1 INTRODUCTION

Conventional soil mechanics theory treats soil as ei-

ther fully saturated or dry. However, a large number

of engineering problems involve the presence of un-

saturated soil zones where the voids between the soil

particles are filled with a mixture of air and water.

These zones are usually ignored in practice and the

soil is assumed to be either fully saturated or com-

pletely dry. But the test results indicated significant

differences between the mechanical behaviour of

unsaturated soils and the mechanical behaviour of

fully saturated or completely dry soils.

The critical-state concept has been well established

as a useful framework within which fully saturated

soil behaviour can be interpreted (Schofield and

Wroth, 1968). The critical-state behaviour is de-

scribed as a state of soil where its volume does not

change under large shear strains. Saturated critical

state classically can be expressed through the devia-

tor stress, q, the mean effective stress, p′, and the

specific volume, υ:

q Mp (1)

lnv p (2)

Where, M = slope of the critical-state line in (q : p′)

space, Γ = intercept at p′=1 kPa, and λ = slope of the

critical-state line in (v : lnp′) space. So far many

studies have been conducted on critical state of satu-

rated soils (Schofield and Wroth, 1968; Wood, 1991;

Maatouk et al., 1995; Newson, 1998), while the crit-

ical state behaviours of many types of soils are well

known in this state. But behaviuor of unsaturated

soils are not known completely.

It is well known and understood that the mechanical

behaviour of saturated soils can be interpreted and

explained by a single stress state variable, called the

effective stress (Terzaghi, 1936). Unsaturated soils

are characterized by the presence of air phase, water

phase and air–water interface in voids. There are dif-

ficulties in applying the same approach to unsaturat-

ed soils due to additional phase (Jennings & Bur-

land, 1962) and it is thus difficult to define

convenient stress state variables for unsaturated

soils. During the past three decades there has been

Mechanical behaviour and critical state parameters of an unsaturated dense silty sand

M. Maleki Department of Civil Engineering, Bu-Ali Sina University, Hamedan, Iran, Maleki@basu.ac.ir

M. Bayat Department of Civil Engineering, Bu-Ali Sina University, Hamedan, Iran, M.Bayat@basu.ac.ir

ABSTRACT: Unsaturated soils with pore water pressures that are negative relative to atmospheric condition

are commonly widespread around the world, especially at shallow depths from the surface. Shear strength and

critical state parameters of these soils are crucial for stability analyses of surface soils such as analyses of

slopes against slope failures and landslides. The unsaturated critical-state equations are presented in terms of

four state variables, namely, mean net stress, deviator stress, matric suction and specific volume. In this paper

a laboratory study on the influence of matrix suction on the shear strength and mechanical behaviour of a

dense silty sand is presented. For this purpose, a set of triaxial tests in saturated and unsaturated conditions

have been carried out. Axis translation technique and double-walled triaxial cell have been used to measure

the soil matric suction and variation of pore air volume respectively. The data for critical-state conditions

from these tests are presented with respect to matric suction, focusing on the critical-state parameters, which

is commonly proposed. The results indicated that the mechanical behavior of silty sand depend non-linearly

on the matric suction. On the other hand, it is necessary to present a new definition of critical state line equa-

tions in different coordinates.

KEYWORDS: shear strength; unsaturated soils; constant water content triaxial test; matric suction; volume change

an increasing use of two independent stress variables

to describe the behaviour of unsaturated soils

(Coleman, 1962; Bishop and Blight, 1963; Burland,

1965; Autchison, 1967; Matyas and Radhakrishna,

1968; Barden et al., 1969; Brackley 1971; and Fred-

lund and Morgenstern, 1977). Because unsaturated

soils have an additional phase (the air phase), and it

is therefore no longer possible to interpret their be-

haviour through effective stresses, nor to assume

that water content and volume are linked. For un-

saturated soils, the stress state can be represented by

two stress state variables, the net mean stress and the

matric suction (Fredlund and Morgenstern, 1976).

