Geotechnical Testing Journal

Geotechnical Testing Journal H. Jebali,1 W. Frikha,1 and M. Bouassida2

DOI: 10.1520/GTJ20160067

3D Consolidation of Tunis Soft Clay Improved by Geodrains VOL. 40 NO. 3 / MAY 2017

Geotechnical Testing Journal

doi:10.1520/GTJ20160067

Vol. 40

No. 3

/

May 0000

/

available online at www.astm.org

H. Jebali,1 W. Frikha,1 and M. Bouassida2

3D Consolidation of Tunis Soft Clay Improved by Geodrains Reference Jebali, H., Frikha, W., and Bouassida, M., “3D Consolidation of Tunis Soft Clay Improved by Geodrains,” Geotechnical Testing Journal, Vol. 40, No. 3, 2017, pp. 1–10, http://dx.doi.org/10.1520/GTJ20160067. ISSN 0149-6115

ABSTRACT Manuscript received April 5, 2016; accepted for publication December 20, 2016; published online February 16, 2017. 1

Universite´ de Tunis El Manar – Ecole Nationale d’Inge ńieurs de Tunis. LR14ES03-Inge ńierie Ge ótechnique. BP 37 Le Belve ´de `re, 1002 Tunis, Tunisie

This paper presents an experimental study carried out on undisturbed cored samples of Tunis soft soil extracted at 17.25 m depth at the lagoon of Sejoumi. Three series of oedometer tests were performed: the first one was a standard test on Tunis soft soil, the second one was performed on the same soil improved by a prefabricated vertical drain Mebradrain 88 (Mb88) type during which vertical drainage was prevented. The third series comprised similar tests to those of series two, during which horizontal and vertical drainage were allowed. The assessment of Carillo’s theory was studied by quantifying the effect of

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Universite ´ de Tunis El Manar – Ecole Nationale d’Inge ńieurs de Tunis. LR14ES03-Inge ńierie Ge ótechnique. BP 37 Le Belve ´de `re, 1002 Tunis, Tunisie, (Corresponding author), e-mail: [email protected]

radial and vertical consolidation from the observed global degree of consolidation of improved Tunis soft soil specimens by geodrains. The rate in decrease of coefficients cr and kr was greater than that recorded for coefficients cv and kr, respectively. Using the Carillo’s theory, a lower degree of consolidation which starts from 10 % is obtained; however, when using simple approximate methods by considering recorded measures from series 3, higher degrees of consolidation starting from 70 % were obtained. Keywords coefficient of consolidation, hydraulic conductivity, geodrains, degree of consolidation

Nomenclature Cc ¼ compression index Cs ¼ swelling index cr ¼ radial coefficient of consolidation cv ¼ vertical coefficient of consolidation e(0) ¼ (initial) void ratio Ic ¼ consistency index

C 2017 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. Copyright V

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Ip ¼ plasticity index kr ¼ radial hydraulic conductivity kv ¼ vertical hydraulic conductivity PVD ¼ Prefabricated Vertical Drain RD ¼ radial drainage VD ¼ vertical drainage U ¼ global degree of consolidation Ur ¼ radial degree of consolidation Uv ¼ vertical degree of consolidation V & RD ¼ vertical and radial drainage Wl ¼ liquid limit Wp ¼ plastic limit r0 ¼ Vertical effective stress.

Introduction In recent years, considerable attention has been devoted worldwide to the problem of building structures on highly compressible saturated soils and to the development of soil improvement techniques for increasing bearing capacity, reducing settlements, and accelerating consolidation of soft soils. Prefabricated verticals drains (PVD) with preloading method was considered the most practiced improvement technique to accelerate the consolidation of soft soils and, hence, to increase their bearing capacity (Indraratna et al. 2009). In Tunisia, the PVD associated with preloading became of current use since the 1990s to accelerate the consolidation of Tunis soft soil for numerous infrastructure projects (Bouassida and Hazzar 2008; Kanoun and Bouassida 2008). Sridhar and Robinson (2011) proposed a method for the determination of the coefficient of radial consolidation (cr) using the “log t” method from the compression data obtained from radial drainage consolidation tests. The method is validated by comparing the experimental data with theoretical predictions. Yune and Chung (2005) developed a consolidometer for peripheral radial drainage measurement of Korea reconstituted and undisturbed clays. These authors concluded that there is no noticeable difference in compression curves recorded either from radial and vertical drainage. In the over-consolidated state, the effect of drainage direction is hardly observed; cr values for the normally consolidated state are higher than cv values. Such a result reflects that the anisotropy of permeability (i.e., higher permeability in horizontal direction) revealed noticeable in virgin compression. A higher anisotropy is also observed for undisturbed samples (cr/cv ¼ 1.7) than for reconstituted ones (cr/cv ¼ 1.3). From the tests carried out by Seah and Juirnarongrit (2003), it was concluded that the ratios of kr/kv and cr/cv increased from 1.5 to 3 with increased effective vertical stress from 20 to 500 kPa. The ratios of kr/kv and cr/cv are close to unity at in situ effective stress with an over-consolidation ratio of 2.

