Introduction

Soils originating from the weathering of non-sedimentary rocks do not undergo any sorting in their grading, typically resulting in well-graded particle size distributions. Weathering may influence the composition of soil in one or more aspects, e.g. particle size, particle size distribution, mineralogy or particle morphology, all of which influence its mechanical behaviour. As the heterogeneity of weathering processes adds to the difficulties encountered studying these soils, it would be desirable to establish which parameters are more likely to influence the basic engineering behaviour, and this paper considers the compressibility.

While the mechanisms of compression in uniform sands are well understood (e.g. Coop and Lee 1993), some uncertainties still remain in describing the behaviour of binary mixtures (e.g. Thevanayagam and Mohan 2000). For example, there is agreement (e.g. Lade and Yamamuro 1997; Carrera et al. 2011) that with increasing fines, the mechanisms of compression evolve from those of a granular soil to those of a fine-grained soil, the minimum value of compressibility and lowest location of the normal compression line in the volume:stress plane being at an intermediate or transitional mixture. However, it is less clear what this value of fines should be for different soils (Zuo and Baudet 2015) and how the nature of the fines influences the mechanics of compression. The approach proposed by Thevanayagam and Mohan (2000) suggests using the traditional definition of void ratio at the two mixture extremes and an inter-granular or inter-fine void ratio for intermediate cases, depending on whether the mechanics are fines or coarse grain-dominated, but it remains rather subjective when to use one definition or the other as the transitional fines content is highly variable and difficult to predict (Zuo and Baudet 2015). This type of approach may also only be used if the particle size distribution is binary and there is sufficient separation of the two grading sizes. The plasticity of the fines may also influence the role that they have, requiring modification of the definition of the inter-granular or skeletal void ratio (e.g. Thevanayagam et al. 2002).

However, considerable work is still needed to shed light on the behaviour of well-graded soils. Recent studies focusing on the behaviour of very well-graded soils with fractal gradings gave contradictory results. Altuhafi and Coop (2011) found that no breakage could be observed after one-dimensional compression in soils having an initial fractal grading, despite the considerable volumetric change observed. They put forward the hypothesis that particle rearrangement and abrasion at the grain contacts could be the mechanisms responsible for the plastic volumetric strain. This appeared to be confirmed when analysing the particle morphology, which showed some changes in particle roughness but no major splitting. Minh and Cheng (2013) could reproduce qualitatively the experimental results published by Altuhafi and Coop (2011), using discret element models (DEMs) that assumed no particle breakage. From the work of Coop et al. (2004), it was found that in shearing, a stable grading was only reached at shear strains in excess of a few thousand percent, and so it is possible that even an initially fractal grading may undergo breakage during shear, as Miao and Airey (2013) found, although their “fractal” grading was a limited one that did not include fines.

According to the international standards, upon which many national classification systems are based, including the Geotechnical Engineering Office (GEO 1988) classification system in Hong Kong, a weathered rock can be classified based on the degree of chemical decomposition undergone by its minerals. In these classification systems, six grades are identified, from fresh rock to residual soil. The weathered grades of granitic saprolites having a soil-like appearance are highly decomposed granite (HDG), completely decomposed granite (CDG) and residual soil (RS), which correspond to grades IV–VI. In Hong Kong, to this general classification, a description of the “consistency” of the soil is added, e.g. “weak”.

Baynes and Dearman (1978) proposed a qualitative trend between the weathering degree and the soil in situ bulk density, based on data collected by Lumb (1962), and suggested a distinction between a “granular domain” in the initial stages of weathering and a “clay matrix domain” thereafter. As the compression mechanisms of a saprolitic soil can be expected to be different for these two domains and to span the mechanical behaviours discussed above, it would be desirable to find a trend analogous to that of Baynes and Dearman, but based on mechanical parameters. However, this could only be an approximate trend as weathered soils are generally well-graded and are seldom found in nature having a perfectly fractal or binary grading, which are idealisations often used in research to establish general frameworks.

In this work, one-dimensional compression tests were carried out on granitic saprolitic soils with different weathering degrees. Isotropic and one-dimensional compression tests on other saprolites from Hong Kong and around the world were reanalysed and compared with those tested here to establish general trends.

