Shear Modulus and Damping Ratio of Organic Soils

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Shear Modulus and Damping Ratio of Organic Soils Article in Geotechnical and Geological Engineering · April 2008 DOI: 10.1007/s10706-008-9224-1

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Geotech Geol Eng DOI 10.1007/s10706-008-9224-1

ORIGINAL PAPER

Shear Modulus and Damping Ratio of Organic Soils P. Kallioglou Æ Th. Tika Æ G. Koninis Æ St. Papadopoulos Æ K. Pitilakis

Received: 18 May 2007 / Accepted: 11 May 2008 Ó Springer Science+Business Media B.V. 2008

Abstract The paper presents results from a laboratory investigation into the dynamic properties of natural intact and model organic soils by means of resonant-column tests. The natural intact organic soils were sands, cohesive soils and peats with varying content of calcium carbonate. The model organic soils were formed in laboratory by mixing kaolinite and paper pulp. The influence of various soil parameters, such as strain level, confining stress, void ratio, plasticity index, organic content and secondary consolidation time on shear modulus, G, and damping ratio, DT, is presented and discussed. The test results on natural organic soils show that only high organic contents (OC C 25%) have significant influence on G and DT at both small and high shear strains. For the model organic soils, however, a significant influence of even lower values of organic content (5% B OC B 20%) on G at small strains and DT at both small and high strains is observed. Keywords Shear modulus Damping ratio Dynamic properties Resonant-column Organic soils Peat

P. Kallioglou (&) Th. Tika G. Koninis St. Papadopoulos K. Pitilakis Department of Civil Engineering, Laboratory of Soil Mechanics, Foundations’ & Geotechnical Earthquake Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece e-mail: [email protected]

1 Introduction It is well known in Geotechnical Engineering that among the key parameters controlling the response of soil to dynamic loading is shear modulus and damping ratio. It is also widely accepted that the response of soil to both static and dynamic loading depends mainly on the level of strain induced to it. Soil behaviour ranges from linear elastic to inelastic, depending on the level of strain, and may be divided in three zones (Dobry 1991; Jardine 1992; Hight and Higgins 1994). At small shear strains, c, the stress– strain relation is linear elastic, soil shear stiffness has its maximum value, G = Gmax, and damping ratio its minimum value, DT = DTmin. The upper strain limit of this range is called linear elastic threshold shear strain, cet , and depends on soil type. When the strain exceeds the linear elastic threshold shear strain, but remains below another upper strain limit, the stress– strain relation becomes non-linear elastic, and is accompanied by stiffness degradation and damping increase. The latter upper strain limit is called volumetric threshold shear strain, cvt , and depends also on soil type and stress state. When the strain exceeds the volumetric threshold shear strain, cvt , the stress–strain behaviour becomes inelastic with significant stiffness degradation, damping increase and plastic strains development. Consequently, passage from elastic to inelastic behaviour corresponds to cvt , defined as the strain at which excess pore water pressures or plastic strains start to build up.

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Organic soils, which according to their definition contain a varying proportion of organic matter, include peat (remains of dead vegetation in various stages of decomposition), gyttja (plant and animal remains deposited in lakes) and organic clays, silts and sands. Table 1 presents a classification system of soils according to the content of the organic matter, proposed by Karlsson and Hansbo (1981). Organic soils have long been recognized as problematic materials, because of their low shear strength, high compressibility and permeability and considerable secondary consolidation deformations. They are characterized by an inhomogeneous and anisotropic structure and differ greatly from inorganic soils with respect to their engineering properties. There are, however limited experimental data, regarding the dynamic properties of such soils. Most of the previous investigations were concerned with the dynamic properties of soils with very high organic contents, such as peats (Shannon and Wilson 1967; Kramer 1993, 1996, 2000; Stokoe et al. 1996; Boulanger et al. 1998; Wehling et al. 2003).

2 Objectives and Scope With expanding urban development, there is an increasing demand of building large infrastructure constructions at sites with even problematic soils. For example, organic soils and peats are often encountered within the foundation soil of large embankments and Table 1 Classification of soils according to the organic content (Karlsson and Hansbo 1981) Soil group

Organic content Examples of in weight % of designations dry material (\2 mm)

Low-organic soils

2–6

Gyttja-bearing clay Dy-bearing silt Humus-bearing sand

Medium-organic soils 6–20

Clayey gyttja Silty dy Humus-rich sand

High-organic soils

[20

Gyttja Dy Peat Humus-rich topsoil

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bridges. The design of these constructions requires the knowledge of the engineering behaviour of such soils and more particular, the seismic design requires the knowledge of their shear modulus and damping ratio. This paper presents the results of a laboratory study on the dynamic properties of natural and model organic soils by means of resonant-column (RC) tests. The tests were carried out in the context of site seismic response studies in Greece and Cyprus and also an investigation into the dynamic problems of seismically problematic non liquefiable soils, considered in the Greek Seismic Code (GSC 2000).

