The relationship between sea-level change, soil formation and stress history of a very soft clay deposit

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Introduction
The sea-level change in the Southern Hemisphere along the Brazilian coast in the Quaternary has been studied by numerous authors from different sources (e.g., [1][2][3][4][5][6][7]).Considerable discussion ensued regarding the existence of secondary oscillations and the date of sea-level highstand.
A comprehensive geological-geotechnical characterisation of a very soft clay deposit in the surroundings of Rio de Janeiro city has been conducted in recent years.The data have provided evidence supporting one of those hypotheses, as shown below.
The soil formation and cause of the overconsolidation of the deposit have also been discussed over the years.The available data have been examined and a clear explanation resulted from the analysis, as shown below.

Sea-level change, the hypotheses for the Brazilian coast
Flemming et al. [8] and Locat et al. [9] presented the eustatic sea-level that has varied over the last 25,000 years (Figure 1a, a magnification of the last 10,000 years in Figure 1b).These authors noted that the minimum sea-level may be about 120 m (last glacial maximum) below present sea-level, which corresponds to the maximum Wisconsinian glaciation.Also, most of the rise in eustatic sea-level due to ice melting during the Holocene was reached about 7000 years ago, and since then the sea-level has only risen approximately four metres.The insert in Figure 1a shows the variation of eustatic sea-levels during the last 500,000 yr, where a number of minimum sea-levels (corresponding to their maximum glacial periods) can be observed.
If the average trends of sea-level change are estimated from the figure, the values obtained are 11 mm/yr for the period 16,000-7000 yr BP (before present) and 0.4 mm/yr since 7000 yr BP.Masson-Delmotte et al. [10] reported average rates of global mean sea-level change of 10 to 15 mm/yr in the period 22,000-7000 yr BP.Reference must also be made to Lambeck et al. [11], Masson-Delmotte et al. [10] and Church et al. [12] for comprehensive studies on this matter, including rates in very recent years.
However, a steady rise might not have occurred in some places.In fact, a maximum (highstand) was reached, followed by a smooth decline in the Southern Hemisphere (e.g., [5]).According to Angulo et al. [7], Delibrias and Laborel [13] were the first to anticipate regional differences in sea-level history, indicating a highstand of at least one metre higher than at present in Brazil, unlike the Northern Hemisphere.
It is worth mentioning that at least one reference indicates a similar qualitative behaviour of a drop in sea-level after a highstand (around 6000 yr BP) in the Northern Hemisphere, which occurred in the Shanghai region (Ye et al. [14], quoting Wang and Wang [15]).
Concerning the Brazilian coast, the trend suggested by Suguio et al. [2] is that in around 6800 yr BP the present sea-level would have been reached, then rose to a maximum sea-level around 5100 yr BP.The continuous drop in sea-level to the present would have been interrupted twice, approximately 3900 yr BP and 2800 yr BP, when transgressions (or high-frequency sea-level oscillations) would have occurred.Angulo and Lessa [5] claimed that the trend suggested by them (illustrated in Figure 2) is more similar to the trends detected in other coastal regions of the Southern Hemisphere, where there has been a steady drop in sea-level.
Later, Angulo et al. [7] provided more arguments regarding the reliability of the indicators that they used, and after analysing a large number of vermetid (small to medium-sized sea snails, marine gastropod molluscs) samples, suggested the trend illustrated in Figure 3.These authors also compared the trend in Figure 3 with the predictions obtained from a geophysical model employed by Milne et al. [6], and found a difference in relation to the highstand date.Since the trend in Figure 3 was due to only one sample older than 6000 cal.yr BP (indicated in the figure), Angulo et al. [7] argued that if it was removed, the prediction by Milne et al. [6] for paleo-sea-levels older than 5800 cal.yr BP would represent an extension of the observed trend (Figure 4).There is, however, a difference between the predicted paleo-sea-level and the obtained trend, which seems to show a very gentle decline over time from 4000 to 2000 cal.yr BP (Figure 4).Sea-level envelopes for the region between 8°S and 26°S, plotted with the paleo-sea-level behaviour predicted by Milne et al. [6], from geophysical simulations (adapted from Angulo et al. [7]).Milne et al. [6] 3. The test site