Soils tested

The soils tested in this work were a saprolite from the Sha Tin Granite sampled along a slope profile and a saprolite from the Kowloon Granite, sampled at shallow depths. According to the GEO (1988) classification system, the soils tested belonged to grades IV–VI. In the Sha Tin Granite, several Mazier samples were taken from two boreholes, one covering depths between 6.5 and 27 m [at borehole A (BHA)], while the other only reached shallow depths (BHB). However, this would correspond to a depth of approximately 40 m for the other borehole, due to the difference in ground level, which explains it being less weathered despite the shallower depth. Although it is expected that the weathering would generally be larger at the surface and decrease with depth, this was not rigorously observed. This type of non-uniformity is a typical feature of weathering and might be explained by preferential water flow, such as along discontinuities. Two block samples were taken in the Kowloon Granite, both above a 2-m depth. The two samples were taken in two different trial pits (TPs), TPA and TPB, but were close together and belonged to the same geological formation. The acronyms used for the soils tested and their depths are reported in Table 1.

Table 1 Depths of the samples tested and the acronyms used (BH borehole, TP trial pit)
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Gradings and mineralogy

To limit the heterogeneity of the dataset taken from the literature, only saprolitic soils originating from granites were taken into consideration. In Table 2, the details of the dataset available are listed. As mentioned above, the soils tested specifically for this research were from the Sha Tin Granite, where the soil was sampled at different depths with weathering degrees ranging from HDG to CDG, and the Kowloon Granite, which was sampled at shallower depths and included both CDG and RS. Besides these soils, a number of the other sets of data considered were from Hong Kong. In particular, the data from Fung (2001), Zhang (2011) and Madhusudhan and Baudet (2014) are also from the Kowloon Granite, while the data from Ng and Chiu (2003) and Yan and Li (2012) are from the Mt. Butler and the Needle Hill Granites, respectively. The other data considered are from Korea (Lee and Coop 1995 and Ham et al. 2010), Portugal (Viana da Fonseca 1998 and Viana da Fonseca et al. 2006) and Japan (Ham et al. 2010).

Table 2 Details of the soils used as a dataset
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In Fig. 1, the gradings of these soils are presented. The solid symbols refer to the soils tested in this work, while the open symbols are for the other saprolites from Hong Kong, and the cross symbols are for saprolites from other locations in the world. To have an easier, although coarser, means of comparison, the particle size distributions were divided into three parts, i.e. gravel, sand and fines, which are the sum of the silt and clay fractions. The grading curves of the soils tested for this work are presented in Fig. 2 and the others can be found in the relevant references. In Viana da Fonseca (1998), a great number of grading curves was presented, and the limits of the envelope formed by these curves are shown as a hatch-shaded diamond area in Fig. 1. The envelopes proposed by Lumb (1962) for the HDG, CDG and RS, which were based on a large dataset from Hong Kong, are superimposed on Fig. 1 to provide a reference regarding the weathering degrees. In general, most of the soils analysed fall in or close to the envelopes proposed by Lumb, except for those soils plotting on the fines-axis, for which a possible explanation will be given later in this section. As the weathering degrees of the soils outside Hong Kong were generally not specified, the agreement might be, to some extent, fortuitous. However, except for the Sha Tin Granite, where only one sample was identified as HDG on the borehole log but a few actually plot in that area, all the other data from the literature in Hong Kong were described as CDG and also plot in the CDG area.

Fig. 1
figure 1

Gradings of granitic saprolites from several locations worldwide, superimposed with the change in grading hypothesised by Irfan (1996). 1Lee and Coop (1995), 2Viana da Fonseca (1998), 3Fung (2001), 4Ng and Chiu (2003), 5Viana da Fonseca et al. (2006), 6Ham et al. (2010), 7Zhang (2011), 8Yan and Li (2012) and 9Madhusudhan and Baudet (2014)

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Fig. 2
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Particle size distribution of the soils tested for this research

