Unified Compression Model for Venice Lagoon Natural Silts Giovanna Biscontin, M.ASCE1; Simonetta Cola2; Juan M. Pestana, P.E., M.ASCE3; and Paolo Simonini4 Abstract: Over the last 50 years, the city of Venice, Italy, has observed a significant increase in the frequency of flooding. Numerous engineering solutions have been proposed, including the use of movable gates located at the three lagoon inlets. A key element in the prediction of performance is the estimation of settlements of the foundation system of the gates. The soils of Venice Lagoon are characterized by very erratic depositional patterns of clayey silts, resulting in an extremely heterogeneous stratigraphy with discontinuous layering. The soils are also characterized by varying contents of coarse and fine-grained particles. In contrast, the mineralogical composition of these deposits is quite uniform, which allows us to separate the influence of mineralogy from that of grain size distribution. A comprehensive geotechnical testing program was performed to assess the one-dimensional compression of Venice soils and examine the factors affecting the response in the transition from one material type to another. The compressibility of these natural silty clayey soils can be described by a single set of constitutive laws incorporating the relative fraction of granular to cohesive material. DOI: 10.1061/共ASCE兲1090-0241共2007兲133:8共932兲 CE Database subject headings: Soil compression; Soil settlement; Soil properties; Geotechnical models; Model verification; Silts.
Introduction The historical city of Venice, Italy, is a collection of hundreds of islands in a large lagoon connected to the Adriatic Sea by three inlets 共i.e., Malamocco, Lido, and Chioggia, Fig. 1兲. Venice Lagoon is suffering a rapid deterioration, including dramatic changes in the water and sediment balance in the basin, which is severely affecting both the natural environment and human activities in the area. The problem dates back to the early 1300s when the Venetians started to divert the three major rivers flowing into the lagoon to protect against silting of the basin and therefore avoid the loss of their prosperous harbor. More recently, the development of an industrial area adjacent to the port after World War II increased the demand for fresh groundwater. Groundwater extraction resulted in an accelerated rate of land subsidence between 1945 and the late 1970s and was eventually stopped 共Butterfield et al. 2003兲. During the same period, the city of Venice observed an increase in the frequency of flooding with a record tidal level of nearly 2 m measured in November of 1966. Other factors compounding the problem include the deepening of the inlets to allow for larger ships required by the increased 1
Assistant Professor, Dept. of Civil Engineering, Texas A&M Univ., 3136 TAMU, College Station, TX 77843-3136 共corresponding author兲. E-mail:
[email protected] 2 Assistant Professor, Dept. IMAGE, Univ. of Padova, via Ognissanti, 29, 35129 Padova, Italy. E-mail:
[email protected] 3 Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, 420 Davis Hall, Berkeley CA 94720-1710. E-mail:
[email protected] 4 Professor, Dept. IMAGE, Univ. of Padova, via Ognissanti, 29, 35129 Padova, Italy. E-mail:
[email protected] Note. Discussion open until January 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on February 13, 2006; approved on September 11, 2006. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 133, No. 8, August 1, 2007. ©ASCE, ISSN 10900241/2007/8-932–942/$25.00.
port activity in Venice and sea level rise 共Harleman et al. 2000兲. Numerous engineering solutions have been proposed, including the use of tilting flap gates located at the three Lagoon inlets to prevent flooding from exceptionally high tides. To design the foundation of these movable gates, an extensive study on the characterization of foundation soils has been undertaken. Within these studies, a test site has been selected at the Malamocco Test Site 共MTS兲 which is considered representative of the whole lagoon area. Preliminary data documenting laboratory investigations and the applicability of some in situ testing methods have already been published 共e.g., Simonini and Cola 2000; Biscontin et al. 2001; Cola and Simonini 1999, 2002; Simonini 2004兲. This paper presents a new set of constitutive laws accounting for the ratio of granular to cohesive material to describe the behavior of “transitional” soils with similar mineralogy in one-dimensional compression based on the framework proposed for cohesionless soils 共Pestana and Whittle 1995; Pestana 2002兲.
