Relationship Between Petrographic Characteristics and the Engineering Properties of Jurassic Sandstones, Hamedan, Iran

ORIGINAL PAPER

Relationship Between Petrographic Characteristicsand the Engineering Properties of Jurassic Sandstones,Hamedan, Iran

M. Heidari • A. A. Momeni • B. Rafiei •

S. Khodabakhsh • M. Torabi-Kaveh

Received: 16 June 2012 / Accepted: 12 November 2012 / Published online: 4 December 2012

� Springer-Verlag Wien 2012

Abstract To study the relationship between engineering

properties and petrographic characteristics, 20 rock sam-

ples were collected from Jurassic sandstones in the

Hamedan region, western Iran. The specimens were tested

to determine uniaxial compressive strength, point load

strength index, tangent modulus, porosity, and dry and

saturated unit weights. Samples were also subjected to

petrographic examination, which included the observation

of 11 parameters and modal analysis. Based on the results

of a statistical analysis, polynomial prediction equations

were developed to estimate physical and mechanical

properties from petrographic characteristics. The results

show that textural characteristics are more important than

mineral compositions for predicting engineering charac-

teristics. The packing density, packing proximity and grain

shape are the petrographic properties that significantly

affect the engineering properties of samples. Multivariate

linear regression analysis was performed, employing four

steps comprising various combinations of petrographic

characteristics for each engineering parameter. The optimal

equation, along with the relevant combination of petro-

graphic characteristics for estimating the engineering

properties of the rock samples is proposed.

Keywords Jurassic sandstone �Petrographic characteristics � Texture � Iran

1 Introduction

Sandstones include a wide range of rock types with variable

mineralogy, petrographic characteristics and mechanical

properties. Large variations in the physical and mechanical

properties of sandstones have been attributed to variations

in petrographic characteristics (Bell 1978a; Howarth and

Rowlands 1986; Shakoor and Bonelli 1991). Thus, in

addition to the values of engineering indexes, petrographic

characteristics that are known to affect physical and

mechanical properties can be used to predict the engineer-

ing properties of sandstones. These properties include grain

size and shape, degree of interlocking, types of contacts,

packing density, packing proximity, mineral composition

and amount and type of cement and matrix. These proper-

ties can be readily measured in the laboratory and are

commonly determined from analyses of thin sections.

Jurassic sandstone is widely exposed in the Hamedan

region of western Iran, where they are a source of barrow

material. According to the definition of Pettijohn et al.

(1987), most of the sandstones in the Hamedan region are

sublitharenites, quartzarenites and subarkoses, making them

suitable for geomechanical studies. The petrographic

parameters studied here include: (1) grain and matrix mineral

composition; (2) degree of packing of sandstone, which can

be expressed in terms of packing density (Pd), packing

proximity (Pp), porosity (n), dry unit weight (cd) and satu-

rated unit weight (csat); and (3) the types of grain contacts. In

addition to linear regression, multivariate linear regression

analyses were performed to obtain best-fit curves between

petrographic parameters and engineering properties.

Empirical predictive models, based on multivariate statisti-

cal analysis and thin section data, correlated strongly with

physical and mechanical properties, and, thus, can be used to

estimate the engineering properties of the sandstones.

M. Heidari (&) � B. Rafiei � S. Khodabakhsh �M. Torabi-Kaveh

Department of Geology, Faculty of Sciences, Bu-Ali Sina

University, Mahdieh Ave., 65175-38695 Hamedan, Iran

e-mail: [email protected]

A. A. Momeni

Department of Geology, Shahrood University of Technology,

Shahrood, Iran

123

Rock Mech Rock Eng (2013) 46:1091–1101

DOI 10.1007/s00603-012-0333-z

2 Geological Setting

The study area is located in the Sanandaj–Sirjan struc-

tural zone in western Iran, between longitudes of

48�3503700E and 48�3504800E, and latitudes of 34�4502000Nand 34�4503900N (Fig. 1). Samples were collected from

the Ekbatan Dam site, 5 km east of Hamadan city. The

oldest rock units are Jurassic slates and phyllites, which

are disconformably overlain by Jurassic sandstones. Two

sandstone units were observed in the study area (Fig. 2):

