Deashis Das,Brijes Mishra,Neel Gupta

a RESPEC,Lexington,KY 40508,USA

b West Virginia University,Morgantown,WV 26506,USA

c RESPEC,Rapid City,SD 57703,USA

Keywords:Shale strength XRD (X-ray diffraction)SEM (scanning electron microscopy)Grain size Quartz content Grain shape

ABSTRACT Ground failure is a major contributor to fatalities in underground mines in the US.Underground coal mines in the Northern Appalachian have weak roof rock composed of shale,which is prone to failure under high horizontal stress.Understanding the relationship among strength,specimen size and rock petrographic parameters is essential for developing an effective ground control plan.Size effect studies have found that rock strength varies with specimen size.This paper attempts to understand this strength variation using three specimen sizes(254-mm,508-mm,and 762-mm).The specimen strength was measured and the major petrographic parameters affecting the strength,namely grain size,grain shape,quartz content,clay content,etc.were analyzed using X-ray diffraction (XRD) and scanning electron microscopy(SEM).The petrographic parameters were then correlated with the strength of the three differently sized specimens.The results showed that 508-mm specimen had the lowest strength.Quartz content of the 508-mm specimen was lower than that of 254-mm and 762-mm specimens.Clay content and average grain size of the 508-mm specimen were higher than those of 254-mm and 762-mm specimens.These results clearly show that grain size,quartz content and clay content contribute to strength variation observed in differently sized shale specimens.

1.Introduction

From 2000 to 2018,nearly 31% of occupational fatalities in underground mines in the US occurred due to fall of ground,making it the leading cause of fatalities in this environment (Fig.1).Cutter roof failure observed in stack rocks is a major contributor to groundfall [1].This interbedded layer of shale and sandstone makes the roof vulnerable to high horizontal stresses,ultimately resulting in groundfall.Characterization of the roof shale and understanding its strength variation with size is necessary for the development of a proper ground control plan,which in turn will reduce the occurrence of groundfall.

Literature was reviewed to understand the variation of rock strength with size.As there are limited studies on shale,therefore other rocks were studied.There has been only one size effect study conducted for shale.The study was performed by Hodgson and Cook [2] and no significant correlation of strength with size was observed.However,size effect study on other rocks showed that the strength of rock decreases with increase in the size of the specimen [3–10].

The other part of the literature study comprised of identifying the petrographic parameters affecting rock strength and understanding ways to analyze these parameters.It was found that to analyze the petrographic parameters,shale needed to be observed at micro scale.Hence,X-ray diffraction (XRD) technique was employed to analyze the compositional parameters such as quartz content and scanning electron microscopy(SEM)was employed to analyze the petrographic parameters such as grain size and grain shape.A significant amount of literature to understand petrographic parameters of different rocks and to assess the correlation of strength with these petrographic parameters was also reviewed.There has been extensive research on granite [11,12],sandstone[13–15],coal measure rocks [16–19] and shale [20].However,most of the petrographic analysis work done in shale rock,as well as other rocks were qualitative [21–23].Our research attempts to develop a method to quantitatively estimate the grain size and grain shape by developing a novel etching process suitable for shale and then visualizing the etched specimen under SEM.The complex microstructure,wide variation in grain size and softness of shale make it difficult to analyze the grains quantitatively;this paper also attempts to address this issue.

Fig.1.Number and percentage of occupational fatalities by accident class at underground mining locations,2000–2018 (Source:CDC-NIOSH).

2.Methodology

This study is divided into three major segments:

(1) Uniaxial compressive strength test:this section deals with the UCS tests performed on 254-mm,508-mm and 762-mm shale specimens.The difference in strength was noted.

(2) X-ray diffraction test:this section encompasses the XRD test on the shale specimens.The composition parameters such as quartz content,calcite content,and clay content,were obtained and the relationship of these parameters with strength of the shale specimens was observed.

(3) Scanning electron microscopy imaging:this section discusses a new method of specimen preparation focusing on quantification of grain parameters.In addition,this section contains calculation of the grain parameters,such as grain size and grain shape,which were then correlated with strength of the shale specimens.

2.1.Uniaxial compressive strength (UCS) test

To get an estimate of the strength of each shale specimen,uniaxial compressive strength tests were conducted.There were seven specimens of each size (254-mm,508-mm,and 762-mm),collected from the Marcellus shale outcrop in the New York region.UCS tests were performed on the servo-hydraulic Material Test System (MTS 440) in the Rock Mechanics Lab at West Virginia University (WVU).We followed ASTM D7012 standard to adhere to the testing requirements,which included specimen preparation,specimen size and shape restrictions and loading rate parameter.

