strength and dilatancy of sands mixed with jute fibre

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Strength and Dilatancy of Sands mixed with Jute Fibre Pankaj Bariker & K.V.S.B. Raju University Visvesvaraya College of Engineering (U.V.C.E), Bangalore University, Bangalore, Karnataka, India ABSTRACT In the present study an attempt is made to evaluate the Strength and Dilatancy parameters of Sands mixed with Jute Fibres. A series of direct shear tests were performed on sample of Sands with mixture of Clean Sand and Sand mixed with 0.25% and 0.50% of Jute Fibres at three different relative density states namely loose, medium dense and dense state respectively, the effect of stress level is also bought out by varying the effective normal stress. The tests were conducted on dry sand having different relative densities (i.e., 20%, 50%, & 80%) subjecting them to different constant values of vertical normal stress ranging from 50kPa to 400kPa. At each stress level and density state for each case of sand Jute fibre mixture,peak frictional angle and dilatancy angle were found out by conducting direct shear tests. A series of direct shear tests were conducted up to shear strain of 40%. The stress strain response was observed and recorded, and the shear strength and dilatancy parameters were obtained for each relative density and normal stresses. It was found that as the percentage of Jute fibre was increased the peak friction angle and dilation angle were found to increase. Also in the present work a correlation between peak friction angle, dilatancy angle and critical state friction angle was obtained for sands mixed with Jute fibre. The present data was also compared with those of established correlations by Bolton (1986) and Kumar et.al (2007). 1 INTRODUCTION

The basic contributions to soil strength may be said to consist of two parts, the internal frictional resistance between grains, which is a combination of rolling and sliding friction and another part known as ‘interlocking’. Interlocking, which means locking of one particle by the adjacent ones, there by resisting movements to contribute a large portion of the shearing strength in dense sands, while it does not occur in loose sands.Which, depends on the size and shape of the particles, their arrangement, particle-to-particle friction, associated pore spaces, and the degree of saturation. When deformations occur in granular materials, the external forces may produce internal fabric changes, which is caused by rolling, particles sliding and interlocking, these changes will produce a different response of the material behavior. Such considerations are extremely significant in the design of soil structures such as retaining walls, foundations systems, and dams, because the analysis of these systems are based on the strength and deformation behavior of the material at bottom or near to them.

Reynolds (1885) the earliest to monitor a change in volume during shear for sands. Later, he showed that the dense sands exhibit expansion in volume during shear, and loose sands contract during shear deformation.Casagrande (1936)demonstrated that irrespective of the relative density of sand, atconsiderable level of shearing strain, a state finally emerges where the materialstarts shearing at constant volume and at constant shear stress. Which isoften termed as the critical and the corresponding values of internal frictionangles and void ratio are often defined as the critical friction angles (øcv) and thecritical void ratio

(ecr), respectively. Taylor (1948), Skempton andBishop (1950) worked to separate the strength component (øcv)

purely on anaccount of friction from that (øp-øcv) due to an expansion of the material; where øp is the angle of

internal friction corresponding to peak stress ratio.

Vesic (1963), Bishop (1966) and Lee and Seed (1967) demonstrated that the Mohr- coulomb failure envelope remains curved at low stress level, and amount of curvature depends on the relative density of the sand. With dense sands possessing more curvature than loose sands.Schanz and Vermeer (1996) concluded that the value of øcv doesn’t depend on the stress level, but øp is

dependent on the stress state and the corresponding rate of dilation, and mentioned that the rate of dilation becomes maximum near the peak stress state.

Bolton (1986) conducted tests both in Plane and Triaxial conditions and found the ideal method of determining øcv i.e., by drawing a plot between øp, corresponding Rate of dilation (at øp) and Rd i.e., the value of øp associated with zero rate of dilation, which is termed as øcv. He proposed a much simpler relationship among øp, øcv and ψp. Where, ψp is the angle of dilatancy which indirectly quantifies the rate of dilation.

[1]

…...for plane strain condition [2]

…..for triaxial condition [3]

The quantity IR, is referred to as dilatancy index and its magnitude is related to the relative density (Rd) and the effective stress (σv’) by the relation:

[4]

In the above equation σv’is expressed in kPa and Rd

in decimal; Q and R are constants.

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In Equation [4], the effect of stress level is incorporated. Bolton (1986) recommended the values of R = 1 and Q = 10. Later, Salgado et al. (2000) recommended the value of Q = 9.0 and R = 0.49 based on his test results on clean Ottawa sand.

Simony and Houlsby (2006) conducted a number of direct shear tests on large direct shear box apparatus to investigate the strength and dilatancy of sand - gravel mixtures. They concluded that addition of different proportion of gravel to sand causes an increase in peak frictionangle, peak dilatancy angle and critical state friction angle.

