International Journal of Rock Mechanics & Mining Sciences 88 (2016) 23–28

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International Journal ofRock Mechanics & Mining Sciences

http://d1365-16

n CorrE-m

journal homepage: www.elsevier.com/locate/ijrmms

Effect of water saturation and loading rate on the mechanicalproperties of Red and Buff Sandstones

Eunhye Kim a,n, Hossein Changani b

a Department of Mining Engineering and Center for Underground Construction and Tunneling, Colorado School of Mines, CO, USAb Department of Mining Engineering, University of Utah, UT, USA

a r t i c l e i n f o

Article history:Received 29 August 2015Received in revised form30 April 2016Accepted 7 July 2016Available online 22 July 2016

Keywords:Water saturation effectLoading rate effectPorosity effectDynamic mechanical strengthSplit Hopkinson Pressure Bar (SHPB)

1. Introduction

A number of different parameters influence the mechanicalbehavior of geomaterials, and understanding the mechanical be-havior of geomaterials is important for not only academic researchbut also various industrial applications.1 As typical geomaterialsare heterogeneous in pore size and are hydrated to various degreesin nature, understanding the fracture behavior of geomaterials ofdifferent porosities and water contents under different loadingconditions is crucial to understanding the role that geomaterialcharacteristics play in fracturing processes.2–4 For example, it isimportant to know how the porosities and water contents ofgeomaterials influences how much energy is needed to disruptthem. In addition, as the rate of loading has a significant effect onrock fragmentation processes, including drilling, blasting, hy-draulic fracturing, crushing, and grinding, and on failure modes,including rock bursting, impact failure, and others,5 informationabout the mechanical properties and behaviors of geomaterials atdifferent loading rates can significantly affect the safety of un-derground construction, the optimum energy cost, the pro-ductivity of excavation and energy extraction, and the design ofimpact-resistant engineered infrastructures and constructions.6–9

In the oil and gas industry, the main task of reservoir engineers is

x.doi.org/10.1016/j.ijrmms.2016.07.00509/& 2016 Elsevier Ltd. All rights reserved.

esponding author.ail address: ekim1@mines.edu (E. Kim).

to increase the productivity of wells. Induced hydraulic fracturingis a technique that is typically used to generate fractures in rockreservoirs. At the beginning of this process, a device known as aperforating gun is lowered into a well to a designated location inthe reservoir rock, and a charge is fired to perforate the steelcasing, cement, and rock formation. This perforation stage createssmall cracks or fractures in the rock. A mixture of water, sand, andchemicals is then injected into the wellbore under high pressure tokeep the fractures open. In all steps of this process, knowledge ofthe effects of porosity and water content on the dynamic behaviorof the reservoir rock may be useful in predicting the geomaterialproperties and behaviors.

For many years, many researchers have studied the mechanicalbehavior of various types of geomaterials under different condi-tions. While a considerable amount of work has been done on theeffect of porosity on the dynamic fracture mechanics of metals,composites, and ceramics,10 only a very limited amount of workhas been done on geomaterials with different porosities underdynamic loading conditions.11,12 As many engineers and scientistsstudying rock mechanics thought that the force applied on a rockbreaks a rock sample with the similar mechanism in static anddynamic loading conditions, many tests have been performedunder static loading conditions. However, some researchers re-ported that there were significantly different rock failure me-chanisms between static and dynamic loading tests.13–16 Ad-ditionally, sometimes it is not easy to obtain relevant rock sampleshaving similar mineral compositions with remarkably different

Table 1Porosities of Red and Buff sandstones estimated from weight differences betweendry and fully saturated samples and the 300-point count method using magentaepoxy-stained samples.

Type Porosity estimated fromweight difference (n¼40)

Porosity estimated from 300-point count method

Red sandstone 5.5% (70.03) 4.7%Buff sandstone 22.7% (70.04) 18.0%

E. Kim, H. Changani / International Journal of Rock Mechanics & Mining Sciences 88 (2016) 23–2824

porosities essential to get accurate rock porosity effect on me-chanical properties and behaviors.

