Propagation of shock waves in dry and wet sandstone:Experimental observations,theoretical analysis and meso-scale modeling

Chung Liu,Yng Wu,Xin-feng Zhng,*,Ji-jie Deng,Chen-yng Xu,Wei Xiong,Meng-ting Tn

aSchool of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing,Xiaolingwei 200,Nanjing,China

bNO.208 Reseach Institute of China Ordnance Industries,Beijing,China

Keywords:Dynamic impact Shock wave Meso-scale simulation Sandstone

ABSTRACT Methods of experimental observations,theoretical analysis and meso-scale modeling were used to study the propagation processes of shock waves in dry and wet sandstone under dynamic impact in this paper.According to the results from the dynamic impact experiments with velocity of 0.2-0.5 km/s,it was found that the velocity of shock wave increases linearly with water content.Additionally,the velocity of the shock wave in the sandstone showed a linearly increased regularity with the increasement of the impact velocity,which was proved by theory in this paper.Furthermore,meso-scale simulation models were performed and the simulation results showed that sandstone's porosity reduced the shock waves velocity compared to nonporous materials.Pore space filled with water counteracts the effects of porosity,resulted in larger shock wave velocity.

1.Introduction

Porosity and water content are typical properties for sandstones of the uppercrust of Earth such as sandstone,which is comprised of one or more mineral composition with a certain texture and structure of aggregates.Sandstone structurally has a lot of defects which makes it classified as heterogeneous,discontinuous and anisotropic.And it is the same with numerous planetary.Planetary materials have high amount of empty pore space and porosities of some of them up to 75%(Britt et al.,2002[1]),the water content are deferent between planets.The analysis of shock waves propagation into wet and dry porous materials is necessary in order to have a better understanding of dynamic destruction processes on these types of planetary materials.Thereby we can have a clearer insights about the mechanisms of subsurface damage and effect of porosity and water content on sandstone fracture and deformation.

For a better understanding of the multiple processes occurring in meteorite impacts,the MEMIN(Multidisciplinary Experimental and Modeling Impact Research Network)(Poelchau et al.,2013[2],Hoerth et al.,2013[3],Sommer et al.,2013[4],Dufresne et al.,2013[5],Güldemeister et al.,2013[6],Buhl et al.,2013[7])apply different methods,in particular,studying the natural craters and performing laboratory experiments and numerical simulations.They analyze the cratering shape,ejecta cloud and propagation of shock waves of wet and dry porous materials.Impact cratering experiments were carried out in porous sandstones which showed that pore with have great of influence for shock wave velocity and cratering volume(Kenkmann et al.,2011[8]).Hypervelocity impacts on dry and wet sandstone were studied by using meso-scale simulations to understand the influence of porosity on the mechanical behavior of sandstone(Durr et al.,2013[9]).Baldwin et al.(2007[10])studied the macroscopic response of sandstone with different microscopic characteristics under hypervelocity impact by scaling impact cratering experiments and determined give the equation of state.Buhl et al.(2013[11])investigated the particle size distribution and strain rate attenuation in hypervelocity impact and shock recovery experiments.Kirk et al.(2014[12])studied the Hugoniot of two geological materials,namely Lake Quarry Granite and Gosford Sandstone by a series of plate impact experiments using a 50.8 mm smooth bore single stage light gas gun.Miljkovic et al.(2007[13])combined sandstone flyer plate impact test data with high pressure quartz data to produce a synthetic Hugoniot.Chapman et al.(2006[14])performed a series of plate impact experiments on quartz sand of 230μm average grain size,at various levels of water saturation to obtain Hugoniot data,and high levels of water saturation were found to strongly influence the Hugoniot.Wang et al.(2010[15])performed impact compressive experiments on dry and wet sandstone conducted with modified Ф75 mm Split Hopkinson Pressure Bar(SHPB)apparatus;they found that water content can influence the damage patterns of sandstone and the impact damage of dry sandstone is more severe than that of wet sandstone.Ju et al.(2009[16])and Yu et al.(2011[17])studied the porous media stresswave propagation and change of the internal pores by SHPB shock compression tests and CT scanning electron microscope.Lou(1994[18])analyzed the dynamic fracture behavior of dry and waterlogged granites by SHPB experiments.Luo et al.(2012[19])presented relationship between macroscopic and meso-scale mechanical parameters of in homogenous sandstone material by numerical simulation.