The uniaxial compressive strength(σu)of the test specimen was calculated as follows:

where σuis the uniaxial compressive strength of the specimen tested (UCS);Pthe failure load;andAthe cross-sectional area of the specimen.

2.2.X-ray diffraction test

The UCS tests determined the strength of differently sized shale specimens.However,compositional analysis technique such as XRD showed the factors causing variation in the strength.The local geology of the Marcellus shale indicated the presence of clay in the shale rock.This necessitated preparation of powdered specimens for proper identification of clay along with other minerals.Reducing the size of the specimen particles provides random orientation and proper quantification of the clay.The clay particles in bulk specimen have a preferred orientation that makes their detection difficult [24].

For XRD powder specimen preparation,the laboratory standard of the Mineral Processing Lab of WVU was followed.For sieving,the smallest size sieve available was obtained.Ten different powdered specimens of each size of shale specimen were prepared.The following contains a brief description of the methods employed to obtain these specimens.

(1) Crushing:The intact rock specimen was placed into a jaw crusher.The two jaws of the crusher,with one jaw fixed and the other reciprocating developed the mechanical pressure on the rock.A minimal gap left between the lower ends of the two jaws allowed recovery of the crushed particles of the smallest size.

(2) Grinding:Then,the crushed specimen was placed into a ball mill,which works on the principle of impact and attrition.Impact of the balls reduces the size of the specimen.The ball mill runs on crushed rock for 20 min,reducing the particles to micron scale.

(3) Sieving:The crushed particles were sieved with a No.325 mesh (44 μm) to obtain fine particles with a size range below 44 μm.

The XRD test was run using the PANalytical X’Pert Pro X-ray Diffractometer of the WVU Shared Research Facilities and the analysis of the obtained data was performed using Highscore software.

2.3.Scanning electron microscopy

SEM imaging analysis investigated the relation between strength and the grain parameters of the differently sized shale specimens.Shale is soft and has a very complex microstructure.Several iterations were performed to visualize the grains to the maximum extent and then the grain parameters were quantified.The section below discusses the optimized specimen preparation technique and the image processing technique in detail.

2.3.1.Specimen preparation technique

It is a challenge to perform petrographic analysis on shale rock due to its complex structural heterogeneity.The range of variation of grain size is large (in some cases from micrometer to millimeter),and the presence of matrix materials makes it difficult to delineate the grain boundaries.The first step of specimen preparation was cutting the rock cores.A low speed saw cut the shale rock cores into smaller sizes(preferably 254 mm×254 mm×127 mm)as shown in Fig.2.This ensured that there was no development of fractures during cutting and thereby maintaining a pristine specimen.

After cutting,the sample was polished.Several methods of polishing for varying amounts of time were attempted.The final method involved the use of two 30.48 cm diameter diamondlapping films (DLFs) of 15 and 6 μm for 3 and 2 min,respectively.The films were firmly fixed on the disc of the polishing machine shown in Fig.3.The disc then rotated at a speed of 250 rpm,with the specimen manually held against the surface of the film to touch the film surface.This process used water as a lubricant to dissipate the heat produced.Subsequently,a polishing cloth with diamond paste of 0.5 μm polished the specimen for 2 min.Instead of water,green lube was used as a lubricating agent.Green lube is a medium viscosity hexylene glycol-based lubricant used for metallographic preparation.After each polishing step,the polished specimens were placed in a beaker containing deionized water and then into an ultrasonic bath.

Fig.2.Isomet low speed saw for specimen cutting (WVU Advanced Engineering Research Building).

Etching was performed after polishing the specimen.Etching was necessary to visualize the grain boundaries distinctively.As the specimens contained a dominant percentage of calcite (from XRD result),etching helped in visualization of the grain boundaries by dissolving the calcite matrix present between grains.Different acids with different concentrations were used to find the optimum acid and concentration which would show the maximum amount of grain boundaries.Optimum result was obtained by exposing the polished shale specimen to 0.2 M hydrochloric acid (HCl) for 1 min.Following the etching process,the specimen was washed with deionized water and placed inside an oven at 70 ℃for 5 min.The length of exposure time to acid during etching is critical.When etching lasted longer than 1 min,there was a large deposition of chloride on the boundaries that distorted the visualization of grains.In addition,acid destroys the shale surface.Fig.4 shows an image of a polished specimen etched with 0.2 M HCl for 1 min.