In this study, to fill in some of the gaps that exist in knowledgeof the effects of porosity and water content on the mechanicalstrength of geomaterials, we examined and compared the com-pressive strength, tensile strength, and Young's modulus of dryand saturated Red and Buff sandstones under static, fast, and dy-namic loading conditions. Our results provide insights into howthe mechanical behaviors and properties of geomaterials are af-fected by the water content and loading rate.

2. Materials and methods

2.1. Sample preparation

Red (smaller grain size, 4.7–5.5% porosity) and Buff (larger grainsize, 18.0–22.7% porosity) sandstone samples with L (length)/D(diameter) ratio of �0.4 were prepared for tensile tests and withL/D ratio of �2 for compressive tests using coring, cutting andgrinding machines. The Red and Buff sandstone samples weresoaked in water for 48 h in a vacuum chamber (25 cm Hg). Half ofthe fully saturated samples were placed in a dry oven at 105 °C for48 h to prepare dry sandstone samples.

2.2. Porosity measurements

To estimate porosity, thin section analyses of Red and Buffsandstone samples were performed by TerraTek (Fig. 1). Thesandstone samples were impregnated with a low-viscosity fluor-escent red-dye epoxy resin under a vacuum to highlight the por-osity, mounted on standard (24 mm�46 mm) thin section slides,and ground to a 30-mm thickness. The thin-sectioned sampleswere stained with a mixture of potassium ferricyanide and Ali-zarin Red and digitally imaged under plane- and cross-polarizedlight using a Nikon polarizing binocular microscope equipped witha Spot Insight digital camera. Void areas stained with pink colorwere regarded as pore spaces and used to evaluate the porosity ofthe Red and Buff sandstone samples.

In addition, the porosities of Red and Buff sandstones wereestimated with the weight difference between the dry and satu-rated samples (Table 1). The porosity of rock is the ratio of theporous volume of the rock occupied by air and water divided bythe total volume, expressed as follows:

Fig. 1. The magenta epoxy was seen between framework grains: (A) cross-laminated R

=( + )

( + + ) ( )P

V VV V V 1

w a

w a s

where Vw is the water volume, Va is the air volume, and Vs is thevolume that the solid material occupies. The rock sample poros-ities were determined by the water saturation method suggestedby the International Society of Rock Mechanics.17

2.3. P and S wave velocity measurements

To estimate Young's modulus, the longitudinal (P wave) andtransverse (S wave) wave velocities of Red and Buff sandstonesamples were measured. P and S wave velocities are intrinsicproperties of solid materials. The ultrasonic pulse velocity tech-nique was used to measure the P and S wave velocities of the rocksamples. A frequency of 1.0 MHz was used to measure the P and Swave velocities of cylindrical rock samples with 3.175-cm and5.46-cm diameters and L/D ratio of 2.0. All samples used in thisstudy were prepared in accordance with ASTM D2845.18 The dis-tance between the two transducers, the sample's length divided bythe delay or arrival time, measured by an ultrasonic machine, gavethe corresponding wave velocity in the geomaterial specimens.The P and S wave values and calculated dynamic Young's modulusobtained were shown in Table 2. The dynamic elastic properties ofthese types of sandstones (the dynamic Young's modulus (E), bulkmodulus (K), and shear modulus (G)) were calculated as a functionof P wave velocity (Vp), the S wave velocity (Vs), and the rockdensity (ρ) using the following equations:

ρ=

( − )

( − ) ( )E

V V V

V V

3 4

2

s p s

p s

2 2 2

2 2

ρ=

( − )( )K

V V3 4

3 3p s2 2

ed sandstone and (B) cross-laminated Buff sandstone. Scale bars indicate 250 mm.

Table 2P- and S-wave measurements of Red and Buff sandstones. The values in parentheses are the Standard Errors of the Means (SEM).