the Lower Sandstone Unit composed mainly of wackes,

and the Upper Sandstone Unit consisting of arenites. The

rocks studied are affected by diagenetic processes such as

Fig. 1 The location of the study

area in the structural zones of

Iran and Hamedan city

Fig. 2 Stratigraphic column of Jurassic strata in the Ekbatan Dam

section

Table 1 Measured petrographic data for twenty numbers of the

sandstone specimens

Sample no Quartz Feldspar Lithics Mica Cement Matrix

S1 60.4 2.2 19.8 0.0 13.5 1.0

S2 81.2 3.7 7.5 0.0 4.2 1.0

S3 82.5 3.0 4.1 0.0 5.7 2.0

S4 77.3 1.0 8.0 1.0 5.1 1.0

S5 77.5 1.5 13.2 1.0 3.1 1.5

S6 68.4 1.5 20.0 – 8.5 1.0

S7 61.6 6.0 15.5 – 10.6 1.0

S8 70.4 2.5 17.0 1.0 3.3 2.0

S9 67.9 3.0 7.6 1.0 17.5 1.0

S10 72.2 4.0 5.9 1.0 4.6 1.0

S11 68.4 5.5 7.6 1.0 5.2 2.0

S12 71.6 1.1 14.9 1.0 6.9 1.0

S13 60.2 3.0 15.9 – 18.2 1.0

S14 67.1 4.2 6.5 1.0 2.8 1.0

S15 88.1 2.6 1.4 1.0 4.1 1.0

S16 74.9 1.8 11.5 0.0 6.5 2.0

S17 70.0 4.2 7.1 1.0 6.4 1.0

S18 89.2 5.0 1.0 1.0 2.0 1.0

S19 90.0 2.4 2.5 0 3.0 1.0

S20 83.6 1.5 1.6 1.0 6.5 1.0

Min 60.2 1.00 1.00 0.00 2.00 1.00

Max 90.0 6.00 20.0 1.00 18.20 2.00

Ave 74.12 2.98 9.43 0.70 6.88 1.22

Med 71.9 2.80 7.60 1.00 5.45 1.00

SD 9.29 1.46 6.13 0.47 4.65 0.41

CV 0.12 0.49 0.65 0.66 0.67 0.33

Min minimum, Max maximum, Ave average, Med medium, SD

standard deviation, CV coefficient of variation

1092 M. Heidari et al.

123

compaction, cementation, precipitation of dolomite cement,

fracturing, vein formation and pyrite formation.

3 Materials and Methods

Eighty-four samples were obtained from Jurassic Sand-

stone at the Ekbatan Dam site (Fig. 1). The engineering

properties of the samples (dry unit weight, saturated

unit weight, point load strength index, porosity, uniaxial

compressive strength and tangent modulus) were deter-

mined in accordance with methods suggested by the

International Society for Rock Mechanics (ISRM) (1981).

Sample textures were observed under an optical polarizing

microscope. The relative percentages of three types of

grain-to-grain contacts (i.e., concave–convex, long and

sutured) were determined along traverses in each thin

section. The number of grain-to-grain, grain-to-void, grain-

to-cement and grain-to-matrix contacts was counted along

the same traverses. The field of observation was set to

include 100–150 grains per image, enabling the observa-

tion of textural features for each area.

More than 100 randomly selected grains were studied

per thin section to determine the mean grain size. The

average of measurements along two perpendicular tra-

verses, passing through the centre of each grain, provided

the average size of the grains in each thin section. Five

random fields of view per thin section were used to eval-

uate the average grain size. Grain shape, measured in term

of roundness, was quantified for 100 randomly selected

grains per thin section. The degree of clastic particle

roundness, determined by the sharpness of particle edges

and corners, was determined using the scale developed by

Powers (1953). Packing density and packing proximity

were quantified according to Kahn’s (1956) method.