Basic Properties of Venice Lagoon Soils The sediments of the Quaternary Basin comprising the whole Venetian Lagoon area, reach depths of approximately 800 m, and were deposited over the past 2 ⫻ 106 years. The subsurface soils of the Venice Lagoon down to 50– 60 m are characterized by a complex system of interbedded sands, silts, and silty clays deposited during the last glacial period of Pleistocene 共Würm兲 when the rivers transported fluvial material from the Alpine ice fields. The Holocene is only responsible for the shallowest lagoon deposits, about 5 – 15 m thick. The depositional patterns of these sediments are rather complex due to the combined effects of geological history and human action, which modified significantly the morphology of the lagoon, inlets and channels over the past several centuries. Fig. 2 summarizes gradation and index properties from all samples collected from ground level 关approximately 10.5 m below mean sea level 共MSL兲 at MTS兴 down to a depth of 56 m below MSL. For classification purposes, the soil types in the
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Fig. 1. General view of Venice Lagoon and location of the MTS 共Cola and Simonini 2002, with permission from NRC Press兲
whole lagoon area have been reduced to three main groups: medium to fine sand 共SP-SM兲, silt 共ML兲, and very silty clay 共CL兲 according to the Unified Soil Classification System, and their typical grain size distributions are reported in Fig. 3. These three classes constitute over 95% of the Venetian soils and occur approximately in proportions of 35% SM-SP, 20% ML, and 40% CL. The remaining 5% of the soils are medium plasticity clays and peats 共CH, OH, and Pt兲. Subsurface profiles are characterized by irregular alternation of the three soil types, with a few thin layers of compacted peat. Additional characteristics include: • Silty and sandy fractions have a significant presence with percentages of silt exceeding 50% in 65% of samples analyzed; • Sands are relatively uniform, but finer materials become more widely graded: the coarser the materials, the lower the coefficient of uniformity. • Atterberg limits are characterized by average values of liquid limit 共LL兲 and plasticity index, equal to 36± 9 and 14± 7%, respectively 共w0⫽natural water content兲. The cohesive soils are generally characterized by low activity: the great majority of samples fall in the range 0.25⬍ A ⬍ 0.50. • The overconsolidation ratio 共OCR兲 was estimated from the preconsolidation stress, ⬘p, from one-dimensional 共1D兲 consolidation tests carried out on CL samples. Due to the very gradual transition to the virgin compression regime, estimates of ⬘p had high uncertainty, excluding a few of more plastic
silty-clay samples with higher clay content. Additional data from the flat dilatometer 共Marchetti 1980兲, are reported in Fig. 2 to provide a reasonably continuous OCR profile. A general decrease of OCR with depth shows the deeper formations remaining only slightly overconsolidated. The higher OCR values near the ground surface correspond to the caranto layer, a highly overconsolidated oxidized silty clay dating to the last Wurmian glaciation. Except for caranto and some thin deeper layers, the cohesive soils are generally slightly overconsolidated. Despite the highly heterogeneous soil conditions, the basic material properties vary over a relatively narrow range due to the common mineralogical origin and depositional environment 共Cola and Simonini 2002兲. Typical mineralogical compositions of the soils at Malamocco are compared in Fig. 4 共Curzi 1995兲. Sand composition is mostly carbonatic and siliceous, with a predominance of calcite and dolomite crystals, especially at higher depths. When the carbonate and quart-feldspar fractions decrease the clay minerals increase, although they never exceed 30% in any sample. Silt and clay particles were generally formed by mechanical crushing in a continental environment and are aggregated in an irregular assemblage, characteristic of a predominant flocculated structure. Clay minerals are mainly composed of illite— prevalently 2M muscovite—with chlorite, kaolinite and smectite as secondary materials.