General
The Sarapuí II test site is situated on the left bank of the Sarapuí River, some 7 km from Rio de Janeiro city, with average coordinates 22°44′27″S and 43°16′49″W.The test site was established some fifteen years ago after deactivating the Sarapuí I test site (1.5 km from Sarapuí II, on the same bank), which was set up in the mid-1970s, after a significant number of studies (e.g., [16][17][18][19][20][21]).
The initial studies on the Sarapuí II test site were related to pile behaviour in soft clays [22][23][24].Joint research projects between the Brazilian national oil company's research centre (Petrobras-Cenpes) and the Alberto Luiz Coimbra Post-graduate and Engineering Research Institute of the Federal University of Rio de Janeiro (Coppe/UFRJ), have been undertaken on the test site since 2008.Those projects include the development of the torpedo-piezocone [25] and execution of load tests on model torpedo piles (e.g., [26]).Some of the geological-geotechnical characteristics of the deposit were presented elsewhere [27] and are summarised below.

Soil profile
The thickness of the very soft soil in the test site area ranges from 6.5 m to 10 m.An underlying layer of yellow clayey-silt has also been characterised.The water level varies in the range ± 0.3 m relating to ground level.The ground surface is covered by roughly 0.15 m of thick roots.The upper sample (Figure 5a) shows the top 15 cm consisting of thin roots mixed with the topsoil.Accordingly, the top of this layer, which corresponds to elevation 0.52 m, was assumed as the ground level.The transition between this layer and the underlying soil layer is reasonably well defined, as can be observed in Figure 5a.Figures 5b and 5c illustrate the presence of a significant number of wood fragments, between 1.38 m and 1.44 m in depth.Small shell fragments are present throughout the profile.However, between the depth of 1.0 m and 1.6 m and between 5.2 m and 6.0 m, a large quantity of larger fragments (in many cases closed and intact shells) is noticeable.Figures 5d to 5g illustrate an interesting feature of the profile.The top of a sample slice 12 cm in height (from 1.38 m to 1.50 m in depth) in Figure 5d shows brown-dark grey clay, with no shells.The bottom of the same slice is shown in Figure 5e where a large number of shells-some of them closed and intact-are being removed from the sampler.Figure 5f illustrates the bottom of the sampler after removing the shells, and Figure 5g shows the removed washed shells.Figure 5h depicts shells still inside a slice of the sampler (5.86-6.00m depth), and in Figure 5i the removed washed shells.To the authors´ knowledge, it is the first time a quantity of shells in a soft clay was so significant that they were detected by the profile of cone resistance (q t ) from six piezocone tests [28] in the area, as shown in Figure 5j.The layer where the roots are mixed with the topsoil also shows an increase in q t .

Geological-geotechnical data
Geological-geotechnical data are summarised in Figures 6 and 7.The soil is silty clay, with 60% clay, 35-40% silt and 0-5% sand on average.It is a high plasticity soil (plasticity index in the range 60-170%), very soft, with organic content decreasing with depth, from 12-16% to 6%.The material is slightly overconsolidated (overconsolidation ratio of 2.0) from approximately 3 m in depth (this subject is discussed further in the paper).Sensitivity from vane tests is in the range 4-8 in most of the data.It should be pointed out that the values below the depth of 8.0 m correspond to the underlying layer of yellow clayey-silt.Further details about the soil deposit can be found in Jannuzzi [29] and Jannuzzi et al. [27].

