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International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–38
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International Journal of
Rock Mechanics & Mining Sciences
1365-16
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Geostatistical relationships between mechanical and petrophysical
properties of deformed sandstone
Reza Alikarami a,b,n, Anita Torabi a, Dmitriy Kolyukhin a, Elin Skurtveit a,b,c
a Uni CIPR, Uni Research, P.O. Box 7810, N-5020 Bergen, Norway
b Earth Science Department, University of Bergen, P.O. Box 7800, N-5020 Bergen, Norway
c Norwegian Geotechnical Institute, NGI, Sognsveien 72, N-0855 Oslo, Norway
a r t i c l e i n f o
Article history:
Received 20 September 2012
Received in revised form
29 April 2013
Accepted 10 June 2013
Keywords:
Faulted sandstone
Correlation
Uniaxial compressive strength
Elasticity
Permeability
Cementation
09/$ - see front matter & 2013 Elsevier Ltd. A
x.doi.org/10.1016/j.ijrmms.2013.06.002
esponding author at: Uni CIPR, Uni Research, P
. Tel.: +47 55 58 36 78; fax: +47 55 58 82 65.
ail address: reza.alikarami@uni.no (R. Alikaram
a b s t r a c t
Petrophysical and mechanical properties of sandstone reservoirs are likely to change as a result of
faulting. In this paper, we investigate the distribution of deformation features (structures) such as
fractures and deformation bands in the Navajo and the Entrada sandstones in the fault core and damage
zones of two faults in two localities in southeast (Cache Valley) and central (San Rafael Swell) Utah. These
two localities had different degree of calcite cementation and hence are of interest to study the
mechanical and petrophysical properties of these localities, in order to find out the impact of
cementation on these properties and their possible relations. We have performed in-situ measurements
by Tiny-Perm II and Schmidt hammer to examine the distribution of permeability and strength/elasticity
of rock within the damage zone of these faults. We have studied the statistical relation between (i) Tiny-
Perm II measurements and Schmidt hammer values, (ii) permeability and uniaxial compressive strength,
and (iii) permeability and Young's modulus of deformed rocks. The statistical results demonstrate that
there are correlations between the studied parameters, but the dependencies vary with the degree of
calcite cementation in mineralogically similar sandstones (quartz sandstone). Statistical results demon-
strate to first approximation that an exponential law is more suitable for description of the relations (i),
(ii) and (iii) of non-cemented Navajo sandstone whereas for cemented Navajo sandstone these relations
are better approximated by power law.
& 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Rock deformation starts by either fracturing or formation of
deformation bands depending on the initial porosity of rock [1,2].
Deformation of low porosity rocks typically occur by fracturing
where the energy needed for cracking/fracturing is less than the
energy required for shearing and rearrangement of grains [1].
Fractures are either tensile fractures or shear fractures. Tensile
fractures or joints are fractures with no visible differential dis-
placement on two sides of them, whereas shear fractures are
fractures with relative displacement parallel to fracture plane [3].
In this study, the term fracture has been equally used for both
types. When the space between fractures walls is filled with
secondary minerals such as calcite or quartz, they are called veins.
Contrary to low porosity rocks, deformation of porous rocks occur
by grain sliding and rearrangement of grains as well as by grain
size reduction and crushing, which leads to nucleation of different
ll rights reserved.
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i).
types of deformation bands at the transition between elastic and
plastic deformation [1,2,4]. Deformation bands are small-scale
mm-thick tabular structures with millimeter to centimeters dis-
placement, and the most common types of deformation bands,
cataclastic bands involve grain crushing and compaction [4] and
may form in the damage zone of faults. These bands were
observed in our studied localities.
Fractures and deformation bands, depending on their types can
affect the petrophysical properties of rock, such as porosity and
permeability [5], and its mechanical properties, such as compres-
sive strength and elasticity [6], in different ways. For instance,
porosity and permeability are reduced within cataclastic bands
(especially compaction bands) with respect to their host rocks,
while compressive strength and Young's modulus of the material
inside the band could be higher than the adjacent host rocks
[1,4–9]. In dilation bands, with band perpendicular extension
and favorable creation condition of low mean stress [1,4,10],
while porosity increases and compressive strength and elasticity
decrease, depending on pore tortuosity and change in specific
surface area, permeability may decrease or increase [10–12].
Fractures on the other hand tend to increase porosity and effective
permeability [8,9,13] and decrease the effective rock strength and
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R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–3828
elasticity (if applied compressive stress is not normal to the
fracture) [6,14]. One of the main aims of this study is to under-
stand the possible impact of these deformation structures (frac-
tures and deformation bands) on the petrphysical and mechanical
properties of deformed sandstone reservoirs in the damage zone
of faults. Therefore, our measurements are considered to show the
effective properties of the damage zone although we have avoided
measuring on the fractures. From now on we use petrphysical and
mechanical properties, such as permeability, compressive strength
and Young's modulus, as of/equal to effective permeability, effec-
tive compressive strength and effective Young's modulus.
In general, in pressure sensitive rocks such as porous sand-
stones subjected to volumetric deformation, depending on the
stress level, petrophysical properties such as porosity and perme-
ability as well as mechanical properties such as rock strength and
elasticity may change. For instance higher overburden/confining
pressure is likely to be accompanied by compaction, which results
in lower permeability [15–21] and higher rock strength/elasticity
[21–24]. Another important aim of the present study is to under-
stand the possible relation between petrophysical and mechanical
properties of deformed rock. Dependence of rock strength on
porosity has been studied in porous rocks such as sandstones and
chalks by many researchers [25–30]. Palchik [25] has studied the
relationship between uniaxial compressive strength and porosity
by uniaxial compression test, and Palchik [26] has studied the
application of Mohr–Coulomb failure criterion to the porous sandy
shales. He found that an increase in porosity leads to a decrease in
the cohesion, friction angle and peak axial stress of cylindrical
samples from southern part of Donetsk city (Ukraine) during
triaxial compression tests. Palchik and Hatzor [27] have examined
the influence of porosity on tensile and compressive strength of
porous chalks (Adulam chalks) by means of uniaxial compression,
point load and indirect tension Brazilian tests using dry cylindrical
specimens. They reported that the tensile and compressive
strengths are inversely relatedto porosity through exponential
relations. Schöpfer et al. [29] employed the Discrete Element
Method (DEM) to investigate the effect of porosity and crack
density on elasticity and strength of rock which was represented
by bonded, spherical particles. He found that higher porosity and
crack density decrease the elasticity and strength of rock.