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Fig. 2. Soil profile, basic properties and stress history at the MTS 共Cola and Simonini 2002, with permission from NRC Press兲
Model Formulation Limiting Compression Curve for Two-Phase Model Pestana and Whittle 共1995兲 proposed a compression model for freshly deposited cohesionless soils able to describe the nonlinear
Fig. 3. Typical grain-size distributions of the soil groups SM-SP, ML, and CL 共Cola and Simonini 2002, with permission from NRC Press兲
compression response over a wide range of confining stresses and densities. The model assumes that soils compressed isotropically from different initial formation densities, approach a unique response at high stress levels, referred to as the limiting compression curve 共LCC兲. Similar response is predicted for 1D compression as the lateral earth pressure coefficient K0 approaches a constant value in the LCC regime 共e.g., Hendron 1963;
Fig. 4. Typical mineralogical composition of sediments 共Cola and Simonini 2002, with permission from NRC Press兲
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fc =
Vc Wc = Vc + Vg Wc + 共Gc/Gg兲Wg
共2兲
where Vw, Vc, Vg and Ww, Wc, Wg⫽volumes and weights of the water, clay, and granular components 共i.e., silt and sands兲, respectively, and Gc and Gg⫽specific gravity of the clay and sand/silt particles. For most practical purposes, Gc ⬵ Gg = Gs and the volumetric clay fraction f c can be approximated by the gravimetric clay fraction FF FF =
Wc Vc ⬵ = fc Wc + Wg Vc + Vg
共3兲
The void ratios of the clay–water and granular phases, ec and eg, respectively, can be determined from the overall void ratio, e, and the volumetric clay fraction according to the following relationships:
eg = Coop and Lee 1993兲. More recently, the model was revised to include a better description of the elastic stiffness and the transitional regime 共Pestana 2002兲 and has been used to model the shear stiffness of granular materials for dynamic analyses 共Pestana and Salvati 2006兲. For 1D compression, the behavior is linear in a double logarithmic void ratio–effective stress space 共cf., Fig. 5兲. The K0–LCC is completely described by the slope, c, and the location given by the reference vertical stress at a void ratio of one, v⬘r, or the reference void ratio at a stress of 1 atm, e1v, given by e=
冉 冊 ⬘v
v⬘r
−c
= e 1v
冉 冊 ⬘v pat
−c
G sw Vw e e = = ⬇ Vc f c FF FF
共4a兲
Vw + Vc e + f c e + FF Gsw + FF = ⬇ = Vg 1 − f c 1 − FFc 1 − FFc
共4b兲
ec =
Fig. 5. Idealized 1D compression response of soils with different initial density
where w⫽water content of the fully saturated soil. According to Eq. 共4b兲, the value of eg is a function of water content and clay fraction FF. If one of these variables is high, eg may be greater than the maximum void ratio, eg,max, of the granular phase alone. In these conditions 共eg Ⰷ eg,max兲, the grains behave as “rigid inclusions” in the clay–water phase and provide insignificant contribution to the overall compressibility, the latter being controlled only by the clay matrix, and the location of the K0–LCC becomes a function of the clay fraction e1v = ec1vFF
共1兲
where e⫽current void ratio; ⬘v⫽vertical effective stress; and pat⫽atmospheric pressure. Pestana 共1994兲 suggested that the same model could be used to describe the 1D compression response of saturated soils containing a mix of cohesive and granular soils. Following a two-phase model proposed by Mitchell 共1976兲 and sketched in Fig. 6, these soils can be idealized as a combination of two phases: 共1兲 the clay–water phase, also referred as the clay matrix and 共2兲 the granular phase 共i.e., silt+ sand fraction兲. The volumetric clay fraction f c共0 ⱕ f c ⱕ 1兲 is given by
where ec1v⫽reference void ratio for the K0–LCC of the clay– water phase only. The reference void ratio ec1v for the clay–water phase and the slope, c, of the K0–LCC line are uniquely dependent on the specific mineralogy of the clay phase. For soil specimens having different clay contents but same clay mineralogy, the location of the K0–LCC lines changes according to Eq. 共5兲, but the slope, c, remains unaffected. When these compression curves are normalized by their respective e1v they converge to the same normalized K0–LCC, independently of the clay fraction. On the other hand, if the saturated clay fraction is small, the grains of the granular fraction are in mutual contact, and the clay matrix is interlocked in the voids of the granular skeleton. In this case, the overall compressibility is controlled by the granular phase alone. The overall void ratio is therefore related to FF and eg by Eq. 共4b兲 and the 1D compression curve becomes a straight line, characterized by the slope c of the granular fraction. The K0–LCC line position changes according to e1v = eg1v共1 − FF兲 − FF
Fig. 6. Biphase conceptual model
共5兲
共6兲
where eg1v⫽reference void ratio for the K0–LCC of the granular phase only. Normalizing each compression curve by its reference void ratio e1v results, again, in convergence to the normalized K0–LCC, independently of clay fraction. It is to be expected that the transition from a mechanical behavior controlled by the coarse fraction towards one totally governed by the fine fraction does not occur at the FF threshold value predicted by the intersection of Eqs. 共5兲 and 共6兲 but gradually, in a relatively large FF range.