Kumar et al. (2007) examined further the correlations between øp, øcv, ψp and IR by conducting a number of direct shear tests on Bangalore (quartz sand). The effect of stress level and density onøp, ψp were incorporated. A correlation between øp and ψp and between øp and σv’similar to that of Bolton (1986) and Salgado et al.(2000) were suggested as following.

[5]

[6]

[7]

In the above equation σv’ is expressed in kPa and Rd

in decimal.

The objective of the present study was to examine further these correlations. For this purpose a number of direct shear tests were conducted onBangalore (quartz) sand mixed with 0.25% and 0.50% of Jute Fibres, by varying the magnitude of normal stress in between 50 kPa and 400 kPa. Three different relative densities of sands were employed.All the tests were continued up to a substantial value of the horizontaldisplacement so that the critical state was achieved in all the tests. The valuesof øp and ψpwere determined in all the tests for different combinations of σv’and Rd. All the test results were compared with the recommendations of Bolton (1986),and Kumar et al. (2007) so as to suggest correlationswhich providebetter estimation with regard to the present experimental work on sand - jute fibre mixtures.

2 PROPERTIES OF MATERIALS

2.1 Bengaluru Sand

The Bengaluru sand was found to be generally comprising of sub – angular grains as can be seen from the scanning electron micrograph provided by Kumar et al. (2007). The grain size distribution of the chosen (Bengaluru) sand is shown in Figure1. It can be noticed that the materialhardly comprises of any fraction of silt. The average specific gravity (G) of the sand particles was found to be 2.73. The maximum and minimum unit weights of this sand were found to be 17.04 kN/m3 and 14.53 kN/m3, respectively.

The values of the different parameters associated with the grain size distribution curve of the material are as follows: D10 = 0.29 mm, D30 = 0.46 mm, D50 = 0.70 mm, D60 = 0.80 mm, Cu = 2.76 and Cc = 0.90; D10, D30, D50 and D60 are the sizes corresponding to respective

percentage of finer, and Cu and Ccare the uniformity coefficient and the coefficient of curvature of the material, respectively. As per the Indian Standard for classification of soils (IS 1498-1970, reaffirmed 2002), Bengaluru sand was found to be poorly graded.

Figure 1. Grain Size Distribution Curve of Sand Sample

2.2 Jute Fibre Use ofnatural Fibre in civil engineering for improving soil properties is advantageous because they are cheap, locally available and eco-friendly. The natural fibre reinforcement causes significant improvement in Tensile Strength, Shear Strength and other engineering properties of the soil as per H.P.Singh et.al (2013). Over the last decade the use of randomly distributed natural and synthetic fibre has recorded a tremendous increase. Keeping this in view an experimental study was conducted on locally available (Bengaluru, Karnataka, India) Sand mixed with Jute fibre.

In the present investigation the diameter and length of Jute fibre used are<1 mm and 5mm respectively. The content of Jute fibre by dry weight of the sand was taken as 0.25% and 0.5% respectively. 3 TEST RESULTS AND DISCUSSION A number of direct shear tests were conducted on chosen dry sand at three different values of unit weight, namely, 14.97 kN/m3, 15.68 kN/m3 and 16.47 kN/m3 at its loose, medium dense, densest states i.e., at relative densities of 20%, 50%, 80% respectively, mixed with 0.25% and 0.50% of jute fibre correspondingly. The size of shear box was 60 mm x 60 mm and the sample height was kept equal to30.77 mm for all the tests. All the samples were sheared at a uniform relativehorizontal movement of 0.625 mm/minute between the upper and lower box. Thevertical effective normal stress on all specimens werevaried between 50 kPa and 400 kPa. The samples of a given density were prepared by either rainingthe material from a constant height of fall (for loose to medium dense sand) orwith the tamping technique using a fixed number of blows (for dense sand). All the tests were continued up tou/H = 40%; where H is the initialheight of the sample and u is the horizontal displacement at any time.

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3.1 Test Results For all the tests, the variation of the horizontal (shear) force (Ph) and the corresponding change (v) in the vertical height of the sample with increase in the horizontal displacement (u) was continuously monitored at regular linear strain interval, volumetric strain simply becomes equal to v/H. The corresponding test results are shown in Figures 3 - 6 in terms of

(i) The variation of Ph/Pv with u/H, and (ii) The variation of v/H with u/H.

Where, Pv is the magnitude of the vertical force. From these plots the values of friction angles (ø) and dilatancy angles(ψ) were determined using the following expressions.

