the behavior of water saturated sand under shock loading(1)

8/12/2019 The Behavior of Water Saturated Sand Under Shock Loading(1)

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The Behaviour of Water Saturated Sand under Shock-loading

D. J. Chapman, K. Tsembelis, and W. G. Proud

PCS, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE. UK.

ABSTRACT

A series of plate impact experiments have been performed on quartz sand of 230 m average grain size, atvarious levels of water saturation to obtain Hugoniot data. Manganin stress gauges were inserted in anvilssurrounding the sand samples. Shock-velocity was calculated from the time of arrival and the Hugoniot data wasinferred using impedance matching techniques. Low levels of water saturation (10%) did not significantly affectthe shock response compared to dry sand. High levels of water (20-22%) saturation were found to stronglyinfluence the Hugoniot.

INTRODUCTION

The shock properties of geological materials are of relevance to a diverse range of applications, includingplanetary impact, oil and gas recovery, mining and earthquakes. Geological materials are often added to mortarsand cements to form concretes. The quartz sand investigated here is used in the construction industry. Theresearch presented forms part of a larger effort to characterise concretes and construction materials under shockcompression.

The shock response of granular materials such as sand presents a complex problem. The sand aggregate iscomposed of independent grains surrounded by voids. The sand will compact from its initial state in a mannerwhich is determined by the initial porosity, grain morphology, and the strength of the particle. The strength of thesand aggregate will be substantially different from that of the quartz bulk material due to effects of intra particlemorphology, and significant surface energies [1]. Further to this we expect the state of stress within each particleto depend on the configuration of inter-particle contacts. As the compaction process progresses, viscoplastic flow

of the grains to fill the voids increase the area of inter-particle contact. Consequently, until full compaction hasoccurred the deformation is predominantly the localised shearing of grains to fill voids, and the contribution fromthe compression of the bulk material is not significant. The relatively small grain size (sand investigated here hasan average grain size of 230 m) will favour ductile deformation rather than brittle failure of the grains. Thismorphology dependant deformation makes it unlikely that a single universal porosity parameter can quantitativelydescribe all states of deformation, and limits the success of modelling using compaction models such asHermanns P- [2]. To this end, the time resolved data presented will provide stringent validation test for anysuch compaction model. However, it should be highlighted that the experimental data still averages over manygrains and gives no information on the microscale processes occurring.

We present an experimental study into the effects of water saturation on the Hugoniot of sand. There is little workin the open literature that addresses how the Hugoniot of sand varies with water saturation [3, 4]. However, workby Hiltl et al[5, 6] on a sandstone with similar a grain size to the sand investigated here demonstrates that water

saturation acts to homogenize the material and prevent the localization of stress at contact points.

Almost universally, the principal Hugoniot of highly porous granular materials have been developed from directmeasurement of shock-velocity. The work presented here uses a plate-impact reverberation technique. Sensorsare embedded in anvils surrounding a cavity containing the sample. This is similar to methods employed by otherauthors [3, 4, 7-9]. The method has the disadvantage that no in-material stress data is obtained directly and mustbe inferred using the jump condition (eq. 1).


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PSX uU0

= (1)

where xis the longitudinal stress, 0 the initial density, US the shock-velocity, and uPthe particle velocity. Thestress values obtained should be treated with caution as the method represents an approximation, neglectingmaterial strength and assuming a steady state.

MATERIAL DESCRIPTION

The material under investigation was a quartz-based sand provided by the Concrete Structures Section (CSS),Department of Civil & Environmental Engineering, Imperial College, London, UK. This has a dry density of1520 50 kg m

-3and an average particle size of 230 m. Fig. 1 shows the particle size distribution measured

using a laser particle size analyzer. Mie scattering of a visible laser beam is used to back-calculate a fit to theparticle size distribution which would generate the observed scattering. All particles are assumed to be spherical.The density for the single crystal quartz is 2650 kg m

-3[10]. This suggests that the sand is 43% porous neglecting

any impurities.