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One-Dimensional Compression Response During the 1D compression process, the change of the volumetric strain d p can be decomposed into the elastic dep and plastic d pp components. The elastic component dep may be determined from dep =
冉
冊
dp⬘ 3共1 − 2兲 1 1 + 2K0 = d⬘v 3 Ke 共1 + 兲 Ge
共7兲
where p⬘ and ⬘v⫽mean and vertical effective stresses; K0⫽coefficient of lateral earth pressure at rest; Ke and Ge⫽elastic bulk and shear modulus; and ⫽elastic Poisson’s ratio. The elastic shear stiffness, also referred to as Gmax, can be described by the following relationship 共Jamiolkowski et al. 1994兲:
冉 冊
Gmax Gb p⬘ = 1.1 pat e pat
n
共8兲
where Gb⫽material constant, and the exponent n may vary between 0.4 and 0.8. Plastic deformation is controlled by the proximity of the current stress ⬘v to the corresponding vertical stress ⬘vb on the K0–LCC at the same void ratio: d pp =
d⬘ e c共1 − ␦b 兲 v 1+e ⬘v
␦b = 1 − ⬘v/⬘vb,
0 ⱕ ␦b ⱕ 1
冉 冊
⬘vb e 1v = pat e
共9a兲 共9b兲
1/c
共9c兲
where ⫽model parameter controlling the curvature of the compression curve. If we ignore, momentarily, the elastic contribution during the compression loading and substituting Eq. 共9c兲 into Eqs. 共9b兲 and 共9a兲, we obtain d p = −
再 冋 冉 冊 册冎
⬘ e e de ⬵ c 1 − 1 − v 1+e 1+e pat e1v
1/c
d⬘v ⬘v 共10a兲
This equation can be rearranged to read
再 冋 冉 冊冉 冊 册 冎
⬘v de de/e1v = ⬵ − c 1 − 1 − e e/e1v pat
e e 1v
1/c
d⬘v ⬘v 共10b兲
Eq. 共10b兲 implies that normalized curves will converge to the same K0–LCC 共for the same c兲, and that the transitional regime can be approximately described with a unique parameter for values of vertical effective stress above the initial vertical effective stress 共i.e., the equation assumes that the soils are freshly deposited兲. On the basis of the previous equations the model is completely defined by six independent parameters, namely three parameters for the elastic strain component, Gb, n, , and three for the plastic one, e1v, c, . However, for a group of samples sharing the same mineralogy, and consequently the same c, the values of e1v can also be related to the position of the K0–LCC for the pure clay 共ec1v兲 and/or the pure granular soil 共eg1v兲 depending on FF. For example, using the assumption of rigid granular inclusions 共i.e., large eg and large FF兲 and Eqs. 共4a兲 and 共5兲, we obtain that
Fig. 7. Maximum shear stiffness Gmax from laboratory tests as a function of mean effective stress p⬘
the change in normalized void ratio 共de / e兲 is only a function of the clay water phase. Hence, still ignoring the elastic component, we have
再 冋 冉 冊 册冎
⬘ de dec e = ⬵ − c 1 − 1 − v e ec pat FFec1v
1/c
d⬘v ⬘v
共11兲
Therefore, to describe a whole class of soils with the same mineralogy, but different grain size distribution, parameter e1v may be estimated from the clay fraction FF. The proposed formulation assumes that the Venetian soils exhibiting very low OCRs can be described by the formulation for freshly deposited soils above the value of the current effective stress. Similarly to sands, for these silty-clayey soils the compression in the transitional regime 共i.e., before the LCC兲 is relatively insensitive to the elastic response and it is difficult to assess the value of the preconsolidation pressure by visual inspection of the void ratio vs. vertical effective stress curve. As a result, the compression curve can be described with reasonable accuracy by assuming “freshly deposited” material response above the current vertical stress up to the LCC. The transition to the LCC is not necessarily related to the preconsolidation pressure as it is the case for high clay content materials. Although further research is required to fully ascertain this fact, preliminary results indicate that for clay contents larger than 25–30% the “break” in the compression curve represents the preconsolidation pressure, but this may be a function of clay mineralogy 共i.e., activity兲.