There are also extensive studies on how rock's permeability and
porosity are related. The base for most of the porosity–perme-
ability models is the Kozeny–Carman equation which links perme-
ability to the pore geometry characteristics, i.e., porosity, hydraulic
radius, tortuosity and specific surface area [12,31–33]. Pape et al.
[32] derived the permeability from industrial porosity logs
employing a fractal pore space geometry in which effective radius,
tortuosity and porosity are connected through the fractal dimen-
sion D. Afterwards, they estimated the permeability using a
power-law relation between permeability and porosity.
While there are extensive studies on the dependence of
permeability and rock strength on porosity and overburden
pressure, there is no study on the possible relationship between
permeability and rock strength, the properties that can be
obtained from in-situ field measurements. In the present work,
we have studied this relationship, the connection between fluid
flow characteristics and mechanical properties of sandstone, in
order to be able to forecast these properties from each other. This
is of great importance in understanding of the behavior of rock
when subjected to stress and has implications for fluid flow and
storage underground. We have performed two field studies in
southeastern and central Utah on faulted Navajo Sandstones. The
Navajo Sandstone is a producing petroleum reservoir and cur-
rently a candidate reservoir for CO2 storage in Utah, USA. In the
studied localities, the Navajo Sandstone show different degree
of calcite cementation from non-cemented to fairly cemented
sandstone. We conducted extensive permeability (by a Tiny-Perm II)
and hardness measurements (by a Schmidt Hammer) at the
damage zone of the studied faults to examine the distribution of
rock permeability and compressive strength/Young's modulus in
faulted sandstone reservoirs. We employed geostatistical analysis
on the field measured data such as Tiny-Perm II–Schmidt Hammer
values (TP–HR) as well as calculated data such as permeability–
uniaxial compression strength (K–U) and permeability–Young's
modulus (K–E) to find out if there is any relation between these
parameters, and whether this relation is statistically significant.
We employ different statistical approaches to suggest the most
suitable relations. We examine linear, exponential and power law
statistical relations on our data. Our statistical method is based on
using maximal likelihood estimation to find the best relations,
and testing the relations significance level. Our main goal in the
present study is to find out the possible relations between
mechanical and petrophysical properties of deformed sandstone
such as TP–HR, K–U and K–E. We also compared the results from
two studied localities to find out the effect of cementation on
permeability and compressive strength/Young's modulus of rock
as well as on the relations between these rock properties.
2. Methods
We have performed two extensive structural field studies on
faulted Navajo and Entrada Sandstones in southeastern (Cache
Valley) and central (San Rafael Swell) Utah, USA. We have
measured in-situ permeability by a Tiny-Perm II and rock hardness
by Schmidt hammer type N in the damage zone and core of the
studied faults. The Tiny-Perm II and Schmidt hammer values were
used in empirical relations to calculate permeability, uniaxial
compressive strength and Young's modulus.
2.1. Rock permeability and compressive strength/Young's modulus
We have measured in-situ permeability and rock hardness in
the damage zones and fault cores at every 2 m along the scan-lines
almost perpendicular to the faults. Tiny-Perm II is a portable air
permeameter used for measurement of rock matrix permeability
on outcrops. A portable permeameter is basically an annulus through
which air can be released into porous media. The permeameter
measurements are localized with a depth of investigation of less
than four times the internal radius of the tip seal [34]. This means
that the investigation depth of the Tiny-Perm II, with the inner tip
diameter of about 9 mm, is less than 18 mm. Within fractured
zones, we put the Tiny-Perm II on the intact portion of deformed
rock with distance more than the investigation depth of Tiny-Perm
II to the fractures. For measuring the permeability of deformation
band we put the Tiny-Perm II on the deformation band. We did not
observe any visible slip surface in the deformation bands. We used
the empirical relation (Eq. (1)), provided by the user's manual
of the instrument, to convert the Tiny-Perm II readings to the
permeability. The relation used to calculate the permeability is
given by:
TP ¼−0:8206logðKÞ þ 12:8737 ð1Þ
where TP is the Tiny-Perm II reading, and K is the permeability in
mD. The recommended permeability measurement range for rock
is approximately from 10 mD to about 10 D by the manufacturer.
For Tiny-Perm II measurements we took three readings on each
test spot, to examine the repeatability and minimize the possible
user based errors, and then used the average value of the readings
to calculate the permeability of the spot.
In-situ values of rock hardness have been measured by Schmidt
Hammer type N. Schmidt hammer is a device that has been used
N
UT
Fault Core
FootwallHanging-wall
Navajo SSt.
Scan line
Measurement spot
Scan line
109° 29’
38° 44’
109° 32’ 38° 40’
S.R. Mb.
D.B. Mb.
20 m
50 cm
2 km
Fig. 1. (a) Field work location, Cache Valley (outside the Arches National Park), Utah, USA, with principal structural features of the area, map is modified after [54],
(b) Studied fault with indications of Navajo Sandstone at footwall and Slick Rock Member (S.R. Mb.) and Dewey Bridge Member (D.B. Mb.) at hanging-wall and (c) Scan line
with a measurement spot.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–38 29
to estimate the rock hardness and elastic properties or compres-
sive strength of rocks mass [35,36]. Different empirical relations
between Schmidt hammer rebound values and rock strength or/
and Young's modulus have been proposed by different researchers
[37–41]. Based on rock mineralogy (sandstone) and hammer type
(N type), we employ the empirical relation provided by Katz et al.
[37] (Eqs. (2) and (3)) to convert the Schmidt Hammer rebound
values (HR) to uniaxial compressive strength U (MPa), and Young's
modulus E (GPa), respectively:
lnðUÞ ¼ 0:792þ 0:067ðHRÞ70:231 ðR2 ¼ 0:96Þ ð2Þ
lnðEÞ ¼−8:967þ 3:091lnðHRÞ70:101 ðR2 ¼ 0:99Þ ð3Þ
Schmidt hammer measurements have been acquired mostly on
the same locations as the permeability measurements had been
performed. The International Society for Rock Mechanics (ISRM)
[42] recommended averaging the upper 50% of at least twenty
single impact readings, after eliminating any reading from points
that show signs of cracking. American Society for Testing and
Materials (ASTM) [43] suggested taking at least ten single impact
readings, discarding those differing from the average by more than
seven units, and averaging those left. In this work we followed the
ASTM [43] method. Schmidt hammer rebound values obtained
along non-horizontal directions are normalized using the correc-
tion curves provided by the manufacturer based on ISRM [42] and
ASTM [43] standards.