Packing density and packing proximity were determined

along ten traverses per thin section. Modal analyses were

based on 150 randomly selected points per thin section,

using the point-counting method described by Hutchinson

(1974). Quartz, feldspar, rock fragments, mica, calcite,

matrix and cement contents were determined for each thin

Fig. 3 Photomicrographs of

texture of the sandstones on

thin-sections under crossed-

nicols. a Calcite cement,

b dolomite cement, c silica

cement (quartz crystals and

chalcedonyic), d ferruginous

(iron oxides) cement

Fig. 4 Grain composition of studied sandstones based on Pettijohn’s

classification (1987)

Relationship Between Petrographic Characteristics 1093

123

section. The porosity measured was the ‘‘total porosity’’,

which is determined using the following formula:

n ¼ 1� cd=Gsð Þ; ð1Þ

where n = total porosity, cd = dry unit weight, and

Gs = density.

Previous studies (Bell 1978a; Ulusay et al. 1994; Bell

and Lindsay 1999) used the same method to measure

porosity, thereby enabling a comparison with the present

results.

4 Results and Discussion

4.1 Mineral Composition

Table 1 summarizes the results of petrographic analyses

and provides a statistical summary of mineral composi-

tions. These sandstones are composed mainly of quartz,

with smaller amounts of feldspar and rare mica. The con-

tent of rock fragments by volume is 1–20 %, and that of

cement is 2.0–18.2 % (Table 1). Three types of cement

Table 2 Some indices related to textures of the samples

Sample no Mgs (mm) Grain shape % Type of grain contact % Pd % Pp %

Angular Round Long Concave/convex Sutured

S1 0.18 78 22 49.5 35.6 10.2 97.1 85.0

S2 0.28 70 30 45.7 30.8 10.6 81.4 68.0

S3 0.44 86 14 41.5 40.2 5.7 96.0 82.0

S4 0.47 89 11 43.5 46.0 8.1 97.8 87.0

S5 0.65 62 38 35.5 41.0 21.1 91.1 79.0

S6 0.39 90 10 68.6 15.0 11.5 92.3 83.0

S7 0.38 77 33 25.1 41.4 17.1 85.3 69.0

S8 0.45 79 21 45.8 24.7 23.3 86.2 81.2

S9 0.47 82 18 49.8 26.6 17.5 90.3 79.3

S10 0.55 84 16 35.4 28.3 24.6 90.5 70.3

S11 0.37 86 14 68.3 24.5 5.0 96.6 84.2

S12 0.55 75 25 47.6 22.1 23.4 95.3 88.7

S13 0.58 79 21 42.5 27.4 18.2 86.1 69.4

S14 0.75 80 20 51.5 31.2 13.2 96.4 86.3

S15 0.66 85 15 50.6 21.1 22.5 90.7 83.1

S16 0.65 66 34 45.8 25.5 20.9 96.8 77.8

S17 0.39 85 15 61.4 20.4 12.2 90.7 84.5

S18 0.25 67 33 60.6 28.4 6.3 84.9 78.8

S19 0.19 87 13 57.5 18.2 22.7 97.7 88.1

S20 0.45 67 33 58.5 30.4 6.5 83.3 70.5

Min 0.18 62 38 25.1 15 5 81.4 68

Max 0.75 90 38 68.6 46 24.6 97.8 88.7

Ave 0.455 78.7 21.8 49.23 28.94 15.03 91.32 79.76

Med 0.45 79.5 20.5 48.55 27.85 15.15 90.9 81.6

SD 0.15 8.38 8.78 11.04 8.34 6.83 5.30 6.825

CV 0.34 0.10 0.40 0.22 0.28 0.45 0.05 0.08

K–S 0.96 0.85 0.77 0.94 0.81 0.72 0.59 0.67

Mgs mean grain size (mm), Pd packing density, Pp packing proximity, K–S Kolmogorov–Smirnov test asymptotic significant

Fig. 5 Grain-contact types: concavo-convex (1), sutured (2) and long

contacts (3)


123

were recognized: siliceous, carbonate and ferruginous

(Fig. 3).

The studied sandstones can be classified as sublithare-

nites, quartzarenites and subarkoses (Fig. 4), based on the

scheme proposed by Pettijohn et al. (1987).

4.2 Sandstone Texture

The results of the textural analysis are summarized in

Table 2. Mean grain size ranged from 0.18 to 0.75 mm,

indicating that the majority of samples were medium-

grained sands. Most of the sandstones were moderately

sorted, and more than 78 % of grains were angular in

shape. Table 2 shows that for all parameters, the mean and

average values are similar among all the samples. All the

data sets have a normal distribution (Table 2), as revealed

by the Kolmogorov–Smirnov test (Kolmogorov 1933;

Smirnov 1939).