Calibration and Validation of the Model In order to evaluate the proposed model ability to capture the one-dimensional compression of Venetian soils, experimental results from an existing database and from a new laboratory investigation have been considered. Parameter Calibration Cola et al. 共1998兲 and Cola and Simonini 共2002兲 published experimental values of Gmax for specimens from the MTS obtained with a bender element system in a triaxial cell or in the resonant column apparatus. In Fig. 7 the experimental values of Gmax / p⬘at are normalized by 1 / e1.1, and related to the normalized mean
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Table 1. Properties of Undisturbed Specimens Type of soil
Sample
Deptha 共m兲
CF 共%兲
LL 共%兲
W0 共%兲
e0
MSM10-3 CL 13.37 48 0.622 21 MSM10-6 CL 17.09 40 0.903 30 MSM10-7 CL 15.28 29 0.634 22 MSM10-14 CL 27.56 50 1.091 40 MSM10-19 CL 33.48 22 1.098 38 MSM10-28 CL 39.53 25 0.667 24 MSM10-43 CL 51.94 40 0.675 24 MSM10-48 CL 81.15 30 0.899 32 MSM10-52 CL 94.07 32 0.670 24 MSgM1-2 CL 13.65 44 0.643 23 MSgM1-3 CL 15.79 35 0.641 23 MSgM1-10 CL 27.5 41 1.161 46 MSgM1-18 CL 39.8 31 0.725 24 MSgM1-22 CL 49.22 30 1.214 43 MSgM1-22B CL 49.22 30 1.224 43 MSgM1-24 CL 52.25 42 0.696 24 MSgM2-11mb CL 26.72 41 0.984 41 MSgM2-6 ML 18.15 1 0.852 31 MSgM2-9b ML 24.00 0.4 0.816 32 MSgM2-13b ML 30.70 2.5 0.745 27 MSgM2-16b ML 35.60 7 0.645 20 MSgM2-12b ML 28.60 2.7 0.965 30 MSgM2-25b ML 54.60 8 0.756 25 MSgM2-23m ML 50.20 11.4 0.93 35 MSgM2-9a SP-SM 23.70 3 0.721 26 MSgM2-18a SP-SM 37.70 0 0.907 29 MSgM2-19 SP-SM 40.80 0 0.801 30 MSgM2-21 SP-SM 46.50 0 0.775 30 MSgM2 23a SP-SM 50.00 0 0.84 27 a Depth from mean sea level 共sea bottom at 10.13 m for MSM10/MSgM1 and at
effective stress p⬘ / pat. The data, grouped by class of material and test type, show a relatively large scatter. However, a constant Gb = 538 with an exponent n = 0.66 can be reasonably assumed as representative of the trend for all data. Given the difficulty in obtaining experimental measures of Poisson’s ratio, a unique value = 0.15 was assumed for all the Venetian materials. Variations in Poisson ratio have a minor effect on the predicted response. Three series of 1D compression tests were considered in this study: 1. Tests on undisturbed natural samples, belonging to the three soil classes SM-SP, ML and CL, whose results have been
Table 2. Characteristics of 1D High Stress Compression Tests on Reconstituted Samples Sample MSgM2 MSgM2 MSgM2 MSgM2 MSgM2 MSgM2 MSgM2
9b 13b 25b 18a 19 21b 23a
Soil type
CF 共%兲
e0
FF
ML ML ML SP-SM SP-SM SP-SM SP-SM
0.4 2.5 8 0 0 0 0
0.780–1.270 0.570–0.915 0.635–0.897 0.686–0.980 0.725–0.981 0.645–0.889 0.731–1.022
0.04 0.11 0.10 0.01 0.01 0.01 0.01
PL 共%兲
D50 共mm兲
35 20 0.0021 38 19 0.0031 29 19 0.0070 49 29 0.0020 30 25 0.0065 30 20 0.0071 42 20 0.0030 36 23 0.0058 38 19 0.0083 34 20 0.0023 32 19 0.0042 56 32 0.0026 31 20 0.0048 62 34 0.0049 62 34 0.0049 41 22 0.0030 46 31 0.0042 ND ND 0.048 ND ND 0.045 ND ND 0.035 ND ND 0.045 ND ND 0.060 ND ND 0.047 ND ND 0.031 ND ND 0.088 ND ND 0.112 ND ND 0.141 ND ND 0.116 ND ND 0.200 2.05 m for MSgM2兲.