1 2 3( )3

ap u

(3)

a ws u u (4)

Where, ua = pore air pressure and uw = pore-water

pressure. These variables have been suggested as the

critical state variables for unsaturated soils by sever-

al researchers (Wheeler and Sivakumar 1995;

Maatouk et al., 1995; Rampino et al., 1998; and Ad-

ams and Wulfsohn, 1997) and one critical-state line

in q−p′ space for the unsaturated soil can be consid-

ered as follows:

0q Mp q (5)

0 lnv v p (6) Where q0 = final intercept of the CSL with the q ax-is; and v0 is the specific volume of the soil at critical state with p = 1 kPa (as a reference pressure). Experimental and theoretical difficulties delayed

considerably the development of an understanding

of the critical state behaviour of unsaturated soil. It

is only during the last few years that theoretical

frameworks and constitutive models have been pro-

posed to describe the mechanical behaviour of un-

saturated soils. However, the proposed models have

been based on limited experimental data.

This paper presents test data from triaxial tests on a

silty sand, tested under unsaturated conditions with

measurements of matric suction.

1 MATERIALS AND METHODS

1.1 Soil sample and specimen preparation

The engineering index and properties of the tested soil are presented in Table 1 and the grain size-distribution is shown in Figure 1. The soil consists of 51% sand, 20% silt and 29% clay.

Table1. Classification properties of soil

Liquid limit %

Plastic limit %

Plasticity index %

Specified gravity (Gs)

Clay percent %

Silt percent %

Soil type: (unified system)

16

-

NPI

2.67

29

20

SM

The soil is classified as SM according to the Unified Classification System. Previous investigations have indicated that sample preparation methods affect the behaviour of soils (Ladd, 1974; Mulilis et al., 1977) and thus the choice of a proper sample preparation technique is important in determining the resistance of specimen. Current field sampling techniques are not readily able to produce high-quality undisturbed granular soil specimens for laboratory testing at an affordable cost. Accordingly, numerous sample reconstitution methods have been developed for use in the labora-tory. Among these methods, wet compaction tech-nique has the advantage that it is relatively easy to control the global specimen density achieved, even for loose specimens (Frost and Park., 2003). In this work, wet compaction technique has been used for preparation of samples.

Figure 2. Typical soil water characteristic curves (SWCCs) ac-

cording to states of saturation in unsaturated soil (Kim and

Sture, 2008).

Figure 1. Grain size distribution of the soil.

There is a significant difference between the SWCCs

response for drying and wetting curves in unsaturat-

ed state (Figure 2). In other words, the initial water

content condition can influence the behaviour of un-

saturated soils (Chan and Tae 2010).

In this work, for specimens preparation, dry sand

(from Shooshab river), kaolinit and silt have been

mixed with respect to the considered different

weight ratios and the required amount of dry soil

mass and water for each layer of specimens have

been determined exactly. Triaxial soil specimens

were formed by dynamic compacting soil at a nomi-

nal water content of 7% in seven uniform layers, us-

ing a specially fabricated unit. This procedure pro-

duced uniform 38 mm diameter by 70 mm long

cylindrical specimens all having the same structure.

This length to diameter ratio of 2 selected in order to

minimize the effects due to end platens of the appa-

ratus and to reduce the likelihood of buckling during

testing. The physical properties of specimens are

given in Table 2.

Table2. Physical properties of compacted soil specimen

1.2 The triaxial apparatus

In the current study, the triaxial compression test ap-paratus developed at Bu-Ali Sina university, used to determine the critical-state parameters of unsaturated soils (Figure 3).

The matric suction is generally controlled by using the axis translation technique (Fredlund and Ra-hardjo, 1993; Alonso et al., 1990; Aversa and Nico-tera, 2002). Triaxial tests were conducted using two conventional triaxial cells made for unsaturated soil testing (Fredlund and Rahardjo, 1993). The appa-ratus has ability to control and measure the pore air and pore-water pressure in the soil specimen inde-pendently by using axis translation technique. The pore-water pressures (uw) was controlled through a saturated ceramic disks with a high air entry value. For that purpose, two ceramic disks with air entry value of 500 kPa were sealed onto the base and up-per pedestals of the triaxial cell. The constant pore air pressure was applied to the base and upper pedestals by coarse corundums that were sealed in the middle of ceramic disks (Figure 4). This two-way flows of water and air causes an ac-ceptable decrease in test time and also production of homogeneous specimen.

1.3 Testing program and procedures

The unsaturated stress–strain behaviours of soil specimens were determined by constant water con-tent triaxial test (CW). In this work, for unsaturated triaxial test, soil specimens were enclosed in two rubber membranes with two slotted aluminium

Wet unit weight (kN/m3)

Dry unit weight (kN/m3)

Initial Sr %

Moisture content %

Void ratio

Porosity

19.23

17.97

40.8

7

0.46

0.32

Figure 1. Grain size distribution of the soil.