Grain contacts were classified as tangential, long,

concavo–convex, sutured or floating. In well-sorted sand-

stone, the presence of three or more inter-grain contacts per

grain suggests that porosity has been reduced by pressure

solution (Bell 1978a). Therefore, the presence of large

numbers of long, concavo-convex and sutured contacts in

the present samples (Fig. 5) reflects the influence of pres-

sure solution. The most common types of contacts are long

and concavo–convex. A reduction in pore space due to

pressure solution is also indicated by the presence of sec-

ondary quartz overgrowths around primary quartz grains.

High values of packing density and packing proximity,

combined with low contents of cement and matrix, indicate

that grains are tightly packed (Ulusay et al. 1994). How-

ever, in the present study, few significant relationships

were found between cement and matrix content, and

packing density and proximity (Fig. 6).

Long contacts are the most common type of contact in

the studied sandstones, making up approximately 49 % of

the total contacts, followed by concavo-convex contacts

(28 %) and sutured contacts (15 %) (Fig. 5). Sutured

contacts indicate diagenesis and deep burial, whereas long

and concavo-convex contacts indicate intermediate depths

(Bell 1978b). More than 78 % of the measured grains have

concavo-convex and long contacts (Table 2), suggesting

that the sandstones have undergone substantial compaction.

There are relatively few non-contacts (i.e., grain–cement,

grain–matrix and grain–void boundaries).

4.3 Engineering Properties

Table 3 provides a summary of the physical and mechan-

ical properties of the rock samples. The values of dry

density (cd) and saturated density (csat) vary from 21.50 to

25.90 (kN/m3) and 22.26 to 27.20 (kN/m3), respectively.

Porosity (n) varies widely from 3.40 to 17.50 %. The mean,

medium and coefficient of variation (CV) values for uni-

axial compressive strength (UCS) are 69.77, 69.35 and 0.23

(MPa), respectively; the values for the tangent modulus

(Et) are 8.36, 7.72 and 0.23 (GPa), respectively. Based on

the Young’s modulus and UCS values, the sandstones are

classified as CL, DL or CM, with a low to medium mod-

ulus ratio, according to the Unified Classification System of

Deere and Miller (1966).

5 Correlation Between Petrographic Parameters

and Engineering Parameters

To verify the relationship between mineral characteristics,

and the physical and mechanical properties of the samples,

we examined the strengths of linear correlations. Feldspar,

mica and matrix in sandstones were excluded from the

analyses because they occur in negligible amounts. Mul-

tiple regression and correlation analyses were performed to

determine if the combined petrographic variables could

better explain the mechanical and physical properties of the

sandstone than could one petrographic parameter alone.

Stepwise multivariate linear regressions were then applied

Fig. 6 Cement percent versus a percent of packing proximity (Pp),

b percent of packing density (Pd)


123

Table 3 The physical and mechanical properties of the twenty samples of the Ekbatan sandstones

Sample no cd (kN/m3) csat (kN/m3) n (%) Is(50) (MPa) UCS (MPa) Et (GPa)