For both Tiny-Perm II and Schmidt Hammer we polished the
rock surface by using a geological hammer to minimize weath-
ering effects and also to make the test spot smooth and flat. We
have avoided measuring permeability and hardness on fractures,
although one could expect small fractures around the measure-
ment spots. These small fractures could affectthe permeability of
the intact rock as well as its strength and elasticity. Hence, the
measured properties here are considered to be effective properties
of the whole media that is affected by our measurements. Based
on the permeability and rock strength/Young's modulus, we
evaluate the possible relationship between them in footwall and
hanging-wall of both faults using the field data and suitable
statistical tests.
2.2. Statistical method
First, we statistically evaluate the correlation between the two
parameters of interest. Let xi¼{HRi, Ui, Ei, ln HRi, ln Ui, ln Ei},
yi¼{TPi, Ki, ln TPi, ln Ki}. Dependence of vectors x, y is characterized
by correlation coefficient
rxy ¼
∑Ni ¼ 1ðxi−〈x〉Þðyi−〈y〉Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
∑Ni ¼ 1ðxi−〈x〉Þ2∑Ni ¼ 1ðyi−〈y〉Þ2
q ð4Þ
In the formulas, bold fonts indicate vectors, and mean values are
denoted by hi. Statistical significance of the correlation coefficient
ðrxy≠0Þ can be tested using the t-test [44]
_
t
�� ��¼ ��� rxy
ffiffiffiffiffiffiffiffiffiffi
N−2
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1−rxy2
p ���≥tðN−2;αÞ ð5Þ
where N is the overall sample size and α is the significance level.
A default value of α¼5% is used in all our calculations. Statistical
analysis is performed by using the regression
yi ¼ γðxiÞ þ εi; i¼ 1;…;N ð6Þ
with linear function γðxiÞ ¼ bxþ a. The random residuals εi are
assumed independent and normally distributed with zero mean
and standard deviation s. Regression parameters a, b are esti-
mated by maximal likelihood estimation method with likelihood
function
jða; b; sjy; xÞ∝ðs2Þ−N=2exp − ∑
N
i ¼ 1
½yi−γðxiÞ�2
2s2
 !
ð7Þ
Calcite cement
Fig. 2. Electron microscope (SEM) images of Navajo Sandstone from the (a) Cache Valley and (b) San Rafael Swell localities. The arrows indicate the calcite cement (light grey
color) preserved in the pore spaces.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–3830
To validate the quality of regression approximation we apply
two tests based on using F-test statistics. Hypothesis H0 is
considered against alternative hypothesis H1. In the first statistical
criterion (F-test 1)
H0 : b¼ 0; H1 : b≠0 ð8Þ
H0 states that there is no significant correlation between x and y,
and H1 states that there is a significant correlation (positive or
negative) between x and y. The test function is
F−test 1 :
ðSYY−RSSÞ
s2
4F1;N−2ðαÞ ð9Þ
where
SYY ¼ ∑
N
i ¼ 1
½yi−〈y〉�2; RSS¼ ∑
N
i ¼ 1
½yi−_γ ðxiÞ�2; s2 ¼
RSS
N−2
ð10Þ
where SYY is the sum of squares for y's, RSS is the residual sum of
squares and s2 is the residual mean square. If Eq. (9) holds then
null hypothesis related to reduced model H0 is rejected with (1−α)
100% confidence [45,46].
In this study we use also another statistical test using
F-distribution and checking the improvement of regression appro-
ximation estimation in comparison with mean value approxima-
tion [44]. The corresponding test function is
F−test 2 :
SYY
s2ðN−1Þ 4FN−1;N−2ðαÞ ð11Þ
3. Structural geology of the studied localities
3.1. Fault in Cache Valley outside the Arches National Park
Cache Valley is located at the eastern border of Arches National
Park, Utah, USA. A salt diapir exists below this area, which formed
during the salt movement period from the Pennsylvanian through
the Triassic [8,47]. The lateral flow and diapiric rise of the salt
caused folding overlying strata, which has resulted in a salt
anticline [8,47].
The normal faults of the area may have been formed during the
relaxation of compression at some time later [8]. In Cache valley we
studied a normal fault with some small sub-parallel faults. The main
fault is striking NW and dips toward SW with the measured dip of
about 721. Based on our own and Braathen et al. [48] field
observations the fault displacement is about 30 m. The fault cut
through the Navajo Sandstone at the footwall and Slick Rock
Member and Dewey Bridge Member of Entrada Sandstone at the
hanging-wall (see Fig. 1). Navajo Sandstone is a massive eolian
sandstone, and it shows high-angle cross-beddings at the Cache
Valley. It is generally well-sorted fine-grained, with medium to
coarse grains of sand along the crossbedded laminae [47]. Navajo
Sandstone at the Cache Valley is almost clean sandstone with small
patches of calcite cement in some grain contacts (see Fig. 2a). The
Dewey Bridge Member of Entrada Sandstone is divided into lower
and upper subunits in the Arches National Park area. The lower unit
is medium to thick beds of resistant, fine-grained sandstone, and
the upper unit is muddy-looking mostly fine- grained, silty sand-
stone [50]. The Slick Rock Member of the Entrada Sandstone is a
massive, well-indurated sandstone. The sandstone is very fine to
fine-grained with some area of medium to coarse sand grains. The
sand grains have been slightly cemented with calcite and iron oxide
[49]. Deformation elements within damage zone of the fault include
deformation bands and fractures but the dominant structure in
Navajo and Entrada Sandstones is deformation band.
3.2. Fault in San Rafael Swell
The studied fault at the San Rafael Swell which is located at the
central Utah, USA is presented in Fig. 3. The Swell is a monocline
composed of Phanerozoic sedimentary sequence [9]. A NW-SE s1
direction is proposed for the formation of the San Rafael mono-
cline fold [51,52]. The origin and timing of faults in this area are
somehow uncertain, but it is suggested that they formed in
response to the San Rafael Swell uplift during Laramide age
between 66.4 and 37 Ma [9,53].
The studied fault in San Rafael Swell is located to the north of
the steepest part of the San Rafael Monocline and cuts through
calcite cemented Navajo Sandstone both in footwall and hanging-
wall. The amount of calcite cement occupying the pore space of
the Navajo Sandstone is fairly high in this locality (see Fig. 2b). The
fault strikes NW and dips westward with a dip angle between 601
and 841 (based on the measurements on separate slip surfaces).