3 Testing Procedure The tests have been performed in the RC apparatus, designed by Drnevich at University of Michigan (Drnevich 1967). The apparatus is of fixed-free type and allows both the longitudinal and torsional vibration of a solid cylindrical specimen (diameter 35.7/ 71.1 mm and height/diameter ratio 2:1). The specimen is placed in a triaxial cell, installed on a concrete base, which is fixed to the ground (passive end). It is surrounded by fluid (water) and subjected to an isotropic confining stress, ro, (up to 700 kPa) and back pressure, ub. The dynamic excitation (force or moment) is subjected to the specimen by means of a system of magnets and coils, connected to the top base plate attached to the specimen (active end). The simple harmonic longitudinal or torsional vibration applied to the active end, produces longitudinal or shear waves respectively, which propagate down to the specimen base (passive end), where they reflect. The excitation frequency is changed until resonance in the first mode of vibration is achieved, and this occurs at a phase of 180o between excitation and velocity of active end. The resonance frequency, amplitude of vibration and acceleration are measured at the active end of the specimen. These values with the characteristics of the specimen (geometry and mass) and the apparatus (mass and stiffness of active end) together are used for the estimation of propagating longitudinal and shear wave velocity, Vp and Vs, Young’s and shear modulus, E and G, longitudinal and shear damping ratio, DL and DT, and axial and shear strain, e and c, respectively. In this paper results for the torsional vibration are only presented. Calculations were made according to ASTM D4015-92.

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Each specimen, after it had been trimmed to its nominal dimensions, was installed in the triaxial cell base and then enclosed by a membrane. The apparatus was assembled and saturation of the specimen followed by increasing both the back and cell pressure, but keeping a constant effective stress (r0 o & 30 kPa). Saturation degree was evaluated by estimating Skempton’s parameter B. After the completion of saturation procedure, the specimen was consolidated at various levels of r0 o. Length and volume changes of the specimen were continuously measured. Two types of dynamic excitation were imposed: small-strain loading and a sequence of loadings with increasing strains. The former was applied sometimes during consolidation stage and always after the completion of primary consolidation, whereas the latter was applied always after the completion of primary consolidation. As the test is considered to be non-destructive, r0 o was usually increased to the next level, in order to assess the dependence of dynamic properties on r0 o.

4 Tested Soils The tested soils were intact natural organic soils, retrieved from various sites in Greece and Cyprus, using either rotary core or thin wall tube sampling (shelby plastic or metal), as well as model organic soils. The latter soils were formed in laboratory in order to study the effect of the organic matter on the dynamic properties, as in natural organic soils there is always the combined effect of natural sedimentation process, stress history, soil composition and structure. The organic content, OC, of the soils was measured by ignition in a muffle furnace at 440 or 750°C, (ASTM D2974-00). The natural organic/peaty soils are classified according to their organic content, Table 1, and their plasticity into the following groups: (i)

Calcareous organic sands. Table 2 and Fig. 1 present the physical properties and the grading curves of the sands respectively. These belong to the recent holocene–pleistocene marine and fluvial deposits, encountered near the coastal zones of Aegion (S1), Larnaca (S2s, S3s, S5s) and Limassol (S4), as well as at Nissi peatland deposits (Cristanis 1994), the latter being deposited in the intramontane basin of Edessa (S6).

The sands were normally consolidated, apart from sand S1 (OCR = 4), and non-plastic (NP). The organic matter of the samples, apart from S6, consisted of semidecomposed roots and seaweeds, which although they were very of light weight, as compared to the mineral mass, they covered a significant part of the sample volume (up to 1/3 of the specimen volume for soil S5s). All sands were also characterized by the presence of high calcium carbonate content, CC, ranging between 22% and 55%. This was determined using either HCl method or radiographic method (RD) as a percentage of the dry mass of the soil. (ii) Organic cohesive soils. Table 3 and Fig. 1 present the physical properties and the grading curves of the soils respectively. These belong either to the recent holocene–pleistocene marine and fluvial deposits, encountered near the coastal zones of Aegion (C1, C2 & C3), Volos (C4), Argostoli (C6) and Larnaka (C8s and C9s), or at the lake deposits of Volvi (C5) and Drama (C7s) basins. The soils were normally consolidated to slightly overconsolidated (OCR = 1–1.5). The organic matter of the samples either had an amorphous structure within the mineral matrix, or consisted of semidecomposed roots and seaweeds (C8s and C9s). In the latter case, although the mass of the organic matter was small, as compared to the mineral mass, it covered up to 1/3 of the sample volume. Some soils (C1, C2, C3, C8s and C9s) were also characterized by the presence of high calcium carbonate content, ranging between 21% and 36%. (iii) Peats. Two natural peats, P1 and P2s were tested. Table 4 presents the physical properties of the soils. Peat P1 had an amorphous structure and was retrieved from Philippi peatland, located in the intramontane basin of Drama in northern Greece (Cristanis 1987). Peat P2s had a highly fibrous structure and was retrieved from the lignite deposit basin of Ptolemaida-Kozani in northwestern Greece. Both peats are considered to be non-plastic (NP), since it was not possible to perform Atterberg limits tests due to their nature. They were also normally consolidated. Although their ash content was between 38% and 52%

123

123

4.0–4.5

S2sc

2.673 0.065

–

16

17

19

20

18

19

co (kN/m3)

59

52

29

26

40

27

Sr FCe (%) (\75 lm) (%)

1.680

1.448

0.852

0.699

94 53

98 45

94 32

98 18

1.018 100 26

0.704 100 23

wo eo (%)