0

5

10

15

20

25

56.09 83.26 123.6 183.4 272.3 404.2

%v

ol.fraction

Particle Size (m)

Figure 1.Particle size distribution for the quartz based sand. Table1. Saturation density, Linear fit coefficients andcorrelation coefficient for the linear fit to the shock-velocitydata.

For the purpose of this investigation saturation was defined as the percentage of the total mass that is composedfrom water. This implies that if all the voids were filled with water the maximum theoretical saturation and densityobtainable would be 22% and 1950 kg m

-3 respectively. However, in practice the sample cell dimensions used

(narrow) in the plate-impact targets prevented optimum grain packing. The density obtained in the dry samplesfor example was 1430 50 kg m

-3. Consequently the density of samples at the various saturations is lower than

would be achieved by optimum packing and the samples contained voids filled with air. The saturationsinvestigated were 0%, 10%, 20% and 22%. Table 1 summarises the saturations and densities obtained.

EXPERIMENTAL METHODS

The Hugoniot data was determined using a plate-impact reverberation technique. Plate-impact experiments wereconducted using the 50 mm bore 5 m length single stage light gas gun at the University of Cambridge [11].Impact velocities were measured to an accuracy of 0.5% using a sequential pin-shorting method and the targetwas aligned with the impactor to less than 1 mrad by means of an adjustable specimen mount. Longitudinalstress was measured during impact using commercially produced manganin piezoresistive gauges(Micro-Measurements LM-SS-210FD-050 option SP60 and Micro-Measurements LM-SS-125CH-048). The outputvoltage was recorded on a fast (5 GS s-1) digital storage oscilloscope. This voltage time data was then reduced tostress histories according to Rosenberg et al [12]. However, manganin gauges exhibit a hysteresis in thepeizoresistive response upon unloading due to work hardening of the gauge element. If the peak stress

Saturation% H2O

by weight

Density(kg m-3)

C0(km s-1)

SCorrelationcoefficient

0 % 1430 50 0.53 1.64 0.899

10 % 1530 50 0.23 2.26 0.971

20 % 1810 50 0.71 2.90 0.951

22 % 1840 50 0.32 4.92 0.979


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experienced by the gauge is greater than 1.5 GPa (the Hugoniot Elastic Limit of the gauge) any subsequentrelease values need to be adjusted for this hysteresis according to the methods of Yaziv et al[13].

Figure 2. Schematic of the plate impact.

The plate impact configuration is shown in Fig. 2. Projectiles were constructed from either a lapped PMMA orlapped Cu discs, (termed the flyer) and affixed to a polycarbonate sabot. To the rear of the flyer plate a recessallowed for complete release. In each experiment the flyer plate material used was the same as that of the anvilsused in the target. The target was constructed as shown in Fig. 1. with the sand contained laterally by analuminium annulus and longitudinally by anvils. A gauge, G1, was embedded within the front driving anvil, 1-2 mmfrom the impact face, and 1-2 mm from the 3.2 mm sand cavity. To the rear of the cavity a further gauge G2 wasbonded 1mm into the back anvil. Gauges were incorporated into the samples using a slow curing epoxy. Thegauge package was typically ~100 m thick and the rise-time was ~30 ns as only the manganin element wasimpedance mis-matched. This afforded good resolution to obtain evidence of any precursor wave in thecompaction process. The PMMA anvils had similar impedance to the sand providing a favourable environmentwhere gauge hysterisis was kept to a minimum. However, to obtain data at higher stresses and particle velocitiescopper anvils were also used. The impedance difference between the gauge package and the copper anvilscaused the stress to ring up over ~300 ns; this is the effective time resolution of the gauge.