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The data on Fig. 1 are quite scattered and this may result from the variability of grain size in the parent rock, although this will, to some extent, be bounded by the description that they are all granites and not rhyolites or pegmatites. Unfortunately, most authors have not stated whether or not they have curtailed their grading curves at the larger particle sizes for testing. In the tests conducted here, the gradings were curtailed at 6.3 or 5 mm and the effect that this has on the grading is indicated in Table 2 and Fig. 1 as it is for Lee and Coop (1995) where this information is also available. Unfortunately, it is not possible to know exactly the consequences of the curtailing on correlations between grading and mechanical behaviour, since both the grading descriptors and the compressibility are likely to change as a result. The “intact gradings” are presented in Fig. 1 with grey symbols and, on Fig. 2, the intact and curtailed grading curves for this research are compared in detail. Although in only one case (6) was there no curtailing and the amount of discarded particles for some of the other tests in this research might seem significant, the particles larger than 6.3 mm might be more appropriately considered as “rock lumps”, since the maximum size of the mineral grains in the parent rocks was not larger than 2–5 mm. Even so, gravel makes up the majority of the grading curve in most cases. The soils tested by Ham et al. (2010) and Zhang (2011) were curtailed at a relatively small particle size of 2 mm so they plot on the fines-axis in Fig. 1 and would explain their anomalous position with respect to the envelopes proposed by Lumb (1962). However, it is not known what proportion of coarser particles were discarded, although the low proportion of fines in Ham et al. (2010) is more typical of a less weathered soil and the resulting curtailment leaves the soil with a relatively unusual grading as a more poorly graded soil than the others, composed mostly of sand. As discussed later, this may have an impact on their behaviour that influences their agreement with the correlations investigated.

In Fig. 3, the mineralogical compositions of the soils are presented, which, in the present work, were determined by means of X-ray diffraction (XRD) analysis carried out on bulk soil samples, which were dried at 50 °C and milled to <60 µm. These were not available for every soil analysed and, in addition, the data for the Mt. Butler and Kowloon Granites were taken from a different source than the gradings data (Irfan 1996). The minerals were divided into three groups, similar to the gradings: quartz, feldspars and others, which include both the micas retained from the parent rock and the products of the weathering, such as clay minerals. Although the data are still quite dispersed, the scatter is slightly less than for the gradings.

Fig. 3
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Mineralogy of granitic saprolites from several locations worldwide. 1Lee and Coop (1995), 2Irfan (1996) and 3Ham et al. (2010)

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Testing methodology

In this research, the soils were tested in conventional oedometers having 50-mm diameter rings. Since the maximum grain size was as large as 20 mm, as already mentioned, the grading curves were terminated at 6.3 mm or, in some cases, 5 mm, as shown in Fig. 2, to ensure a ratio of at least 6 between the ring diameter and the largest size of particles, as suggested by Lacasse and Berre (1988) for well-graded soils, while being able to achieve elevated stresses in a standard equipment. The reconstituted soil was mixed to the required proportions of each particle size, having first separated the soil from each weathering degree into the usual sieve intervals by dry sieving. All the soils considered from other works in the literature were tested in a reconstituted state but it is not known in detail what the preparation processes adopted were.

The parameters used as a reference in this study are the slope of the normal compression line (NCL) in the volumetric plane (λ = Δv/Δlnp′ where v is specific volume and p′ is the mean normal effective stress) and the specific volume on the NCL at 100 kPa (N 100). As can be seen in Table 2, some of the λ values calculated were obtained from oedometer tests (1D), while others were from isotropic compression carried out in triaxial cells (ISO). When comparing the values obtained from oedometer and triaxial tests, it is, therefore, implicitly assumed that the isotropic and one-dimensional NCLs are parallel in the volumetric plane. This means that λ = C c/2.303, where C c is the compression index defined in terms of log10 vertical stress for an oedometer test, so that it is also assumed that K 0 is constant on the NCL. However, since the K 0 values were not available for all cases, the N 100 was determined only for the oedometer tests. The value of the specific volume at 100 kPa vertical stress (N 100) was chosen, since λ was estimated approximately in the stress range 100–1000 kPa. The more commonly used intercept at 1 kPa would be badly affected by small changes in λ. The NCLs were chosen to be straight within the pressure ranges tested when interpreting the data and more importance was given to the tests that reached larger stress, therefore using the slope of the tests after yielding occurred to calculate λ as discussed below.