25

25

8

13

13

12

OCf (%)

42

30

26

46

55

22

CCg (%)

SM

SC-SM

SM

SC-SM

SC-SM

SM

USCS

Black, silty sand with fibrous structure (High organic)

Dark-grey silty-clayey sand with pockets of seaweeds and 7% shells (diameter [2 mm) (High organic)

Dark-grey silty sand with roots and seaweeds (Medium organic)

Dark-grey silty-clayey sand with seaweeds and 4% shells with diameter [2 mm (layer of seaweeds at the base) (Medium organic)

Dark-grey silty-clayey sand with seaweeds (Medium organic)

Dark-grey to black silty sand with seaweeds (Medium organic)

Soil description

Specimens had nominal dimensions: Do = 7.1 cm, Ho = 14.2 cm, apart from those indicated with index s, which had nominal dimensions: Do = 3.6 cm, Ho = 7.1 cm

PL

–

D60 D10

g

f

e

d

c

Calcium carbonate content

Organic matter content

FC: Fines content. Grading tests were conducted without soil pre-treatment for organic and calcium carbonate content

M: Shelby metal tube, PL: Shelby plastic tube

Soils S2s and S3s were retrieved from the same borehole and depth

Estimated in-situ vertical effective stress. Where data were not available, the unit weights, c, above and below ground water table assumed equal to 18 and 20 kN/m3, respectively

b

a

107

2.736 0.095

9.0–9.6

M

S6

87

9.5–10.2

S5s

PL

2.752 0.091 21.0

81

6.7–7.5

6.3

6.7

5.7

S4

2.585 0.170

2.669 0.120

Cu = D50 (mm)

2.685 0.180

M

PL

Gs

S3sc

57

14.0–14.6 134

Sampling r 0 mb (kPa) methodd

S1

Testa Depth (m)

Table 2 Physical properties of natural calcareous organic sands (NP)

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Geotech Geol Eng Fig. 1 Grading curves of natural organic sands and cohesive soils

(ASTM D4427-92) and they may be alternatively described as high-organic soils (ash content greater than 25%), they are referred to as peats in this paper, because of their characteristic structure, odor, colour and high organic content (ASTM D2487-00, Karlsson and Hasnbo 1981). The model organic soils were formed in laboratory by mixing kaolinite (K) and pure paper pulp (P) at contents of 5, 10 and 20% of total dry mass. The paper pulp was initially shredded into very small fibrous pieces and mixed with distilled water by means of a blender. The mixtures were prepared in a slurry condition at an initial water content ranging from 1.25 and 1.75 times the liquid limit of the soils. This condition may be considered as replicating the depositional conditions of young deposits under overburden pressure. To avoid segregation and achieve uniformity, the mixtures were constantly mixed, matured for several days and then were placed in three split moulds (inside diameter: 71.1 mm, height: 270–400 mm), where they were consolidated under one-dimensional conditions to a vertical stress of 50 or 100 kPa. In order to study the effect of the presence of salts in pore water, as it is the case for organic soils near coastal areas, a mixture of kaolinite and 10% paper pulp with distilled water containing NaCl (0.18 N solution) was also prepared. To avoid osmotic effects during the test on this mixture, water with the same salt concentration was used inside the pore water and volume change

measuring system as well as in the cell. Table 5 presents the physical properties of the model organic cohesive soils, as well as kaolinite. As shown in the above table and also exhibited in Fig. 2, the increase of organic content results in an increase of liquid limit, LL, plasticity index, PI, void ratio, e, and soil compressibility, Cc, as in natural organic soils. It may thus be inferred that the behaviour of the model organic soils used in this study resembles that of natural organic soils.

5 Test Results and Discussion It is well known that natural soils are structured materials. As stated by Mitchel (1976), the term ‘‘structure’’ means the combination of ‘‘fabric’’ (particle arrangement) and interparticle ‘‘bonding’’. For the intact organic soils in this work, the presence of organics indicates the existence of an inhomogeneous and inherently anisotropic fabric, while the presence of calcium carbonate, which may act as cementing agent at particle contents, indicates possibly the existence of a bonded structure and thus an extra component of strength and stiffness. The resonant–column test results of each soil group are presented in the following paragraphs. For each group the results for the shear modulus first and for damping ratio then at small and high strains are described and discussed.

123

123

34.2–34.8 334

49.8–50.0 519

20.0–20.6 254

4.5–5.5

56.0–57.0 475

C3

C4

C5

C6

C7s

PL

L

42

54

52

51

29

23

25

26

25

wo (%)

17

17

16

17

18

20

19

19

19

co (kN/m3)

37e

71

103

59

40

39

31

29

27

LL (%)

8e

40

40

30

19

19

12

10

10

PI (%)

21

47

51

26

24

8

23

22

22

CFf (\2 lm) (%) eo

99

94

98

91

Sr (%)

2.547 1.085 100

2.771 1.498 100

2.280 1.059 100

2.650 1.342 100

2.714 0.793 100

2.791 0.644

2.729 0.714

2.683 0.707

2.726 0.734

Gs

25

25

33

6

8

6

13

15

13

OCg (%)

31

36

–

–

–

2

21

23

22

CCh (%)

