This paper examines the interaction between the spatial variations in binder concentration (i.e. cement slurry concentration) and in situ water content, in cement-mixed soil, using field and model data as well as statistical analysis and random field simulation. The field data are first analysed to shed light on the spatial variation in the in situ water content, including its scale of fluctuation. A statistical model is then developed which takes into account the variation in binder concentration and in situ water content. This leads to a two-parameter model for the prediction of the mean, variance and probability distribution function of the strength of the cement-treated soil. The scale of fluctuation for the variation in binder concentration arising from imperfect mixing within a cement-mixed column is then examined using centrifuge model data. This indicates that the scale of fluctuation in binder concentration is much shorter in range than that of the in situ water content. The combined effect of these two scales of fluctuation is then studied by simulating the resulting random field using Monte-Carlo simulations. This indicates that the size of the sampling region has a significant effect on the scale of fluctuation that is captured. If the sampling region is of a similar size to the column diameter, the measured scale of fluctuation reflects that of the binder concentration. As the size of the sampling region increases, so does the measured scale of fluctuation. This explains the wide range of scales of fluctuation that have been reported for cementtreated soil. To capture both scales of fluctuation in core sampling, some boreholes should be sunk at close spacings of less than a column diameter, in order to capture short-range variation.

Although there has been a substantial body of research on the chemical stabilization of sewage sludge, most of these results are project-specific and relate mainly to the use of new binders and sewage sludge from specific sources. In this sense, much of the work to date is context-specific. At present, there is still no general framework for estimating the strength of the chemically treated sludge. This paper proposes one such general framework, based on data from some recent studies. An in-depth re-interpretation of the data is first conducted, leading to the observation that sludge, which has coarse, hard particulate inclusions, such as sand, premixed into it, gives significantly higher strength. This was attributed to the hard coarse particles that lower the void ratio of treated soil, are much less susceptible to volume collapse under pressure, and contribute to the strength through frictional contacts and interlocking. This motivates the postulation of a general framework, based on the premise that coarse, hard particulate inclusions in the sludge which do not react with the binders can nonetheless contribute to the strength of the treated soil. The overall void ratio, defined as the volume of voids in the cementitious matrix normalised by the overall volume, is proposed as a parameter for quantifying the combined effect of the coarse particulate inclusions and the cementitious matrix. The binder-sludge ratio is another parameter which quantifies the strength of the cementitious matrix, excluding the hard particulate inclusions. Back-analysis of the data suggests that the significance of the binder-sludge ratio may diminish as the content of hard particulate inclusions increases.