Due to complexity of the locality and the fact that the fault has
displaced Navajo versus Navajo at the observed slip surface, the
type (sense of movement) and displacement of the fault is
uncertain. However, based on elevation difference between two
sides of the fault (measured by a GPS) and the dip direction of the
fault; we estimated the displacement to be at least 20 m and the
movement to have a Normal component. Presence of major strike-
slip faults in the area, deformation bands showing indication of
strike-slip movements in the vicinity of this locality (not studied in
this work, see Fig. 3d) and a number of normal faults around the
locality [9,53] support our observations.
Faults to the north of our study area, the Chimney Rock fault
array and the Big Hole fault, occur in four sets of opposite dipping
N
5 km
1 m
Footwall Hanging-wall
UT
Slip surface
110° 30’ 110° 26’
39° 00’
39° 07’
DB
Be
ddi
ng
DBs
Fractures/Veins
Fig. 3. (a) Field work location, San Rafael Swell, Utah, map is modified after [54] (b) Fault slip surface and the damage zones at footwall and hanging-wall, (c) deformation
bands and two sets of fractures observed in the damage zone of the studied fault. (d) Deformation bands have displaced beddings in Navajo Sandstone, observed in the
vicinity of the studied locality (not included in this study).
Table 1
Distribution of deformation elements (fractures and deformation bands) along
scan-lines at the fault located in Cache Valleya.
Length
(m)
No. of
bands
No. of
fracs
Avg. band
density
(bands/m)
Avg. frac.
density
(fracs/m)
Total scan-line 155.5
(177)
257 43 1.67 0.28
Footwall
(Navajo SSt.)
76 (99) 191 12 2.51 0.16
Hanging-wall 78 66 31 0.85 0.40
Slick Rock Member 20 61 5 3.05 0.25
Dewey Bridge Member 58 5 26 0.09 0.45
a In the length column numbers in the parentheses present thetotal length of
scan-line, and number outside the parentheses, present the total scan-line minus
covered section length. Hanging-wall is divided into two members of Entrada
Sandstone: Slick Rock Member and Dewey Bridge Member.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–38 31
fault pairs with the orientation ENE and WNW, they are mainly
normal faults [9,53,55] with some oblique movements [53]. Two
different mechanisms for fault formation is suggested for this area
[9,55]; an early phase of development of deformation bands with
associated slip surfaces and a later stage of fracturing and faulting,
which has overprinted the early structures [9,55]. In consistency
with these previous studies [9,55], the observed fault, deformation
bands, fractures and veins suggest at least two phases of deforma-
tion in our studied locality. Similar to these studies, we suggest that
fractures and faults have overprinted early deformation bands. This
fault is more fractured relative to the fault in Cache Valley.
4. Results
We present our data collected from the studied faults at two
localities in Cache Valley (non- cemented Navajo Sandstone) and
San Rafael Swell (cemented Navajo Sandstone). We first present
the distribution of structural elements, then the mechanical and
petrophysical properties based on the field measurements and at
the end the statistical results based on our geostatistical analysis.
4.1. Distribution of structural elements
The density of deformation elements along the scan-lines at
both studied areas decreases away from the fault. Table 1 sum-
marizes the distribution of deformation elements along scan-lines
across the fault zone located at Cache Valley. At the damage zone
of the Cache Valley fault, the length of scan-line at the footwall is
about 99 m, but because of vegetation and coverage we could not
scan some part of the scan-line, so the length of the covered
section (see Fig. 4a) is deducted from the total length of scan-lines
at the footwall which is presented in parentheses in Table 1. The
thickness of fault core is about 1.5 m, which is included in the total
length of scan line, but it is not included in footwall or hanging-
wall length.
At the Cache Valley fault, deformation elements included
deformation bands and fractures. Totally about 300 deformation
elements have been observed, among them 257 are deformation
bands and 43 are fractures. Deformation bands are spread in
Navajo Sandstone and Slick Rock Member of Entrada Sandstone,
and are rarely presented in the Dewey Bridge Member of Entrada
Sandstone. But fractures are concentrated to the area close to the
fault core, in the distance of about 3–4 m, in Navajo Sandstone and
Slick Rock Member, while they are distributed in the Dewey Bridge
Member (see Fig. 4a). The distribution of deformation elements
along scan-lines across the fault zone located at San Rafael Swell is
summarized Table 2. In this locality, the damage zone of the fault
is highly cemented by calcite and its structural elements include
deformation bands, fractures and veins at the footwall and
hanging-wall of the fault. The average band density and fracture
density is higher at the footwall (see Table 2).
0
5
10
15
20
25
30
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181
In
te
ns
ity
 (/
m
) 
D (1m bins)
Deformation element at the fault located in Cache Valley
Deformation bands
Fractures
Main fault Small fault
Hanging-wall Footwall
Covered part
Small fault
Small fault
1
10
100
1000
10000
0
10
20
30
40
50
60
70
40 80 120 1600 20 60 100 140 180
K
 (m
D
)
E
 (G
P
a)
Distance along scan-line (m)
Permeability and Young's Modulus (the fault located in Cache Valley)
Young's Modulus
Permeability
Main Fault
Covered part
Fig. 4. (a) Intensity of deformation elements and (b) distributions of permeability and Young's modulus, along scan-lines at the fault zone located in Cache Valley.
Table 2
Distribution of deformation elements (fractures and deformation bands) along
scan-lines at the fault located in San Rafael Swell.
Length
(m)
No. of
bands
No. of
fracs
Avg. band
density
(bands/m)
Avg. frac.
density
(fracs/m)
Total scan-line 68 226 218 3.32 3.21
Footwall
(Navajo Sst.)
27 160 118 5.93 4.37
Hanging-wall
(Navajo Sst.)
41 66 100 1.61 2.44
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–3832
The separation of deformation bands and fractures/veins are
based on visual inspection of the deformation structures in the
field and some have also been examined by thin section analysis.
Deformation structures that seemed outstanding cataclastic band
with or without calcite cementation, typically less weathered than
the surrounding rock are classified as deformation bands. Other
structures, such as open fractures and calcite veins are classified as
fractures and include both pure tension fractures and shear
fractures with minor shear displacement that has not been
captured. At the fault located in San Rafael Swell, because of
coverage in some sections of damage zone along the primary scan-
line, we had to slightly move the scan-line up and down in the
same direction. Fig. 5a, presents the intensity of deformation
elements (fractures and deformation bands) at the fault located
in San Rafael Swell.
