Use of fall-cone flow index for soil classification: a new plasticity chart

Vardanega et al. (2021) proposed a new plasticity chart for soil classification using flow index and fall-cone liquid limit as measured from fall-cone tests. The new plasticity chart is of great significance as it allows soil classification to be performed without thread-rolling tests, which may well introduce the operator's influence. The discussers examined the applicability of this new plasticity chart to several soils containing diatoms with unique particle morphology and porous structure. The classification results based on the classic Casagrande plasticity chart and the new plasticity chart are compared and discussed herein.

The soils tested herein include natural diatomaceous earth (DE) and artificial diatomite–kaolin mixtures (DKM) with varying diatomite contents. The DKM were included to investigate how diatomite content affects soil consistency limits. The particle compositions of the soils studied following the ASTM standard (ASTM, 2021) are given in Table 2. Natural DE was collected at the depth of 4·0 m from the lacustrine deposits of Shengzhou, Zhejiang Province, China. DKM were prepared by adding diatomite to kaolin clay (RP-2, Active Minerals International), with the content of diatomite being 0, 20, 40, 60, 80 and 100%. All the diatomite contents in this paper are based on the dry mass ratio. For convenience, the mixtures are labelled in the form of ‘diatomite content: kaolin content’. For example, 40D:60K stands for the mixture with 40% diatomite and 60% kaolin clay. The mixture 100D:0K in fact is pure crushed DE consisting of whole and broken frustules (Fig. 7) from Changbai Prefecture, Jilin Province in China.

The consistency limits of the soil studied were determined through thread-rolling and fall-cone tests following ASTM (2017) and BSI (1990). All samples were soaked in deionised water for 7 days before the test to allow full infiltration of water into the intra-skeletal pores of the frustules. Values of the flow index (FI_c) were calculated from fall-cone test data using equation (3).

Table 2 presents the consistency limits as well as the soil classifications according to the classic Casagrande plasticity chart and the new plasticity chart. Also given in this table are the corresponding results for DKM soils from the literature. It is revealed that the classifications of both natural DE and DKM according to the new plasticity chart are identical to those following the Casagrande plasticity chart. This confirms the effectiveness of the new plasticity chart, which allows soil classification to be conducted based on FI_c from the fall-cone test as an alternative to the plasticity limit from the thread-rolling test. This has important practical implications, especially when considering the non-plastic nature of pure diatomite (100D:0K).

Figure 8 indicates that the natural DE is positioned above the A-line and corrected (adjusted) A-line, with its I_P and w_L varying considerably. In addition, the natural DE was classified as clay (CE) according to the new plasticity chart. However, the particle size analysis reveals the dominant silt-sized particles, and the soil was classified as silt accordingly. Such inconsistency between the soil classification according to the plasticity chart and the particle composition is possibly due to the high content of diatoms with extremely high water-holding capacity. Owing to the non-plastic nature of pure diatomite (100D:0K), existing methods fail to measure its consistency limits. Although some successful cases have been reported (Kim, 2012; Wiemer et al., 2017), they cannot be applied to the current study due to the different diatom types and their fragment levels. It is found from the plasticity chart in Fig. 8 that the increasing content of non-plastic diatomite leads to a dramatic increase in w_L and w_P, but only a slight reduction of I_P, with the data of Wiemer et al. (2017) being the only exception. This conclusion is different from the previous study (Shiwakoti et al., 2002) in which sand particles were added to kaolin clay. Although the adding of both non-plastic diatomite and sand ultimately led to the non-plastic nature of the mixture, the sand affected the w_L and w_P of the mixture differently from the diatomite. The natural DE and DKM are distinguished by the extremely high liquid limit that increases with diatom contents. However, such an increase is the result of high fluid holding capacity due to the intra-skeletal porosity of diatoms instead of plasticity (e.g. Shiwakoti et al., 2002; Bandini & Al Shatnawi, 2017), as proved by the very limited I_P value changes of DKM mixtures (Table 2). Note that although the studied soil can be classified as clay with an extremely high liquid limit according to the new plasticity chart, a large amount of water is in the intra-skeletal pore spaces, and thus it barely interacts with soil particles (Bandini & Al Shatnawi, 2017). Consequently, current results show that the consistency limits of diatomaceous soil do not provide information on the soil property as they are conventionally expected to do. Caution should be used when classifying diatomaceous soil according to the Casagrande plasticity chart and the new plasticity chart, as well as deriving the fundamental soil parameters from w_L, w_P and I_P.