Apparently,the presence of water affects the dynamic damage characteristics,such as shock wave propagation and attenuation.In this article,We focused on quantifying the effects of dryness and wetness on shock wave propagation.And dynamic experiments were carried out to have a better understand of the deformation mechanisms associated with dry and wet sandstone.Also,based on a mixture of the superposition principle and the equation state of the porous material,theoretical model was established which can reflect the Hugoniot curve of porosity and pore space saturation of sandstones.Based on the electron micrograph of meso-structure of typical sandstone materials,simulation models of compressive processes of sandstone materials were conducted in meso-scale level with AUTODYN@software.Also,the influences of different porosity and water content on the impact compression properties of sandstone materials were studied by meso-scale simulation models built in this article.Finally,some interesting conclusions about the effect of microscopic model on shock wave velocity in rocks are obtained through experiments,theoretical and simulation analysis.

2.Experiments

2.1.Sample preparation

In order to obtain the influence of water content ratio properties on shock wave propagation,Yellow Sandstones impact Experiments were carried out.The bulk density of the Yellow Sandstone was 2.20±0.04g⋅cm-3,which was determined by scaling the weights and volumes of dried sandstone samples.Additionally,the porosities of the sandstones were calculated for six dry samples with an average value of 20%.

In order to reduce the influence of sparse waves at the boundary on the Yellow Sandstone sample,the sample size was set asФ 50 mm×8mm.The photographs of the Yellow sandstone samples are shown in Fig.1.The preparation process of samples is described as follows:

(1)Preparation for dry Yellow Sandstone samples.The initial Yellow Sandstone samples were placed in the electric thermostatic drying oven at a constant temperature of 40-60oC for 48 h.The weights of the samples M1were measured after drying,which are listed in Table 1.

(2)Preparation for water saturated Yellow Sandstone samples.Part of dry sandstones were saturated in a chamber with water for two weeks.During this period,air bubbles were released from the water and the water saturations reached approximately to80%.The photograph of the water saturated Yellow Sandstone is shown in Fig.2.The weights M2,diameters d,thickness h,as well as water saturations were listed in Table 1.

2.2.Launcher and flyer plates

The sabot,with a shear ring at one end to control the initial velocity of the flyer plate,was made of aluminum 2A12,as shown in Fig.3.To eliminate the disturbance of the reflected waves produced in the impact process,the head portion closed to the flyer plate in the sabot was hollow.Furthermore,copper,with density of 8.92g cm-3,was selected as the material of flyer plates.And the accelerator in the experiments is shown in Fig.4.

2.3.Experiments components

Table 1 Characteristics of Yellow Sandstone samples.

The PVDF piezoelectric film sensors with insulating treatment were pasted on the center surfaces of the sample.Also cover plates were designed in the test components,in order that we can obtain accurate and stable shock wave data,as shown in Fig.5.The cover plates can bring the PVDF sensors into close contact with the sandstone samples and offer help to obtain accurate shock wave signals.Additionally,sixteen discharge holes were designed on the connection between the nylon shell and the barrel to avoid unexpected trigger of the piezoelectric sensors by high pressure gas released from the barrel.

3.Theoretical analysis

Sandstone can be regarded as a substance made of three media with each having initial density and moisture.The initial density of the sandstone is given by:

The initial volume ratio is determined as follows:

Theoretical analysis is mainly based on the following assumptions:

(1)The three medium in the sandstone material have the same pressure state and particle velocity,and solid particles in the model are uniformly defined as SiO2.

(2)In the case of high-velocity impact,the inter granular cementation pattern of sandstone is negligible.

(3)The components of sandstone material are homogeneous and isotropic.The distribution of the material in the pores is considered similar in all directions.

If material shock velocity USis known as a function of particle velocity UPgiven by:

The porous material equation of state(Afanas et al.,2002[20])can be expressed as:

where η =1-ρm0v/α.(vm，pm)is a variable shock adiabatic curve in sandstone material(Afanas et al.,2002[20])and can be expressed as:

where m1=v1ρ1，0/ρ0and m3=v3ρ3，0/ρ0.Due to the existence of mixing free energy in mixtures,Eq.(5)cannot be solved directly.Therefore,the equation of state(EOS)of mixture is difficult to be obtained without a simplification.The mass average method(Tang et al.,2008)is used to simplify the equation of state of the mixture.The superposition principle was used to calculate the material parameters of shock wave under the impact load.

Assuming that there are n components in material,the ratio of the mixture volume and internal energy in the superposition principle are given respectively by(Tang et al.,1999[21]):

Therefore,

Particle velocity Upican be written as:

Combining Eq.(6),Eq.(9)can be rewritten as:

Finally,the particle velocity can be derived as:

Shock wave velocity of each component USican be written as:

Based on Eqs.(6)-(12)the relationship of shock wave can be derived as:

Eqs.(6)-(12)are used to determine basic parameters of the shock wave,based on the mass average method and the principle of superposition.The shock adiabatic relationship of mixture will be determined if relationship of USto UPis obtained.