The obtained results from tests performed by Jia (2010) showed that the horizontal coefficient of consolidation (cr) is greater than the vertical coefficient of consolidation (cv). This result is almost due to the recorded anisotropy of hydraulic conductivity. The ratio between the horizontal and vertical hydraulic conductivities is about 1.65. Hsu and Tsai (2016) presented analytical and experimental investigations of the combined and radial consolidation drainage under linear time-dependent loading by taking account of the loading-dependent coefficients of vertical and radial consolidation using a viscoelastic approach. The results indicate that for any given effective pressure, the coefficient of radial permeability kr exhibited higher values compared with the coefficients of vertical permeability kv for the tested soils. Likewise, cr values were generally higher than cv values owing to higher values of kr. Azari et al. (2016) applied an elastic–viscoplastic model to model a soft soil improved by vertical drains and compared their simulation results with field measurements. Their results showed that the distribution of the overconsolidation ratios in the disturbed zone greatly influenced the viscoplastic strain rates, creep strain limits, and consolidation. Parsa-Pajouh et al. (2016) evaluated the efficiency of several proposed formulations for plane-strain modeling of vertical drain-assisted consolidation through an integrated numerical and experimental investigation. By comparing the predicted and measured pore pressures in well-controlled laboratory tests, the advantages and disadvantages of these formulations were discussed. The authors mentioned that the stress–strain behavior of natural soft soils is highly nonlinear and very complex owing to different fundamental features of soil, such as anisotropy and creep. Rujikiatkamjorn et al. (2016) mentioned that previous studies on different aspects of soil disturbance due to driving vertical drains are limited. An extensive soil characterization was carried out while installing drains at Ballina (Australia), to obtain more realistic smear zone. Soil disturbance was evaluated by determining the change in the coefficient of permeability, the water content, and volume compressibility away from the drain. The characteristics of the smear zone were compared to the data available from past literatures and indicated that the radius of the smear zone was about 6.3 times the equivalent mandrel radius, which was larger than that observed in the laboratory using reconstituted specimens. The objective of this paper is to measure the coefficient of consolidation and hydraulic conductivity of improved Tunis soft soil by geodrains when subjected to vertical and horizontal drainage. These measurements will serve to compare between the predictions of global degree of consolidation using the Carillo’s theory and measurements from the oedometer test performed on Tunis soft soil improved by central geodrain. Obtained results are discussed and then interpreted.

ON JEBALI ET AL. ON IMPROVEMENT OF TUNIS SOFT SOIL

Determination of Radial and Vertical Coefficients of Consolidation In the presence of PVD (Prefabricated Vertical Drain), the radial drainage mostly controls the consolidation of soft soil while the role of vertical drainage is negligible. Therefore, the commonly adopted consolidation theories for designing prefabricated vertical drains using the unit cell model were those of Barron (1948) (Kjellman, 1948a) and Hansbo (1981). Because the solutions considering both vertical and radial drainage are complicated, those most used in practice ignore the effect of vertical drainage, such as Barron’s theory (Kjellman, 1948b). Barron (1948) developed solutions for two types of boundary conditions at the surface of improved soil: (i) “free vertical strain,” resulting from a uniform distribution of vertical load, and (ii) “equal vertical strain,” which results from imposing the same vertical deformation. However, in some cases, the vertical drainage by PVD has a considerable effect on the degree of consolidation of improved soil; Terzaghi (1943) initially suggested the well-known simple method for one-dimensional (1D) vertical consolidation theory, which applies for unimproved soil. Theory which applies for unimproved soil when subjected to such load the dissipation of excess pore pressure is assumed to occur vertically. Furthermore, for most cases in practice, the soil is not homogeneous, and the deformation of PVD improved soil does not occur in 1D condition. Carillo’s theoretical solution (1942)

FIG. 1 Gradation curve of Tunis soft soil.

was suggested by combining the vertical and radial drainage effects to predict the global degree of consolidation, U as: ð1 UÞ ¼ ð1 Ur Þð1 Uv Þ