[8]

[9]

The peak values of ø and ψ were designated by øp

and ψp, respectively. The variation of øp and ψp with increase in σv’ were also illustrated in Figures 11 - 13. Following observations were drawn from Figures 2 - 13:

The peak values of ø and ψfor all tests in each case of mixture occur almost at the same value of the horizontal displacement. The magnitude of the u/H corresponding to øp increases with increase in σv. An increase in the relative density of the material causes a marginal decrease in the value of u/H associated with øp.

For a given relative density of the material, the behaviour of the material at low stress level always remains same as that of a dense sand which indicates a well-defined peak corresponding to øp

and then followed by a decrease in the shear stress which ultimately leads to the critical state of the material at very high values of horizontal displacement; in such cases the material initially shows a decrease in volume followed by an increase in volume.

At low values of σv, the rate of dilation becomes maximum corresponding to øp and subsequently the value of dilatancy angle again decreases and finally becomes equal to zero in the critical state. On the contrary at very high values of σv, the behaviour of the material remains similar to that of loose sand where the shear stress increases continuouslyto yield the critical state at very high values of horizontal displacement. Insuch cases the material experiences a continuous decrease in volume until reaching the critical state.

The values of øpas well as ψp decrease with increase in the value of σv. As compared to loose sand, the effect of σv on the changes in the values of øp and ψp was seen to be more significant in the case of dense sand.

By adding jute fibre to sands, the values of øp and ψpincreases. But the values of øpas well as ψp decrease with increase in the value of σv.

The values of øp and ψpincreased significantly with increase in Jute fibre content.

For a given value of σv, an increase in the relative density of the materialcausing an increase in the values of both øp and ψp.

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Figures 2. The Observed variation for Sand with ϒ= 14.97 kN/m3.


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Figures 5. The observed variation for Sand of ϒ= 14.97 kN/m3mixed with 0.25% Jute fibre.


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Figures 8. The Observed variation for Sand of ϒ= 14.97 kN/m3mixed with 0.50% Jute fibre.


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3.2 Correlation between øp and ψp For different chosen values of σv and relative density (Rd) of the material mixed with different Jute fibre content, the obtained values of øp were plotted against the corresponding values of ψp.All the data points are indicated from Figures 11 to 13. It can be noted that the relationshipbetween øp and ψp can be best described by the following expression: 3.2.1 Sands with 0% Jute fibre

[10]

It can be observed from Figure 11.That, the value of

øcv for the chosen sand sample was found to be equal to

31.21˚ (i.e., τ/σv= 0.58).It can also be noticed from

Figures 2 - 4 that the value of τ/σvat very large value of

u/H (35-40%) remains very close to 0.58 indicating the achievement of the same critical state in all tests.

Figure 11. Correlation between øp and ψp for sands mixed with 0% fibre.

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3.2.2 Sands with 0.25% Jute fibre

[11]

It can be noticed from Figure 12. That, the value of



Figures 5 – 7 that, the value of τ/σvat very large value of


Figure 12. Correlation between øp and ψp for sands mixed with 0.25 % fibre.

3.2.3 Sands with 0.50% Jute fibre

[12]

It can be noticed from Figure 13. That, the value of



Figures 8 - 10 that, the value of τ/σvat very large value of


Figure 13. Correlation between øp and ψp for sands mixed with 0.50 % fibre.

A comparison of Equations [10], [11] and [12]with [1] indicates that the recommendation of Bolton (1986) remains marginally different from the present experimental result. It should be mentioned that Bolton’s expression relating øp,øcvand ψp is operationally indistinguishable from Rowe’s Stress- Dilatancy relations.

3.3 Correlation between øp and σv It is observed from Figures 14 to 16 that the value of øpreduces with increase in the value of σv. Bolton provided Equation [2] (for the plane strain case), where IR (dilatancy index) is defined by Equation [4] with Q = 10 and R = 1. From the regression analysis, it was found that the following relationship holds quite well for the present data: 3.3.1 Sands with 0% Jute Fibre

[13]

Where, with σvexpressed in

kPa and Rd in decimals.

Figure 14. Correlation between øp, ψp and σvfor sands

mixed with 0% fibre.

3.3.2 Sands with 0.25% Jute Fibre

[14]

Where, with σvexpressed

in kPa and Rd in decimals.

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Figure 15. Correlation between øp, ψp and σvfor sands mixed with 0.25 % fibre.

3.3.3 Sands with 0.50% Jute Fibre

[15]

Where, with σvexpressed

in kPa and Rd in decimals.

Figure 16. Correlation between øp, ψp and σvfor sands mixed with 0.50 % fibre.

