Deformability determination of coarse-fragmental soils Текст научной статьи по специальности «Физика»

DEFORMABILITY DETERMINATION OF COARSE-FRAGMENTAL SOILS

Nazarov K. I., Engineer, JSC Hydroproject. Khidoyatov Z. D., Senior Lecturer, Tashkent Institute of Architecture and Construction E-mail: [email protected]

DEFORMABILITY DETERMINATION OF COARSE-FRAGMENTAL SOILS

Abstract. The definitions of strain properties of non-cohesive soils are given in the paper; these properties make it possible to account for lateral friction in the process of testing and to obtain soil strains corresponding to its work in full-scale conditions.

Keywords: sample, soil, coarse-fragmental soils, deformability, friction, odometer, stress, stamp.

Deformability determination of coarse-fragmental soils is usually carried out on an odometer with a rigidly fixed bottom and a movable upper stamp through which a vertical load is applied to the sample.

The disadvantage of this method is that it does not take into account the lateral friction of soil against the walls of the device in which the sample is tested. The stresses in the sample decrease from the surface to the rigid bottom not only due to the friction of the particles, but also due to the friction against the walls of the device. The value of friction against the walls of the device is in functional dependence on the load applied to the sample of tested material, its grain composition, the particle shape factor, etc. The results of compressibility obtained on such devices do not allow us to estimate the actual compressibility of soils.

The method for determining the compressibility of soils in the odometer takes into account lateral friction. The method we have developed for determining the strain properties of non-cohesive soils makes it possible to take into account lateral friction in the process of testing and to obtain soil strains corresponding to its work in fill-scale conditions.

In this method, an account of soil friction against the walls of the device is conducted by parallel testing of two samples of soil of equal height. The first sample is tested in the odometer of conventional type with a movable top stamp and a bottom rigidly fixed to the walls. The stresses applied to soil continuously decrease along the depth of the sample down to its base (Fig. 1) due to the friction of the particles and their friction against the walls of the device. The value of friction against the walls of the device is in functional dependence on the load applied to the sample, as well as on a number of other factors: material, density, grain composition, particle shape factor, etc.

The second sample is tested in the odometer of the same diameter as the first one, but here both the upper stamp and the lower stamp are movable and the pressure is transferred

to the sample through both stamps. Here, at the top of the sample and at its base the stresses are equal to the applied load and they decrease according to the same law from both surfaces of the sample to its middle (Fig. 1, b).

In accordance with the above, in the second sample the average stress is two times greater than in the first one, due to the reduction of lateral friction. Parallel testing of soil on two devices of the same diameter makes it possible to eliminate lateral friction and to calculate the actual soil strain according to:

kh —

— - (1 - e« )

id = i2 + (i2 -i,)-«-— (1)

-kh R \2

0.5 - (1 - e « )2 where id - is the actual relative soil strain; i2 - is the relative

strain at load application on the sample with two movable

stamps; il - is the relative strain at load application on the

sample with one movable stamp; e - is the base of natural

logarithm; R - is the radius of the device; h - is the height of

the sample; k - is the friction coefficient.

In the general case, soil friction against the walls of the device "t" is determined by the normal compressive stresses V" occurring between them.

t = f (a) (2)

Without changing the generality, the following can be written

t = ka (3)

where k is taken as a function V".

Consider the equilibrium of the elementary soil layer of a thickness of dx in the odometer; the layer is subj ected to compressive stresses equal to c of the top surface. The equilibrium equation of this layer has the form:

nR da = -2nRk ■ adx

da 2k ,

— =--ax ;

a R

r da 2k x ,

I — =--I ax ;

aR

(4)

a

0

Section 9. Technical sciences

Figure 1. Determination of the scale effect of strain of coarse-fragmental soils due to friction against the side surfaces of the samples: a) scheme of experiments, b) graphics of deformability: 1 - experiment I; 2 - experiment II; 3 - real curve

ax 2k ax

ln— =--x ^ — = e

<rn R

°0

2k

<7,

1 n-

_2k

-RXdx = f

2k

R dx = -2x ■ R

R

dx = — dz x = 0 ^ z = 0 x = h ^ z =--h

2k R

2-dx = dz R 2k

a.

h J

--h k dx = a J ezdz = -aR(e^

0

^ 2kh

h

n 2kh

^ (i - e-T

2kh

- i)

(5)

The second odometer

i h a0R

h ^ <yp = —— 2 cp 2hk

C ^ h = 0 ; U =Uo

1/2

ezdz = -

2hk'

_ 5kh R

+ C

kh

a°R- (1 - e ^).

■p -o Op = (i -eR ). (6)

As a result of the tests two compressibility curves a + i are obtained. Sectioning these curves in an arbitrary point with horizontal lines, two values of stresses a applied to both samples are obtained; the samples strains are equal. The equality of

strains is a consequence of the equality of the average compressive stresses. In accordance with this, it can be written:

r R 2kh r R kh

aiR (1 - e^) ^ (1 - e"R)

, , , , (7)

2kh kh The average stress in the odometer with two movable

stamps (the right side of the equation) is calculated taking

into account the fact that with such an experiment scheme,

the strains and stresses in the sample are symmetrical about

its midpoint. Solving this equation, we get

K = -Rln(2^>-1). (8)

h

With known value of "k", corresponding to stress range (a1 ) it is possible to calculate the average stresses in the same range for each sample

R ""

a

Cp(1)

-a'Wh(1 -e R)

(9)

At small changes in stresses, the strains proportional to them, can be written as:

= K(i2 -ii)

| Ocp(2) Ocp(1)

Ocp(2) °cp(\)

Hence

Tcp(2) = K(i0 - i2)

¡0 — ¡2 +(i2 — ¡1 ) R

"-a0 kh

cp(2)

¡0 ¡2

°cp(2) Ucp(\)

"0 " cp(2)

kh

1 - e

/

R kh

kh

1 - e

R 2kh

— ¡2 + (¡2 - h)-

kh R

i _2kh \ 1 - e R

v J

kh R

- (1 - e R)

(10)

-- 11

1 -e R-- + -e

2kh R

22

kh

¡0 = ¡2 + (¡2 - ¡1) —

0.5(1 - e

-(1 -eR )

-kh R )2

Conclusion

Experiments conducted with conventional odometers at load transfer through one movable stamp have shown that the relative settlement obtained at different values of density is 1.8-2 times less than at load applied to the sample from two sides. This is explained by the fact that the friction of soil against the walls of the device reduces the stresses acting on soil.

1.

2.

References:

Ibragimov K. I., Nazarov K. I. Strength and Deformability of Coarse-Fragmental Soils // Proceedings of the 1st Central Asian Geotechnical Symposium "Geotechnical problems of construction, architecture and geo-ecology at the turn of the twenty-first century". - Astana, - May 25-28. 2000.- P. 192-195.

Ibragimov K. I., Nazarov K. I. Strength and Deformability of Stone-Earth Dams Erected from Loam-Pebble Soils. TASI.-Tashkent. 2001.

--x

kh