(1)

in which Ur and Uv are the radial and the vertical degree of consolidation, respectively. Theoretically speaking, Carillo’s formula given by Eq 1 is only valid for an instantaneously applied load. The consolidation of soft soil is related to the dissipation of excess pore pressure generated by the surcharge load. For radial consolidation problem with centered vertical drain in oedometer cell, the governing differential equation of excess pore pressure is written (Sridharan et al. 1996): 2 @ðDur Þ @ ðDur Þ 1 @ðDur Þ þ (2) ¼ cr @t @r 2 r @r where: cr ¼ the coefficient of radial consolidation of soft soil, and Dður Þ ¼ Du(r, t) is the excess of pore pressure at radius r from the drain axis, at time t. The solution of Eq 2 that uses the condition of equal vertical strain without smear effect is given by (Barron 1948): 8Tr Ur ¼ 1 exp (3) FðnÞ The smear zone is defined as the disturbed zone of soft soil immediately adjacent to the vertical drain. F(n) is a Barron’s function given by:

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2 @ðDuz Þ @ ðDuz Þ ¼ cv @t @z 2

TABLE 1 Atterberg limits of Tunis soft soil extracted at the lagoon of Sejoumi. WL (%) 48.5

Wp (%)

Ip (%)

Ic

28.7

19.8

0.5

FðnÞ ¼

2 n2 3n 1 lnðnÞ n2 1 4n2

(4)

where n is the drain spacing ratio given by: n¼

D dw

Tr ¼

cr t D2

(6)

where t denotes the time. For the vertical consolidation problem, the differential equation of one-dimensional consolidation for the excess pore pressure is written (Terzaghi 1943):

FIG. 2 Types of performed oedometer tests.

where: D(uz) ¼ Du(z, t) is the excess pore pressure depending on the depth z and time t, and cv ¼ the coefficient of vertical consolidation. The solution of differential Eq 7 leads to the equation of vertical degree of consolidation Uv as follows: Uv < 50 %: rffiffiffiffiffiffi 2 TV UV ¼ p

(5)

D and dw denote the equivalent diameters of unit cell and of PVD, respectively. Tr is the dimensionless time factor of radial consolidation defined by:

(7)

(8)

Uv > 50 %: UV ¼ 1

8 TV p2 exp 4 p2

(9)

Tv denotes the time factor of vertical drainage: Tv ¼

cv t H2

(10)

where H is the drainage distance that is equal half of the thickness of specimen drained at top and bottom sides.


FIG. 3 Impervious membrane covering the porous stone.

Studied Soil Tunis soft soil specimens investigated in this study were extracted from the Sejoumi’s lagoon at depth of 17.25 m. Those assumed undisturbed samples are gray colored, having a characteristic smell and containing shell debris. From the grain size analysis performed by hydrometer and sieve methods in accordance with standards NF P 94-056 (AFNOR 1995a) and NFP 94-057 (AFNOR 1995b), it was found that Tunis soft soil presents 85 % of particles with dimension less than 80 lm; it also includes non-negligible fraction of silt (Fig. 1). Atterberg limits’ tests had been performed according to the NF P 94-051(AFNOR 1995c) on extracted specimen. Obtained results in Table 1 indicate that the tested Tunis soft soil is moderately plastic and has medium consistency.

Consolidation Tests Three series of oedometer tests were carried out on the extracted Tunis soft soil specimens (Fig. 2). Those tests consisted in gradually applied increments of vertical load subjected to the specimen and measurements of the settlement versus time. For each increment load, the decrease in thickness of the sample versus time was recorded. Duration of the applied increment of load depends on the soil and its consolidation properties; it often required 24 h, which was considered a sufficient time for the primary consolidation that ends when constant settlement is observed. Accordingly, the creep settlement is not addressed in the present study, which only focused on the primary consolidation. The next increment of load was applied (roughly the double of previous load) up to the maximum load (25, 50, 100, 200 kPa). When the primary consolidation at prescribed stress level was completed (200 kPa) the sample was unloaded in one or several steps until the increment of load of 25 kPa was dismounted and the swelling of specimen can be measured.