CH

CH

MH

CH

CL

CL

CL

CL

CL

C9s was similar to C8s, but it had a thick layer of sand at the base (High organic)

Grey clay with abundant seaweeds, shells and thin horizontal layers of sand (High organic)

Black clay (High organic)

Dark grey clay with sand and shells (Medium organic)

Grey clay with sand (Medium organic)

Brown-red clay (Medium organic)

Dark-grey clay (Medium organic)

Dark-grey clay (Medium organic)

Dark-grey to black clay with sand (Medium organic)

USCS Soil description

Specimens had nominal dimensions: Do = 7.1 cm, Ho = 14.2 cm, apart from those indicated with index s, which had nominal dimensions: Do = 3.6 cm, Ho = 7.1 cm

99

PL

PL

R

PL

PL

PL

Sampling methodd

h

g

f

e

d

c



CF: Clay Fraction. Grading tests were conducted without soil pre-treatment for organic and calcium carbonate content

Determined using the whole specimen mass

M: Shelby metal tube, PL: Shelby plastic tube, R: Rotary core

Soils C8s and C9s were retrieved from the same borehole and depth

Estimated in-situ vertical effective stress. Where data were not available, the unit weights, c, above and below ground water table assumed equal to 18 and 20kN/m3, respectively

b

a

C9sc

C8sc 11.0–11.5

47.0–47.6 461

C2

100

13.6–14.2 130

r 0 mb (kPa)

C1

Testa Depth (m)

Table 3 Physical properties of natural organic cohesive soils

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Geotech Geol Eng Table 4 Physical properties of natural peats (NP) Testa Depth (m)

r0 mb Sampling (kPa) methodc

Gs

wo eo (%)

co (kN/m3)

Sr OCd (%) (%)

CCe (%) HCl/ RD

USCS Soil description

P1

85.8–86.0 682

PL

2.137 101 2.297 13

96

48

–

Pt

Black, clayey peat with amorphous structure

P2s

35.4–35.9 548

R

2.441

86

62

–

Pt

Brown-black, peat with shells and intense fibrous structure (fibers with horizontal orientation)

58 1.953 14

a

Specimens had nominal dimensions: Do = 7.1 cm, Ho = 14.2 cm, apart from that indicated with index s, which had nominal dimensions: Do = 3.6 cm, Ho = 7.1 cm

b

Estimated in-situ vertical effective stress. Where data were not available, the unit weights, c, above and below ground water table assumed equal to 18 and 20 kN/m3, respectively

c

PL: Shelby plastic tube, R: Rotary core

d


e


Table 5 Physical properties of model organic cohesive soils and kaolinite Mixture

Testa

wob (%)

cob (kN/m3)

Kaolin

K

49

Kaolin + 5% paper pulp

P–5

56

Kaolin + 10% paper pulp

P-10-A

Kaolin + 10% paper pulp + NaCl Kaolin + 20% paper pulp

Srob (%)

OCc (%)

1.331

99

0

1.512

98

5

OH

2.580

1.818

98

10

OH

–

2.580

1.520

100

10

OH

–

2.369

2.177

94

20

OH

CF (%) (\2 lm)

Gs

eob

28

49

2.692

44

–

2.616

90

58

–

16

112

71

14

210

122

LL (%)

PI (%)

17

54

16

70

69

15

P-10-Bd

59

P-20

86

a

Specimens had nominal dimensions: Do = 7.1 cm, Ho = 14.2 cm

b

Initial parameters at resonant–column tests

c


d

Mixture prepared with solution of distilled water and NaCl (0.18 N)

5.1 Calcareous Organic Sands Figure 3a presents the variation of small-strain shear modulus, Gmax, with isotropic effective stress, r0 o, at 24 h confinement time for the tested calcareous organic sands. It should be noted that c values for small size (index s) specimens (c = 26 9 10-6 72 9 10-6) are one order higher than the corresponding values for large size specimens (c = 0.9 9 10-6 – 15 9 10-6). The insitu mean effective stress, r0 oinsitu, also indicated in the above figure was determined using the value of the coefficient of earth pressure at rest, ko, estimated either from ko triaxial tests or using Jaky’s (1944) equation for normally consolidated soils (1 – sin u0 ). It is

USCS

CH

shown that Gmax increases linearly with increasing r0 o in a log–log plot. Lower values of Gmax are indicated for the high-organic sands S5s and S6. Moreover, the Gmax values for the medium-organic sands S2s and S3s (small specimens) measured at higher strains, are either comparable (S2s), or even higher (S3s) than the corresponding values of the other medium-organic sands (S1 & S4). This may be attributed to the higher content of calcium carbonate of sands S2s and S3s, indicating a larger component of stiffness due to the interparticle bonding. Considering the test results at effective confining stresses equal to and above the r0 oinsitu, the shear modulus of the sands can be expressed as a function of effective confining stress, shear strain, void ratio,

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Fig. 2 Variation of (a) organic content, OC, with liquid limit, LL, and (b) compression index, Cc, with void ratio, eo, for model organic soils

organic content and calcareous content by the following expression: G ¼ AðcÞ f r0o gðeÞ hðOC Þ kðCC Þ ð1Þ where: A(c), f(r0 o), g(e), h(OC) and k(CC) are functions of c, r0 o, e, OC and CC respectively. The regression analyses of these data resulted in Eq. 2. G¼

830 0:045 ro0ð0:681c Þ e0:99 1 þ 17:35 c0:597 OC 0:104 CC 0:657 R2 ¼ 0:922

ð2Þ

where: c, OC and CC are expressed as percentages (%) and r0 o and G are expressed in kPa. The normalized G values predicted from the above equation are compared with the experimental data at a shear strain close to the minimum shear strain used in the tests on both large and small size specimens, c = 6.6 9 10-5, in Fig. 4.