Results and discussion

Correlation between compressibility and grading descriptors

Figure 4a–c shows the one-dimensional compression tests carried out in this work. Explanations of the sample names are given in Table 1. For each soil, a number of tests were carried out covering a wide range of initial specific volumes when preparing the reconstituted samples. The samples were created either by gentle moist tamping, which was carried out by manually varying the water content from 8 to 60 %, or by mixing to a slurry for the soils having a larger amount of fines. The range of initial specific volumes that could be achieved changed with the soil, due to the differences in their initial gradings, since more efficient packing modes are obtained as the mean particle size reduces and the grading curve becomes flatter. However, it is clear that after yielding, each soil defines a unique NCL, which have been indicated in Fig. 4. In some cases, only one loose specimen and one dense one were tested, but the NCL was, nonetheless, well-defined. This is because exactly the same grading was used for all the specimens within each weathering degree, which corresponded to the average grading curve calculated for that soil from a much larger sample so that any minor heterogeneity would not cloud the trends further. The NCLs from the literature data were derived in the same way.

Fig. 4
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One-dimensional compression tests and NCLs a sh ewCDG and evwCDG of the Sha Tin Granite, b dp ewCDG and HDG of the Sha Tin Granite and c ewCDG and RS of the Kowloon Granite

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Rocchi et al. (2015) have shown that for a granitic saprolite, the characteristic dominating the behaviour in compression is grading, rather than mineralogy or particle morphology. For this reason and because the mineralogy and particle morphology were not always available for the dataset analysed, the changes in the NCL slope and intercept were correlated with several grading descriptors that are more commonly used in engineering practice.

Among the parameters considered were the mean size D 50, the amount of fines, the coefficient of uniformity c u, the coefficient of curvature, the fractal dimension (if appropriate) and the breakage potential B p, (as defined by Hardin 1985). However, all these parameters describe the initial grading curve with one value only, whereas two are really required, one describing the shape of the curve (well- or poorly graded) and the other defining its location arising from the size of the particles. An attempt to define such a parameter for sedimentary soils was made by Cola and Simonini (2002), who proposed the grain size index I GS. This is the ratio of D 50 and c u, where the former is normalised by 1 mm (D 0) to make it dimensionless, i.e. I GS = (D 50/D 0)/c u. This parameter, therefore, includes both the location of a grading curve and its shape. However, it did not show any evident improvement in the trends observed when it was considered and so only the three most common parameters are presented here, D 50, % fines content and c u.

In Fig. 5, the results are analysed with respect to D 50. For a uniform granular material, a trend would be expected for soils with larger particles to be more compressible, as breakage increases with particle size (Weibull 1951) and sands becomes more compressible. As the yield stress in compression reduces with increasing particle size, the intercept N 100 would also be expected to increase with size (McDowell 2002). From a consideration of mixed binary soil gradings, as discussed above, decreasing D 50 would again be expected to cause a reduction of λ down to a minimum after which it might be expected to increase again. Examining only the data from this study (the solid symbols) in Fig. 5a, a reasonably clear trend can be seen for λ to reduce with particle size down to a size below 1 mm, while below this value, λ may be less sensitive to changes in D 50. Most of the data from other sources plot reasonably close to this trend, especially for the other Hong Kong soils. With the exception of Viana da Fonseca et al. (2006), the data that present some scatter are mainly for soils where the maximum size has been curtailed significantly, notably the data of Ham et al. (2010), as this directly affects the D 50 values, and may have an effect on λ too. Zhang and Baudet (2013) observed that D max might be more significant for breakage, and, therefore, the compressibility of a mixture, than its amount of fines. With the sparsity of data at the finer sizes, the trend identified is slightly tentative, but the two parts of the trend proposed might mark a change in the compression mode, and the reduction of λ with decreasing D 50 is what is commonly seen for the binary soil mixtures typically used in research (e.g. Carrera et al. 2011). Within the limited dataset, it is not possible to see if the trend reaches a minimum and reverses direction as is observed for binary mixtures.

Fig. 5
figure 5

Trends with mean size: a NCL slope and b NCL intercept. 1Lee and Coop (1995), 2Viana da Fonseca (1998), 3Fung (2001), 4 Ng and Chiu (2003), 5Viana da Fonseca et al. (2006), 6Ham et al. (2010), 7Zhang (2011), 8Yan and Li (2012) and 9Madhusudhan and Baudet (2014)

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Given any pair of points 1 and 2 in Fig. 5a, the null hypothesis (H 0) was formulated so that D 50 and λ are not correlated, i.e. if D 50(1) > D 50(2), then λ(1) > λ(2), λ(1) = λ(2) and λ(1) < λ(2) have the same probability to be true. Then the joint probability P(A|B) = 1/3 considering A D 50(1) > D 50(2) and B λ(1) > λ(2) as independent events, i.e. no correlation between D 50 and λ. For this null hypothesis, p = 0.33, which is much larger than the significance level α = 0.05 usually set. However, carrying out a statistical analysis of the dataset assuming the alternative hypothesis (H 1) “if D 50(1) > D 50(2) then λ(1) > λ(2) or else if D 50(1) < D 50(2) then λ(1) < λ(2)”, this was true for 60 % of the sample, which is much larger than the probability of H 0. When excluding the data for those soils whose gradings were curtailed at 2 mm, the probability improved to about 66 %.