4.2. Mechanical and petrophysical properties
We have investigated the distribution of in situ Tiny-Perm II
(converted to calculated permeability using Eq. (1)) and Schmidt
hammer (converted to uniaxial compressive strength and elasti-
city using Eqs. (2) and (3)) measurements in the damage zone of
two studied faults. Our data indicates that we had reasonable
variations in our measurements. The average standard deviation of
Tiny-Perm II measurements in non-cemented Navajo Sandstone
(Cache valley fault) is about 0.04 with highest standard deviation
of about 0.17 and lowest standard deviation of 0.005. In cemented
Navajo Sandstone (San Rafael Swell fault) the average standard
deviation of measurements is about 0.08 with the highest and
lowest standard deviations of about 0.22 and 0.01 respectively. The
average standard deviation of Schmidt hammer measurements in
non-cemented Navajo Sandstone is about 1.6 with highest stan-
dard deviation of about 3.3 and lowest standard deviation of about
0.5. In cemented Navajo Sandstone average measurements stan-
dard deviation is about 1.6 with the highest standard deviation of
about 4.2 and lowest standard deviation of about 0.4.
Table 3 summarizes the field measurements and calculated
mechanical and petrophysical properties of rock at the fault zone
of Cache Valley fault. At the footwall (Navajo Sandstone) of Cache
Valley fault the mean value of permeability is about 380 md with
the maximum and minimum of about 3360 md and 6 md respec-
tively (see Table 3). At the hanging-wall, the mean value of
permeability for the Slick Rock Member, it is about 292 md, while
for Dewey Bridge Member is about 9 md. Compressive strength
mean value of Navajo Sandstone at the footwall is about 52.5 MPa
with the Young's modulus mean values of about 18 GPa. At the
hanging-wall, compressive strength mean value of Slick Rock
Member is about 36.5 MPa and mean value of Young's modulus
is about 12.5 GPa, and for Dewey Bridge Member compressive
strength and Young's modulus mean values are about 79.5 MPa
and 27.5 GPa respectively. For more information about the rock
hardness values measured with Schmidt hammer and correspond-
ing compressive strength and Young's modulus see Table 3. Fig. 4b
presents the distributions of permeability and Young's modulus at
the fault zone of the Cache Valley fault. The highest value of
permeability and the lowest value of Young's modulus are mea-
sured/calculated around the fault core (see Fig. 4); this might be
due to the presence of more fractures around this area.
Intensity of deformation elements along scan-lines at the
footwall and hanging-wall of the fault studied in San Rafael Swell
is presentedin Fig. 5a and Fig. 5b presents the distributions of
permeability and Young's modulus along scan-lines at the fault
zone of this fault.
Table 3
Mechanical and petrophysical properties of rock at the damage zone of the fault located in Cache Valleya.
Hanging-wall Footwall
Dewey Bridge Member Slick Rock Member Navajo Sandstone
TP HR K (md) U (MPa) E (GPa) TP HR K (md) U (MPa) E (GPa) TP HR K (md) U (MPa) E (GPa)
Mean 12.1 52.5 8.8 79.7 27.4 10.9 39.9 292.3 36.4 12.7 10.8 46.5 380.1 52.6 18.1
Max 12.7 62.1 92.6 141.6 44.5 11.4 50.2 1697.4 63.8 23.0 12.2 55.1 3359.9 88.6 30.7
Min 11.3 43.9 1.6 41.8 15.2 10.2 29.1 70.9 15.5 4.3 10.0 30.3 5.9 16.8 4.8
a Empirical relations (1), (2) and (3) are used to calculate rock permeability (K), uniaxial compressive strength (U) and Young's modulus (E) respectively, from Tiny-Perm
II measurements (TP) and Schmidt hammer rebound values (HR).
Table 4
Mechanical and petrophysical properties of rock at the fault zone of the fault
located in San Rafael Swella.
Hanging-wall Footwall
TP HR K
(md)
U
(MPa)
E
(GPa)
TP HR K
(md)
U
(MPa)
E
(GPa)
Mean 11.0 45.0 193.8 58.5 19.8 11.4 45.0 69.3 51.9 18.1
Max 11.8 62.2 1916.9 142.5 44.7 12.2 57.4 563.0 103.3 34.9
Min 10.2 20.9 21.9 9.0 1.5 10.6 29.5 7.6 15.9 4.5
a Empirical relations (1), (2) and (3) are used to calculate rock permeability (K),
uniaxial compressive strength (U) and Young's modulus (E) respectively, from Tiny-
Perm II measurements (TP) and Schmidt hammer rebound values (HR).
0
5
10
15
20
25
30
1 6 11 16 21 26 31 36 41 46 51 56 61 66
In
te
ns
ity
 (/
m
) 
D (1m bins)
Deformation elements at the fault located in San Rafaell Swell
Deformation bands
Fractures/Veins
Main Fault Small Fault
Hanging-wall Footwall
1
10
100
1000
10000
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35 40 45 50 55 60 65
K 
(m
D)
E 
(G
Pa
)
Distance along scan-line (m)
Permeability and Young's Modulus (the fault located in San Rafael Swell)
Young's Modulus
Permeability
Main fault
Fig. 5. (a) Intensity of deformation elements and (b) distributions of permeability and Young's modulus, along scan-lines at the fault zone located in San Rafael Swell.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–38 33
The mechanical and petrophysical properties of rock at the
fault zone of San Rafael Swell fault are summarized in Table 4. At
the footwall of the fault located in the San Rafael Swell mean value
of permeability is about 69 md with the maximum and minimum
of about 563 md and 7.5 md respectively. Mean value of perme-
ability at the hanging-wall is about 194 md, the maximum
permeability is about 1917 md and minimum permeability is
about 22 md. Compressive strength and Young's modulus mean
values for footwall are about 52 MPa and 18 GPa respectively, and
at the hanging-wall of the fault compressive strength and Young's
modulus mean values are about 58.5 MPa and 20 GPa respectively.
For maximum and minimum values of rock hardness and corre-
sponding compressive strength and Young's modulus, see Table 4.