S1 24.82 25.91 3.40 4.34 92.5 11.5

S2 21.5 22.7 17.50 4.08 53.4 6.1

S3 24.52 25.4 8.84 4.1 88.7 –

S4 25.31 25.80 4.10 5.56 89.4 8.42

S5 25.50 26.42 7.30 4.48 61.3 8.20

S6 25.11 26.29 6.40 4.89 85.2 7.78

S7 21.70 22.26 14.98 3.66 44.9 12.36

S8 24.91 26.1 6.65 3.98 75.8 7.66

S9 24.52 25.77 8.60 4.71 73.3 7.30

S10 21.68 23.36 15.86 3.17 54 6.25

S11 25.6 27.2 10.58 3.99 68.2 6.22

S12 25.9 26.65 6.26 4.69 90.4 7.33

S13 24.50 25.6 9.33 3.30 45.2 7.28

S14 24.92 25.3 5.62 5.02 65.3 7.41

S15 25.67 27.03 6.11 3.85 59.7 8.10

S16 23.54 24.92 8.28 3.72 68.8 8.38

S17 25.50 26.8 5.87 4.42 70.7 –

S18 22.46 24.65 9.21 3.35 46.3 12.31

S19 25.52 26.8 5.36 5.5 92.5 10.36

S20 23.11 25.5 11.42 3.88 69.9 7.65

Min 21.50 22.26 3.40 3.17 44.90 6.10

Max 25.90 27.20 17.50 5.56 92.50 12.36

Ave 24.31 25.52 8.58 4.23 69.77 8.36

Med 24.86 25.78 7.79 4.09 69.35 7.72

SD 1.45 1.37 3.85 0.67 16.18 1.95

CV 0.05 0.05 0.44 0.16 0.23 0.23

K–S 0.16 0.49 0.59 0.90 0.90 0.15

cd Dry density, csat saturated density, n porosity, Is(50) point load strength index, UCS uniaxial compressive strength, Et tangent modulus,

K–S Kolmogorov–Smirnov test asymptotic significant

Table 4 The linear relationships between petrographical characteristics with physical and mechanical properties

Petrographical characteristics Physical properties Mechanical properties

cd (kN/m3) csat (kN/m3) N (%) Is(50) (MPa) UCS (MPa) Et (GPa)

Mean grain size (mm) 0.19 0.08 -0.08 -0.09 -0.23 0.17

Angular 0.38 0.23 -0.27 0.38 0.41 0.19

Round -0.48 -0.34 0.36 -0.41 -0.48 -0.26

Pd 0.62 0.48 -0.63 0.57 0.69 0.71

Pp 0.82 0.74 -0.84 0.70 0.74 0.69

Long 0.38 0.53 -0.34 0.25 0.30 -0.04

Concavo-convex -0.26 -0.33 0.14 0.00 -0.09 0.24

Sutured 0.09 0.00 -0.03 -0.05 -0.08 0.00

Quartz (%) -0.05 0.12 0.01 0.07 0.04 0.07

Lithics (%) 0.15 -0.03 -0.17 0.04 0.22 0.05

Cement (%) 0.00 -0.03 0.00 -0.12 -0.12 0.03


123

to reduce the number of variables in the multivariate linear

regression equation without reducing predictability.

5.1 Linear Regression and Correlation Analysis

Eleven petrographic variables were analysed separately for

correlations with mechanical and physical parameters. The

results are set out in Table 4, which clearly shows a distinct

correlation for some parameters.

Most petrographic characteristics are only weakly rela-

ted to dry and saturated unit weight, probably due to the

limited range in unit weight (Table 3). Dry density was

inversely related to the percentage of round grains (r =

-0.48) and showed a significant correlation with packing

proximity (r = 0.82). The saturation density showed a

statistically significant correlation with packing proximity

(r = 0.74). The packing proximity, packing density and

long contacts all showed a statistically significant correla-

tion with unit weight (95 % confidence level). We also

found a statistically significant inverse correlation between

porosity and each of packing proximity (r = -0.84) and

packing density (r = -0.63) (Table 4).

Uniaxial compressive strength has a statistically signif-

icant correlation with packing proximity (r = 0.74),

packing density (r = 0.69) and grain roundness (r =

-0.48). Similar results were obtained for the point load

strength index. Samples tend to show an increase in

strength with increasing packing proximity and packing

density (Table 4), as also noted by Bell (1978a) for the Fell

sandstones, Northumberland, England. The petrographic

characteristics with the greatest impact on the tangent

modulus were packing density (r = 0.71), packing prox-

imity (r = 0.69), concavo-convex contacts (r = 0.26) and

roundness (r = -0.26).

5.2 Multiple Linear Regression and Stepwise Multiple

Regression

Significant variables in multi-variable linear relationships

were considered using a multiple regression and correlation

analysis performed with the EViews 5 software, to deter-

mine if multiple variables would define stronger relation-

ships than single variables. The performance of the

stepwise method developed in this study was assessed

using standard criteria for evaluating statistical perfor-

mance, including the correlation coefficient (r), the root

mean square error (RMSE) and the mean absolute error

(MAE). These three criteria were calculated with the fol-

lowing equations:

R ¼Pn

i¼1 Xi � X� �

Yi � Y� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1 Xi � X� �2

Yi � Y� �q 2

ð2Þ

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1 Xi � Yið Þ2

n

s

ð3Þ

Table 5 Statistical performance evaluation criteria for each MLR stepwise in prediction of engineering properties

Dry unit weight (kN/m3) Saturation unit weight (kN/m3)

Input combination R RMSE MAE Input combinations R RMSE MAE

(i) Pp, Pd 0.82 0.799 0.607 (i) Pp, long 0.77 0.899 0.736

(ii) Pp, Pd, round 0.82 0.791 0.592 (ii) Pp, long, Pd 0.78 0.890 0.712

(iii) Pp, Pd, round, angular 0.83 0.774 0.562 (iii) Pp, long, Pd, round 0.78 0.925 0.756

(iv) Pp, Pd, round, angular, long 0.83 0.770 0.571 (iv) Pp, long, Pd, round, concavo-convex 0.78 0.934 0.750

n (%) Is (50) (MPa)


(i) Pp, Pd 0.84 1.977 1.559 (i) Pp, Pd 0.70 0.467 0.420

(ii) Pp, Pd, round 0.85 1.958 1.565 (ii) Pp, Pd, round 0.71 0.465 0.422

(iii) Pp, Pd, round, long 0.85 1.953 1.571 (iii) Pp, Pd, round, angular 0.71 0.462 0.411

(iv) Pp, Pd, round, long, angular 0.86 1.903 1.457 (iv) Pp, Pd, round, angular, long 0.71 0.461 0.416

UCS (MPa) Et (GPa)


(i) Pp, Pd 0.76 10.15 9.09 (i) Pp, Pd 0.75 1.25 0.98

(ii) Pp, Pd, round 0.77 10.03 8.81 (ii) Pp, Pd, round 0.77 1.19 0.93

(iii) Pp, Pd, round, angular 0.77 9.94 8.64 (iii) Pp, Pd, round, concave/convex 0.84 1.01 0.828

(iv) Pp, Pd, round, angular, long 0.77 9.93 8.59 (iv) Pp, Pd, round, concave/convex, angular 0.85 1.00 0.773


123

MAE ¼Pn

i¼1 Xi � Yij jn

; ð4Þ

wherethere are the means of the observed and pre-

dicted data, respectively; and n is the number of data

points.

A standard t test was used to assess the confidence level

of the regression analysis. The formula used for the t test is

a ratio where the numerator is simply the difference

between the two means or averages, and the denominator is

a measure of the variability or dispersion among scores

(Sharma et al. 2011). The formula for calculating the t test

is as follows:

t ¼ M1 �M2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

S2p

n1þ S2

p

n2

� �r ! S2p ¼

SS1 þ SS2

df1 þ df2

; ð5Þ

Table 6 Computed t value of all parameters for engineering properties in five steps