Due to the several parameters that should influence λ, it is unlikely that any simple relationship like that in Fig. 5 will completely describe the phenomenon, and the formulation of a complete model would be highly complex, perhaps including not only the location of the grading curve but details of its shape, the particle morphologies, mineralogies and strengths as well as the parent rock crystal size. Unravelling the effects of all these possible factors would require an extremely large dataset that does not currently exist, nor is likely ever to, and so it is still useful to identify the effect that simple indices such as D 50 have, even if the relationships derived are inevitably scattered. The agreement of the trends with what would be expected from the literature for other, simpler soils helps improve confidence in them. Any cause of systematic error that adds to the scatter, such as D max, is difficult to identify due to the reduced dataset.

The trend for N 100 in Fig. 5b is quite similar to that for λ, with slightly less scatter. It is possible that this is due to some extent because only oedometer tests were considered. The reducing value of intercept with decreasing D 50 is, again, typical of what is seen in the literature for binary soil mixtures (e.g. Carrera et al. 2011) but the data do not indicate whether at even finer gradings the intercepts would start to increase again as is commonly observed.

In Fig. 6, the data are presented with respect to the amount of fines, since in binary mixtures this is used as an indicative parameter to predict the type of behaviour, i.e. granular-, intermediate- or fines-dominated. Although the data for gradings curtailed at a smaller size agree better with the trend proposed than in Fig. 5, the data scatter is, overall, much greater, as shown by the 30 % value of probability, calculated similarly for D 50. The labels adjacent to the data points indicate the plasticity index, where known. A consistent trend compared to that seen in Fig. 5 can be observed, with λ reducing as fines content increases, but, again, no evidence of a minimum within the range of data could be found. Although there is only one data point for a large amounts of fines, its value is similar to the average for the points at around 30–40 % fines, which might suggest an approximately constant trend. This could be because the plasticity index has similar values for these soils, with the exception of only one data point for the Kowloon Granite, which plots well outside the trend. The variability of the λ values in the granular matrix domain, i.e. values below 10 % of fines, is, then, strikingly more than that observed in the fines matrix domain, where the clay mineralogy might be more important. This is probably because the dataset chosen was carefully selected to include only granitic saprolites, which are, then, more likely to result in similar mineralogical compositions with weathering. The conclusions drawn by Rocchi et al. (2015), i.e. that grading and not mineralogy dominates the compressibility, seems, therefore, to be confirmed based on the dataset analysed here. Similar to the considerations made for D 50, N 100 is expected to reduce with increasing % of fines, which is observed in Fig. 6b.

Fig. 6
figure 6

Trends with % fines: a NCL slope and b NCL intercept. 1Lee and Coop (1995), 2Viana da Fonseca (1998), 3Fung (2001), 4Ng and Chiu (2003), 5Viana da Fonseca et al. (2006), 6Ham et al. (2010), 7Zhang (2011), 8Yan and Li (2012) and 9Madhusudhan and Baudet (2014)

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In Fig. 7, the results are analysed with respect to c u. In a granular soil, it is expected that soils with uniform gradings would compress more because of fewer points of contact among the particles (lower coordination numbers) resulting in higher forces acting across the contacts, a trend which can possibly be seen in Fig. 7. However, an approximately linear trend is observed for both λ and N 100, with no break or change visible within the scatter that might indicate the two different domains. In one case, c u was defined as D 70/D 20 due to difficulty in establishing D 10 from the grading curve. However, this does make this value of c u less reliable and it is identified with asterisk on the figure. Although the scatter of data seems to be noticeably worse on this plot than those either for D 50 or fines content, the hypothesis that the higher the c u value, the larger λ gave a probability of 72 %. The soils having a curtailed D max have been included and agree with the trend; when these are excluded, the trend is actually worse and p = 0.35. This could be because c u describes the shape of the grading curve and not its position and so it is not so badly affected by a change to D max. Once again, the trend for N 100 is less scattered than for λ, possibly because only oedometer tests have been included.