Type Sample size (Diameter, cm) Number of samples P-wave velocity (m/s) S-wave velocity (m/s) Calculated Young's modulus (GPa)

Red sandstone 3. 175 (AX) 40 3977.0 (76.9) 2773.1 (77.2) 38.5 (71.1)5.45 (NX) 20 3943.5 (79.7) 2757.3 (76.5) 37.9 (70.2)

Buff sandstone 3.175 (AX) 40 2100.3 (722.2) 1436.8 (712.4) 8.9 (70.2)5.45 (NX) 20 2052.4 (727.7) 1468.8 (718.4) 8.6 (72.3)

Absorber

Gas gun

Oscilloscope

Data acquisition system

ACAmplifier

Transmitted wave Reflected wave

Incident wave

Laser module

StrikerSample

Space

Time

Incident bar Transmitted bar

Fig. 2. Schematic illustration of Split Hopkinson Pressure Bar system.

E. Kim, H. Changani / International Journal of Rock Mechanics & Mining Sciences 88 (2016) 23–28 25

ρ= ( )G V 4s2

2.4. Static and fast loading compressive tests

Static compressive strength was measured by applying a uni-axial load to a cylindrical specimen under standard conditions.Sandstone specimens with two different diameters, AX and NX,were prepared with length-to-diameter ratios of 2:1, in ac-cordance with ASTM standards. The sample diameter, as suggestedin the standard, was selected to be more than ten times themaximum grain size. Small-diameter specimens were used tocompare the corresponding static compressive strength with dy-namic strength of a similar L/D ratio. After coring samples fromrock blocks, each core was cut perpendicular to its axis at ap-proximately a 2:1 L/D ratio, and the sample ends were then grounduntil they were parallel, in accordance with ASTM D7012.19 Allstatic unconfined strength measurements were performed using aload frame equipped with an MTS Teststar IIM control system andMultipurpose Testware. For unconfined compressive strength(UCS) samples, the assigned loading rate fell within acceptablelimits (0.5–1 MPa s�1 or slightly less). With regard to the specificprocess employed for UCS testing of rock samples, this controlsystem updated all transducer values at the system rate of4096 Hz, and the axial force and displacement were added to thedata file at 2-s intervals. A failure detector was programmed foruse in the testing process. The maximum force transducer valuewas updated with a new maximum value for every increment of113.4 kg (250 lb), and then the maximum force was recorded to anoutput file along with the 2-s data stream. Fast loading compres-sive tests were performed under the same experimental condi-tions as the static compressive tests, except for the loading rate.The loading rate for the fast compressive tests was �200–250 kN s�1 whereas the rate for the static compressive tests was1.3 kN s�1.

2.5. Static loading indirect tensile tests

The indirect tensile strength of the rock samples was de-termined by the Brazilian method. In this method, the compressiveload was applied to a disk-shaped sample. As tensile strengthvalues can be affected by the geometry of rock specimen, to reducethe effects of these factors, disk specimens were prepared with

thickness-to-diameter ratio of 0.3–1.20 The tensile strength of rockwas calculated using the following equation:

σπ

= ( )P

Dt2

5t

where P is the maximum load at failure, D is the diameter of thespecimen, and t is the height or thickness of the specimen. Theloading rate used in the static tensile tests was �0.06–0.08 kN s�1.

2.6. Dynamic loading compression and indirect tensile tests usingSplit Hopkins Pressure Bar (SHBP)

Dynamic compressive tests and indirect tensile tests of dry andwater-saturated Red and Buff sandstone samples were performedwith a Split Hopkinson Pressure Bar (SHBP) (Fig. 2) as described.6

The dimensions of the samples tested under dynamic loading wereprepared with the same way used in the static compressive andtensile tests. Also, the stress calculation equations for dynamicloading tests were the same as the equations for static loading. Tomeasure the dynamic compressive and tensile strengths of thesamples, the wave transformations were recorded in a data ac-quisition system at a 10-MHz sampling rate. The striker velocitywas measured with an oscilloscope and a laser module.

Young's modulus has been used in evaluating rock deformationunder various loading conditions, of which value can be de-termined with stress–strain ratios under uniaxial load. In the ty-pical stress–strain curve for any sample, the modulus at the be-ginning of the loading cycle is low (due to crack closure andseating of the platens), and then, in the linear stress–strain part ofthe curve, the modulus becomes constant. Based on the stress–strain curves of rock samples, the Young's modulus values of dryand saturated Red and Buff sandstone samples were calculated bylinear interpolation along the linear portion of the curve.