HUGONIOT DETERMINATION

Hugoniot measurements employed the impedance match method [14] which is schematically demonstrated inFig. 3. An idealized gauge response and simplified X-T diagram is shown in Fig. 4. The symmetric impact of thefront anvil and flyer results in state A. Shocks moves both forward into the front anvil and backwards into theflyer. The dimensions of the projectile were chosen so that longitudinal release from the rear of the projectilewould not occur during the time of interest. The shock traverses the front anvil passing through the location of G1where state A is recorded and is incident on the anvil sand cell boundary. The anvil will either be reloaded orreleased depending upon the relative impedance of the anvil to that of the sand sample, resulting in state B. Therelease case is represented in Fig 3 where state B is the intersection of the release isentrope of the anvil from

state A and Hugoniot of the sand. In Fig. 3 and for the purpose of the data analysis the release isentrope of theanvil was approximated by the Hugoniot. This is a good approximation for the Cu anvils but less so for thePMMA. A release fan representative of state B passes back into the front anvil and is registered at G1. Theshock/compaction front moves through the sand sample, eventually incident on the rear anvil. Again, dependingupon the relative impedance of the anvil material to the sand, the sand is either reloaded or released by the rearanvil. The reload case is demonstrated in Fig. 3 and is labelled state C. A shock and re-shock at state C passinto the rear anvil and back into the sand, respectively. The shock moving into the rear anvil is measured by G2and can be used to ascertain off-Hugoniot points of the sand after the initial shock. The time of arrival at thegauges can be used to calculate a transit time for the shock through the sand if the shock velocity in the anvils is

PMMA Flyer~ 15 mm thick

V

PMMA front anvil~ 2-3 mm thick

PMMA rear anvil~ 21 mm thick

Aluminium annulus

Gauge 1(G1)

Gauge 2(G2)

Sand cavity~ 3.2 mm thick

Recess

PolycarbonateSabot


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known. It can be shown from conservation of momentum that the line passing through points O and B has slope0Us. Consequently, the particle-velocity of state B can be determined from the intersection of the line withgradient 0Usand the anvil Hugoniot (release isentrope). The sand Hugoniot can be constructed by repeating thisprocedure at different impact velocities.

Figure 3. Impedance match method for Hugoniot measurement. Figure 4. Idealized Gauge response and simplifiedX-T diagram using anvils of higher impedance than

the sand

The above analysis disregards any material strength, treating only a single shock moving through the sand bed.In practice, the stress profile will be complex, with compaction processes occurring and possibly low amplitudeprecursors moving through the skeletal bed of quartz. These precursors will reverberate between the boundariesand act upon the main shock front. However, these perturbations have a minor influence on the main transit timeof the shock front in comparison to the general experimental uncertainty. The shock-velocities are measured asan average of the transit time through the entire sample. If a steady state is not achieved in a short timecompared with the transit time (certainly possible considering the granular bed compaction) this will add additionaluncertainty in the measured shock-velocity. It has been demonstrated for a similar unsaturated sand thatshock-velocities measured in 1mm, 3mm, and 5 mm beds of sand are the same to within experimental error. Thisimplies that the time taken to achieve a steady state is short compared with the transit time.

RESULTS AND DISCUSSION

Table 2 contains the details of the experiments performed. The shock-velocities were calculated using the transittime measured between half-stress points on the rising stress profiles. This avoids complications associated withthe ramping nature of the stress profiles in G2 and minimizes uncertainty. Particle velocities were obtained usingthe impedance matching method discussed above, whereas the longitudinal stress was inferred using the simple

jump condition (eq. 1).

Fig. 5 shows the gauge traces obtained for 0% and 22% saturated sand in PMMA cells at 919 m s-1and 955 m s-1respectively.The trace from G1 for the dry sand rises to the PMMA on PMMA state (state A) and then releases tostate B, which lies on the sand Hugoniot. The PMMA on PMMA level obtained agrees with the values expectedwithin the experimental accuracy. G2 is observed to rise to a stress above that of the release of G1 due to the

reload from the higher impedance PMMA rear anvil. The reload of the G1 after about 3 s is to a level consistentwith that in the rear gauge. The time of arrival of this reload would enable the shock-velocity in the compressedstate to be determined if the density of the previously shocked material was known. This calculation is notundertaken but the traces would provide good validation for any compaction model. It should also be pointed outthat the release level observed in G1 will be subject to a small degree of hysterisis. This has not been taken intoaccount in the presented stress trace, and would act to further lower the observed stress.