Fig. 7
figure 7

Trend of compressibility with the coefficient of uniformity: a NCL slope and b NCL intercept. 1Lee and Coop (1995), 2Viana da Fonseca (1998), 3Fung (2001), 4Ng and Chiu (2003), 5Viana da Fonseca et al. (2006), 6Ham et al. (2010), 7Zhang (2011), 8Yan and Li (2012) and 9Madhusudhan and Baudet (2014)

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Breakage

To shed light on the mechanisms of compression, the particle breakage was analysed in detail. The breakage was studied quantitatively in terms of relative breakage (B r), as defined by Hardin (1985), and in terms of changes of shape using a Qicpic laser scanner (Sympatec 2008). The parameters used for describing the shape of the particles were the aspect ratio (AR) and the convexity (C), which Zhang and Baudet (2013) suggested to be the most appropriate shape descriptors to indicate catastrophic particle breakage as opposed to chipping of the asperities. The aspect ratio is defined as the ratio of the minimum Feret diameter to the maximum one, where the Feret diameter is the distance between any pair of parallel lines that touch two points on the particle perimeter without cutting through the particle silhouette (i.e. between apexes on the perimeter). The convexity is the ratio between the area of the particle silhouette and its convex hull, which is defined as that area which would be enclosed by an elastic rubber band if it were to be stretched around the particle silhouette (i.e. an area that includes all re-entrant parts of the silhouette).

Hardin (1985) defined B r as the ratio of total breakage, B t, which is the area between the grading curves before and after testing, considering only that part above 74 μm, and the breakage potential, B p, which is the area between the initial grading curve and a cut-off at 74 μm. Coop and Lee (1993) showed that the sand particles begin to undergo significant breakage when reaching the NCL and thereafter a logarithmic trend between B r and the mean effective stress could be observed. Even if many of the tests reached the same maximum stress, a similar trend can still be observed in Fig. 8. However, Altuhafi and Coop (2011) showed that the amount of breakage measured not only depends on the stress reached, but also on the initial specific volume. Particles in a loose state have fewer points of contact between each other and, therefore, experience larger stresses. For this reason, only tests having a value of specific volume between 1.9 and 2.1 are presented at the highest stress level to limit the data scatter. For the other tests, the v 0 is indicated in the label. The dp and sh ewCDG seem to plot slightly lower than the evwCDG and possibly the HDG, therefore suggesting that the breakage is less for the more weathered soils. This result might seem counterintuitive, but it arises from the better graded nature of the more weathered soils. Although it might seem that the breakage changes for different weathering degrees, when taking only the tests at the highest stress level, which represent the majority, and comparing them with their initial specific volumes, no real difference between the different degrees of weathering can be observed (Fig. 9).

Fig. 8
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Particle breakage for the soils studied in this research. Trend with vertical stress

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Fig. 9
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Particle breakage for the soils studied in this research. Trend with specific volume

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In Fig. 9, it is evident that despite the different particle size distributions of each soil, the breakage undergone is very similar, and the trends only differ at high values of the initial specific volume, where some scatter can be observed in the data, but without any clear effect of degree of weathering. This contrasts with Ham et al. (2010) who emphasised the effect of weathering degree on the strength of grains of granitic saprolites. However, their conclusions were mainly based on single particle crushing tests, while they did not calculate a global breakage for the different weathering degrees. As already mentioned, Zhang and Baudet (2013) observed that D max seems to dominate breakage rather than the amount of fines in a mixture, which might explain the similarity of the data, since D max changes little with weathering (Fig. 2). Although it might be regarded as just another gradings descriptor like c u or D 50, Hardin intended that the value of B p should represent the propensity of a soil to undergo particle breakage. When comparing the λ values with the corresponding B p values (Fig. 10), there is, indeed, a clear trend for the soils tested in this work (solid symbols), even if the B r values were actually similar. This trend is not as evident for the soils from the literature, but B r values were not available for many of them to examine how much breakage they underwent.

