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STRESS-STRAIN BEHAVIOUR OF COMPACTED RESIDUAL

SOIL IN DIRECT SHEAR TEST

Mohd. Raihan Taha1

, Syed Abdul Mofiz2

and Md.Kamal Hossain3

ABSTRACT

This paper reports the shear strength and deformation characteristics of compacted residual granite soil.

Nine series of tests were conducted using computer control direct shear box apparatus with normal stress

level ranging between 0.05 to 0.4 MPa. The influence of moisture content on the shear strength properties

is specifically discussed. A relationship between the angle of internal friction and moisture content for

residual soil is also proposed. Test results are then used to calculate the non-linear (hyperbolic) model

constants and analyse the stress-strain response of the compacted residual soil under direct shear loading.

Comparison of numerical predictions and results of direct shear tests are made for verification of the model

parameters. It is observed that the predicted stress-strain behaviour using model constants showed fairly

reasonable agreement compare to that of the laboratory test results.

INTRODUCTION

In tropical or semi-tropical area compacted residual soil has been widely used as fill material for

different geotechnical structures such as road pavements, embankments, retaining structures, land

reclamation and landfills. The assessment of the properties and prediction of the behaviour of such fills

have often been based on limited information. In spite of various semi-empirical test methods developed to

correlate engineering experience, proper design and construction uncertainty still remains. The variation of

strength parameters and compressibility of residual soils are mainly caused by differences in moisturecontents, which are most likely to occur in such soils. Because of the seasonal variations in rainfall, the

degree of saturation changes throughout the year. This results in seasonal variation in strength, which have

considerable influence on the geotechnical structures. Still, the failure mechanism, effect of moisture on

shear strength, and dilation-contraction behaviour of tropical soil composites are not yet well understood

due to limited studies. This paper describes the experimental results of nine series of direct shear test on

compacted granite residual soil. The effect of moisture contents on the cohesion intercept, angle of internal

friction and volume change properties are specifically discussed. The test results are then used to evaluate

the non-linear elastic model parameters. Finally, these model constants are used to evaluate the mechanical

stress-strain characteristics of the residual soil in direct shear test. Comparisons between model prediction

and laboratory test results are also discussed.

PROPERTIES OF SOIL

The soil used in this study was obtained from a granite soil formation. The soil is reddish in colour. It is

classified as CH in Unified Soil Classification (USC) system with liquid limit LL= 73%, plastic limit

PL=39% and particle specific gravity Gs=2.63. It contains 64 % silt and clay, 36% sand and no gravel. The

maximum dry density, γ d = 14.42 kN/m3

and optimum moisture content, wopt =24.6% were found from the

standard compaction test.

1Associate Professor, Department of Civil & Structural Engineering, Universiti Kebangsaan Malaysia, UKM Bangi

43600, Selangor Malaysia.2 Research Assistant, Department of Civil & Structural Engineering, Universiti Kebangsaan Malaysia, UKM Bangi

43600, Selangor Malaysia.3 Research Assistant, Department of Civil & Structural Engineering, Universiti Kebangsaan Malaysia, UKM Bangi

43600, Selangor Malaysia

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SAMPLE PREPARATION

The soil was first dried under laboratory air dry conditions, then ground and passed through 2 mm sieve.

The dry powder was carefully wetted with a spray gun to the standard optimum moisture content. The

moist soil was then stored in sealed plastic bags in moist room for about a week before use. The moist

residual soil was then compacted in the shear box mould through machine compaction procedure to thedesired height, moisture content and unit weight.

TEST PROGRAM

The experimental program consists of nine series of direct shear test using a 100-mm x 100-mm standard

shear box. The soil specimens were prepared at moisture contents between 18 to 34 percent. In this study

four tests were conducted with moisture content on the dry side of the optimum moisture content and other

five tests on the wet side. Each series of tests were carried out at normal pressure varying between 0.05 -

0.40 MPa. During shearing, the machine strain rate was set at 0.10 mm/min. The vertical displacements,

shear displacements and shear force were monitored using linear variable differential transducers (LVDT)

and proving ring with LVDTs. A computer control data acquisition system was used to record the shearforce, vertical and shear displacements.