Age of deposit and rate of deposition and the relationship with change in sea-level
Almeida and Marques [21] quoted Antunes [30] to refer to the age of the Sarapuí deposit.In fact, the latter suggested that the sediments were formed in the last 6000 years.However, this suggestion was based on a literature survey-with available dating over a much broader region-and field observations, and no dating was available in the area where the Sarapuí deposit is located.
In the study reported herein, fifteen samples from radiocarbon analyses of the actual soil and the shells and wood (referred to as peat by Beta Analytic [31]) in the soil were dated by Beta Analytic [31], and a detailed picture of the age of the deposit could be obtained (Figure 8, see also Table 1).When shells or wood were present inside the sample they were dated in addition to the actual sediment.Both the conventional radiocarbon age and the calendar calibrated radiocarbon age (calibration is needed to convert radiocarbon age to calendar age) have been included in the table.The deposition rate was assessed based on the intercept of radiocarbon age in the calibration curve, also included in the table.The values obtained from the sediment and wood are found to be virtually the same for the samples at 6.10 m depth, but for the sample at 0.52 m depth the difference in values from the sediment and wood exceeded 1000 years.The difference between the values obtained from the sediment and shells was 660 years at a depth of 1.57 m and 2080 years at 4.40 m.This means that the shells came from the upper soil.Since the most reliable data are those obtained from the sediment, it can be said that the age of the deposit is in the range 12,630-2300 cal.yr BP (considering the first intercept of radiocarbon age from the calibration curve and including the very soft grey Holocene clay and the yellow Pleistocene clayey-silt, see Table 1).The general aspect of the data plotted in Figure 8 might suggest a linear variation of age versus depth, i.e. a deposition rate of 0.9 mm/yr.However, a closer look at the data in Figure 8, and especially in Table 1, shows some significant variations in the deposition rate between 6.4 mm/yr and 0.5 mm/yr.It is also noticeable that from roughly 1.5 m to 5.0 m in depth a reasonably uniform deposition rate of 0.9 mm/yr could be considered.This figure is similar to the deposition rates in shallow-water marine deposits reported by Skempton [32], as seen in Table 2, although these deposits are much thicker, and most of them have been deposited in the Pleistocene, not the Holocene, with the exception of the Oslofjord data.It is also 40-50% of the rate of estuarine deposits from the Holocene (see Table 2).The deposition rate of the depth interval 5.0-8.0 m (approximately) is very variable, 6.4, 0.6 and 6.4 mm/yr, with a general trend of higher deposition rates than the values discussed previously.The higher figure (6.4 mm/yr) is nearly three times as much as the deposition rates for the Holocene estuarine clays quoted by Skempton [32].
Locat and Lefebvre [33] also presented sedimentation rates for various deposits in different parts of the world, and found values between 25 mm/yr and 1 mm/yr, the smaller figures for more recent data, which is consistent with the data obtained herein.
Regarding Brazilian data, Bastos et al. [34], for example, obtained deposition rates between 0.4 and 0.8 mm/yr for Vitoria Bay sediments, dated between 7240 and 1010 cal.yr BP.These values are roughly 50% to 80% of the values obtained in the upper part of the Sarapuí II deposit, in the same age range.[6] and Angulo et al. [7] for Brazilian data.Figure 9 shows data from different authors: the trend suggested by Suguio et al. [2] for the city of Salvador, Bahia State (12°58′13.38″S),which has the largest set of data from those authors; the trend suggested by these authors for the town of Angra dos Reis, Rio de Janeiro State (23°00′36.18″S),which is nearer the Sarapuí II site; Angulo and Lessa's [5] suggestion for the Brazilian coast (see Figure 2); the prediction of Milne et al. [6] of paleo-sea-level for the Rio de Janeiro region (see Figure 4); Angulo et al. [7] envelopes (see Figure 4); variations in eustatic sea-levels over the last 25,000 years (modified after Flemming et al. [8], by Locat et al. [9], Figure 1); and elevations and corresponding ages of the dated samples of Sarapuí II site (from Figure 8).
It is worth noting that the reasonably uniform sedimentation rate (period 7000 cal.years BP to present) is consistent with a steady drop in the sea-level, as suggested by Angulo and Lessa [5], as well as with the geophysical model proposed by Milne et al. [6], supported by Angulo et al. [7].In other words, the hypothesis of the two periods of high-frequency sea-level oscillations, also indicated in Figure 8, is not supported by the uniform sedimentation rate.Also, the highstand occurrence (around 7000 cal.years BP) is directly related to the change in the rate of sediment deposition, i.e., supporting the Milne et al.'s [6] model.