A

B

O V

Stress

Particle Velocity

Flyer Hugoniot

AnvilHugoniot

Slope = 0Us

Sand Hugoniot

C

ShockedSand

Hugoniot


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Shot SaturationH20 % mass

AnvilMaterial

Impact Velocity(km s

-1) 0.5%

Shock Velocity(km s

-1) 5%

Particle Velocity(km s

-1) 5%

LongitudinalStress (GPa) 7%

1 0% PMMA 0.499 1.08 0.34 0.53

2 0% PMMA 0.919 1.56 0.58 1.28

3 0% PMMA 0.915 1.33 0.60 1.14

4 0% PMMA 0.915 1.56 0.57 1.28

5 0% PMMA 0.921 1.54 0.58 1.28

6 0% Cu 0.494 1.20 0.47 0.81

7 0% Cu 0.851 1.80 0.79 2.05

8 10% PMMA 0.499 0.99 0.34 0.52

9 10% PMMA 0.925 1.43 0.58 1.27

10 10% Cu 0.494 1.39 0.47 0.99

11 10% Cu 0.811 1.97 0.75 2.25

12 20% PMMA 0.497 0.73 0.29 1.42

13 20% PMMA 0.904 1.81 0.44 2.25

14 20% Cu 0.494 1.60 0.45 1.97

15 20% Cu 0.805 3.47 0.71 2.70

16 22% PMMA 0.499 1.74 0.26 0.84

17 22% PMMA 0.955 2.29 0.46 1.96

18 22% Cu 0.502 2.57 0.44 2.01

19 22% Cu 0.911 4.14 0.76 5.76

Table 2. Summary of the experiments performed. There is a 5% uncertainty in the measured values for shock-velocity and

particle-velocity and 7% in calculated longitudinal stress.

-0.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5

G1 Dry, 1.52 g cm-3

, 919 m s-1

G2 Dry, 1.52 g cm-3

, 919 m s-1

G2 22% sat., 1.84 g cm-3

, 955 m s-1

Long

itu

din

als

tress

(GPa

)

Time (s)

G1 22% sat., 1.84 g cm-3

, 955 m s-1

T

-5

0

5

10

15

20

25

51 52 53 54 55 56 57

Gauge 1 Gauge 2

Longitudin

alstress(GPa)

Time (s)

Cu on Cu

release

T

Figure 5.Gauge traces obtained for 0% and 22% saturated sand in Figure 6. Gauge traces obtained for dry sand in a

PMMA cells at 919 m s-1

and 955 m s-1

respectively. copper cell at 851 m s-1

.

The G1 trace in Fig. 5 for the 22% saturated sand is observed to rise to the PMMA on PMMA level but is thenobserved to rise still further in stress when the reload from the higher-impedance saturated sand arrives at the G1location. The transit time through the sand bed (T) is observed to be significantly less for the 22% saturatedsand than the dry sand. This translates to a significantly higher shock-velocity. A slight relaxation in stress (2-5%)approximately 0.75 s after the initial peak value occurs in all the sand saturations which may be due to thefracture of the sand grains. However, this is not significant when compared with the experimental stressuncertainty.

Fig. 6 shows gauge traces from an experiment on dry sand using copper anvils. Again the stress is observed torise to the copper on copper level and then release to a level indicative of the Hugoniot of the sand, i.e. state B.