The applied vertical load was doubled at each increment until the maximum required load is attained (50, 100, 200, 400, 800 kPa). The specimen was again unloaded. At the end of the test, the sample was carefully removed, then its thickness and water content were measured. Series 1 (VD): It included two standard oedometer tests performed according to XP P 94-90-1 (AFNOR 1997). Each test was carried out on a cylindrical sample of saturated soil with 70 mm diameter and 19 mm thickness. The soil sample was logged in a metal ring and was placed on a porous stone. The loading cap also has a porous stone, so the sample was sandwiched between two porous stones at the top and bottom of the sample to allow vertical drainage (VD) (Fig. 2a). When preparing the sample, filter papers were placed between the soil and the porous stones. The sample was then placed in the consolidation cell that was mounted a testing apparatus. Water was added into the cell around the sample, so the sample remains saturated during the test. Series 2 (RD): It included two oedometer tests performed on Tunis soft soil improved by a single geodrain (Mebradrain 88) of sizes (thickness ¼ 0.5 cm, width ¼ 1 cm, and length ¼ 19 mm). The portion of geodrain was placed before the placement of soft soil sample. Hence, the disturbance of soft soil and consequent smear zone are not taken into account in the present study. In those tests, only radial drainage (RD) was

FIG. 4 Tunis soft soil improved by geodrain.

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TABLE 2 FIG. 5 Standard oedometer test results of series 1.

Values of compression and swelling indices of Tunis soft soil.

Series of Tests

allowed; vertical drainage was prevented by means of an impervious membrane, which covered the porous stone at the top and the bottom sides of the specimen (Figs. 2b and 3). Series 3 (V&RD): It included oedometer tests performed on Tunis soft soil improved by a single geodrain (Mebradrain 88) type sized identical to that used in Series 2. In those tests, the vertical and radial drainage were both allowed (Figs. 2c and 4). Results of standard oedometer test carried out on Tunis soft soil (series 1) are displayed in Fig. 5. They show the variation of void ratio e plotted as a function of the vertical effective stress in the logarithmic scale for loading-unloading-reloading sequences.

FIG. 6 Oedometer curves obtained from three experimental series.

1: VD

2: RD

3: V&RD

Cc

0.16

0.16

0.30

Cs

0.022

0.022

0.023

From this typical oedometer curve in (e-logr0 ) plan, compression and swelling indexes and preconsolidated stress are determined. The initial void ratio e(0) is equal to 0.85 for the three series. The curves of all performed oedomter tests in the three Series (1, 2, and 3) plotted in (e-logr0 ) plan are shown in Fig. 5. Measured compression Cc and swelling Cs indices are determined from the three series of tests (VD, RD, and V&RD) and plotted in Fig. 6. Table 2 summarizes the obtained values of Cc and Cs. It has been noticed that the compression index obtained from series 3 (V&RD) is roughly the double of that recoded in series 1 (VD) and 2 (RD). This can be explained by the allowed vertical and radial drainage paths from which follows enhanced consolidation of the compressible soil. From Table 2, it is understood that the swelling is only attributed to vertical infiltration of water during unloading of samples.

Study of Three Dimensional (3D) Consolidation COEFFICIENTS OF CONSOLIDATION

The coefficient of vertical and radial consolidation cv and cr were determined from the evolution of settlement versus time


FIG. 7 Determination of cr by Casagrande’s method.

levels of load (50 to 800 kPa) plotted in Fig. 8. This result shows a decreased trend of cr and cv as the consolidation stress increases. HYDRAULIC CONDUCTIVITIES

for each increment of recorded loading (from 50 to 800 kPa). The results obtained from series 1 and 2: cv and cr were determined by the logarithmic method, which uses the plot of sample thickness of sample versus the logarithm of time: log (t) (Casagrande 1938). Hence, as shown for example in Fig. 7, one can determine t50 that is the time corresponding to 50 % of primary consolidation. Fig. 7 illustrates an example of determination of cr by the Casagrande’s (logarithmic) method for an applied load of 100 kPa. Coefficient of vertical consolidation cv has been determined from tests performed in series 1 (VD) and the coefficient of radial consolidation cr has been determined from the test performed in series 2 (RD) by the Casagrande’s method for all

FIG. 8 Coefficients of consolidation cr and cv versus consolidation stress.

