Discussion: Scale effects during cone penetration in spatially variable clays Free

The first discussion contributor found the paper by Zhang et al. (2022) interesting because the contributor had previously proposed, based on empirical considerations, a magnitude for the cone factor applicable to both inorganic and organic soft clay deposits (Mesri, 2001). Because the undrained shear strength of soft clay deposits depends strongly on the mode and rate of shear (e.g. Terzaghi et al., 1996), Mesri (2001) selected to compute a cone factor for the mobilised undrained shear strength (e.g. Bjerrum, 1973)

where q_t is the corrected cone tip resistance; σ_v0 is total vertical stress at cone tip depth; and for both inorganic and organic soft clays

Because for soft clay deposits, independent of plasticity index (Mesri, 1975, 1989)

and (Terzaghi et al., 1996)

then

where s_u(TC) is the undrained shear strength for triaxial compression (TC) mode and rate of shear. Zhang et al. (2022) reference a value of N_k(TC) = 12 to Low et al. (2010), and compute for rigidity index I_r = G/s_u = 100, a value of N_k(TC) = 10·16. For computing undrained shear strength from push cone penetration tip resistance for engineering applications, the numbers 12, 10 and 11 are quite similar.

Zhang et al. (2022) refers to ‘soil layering’ in previous studies; however, it describes the present work for ‘spatially variable soil properties’ or ‘spatially variable clays’, or ‘heterogeneous’ marine soft clay deposits. As the authors do not describe laboratory or field measurements of fabric, structure, minerology, or mechanical or hydraulic properties that have resulted in the values of ‘scale of fluctuation (SOF)’ or coefficient of variation (COV) in Table 1, the meaning of a ‘heterogeneous’ marine soft clay deposit is unclear. Furthermore, Table 1 also includes the New Liskeard varved clay which is a lacustrine deposit.

Because of salt flocculation of clay mineral particles in a marine environment, flocculated clay mineral particles and silt-sized particles sediment together and result in a more or less homogeneous isotropic fabric in marine soft clays. According to Terzaghi et al. (1996; pp. 57–58) a lacustrine sediment is composed of light-coloured summer layers consisting of silt with some clay, and dark-coloured winter layers consisting chiefly of clay (see also Kenney (1963)). Neither a typical marine soft clay deposit nor a varved clay deposit (e.g. illustrated in Fig. 12.2 of Terzaghi et al. (1996)), or illustrated by Kenney (1976), should be described as ‘heterogeneous’ or ‘spatially variable clay’.

In cases where the authors’ ‘heterogeneous’ soil is actually modelling ‘alternate occurrence of weak and strong soils’ and ‘the weakest path mechanism’, the authors’ analytical work, with realistic assumptions on the hydraulic and mechanical properties of the silty and clayey varves, could be useful for characterising and modelling of in situ tests, such as push cone penetration or vane shear in distinctly segregated varved clay deposits.

The authors thank the discussers for their interest in their paper (Zhang et al., 2022) and for the constructive comments made. The points are mainly related to (a) the appropriate value of the cone resistance factor, N_k; (b) the geological nature of spatial variability in soft clay. Responses are made to these points in turn below.

The authors value the additional discussion of the cone factor, by which the result (N_k(TC) in the discussion, given as 11) is close to the numerical result (10·16) for the selected rigidity index, I_r = 100 obtained in the study.

It has been widely accepted that the cone resistance factor is affected by many factors such as soil stiffness, stress and strength anisotropy, shear rate and sensitivity. However, the purpose of the work in the paper was not to provide direct values of N_kt for use in site characterisation, but to investigate how N_kt might be affected by local strength variability. As such, the simplest soil model (uniform strength, isotropic, constant volume elastic–perfectly plastic soil with no strain rate effect) was utilised and so the value of N_kt calculated in the paper was not intended to reflect reality. The authors agree that in engineering design the effects of shear rate and anisotropy (and other factors) will affect the appropriate cone factor and should be considered.

The authors agree with the discussion contributors that the paper does not specify the geological nature of spatial variability of offshore clays, and Table 1 is likely to include sediments from a range of depositional (and post-depositional) environments. The view of the discussion contributors appears to be that marine clay is spatially uniform (based on expectation of flocculation during geologically stable fluvial deposition) and only lacustrine sediments (because of the interannual changes in sedimentation) have consistent horizontal layering. The authors’ experience in characterising a range of fine-grained offshore soils suggests that this is not always true. The authors are not geologists and prefer not to speculate regarding the different geological processes, but they strongly agree that the nature of different forms of spatial variability – either as specified in geostatistical terms as vertical and horizontal scales of fluctuation (as in this paper) or in terms of regular layer thicknesses associated with repeating depositional changes (as in the referenced varved lacustrine deposits) – warrants further study. Once this is done, the work reported in the paper under discussion could be extended to quantify the relative performance of cone penetrometers and different foundation types for geologically likely conditions, as suggested by the discussion contributors.