4.Numerical simulaion

4.1.Meso-scale model

Finite element dynamic analysis software AUTODYN@was used for meso-scale studies.To simulate the impact processes in solid materials,models were modified to include particle morphology,porosity and water.Meso-scale image was obtained by scanning electron microscopy(SEM).The sample material for SEM scanning is mostly beige but streaky brownish,well-sorted sandstone,which shows a quartz content of approximately 72vol%,along with approximate porosity of 20 vol%porosity and an average particle size of about 100±25μm.The SEM photograph of sandstone with different sizes is shown in Fig.6(Kowitz et al.,2013[26]).The model was established by SEM images,and it was mainly reflected in the microscopic particles of irregular shape,size,distribution and porosity.

Due to the irregular nature of sandstone particles,a geometric model of sandstone material in meso-scale was established based on the following steps: first of all meso-structure photograph was obtained by using scanning electron microscopy(SEM)to observe the meso-structure of sandstone material,the vectorization of meso-structure photograph was then carried out to define the sandstone particles were as an irregular oval,and then the vector graphics were improved manually(Fig.6(d)),which can reflect the distribution law, finally,the geometric model of meso-structure of sandstone material was obtained.Several factors were simplified,in numerical simulations so that the model can reflect the mesostructure characteristics effectively,described as follows:

(1)The emphases of present research was to investigate the influence of porosity on the impact performance and the effect of the cementing form of grains was neglected.

(2)The sandstone particle material in the model is uniformly defined as SiO2.

(3)For the dry sandstone,empty spaces between particles are considered as porosity,as shown in Fig.7.The point contact and line contact exist between certain particles.According to the area of porosity,the corresponding number of particles are filled randomly with corresponding area.

(4)In the meso-scale model of wet sandstones,the emptyspaces between particles was filled with water where the particles and water are in direct contact.In this research,the porosities of 10%and 20%of sandstone containing 50%water and saturated water(100%water)are generated respectively as is shown in Fig.8.Compared with the dry sandstone,the pores in wet sandstones are partially or completely replaced by water.

Material model boundaryconditions imposed in the simulations are as follows:

(1)A rigid wall with a constant initial velocity is created.

(2)Non-impact interface was used for establishing the Euler out flow boundary conditions,which ensure the free flow of the shock wave at the boundary surface,and the wave reflection does not occur.

4.2.Material model and parameters

The equation of state and constitutive relationship used in the numerical analysis have great influences on mechanical properties of the material.After comparing recent research results,Burgers Rheological constitutive model(Wang et al.,2012[22])was used to simulate the impact of SiO2compression process in this paper:

Mie-Gruneisen equation of state and the P-αmodel were used in this paper(Borg et al.,2006[23]).Material equation state of SiO2can be expressed as:

Material model parameters for sandstone are presented in Table 2(Trunin,2005[24]).

5.Results

5.1.The dynamic impact experiment results

Dynamic impact experiments on dry sandstone as well as water saturated were carried out.Two PVDF piezoelectric film sensor is connected with the two-channel oscilloscope to capture the voltage signal corresponding to the shock wave propagation in sandstone specimen.The typical voltage-time signal as the effective shock wave propagation in the sandstone was shown in Fig.9.

The shock wave velocity USis calculated as:

whereΔt=t1-t2is the time duration for shock wave propagation between t1and t2instances.Based on the described method,physical parameters of dry and wet sandstone in the impact compression process are determined,as presented in Table 3.(see Table 4).

In the experiment researches of this article,the shock wave propagate velocity measurement results of water saturated percentages are showed to be 90%,75%and 81%,which shown that the water in the sandstone has a significant effect on shock wave propagation.It can be concluded that from the experiment results:(1)When compared the fourth,the fifth,the sixth experimental results,it can be found that under the same water content,the velocity of the shock wave in the sandstone showed a linearly increases with the increase of the impact velocity(from 1228m/s to 1750 m/s).(2)There is an obvious effect of water content on sandstone materials shock response.We can find that the shock wave velocity in dry rock is smaller than it in water-bearing rock.The addition of water increases the propagation velocity of shock wave in sandstone material.(3)Comparing the first and second experimental results with the forth one,it's shown that the shock wave velocity(1955 m/s)of the sandstone of 90%water is greater than the shock wave velocity(1800 m/s)of 75%water under the same impact velocity.Additionally,The shock wave velocity of the dry sandstone with a value of 1228m/s and much smaller than that of water saturated sandstone.The comparison shows that the velocity of shock wave increases linearly with the increase of water content.Also the same results can be obtained by analyzing the results of the third and the sixth experimental.The reason is that the porosity of the rock reduces the velocity of the shock wave.Theincrease in water content results in the shock wave attenuation rate decrease.When the porosity in the rock are filled with water,it will be more conducive to the propagation of shock waves.

