Statistical sample size for quality control programs of cement-based solidification/stabilization

Abstract

Sampling requirements for the quality control (QC) of cement-based solidification/stabilization (S/S) construction cells do not currently consider the reliability of the hydraulic conductivity sample nor the explicit risk associated with actual flow through the cells. This thesis addresses the issues associated with sampling requirements of a cement-based S/S construction cell during a QC program via probabilistic simulation and via theory taking into account the spatial variability associated with hydraulic conductivity of the entire cement-based S/S system. The sampling requirements are determined by considering a hypothesis test, having null that the constructed material is unacceptable, and targeting acceptable probabilities of making erroneous decisions. Two types of errors that may result in the hypothesis test are: 1) a Type I error where the sample data rejects the null hypothesis even though the null is correct, and 2) a Type II error where the sample data fails to reject the null hypothesis even though it is false. Probabilistic simulations are performed to examine the influence of a soil-cement material’s mean, variance, and correlation length on sampling requirements for a QC program of cement-based S/S construction cells. It is found that to achieve target Type I and Type II error probabilities, samples should be collected at higher frequencies when the mean hydraulic conductivity is close to the regulatory value, coefficient of variation is 1.0 or less and the correlation length is at an intermediate value. An example is presented to illustrate how the results can be used in practice. An analytical approach is also presented for selecting the sample size for cement-based S/S construction cell’s QC program. Analytical solutions are developed to compute the probabilities of Type I and Type II errors as a function of the number of samples taken and the statistics of the hydraulic conductivity field. The solutions are verified by probabilistic simulations. A set of hydraulic conductivity field data of an existing cement-based S/S system is statistically analyzed to assess its spatial variability. A lognormal distribution is found to be a reasonable fit to the data. Recommendations are provided for conservative QC sampling requirements for that system.