3. Results and discussion

In this study, we examined the effects of porosity and hydrationon the mechanical strength and behavior of Red and Buff sand-stones, as these two sandstones exhibit relatively homogenousgrain and pore sizes, which are relevant to their behavior in me-chanical strength tests.6,7 To measure the porosities of the Red andBuff sandstones, we used two methods: measuring the weightdifference between dry and hydrated samples and 300-pointcounting of thin-section samples stained with magenta epoxy. Theporosity values of the Red and Buff sandstones estimated using thetwo methods were quite similar. The porosity of the Red sandstonewas 5.5% as estimated from the weight difference measurementand 4.7% as estimated from the 300-point count measurement.The corresponding porosity estimates of the Buff sandstone were22.7% and 18.0%, respectively (Table 1). These results indicate thatthe porosity of the Buff sandstone is much higher than that of theRed sandstone. The results also indicate that both the weight dif-ference method and the 300-point count measurement methodare reliable ways to estimate the porosity of sandstones.

0

50

100

150

200

250

Red sandstone Buff sandstone

Static compressive strength

DrySaturated

0

50

100

150

200

250

Red sandstone Buff sandstone

Fast compressive strength

DrySaturated

Stre

ngth

(MP

a) *

(A)

(B)

Stre

ngth

(MP

a)

*

*

*

0

100

200

300

Red sandstone Buff sandstone

Dynamic compressive strength

DrySaturated

(C)

Stre

ngth

(MP

a)

*

*

Fig. 3. Static, fast and dynamic compressive strengths of dry and saturated Red andBuff sandstones. *Po0.05; Student's two-tailed t-test (4rnr11).

Table 3Mechanical strengths of dry and water-saturated Red and Buff sandstones (units:MPa). The values in parentheses are the SEMs (4rnr11).

Experiment type Red sandstone Buff sandstone

Dry Saturated Dry Saturated

Compressive test Static 195.2(73.4)

153.6 (71.2) 74.5(71.2)

62.3 (70.8)

Fast 219.5(73.2)

170.7 (72.5) 85.8(70.6)

67.5 (71.1)

Dynamic 278.2(77.7)

221.7 (76.2) 173.2(712.5)

136.8 (73.9)

Tensile test Static 26.6(70.6)

16.2 (70.5) 8.0(70.2)

5.3 (70.2)

Dynamic 97.9(72.7)

75.2 (72.3) 26.9(71.2)

21.8 (70.8)

E. Kim, H. Changani / International Journal of Rock Mechanics & Mining Sciences 88 (2016) 23–2826

3.1. Compressive strength of Red and Buff sandstones

The effects of water saturation (hydration) on the static, fast,and dynamic compressive strengths of the Red and Buff sand-stones were examined. The maximum strength (MPa) was greaterfor the dry samples than for the saturated samples, regardless ofthe porosity (Fi. 3). This confirms that water reduces the cohesionof geomaterials, resulting in a decrease in the compressivestrength (approximately 20% in this study). The Red sandstoneexhibited compressive strengths approximately 1.6–2.6 foldgreater than the Buff sandstone in both the dry and saturatedsamples under static, fast, and dynamic loading conditions. Inter-estingly, the differences in the compressive strengths of the Redand Buff sandstones decreased with increasing loading rate. Understatic and fast compressive loading, the strength of the Redsandstone was approximately 2.6 greater than that of the Buffsandstone, whereas under dynamic loading, the strength of the

Red sandstone was only 1.6 times greater. The results support theconclusion that the degree of strength increase with increasingloading rate is greater in higher-porosity geomaterials; the por-osity of the Buff sandstone is higher than that of the Red sandstone(Fig. 3, Table 3). The underlying mechanism of the higher dynamicincrease factor (DIF) with higher rock porosities is not fully un-derstood to date, but the behind mechanism can be explained asbelow. Not only the force applied to the rock is used to break therock but also the force is absorbed by the rock. The absorbed en-ergy is significantly higher in a dynamic loading than a staticloading condition. In a static loading condition, the force pre-dominately goes through the weak points of the rock resulting inslow crack propagations whereas in a dynamic loading condition,the most force can go through the grains or solid parts of thesample along the shortest route as the applied force is typicallygreater than the grain strength, and less force passes through theweaker points of the sample. For this reason, more force is used tobreak solid grains instead of breaking the weak points of a samplein dynamic loading tests when compared with static loading tests.Thus, as more weak points exist in higher porosity samples thanlower porosity rocks, more drastic increase of DIF (the ratio ofdynamic strength to static strength) can be observed in higherporosity rocks. Our data are consistent with evidence from otherstudies that geomaterials with higher porosities display higherdynamic increase factors (DIFs). In addition, the DIFs calculated inthis study were within the range of values reported by otherresearchers.9,13,21–23 This might be caused by various rock typeshaving different mineral compositions, degrees of cementation,and grain sizes, among other mechanical and structural char-acteristics of geomaterials.