Finally,the etched specimen was coated with Au to prepare the specimen for imaging in SEM.The organic matter in shale absorbs the incident electrons when imaged in SEM,degrading the quality of the obtained image.Coating prevents electrons from accumulating on the surface of the shale specimen.Fig.5 summarizes the specimen preparation steps for SEM imaging.

2.3.2.SEM imaging

A Hitachi S-4700 Scanning Electron Microscope was used to image the surface of the prepared specimens,with both SE (secondary electron) and BSE (back scattered electron) multiscale imaging.Fig.6 depicts a BSE image,noting different observations.Fig.6 illustrates that there is no significant variation in the contrast of individual grains as most of the grains are calcite.Grains with higher density are lighter,and pores are darker.Fig.6 also shows a pyrite framboid,which has a higher density as compared to other grains and is lighter in contrast.There are few pores in the specimen relative to the area imaged.The grains have a high range of variation in size and most of them are in the micron scale.Grains are relatively circular in shape.

2.3.3.Image processing technique

This study digitized the grain boundary in the image (Fig.7a)obtained from SEM in AutoCAD,darkening the grains completely(Fig.7b) for easier thresholding.The automation of this process is difficult,as the specimen is homogeneous and there is no significant difference in contrast between different grains.Using the classification technique of ImageJ2,individual information about each grain in a heterogenous specimen can be obtained [25].

The following steps were completed in ImageJ2 for analysis:

(1) Scale setting;

(2) Checking the measurement scale;

(3) Converting image to greyscale (8 bit);

(4) Thresholding the image;

(5) Removing the scale bar;

(6) Noise removal–Removing outliers;

(7) Separating the grain boundaries;

(8) Binary Erosion;

(9) Minimum filter;

(10) Analyzing the particles–Selecting the parameters for measurement;

(11) Measurement.

Two major steps in this process were thresholding and grain boundary separation,discussed below in detail.

2.3.3.1.Thresholding.Thresholding is a technique for dividing an image into two (or more) classes of pixels,typically called the“foreground” and “background”.A grayscale image is divided into two classes:black (pixel intensity 0) and white (pixel intensity 255).Fig.8a shows an SEM image digitized in AutoCAD.The intensity histogram,shown in the small box at the left top corner,gives the distribution of the intensities of different grains present in the grayscale image.The intensity histogram is a curve with two black vertical lines at 0 and 255,indicating that there are grains with intensities other than 0 and 255.However,after thresholding the image as seen in Fig.8b,the curve is not visible.Only two vertical black lines are visible at the 0 and 255 positions.This shows that there are only two intensities in the thresholded image:0 and 255.

2.3.3.2.Grain boundary separation.One problem that arises during petrographic analysis is grain boundary separation.To address this issue,the minimum/maximum filter in ImageJ2 was implemented.In some cases,the grain boundaries of two adjoining grains were too close to be differentiated by pixels.After thresholding,the boundaries would merge together and form a combined grain.The minimum filter reduced the size of each grain by 0.5 pixel,which then separated the grains.It should be noted that the loss in grain size was kept at minimum while increasing the grain numbers.Fig.9 depicts an illustration of the min/max filter with a total of 122 grains counted without filter and 188 grains after the application of the filter.

Fig.3.Specimen polishing machine (WVU Advanced Engineering Research Building).

Fig.4.BSE (back scattered electron) image of polished specimen etched with 0.2 M HCl and magnified view of a small area to show the grains.

2.3.4.Grain parameters

Two major grain parameters were analyzed:grain size and grain shape.The method of estimation of these parameters is discussed below.

2.3.4.1.Grain size.The grain size was measured using Feret’s diameter.Feret’s diameter represents the perpendicular distance between two parallel outer tangents to an object (Fig.10).One can obtain the longest diameter of an object by selecting the largest Feret’s diameter measured in 32 different directions (e.g.,at an angular resolution of 5.7°).Minimum Feret’s diameter is defined by taking the shortest from 32 Feret’s diameters.The maximum and minimum diameters are not necessarily orthogonal [26].

2.3.4.2.Grain shape.There are two secondary geometrical parameters in the analysis of grain shape:aspect ratio and form factor.Aspect ratio defines the elongation of the grains,which is measured as the ratio of the grain’s maximum and minimum Feret’s diameter.The grains will be more elongated with a higher aspect ratio.Form factor estimates the roughness of the grain’s perimeter.It is a measure of the grain’s deviation from circularity.The circularity shape factor (form factor) of the grain is defined as:

The value of form factor ranges from 0 to 1,with 0 for very rough objects and 1 for a perfect circle.