Steps Engineering indices Constant Petroghraphical parameters

Pp Pd Long Concave–convex Round Angular

Steps (i) cd 4.54 6.18 – – – – –

csat 4.69 4.69 – – – – –

N 8.30 -6.80 – – – – –

Is(50) -1.04 4.25 – – – – –

UCS -2.37 4.73 – – – – –

Et -2.64 – 4.09 – – – –

Steps (ii) cd 3.10 3.89 -0.18 – – – –

csat 4.95 3.67 1.49 – – –

N 5.17 -4.42 0.36 – -1.79 – 1.09

Is(50) -0.80 2.44 0.17 – – – –

UCS -2.44 2.09 1.13 – 1.79 – –

Et -2.57 1.33 1.65 – – – –

Steps (iii) cd 2.83 3.57 -0.27 – – -0.59 –

csat 3.60 2.59 -0.55 1.19 – – –

N 4.47 -4.34 0.25 – – -0.56 –

Is(50) -0.45 2.23 0.10 – – -0.34 –

UCS -1.62 1.84 0.99 – – -0.61 –

Et -2.82 1.67 1.86 – – 1.23 –

Steps (iv) cd 1.82 3.24 -0.21 – – -0.94 -0.81

csat 2.57 2.54 -0.43 1.21 – 0.36 -

N 4.04 -3.82 0.33 0.26 – -0.46 1.04

Is(50) -0.56 2.21 0.07 0.63 – 0.31 0.42

UCS -0.12 1.63 1 – – -0.67 -0.52

Et -3.14 2.47 1.22 – 2.19 0.73 –

Steps (v) cd 1.74 3.01 -0.35 -0.40 – -0.99 -0.88

csat 2.50 2.46 -0.37 0.81 -0.27 0.40 –

N 0.60 -3.77 0.41 0.56 – 0.72 0.86

Is(50) -0.34 2.05 -0.03 -0.28 – 0.14 0.26

UCS -0.01 1.50 0.82 -0.18 – -0.66 -0.54

Et -0.55 2.22 1.18 – 2.23 -0.42 -0.65

Table 7 The best MLR equations to predict the engineering properties

cd (kN/m3) = 20.794 ? 0.165Pp - 0.013Pd - 0.094

Round - 0.081Angular

Et (GPa) = -9.347 ? 0.109Pd ? 0.173Pp - 0.064 Round ? 0.088

Concave–Convex - 0.094 Angular

csat(kN/m3) = 14.731 ? 0.162Pp ? 0.029long - 0.040Pd UCS (MPa) = -89.012 ? 1.149Pp ? 0.785Pd - 0.211 Round

n (%) = 20.017 - 0.544Pp ? 0.072Pd ? 0.205

Round ? 0.038 Long ? 0.241 Angular

Is (MPa) = -1.142 ? 0.064Pp ? 0.004Pd - 0.005 Round


123

where M1 and M2 are the means of groups 1 and 2,

respectively; Sp2 is the pooled variance; SS1 and SS2 are the

sum of squares for each group; n1 and n2 are the number of

scores in each group; and df1 and df2 are the degrees of

freedom for each group (df1 = n1 - 1 and df2 = n2 - 1).

The t value is positive if the first mean is larger than the

second, and vice versa. Once the t value is computed, it is

compared with the tabulated value. If the computed value

is larger than the one tabulated, this indicates a strong and

significant correlation. A risk is set to test the significance.

Fig. 7 Comparison of the best predicted engineering properties by MLR and experimented values


123

In most cases, the ‘‘rule of thumb’’ is to set the alpha level

at 0.05 (i.e., a 95 % confidence interval).

The results of stepwise multiple regression and the

computed t value for each engineering property are listed in

Tables 5 and 6, respectively. The coefficient of multiple

determinations (R) for the relationships with dry density,

saturated density, tangent modulus and porosity is high

when compared with those obtained for other relationships.

The relationship between Is(50) and UCS is characterized by

a moderate R value. Density, porosity and tangent modulus

are therefore better explained when multiple petrographic

variables are considered.

In the first step, one of the 11 variables predicted a dry

unit weight with R = 0.82 (Table 5). For the tangent

modulus, an increase from two to five variables resulted in

an increase in R of 0.10 (Table 5). When UCS was

regressed against packing proximity, packing density and

grain roundness, R was 0.77. The analysis showed that

these three variables are good predictors of the UCS. In

contrast, two variables, packing proximity and packing

density, could be used to predict UCS with R = 0.76.

Reducing the number of variables in the analysis from

three to two caused only a very small loss in predictive

capability. A similar assessment may also be made for the

other properties given in Table 5. The statistical perfor-

mance evaluation criteria of multiple linear regression

(MLR) for engineering properties are presented in Tables 5

and 6, which show that increasing the number of variables

input into the regression models improves the estimating

ability of UCS and Et. A stepwise multiple regression

performed for the point load strength index indicates that

five variables collectively predicted this mechanical prop-

erty with R = 0.71. Considerable effort can be saved, with

only a small loss in accuracy, if two variables (packing

density and packing proximity) are used (R = 0.70).

The results of the five-step t test relating to engineering

properties are shown in Table 6. Only in the first step is the

calculated t value much greater than the tabulated value at

the 95 % confidence interval. The most suitable equation,

which represents a comparison of the best predictions of

engineering properties by MLR and experimental values, is

presented in Table 7 and Fig. 7.

Based on the T-ratio probabilities, porosity had one

significant predictor (t [ 5.17), which is the regression

constant (Table 6). The calculated R values indicate that

the regression is significant (R = 0.84). Therefore, a rough

estimate of porosity can be made using the prediction

equation. The point load strength index showed moderate

predictor values, and uniaxial compressive strength had

only one significant predictor (t = –2.44), which is the

regression constant (Table 6). The calculated R values

indicate that the regression is not highly significant

(r = 0.76).