Vertical and radial hydraulic conductivities (kv and kr) are determined by the variable head permeability test. In fact, oedometer apparatus (in series 1 and 2) is equipped with a conventional measuring device (tubing connected to the base of the specimen). The measurements are performed for different levels of applied load from 100 to 800 kPa (100, 200, 400, and 800 kPa). The minimum value of 100 kPa was chosen to avoid any swelling of the specimen when subjected to moderate consolidation stress. Fig. 9 shows the variations of vertical and radial hydraulic conductivities in function of applied load. It is noticed that each permeability decreases when the consolidation stress increases in similar trend as observed for the respective coefficients of consolidation. Fig. 10 shows opposite variations of the ratios cr/cv and kr/kv when the consolidation stress varies from 100 to 800 kPa. Variation of ratio cr/cv in function of the consolidation stress shows that as the applied load increases the ratio cr/cv decreases. The rate in decrease of coefficient cr is greater than that recorded for coefficient cv. In fact, the ratio cr/cv equals 36 for a consolidation stress of 100 kPa and slows down up to 12 when the consolidations stress equals 800 kPa. Fig. 10 also shows the variation of ratio kr/kv in function of the effective consolidation stress. It is noticed that this ratio is

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8


FIG. 9 Radial and vertical coefficient of permeability versus consolidation stress.

variable when the applied load increases. The rate in decrease for kv is greater than that recorded for kr. It is also remarked that the kr/kv ratio increases with the consolidation stress. Ratio kr/kv is equal to 4 for the consolidation stress of 100 kPa and tends to 12 when the consolidation stress equals 800 kPa. Obtained results show that the assumption made by many authors, e.g., cr/cv ¼ kr/kv is only valid at high levels of consolidation stress (Jia and Chai 2010).

DEGREE OF CONSOLIDATION

In this paper, the global degree of consolidation U(t) is predicted by two methods. The first one uses the measured

FIG. 10 Ratios kr/kv and cr/cv versus consolidation stress.

settlement at different levels of applied load in series 3 (case of vertical and radial drainage, V&RD): UðtÞ ¼

sðtÞ s1

(11)

where s(t) and s1 denote the settlements at given time, t, and at the end of consolidation, respectively. The second method consists in calculating U by the Carillo’s Eq 1. The radial degree of consolidation Ur is estimated from the experimental results of series 2 (case of radial consolidation RC) and Eq 3. The vertical consolidation Uv is obtained from recorded results in series 1 (case of vertical consolidation VC) by using Eqs 8 and 9.


FIG. 11 Variation of global degree of consolidation.

Figs. 11a, 11b, 11c, and 11d illustrate the variation of global degree of consolidation U in function of time for vertical consolidation stress of 100, 200, 400, and 800 kPa. For applied loads (100, 200, 400, and 800 kPa), it is noted that the degree of consolidation as predicted by the Carillo’s theory reaches 100 % at a time less than 24 h, while the global degree of consolidation U, estimated from Eq 11 by using measurements of Series 3 results, reaches 100 % in 24 h. One can also noticed that using the Carillo’s theory, a lower degree of consolidation, which starts from 10 %, is predicted; however, when using simple approximate methods by considering recorded measures from series 3, higher degrees of consolidation starting from 70 % are obtained. Comparing the recorded and predicted global degree of consolidation U, it follows that the evolution of global degree of consolidation U predicted by the Carillo’s theory is overestimated with respect to that deduced from the recorded settlement from series 3. The final global consolidation degree U is identical using the two methods.

Conclusions This paper presented an experimental study conducted on Tunis soft soil, in which three types of oedometer tests were executed: first, a standard oedometer test; second, an oedometer test on soil specimen improved by a geodrain element during which vertical drainage was prevented; and third, a

similar test to the second one where horizontal and vertical drainage were allowed. Measurements of coefficients of permeability kv and kr were determined by the variable head permeability test. In addition, coefficients of vertical and radial coefficients of consolidation cv and cr were determined from the evolution in time of settlement at different levels of consolidation stress. Comparison between the ratios kr/ kv and cr/cv demonstrated that equality between the two ratios only happens at high level of stress consolidation, contrarily to the common assumption made in previous studies. Predictions of the global degree of consolidation showed that the Carillo’s theory leads to overestimated results with respect to predictions from recorded settlements. Furthermore, the effect of vertical and radial consolidations from the observed global consolidation of improved Tunis soft soils was discussed. Subsequent researches were conducted to study the soft soil creep, such as the study carried out by Mitchell and Soga (2007), who found that different soil types exhibit viscoelastic behavior with varying amounts of timedependent deformation, as exhibited by secondary compression or creep. Moreover, they showed that more plastic clay soil results in more pronounced viscoelastic behavior. In addition, the specimens with higher plasticity indices exhibited more volumetric strain in the steady-state creep rates. Due to this, the creep behavior of Tunis soft soil should be studied in forthcoming research work.

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ACKNOWLEDGMENTS

The authors gratefully appreciate the help provided by Dr. Samia Boussetta during the experimental work carried out at the soil mechanics laboratory of the National Engineering School of Tunis.

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