Fig. 10
figure 10

Trend of compressibility with breakage potential. 1Lee and Coop (1995), 2Viana da Fonseca (1998), 3Fung (2001), 4Ng and Chiu (2003), 5Viana da Fonseca et al. (2006), 6Ham et al. (2010), 7Zhang (2011), 8Yan and Li (2012) and 9Madhusudhan and Baudet (2014)

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In Fig. 11, the breakage is analysed for each grading component in a differential way. For this purpose, the difference in the cumulative mass before and after the test, defined as Δ in the inset of Fig. 11a, was calculated for the different grain sizes. For the stress level reaching 7 MPa, there is a net gain in mass for each size component except for the maximum. This, of course, does not mean that there is no breakage for components of the grading curve where there is a net gain, as can be seen if the difference in passing mass is calculated (δ in Fig. 11b). When comparing the cumulative curves, Δ is greatest at a 2-mm size, where a peak is visible for all soils except the sh ewCDG. This peak corresponds to the change between negative and positive values in δ in Fig. 11b. It is possible that the particles larger than 2 mm experience the largest change simply because they represent the majority of the retained soil in the grading curves for these soils. In Fig. 11b, however, it can be seen that the highest net gain is for the grain size 0.3–0.6 mm. Nakata et al. (1999) showed that catastrophic splitting is essentially of two types, according to the strength of the mineral. Strong minerals have a single and well-defined peak strength, and particle breakage typically results in two large pieces being left after breakage, while weaker minerals like feldspars suffer progressive breakage of the particle asperities resulting in numerous grain pieces and multiple peaks in its strength. Although in this research the particles of the soils tested consisted of aggregates of different minerals, it would appear that the main mechanism of breakage is progressive failure of the particles as the greatest loss is at the 2–5-mm size, while the maximum net gain is at 0.3–0.6 mm.

Fig. 11
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Change in the grading components as a result of breakage: a cumulative curves and b histograms

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In Fig. 12, the shape descriptors described above were analysed for the particles retained in the sieves immediately below and above 2 mm, before and after testing. The comparison could also be carried out using all the particles that are below or above 2 mm. However, the maximum size that can be analysed by the Qicpic apparatus is 4 mm and the resolution of the descriptors depends on the ratio between particle and pixel size, i.e. the greater, the better. In both Fig. 12a, b, it can be observed that the change of shape is significantly larger for particles >2 mm. These changes of shape reduce progressively to zero with reducing particle size, as shown in the insert in Fig. 12a. It would, therefore, appear that particles larger than 2 mm experience catastrophic splitting, while the remainder of the grading is less affected by breakage and probably changes morphology more as a consequence of particle chipping and abrasion.

Fig. 12
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Change in the particle morphology as a result of breakage: a aspect ratio and b convexity

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The sh ewCDG presents a different mode of breakage in Fig. 11, as there is no clear peak at 2 mm or any other grain size. The values of Δ and δ describe a flatter curve which has lower values than the others. Figure 13 shows the aspect ratio values below and above 1 mm, where a slight change in slope can be observed in Fig. 11. A significant change in the shape distribution before and after testing is seen in both cases. This might indicate that breakage is experienced similarly across the whole particle size distribution. However, further research is needed to investigate how breakage evolves for soils having greater amounts of fines and to explain how different breakage modes can result in similar overall values of B r.

Fig. 13
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Change in the particle morphology as a result of breakage for the sh ewCDG

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Conclusions

The compression of reconstituted samples of weathered granitic saprolites were studied based on a number of tests carried out on a range of weathering degrees and an analysis of the existing literature. A trend of reducing compressibility with reducing D 50 was found, as might be expected either from considerations of grading change or particle breakage. It appeared that while there was a clear reduction of compressibility in the granular matrix domain identified by Baynes and Dearman (1978), there was no clear change in the fines matrix domain. In contrast, a monotonic linear trend was found with increasing c u, although more scatter was observed in this case, perhaps indicating the inability of c u to distinguish the domains. The maximum size appears to be also an important factor when analysing the behaviour with respect to the grain size.

When analysing the breakage in an attempt to illustrate the mechanisms of compression, it was found that the relative breakage undergone by the soils tested was rather similar, despite the differences in their grading curves and degrees of weathering. When studying breakage in more detail, it was observed that the larger particle sizes, which also represented the majority of the soil by mass before testing, experienced the most breakage. In addition, comparing the particle morphology of the different grain sizes before and after testing, it was observed that these particles experienced catastrophic breakage, while the smaller grains probably changed as a result of smaller scale particle damage such as chipping.