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Asger Eriksen and Waleed Al-Nuaimy describe a statistical basis for assessing the risk of unexploded bombs during site investigations and piling.

The threat of buried unexploded bombs (UXB) to land developments in some areas of the UK has been well publicised. A formalised statistical approach to assessing this risk for land owners, developers or consultants is, however, lacking.

This note introduces a statistically rigorous method for quantifying these risks so the potential impact of a few boreholes on a site or a dense grid of clustered piles can be accurately quantified.

Large areas of Europe were bombed heavily during the Second World War, and bombs which failed to explode can still pose a danger to construction work. But there is no regulation, guidance or industry consensus on good practice to assist professionals who need to assess the degree of risk of such sites.

The authors recommend the following steps:

1 Determine the overall risk of UXB in an area from anecdotal evidence or by downloading public domain regional risk maps 1.

2 If a risk is indicated or unknown, conduct or commission a desktop study of available site-specific evidence including records of known enemy air raids, the Ministry of Defence's offi cial register of abandoned UXB, contemporary aerial photographs, the presence of strategic targets such as munitions facilities and fi ring ranges, to name but a few.

3 If the potential for UXB is highlighted by the desk study, then the risk of detonating any UXB should be formally assessed. This involves a review of development plans including site investigation methods (eg boreholes, CPTs), foundation designs (eg raft or piled), records of post-war land use, composition of made ground and near-surface geology. To date, sites have been qualitatively ranked as low, medium or high risk in terms of the likelihood of detonating UXB. The qualitative and often subjective nature of this ranking process has been brought into question and is the focus of this note.

4 If a significant threat exists then the process moves towards appropriate risk mitigation. A new Ciria steering group has recently been set up to standardise UXB risk mitigation methodologies.

Assessment of sampling theory applied to UXB Published techniques to compute the probability of detonating at least one of several potentially buried UXB have been investigated.

The discussion of sampling theory presented in CLR 4: Sampling strategies for contaminated land 2. relies heavily on a single reference in this area, Statistical basis for sampling contaminated land (Ferguson, 1992 3).There are no (published) analytical expressions to compute the probability of detecting a hot-spot, nor for the number of samples required to achieve 95% detection probability. Rather, the figures and mathematical expressions presented are the result of curve fitting to numerical simulation results. The Elipgrid software 4, for example, deals only with single hot-spots.

These results are of limited relevance to understanding the risk of UXB, as the desired result is to not disturb the hot-spots rather than to detect them with a 95% probability.

Furthermore, they are unable to deal with multiple elliptical hot-spots, nor are they suitable for multiple hot-spots with a nonherringbone sampling pattern.

The problem is complicated by the fact that a UXB detonation can be initiated without a direct strike, by impacting the surrounding ground with signi. cant shock forces such as caused by piling and drilling (Figure 1). The authors are not aware of any published literature that refers to a 'zone of influence' surrounding a hot-spot.

A more robust solution is thus required to be capable of dealing with the following issues:

multiple hot-spots (user-defined number of UXB derived from desk study);

target of user-defined shape and size;

random and regular sample locations;

grouped (clustered) samples on a regular grid;

zone of variable influence around a UXB (up to 2m) where sampling risks detonating it;

computing the probability of detonating a UXB with a given grid spacing; and

computing the grid spacing (and number of samples) required to achieve a given probability of detonation or detection.

Geophysical contractor Zetica's approach (UXB probability calculator - UXB-PC) computes the probility of detecting multiple ellipsoidal UXB by means of either random (boreholes or CPT for site investigations) or regular grid (pile layout) sampling.

In the case of uniform simple random sampling, the probability of striking at least one of multiple UXB can be computed both analytically in closed form using probability theory, as well as numerically using Monte Carlo simulation, and results are almost identical.

The Monte Carlo method encompasses any technique of statistical sampling employed to approximate solutions to such quantitative real life problems.

This numerical simulation is carried out with user-defined parameters (such as the expected number of UXB per hectare, the expected UXB dimensions and the sampling density and type) and the sampling experiment is repeated 100,000 times, presenting the mean of the probabilities computed. The results are stable to within +/- 1%.

Monte Carlo analysis is similarly carried out when the UXB fuses are assumed to be surrounded by a spherical zone of in. uence, with the probability of detonation decreasing linearly from 100% at the edge of the bomb to 5% at the zone boundary.

UXB-PC has been validated against published benchmarks in the . eld as discussed below. This work is presented as a contribution to objectively quantify the probability of detonating a buried UXB by regular or random sampling.


The methodology employed was validated by comparing results of two sampling scenarios with results from three sources generally accepted as industry standards 1, 2, 3 . These scenarios present only single elliptical hot-spots with no zone of in. uence (as Elipgrid cannot handle multiple hot-spots), and the corresponding results are shown above (Scenario 1 and Scenario 2).

The results indicate that UXBPC is an effective alternative for published procedures that rely on looking up values on a set of best-fit curves. It also successfully computes the probabilities of detection for a given number of samples, with single and multiple hot-spots of arbitrary aspect ratio. Indicative results are presented for random sampling, as assumed for site investigation boreholes, and regular grids, as assumed for piles (see panel).


Existing techniques for assessing the risk of disturbing contaminated land are incapable of dealing with scenarios involving unexploded bombs buried at a development site.

Introduced here is UXB-PC, a quantitative technique for objectively calculating the probability of detonating UXB during intrusive works.

Input parameters are the number and dimensions of possible UXB as supported by documentary evidence and details of the intrusive method to be used, ie randomly located individual boreholes/CPTs or a regular grid of piles.

Figure 4 shows a monogram of grid spacing for intrusive works versus probability of detonation for a 1ha site expected to contain one UXB with fractional area of 0.016%, both with and without the 2m zone of influence.

The additional risk posed by the zone of inflence can be signficant.

The method provides a quantitative and validated measure of the risk of striking a UXB which can be combined with other land development and construction risks.

Asger Eriksen is chief executive of'cer of Zetica and Waleed Al-Nuaimy is lecturer at University of Liverpool.


1 UXB risk maps, Zetica website, www. htm

2 Department of the Environment (1994).

Sampling strategies for contaminated land, Contaminated land research report, CLR Report No 4.

3 Ferguson CC (1992). The statistical basis for spatial sampling of contaminated land, Ground Engineering, Vol 25, No 5, pp 34-38.

4 Elipgrid-PC software, Oak Ridge National Laboratory, US Department of Energy.

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