determination of physicomechanical properties of soft soils from

8/11/2019 Determination of Physicomechanical Properties of Soft Soils From

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results obtained by these methods allow the construction of

a single curve describing the uniaxial compression sxexover a wide range of strain rates and load amplitudes.

2. Experimental

The sand investigated was quartz sand with a particle

distribution centred between 150 and 212 mm, where 82%

by mass of the particles lay. The granular composition of

this sand is presented inTable 1. The theoretical maximum

density of the quartz used was 2.55 g/cm3; the dry sandpour density was 1.5 g/cm3 the sand beds used in the

experiments were 4573% porous.

2.1. Experimentalmodified Kolsky method

The intermediate strain rate experiments were conducted

in the Research Institute of Mechanics of Nizhny

Novgorod State University as part of a wide spectrum of

research into dynamic properties. The experimental set-up

(Fig. 1) successfully allowed the use of a modified Kolsky

method based on the use of the split Hopkinson pressure

bar (SHPB)[10].

Recent dynamic tests on soft soils have met with

considerable success using a modification of the Kolsky

method [1012]. The main difference between the present

test modification and the original SHPB scheme used in

compression tests is that a soil specimen is located inside a

rigid jacket, which confines its radial strain. This config-

uration is called a passively confined or jacketed test.

The stresses involved in the deformation of a soil

specimen, placed in a metal-confining jacket, loaded in a

SHPB system are shown in Fig. 2. During the jacket-

confined tests, the axial stresses in the soil specimen are

usually not higher than 300 MPa due to the significant

difference between the impedances of the bars and speci-

men. These stresses must be lower than the yield strength of

the jacket material. The maximum elastic radial strain of

the jacket, using an analysis based on a thick-walled pipe

under internal pressure loading[13], is greater than but of

the same order as the strain seen in these experiments. The

maximum circumferential strains of the jacket, as measured

by the strain gauges, were not more than 0.05%; long-

itudinal strains in some of the specimens were as high as

10%. In such circumstances, the radial strain may be

neglected in comparison to the longitudinal strain.

Effectively, the strain state of the specimen may be

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Table 1

Fraction of sand mass in various size fractions

Minimum dimension of granule (mm) The granules lie in the range between the size value in that column and the size value in the column to the right

1.6 1 0.63 0.4 0.315 0.2 0.16 0.1 0.063 0.05 o0.05

% Mass of fraction 0.03 0.375 4.425 22.955 18.035 40.09 9.22 3.31 0.42 0.215 0.265

This was obtained by sieving six separate samples of sand taken from different locations within the bulk sample.

Fig. 1. The experimental setup for the Kolsky bar system. For clarity, the dimensional parameters are indicated in Fig. 2.

A.M. Bragov et al. / International Journal of Impact Engineering 35 (2008) 967976968


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considered one-dimensional and the stress state bi-axial.

Then the main components of the stress and strain tensors

will be

s1 sx; s2 s3 sr; 1 x; 2 3 0, (1)

where sx and ex are longitudinal stresses and strains

obtained using the Kolsky analysis, and sr the radial

stresses found in the sample jacket. Inertia plays a minor

role in these strain rates for these samples stresses. This

effect is ignored in these experiments; however, inertia is

important in the shock wave experiments.

To determine the value of radial stress sr, an approx-

imation to a thick-walled cylinder was assumed, and

formula (2) was used. The expression relates the stress in

the jacket,srto the internal pressure, Pi, causing the small

elastic strain in the jacket:

sr Pi 1

2R22ER21 R

22y, (2)

where Eis the Young modulus of the jacket material, andR1 and R2 are the external and internal radii of the jacket,

respectively. The above expression gives the radial stress

component sr, based on the circumferential strain (eY).

Having both components of stress in the sample, sx(t)

and sr(t), allows a wide spectrum of properties of the test

material to be calculated.

The maximum shear stress t will occur at the planes

inclined 451to the longitudinal axis, and the value on these

planes will be

t sx sr=2.

The pressure,P, in the specimen can be expressed in termsof the main stresses as

P sx 2sr=3. (3)

The volumetric strain will take the following form:

y x. (4)

Expressions (3) and (4), describe the uniaxial compression

diagram, and allow the volumetric compressibility curve of

soil to be calculated.

The stress and strain levels during the compression

process are determined by

sit sxt srt, (5)

it xt

1 n

2

3xt. (6)

By eliminating time as a parameter, it is possible to

construct the major time-invariant characteristic of soil

material in its stress strain curve siei.