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Fig. 3 Variation of (a) small-strain shear modulus, Gmax, and (b) small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, for natural calcareous organic sands

The normalized shear modulus, G/Gmax, is plotted versus shear strain in Fig. 5a for all sands at an effective isotropic stress approximately equal to or higher than r0 oinsitu. For sands S2s, S3s and S5s, the measured G values were normalized by the Gmax value, determined from equation (2) at c = 10-6. For medium-organic sands, the degradation G/Gmax curves agree with the range of corresponding curves presented in literature for reconstituted inorganic sands containing fines (Kallioglou 2003). Highorganic sands exhibit higher linearity in G/Gmax curves than medium-organic. The magnitude of r0 o affects the position of the G/Gmax curves both for medium-organic and high-organic sands, Fig. 6a. In

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Fig. 4 Comparison of normalized shear modulus, G/[g(e) 9 h(OC) 9 k(CC)], obtained from Eq. 2 with the corresponding results from the tests on natural calcareous organic sands

Fig. 6 Effect of effective isotropic confining stress, r0 o, on variation of (a) normalized shear modulus, G/Gmax, and (b) damping ratio, DT, with shear strain, c, for natural calcareous organic sands S4 and S6

Fig. 5 Variation of (a) normalized shear modulus, G/Gmax, and (b) damping ratio, DT, with shear strain, c, for natural calcareous organic sands at effective isotropic confining stress, r0 o, approximately equal to or higher than insitu stress, r0 oinsitu

particular, at a given shear strain level, c, an increase of r0 o results in an increasing linearity of G/Gmax curves. The influence of r0 o on G/Gmax-c curves is limited at stress levels lower than r0 oinsitu or of the order of 90 to 140 kPa and diminishes at stresses exceeding the latter range. The variation of small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, at 24 h confinement time is plotted in Fig. 3b. DTmin remains either constant, or decreases with increasing r0 o. The range of DTmin values is from 1.4% to 1.8% for the medium-organic and from 2.5% to 4.1% for the highorganic sands at c B 10-5 for the range of stresses examined (r0 o = 30–400 kPa). These ranges compare with the corresponding range of DTmin between 0.7% and 1.9% for inorganic sands containing fines

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(Tika et al. 2004). A small increase in DTmin of cemented over non-cemented sands has been reported in literature (Chiang and Chae 1972; Saxena et al. 1988). Since, however, all sands tested in this work contained calcium carbonate, the higher DTmin values observed for the high-organic sands indicate that the organic matter starts to have an influence on DTmin at an organic content exceeding 25% approximately. The variation of damping ratio versus shear strain is plotted in Fig. 5b. The DT versus c curves for the medium-organic sands are within the range of corresponding curves presented in literature for inorganic sands containing fines (Kallioglou 2003), whereas for the high-organic sands exhibit higher linearity than the medium-organic sands. The magnitude of r0 o affects the position of the DT curves both for medium-organic and the high-organic sands and at a given shear strain level, c, with an increase of r0 o resulting in a decrease of DT, Fig. 6b. 5.2 Organic Cohesive Soils 5.2.1 Natural Intact Organic Soils Figures 7a and 8a present the variation of small-strain shear modulus, Gmax, with isotropic effective stress, r0 o, at 24 h confinement time for the tested mediumorganic and high-organic cohesive soils respectively. It should be noted that the tests on the high-organic soils of this group were conducted on small size specimens and the c values (c = 53 9 10-6 – 230 9 10-6) are up to two orders higher than the corresponding values for the large size specimens of medium-organic soils (c = 1.2 9 10-6 – 10 9 10-6). The insitu mean effective stress, r0 oinsitu, also indicated in the above figures, was determined using the value of the coefficient of earth pressure at rest, ko, estimated either using Jaky’s (1944) equation for normally consolidated clays (1 – sin u0 ), or as function of PI and OCR for overconsolidated clays (Brooker & Ireland, 1965). The angle of shearing resistance, u0 , was evaluated from the empirical correlation of u0 and PI (Kenney 1959). A linear relation between Gmax and r0 o in a loglog plot is observed for each tested soil for both normal consolidation and overconsolidation states. Kallioglou et al. (2008) studied the small-strain stiffness of natural intact inorganic cohesive soils with calcium carbonate content less than 5% and expressed Gmax by the following equation:

123

Fig. 7 Variation of (a) small-strain shear modulus, Gmax, and (b) small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, for medium-organic cohesive soils

e0:63 Gmax ¼ ð6290 80 PI Þ r00:50 o

ð3Þ

where: Gmax and r0 o are expressed in kPa and PI as percentage values (%). Kallioglou et al. (2008) also confirmed that the above equation holds for the laboratory Gmax value of natural intact inorganic cohesive soils containing calcium carbonate up to a content of 25%. To account for the effect of stress history, void ratio and soil composition and plasticity on Gmax, Gmax values at r0 oinstitu for large size specimens only were normalized by the void ratio and plasticity index functions of the above equation and plotted versus r0 oinstitu at c B 10-5 in Fig. 9. As indicated in the