In addition to DE, the new plasticity chart appears also to be inapplicable to peat with a porous and compressible nature due to the open cellular structure of the organic solids. Previous studies have confirmed the inappropriateness of Atterberg limits to peat (O'Kelly, 2015; O'Kelly et al., 2018) and their adoption could be misleading. The ΔI_P–ΔI_Pc plots in Fig. 4 quantify the deviations of data points from the A-line. Interestingly, the discussers found that the data points with the most significant deviations from the A-line are those representing peat from the southwest of England (Vardanega et al. (2019) data in Table 1). Consequently, it is reasonable to expect that a minor modification of equation (5) with the data of peat excluded will lead to more accurate predictions, considering the notional nature of Atterberg limits for peat.

The discussers kindly welcome ongoing comments and discussions from the authors.

The authors welcome the discussion on their paper proposing a new classification chart for plastic soils. The authors appreciate the opportunity in this reply to respond to and clarify some of the points raised by the discussers.

The need to update the Casagrande plasticity chart due to the preference in various codes employing the cone penetrometer device over the Casagrande cup device for liquid limit (w_L) determination (as suggested in Dragoni et al., 2008), or to change the function of the A-line (e.g. Reznik, 2017), or to develop new soil classification methods (e.g. Polidori, 2003, 2004, 2007; Jang & Santamarina, 2016; Moreno-Maroto & Alonso-Azcárate, 2018) has been the subject of considerable research efforts. The original paper (Vardanega et al., 2021) sought to do two things: (a) remove the need for the thread-rolling test for the plastic limit (w_P) from the classification system by using the fall-cone flow index (FI_c) from Sridharan et al. (1999), and (b) adjust the A-line and U-line equations (equations (1) and (2)) (based on the work of Casagrande (1947), as given in Howard (1984)) using equation (5) and the equations developed in the paper by O'Kelly et al. (2018) for linking the fall-cone liquid limit with the Casagrande cup liquid limit. The authors acknowledge that any deficiencies in the original Casagrande classification methodology will not be overcome by the achievement of aims (a) and (b).

The discussers introduce the idea that both the traditional Casagrande approach for soil classification, incorporating the thread-rolling test for the plastic limit, and the updated version based on flow index do not correctly classify two soil types: DE and peat soils. As demonstrated by the discussers for DE soils (but also for peat soils, cf. Skempton & Petley (1970)), consistency limits can be determined in the laboratory for these soils, but the Casagrande classification system (traditional or revised) alone does not give sufficient insight into the behaviour of these materials in the field (O'Kelly, 2015, 2016). While noting this, the authors would also contend that the Casagrande system for classification has this drawback to some extent for all natural materials, as it is based on remoulded soil parameters (w_L and w_P), testing only the fraction of the disaggregated material that passes the 425 μm sieve size. It is acknowledged that this drawback is considerably more marked for the DE and peat soil types referred to in the discussion. In the case of peats, more useful tests for soil classification purposes may be organic content, fibre content, natural water content and degree of humification (decomposition), as elaborated in the papers by Edil & Wang (2000) and O'Kelly (2015, 2016). Users of any soil classification framework should be aware of its inherent limitations and potential drawbacks in indicating relevant soil field behaviour. The authors’ response to the discussers’ specific comments is given in the following sections.

