.71 ©2005 International Society of Arboriculture Probability of occupation 1/1 1/2 1/7.2 1/14.4 1/72 1/144 1/720 1/17,280 1/120,960 A small, dead branch of less than 10 mm (0.4 in.) diameter is unlikely to cause significant harm even in the case of direct contact with a target, while, on average, a falling branch with a diameter greater than 150 mm (6 in.) is likely to cause harm in the event of contact with all but the most robust target. The increased potential for injury in relation to the size of tree or branch is proportional to a degree, yet the tree or branch will reach a size where the increased severity of injury is no longer significant. Similarly, most property likely to be affected by tree failure can incur only a limited level of damage before further damage is likely to be inconsequential (i.e., when it is beyond economic repair). The mass of a falling tree or branch contributes to the force that will occur upon impact with a target but does not alone determine the potential severity of harm. The distance and orientation when falling will influence the force upon impact. Other trees or branches might impede the path of a falling tree or branch, and it might be predicted that the failure of a branch will result in it being hung up without presenting an immediate danger or that it might fall unim- peded. Additionally, a tree or branch may be decayed to such an extent that it will disintegrate or exert only a minor force upon impact. For these reasons, it is probably unrealistic to calculate the effect of the height from which a branch could fall, but it is necessary to be aware that factors other than mass will contribute to the force upon impact, although these factors might be recorded only where they are particu- larly significant in a given situation. The system categorizes impact potential by the diameter of tree stems and branches. An allometric biomass equation derived from dry weight measurements of trees of different stem diameters (Tritton and Hornbeck 1982)
March 2005
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