The relation between axial and radial components ofstress will be

srt xsxt n

1 nsxt.

The factor of lateral pressure, linking the principal stress

directions is defined as

xt srt

sxt (7)

and also the dynamic Poisson ratio

nt srt

sxt srt. (8)

It should be noted that the term dynamic Poisson ratio as

used here refers to a ratio of stresses in a dynamic, inelastic

deformation process, unlike the more classical situation of

a homogeneous material undergoing elastic loading. In the

experiments, the longitudinal strain pulses were measured

in the pressure bars and the shear strains in the jacket. A

typical result is shown inFig. 3. Computer analysis, using

in-house programmes[14]use these pulses to obtain a set of

parametrical functions tsxexsrtPYx. After first

synchronizing, the time bases of the stress pulses,effectively removing the transmission time along the bars,

then eliminating time it is possible to derive a set of

parameters such as: sxex, siei, PY and tP, xP, etc.

Test samples were placed in jackets and capped by circles

of thin paper to prevent the sand falling out. These paper

inserts had little friction with the jacket and did not

influence the test results. The jackets had a wall thickness

of 10 mm and a 10 mm working length. To centre the ends

of the pressure bars into the sample the jackets had a

thinner section outside of the working length to aid

alignment. The bars were pressed into the sample to make

a good contact, but no static external load was applied to

the samples during the test procedure. Empirical evidence,

supported by numerical simulation, has shown these

sleeves do not influence the stress deformation of the

jacket. The length of a sample was about equal to the

working length of the jacket. During compression, the

jacket had a uniform expansion along its length [14,15].

Depending on the loading stress investigated, the jackets

were made from either an aluminium alloy or steel. For

stress amplitudes up to 100 MPa, specimens used alumi-

nium alloy jackets, for higher stresses, steel jackets. The

larger deformation of the aluminium alloy, compared with

steel, allows more precise measurements, at small pressures,

of the strain on the external surface of the jacket.

ARTICLE IN PRESS

Fig. 2. Stress components and parameters in a soil specimen and in the

confined jacket. The terms are defined in the text.

A.M. Bragov et al. / International Journal of Impact Engineering 35 (2008) 967976 969


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2.2. Experimentalplate impact studies

Plate impact experiments were performed using a single

stage light gas gun at the Cavendish Laboratory [16]. This

has a 5 m long; 50 mm bore barrel and uses air or helium at a

pressure up to 350 atmospheres as the propellant, achieving

velocities up to 1200 m s1. The projectiles used in this study

consisted of a plate of copper 10 mm thick, 48 mm diameter,

mounted on the front of a polycarbonate sabot.

The sample consists of a 3 mm bed of sand inside a cell

made up of copper plates. The cell is in four parts as shown

in Fig. 4. A cover plate 2 mm thick fronts the cell, amanganin stress gauge is mounted in epoxy between this

plate and the copper plate behind it. This second plate was

either 2 or 3 mm thick. The third plate has a 3 mm recess

into which the sand is loaded. The recessed plate has a

1 mm thick rear face after which a second stress gauge is

located. The rear plate is 10 mm thick copper. The sand

was poured into the recess, the cell was tapped several

times to allow the sand to settle, the sand was then

smoothed off to produce a filled, flat-faced sample, level

with the top of the recess, finally, the cover plates were

fixed into position. The sand in this sample was not under

external load prior to impact, but was of a well-defined

density.

In these experiments, the sample mount was aligned to

an accuracy ofo1 mm, an angle ofo1 mrad, to the end of

the barrel using a dial gauge prior to each experiment thus

allowing a highly planar impact. The impact velocity is

measured using a sequential array of shorting pins

mounted at the end of the barrel to an accuracy of 0.1%.

The gauges act in two ways, firstly as time of arrival

sensors and secondly by recording the stress history. The

gauge at the front of the cell records the initial stress in the

copper, followed by the release down to the shock level

produced in the sand. The rear gauge initially records the

stress from the compacted sand into the rear copper block.

Given the high rate of loading, there is little time for bulk

lateral movement of the sand. In non-porous systems, the

material does not have time to move laterally and the

system is defined as being inertially confined. For the sand

in the shock-wave experiments, this effect will act as a

confinement. However, just as in the Kolsky system

described above, the lateral strain will be very small. There

will be some small lateral movements within the sample as

the grain pores collapse but no bulk lateral motion of the

material was observed. Overall, the loading system here is

one-dimensional strain in the longitudinal direction with a

bi-axial longitudinal and lateral stress state, again analo-

gous to the Kolsky system.