4.3. Statistical results
In this section we present the results of statistical analysis of
different datasets for cemented and non-cemented Navajo Sand-
stones. Tables 5–8 present the correlation coefficients, parameters of
optimal linear regressions and corresponding confidence intervals for
ln TP–HR, ln K–U, ln K–E relations (exponential law dependencies) in
comparison with ln TP-ln HR, ln K–ln U, ln K–ln E relations (power
law dependencies). First statistical test (F-test 1 defined by Eq. (9)) is
satisfied for all relations in both locations (Cache Valley and San
Rafael Swell) and it is just presented for the Cache Valley locality.
Second statistical test (F-test 2 defined by Eq. (11)) is not satisfied for
all relations, hence, its significance becomes more crucial for the
evaluation of some of the relations, and therefore it has been
presented for all relations for both localities.
In the Cache Valley location we apply the statistical analysis
just for the footwall (Navajo Sandstone) as the range of perme-
ability in Dewey Bridge Member of Entrada Sandstone is below the
recommended permeability measurement range for Tiny-Perm II,
and there are only three TP and HR measurements on the Slick
Table 6
Results of statistical analysis, non-cemented Navajo Sandstone, footwall of the fault located in Cache Valley, power law relations.
Relation ln TP (ln HR) ln K (ln U) ln K (ln E)
rxy 0.7113 −0.7509 −0.7064
t-test (R) , α¼5% Yes (4.32141.728) Yes (4.79441.728) Yes (4.27741.728)
a 1.640370.3527 14.351073.6843 10.972672.5852
b 0.197070.0935 −2.319270.9794 −1.966170.9461
F-test 1, α¼5% Yes (19.45844.381) Yes (24.56544.381) Yes (18.91944.381)
F-test 2, α¼5% No (1.923o2.155) Yes (2.17842.155) No (1.896o2.155)
F-test 2, α¼10% Yes (1.92341.814) Yes (2.17841.814) Yes (1.896o1.814)
Table 7
Results of statistical analysis, cemented Navajo Sandstone, damage zone (footwall and hanging-
wall) of the fault located in San Rafael Swell, exponential relations.
Relation ln TP (HR) ln K (U) ln K (E)
rxy 0.6847 −0.5812 −0.6104
a 2.251970.0515 6.322070.7600 6.439070.7519
b 0.003670.0011 −0.028070.0115 −0.087870.0334
F-test 2, α¼5% Yes (1.84341.621) No (1.479o1.621) No (1.561o1.621)
F-test 2, α¼10% Yes (1.84341.456) Yes (1.47741.456) Yes (1.56141.456)
Table 8
Results of statistical analysis, cemented Navajo Sandstone, damage zone (footwall and hanging-
wall) of the fault located in San Rafael Swell, power law relations.
Relation ln TP (ln HR) ln K (ln U) ln K (ln E)
rxy 0.7023 −0.6721 −0.6886
a 1.836970.1717 11.030872.0636 8.894571.3298
b 0.152370.0453 −1.645970.5321 −1.522770.4705
F-test 2, α¼5% Yes (1.93241.621) Yes (1.78641.621) Yes (1.86341.621)
F-test 2, α¼10% Yes (1.93241.456) Yes (1.78641.456) Yes (1.86341.456)
Table 5
Results of statistical analysis, non-cemented Navajo Sandstone, footwall of the fault located in Cache Valley, exponential law relations.
Relation ln TP (HR) ln K (U) ln K (E)
rxy 0.7546 −0.8504 −0.8266
t-test (R) , α¼5% Yes (4.82741.725) YES (6.44541.725) YES (5.94441.725)
a 2.162170.0932 8.531470.9122 8.371270.9515
b 0.005070.0021 −0.062070.0184 −0.164370.0537
F-test 1, α¼5% Yes (25.13244.381) Yes (49.63044.381) Yes (40.97244.381)
F-test 2, α¼5% Yes (2.20742.155) Yes (3.43142.155) Yes (2.99942.155)
F-test 2, α¼10% Yes (2.20741.814) Yes (3.43141.814) Yes (2.99941.814)
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–3834
Rock Member of Entrada Sandstone. Figs. 6 and 7 present field
measurements and estimated regressions for considered relations.
4.3.1. Non-cemented Navajo Sandstone at the footwall of the fault in
the Cache Valley
Applied statistical relations (ln TP–HR, ln K–U and ln K–E) on
field measurements and estimated regression parameters from the
footwall of the fault in the Cache Valley are presented in Fig. 6.
The results of statistical analysis of data collected from Navajo
sandstone in footwall of the this fault are summarized in
Tables 5 and 6. Table 5 presents correlation coefficients and
regression coefficients for ln TP–HR, ln K–U, ln K–E relations (expo-
nential law dependences) and corresponding results of regressions
quality testing based on two statistical criterions F-test 1 (first
statistical test defined by Eq. (9)) and F-test 2 (second statistical
test defined by Eq. (11)). For F-test 1 significance level of 95% is
used (α¼5%) while the results for F-test 2 are given for two
significance levels of 95% (α¼5%) and 90% (α¼10%).
The correlation coefficient intervals for ln TP–ln HR, ln K–ln U,
ln K–ln E relations (power law dependences) and dependence
validation based on criterion F-test 1 and F-test 2 are presented
in Table 6. The validation of determined dependences is per-
formed. The t-test (Eq. (5)) and F-test 1 are satisfied with the
significance level of 95% for all studied relations.
4.3.2. Cemented Navajo Sandstone at the damage zone of the fault in
San Rafael Swell
Best approximationsfor ln TP–HR, ln K–U and ln K–E for
cemented Navajo Sandstone at the damage zone of the fault in
San Rafael Swell are presented in Fig. 7. Tables 7 and 8 summarize
the results of statistical analysis of data collected from the damage
zone of the fault located in San Rafael Swell and present the
intervals of regression coefficients for exponential law and
power law relations and dependence validation based on F-test 2
(Eq. (11)).