Table 2 Parameters of sandstone material.

5.2.Theoretical calculations and numerical simulation results

Dry sandstone can be considered as a mixture of quartz grains and air,and 20%dry sandstone porosity,which means the air take 20%volume of the mixture,the material parameters as presented in Table 2.The comparison between the available experimental data[5,6]and calculation and simulation results is shown in Fig.10.

In low impact velocity regime,due to the presence of cementation between the particles in the sandstone material,the particles and porosity are not easily crashed or collapsed,and since the calculations and simulation results ignore the effect of interparticle cementation,the experimental results are larger than the theoretical calculation.In high impact velocity regime,there are intense collision between the particles,and cementation is negligible,therefore,the results of experiments,theoretical calculations and simulations agree well with each other,showing almost a linear relationship.

For further investigation of the dry sandstone impact response of different porosities,and exploring the influence of porosity on the velocity of the shock wave,shock compression properties of 10%and 20%porosity sandstone were calculated as shown in Fig.11.The 10%and 20%porosity curves in high-velocity region are linear and parallel to each other.But for the same impact conditions,with the increase in porosity,the shock wave attenuation rate increases as shown in Fig.11.Increase in porosity of the sandstone,results in local gap increases between the particles.The presence of voids between the particles affect the interaction of particles by the process of shock wave propagation in sandstones,so that the shock wave energy is largely consumed and scattered through the pore deformation and crush,therefore affecting the propagation of shock waves;therefore,the higher the porosity,the larger the shock wave attenuation rate and the lower the velocity of the shock wave.

Comparison between the dry and wet sandstone Hugoniot parameters is shown in Fig.12.It can be seen that the curve of wet sandstone material is higher than the dry sandstone,implying that shock wave propagation velocity attenuation rate is smaller than in wet sandstone for the same impact conditions.The curve of 90%saturated sandstone material was significantly higher than that of the 50%wet sandstone,implying that the higher moisture content results in smaller rate of shock wave attenuation for the same porosity content.In the dry sandstone,there exists considerable porosity,which will affect the interaction between the particles,there by affecting the propagation of shock waves.Fig.13 shows that the shock wave propagation velocity is significantly larger when the pores are filled with water.

Table 3 Sandstone material dynamic impact compression test results.

Table 4 Hugoniot parameters obtained from meso-scale simulations and experimental.

Figs.12 and 13 show that with the same water content and different porosity,the US-UPdata increase with the increase in porosity.This implies that for the sandstone with the same water content,increase of porosity results in increase of shock wave attenuation rate increase and decrease of shock wave velocity.The main reasons are as follows:The pores in the rock will reduce the velocity of the shock wave.What is more,compaction of pores in rock material will consume the energy of shock wave.For aqueous sandstone under the same porosity,the higher water content results in the smaller shock wave attenuation rate.The water filling the pores can buffer energy dissipation due to pore collapsing,so that the shock wave propagation is faster in sandstone material.

6.Conclusions

This article studies the effects of the pores and water contents on the dynamic behavior of sandstone material under impact load,through combination of experimental observations,theoretical calculations and numerical simulation.Sandstone material impact compression experiments were performed,using the high pressure chamber launch platform to accelerate the flyer plate and shock compression of sandstone specimens at different impact velocity.Data obtained from the dynamic impact experiments on dry and wet porous sandstone material were used to analyze the shock wave propagation of dry and wet sandstones.Also,the theoretical model were used to describe the dynamic response characteristics of sandstone material.Combining the equation of state of the porous material with the superposition principle,the impacting compression property was discussed and the Hugoniot curve for sandstones of different porosity and water contents were determined.The calculation result of theoretical models and the experiment data were in good agreement.At last,based on the electron micrograph material meso-scale structure,simulation models were built with AUTODYN@software to study the influence of meso-scale characteristics on the macroscopic mechanical properties.The Hugoniot parameters are found from the simulation results agree well with theoretical model results and experiment results.The main conclusions are as follows:

(1)Under the same water content,the velocity of the shock wave in the sandstone showed a linearly increases with the increase of the impact velocity.

(2)There is an obvious effect of water content on sandstone materials shock response.Compared to dry sandstone,the addition of water increases the propagation velocity of shock wave in sandstone material.

(3)Fordry sandstone,higher porosity results in the higher shock wave attenuation rate and smaller propagation velocity in the material.

(4)For aqueous sandstone at the same porosity,the increase in water content results in the shock wave attenuation rate decrease and shock wave velocity linearly increases.

Acknowledgments

This project is Supported by NSAF(Grant No.U1730101)and the National Program for Support of Top-notch Young Professionals of China(2014)and the Funding of Science and Technology on Transient Impact Laboratory(Grant No.61426060101162606001)and the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX18_0460).