3. Results

As stated above, for Kolsky experiments at different

load magnitudes, the pressure bars and jackets were made

from an aluminium alloy or high-strength steel. The

parameters of a loading pulse were varied by changing

ARTICLE IN PRESS

Fig. 3. Typical initial and reflected strain pulses in the pressure bars (pulses 13) and also in a jacket (pulse 4). The levels of the strain are small, within the

elastic limits of the bars and jacket. The longitudinal strain in the much softer sand sample is considerable.

Fig. 4. The cell. All cell components are made from copper (Cu 101).



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the velocity and length of the striker bar. The experiments

can be divided into three groups:

low striker velocity (Vp 1012 m/s)sample stress up

to 80 MPaaluminum alloy pressure bars and jacket;

medium striker velocity (Vp 1822 m/s)sample

stress up to 150 MPaaluminum alloy pressure bars

and a steel jacket and

high striker velocity (Vp 2834 m/s)sample stress up

to 500 MPasteel pressure bars and jacket.

Overall 810 experiments were conducted in each group.

The major characteristic of soils were obtained using the

analysis defined above. The results in each group wereaveraged. In Fig. 5, the average curves of sand compres-

sibilities, from the third group, are shown.

In Fig. 6, the average dependence of shear stress with

pressure tPis given. The curve is practically linear in the

loading part of the cycle and almost linear in the unloading

cycle. This behaviour may be described using a Mohr

Coulomb equation: t C+(tan f)P, where C is the

effectively the shear strength or resistance of the unloaded

material, P is the applied pressure, and tan f gives a

measure of the increase in shear resistance with applied

load, f being called the internal friction angle. It is

necessary to note that the value of the specific coupling, C,

is rather small, indicating a soft material, and so has a large

percentage error associated with it. However, from a

practical viewpoint it can be neglected. In Fig. 6,

tanj 0.64; while the lateral thrust factor was determined

to be x 0.33 (Fig. 7).

The final results both in sxe and Pe axes are shown in

Fig. 8. The results show that the loading of the diagrams is

non-linear especially at higher stresses within the range of

strain rates used. The deformation rate does not strongly

influence the behaviour as all the responses lie, within

experimental error, on the same curve. The existence of

similar deformation diagrams for soft soil media was

predicted by experts in the field of soil dynamics e.g.

Lyakhov [2]. The amplitude of the maximum stresses,

achieved on the diagrams, are wholly determined by value

of the loading pulse. No influence of strain rate on

unloading was found. Comparison of loading and unload-

ing branches leads to the conclusion that the velocity of

waves during unloading considerably exceeds the wave

velocity in the loading cycle, in this range of pressure. Also,

the compressibility of sand decreases slightly with reduc-

tion of particle size for all modes of loading. While overall,

the response is non-linear (see Figs. 5 and 8), the loading

deformation diagrams have two main regions, connected to

the various mechanisms of deformation. The behaviour in

this region is strongly connected to two mechanisms.

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Fig. 5. Averaged curve of sand compressibility from the Kolsky system

using steel jackets and steel bars, for stress loading up to 500 MPa.

Fig. 6. Dependence of lateral stress with pressure for experiments with

loading stresses of 80, 150, and 500 MPa.

Fig. 7. The characteristic of lateral thrustx for experiments with loading

stresses of 80, 150, and 500 MPaU This gives a value of0.33 during the

loading part of the cycle.



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The first mechanism is produced by the significant

difference of acoustic impedances of bars and specimen,

this leads to low stress transmission. The particle velocity

within the sample is small (500 m/s) and the sand is very

porous. In the first stage, the basic mechanism is the

movement of sand particles to fill the pores.

With the removal of pores, the second mechanism

becomes more dominant. The sample is at higher density

so transmits more stress from the bars as there is a lower

impedance mismatch. The particles also begin to interact

intensively with each other. This is accompanied by anincrease of friction at the contact points, elastic deforma-

tion and their partial destruction. Recovered material

shows this fracture of particles during the dynamic loading.

These processes require higher stresses. Therefore in this

second region the compressibility gradually decreases,

while the intensity of stress growth is increased. These

mechanisms coexist over much of the stress range and the

switch between the relative dominance of the mechanism is

not sharp, hence the rounded transition region. Inertia has

only a limited role in this region, given the small particle

size and the low density.

