Quantified Tree Risk Assessment Used in the Management of Amenity Trees

Michael J. Ellison

doi:10.48044/jauf.2005.007

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Figure 1.
Quantified tree risk assessment calculator illustrating Example 1.

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Table 1.

Vehicular occupation. The probability of impact (P) is calculated D3600 ÷ S1000 = T; TV = H3600; H ÷ 24 = P.

Road class	S Average speed (kph)	D Minimum stopping distance plus 6 m vehicle length (m)	T Time that each vehicle occupies length of road ‘D’ (sec)	V No. vehicles/day^{^z} (1 direction only)^{^y}	H No. hours for which a point on the road is occupied each day	P Probability of impact with or by a tree/branch
Motorway	113	102	3.25	30,450	27.5^{^x}	1/1
Trunk road (built-up area)	48	29	2.17	19,200	11.5	1/2.1
Trunk road (non-built-up area)	64	42	2.36	15,500	10.1	1/2.4
Principal road (built-up area)	48	29	2.17	15,000	9.0	1/2.7
Principal road (non-built-up area)	64	42	2.36	7,200	4.7	1/5.1
Minor road (all classes)	64	42	2.36	1,400	0.9	1/27

↵^z Transport Statistics Great Britain (1997).
↵^y For the purpose of assessing the probability of impact, the total number of vehicles occupying all lanes of a motorway traveling in a single direction must be considered.
↵^x Due to the sheer volume of traffic using motorways and the need to consider stopping distances, the vehicular occupation period is theoretically greater than 24 h.

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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	Total occupation per day (seconds)	Probability of occupation
Constant	86,400	1/1
50% occupied	43,200	1/2
100 per hour	12,000	1/7.2
50 per hour	6,000	1/14.4
10 per hour	1,200	1/72
5 per hour	600	1/144
1 per hour	120	1/720
1 per day	5	1/17,280
1 per week	0.71	1/120,960

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Table 3.

Target ranges for structures, pedestrians, and vehicles. Vehicular, pedestrian, and structural targets are categorized by their frequency or monetary value. For example, the probability of a vehicle or pedestrian occupying a target area in target range 4 is between the lower and upper limits of 1/10,000 and 1/500. Using the value of a “hypothetical life” of £1,000,000 the structure value within the target range 4 is £101–2,000.

Target range	Structure (repair value)^*	Pedestrian frequency	Vehicular frequency	Probability ratio^z
1	(a) Very high value (b) Habitable	> 36 per hour–constant	(a) Motorway (b) Trunk road, built-up and non-built-up areas (c) Principal road, built-up area	1/1
2	High value	10–36 per hour	Principal roads, non-built up-area	1/20
3	Moderate–high value	1–9 per hour	Minor roads, moderate use or poor visibility	1/100
4	Moderate value	< 1 per hour	Minor roads, low use and good visibility	1/500
5	Low value	≤ 1 per day	Minor private roads and tracks (no data available)	1/10,000
6	Very low value	≤ 1 per week	None	1/120,000

↵* Structure values represent the likely cost of repair or replacement. Very high = £50,001–1,000,000; high = £10,001–50,000; moderate–high = £2,001–10,000; moderate = £101–2000; low = £11–100: very low = ≤£10.

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Table 4.

Biomass dry weight estimates (Tritton and Hornbeck [1982]).

Dbh^* (mm)	Dry weight (kg) y = ax^b^**	Fraction of dry weight (600 mm) as a ratio
10	0.11263	1/23,505.722
25	1.0713	1/2,471.6699
50	5.8876	1/449.74
100	32.357	1/81.834
150	87.67	1/30.203
200	177.82	1/14.891
250	307.77	1/8.604
300	481.81	1/5.496
350	703.8	1/3.762
400	977.26	1/2.71
450	1305.5	1/2.03
500	1691.4	1/1.566
550	2138	1/1.24
600	2647	1/1

* Diameter at breast height, 1.37 m (4.5 ft).
↵** x = dbh (mm); y = dry weight estimate; a = allometric coefficient 0.1126294414; b = allometric coefficient 2.458309949.

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Table 5.
Impact potential.
Impact potential range Size of part (mm diameter) likely to impact target Impact potential
1^* > 450 1/1
2 251–450 1/2
3 101–250 1/8.6
4 26–100 1/82
5 >10–25 1/2,500
↵* Range 1 is based on a diameter of 600 mm (24 in.).
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Table 6.
Probability of failure. The probability that the tree or selected tree part will fail within a year.
Probability of failure range Probability of failure percentage Probability ratio
1 Very high 51–100 1/1
2 High 11–50 1/2
3 Moderate 1–10 1/10
4 Low 0.1–0.9 1/100
5 Very low < 0.1 1/1,000
Target value Impact potential Probability of failure Risk of of harm
Probability ratio 1/120,000 × 1/1 × 1/1 = 1/120,000
Target value Impact potential Probability of failure Risk of of harm
Probability ratio 1/100 × 1/82 × 1/1 = 1/8,200
Target value Impact potential Probability of failure Risk of harm
Probability ratio 1/100 × 1/450 × 1/1 = 1/45,000