HYPERBOLIC MODEL

In this study, the non-linear elastic (hyperbolic) model (Duncan and Chang 1970; Clough and Duncan

1971) has been used to simulate shear stress and shear deformation behaviour of the granite residual soil.

The frictional resistance and relative shear displacement relationship at any normal pressure is expressed as

ult

s

si

s

h

E

h

τ

τ ∆

+

∆=

1(1)

where τ is the frictional shear resistance, ∆hs is the horizontal shear displacement, E si is the initial shear

tangent stiffness, and τ ult is the asymptotic value of shear at infinite displacement of the hyperbolic curve.

The initial tangent shear stiffness is related to the normal pressure and can be determined as

n

a

n

wsiP

k E

=σ

γ (2)

where k is the shear stiffness number, γ w is the unit weight of water, n is the shear stiffness exponent

number, and Pa is the atmospheric pressure. The different constants in above equation are obtained by

conducting direct shear tests at varying normal stress and following the procedures of Duncan et al. (1980).

The values of k and n are determined by plotting the experimental data of E is / γ w vs σ n /Pa on a log-log scale.

Differentiating shear strength equation with respect to ∆hs and using the Mohr-Coulomb strength

equation, the tangent shear stiffness can be calculated as

is

n

f

hs

ts E c

R

d

d E

2

tan1

+

−=∆

=δ σ

τ τ (3)

This relationship can be used to calculate the value tangent shear modulus for any normal stress condition if

the values of the parameters k, n, c, φ, and R f are known.

The value of stress ratio, R f, can be written by the following equation

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R f

f

ult

=τ

τ (4)

where τ f is the shear stress at failure, and τ ult is the ultimate shear stress. These parameters should be

determined from the shear stress measured during the travelling shear displacement of the shear box in a

direct shear test. The ultimate shear stress is the asymptotic value of the shear stress and is calculated using

the shear stress, τ , and horizontal shear displacement, ∆hs, at 70 and 95 percent of τ f . It can be expressed by

the following equation

τ

τ τ

ult

s s

s s

h h

h h=

−

−

∆ ∆∆ ∆

95 70

95

95

70

70

(5)

Equations 4 and 5 provide a mean for estimating R f from direct shear test results instead of assuming a

value of 0.85 as suggested by Clough and Duncan (1969). This procedure is similar to that outlined by

Duncan et al. (1980) for determining R f from triaxial tests except the shear displacement and shear stress are

used instead of axial strain and deviator stress. Initially, efforts were made to normalise the horizontaldisplacement using the length of the direct shear specimen. This might have provided a better

correspondence between a triaxial stress-strain curve and the shear stress-displacement curve. Hence, the

direct shear test results provide a value of R f that is higher than the value of 0.85 proposed by Clough and

Duncan (1969). Therefore, it is recommended that R f be determined directly from direct shear test results.

RESULTS AND DISCUSSION

The shear stress and shear displacement curves for two representative series of direct shear test, one on

the dry side and the other on the wet side, are shown in Fig. 1 and Fig. 2, respectively. The results indicate

that the shear displacement corresponding to maximum stress increases with normal interface pressure. In

terms of vertical strain, the soil in the dry side exhibits a dilation behaviour for the small normal stress and

gradually decreasing dilation properties for higher normal stress (Fig. 1). On the wet side, contraction

behaviour is more pronounced (Fig. 2). This contraction property may be due to the increasing of moisture

content and vertical settlement, which developed after the application of normal stress on the soil

specimens. It is also observed from the figures that the compacted soil has a strain softening behaviour on

the dry side and strain hardening on the wet side. The shear strength parameters in terms of cohesion

intercept and angle of internal friction were determined by using best-fit straight-line failure envelope. The

failure envelopes with different moisture contents is shown in Fig. 3. The results show that the shear

strength parameters of the residual soil gradually decreases with increasing moisture content. Fig. 4 shows

the cohesion intercept versus moisture content and it indicates on the dry side the cohesion intercept

gradually increases up to the optimum moisture content, and then gradually decreases on the wet side. This

behaviour is similar to the standard compaction curve. The angle of internal friction versus moisture content(Fig. 5) shows that the angle of internal friction decreases with the increases of moisture contents. This may

due to the fact that the soil particle looses its bonding upon increase in moisture content. During shearing

the soil particles becomes more and more slippery and hence the angle of internal friction reduces. A

proposed relationship between angle of internal friction and the moisture content variation is such that:

φ =A(w) b

(6)

where φ is the angle of internal friction, w is the moisture content in percent, constants A = 690;

and b = -0.9933.