Fig.5.Flowsheet summarizing the specimen preparation process for SEM imaging.

3.Results and discussion

3.1.UCS test

The test results showed that axial splitting was the predominant failure mode in the different sized shale specimens (Fig.11).From the work of previous researchers,similar observations have been noted when shale rock undergoes UCS test[27,28].The specimens showed multiple failure cracks that developed along the axial length of the specimen.Axial splitting also indicates that the specimen had a high degree of brittleness.There was a sudden release of stress after the maximum stress point exceeded.

Fig.12 shows a representative stress–strain plot of the three different sized specimens.In all the specimens,a nonlinear curve was observed at the initiation of the test.This is attributed to closure of the pre-existing cracks as a result of loading.This was followed by a linear increase in stress and strain indicating elastic behavior.When peak load reached,specimen failed abruptly with loud noise depicting the brittle behavior of the shale tested.

Box plot of the results of UCS test (Fig.13)shows that the 508-mm diameter specimen has the lowest strength when compared with 254-mm and 762-mm diameter specimens.The mean strength of 254-mm and 762-mm specimens are similar.However,the spread of the strength values for 762-mm specimens was more than that of 254-mm specimens.The 508-mm specimen strength values had the least spread.

Fig.6.BSE SEM image of shale specimen.

Fig.7.SEM image of shale before digitization using AutoCAD and after digitization using AutoCAD.

Fig.8.SEM images of shale before thresholding and after thresholding.

Fig.9.SEM image of shale before application of min/max filter and after application of min/max filter.

Fig.10.Illustration of maximum and minimum Feret’s diameters [26].

One-way ANOVA analysis was conducted with strength as the response variable and specimen size as factor with 3 levels (254-mm,508-mm,and 762-mm).The overall model was significant at 5% level of significance,which proved that there was a significant difference between the mean strength of the three different sizes of specimen.Thereafter,paired comparison assessed any significant difference between different levels of the factor specimen size.It was observed that there was a distinct difference in the strength values between 254-mm and 508-mm and 508-mm and 762-mm specimens at 5% significance level,but the difference of UCS values between 254-mm and 762-mm was not significant.Petrographic parameters of shale were analyzed then to understand this variation in strength.

Fig.11.Axial splitting failure of shale specimen observed post failure.

Fig.12.Stress–strain plot for one of the specimens tested.

3.2.X-ray diffraction — Compositional analysis

X-ray diffraction pattern for the different sized specimens had similar peaks.However,the average mineral content for the different sized specimens varied.A representative diffraction pattern is shown in Fig.14.Almost all the major peaks have calcite in them.Montmorillonite is also widely distributed in the pattern.The major elements detected from the analysis were quartz,calcite,pyrite,fluorite,montmorillonite,apatite.Illite was also found in some specimens.

Fig.13.Box plot of UCS vs.specimen size.

Fig.14.X-ray diffraction pattern from the XRD test.

The average mineral composition of the specimens of different sizes along with respective standard errors is shown in Table 1.

Table 1Average values of quartz,calcite,fluorite,and clay in different sized specimens.

3.2.1.Quartz content

From Fig.15,it is observed that the quartz content is lower for 508-mm specimen as compared to 254-mm and 762-mm specimens.There is not a considerable difference in quartz content of 254-mm and 762-mm specimens.This corroborates the literature review for other rocks,which states that increase in quartz content increases the strength of rock [11,29].Average quartz content is low in 508-mm specimen,which contributes to its lower strength.

3.2.2.Calcite content

Calcite (or carbonate) forms intermediate strong fraction in shales[30].Calcite forms the major component of the shale tested as it forms almost three-fourths of the specimen.Calcite also follows a similar trend as quartz with a lower percentage of calcite in lower strength 508-mm specimens and a comparatively higher percentage in 254-mm and 762-mm specimens.As calcite forms an intermediate strong fraction in shale,a higher percentage gives higher strength as can be seen in the analysis.

Fig.15.Plot showing the correlation between strength of the specimen and its composition.

3.2.3.Fluorite content

Fluorite also follows a similar trend as the above two with lesser fluorite content in weaker 508-mm specimens and more fluorite content in stronger 254-mm and 762-mm specimens.However,as the percentage composition of fluorite is very less (close to 6%)and it not being as hard as quartz,it may not be a major player in influencing the strength of the rock.