The discussers note that for DE soils, a group of soils that was not included in the original database, the soil classifications derived using both the Casagrande plasticity chart and that described by Vardanega et al. (2021) are identical in all cases. It is pleasing to see that the new classification scheme agrees with the Casagrande chart. The discussers further note, however, that the natural DE soils they investigated are misclassified by both charts, with these soils (comprising a majority of silt-sized particles) plotting above the A-line and hence being classified as clays. (Note, solely based on their w_L and I_P values listed in Table 2, all six DKM soils investigated by the discussers also plot above the A-line. On this basis, these soils would also be classified as clay – hence, it would seem their listed I_P values are incorrect.) It should be remembered that there is no theoretical basis for the original formula for the A-line given in Casagrande (1947). More recent experience has shown that, in general, this line divides clays and silts well, the position of soils on the Casagrande chart has become the de facto classification tool for fine-grained soils, with their classification by measurement of particle-size composition rarely carried out. The fact that both charts misclassify the natural DE soils is hence interesting, but not necessarily surprising. As already pointed out, because the proposed new classification chart is derived from the Casagrande chart, any misclassification will naturally persist with use of the new chart.

The discussers also rightly point out that for some DE soils, such as pure crushed DE consisting of whole and broken frustules (i.e. DKM, 100D:0K), which are clearly identified as non-plastic, the new plasticity chart (and the Casagrande chart) would still classify said materials as plastic silts. Although both classification charts should only be used having established the plasticity credentials of the fine-grained test materials, the authors accept that this should be clarified for the new chart, as with the lack of need for a thread-rolling test, this point may be missed. It should, however, be pointed out that the plasticity, or otherwise, of fine-grained soil can generally be judged by touch rather than requiring a plastic limit test. As also pointed out in the original paper (Vardanega et al., 2021), for fine-grained soil identified as being non-plastic, equation (5) in that paper should not be applied to compute a ‘plasticity index’ (plastic range), or from that, a ‘plastic limit’.

The discussers also suggest that the framework should exclude peat soils. The authors note that organic soils were included in the soils studied by Casagrande when developing the soil classification framework (Casagrande, 1947), so it was deemed valid to include such material types in the determination of equations (5) and (6) in the original paper, as the test data is experimentally valid for the database of fine-grained materials studied (notwithstanding the earlier comments about the link or lack thereof to field performance of the obtained data). The authors would like to clarify (as stated in the original paper) that the peat soil data from Vardanega et al. (2019) were determined for soil samples with the peat fibres removed. The authors do agree that the consistency limits are not sufficient alone for classification of natural peat soils for the reasons already mentioned in this reply.

However, as suggested by the discussers, the authors have re-run the correlation analysis presented in the original paper (Vardanega et al., 2021), excluding the peat and high organic content soil data from the TCD database (see Table 3) and the peat soil data from Vardanega et al. (2019) (see Table 1 for the full listing of the source publications for the original analysis). This reduces the number of data points for the correlation from 235 to 208 – that is, the 27 points removed comprise approximately 11·5% of the data points. Fig. 9 shows the updated correlations for the reduced database, which are given as equations (12) and (13) in this reply

Interestingly, the simple linear form of the correlation (equation (12)) has a slightly higher coefficient of determination (R²) than equation (13). Therefore, using the procedure outlined in the original paper (Vardanega et al., 2021), equation (12) is used to update the A-line and U-line, given as equations (14) and (15) in this reply.

Table 4 shows a numerical comparison between equations (10) and (14), and equations (11) and (15). For both sets of equations, the difference of FI_c(%) ranges from around −0·5 to 6 over the w_L range of up to 120%, and from around −0·5 to 102 for the extended plasticity chart with w_L up to 600%. The authors consider that this will not result in a significant change to the classification system presented in the original paper (especially as the current BS 5930 (BSI, 2018) standard only presents the plasticity chart up to w_L of 100%, with very high plasticity being when w_L > 70%). However, a classification chart could be produced using equations (14) and (15), if the user of the revised framework should wish to do so.

The contribution part of this discussion is financially supported by the National Natural Science Foundation of China (nos. 41972285, 41672293, 41972293).