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Figure 1: Shear stress vs shear displacement and dilation vs shear displacement of the compacted

residual soil w = 26% .

0

50

100

150200

250

300

350

400

0 2 4 6 8 10 12 14Shear displacement (mm)

S h e a r s t r e s s ( k P a )

w = 26 %

σn = 0.05 MPa

σn = 0.2 MPa

σn = 0.15 MPaσn = 0.1 MPa

σn = 0.3 MPa

σn = 0.25 MPa

σn = 0.35 MPa

σn = 0.4 MPa

-0.3

0.0

0.3

0.6

0.9

1.2

1.5


D i l a t i o

n

( m m )

0.05 MPa 0.10 MPa0.15 MPa 0.20 MPa0.25 MPa 0.30 MPa0.35 MPa 0.40 MPa

Normal Stress

Figure 2: Shear stress vs shear displacement and dilation vs shear displacement of the compacted

residual soil (w = 34% ).

0

50

100

150

200


S h e a r s t r e s s ( k P a )

w = 34 %

σn = 0.05 MPa

σn = 0.40 MPa

σn = 0.35 MPa

σn = 0.30 MPa

σn = 0.25 MPa

σn = 0.20 MPa

σn = 0.15 MPa

σn = 0.10 MPa

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

1.5


D i l a t i o n

( m m )

0.05 Mpa 0.10 Mpa0.15 Mpa 0.20 Mpa0.25 Mpa 0.30 Mpa0.35 M a 0.40 M a

0

100

200

300

400

0 50 100 150 200 250 300 350 400 450

Normal Stress (kPa)

S h e a r S t r e s s ( k P a )

w = 34 %

w = 24 %

w = 26 %w = 28 %

w = 30 %

w = 32 %

Figure 3:Best fit failure envelope of residual soil

with different moisture content.

25

50

75

100

125

150

16 18 20 22 24 26 28 30 32 34 36

Moisture content, w ( %)

C o h e s i o n i n t e r c e p t ( k P a ) Wet SideDry Side

Figure 4: Variation of cohesion intercept

with different moisture content

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Test results also show that the dilation angle decreases with the increase in normal stress (Fig.6). From this

figure it can also be observed that the dilation characteristics are more pronounced for samples with less

moisture contents. The non-linear elastic model parameters for the compacted residual soil were then

determined from these tests. The effective stress hyperbolic and Mohr-Coulomb strength parameters using

the procedure outlined by Duncan et al. (1980) are shown in Table 1.

Table 1: Summary of the non-linear model constants for direct shear test.

Parameters Value

Normal stress range σ n 0.05 to 0.40 MPa

Shear stiffness number k 17067

Shear exponent number n 0.96

Cohesion intercept c 0.1006 MPa

Friction angle parameter φ 29.03o

Failure ratio R f 0.98

Analysis was made to verify the model parameters by comparing numerical predictions with theexperimental test results for the compacted soil on the dry side of optimum. The measured and predicted

stress-displacement curve is shown in Fig.7. In general, the predicted results indicated fairly good

agreement with the experimental results. However, it is obvious that it could not predict overconsolidation

behaviour and it could only handle strain-hardening materials as assumed in the non-linear model.

Nevertheless, the non-linear elastic model using the model parameters obtained from the direct shear test is

sufficiently accurate for modelling and analysis of different types of horizontal shear governing

geotechnical structures under expected working loads.

Figure 5: Relationship between angle of

internal friction with different moisture

Figure 6: Dilation characteristics of residual soil

in direct shear test under different normal stress.

15

20

25

30

35

40

45

50

16 18 20 22 24 26 28 30 32 34 36 38

Moisture content w (%)

F r i c t i o n a n g l e φ

o φ = A (w)b

A = 690

b = -0.9933

-5

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400 450

Normal stress, σn (kPa)

D i l a t i o n a n g l e , δ

o

w = 18 %

w = 26 %

w = 22 %

w = 30 %

w = 34 %

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