Reply to the discussion by R. Popescu on "Bearing capacity prediction of spatially random c - phi (variant) soils"

Fenton and Griffiths The discussor brings up a number of good points regarding the difficulties in characterizing spatial variability of soils. The main points of concern raised by the discussor are the high coefficients of variation (COVs) considered by the authors and the methodology used to simulate the random soil property fields. It is hoped that the following discussion will shed some light on these concerns. 369 Regarding the range in COV considered by the authors, which was 0.1–5.0, the authors believe that it is still unknown what value(s) of COV should be used in geotechnical characterization. The appropriate COV depends on several things, such as the intensity of site investigation; the level of deterministic site characterization (e.g., higher order trend, layer-wise descriptions); and how the soil variance affects the response quantity, or engineering property, of interest (i.e., is the property itself a measure of some form of local average, or is it highly dependent on microscale “defects”? ). The issue of site investigation intensity is intimately connected to the degree of deterministic site characterization, for example, if only a single value global average property is employed in the design of a footing, then the site investigation results could yield a large COV, particularly if the site is large and the investigation points are widely separated. The COV would then be interpreted as one’s “uncertainty” about the value of the property at the footing if no test results were available near the footing. If a particular test result were available near the footing, then that result would be preferentially used to design the footing, and the corresponding COV would be reduced. In such a case, the site characterization moves away from a single value global average to a more detailed deterministic description that incorporates observation versus footing locations. The COV used for design depends on how the investigation data are used and on where the investigation points are relative to the footing. For one site with considerable data near the footing, the COV to be used might be quite small, whereas for another site with limited data and (or) data well removed from the footing location, the appropriate COV might be quite large. In this sense, the comprehensive results reported by authors such as Phoon and Kulhawy (1999) are really just a start at the characterization of soil variability. They are basically reporting COVs estimated from a particular dataset, reflecting the residual variability about the locally estimated mean (or mean trend). These results tell us little about how to handle uncertainty about the soil properties at some distance from where the soil was actually sampled. There is much that is unknown about this problem, and considerable research that needs to be done before definitive levels of COV can be stated for any given situation. For this reason, the authors chose to perform their analysis over a wide range in COV values. This is not viewed as a recommendation that designers should be considering COVs as high as 5.0, but rather allows the results to be used in the event that a designer determines such a high COV is appropriate. Alternatively, if a lower COV seems appropriate, these results are also included in the paper. It is not clear to the authors why the discussor is introducing the idea of the finite element model size into the choice of COV. The important issue is the estimate of the “point” COV (where point is usually some local average over a small volume) from a set of data collected in the field. How the data are collected, how the statistical analysis is carried out, and how the results are to be used will affect the value of the estimated point COV. Once that value has been determined, it is appropriate to use it in whatever numerical model one chooses. The quality of the numerical model in representing reality is another issue, but the authors have strived to produce a model that reflects the material behaviour as well as possible given current computational resources. In particular, the Local Average Subdivision method employed by the authors correctly reflects the transformation from the true point statistics to the element averages that is consistent with the continuum finite element model. The second issue raised by the discussor has to do with the ability of the authors’ simulation technique to adequately represent the prescribed random fields. The discussor is concerned that the nonlinear transformation, when going from the underlying Gaussian random field to the target soil property, affects the final correlation structure. This transforma-