As the stress wave begins to decrease, the specimen

unloads, i.e., the soil decompacts a little. However, the

transition from active loading to unloading is not

instantaneous; it occurs across a range of strains. Such

behaviour can be partially explained by the dynamic

loading of the gaseous component in the pores. Secondly,

internal stresses in the sand particles can overcome the

coherence forces, as soon as the loading is taken off. The

comparison of the loading and unloading branches of the

diagrams allows the conclusion that the velocity of

unloading considerably exceeds the velocity of compaction

waves for all groups.

In the higher rate plate-impact tests, the data gathered

correspond to a region much higher than the low-velocity

Kolsky experiments. In this shock region, the loading wave

induces considerable stress between the grains while

allowing only limited time for grain movement, fracture

is the dominant mechanism. Fig. 9 shows the data from

shots at velocities of 200, 500, and 969 m s1 using the plate

impact gun with a 10 mm Cu impactor onto copper cells

enclosing a thin sand bed. There are similarities between

the gauge outputs seen in all experiments. The front gauge

shows a rapid rise to a flat-topped pulse. The height of this

pulse is defined by the copper Hugoniot as both the

impactor and target cell are copper, the stress level inthe copper increases with impact velocity. The width of the

initial pulse seen in the front gauge is defined by the

thickness of second plate in the target, which determines

how long it takes the release wave returning from the

coppersand interface to reach the gauge.

In some of the front gauge traces, there is a dip

immediately before the steep initial rise. This is due to

capacitative linking between the gauge and the epoxy

surrounding it, which acts as a dielectric, and the copper

plates on either side of the gauge [17].

The rear gauge shows the stress transmitted into the rear

of the copper cell through the sand. Given the granular

nature of sand, a ramp is seen due to the collapse of pores

in the system. The rear gauge trace shows this ramping in

the first part of its signal (see Fig. 9(a)). As the impact

velocity increases the pore collapse occurs over a shorter

time and the initial ramp seen in the second gauge trace

steepens. In all cases a plateau is reached. This level

corresponds to the stress transmitted by the shock-

compacted sand into the copper. Later, a second rise on

the rear gauge trace is due to stress waves being reflected in

the sand-filled cavity due to impedance mismatches

between the sand and the copper cell. This second rise

gives further information on the compressed sand, the full

analysis of which is not entered upon here.

ARTICLE IN PRESS

Fig. 8. Dynamic curves for dry sand as plotted both in stressstrain (sxe) and pressurestrain (Pe) axes. The characteristic for experiments with loading

stresses of 80, 150, and 500MPa are shownU The curves lie on the same loading path. After reaching a maximum compressive strain, the curves drop in

stress and strain during unloading.



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Sand is a statistical material and, therefore, some

variation can be expected from sample to sample. How-

ever, a repeat experiment at 500 m s1 shows excellent

reproducibility, on the loading cycle as illustrated in

Fig. 10.

By combining the shock speed through the sand,

obtained from the time difference seen when the gauge

starts to record a stress, with the density of the sand, it is

possible to derive a Hugoniot of the material. It should be

emphasized that this is an approximation based on a

hydrodynamic response. This assumption is not without

merit as the sand displays very limited strength compared

with the loading pulse.

For the shock-compacted sand, initial tests using a finite

difference hydrocode suggest that using the fully com-

pacted density of the sand gives predictions which match

the stress level of the first plateau on the rear gauge, thus

indicating the high degree of compaction that has occurred.

It is clear, however, that a model, which takes into account

the kinetics of pore collapse is required in order to describe

ARTICLE IN PRESS

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10

FrontRear

Stress/G

Pa

Time / s

Initial Ramp

First Plateau

Second Rise

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8

FrontRear

Stress/G

Pa

Time / s

0 1 2 3 4 5 6 7 8

Time / s

0

5

10

15

20

Front

Rear

Stress/GPa

Fig. 9. The output of the gauges from experiments with impact velocities of (a) 200, (b) 505, and (c) 969 m s1. The time bases of all experiments are set so

the initial rise of the front gauge is at 0 ms. The stress measured is that in the copper cell.

0

2

4

6

8

10

StressatRearGauge/GPa

Time / s

2 3 4 5 6 7 8

Fig. 10. Reproducibility of plate impact at 500m s1. The rear gauge

traces from two separate experiments are shown.



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the full process. The Hugoniot obtained is shown below,

Fig. 11, in the stress particle velocity space, together with

the variation of shock speed with particle velocity,Fig. 12.

These data is are agreement with previously published data

on sand[18].