U
A
e 1v
FF
8.0 16.6 20.4 7.8 11.4 28.3 14.7 22.2 64.1 7.6 21.3 7.2 15.1 9.9 10.2 15.0 10.9 4.8 3.6 9.6 16.4 2.5 13.8 32.1 4.3 2.6 1.8 1.8 2.1
0.31 0.48 0.34 0.4 0.23 0.4 0.55 0.43 0.59 0.32 0.37 0.59 0.35 0.93 0.93 0.45 0.37 ND ND ND ND ND ND ND ND ND ND ND ND
1.28 1.24 1.08 1.73 1.69 1.17 1.20 1.38 1.83 1.23 1.12 1.68 2.46 2.88 3.00 1.17 1.68 1.53 1.76 1.53 1.32 1.95 1.56 1.43 1.65 1.83 1.77 1.78 1.48
0.78 0.60 0.44 0.78 0.74 0.41 0.60 0.58 0.41 0.70 0.55 0.70 0.53 0.65 0.65 0.63 0.67 0.05 0.04 0.11 0.13 0.05 0.10 0.20 0.04 0.01 0.01 0.01 0.10
partially examined and discussed 共Biscontin et al. 2001; Cola and Simonini 2002兲; 2. Tests on reconstituted samples obtained using SP-SM and ML soils from the first series, loaded up to high stresses, to better evaluate the slope c in the K0–LCC regime; and 3. Tests on reconstructed mixtures of sand and clay prepared at different sand versus clay ratios, also loaded to high stresses, to evaluate the influence of FF on c and e1. All the samples were collected from three boreholes located close together at the center of the MTS, at depths between 13 and 94 m below MSL. Tables 1–3 list the relevant information for all the three series of tests.
Table 3. Characteristics of 1D High Stress Compression Tests on Artificially Reconstructed Mixtures Sample
C11 共%兲
C19 共%兲
e0
FF
M1 M2 M3 M4 M5 M6
0 30 40 50 75 100
100 70 60 50 25 0
0.816 0.680 0.851 0.843 1.022 1.230
0.01 0.21 0.27 0.34 0.50 0.67
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Fig. 8. 共a兲 1D response at high stress; 共b兲 normalized curves of natural SM-SP and ML samples
The first series of tests was carried out using the incremental loading procedure on 70 mm diameter and 20 mm height undisturbed natural specimens from the three soil groups: 18 tests on CL, 7 on ML, and 5 on SP-SM. Sandy specimens were prepared by using a freezing technique, necessary to preserve the initial density conditions. The maximum vertical stress applied to the specimens was approximately 6 MPa, with a few loaded up to 12 MPa. The measured compression curves are shown in the log ⬘v – log e plane in Figs. 8共a兲 and 9共a兲, grouped according to the specimens classification, SP-SM/ML and CL. Even though a first estimate of the slope in the K0–LCC regime, c, had been attempted 共Biscontin et al. 2001兲, the stress level was not sufficiently high to induce a well-defined LCC
regime, with the exception of four plastic specimens 共i.e., MSM10-52, MSgM1-18/22/22b兲. For this reason, the experimental database on natural samples was integrated with the second series of 1D tests 共Vello 2000兲, performed in a very stiff piston-oedometer where the reconstituted SP-SM and ML specimens were loaded up to stress levels of 34 MPa, reaching the crushing regime. Dry specimens were prepared by pluvial deposition directly into the oedometer cell. Crushing of soil particles was confirmed by the changes in grain size distribution measured after each test. Moreover, to evaluate the effectiveness of the testing procedure in reaching the LCC regime, two different initial densities 共loose and dense兲 were tested for each material sample.