3.3.4 Comparison of Results Experimentally measured values of øpwere plotted against those estimated using

I. Bolton’s recommendation, as in Equation [2], II. Kumar et.al, ’s (2007) recommendation, as In

Equation [6], and III. Present correlation, as in Equation [12]

And the corresponding comparison from three different correlations is shown in Figure 17 for all the data points. It can be noted the estimated values of øpfrom the recommendations of Bolton and Kumar et al. are found to be slightly higher than those actually measuredvalues for the present case of sands mixed with 0% Fibre. On the other hand Equation [12] seems to be better.

From above, it should be mentioned that the three different recommendations may provide only a marginal difference in the value of øpand the averages of the three can be adopted for carrying out the analysis where the effect of stress level on øphas to be taken in to consideration. After determining the value of øp, Equation [1] or [10] can then be used to find the value of dilatancy angle (ψp).

Figure 17. Comparison between results of previous research work with present correlation

4 CONCLUSIONS

On conducting series of direct shear tests over Sand - Jute fibre mixtures by varying Jute fibre content from 0.25% to 0.5%. It was found that with increase in normal stress, the peak friction angle (øp) and dilatancy angle (ψp) was found to decrease.

It was found that with increase in density, the peak friction angle (øp) and dilation angle (ψp) was found to increase.

With increase in Jute content from 0.25% to 0.5%, the peak friction angle (øp), dilation angle (ψp)and

critical state friction angle (øcv) was found to increase than when compared to clean sand.

The present study was useful in establishing correlations between peak friction angle (øp), dilation angle (ψp) and critical state friction angle.

From the present study one can estimate the dilation angle and critical state friction anglewhich is a useful parameter in numerical modelling studies of various Geo Structures.

From the present study it is found that, jute fibre will be a good reinforcing material to enhance the strength of Coarse grained soil.

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Also the present work was compared with established correlations of Bolton (1986) and Kumar et.al, (2007) and it was found that the present data compares favorably.

5 REFERENCES Alessandro Simoni and Guy T. Houlsby. (2006): “The

direct shear strength and dilatancy of sand– gravel mixtures”, Geotechnical and Geological Engineering, 24, pp 523-549.

Bishop, A. W. (1966): “The Strength of Soils asEngineering Materials”, Geotechnique, 16(2), pp. 91-128.

Bolton, M. D. (1986): “The Strength and Dilatancy of Sands”, Geotechnique, 36(1), pp. 65-78.

Casagrande, A. (1936): “Characteristics of Cohesionless Soils affecting the Stability of Slopes and Earth Fills”, Journal of Boston Society of Civil Engineers, 23(1), pp. 13-32.

Colliat-Dangus, J. L., Desrues, J. and Foray, P. (1988): “Triaxial Testing of Granular Soils under Elevated Cell Pressure”, Advanced Triaxial Testing of Soiland Rock, ASTM STP 977, ASTM, Philadelphia, Pa., pp. 290-310.

Singh, H. P and Bagra, M. (2013): “Improvement in CBR value of Soil Reinforced with Jute Fibre”, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 2, pp. 3447-3452.

IS-1498-1970, Reaffirmed (2002): “Classification and Identification of Soils for Engineering Purposes”, Bureau of Indian Standards, New Delhi.

Kumar, J. Raju, K.V.S.B. Kumar, A. (2007): “Relationship between rate of dilation, peak and critical state of friction angles”, Indian Geotechnical Journal, Vol 37(1), No.1,53.

Lee, K. L. and Seed, H. B. (1967): “Drained Characteristics of Sands”, Journal of the Soil Mechanics and Foundation Division, ASCE, 93(6), pp. 117-141.

Reynolds, O. (1885): “The Dilating of Media Composed of Rigid Particles in Contact”, Philosophical Magazine, December issue.

Roscoe, K. H., Schofield, A. N. and Wroth, D. P. (1958): “On the Yielding of Soils”, Geotechnique, 9, pp. 22-53.

Salgado, R., Bandini, P. and Karim, A. (2000): “Shear Strength and Stiffness of Silty Sand”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 126 (5), pp. 451-462.

Schanz, T. and Vermeer, P. A. (1996): “Angle of Friction and Dilatancy of Sand”, Geotechnique, 46(1), pp. 145-151.

Taylor, D. W. (1948): Fundamentals of Soil Mechanics, John Wiley and Sons, New York.

Venkatramaiah, C. (1993): “Geotechnical Engineering”, New age International Publishers, Revised Third Edition, pp. 285-289.

Vesic, A. S., and Clough, G. W. (1968): “Behavior of Granular Materials under High Stresses”, Journal of the Soil Mechanics and Foundation Division, ASCE, 94(3), pp. 661-688.

strength and dilatancy of sands mixed with jute fibre

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