Figure 3. Triaxial compression test equipments: (1) unsaturat-

ed control panel; (2) saturated control panel; (3) unsaturated

triaxial cell; (4) saturated triaxial cells; (5) water de-airing

tank system; (6) data logger.

Figure 4. Base plate Components of unsaturated triaxial cell.

Figure 5. Prepared soil specimen enclosed in two rubber

membranes.

sheets separated by layer silicon grease between the membranes. In this way, air which is diffused into cell water through the rubber membrane was elimi-nated (Alonso et al., 1990) (Figure 5). After placing and sealing the specimen inside the triaxial chamber, the wetting process was then started by decreasing the value of matric suction until the specimen was achieves to initial matric suction of 25, 50, 100 and 162 kPa. In this stage, water was absorbed by the soil specimen so that volume of the water in the soil specimen remained constant (i.e. after 3-5 days). The wetting curves during the equalization stage are plotted in Figure 6.

.

After the equalization stage the soil specimen is first consolidated by applying matric suction and net con-fining. During this consolidation stage, the moisture content of the specimen is reached the equilibrium state. In constant water content tests, unsaturated specimens were sheared to failure under constant gravimetric water content conditions. In these tests the pore-water valve was shut off while pore-air was allowed to drain freely from the specimen. During CW tests, matric suction will vary if significant changes in pore-water pressure occur during shearing. The saturated stress–strain behav-iours of soil specimens were determined by means of conventional triaxial compression test apparatus.

The saturated triaxial compression tests were carried out under consolidated and undrained condition. Pri-or the tests, the soil specimens were saturated until a value of pore pressure coefficient (Bw) exceeding 0.95 (ASTM D 854-02, 2002). For this purpose, af-ter taking necessary measurements, the specimens have been first subjected by CO2 at least for 3 hr and then saturated by de-aired water. Specimens have been considered to be fully saturat-ed if B is at least equal or greater than 0.95. In this study, backpressure of 300 kPa has been applied during the tests to achieving the saturation state.

Test 𝜎3 ua uw 𝜎3-ua ua-uw

CW- S 25-25 275 250 225 25 25

CW-S25-50 300 250 225 50 25

CW-S 25-100 350 250 225 100 25

CW- S 50-25 275 250 200 25 50

CW-S 50-50 300 250 200 50 50

CW-S 50-100 350 250 200 100 50

CW-S 100-25 275 250 150 25 100

CW-S 100-50 300 250 150 50 100

CW-S 100-100 350 250 150 100 100

CW- S 162-25 275 250 88 25 162

CW-S 162-50 300 250 88 50 162

CW-S 162-100 350 250 88 100 162

Table-3. Initial stress values for the constant water content tests

Figure 7. Result of undrained tests on saturated specimens: (a) stress-strain relationship; (b) pore water pressure- strain relationship

Figure 6. Wetting curves during equalization stage.

1.4 Tests results

Figures 7(a) and 7(b) show the stress-strain and pore-water volume change versus axial strain for the saturated soil specimens respectively. In most cases, the pore-water volume changes tend to stabilize close to the end of loading (i.e. 20-30% induced strain) that this condition represents a critical state of saturated specimens. The results of the CW triaxial tests carried out under constant net confining stress-es of 25, 50, 100, and 162 kPa are presented Figures 8-11. The specimens were designated using a con-vention similar to that used in the CU tests.

For example, CW-S 50-100 represents a specimen that was tested under the constant water content condition at a net confining stress of 50 kPa and an initial matric suction of 100 kPa, as shown in Table 3. Figures 8(a), 9(a), 10(a) and 11(a) are the stress–strain curves for the unsaturated specimens. It was observed that matric suction has considerable effects on stress-strain curves and for the same net confin-ing pressure, the strength of the unsaturated speci-mens is significantly greater than the strength of a saturated specimen.

Figure 8. Results of constant water test at matric suction of

25 kPa and various confining stresses, plotted against axial

strain: (a) deviator stress, q; (b) suction, s; (c) volume

change.

Figure 9. Results of constant water test at matric suction of

50 kPa and various confining stresses, plotted against axial

strain: (a) deviator stress, q; (b) suction, s; (c) volume

change.