3.2.4.Clay content

Clay is unevenly distributed in the specimens.The average clay tended to be around 20%.Fig.15 shows that the average clay content of 508-mm specimen is higher which strengthens the fact that clay contributes to the decreasing strength of shale.

3.3.SEM imaging–Grain parameter analysis

For estimation of all parameters,we selected approximately 500 grains of each size specimen (254-mm,508-mm,and 762-mm),half of which were selected from the top sections and the other half from the cross-section.12–24 images of each size were needed to produce a total of 500 grains.Only those grains were considered for digitization,which can be visually delineated.Auto-CAD digitized the grains and ImageJ thresholded and processed them.We analyzed the grain parameters after obtaining the final image.

3.3.1.Grain size analysis

Grain size is represented by maximum Feret diameter.Maximum Feret diameter for each grain for each sized specimen was calculated and averaged to obtain an average grain size for each of 254-mm,508-mm,and 762-mm specimens.From the plot in Fig.16,it is notable that the 508-mm specimen has a higher average grain size than the 254-mm and 762-mm specimens.In addition,Fig.16 also shows that the average strength of the 508-mm specimen was lowest as compared to the other two specimen groups.There was no significant difference between the average grain size of 254-mm and 762-mm specimens;their average strength also showed a similar trend.Therefore,one can proposethat grain size affects the strength of rock.Rocks that have a larger grain size have less strength as compared to rocks with a smaller grain size.This has also been seen in the case of granitic rocks[11].

Fig.16.Relationship between shale rock strength and grain size.

3.3.2.Grain shape analysis

Grain shape is represented by aspect ratio(AR)and form factor(FF).Aspect ratio defines the elongation of the grains,and form factor denotes the roughness of the grain boundary.From the literature review,we have learned that circular grains have low compressive strength and grains with a rough surface have higher compressive strength.We calculated the aspect ratio by dividing the maximum Feret’s diameter with minimum Feret’s diameter.One can calculate form factor using the perimeter and area of the individual grains.

Fig.17 shows how the average AR is low for 508-mm specimens and at maximum for 762-mm specimens.Again,the difference in AR of 254-mm and 762-mm specimens is very low.This observation agrees with literature that observed that grains with low aspect ratio have lower strength [31].Earlier reported literature validates these results,as the circular grains are not tightly packed and can disintegrate easily under stress;in contrast,elongated grains pack more tightly and are therefore more difficult to break under stress.

In this analysis,form factor is not in agreement with the earlier findings reported in various literature.A lesser value of form factor portrays a rough surface,which increases the strength of the specimen;however,in this analysis,the 508-mm specimen has the lowest form factor,whereas the 254-mm and 762-mm specimens have higher form factor.In addition,the difference between the form factor values is less,nearly the same for all the specimen sizes.Therefore,it was concluded that form factor cannot be considered an important parameter to quantify strength.

Fig.17.Relationship between shale rock strength and grain shape.

4.Conclusion

This study aimed to understand the reason for the variation of strength in different sized shale specimens.It was found that changing the size of the specimen changes the strength of shale.Next,the causes for the variation of strength of the shale were investigated by analyzing the petrographic parameters.This study used X-ray diffraction method and scanning electron microscopy for petrographic analysis to analyze different parameters such as quartz content,calcite content,clay content,grain size and grain shape.The points below summarize the results of this study.

(1) Strength of the shale specimen changed with the size of the specimen.

(2) Quartz content influences the strength of shale rock.Strength of the rock decreases with low quartz content.508-mm specimen with the lowest strength had minimum quartz content.

(3) Calcite being a major component in composition analysis affected the strength of shale rock.Higher calcite content resulted in higher strength.

(4) Fluorite followed a similar trend as calcite,with weaker specimens having a lower average fluorite content.

(5) Clay was present in the studied shale specimens.Clay being soft reduces the strength of rock.Higher content of clay was observed in 508-mm specimens than in the other two sizes.

(6) Shale has a complex microstructure,so it requires a defined polishing methodology.Polishing should not be done for long,as shale is also very soft.

(7) Etching forms an important part of specimen preparation if grain parameter analysis is to be done.

(8) Grain size is an important factor contributing to the strength of the shale specimens tested.508-mm specimens,which had the lowest strength,had a higher average grain size compared to other specimen sizes.

(9) Grain shape when defined by aspect ratio followed the general trend,showing that rock with grains with higher aspect ratio has a higher strength than the other rock types.However,this trend was not observed when using form factor to define grain shape.