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above figure, at a given r0 institu , the medium-organic o soils (OC = 6–15% and CC = 0–23%) showed either comparable, or lower values of normalized Gmax than the estimated from the above equation. The results for the shear modulus at high strains are shown in Figs. 10a and 11a & b for the mediumorganic and the high-organic cohesive soils respectively at an effective isotropic stress approximately equal to or higher than r0 insitu . For the high-organic o soil C7s the measured G values were normalized by a Gmax value at c = 7 9 10-5, because of the plateau observed in G-c curve at strains c \ 2 9 10-4, Fig. 11a. In the above figures, the G/Gmax-c curves are compared with those presented in literature for

Fig. 8 Variation of (a) small-strain shear modulus, Gmax, and (b) small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, for high-organic cohesive soils

Fig. 9 Variation of normalized small-strain shear modulus, Gmax/[f(e) 9 g(PI)], with insitu mean effective stress, r0 oinsitu, for natural organic cohesive soils

Fig. 10 Variation of (a) normalized shear modulus, G/Gmax, and (b) damping ratio, DT, with shear strain, c, for mediumorganic cohesive soils at effective isotropic confining stress, r0 o, approximately equal to or higher than insitu stress, r0 oinsitu

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curves for the stress range studied (r0 o = 110– 400 kPa). The variation of small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, at 24 h confinement time is plotted in Figs. 7b and 8b for the medium-organic and the high-organic cohesive soils respectively. DTmin either remains constant or decreases with increasing r0 o. The range of DTmin values is between 1.8% and 4.2% for the mediumorganic cohesive soils at c B 10-5 and at r0 oinsitu. This range is similar with the corresponding of DTmin = 1.4–4.7% for inorganic cohesive soils (Kallioglou et al. 2008). No clear effect of the organic content on DTmin is observed possibly due to different composition of natural soils tested. The DT versus c curves for the medium-organic and high-organic cohesive soils, shown in Figs. 10b and 11c respectively, indicate that there is no clear effect of soil plasticity on them. Moreover, these curves differ significantly from the corresponding curves presented in literature for inorganic cohesive soils on the basis of soil plasticity (Vucetic and Dobry 1991). 5.2.2 Model Reconstituted Organic Soils

Fig. 11 Variation of (a) shear modulus, G, (b) normalized shear modulus, G/Gmax, and (c) damping ratio, DT, with shear strain, c, for high-organic cohesive soils at effective isotropic confining stress, r0 o, approximately equal to or higher than insitu stress, r0 oinsitu

inorganic cohesive soils (Kallioglou et al. 2008; Vucetic and Dobry, 1991; Sun et al. 1988). The degradation curves follow the trend of increasing linearity with increasing plasticity; in particular for the medium-organic soils, the G/Gmax curves either agree with, or exhibit a higher linearity than the corresponding curves, proposed in literature for soils of the same plasticity, whereas for the high-organic soils the G/Gmax curves exhibit a higher linearity for c \ 10-3. The magnitude of r0 o was observed to have a negligible effect on the position of the G/Gmax

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Figure 12a presents the variation of small-strain shear modulus, Gmax, with isotropic effective stress, r0 o, at 24 h confinement time for the tested model organic cohesive soils as well as kaolinite for comparison. A linear relation between Gmax and r0 o, in a log–log plot, is observed for each tested soil for both normal consolidation and overconsolidation states. At a given r0 o, Gmax decreases with increasing organic content above 5%. The addition of salt (NaCl) in soil P-10-B results in an increase of Gmax to values equal or above the corresponding for soil P-10-A and even kaolinite. The normalized shear modulus, G/Gmax, is plotted versus shear strain in Fig. 13a at r0 o = 90–110 kPa, apart from soil P-20 for which data at r0 o = 40 kPa only were available. The degradation curves of the model organic cohesive soils are practically coincident with that of kaolinite, irrespectively of organic content (OC = 5–20%) and stress level. This behaviour is in agreement with the results on natural medium-organic cohesive soils showing either negligible or small effect of medium organic content (OC = 6–15%) on degradation curves. It can thus be concluded that for medium-organic soils the plasticity of the mineral soil, rather than of the organic soil, controls the position and

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Fig. 13 Variation of (a) normalized shear modulus, G/Gmax, and (b) damping ratio, DT, with shear strain, c, at effective isotropic stress r0 o = 40–110 kPa for model organic cohesive soils and kaolinite Fig. 12 Variation of (a) small-strain shear modulus, Gmax, and (b) small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, for model organic cohesive soils and kaolinite

shape of G/Gmax curves. The magnitude of r0 o has either a slight (P-10-B), or a negligible effect (P-5 & P10-A) on the position of the G/Gmax curves for the stress range studied (r0 o = 90–200 kPa), Fig. 14a. The presence of salt (NaCI) in soil P-10-B results in higher degradation of G/Gmax curve. The variation of small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, at 24 h confinement time is plotted in Fig. 12b. A slight to moderate decrease of DTmin with increasing r0 o is observed. DTmin increases with increasing organic content and this may be attributed to the increasing flexibility of the soil mass due to the presence of organic fibers.