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Hysterisis effects will be more significant in the copper cells as the gauge undergoes significantly more workhardening before release. G2 is observed to rise to a stress significantly above the release in G1 as aconsequence of the reload of the sand sample by the higher impedance rear copper anvil. The stress is observedto ring-up as the sample is reloaded by sequential reflections between the copper anvils. Some of the tracesrecovered using the copper anvils demonstrated signal oscillations because of the capacitive linkage[15]. It hassince been established that this effect can be reduced by an extra 25 m mylar sheet insulation surrounding thegauge package. This will be used in future work, though it should be noted this increases the gauge packagethickness to ~ 200 m greatly reducing the effective response time due to the stress having to ring-up in the

gauge package. These signal oscillations resulted in the traces only being useful for time of arrival data and noreliable release stress data can be ascertained.

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8

22% sat. 1.84 g cm-3

,

Us = 0.32 + 4.92 Up

20% sat. 1.81gcm-3

,

Us = 0.71 + 2.90 Up

10% sat. 1.53 g cm-3

Us = 0.23 + 2.26 Up

Dry 1.43 g cm-3

,

Us = 0.53 + 1.64 Up

Shock

Velocity(km

s-1)

Particle Velocity (km s-1

)

HP

0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8

22% sat. 1.84 g cm-3

20% sat. 1.81 g cm-3

Dry 1.43 g cm-3

Dianov et al [1], 23% sat. 1.93 g cm-3

Dianov et al [1], dry 1.52 g cm-3

Longitu

dina

lStress

(GPa

)

Particle Velocity (km s-1

) Figure 7.Shock-velocity dependence on particle-velocity Figure 8.Stress dependence on particle-velocity

Fig. 7 shows the measured Hugoniot data in shock-velocity particle-velocity space and Fig. 8 in the stressparticle-velocity space. Fig. 9 also depicts fits to data by Dianov et al[3] for a sands of similar particle size, water

saturation and density (solid lines). Their data was obtained in an analogous manner to ours by measurement ofshock-velocity and application of a simple conservation equation. Simple least square linear fits have beenapplied to the data. The constants and correlation coefficients indicating the quality of fit obtained are presentedin table 1. The data for the 10% saturated sand lies close to that of the dry sand and has been omitted from Fig. 8for clarity. The values obtained for the linear coefficients are heavily dependent on the single high-pressure,high-particle velocity points labelled HP in Fig. 7. More work is required to reduce this dependence; however, theagreement with the published data gives confidence in the results. We would expect that the shock-velocityparticle-velocity dependence would be non-linear for such a porous system. However, we consider the simplelinear fits presented to be adequately representative of the data over the investigated range of particle-velocitiesgiven the small number of points.

The most striking point of interest is that low water saturation (10%) does not significantly effect the shockresponse, although at higher water saturations the measured shock velocity is heavily influenced by the degree ofsaturation. The 10% saturated data appears to lie very closely to that of the dry sand data. At these lowsaturation levels the water presence in the voids is obviously insufficient to modify stress transmission. Thestress is still predominantly transmitted through contact points between grains. There is a marked effect of movingfrom 20 to 22 % saturation. However, this again should be treated with some scepticism until more research canbe performed to substantiate this. The 22% saturated material has a density 1840 kg m-3 which is stillsubstantially lower than that of the theoretical maximum attainable for this saturation 1950 kg m -3. Therefore,there are still a significant number of voids containing air. The presence of air in the voids will significantlyinfluence the compaction process and should be included in any modelling undertaken. The water acts tohomogenise the material, allowing stress to be transmitted though the water filled voids. This is reflected by asignificant increase in shock-velocity when compared with the dry sand for a given input stress.


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The stress data for state B obtained from the release levels in G1 have not been presented here. It is hoped thatcomparison of these values with those inferred from the hydrodynamic equation (eq. 1) will give a usefulindication of the strength of the sand. It is likely to demonstrate that the simple jump condition (eq. 1) used tocalculate the stress values presented in Fig. 8 is a poor approximation. This will be investigated as part of the ongoing research.

CONCLUSIONS

The Hugoniot curves for quartz sand with varying water saturation have been obtained. At low water saturation(10%) the shock response was found to be similar to that of the dry sand. However, at higher water saturations(20% and 22%) the degree of saturation was found to have a significant effect on the measured shock-velocity.Future work will focus on analysis of data which may provide a direct measurement of the stress in the sand andimprove the population of the Hugoniot obtained.