Age of deposit and rate of deposition and the relationship to geological-geotechnical data
In the study herein, another interesting view of the previous discussion could be provided if the age versus depth of Sarapuí II clay were now to be plotted, together with cone resistance (Figures 10a,b,d).The cone resistance profile clearly indicates that, broadly considering, there are at least two layers of very soft soil (Holocene clay) in the profile, one from roughly 5.2 m to 7.5-8 m in depth, with cal.yr BP between 8590 and approximately 7200, which had probably been deposited during transgression, and the upper layer formed during regression.The top of the layer deposited during regression would be around 5.2 m in depth.If now considering the deposition rate, it is noticeable that the depth interval 4.87-5.44m had a deposition rate of 6.4 mm/yr, while all other depth intervals above had a much lower rate, from 0.6 mm to 1.0 mm/yr (except the upper), which seems to be characteristic of the deposit formation's regression phase.Moreover, the depth interval between 6.10 m and 7.19 m (corresponding to the transgression phase) presented the same deposition rate of 6.4 mm/yr.
A similar comparison can be made between the deposition rate and grain size distribution (see Figure 10c).The higher rates are found to be related to a greater sand content, especially in the case of the depth interval 4.7-5.7 m, where there was a deposition rate of 6.4 mm/yr.In other words, the soil deposited during transgression has a greater sand content in the silty clay than during regression.The closer agreement in depth between deposition rate and grain size distribution could be attributed to a longer distance between samples and the piezocone tests.In fact, the same samples were used for both dating and grain size analysis, or samples from boreholes at intervals of 4.0 m or less were taken for this purpose, whereas the average distance between samples and the piezocone tests is 15 m.Also, a closer look at the geotechnical data shows that e o and γ n values also indicate two layers of the Holocene clay.
Therefore, the analysis of both geological and geotechnical data clearly indicates that the regression started indeed around 7000 cal.yr BP, as predicted by Milne et al. [6], and supported by Angulo et al. [7].

Stress history
The proper evaluation of the stress history is a key issue in the design of embankments on soft clays.Therefore, the knowledge of the cause of overconsolidation plays a major role in the interpretation and accuracy of the measured values from in situ and laboratory testing.
Perret et al. [35] and Locat et al. [9] suggested the joint use of three parameters, OCR (overconsolidation ratio or yield stress ratio), OCD (overconsolidation difference, suggested by Olsen et al. [36], according to Perret et al. [35]) and OCG (overconsolidation gradient), in equations 1, 2 and 3, respectively, to identify the consolidation state of a soil.The idealised marine soil profiles in Figure 11 represent secondary consolidation (a) to (d), erosion (e) to (h) and cementation and thixotropy (i) to (l).The less known OCG parameter, defined as the slope of the yield stress-vertical stress relationship, is not sensitive to erosion.  Figure 12 presents those values for the Sarapuí II deposit, obtained from incremental loading (IL) 24h-consolidation tests, where the yield stress was obtained from Pacheco Silva´s [37] method, which provides similar values to Casagrande´s method, but it is easier to apply.Values of OCG were obtained considering only the very good to excellent samples (see below for sample quality), and lines were drawn for the corresponding depth intervals from where the data were taken.The dashed lines represent general trends in the figures.
The samples were obtained from 100 mm in diameter thin wall tube samplers, and the specimens trimmed following the procedures suggested by Ladd and DeGroot [38].The sample quality was assessed on the criterion of Lunne et al. [39] (see also Tanaka  Almost all cases were classified as very good to excellent and good to fair.The few exceptions, classified as poor or very poor, correspond to the cases where shells inside the specimens had to be removed and replaced by disturbed soil. The trend from around 2.5 m depth to the bottom of the very soft soil clearly indicates that secondary consolidation is the controlling process of the overconsolidation.The results obtained from the upper part of the profile seem to indicate a combination of secondary consolidation and erosion.However, there is no geological evidence for erosion, as discussed in previous sections.Also, no embankments were executed in the area where the samples were collected and piezocone tests performed.Thus, other causes may be investigated to provide a suitable explanation.The first is recent water level drawdown, or water level fluctuation during certain periods of the year, which would generate results similar to erosion.However, as aforementioned, there is no geological evidence indicating water level drawdown (or water level fluctuation) with a magnitude of more than 0.5 m, which would, therefore, be unable to generate the high OCR values obtained at a small depth (see also Parry [42,43]).Other possibilities to be investigated in the near future are desiccation/suction caused by the vegetation and bacterial action (see also Jennings [44]; Bjerrum [45]; Jamiolkowski et al. [46]; Ehlers et al. [47]).