However, the addition of salt (NaCl) in soil P-10-B results in a decrease of DTmin. These observations indicate a significant effect of both the organic matter content and pore water chemistry on DTmin. The range of DTmin values at c B 10-5 is between 2.1% and 4.8% and is similar with the corresponding of natural intact organic cohesive soils tested, Fig. 7b. The variation of damping ratio versus shear strain for model organic cohesive soils is plotted in Fig. 13b. The damping ratio curves shift to higher values of DT with increasing organic content. Similarly with the natural organic cohesive soils, these curves differ from the corresponding curves, presented in literature on the basis of soil plasticity (Vucetic and Dobry 1991). The magnitude of r0 o has slight or negligible effect on the position of the DT versus c curves for the stress range studied (r0 o = 90–200 kPa), Fig. 14b.

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Fig. 14 Effect of effective isotropic confining stress, r0 o, on variation of (a) normalized shear modulus, G/Gmax, and (b) damping ratio, DT, with shear strain, c, for model organic cohesive soils

5.3 Peats Figure 15a presents the variation of small-strain shear modulus, Gmax, with isotropic effective stress, r0 o, at 24 h confinement time for the tested peats. The insitu mean effective stress, r0 oinsitu, also indicated in the above figure, was determined using the value of the coefficient of earth pressure at rest, ko, estimated using Jaky’s (1944) equation for normally consolidated soils (1 - sin u0 ). A linear relation between Gmax and r0 o, in a log–log plot, is observed for both soils. The Gmax values of the tested peats (Gmax = 15.9–27.8 MPa at r0 o = 39–374 kPa and wo = 101% for P1 and Gmax = 60.7–73.1 MPa at r0 o = 111–396 kPa and wo = 58% for P2s) are higher than the corresponding values reported in literature for peats (7–11.3 MPa for r0 o = 66–200 kPa and w = 152–240% by Boulanger et al. 1998, and 0.15–11 MPa for r0 o = 1.5–12.5 kPa

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Fig. 15 Variation of (a) small-strain shear modulus, Gmax, and (b) small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, for peats

by Kramer 1993). Obviously, the high Gmax values of peats P1 and P2s may be attributed to their lower water contents, as well as to the fact that for most of the stress range examined, apart from the highest ones, the peats were overconsolidated. The results for the shear modulus at high strains for both peats are shown in Fig. 16a & b at an effective isotropic stress approximately equal to r0 oinsitu. The measured G values were normalized by the G value at c = 2 9 10-5, Fig. 16a. Both peats exhibit strong linearity, similar to those reported for very plastic clays (PI = 200%) and other peats in literature, Fig. 16b. The effect of r0 o on the position of the G/Gmax curves was not studied due to the upper limit of confining pressure (ro \ 700 kPa) in the resonant-column apparatus.

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agree with the lower bound curve presented in literature for peats and high plastic clays with PI = 200% (Vucetic and Dobry 1991). 5.4 Effect of Secondary Consolidation Time on Shear Modulus and Damping Ratio For all the organic soils tested in this work, primary consolidation was completed within 24 h. The effect of time on Gmax and DTmin was studied by conducting tests of long duration under constant confining stress and recording the variation of Gmax and DTmin with secondary consolidation time of soils. A linear increase of Gmax with logarithm of secondary consolidation time was observed. DTmin either remained constant or decreased with logarithm of secondary consolidation time, Fig. 17. The influence of secondary consolidation time on Gmax can be expressed in terms of the following parameter NG (Marcuson and Wahls 1972): NG ¼

Gmax ðtÞ Gmax ðt ¼ 48 hÞ log 48t h Gmax ðt ¼ 48 hÞ

ð4Þ

where Gmax ðtÞ: small-strain shear modulus at a given time t; Gmax ðt ¼ 48 hÞ: small-strain shear modulus at 48 h consolidation time.

Fig. 16 Variation of (a) shear modulus, G, (b) normalized shear modulus, G/Gmax, and (c) damping ratio, DT, with shear strain, c, for peats at effective isotropic confining stress, r0 o, approximately equal to insitu stress, r0 oinsitu

The variation of small-strain damping ratio, DTmin, with isotropic effective stress, r0 o, at 24 h confinement time is plotted in Fig. 15b. As shown, DTmin decreases with increasing r0 o. The range of DTmin values is between 2.3% and 2.4% at c B 10-5 and at r0 oinsitu and agrees with the values for peats given in literature. The variation of damping ratio versus shear strain for peats is plotted in Fig. 16c. As shown, the peats exhibit high linearity in DT curves. These curves

Fig. 17 Variation of (a) small-strain shear modulus, Gmax, and (b) small-strain damping ratio, DTmin, with consolidation time at effective isotropic confining stress, r0 o, equal to and higher than insitu stress, r0 oinsitu

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Similarly, the following parameter ND can be used in order to quantify the effect of secondary consolidation time on DTmin: ND ¼