ACKNOWLEDGEMENTS

This research has been supported by QinetiQ plc and the UK Ministry of Defence (MoD). The authors would liketo thank D. Johnson and R. Flaxman of the Cavendish Workshop for technical assistance and H. Czerski for theparticle size analysis. This research forms part of a larger study including DSTL, OinetiQ plc, MoD, Imperial

College London and Sheffield University.

REFERENCES

1. Graham, R.A., Comments on shock-compression science in highly porous solids, in High-Pressure ShockCompression of Solids IV: Response of Highly Porous Solids to Shock Loading, L. Davison, Y. Horie, and M.Shahinpoor, Editors. 1997, Springer: New York. p. 1-21.

2. Herrmann, W., Constitutive equation for the dynamic compaction of ductile porous materials.J. Appl. Phys., 1969. 40:p. 2490-2499.

3. Dianov, M.D., et al., Shock compressibility of dry and water-saturated sand.Sov. Tech. Phys. Letts, 1976. 2: p. 207-208.

4. Resnyansky, A.D. and N.K. Bourne, Shock compression of dry and hydrated sand, in Shock Compression ofCondensed Matter - 2003, M.D. Furnish, Y.M. Gupta, and J.W. Forbes, Editors. 2004, American Institute of Physics:Melville NY. p. 1474-1477.

5. Hiltl, M., et al., Dynamic response of Berea sandstone shock-loaded under dry, wet and water-pressurized conditions,

in Proc. Int. Conf. on High Pressure Science and Technology (AIRAPT-17), M.H. Manghnani, W.J. Nellis, and M.F.Nicol, Editors. 2000, Universities Press (India) Ltd.: Hyderguda, Hyderabad, India. p. 245-248.

6. Hiltl, M., et al., Shock recovery experiments on sandstone under dry and water-saturated conditions, in ShockCompression of Condensed Matter - 1999, M.D. Furnish, L.C. Chhabildas, and R.S. Hixson, Editors. 2000, AmericanInstitute of Physics: Melville, New York. p. 1251-1254.

7. Resnyansky, A.D. and N.K. Bourne, Shock-wave compression of a porous material.J. Appl. Phys., 2004. 95: p.1760-1769.

8. Resnyansky, A.D., N.K. Bourne, and J.C.F. Millett, Experiment and theory for the characterization of porousmaterials, in Shock Compression of Condensed Matter - 2001, M.D. Furnish, N.N. Thadhani, and Y. Horie, Editors.2002, American Institute of Physics: Melville, NY. p. 717-720.

9. Tsembelis, K., et al., The behavior of sand under shock wave loading: Experiments and simulations, in Behaviour ofMaterials at High Strain Rates: Numerical Modelling, F.G. Benitez, Editor. 2002, DYMAT: Saint-Louis, France. p. 193-203.

10. Marsh, S.P., LASL Shock Hugoniot Data. 1980, Berkeley, California: University of California Press.11. Bourne, N.K., et al., Design and construction of the UK plate impact facility.Meas. Sci. Technol., 1995. 6: p. 1462-

1470.12. Rosenberg, Z., D. Yaziv, and Y. Partom, Calibration of foil-like manganin gauges in planar shock wave experiments.

J. Appl. Phys., 1980. 51: p. 3702-3705.13. Yaziv, D., Z. Rosenberg, and Y. Partom, Release wave calibration of manganin gauges.J. Appl. Phys., 1980. 51: p.

6055-6057.14. Linde, R.K. and D.N. Schmidt, Shock propagation in nonreactive porous solids.J. Appl. Phys., 1966. 37: p. 3259-

3271.15. Rosenberg, Z., On the source of the resistive hysteresis in dynamically loaded piezoresistive gauges.J. Phys. D:

Appl. Phys., 1987. 20: p. 812-813.

the behavior of water saturated sand under shock loading(1)

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