A.6.1 Gy Sampling Principles Applied to Bulk Material

The use of Gy’s incremental sampling approach to collect samples from environmental bulk materials (e.g., soils, sediments, liquids) is a relatively new concept in contaminated site investigation. Important concepts underlying Gy’s sampling principles (and ISM) are reflected by addressing the following questions:

  • What are the differences between bulk material sampling and traditional random sampling of discrete items (e.g., individuals in a room, discrete data sets consisting of 100 distinct points, or even 10,000 distinct points)?
  • How can Gy’s sampling principles be used to collect representative (unbiased) samples from environmental bulk materials?
  • Which heterogeneities are sources of sampling error, identified by Gy’s sampling theory, are addressed by ISM?
  • What is the difference between the heterogeneities present in the bulk material to be sampled and the variability in the analytical results obtained by chemical analysis of collected samples?

The variability observed in measured concentrations within a DU can be directly attributed to heterogeneities in the environmental media that is sampled. This concept applies to individual ISM samples (estimates of the mean) and discrete samples alike. Uncertainty in parameter estimates and corresponding decision errors are closely tied to the underlying sources of variability and the sampling methodology used to obtain a representative sample (e.g., simple random sampling, serpentine, and systematic random within grid).

Gy’s field sampling equation (Pitard 1993, Smith 2006) given below (1) represents the main formula used to compute sample mass, Ms, needed to obtain a representative/unbiased estimate of mean concentration, CDU of the contaminant present in the bulk material of mass, ML, contained in a DU (lot)

s2FE = (1/Ms) - 1/ML) clfgd3,   (1)

The details of the parameters used in equation (1) can be found in Pitard (1993). In mining projects, a detailed investigation is conducted a priorito estimate the parameters used in equation (1), so that an adequate amount of mass of the bulk material can be collected to obtain a representative/unbiased estimate of the mean of the lot.

Ideally, the sample mass, Ms, is calculated using Gy’s experimental equation (1). Based on a CSM, a pilot study, and/or information from similar sites, an initial estimate, s2FE of the variance of the FE, , needs to be estimated or computed beforehand to determine Ms needed to compute a representative estimate of the DU mean concentration, CDU.

Statistical terminology and quantifiable measures (bias, FE, standard deviation of FE, RMSE, 95% UCL) used to assess the performance (accuracy, precision) of the mean estimate, CIS, obtained using ISM are described as follows. Here E represents the expected value operator, Var represents the variance operator, and Abs(x) represents absolute value of the quantity, x.

ML = mass of the DU consisting of particulate material (surface soils)
Ms = mass of the sampled material collected from the DU
CDU (= µ) = mean of the contaminant (e.g., uranium) present in the bulk material of the DU
m = number of increments in an ISM replicate; typical values of m = 36, 50, 64, 100
r = number of replicates of ISM; r ≥ 1
SS = sample support

Sampled mass Ms = m × ISMincr, where ISMincr represents increment mass (same for all increments).

CIS = an ISM estimate of unknown DU mean, CDU

Let X subsript 1, X subsript 2, ... X subsript X subsript rrepresent the analytical values of the r ISM replicates, each replicate made of m increments. Note that each analytical result based on an ISM replicate represents an estimate of the DU mean. The ISM mean estimate, CIS, of the DU mean, CDU, based on r replicates is given in equation (2).

C subscript is = X = X subscript 1 + X subscript 2 + ... + X subscript r/ r