DTmin ðt ¼ 48 hÞ DTmin ðtÞ log 48t h DTmin ðt ¼ 48 hÞ

ð5Þ

The variation of parameter NG with plasticity index of both natural and model organic soils at the insitu mean effective stress, r0 oinsitu, is shown in Fig. 18. The results of medium-organic soils are within the range of inorganic clays given in literature, whereas high-organic soils exhibit higher values of NG. The effect of time on DTmin for the above soils was either negligible (ND = 0 for S1 & C3) or small (ND = 0.15 for C2 & P1, ND = 0.21–0.25 for S6, C1 & C7s) irrespectively of organic content. The variation of NG with of secondary compression index, Ca, obtained from RC tests for model and natural organic cohesive soils, as well as peats is presented in Fig. 19. An increase of NG with increasing Ca is observed. The influence of secondary consolidation time on G/Gmax-c and DT-c curves was studied for the natural high-organic cohesive soil C7s, Fig. 20. It is shown that with increasing consolidation time the G/Gmax curve moves upwards, whereas the DT curve downwards. This influence is stronger for DT curves and it diminishes for G/Gmax curves with increasing consolidation time.

Fig. 19 Variation of NG with secondary compression index, Ca, at effective isotropic confining stress, r0 o, approximately equal to or higher than insitu stress, r0 oinsitu for natural and model organic soils. The numbers in the parentheses indicate the effective stress level.

5.5 Linear Elastic and Volumetric Threshold Shear Strains The variation of linear elastic and volumetric threshold shear strains, cet and cvt , with plasticity index at effective isotropic confining stress, r0 o, approximately equal to insitu stress, r0 oinsitu, for the natural organic, as well as the model organic soils at r0 o = 40–110 kPa, is presented in Fig. 21. As shown, medium-organic soils exhibit similar linear elastic threshold shear strains values, cet, as inorganic soils. For the high-organic soils both threshold shear strains are higher than the corresponding for the mediumorganic soils. For high-organic cohesive soils of high plasticity also the linear elastic threshold shear strains approach the values observed for peats.

6 Conclusions For the tested calcareous organic sands the following conclusions can be drawn: Fig. 18 Variation of NG with plasticity index, PI, at effective isotropic confining stress, r0 o, approximately equal to insitu stress, r0 oinsitu for natural and model organic soils (open symbols indicate medium-organic and closed symbols highorganic soils)

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–

The presence of organic matter starts to have a significant influence on Gmax and DTmin of the sands at contents exceeding 25% approximately. High-organic sands (OC = 25%) exhibit lower

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–

Gmax and higher DTmin values than the mediumorganic sands (OC = 8–13%). The G/Gmax and DT versus c curves for mediumorganic sands are similar with those observed for inorganic sands containing fines, whereas highorganic sands exhibit a higher linearity in both G/ Gmax and DT curves. For both medium-organic and high-organic sands, the magnitude of r0 o affects the position of the G/Gmax and DT versus c curves.

For the tested organic cohesive soils the following conclusions can be drawn: –

Fig. 20 Effect of secondary consolidation time on variation of (a) normalized shear modulus, G/Gmax, and (b) damping ratio, DT, with shear strain, c, for natural high organic cohesive soil C7s at isotropic effective stress r0 o = 360–400 kPa

Fig. 21 Variation of linear elastic and volumetric threshold shear strains, cet and cvt , with plasticity index, PI, at effective isotropic confining stress, r0 o, approximately equal to insitu stress, r0 oinsitu

–

Medium-organic intact soils show either comparable, or lower normalized small-strain shear modulus, Gmax/[f(e) 9 g(PI)], than the corresponding for inorganic cohesive soils. Both intact natural and model reconstituted organic cohesive soils show a decrease of Gmax with increasing organic content. No clear effect of the organic content on DTmin was observed for the natural medium-organic cohesive soils, possibly due to their different composition. An increase of DTmin with increasing organic content was indicated by the model organic cohesive soils. The pore water chemistry may also affect significantly both Gmax and DTmin. Medium-organic cohesive soils (OC = 6–15%) exhibit either similar G/Gmax curves, or a more linear behaviour than the inorganic soils of the same plasticity. High-organic cohesive soils (OC = 25–33%) exhibit higher linearity than the inorganic soils of the same plasticity. For both medium-organic and high-organic cohesive soils, the magnitude of r0 o has negligible effect on the position of the G/Gmax curves. There are indications that the degradation curve may be influenced by pore water chemistry.

Both peats tested exhibit a strong linear response similar to that of very plastic clays (PI = 200%). The influence of secondary consolidation time on Gmax is quantitatively similar for the medium-organic soils to that of inorganic soils and higher for the highorganic soils, as compared with that for the inorganic soils of the same plasticity. Threshold shear strains depend on both soil plasticity and organic content. Medium-organic soils indicate linear elastic threshold shear strain values

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similar to those of inorganic soils of the same plasticity. For high-organic soils both threshold shear strains are higher than medium-organic soils of the same plasticity. As previously recognized, organic soils are inherently variable materials and the results of a laboratory investigation involving a limited number of tests and type of soils are not sufficient to define the behaviour of these complicated materials with great precision. Nevertheless, it is hoped that the findings of this work may contribute to the understanding of the dynamic properties of organic soils, and its results could be applicable to organic soils at other sites, that were formed under similar geologic and depositional conditions.

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