3.2. Tensile strength of Red and Buff sandstones

We also examined the static and dynamic tensile strengths ofthe Red and Buff sandstones under dry and saturated conditions toassess the effects of porosity and water content. Consistent withthe results of the compressive strength tests, the tensile strengthsof the Red and Buff sandstones were greater when dry, under bothstatic and dynamic loading, than when saturated. Intriguingly, thetensile strengths of both dry and saturated Red sandstone sampleswere approximately 3.5 fold higher than the Buff sandstonesamples (Fig. 4). These results suggest that tensile strength is moresensitive to the porosity of geomaterials, as the compressivestrength of the Red sandstone was only 1.6–2.6 times higher thanthat of the Buff sandstone. More interestingly, a more dramaticeffect of the loading rate was observed in the tensile tests of theRed and Buff sandstones than in the compressive tests. When thepercentage differences between the compressive and tensilestrengths measured under static and dynamic loading conditions

0

30

60

90

120

Red sandstone Buff sandstone

Dynamic tensile strength

Dry

Saturated

0

5

10

15

20

25

30

Red sandstone Buff sandstone

Static tensile strength

DrySaturated

Stre

ngth

(MPa

)*

(A) (B)

Stre

ngth

(Mpa

)

* *

*

Fig. 4. Static and dynamic tensile strengths of dry and saturated Red and Buff sandstones. *Po0.05; Student's two-tailed t-test (4rnr11).

0

30

60

90

120

StaticDynamic

0

100

200

300 StaticFastDynamic

Com

pres

sive

st

reng

th (M

Pa)

Dry DrySaturated SaturatedRed sandstone Buff sandstone

Tens

ile s

treng

th

(MP

a)

Dry DrySaturated SaturatedRed sandstone Buff sandstone

43

44132

120

268

364

236 311

12

11

158

Fig. 5. Static, fast and dynamic compressive strengths and static and dynamictensile strengths of dry and saturated Red and Buff sandstones. Each number abovethe error bar indicates increased percentage value of compressive (A) and tensilestrength (B) compared to the static compressive strength. *Po0.05; Student's two-tailed t-test (4rnr11).

Table 4Young's moduli of dry and water-saturated Red and Buff sandstones under com-pressive loading (units: GPa). The values in parentheses are the SEMs (4rnr11).

Experiment type Red sandstone Buff sandstone

Dry Saturated Dry Saturated

Compressive test Static 25.6(70.2)

23.4(70.4)

12.4(70.2)

11.2(70.2)

Fast 23.3(70.3)

21.7(70.3)

12.1(70.1)

11.5 (70.1)

Dynamic 192.5(714.5)

213.6(719.1)

248.8(721.3)

145.6(716.4)

E. Kim, H. Changani / International Journal of Rock Mechanics & Mining Sciences 88 (2016) 23–28 27

were compared, the increase in tensile strength with increasingloading rate was found to be much greater for both the Red andBuff sandstones than the increase in compressive strength, re-gardless of the water contents (Fig. 5, Table 3). Our data suggestthat more drastic DIFs can be obtained in tensile tests with in-creasing loading rate than in compressive tests, which providessome insight into how loading rates and different testing methodsaffect the mechanical behavior of geomaterials.