Since the stress states obtained in the Kolsky method

and the plane shock wave experiments are similar, the

combination of the results obtained by these techniques

allows the uniaxial compression curve sxex to be

constructed over a wide range of strain rates and load

amplitudes.In order to construct the compressibility curvePebased

on the results of a plane shock wave experiment it is

necessary to measure the longitudinal and lateral compo-

nents of the stress tensor. In the case of soils, such lateral

measurements are difficult to perform in the shock regime.

The compaction of the sand produces dramatic variations

in local strain within the sample, eroding stress gauges,

while the effect of inertial confinement of the sand does not

allow valid measurements to be made outside of the

shocked material. Therefore, we propose to determine the

pressure Pfrom the obtained shock wave adiabat sxex as

follows.

From the available experimental data, it was established

that the relation between the shear strength and the

pressure for soft soils loaded up to 500 MPa is close to

linear [2,3,8]:

t C tan fP, (9)

where C is the cohesion (very small for sand) and f is the

internal friction angle.

If the assumption that this relation is also valid at higher

pressures (up to several gigapascals) and the value off is

maintained then the pressure can be calculated. Indirect

evidence of the validity of this assumption is provided

by the results of plane shock wave tests, in which two

stress tensor components were determined for a cement

mortar[19].

For uniaxial deformation, we have

P sx 43t. (10)

Using this formula and the linear relation (10), we obtain

an expression for the pressure as a function of the stresssx:

P sx 4=3a

1 4=3 tan j. (11)

Thus, under the above assumption, this expression

provides the relation Pex (or Pr) for shock-wave

compression, using the shock adiabat sxex and the

previously determined values ofCand tan f. In combina-

tion with the Pex curve obtained using the modified

Kolsky method, this provides the complete Pex relation

for a broad range of load amplitudes.

The coefficients in relation (10), determined using the

modified Kolsky method, are C 0 and tan f 0.643.

The results of plane shock-wave tests [20] gave the

linear shock-wave adiabat, Us c0+Sup, where Us is the

shock wave velocity, up

is the particle velocity, and

c0 510.9 m/s, a term associated with acoustic sound

speed and S 1.71 are constant coefficients. Using this

adiabat and expression (10), it is possible to construct a

compressibility curve Pex or Pr.

The complete sxex (1, 2) and Pr (3, 4) curves are

depicted in Fig. 13, where curves 1 and 3 represent the

dynamic response obtained using the Kolsky method, while

curves 2 and 4 are the shock wave adiabats constructed

using the results of plane impact experiments. As can be

seen, the results obtained by the two independent methods

are in good agreement and complement each other, thus

significantly expanding the domain of determination of the

main laws for the deformation of soils.

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0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Stress/GPa

Up / mm s-1

Fig. 11. Hugoniot of quartz sand in stress/particle velocity (Up) space.

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Us/mms

-1

Us / mm s-1

Fig. 12. Shock velocity as a function of particle velocity.



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4. Conclusions

A method for determining the main parameters in the

high strain-rate compression of soft soils over a wide range

of impact loads and strain rates has been developed. The

experimental data obtained can provide the parameters

and constants necessary for the development of mathema-

tical models of soft soils. The values of the lateral stress in

the shock regime were calculated using parameters

obtained in the lower rate Kolsky method. This is possible

as the upper stresses in the Kolsky experiments overlapped

with the lower stress range of the shock experiments. Theresults of this analysis were consistent. It is important to

extend this analysis to other systems, including low-density

solids to see if this is a general result.

In the case of dry sand using these two complementary

techniques, the generalised curves of a dynamic compres-

sibility have been constructed. Several important conclu-

sions can be found in relation to the sand behaviour.

Firstly, the results across a wide range of strain rates show

no abrupt change in behaviour. Secondly, there is little

strain rate dependence in the pressure range studied.

The compaction process involves two mechanisms, grain

movement and grain fracture. A more in-depth discussion

of the compaction processes was given in the main text but

grain movement dominated the response in low-stress

Kolsky experiments. In the higher stress regime, the

response became dominated by grains locking together

and fracturing, this trend continued into the shock regime.

This technique will now be applied to other materials of

geological interest such as loams, clays, and rocks.

Acknowledgements

This study was supported in part by the Russian

Foundation for Basic Research, Project nos. 04-05-

64614a and 04-01-00454a. MoD, QinetiQ, and [dstl] are

thanked for their support of this research. Mr. D. Johnson,

R. Flaxman, and D.L.A. Cross of the Cavenidsh workshop

gave invaluable support. Dr. Stephen Walley of the

Cavendish Laboratory is thanked for his help in editing

this document and providing an extensive set of references.

References

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Fig. 13. The combined response of sand across the strain rates 102106 s1.



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