The validation of determined dependences is performed. The
t-test (Eq. (5)) and F-test 1 (Eq. (9)) are satisfied with the
1.5 2 2.5 3 3.5
1
2
3
4
5
6
7
8
9
ln E
measured data
y = − 1.9661 y + 10.9726
2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6
1
2
3
4
5
6
7
8
9
ln U
ln
 K
ln
 K
ln
 K
ln
 K
measured data
y = − 2.3192 + 14.3510
3.4 3.5 3.6 3.7 3.8 3.9 4 4.1
2.32
2.34
2.36
2.38
2.4
2.42
2.44
2.46
2.48
2.5
2.52
ln HR
ln
 T
P
measured data
y = 0.1970 x + 1.6403
5 10 15 20 25 30
1
2
3
4
5
6
7
8
9
E
measured data
y = − 0.1643 x + 8.3712
10 20 30 40 50 60 70 80 90
1
2
3
4
5
6
7
8
9
U
measured data
y = − 0.0620 x + 8.5314
30 35 40 45 50 55
2.32
2.34
2.36
2.38
2.4
2.42
2.44
2.46
2.48
2.5
2.52
HR
ln
 T
P
measured data
y = 0.0050 x + 2.1621
Fig. 6. Parameters and function_γ ðxÞ defined as best approximation for (a) ln TP–(HR), (b) ln K–(U), (c) ln K–(E), (d) ln TP–(ln HR), (e) ln K–(ln U) and (f) ln K–(ln E) relations,
non-cemented Navajo sandstone, footwall of the Cache Valley fault.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–38 35
significance level of 95% for all studied relations. The results for the
F-test 2 (Eq. (11)) are given for two significance levels of 95%
(α¼5%) and 90% (α¼10%).
5. Discussion
This study combines field measurements and geostatistical ana-
lysis of petrophysical and mechanical properties such as permeabil-
ity, strength and Young's moduli of deformed rocks exposed in
Navajo and Entrada sandstones in the damage zone of two faults
located in Cache Valley and San Rafael Swell. Using empirical
relations we have calculated the permeability, strength and elasticity
of deformed rock from our in-situ field measurements by Tiny-Perm
II and Schmidt Hammer. Our field measurements indicate that in the
damage zone of both faults permeability and strength/elasticity of
rock change in accordance with the density and type of deformation
structures (fractures and deformation bands).
In the studied damage zone of faults, both compacted (defor-
mation bands) and dilated (fractures) areas exist, which have
influenced our field measurements (see Figs. 4 and 5). In non-
cemented Navajo Sandstone, a cluster of deformation bands (about
8 m from fault core) shows the highest strength/elasticity and
lowest permeability, whereas a zone of fractures (about 1 m from
the fault core) shows the highest permeability and lowest strength
and elasticity (see Fig. 4). The observed deformation bands in non-
cemented Navajo Sandstone are mostly cataclastic bands with
grain rearrangement and moderate grain crushing. In cemented
Navajo Sandstone, most of the fractures/veins have been devel-
oped parallel to the existing cataclastic bands, and cementation
tends to have high influence on permeability and strength of the
fractured zone, i.e. cementation has decreased the permeability
and increased the strength and the Young's modulus of rock.
However, in both cemented and non-cemented Navajo Sandstone
at the damage zones of faults, permeability and strength/elasticity
along the scan-lines suggest reverse distributions (see Figs. 4b and
0.5 1 1.5 2 2.5 3 3.5 4
0
1
2
3
4
5
6
7
8
ln E
measured data
y = − 1.5227 x + 8.8945
2 2.5 3 3.5 4 4.5 5
0
1
2
3
4
5
6
7
8
ln U
ln
 K
ln
 K
ln
 K
measured data
y = − 1.6459 x + 11.0308
3.2 3.4 3.6 3.8 4 4.2
2.3
2.35
2.4
2.45
2.5
2.55
2.6
ln HR
ln
 T
P
measured data
y = 0.1523 x + 1.8369
0 5 10 15 20 25 30 35 40 45 50
0
1
2
3
4
5
6
7
8
E
measured data
y = − 0.0878 x + 6.4390
0 50 100 150
0
1
2
3
4
5
6
7
8
U
ln
 K
measured data
y = −0.0280 x + 6.3220
20 25 30 35 40 45 50 55 60 65
2.3
2.35
2.4
2.45
2.5
2.55
2.6
HR
ln
 T
P
measured data
y = 0.0036 x + 2.2519
Fig. 7. Parameters and function_γ ðxÞ defined as best approximation for (a) ln TP–(HR), (b) ln K–(U), (c) ln K–(E), (d) ln TP–(ln HR), (e) ln K–(ln U) and (f) ln K–(ln E) relations,
cemented Navajo Sandstone, damage zone of the San Rafael Swell fault.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–3836
5b), i.e. when permeability increases, compressive strength and
elasticity decrease and vice versa.
According to the t-tests results (see Tables 5–8) there is a
correlation with the confidence level (significance level) of 95% for
(TP–HR), (K–U) and (K–E) in deformed Navajo sandstone in the
damage zone of two studied faults. Statistical analysis reveal a
positive correlation between TP and HR values (which means if HR
changes then the TP will change in the same direction) and negative
or inverse correlations for K–U and K–E (which means an increase or
decrease in rock strength or elasticity will be a sign of permeability
change in opposite direction). Quality of regression approximations
are validated by applying two tests based on using F-test statistics.
Figs. 6 and 7 present TP–HR, K–U and K–E relationships, and Table 9
summarizes them. Table 9 presents the statistical results of linear,
exponential and power-law relations for all studied data from both
locations based on F-test 2. In Table 9, bold numbers indicate the
dependences with highest values of F-test 2. All relations satisfy
F-test 1 (first statistical test defined by Eq. (9)) with significance level
of 95% (α¼5%), but some relations could not satisfy F-test 2 (second
statistical test defined by Eq. (11)) with significance level of 95%
(α¼5%), and not with significance level of 90% (α¼10%) either. The
dependences with the highest F-statistics or best relations are the
same for both F-test 1 and F-test 2.
Nevertheless almost all kind of considered relations satisfy to
F-test 1 and F-test 2 for TP-HR dependence, the exponential
relation for the non-cemented Navajo Sandstone, and power
law relation for cemented Navajo Sandstone give highest F-test
2 statistics (see Table 9). As Table 9 indicates K–U and K–E
correlations do not follow the linear relation with confidence level
of 95% (α¼5%). With confidence level of 90% (α¼10%), only the K–
E correlation in cemented Navajo Sandstone follows the linear
relation, therefore, linear relation is rejected for K–U and K–E.
Both exponential and power law relations are satisfied with
confidence level of 90% (α¼10%) for K–U and K–E dependences in
both cemented and non-cemented Navajo Sandstone. With con-
fidence level of 95% (α¼5%), for both K–U and K–E exponential
relation is satisfied for non-cemented Navajo Sandstone but in
cemented Navajo Sandstone power law is satisfied for K–U and K–E
Table 9
Results of statistical analysis; comparison of linear, exponential and power-law
relationsa.