6 Conclusions

To study the relationship between petrographic character-

istics and engineering properties, selected sandstones were

quantified using a comprehensive multivariate statistical

evaluation. By quantifying the mineralogy and texture of

the sandstones, we identified the parameters that control

their engineering performance. The results of our study are

summarized below.

1. Among 11 petrographic characteristics, we found that

packing density, packing proximity and the percentage

of long contacts exhibited the most significant corre-

lations with most of the engineering properties

considered in this study. In addition, packing density

and porosity are the two key parameters that influence

UCS, with lower porosity and greater packing density

acting to enhance UCS.

2. In sandstones, which consist almost entirely of quartz,

there is no relationship between mineral composition

and density, strength, porosity or tangent modulus. As

highlighted by Bell (1978a), the engineering properties

of rocks show no relationship to their mineral compo-

sition, which is expected because textural properties

are more important than composition in this case. We

found no significant relationship between cement

content and engineering properties.

3. The use of stepwise regression statistics was important

in reducing the number of variables from 11 to only a

few. Packing proximity and packing density showed

strong correlations with dry unit weight, saturated unit

weight, UCS, point load strength index and porosity.

4. Our results raise the possibility of quantitative predic-

tions of the physical and mechanical properties of the

studied sandstones using petrographic parameters.

However, additional studies are needed to verify these

relationships. These independent variables are only

appropriate for estimating the properties of the studied

sandstones, and the resulting equations are not recom-

mended for the evaluation of sandstones from other

regions.

References

Bell FG (1978a) The physical and mechanical properties of the Fell

Sandstones, Northumberland, England. Eng Geol 12:1–29

Bell FG (1978b) Petrographical factors relating to porosity and

permeability in the Fell Sandstone. Q J Eng Geol 11(2):113–126

Bell FG, Lindsay P (1999) The petrographic and geomechanical

properties of sandstones from the Newspaper Member of the

Natal Group near Durban, South Africa. Eng Geol 53:57–81

Broch EM, Franklin JA (1972) The point load strength test. Int J Rock

Mech Min Sci 9:669–697


123

Deere DU, Miller RP (1966) Engineering classification and index

properties for intact rock. U.S. Air Force Systems Command, Air

Force Weapons Lab., Kirtland Air Force Base, New Mexicom,

Technical Report, AFWL-TR, pp 65–116

Howarth DF, Rowlands JC (1986) Development of an index to

quantify rock texture for assessment of intact rock properties.

Geotech Testing J 9:169–179

Hutchinson CS (1974) Laboratoary handbook of petrography tech-

niques. Wiley, New York, p 527

International Society for Rock Mechanics (1981) Rock characteriza-

tion, testing and monitoring, ISRM suggested methods. In:

Brown ET (ed) Pergamon Press, Oxford, p 211

Kahn JS (1956) The analysis and distribution of the properties of

packing in sand size sediments. J Geol 64:385–395

Kolmogorov AN (1933) On the empirical determination of a

distribution function, vol 4, pp 83–91

Pettijohn FJ, Potter PE, Siever R (1987) Sand and sandstone.

Springer, Berlin, p 306

Shakoor A, Bonelli RE (1991) Relationship between petrophysical

characteristics, engineering index properties and mechanical

properties of selected sandstones. Bull Assoc Eng Geol 28:55–71

Sharma PK, Khandelwal M, Singh TN (2011) A correlation between

Schmidt hammer rebound numbers with impact strength index,

slake durability index and P-wave velocity. Int J Earth Sci

100:189–195

Smirnov NV (1939) On the estimation of the discrepency between

empirical curves of distribution for two independent samples.

Bull Moscow 2:3–16

Ulusay R, Tureli K, Ider MH (1994) Prediction of engineering

properties of a selected litharenite sandstone from its petro-

graphic characteristics using correlation and multivariable sta-

tistical techniques. Eng Geol 37:135–157


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Relationship Between Petrographic Characteristics and the Engineering Properties of Jurassic Sandstones, Hamedan, Iran

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