3.3. Young's modulus estimated with ultrasonic wave measurementsand compressive loading tests

The ultrasonic velocity test method is a nondestructive way tocharacterize geological core samples. This method involves pro-pagating ultrasonic compression and shear waves along thelongitudinal axis of a sample, measuring the velocity of the wavesas they travel through the specimen, and calculating the dynamicelastic properties of the specimen including Young's modulus (theelastic stiffness) (ASTM 2845). P- and S-wave velocity measure-ments were used to estimate the dynamic Young's modulus ofoven-dried specimens. We also calculated the dynamic Young'smodulus from the results of the SHPB tests (dynamic compressivetests) conducted on the same samples. As shown in Tables 2 and 4,the Young's modulus values calculated from the SHPB results were10–20 times higher than those estimated from the ultrasonic ve-locity test results. The Young's modulus estimated from ultrasonic

velocity tests was very close to the value of the Young's modulusobtained from static and fast loading tests.24 In this study, espe-cially for dry samples, the ratio for the high-porosity material (theBuff sandstone) was less than one, but that for the low-porositymaterial (the Red sandstone) was greater than one.

Also interestingly, Young's modulus of the Red and Buff sand-stones were higher for dry samples under static and fast com-pressive loading than for saturated samples. However, the Young'smodulus values under dynamic loading were not significantlydifferent for the Red sandstone, regardless of the hydration con-ditions, whereas the Young's modulus values of the Buff sandstonesamples under dynamic loading were much higher (by approxi-mately 71%) for dry conditions than for saturated conditions(Fig. 6). These results indicate that the hydration effect on Young'smodulus is enhanced by higher porosity under dynamic loadingconditions. The underlying mechanism seems to be similar to thatof more DIF increase in higher porosity rocks. In dynamic loadingtests, it seems that most force passes through the shortest route ofthe sample, whereas in static loading tests most energy goes intobreaking the weak points in the sample. When developing crackfront meets the water, the water can slow down crack propagation.Thus, as more water exists in higher porosity rocks than in lowerporosity rocks, water saturation effect on Young’s modulus isgreater with higher porosity under dynamic loading conditions. Inaddition, these results suggest that Young's modulus can be usedas a parameter in assessing the effects of porosity and hydrationon the dynamic mechanical behavior of geomaterials.

4. Conclusions

Various parameters can be used to characterize geomaterialfracture and strength, and measured mechanical properties ofrocks can differ depending on how stresses are applied. Thecompressive and tensile strengths of Red and Buff sandstonesunder static, fast, and dynamic loading conditions were measured,

0

10

20

30

Red sandstone Buff sandstone

DrySaturated

0

10

20

30

Red sandstone Buff sandstone

DrySaturated

You

ng’s

mod

ulus

(G

Pa)

*(A)

(B)

*

*

*

Static compressive

You

ng’s

mod

ulus

(G

Pa)

Fast compressive

0

100

200

300

Red sandstone Buff sandstone

DrySaturated

(C)*

You

ng’s

mod

ulus

(G

Pa)

Dynamic compressive

Fig. 6. Young's modulus of dry and saturated Red and Buff sandstones under static,fast and dynamic compressive loading. *Po0.05; Student's two-tailed t-test(4rnr11).

E. Kim, H. Changani / International Journal of Rock Mechanics & Mining Sciences 88 (2016) 23–2828

and the effects of porosity and hydration on these parameterswere examined. The main findings of this study are as follows:(1) the Red sandstone exhibited compressive and tensile strengthstwo to four times higher than the Buff sandstone under static, fast,and dynamic loading conditions; (2) the compressive and tensilestrengths of both sandstones increased with increasing loadingrate, and the effect of the loading rate on the tensile strength wasmore pronounced than the effect on the compressive strength;(3) the static, fast, and dynamic strengths of dry samples werehigher than those of saturated samples—on average, water sa-turation reduced the rock strength by approximately 20%; and(4) the Young's modulus determined from compressive loadingtest results was significantly greater for the Buff sandstone whendry than when saturated but the Young's modulus values of the

Red sandstone when dry and when saturated were not sig-nificantly different. The results of this study provide insights intohow the porosities and hydration states of geomaterials affecttheir mechanical properties and behavior at various loading rates.These insights can contribute significantly to improving safety andcost-effectiveness in geotechnical applications.

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