However, the general shape of the stress-strain curves is similar to those of saturated specimens. For example, the shear strength for specimen num-ber (CW-S 100–50) is roughly twice that for speci-men number (CU-S 0–50). This shows that the ma-tric suction contributes to the shear strength of unsaturated soils. The unsaturated specimens showed different failure modes from each other in the final state of loading. Figure 12 presents the shape of the two specimens in the end of test. As shown in the Figure 12, the unsaturated specimens showed a barrel failure mode as saturated specimen

at lowest suction value (i.e. 25 kPa), while unsatu-rated specimens showed a brittle failure mode ac-companied with a shear zone at highest suction val-ue (i.e. 162 kPa).

2 CRITICAL STATE LINES

The definition of critical state used herein is related to state, in which volume, suction (or pore-water pressure) and shear strength are constant when that

Figure 10. Results of constant water test at matric suc-

tion of 100 kPa and various confining stresses, plotted

against axial strain: (a) deviator stress, q; (b) suction, s;

(c) volume change

Figure 11. Results of constant water test at matric suc-

tion of 162 kPa and various confining stresses, plotted

against axial strain: (a) deviator stress, q; (b) suction, s;

(c) volume change

Test (q)cr (ua-uw)cr v=(1+e)cr (Sr)cr (p′′)cr

CW-S 25-25 176 43.5 1.508 47.4 83.7

CW-S 25-50 232 47.5 1.456 52 128.8

CW-S 25-100 379 51.5 1.436 55.1 226.5

CW-S 50-25 190 74 1.55 43.5 88.5

CW-S 50-50 234 78.5 1.51 47.2 128

CW-S 50-100 366 91.4 1.48 50.3 222

CW-S 100-25 234 118.3 1.52 45.8 103

CW-S 100-50 276 121.2 1.48 50 143

CW-S 100-100 410.5 125.2 1.44 54.4 237

CW-S162-25 255 159.2 1.47 51.2 105

CW-S 162-50 315 153.8 1.453 53 155

CW-S 162-100 421 159.2 1.425 56.6 240

soil is subjected to large strain under different stress paths.

Figure 13 shows the stress paths of the saturated se-ries on the (q : p′) plane. Despite having different in-itial mean stresses, the specimens approached a unique critical-state line with a slope M equal to 1.5. These test results of unsaturated specimens seem to support that the net mean stress, p′′, and deviator stress, q, can be used as critical state variables for unsaturated soils (Table 4). The critical state lines for unsaturated tests presents in Figure 14. The criti-

Figure 12. The failure modes of unsaturated specimens; (a)

barreling in specimens at lowest suction value; (b) shear

zone in specimens at highest suction value.

Figure 13. Effective stress path of undrained tests on satu-

rated specimens

Table 5. The critical-state parameters for each matric suc-

tion

Figure 14. Critical state line on the (q : p′′) plane for the

unsaturated specimens.

Table 4. The critical-state parameters for each matric suction

ua-uw (kPa) M q0

0 1.5 16

25 1.375 45

50 1.334 69

100 1.336 92

162 1.278 115

cal-state lines were different for the unsaturated series

of tests as shown in Figure 14.

3 CONCLUSION S

In order to investigate the characteristics of pore pressure, volume change, and stress–strain behav-iour according to an initial matric suction of an un-saturated soil, a series of triaxial experiments was performed. In this triaxial apparatus, the matric suction was con-trolled by axis translation technique and volumetric behavior of specimens controlled by double-walled triaxial cell. The tests include consolidated un-drained tests on saturated specimens and constant water content tests on unsaturated specimens. Based on results, the following conclusions can be de-duced. 1. Soil suction does play a role towards increasing

the shear strength of an unsaturated soil and the

shear strength of the samples increases as a result of

increasing matric suction. The test results indicate a

non-linear relationship between shear strength and

matric suction.

2. The increase in shear strength with respect to ma-

tric suction is then becomes less than the increase

with respect to the net normal stress.

3. The volume change of an unsaturated soil during

shearing is more sensitive to the confining pressure

compared to the initial matric suction of the speci-

men. 4. Based on the test results, the critical state lines for the unsaturated soil specimens with respect to differ-ent matric suction or degree of saturation are not parallel to each other. It has been observed that the intercepts M and q0 are function of matric suction (ua-uw).

ACKNOWLEDGEMENTS

We are thankful to Mr. Ali Mirzaii for collaboration in manufacturing the unsaturated Triaxial apparatus that we used in our research.

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