Fig. 9. 共a兲 1D response at high stress; 共b兲 normalized curves of natural CL samples 938 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / AUGUST 2007
Fig. 10. 共a兲 1D response at high stress; 共b兲 normalized curves of reconstructed SM-SP and ML samples
On the basis on compression curves in Fig. 10共a兲, a K0–LCC average slope equal to 0.24 was estimated for all the SP-SM and ML soils 共referred to as Group 1兲; the slope c = 0.24 also fitted the majority of the curves for the CL samples, excluding the four above-mentioned specimens, which provided an average value c = 0.40 共Group 2兲. This is a particularly interesting outcome of this investigation, confirming the basic idea that the Venetian sediments, characterized by the same mineralogical composition, should have the same c. Each curve was then normalized by its reference void ratio e1v. The normalized compression curves are depicted in Figs. 8共b兲 and 9共b兲 for all natural samples and in Fig. 10共b兲 for the reconstituted ones, showing the two typical slopes in the LCC regime. Fig. 11 shows the variation of the reference void ratio e1v with FF, defined here as the percent by weight smaller than 5 m.
Fig. 11. Reference void ratio e1v versus fine fraction FF
For the silty clays of Malamocco, the value of 5 m appears, in fact, to better take into account the separation between fine and coarse grained materials than the classical value of 2 m, which usually defines the clay fraction. Experimental data at high FF support the hypothesis of Eq. 共5兲 that the reference void ratio e1v is uniquely dependent on FF and the reference void ratio of the clay phase ec1v. The regression on the data is extremely good for Group 2 specimens, while the scatter is larger for Group 1. This is likely due to the heterogeneous nature of Venetian soils, which causes gradation to vary significantly even at the centimeter scale, as shown by Cola and Simonini 共1999兲. The results at high FF also support the existence of two different mineralogical compositions for the samples, since the data align on two different lines, corresponding to different values of ec1v. Eq. 共6兲 is also plotted in Fig. 11 with eg1v = 1.94 for the coarse grained fraction. It fits well the data for sandy and silty specimens at FF less than 0.2. In order to properly evaluate the transition between granular and fine matrix response, the experimental investigation was integrated with the third series of 1D tests 共Table 3兲. The artificial specimens were prepared by mixing different amounts of sand from sample MSgM2-19 and silty clay from sample MSgM2-11b. The clay was homogenized to slurry at a water content equal to 1.5 LL; then the sand was added in percentages equal to 25, 50, 60, and 70% by weight. The mixtures were loaded up to 34 MPa in the stiff-piston oedometer 共Alessi 2001兲. Tests on pure sand and pure clay were also performed. The results of these tests are reported in Figs. 12共a and b兲. All the normalized curves, independently of grain size composition, approach the K0–LCC line characterized by c = 0.24, due to the fact that both MSgM2-19 and MSgM2-11b soils belong to the Group 1. The reference void ratios for the third series of tests are also included in Fig. 11. The data align along a continuous trend in the range 0.20⬍ FF⬍ 0.7, confirming the transition from a response controlled by the granular fraction to one governed by
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Fig. 12. 共a兲 1D response at high stress; 共b兲 normalized curves of reconstructed mixtures of pure sand and clay
the clay matrix occurs gradually. Within this range e1v is affected by both eg1v and ec1v, as the coarse particles are neither in full mutual contact nor floating in the clay matrix. For materials belonging to Group 1 the transition can be described by the following relationship: e1v = eg1v exp共0.25 − 4.76FF兲 + 共ec1v − 0.12兲FF
共12兲
No experimental data are available to estimate the transition for Group 2 materials. In sands, parameter is affected by grain-size distribution and the shape of grains. Experimental values of for Venice soils were determined from a best fit of 1D compression curves of undisturbed specimens and plotted in Fig. 13 as a function of the uniformity coefficient, U. In Fig. 13, data from sands and sandy silts reported by Pestana 共1994兲 are also drawn for comparison. For the poorly graded Venice sands, parameter lies at the upper bound of the existing data, as expected because of their subangular and angular shapes. Moving toward well-graded finer sediments, characterized by higher U, shows a slight increase, described by the following equation:
= 0.486 . U0.137
共r2 = 0.68兲
共13兲
U has a small influence of on the curvature parameter for these soils, suggesting that an average value of = 0.65 could be used for most practical applications. Simulation of 1D Compression of Venice Lagoon Soils In order to evaluate the reliability of the proposed model to reproduce the experimental data, the complete compression curves of typical specimens from the three classes SM-SP, ML, and CL, 共the latter belonging to both the Groups 1 and 2兲, were estimated and plotted in Figs. 14共a–c兲. Model parameters were selected according to the calibration procedure described in the previous section. A good agreement between measured and predicted compression behavior can be obtained, showing the nonlinear compression curves in the transition regime approaching the linear relationship in the log e – log ⬘v plane at large stresses, i.e., the K0–LCC.