Conclusions
The paper addresses the relationship between the sea-level change, soil formation and stress history of a very soft clay deposit near the city of Rio de Janeiro (Sarapuí II).Dating of the very soft organic clay throughout the profile provided values between 8590 and 2300 cal.yr BP.The average deposition rate is 0.9 mm/yr.The upper part of the deposit had a more uniform deposition rate (in the range 0.6-1.0mm/yr) than the highly variable lower part (approximately 5-8 m depth interval).The fairly uniform sedimentation rate (period 7000 cal.years BP to present) is consistent with a steady drop in the sea-level.The very soft organic material overlies a yellow clayey-silt soil from Pleistocene origin (12,240 cal.yr BP).The combination of geological and geotechnical data with engineering properties of the deposit indicates that the paleo-sea-level highstand in the Rio de Janeiro area (and possibly in the region between 8°S and 26°S in the Southern Hemisphere, on the Brazilian coast), an issue under discussion for many years, occurred around 7000 cal.yr BP, as predicted by a geophysical model developed by Milne et al. [6] and supported by Angulo et al. [7].Moreover, it also indicates that the lower part of the Sarapuí II deposit was formed during transgression and the upper part during regression.The overconsolidation of the soft clay deposit (excluding the top 2.5 m, which needs further investigation) could be attributed to secondary consolidation.

Figure 3 .
Figure 3. Paleo-sea-level for the Brazilian coast north of 28° (solid lines and squares) and south of 28° (dashed lines and circles), based on vermetid samples (adapted from Angulo et al. [7]).

Figure 4 .
Figure 4. Sea-level envelopes for the region between 8°S and 26°S, plotted with the paleo-sea-level behaviour predicted by Milne et al.[6], from geophysical simulations (adapted from Angulo et al.[7]).

Figure 5 .
Figure 5. (a) Sample at the top of the profile, upper 15 cm of thin roots mixed with the topsoil; (b) and (c) wood fragments found between 1.38 m and 1.44 m depth; (d) top of slice 12 cm in height (1.38-1.50m depth); (e) shells being removed; (f) bottom of slice, after removal of shells; (g) washed shells removed; (h) shells inside the sampler, sample slice 14 cm in height (5.86-6.00m depth); (i) washed shells removed; (j) cone resistance from six piezocone tests.

Figure 9 .
Figure 9. Data from Sarapuí II clay plotted together with different hypotheses for the sea-level change.Data from Sarapuí II, Milne et al. [6] and Angulo et al. [7] in cal.yr BP, the other data in yr BP.
m = σ´p = yield stress, σ´v o = in situ vertical stress.
Figure12presents those values for the Sarapuí II deposit, obtained from incremental loading (IL) 24h-consolidation tests, where the yield stress was obtained from Pacheco Silva´s[37] method, which provides similar values to Casagrande´s method, but it is easier to apply.Values of OCG were obtained considering only the very good to excellent samples (see below for sample quality), and lines were drawn for the corresponding depth intervals from where the data were taken.The dashed lines represent general trends in the figures.The samples were obtained from 100 mm in diameter thin wall tube samplers, and the specimens trimmed following the procedures suggested by Ladd and DeGroot[38].The sample quality was assessed on the criterion of Lunne et al.[39] (see alsoTanaka [40]; Lunne and Long[41]), based on the ∆e/e o ratio (also included in the figure), where, ∆e = e o − e, e o = initial void ratio, e = void ratio at the vertical effective stress in the field.

Table 1 .
Age of Sarapuí II clay.
a Yellow clayey-silt.