Final Remarks
Fig. 13. Relationship between uniformity coefficient U and parameter
The 1D elastoplastic compression model for cohesionless soils proposed by Pestana and Whittle 共1995兲 and modified by Pestana 共2002兲 has been combined here with a two-phase granular inclusions/clay matrix conceptual approach, in order to describe the 1D compression behavior of a wide range of soils through a single framework. The effectiveness of the proposed model was verified on the Venice Lagoon soils, which are formed by a chaotic interbedding of different clayey/sandy silt sediments, characterized by a common geological origin and narrowly varying mineralogical composition. Comparison between measured and predicted response confirmed the model ability to capture the basic features of the 1D response of such highly heterogeneous soils with a unique approach. The following observations emerge from the investigation on the 1D stress–strain response of soils and the influence of grain size composition on their behavior:
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Fig. 14. Experimental curves versus model predictions for 共a兲 SP; 共b兲 ML; and 共c兲 CL materials
1.
2.
3.
4.
A unique value of c well describes the 1D compression of typical Venetian soils at high pressure, confirming that c is mainly influenced by mineralogy; The assumption of coarse grained particles acting as rigid inclusions in an otherwise clay–water matrix is a good approximation for large fine fractions, FF⬎ 0.7. For very small fine fractions, FF⬍ 0.2, the trend of e1v is affected only by the granular phase. In the range 0.2⬍ FF⬍ 0.7, e1v is affected by both eg1v and ec1v, as the coarse particles are neither in full mutual contact nor floating in the clay matrix. In this case, a new equation has been introduced to predict the reference void ratio as a function of FF, also accounting for the interaction between granular and clay–water phase; In 1D compression the Venetian soils show a gradual transition from the elastic to the plastic range without a “distinct” change of response before the K0–LCC regime; the parameter controlling this transition appears to be slightly influenced by gradation but it can be assumed constant with little loss of accuracy; and For these silty clayey materials, the vertical stress at which the transition takes place is affected by the clay fraction and in situ density. Therefore the break in the compression curve cannot, in general, be directly associated with the preconsolidation pressure as it is the case for high clay content material. Although further research is required to fully ascertain this fact, preliminary results indicate that for clay contents larger than 25–30% the break in the compression curve represents the preconsolidation pressure, but this may be a function of clay mineralogy 共i.e., activity兲.
Notation The following symbols are used in this paper: d p ⫽ volumetric strain; dep, d pp ⫽ elastic and plastic components of the volumetric strain; e ⫽ void ratio; ec, eg ⫽ void ratio of clay-water and granular phases; ec1v, eg1v ⫽ reference void ratio at pat = 1 atm for the K0–LCC in the case of zero sand phase or zero clay-water phase;
eg,max ⫽ maximum void ratio of the granular phase; e1v ⫽ reference void ratio for the K0–LCC at pat = 1 atm; FF ⫽ gravimetric clay fraction; f c ⫽ volumetric clay fraction; Gb ⫽ material constant for estimates of Gmax; Ge ⫽ elastic shear modulus; Gc, Gg, Gs ⫽ specific gravity of clay particles, sand/silt particles, and the soil; Gmax ⫽ maximum shear stiffness; Ke ⫽ elastic bulk modulus; K0 ⫽ coefficient of earth pressure at rest; n ⫽ material constant for estimates of Gmax; p⬘ ⫽ mean effective stress; U ⫽ uniformity coefficient⫽D10 / D60; Vw, Vc, Vg ⫽ volumes of water, clay, and granular components, respectively; Ww, Wc, Wg ⫽ weights of water, clay, and granular components, respectively; w ⫽ water content of the saturated soil; ␦b = 1 − ⬘v / ⬘vb ⫽ relative distance of current stress state from the K0–LCC ⫽ model parameter controlling the curvature of the compression curve; ⫽ elastic Poisson’s ratio; c ⫽ slope of K0–LCC in the log e – log共⬘v / v⬘r兲 space; ⬘p ⫽ preconsolidation pressure; ⬘v ⫽ vertical effective stress; ⬘vb ⫽ vertical stress on the K0–LCC corresponding at the current void ratio; and v⬘r ⫽ reference vertical stress for the K0–LCC at e = 1.
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