Calculated statistical values based on Eq. (11) F-test 2
Linear
relation
Exponential
relation
Power-law
relation
α¼5% α¼10%
Non-cemented Navajo Sandstone (Cache Valley)
TP (HR) 2.1782 2.2066 1.9229 2.1555 1.8142
K (U) 1.4191 3.4315 2.1782
K (E) 1. 4527 2.9986 1.8960
Cemented Navajo Sandstone (San Rafael Swell)
TP (HR) 1.7859 1.8434 1.9322 1.6207 1.4557
K (U) 1.4498 1.4786 1.7859
K (E) 1.5621 1.5607 1.8623
a Eq. (11) and F-test 2 are used to calculate the statistical values for two
significance levels of 95% (α¼5%) and 90% (α¼5%), bold numbers indicate the
dependences with highest statistical values.
R. Alikarami et al. / International Journal of Rock Mechanics & Mining Sciences 63 (2013) 27–38 37
relations. According to the statistical results, the exponential
relation gives the most suitable relation (for the TP–HR, K–U and
K–E) for non-cemented Navajo Sandstone data, while for cemen-
tedNavajo Sandstone, power law relation gives the best approx-
imation for the mentioned relations.
The presence of cement increases the compressive strength and
Young's modulus of Navajo Sandstone and decreases its perme-
ability, but permeability is more sensitive to cementation than the
compressive strength and Young's modulus (see Tables 3 and 4).
This different sensitivity to cementation could be a possible reason
for different type of relation between K–U and K–E in non-
cemented and cemented Navajo Sandstone.
The above statistical relations could be valid for rocks with
similar mineralogy to the non-cemented Navajo Sandstone, which
comprises quartz sandstone in the Cache valley and the cemented
one with mainly calcite cementation in the San Rafael Swell.
Application of these relations to other rocks needs to be done
with care due to the effect of mineralogy, degree of cementation,
weathering and measurement-related bias. Although this study
suggests relations between deformed sandstones permeability and
its strength/elasticity, more work is needed to find out the most
suitable relations for different types of lithologies.
Our calculated permeability values for Navajo Sandstone are
consistent with the permeability values measured and reported by
Antonellini and Aydin [7] and Matthäi et al. [56], and Young's
modulus values calculated from the Schmidt Hammer rebound
values for Navajo sandstone are consistent with the values
reported by Spencer [57].
The results of this study may help scientists and engineers from
different disciplines such as petroleum engineering, geomechanics
and geophysics when there is a need for prediction of either the
petrophysical or mechanical properties of deformed sandstones
(lithologically similar to the Navajo Sandstone). These parameters
may be used as input to fluid flow and/or geomechanical simulators
when dealing with hydrocarbon production or CO2 sequestration.
6. Conclusions
Petrophysical and mechanical properties of sandstone reser-
voirs are likely to change as a result of faulting. In the damage zone
of faults with compacted areas both porosity and permeability
might decrease and rock strength might increase, whereas in
fractured zones of a damage zone porosity and permeability most
probably would increase and rock strength and its elasticity would
decrease. In this study we examine the possible relation between
rock permeability and its strength/elasticity by means of field
study and geostatistical analysis of data gathered from deformed
Navajo sandstone in the damage zones of two faults in Cache
Valley (non-cemented Navajo Sandstone) and San Rafael Swell
(cemented Navajo Sandstone). We examine linear, exponential law
and power law relations to find the most suitable relation for three
pairs of variables TinyPerm–Schmidt hammer (TP–HR), permeabil-
ity–uniaxial compressive strength (K–U) and permeability–Young's
modulus (K–E) in both locations.
Our field measurements and statistical results demonstrate that
1.
 Cementation has strong impact on permeability and mech-
anical properties of Navajo Sandstone. Cementation causes
high reduction in the permeability, while it enhances the
uniaxial compressive strength and Young's modulus of Navajo
sandstone.
2.
 In the damage zone of the fault with non-cemented Navajo
Sandstone in Cache Valley, zones of deformation bands show
the highest strength and Young's modulus and lowest perme-
ability, while zones of fractures around fault core have the
lowest strength and Young's modulus and highest permeability.
3.
 There are strong correlations with significance level of 95%
between TinyPerm–Schmidt hammer (TP–HR), permeability-
uniaxial compressive strength (K–U) and permeability–Young's
modulus (K–E) for Navajo Sandstone in the damage zones of
studied faults.
4.
 Correlation between deformed rock permeability and its
strength/elasticity is negative.
5.
 Linear relation is only valid for TinyPerm–Schmidt hammer
(TP–R). Permeability–uniaxial compressive strength (K–U) and
permeability–Young's modulus (K–E) do not follow linear
relationships.
6.
 For non-cemented Navajo Sandstone, in the damage zone of the
fault in Cache Valley, exponential law relation gives the highest
values of F-test 2 (second statistical test defined by Eq. (11)) for
TinyPerm–Schmidt hammer (TP–HR), permeability–uniaxial
compressive strength (K–U) and permeability–Young's modulus
(K–E) and therefore it is the most suitable distribution for these
relationships.
7.
 For cemented Navajo Sandstone, in the damage zone of the
fault in San Rafael Swell, power law relation is the best relation
with highest values of F-test 2 (second statistical test defined
by Eq. (11)) for TinyPerm–Schmidt hammer (TP–HR), perme-
ability–uniaxial compressive strength (K–U) and permeability–
Young's modulus (K–E).
Acknowledgments
This study is part of project 207806, The IMPACT Project,
funded by the CLIMIT Program at the Research Council of Norway
and Statoil. The financial support from Statoil-VISTA, research
cooperation between the Norwegian Academy of Science and
Letters and Statoil to the third author is acknowledged. The
authors are grateful to Bahar Ghahremany and Donald Seifried
for their field assistance in Utah, USA. Reviewer Atila Aydin is
greatly acknowledged for his constructive comments. The authors
would like to thank Patience Cowie for reviewing the first version
of the manuscript. Alvar Braathen is acknowledged for introducing
us to the field localities in Utah.
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	Geostatistical relationships between mechanical and petrophysical properties of deformed sandstone
	Introduction
	Methods
	Rock permeability and compressive strength/Young's modulus
	Statistical method
	Structural geology of the studied localities
	Fault in Cache Valley outside the Arches National Park
	Fault in San Rafael Swell
	Results
	Distribution of structural elements
	Mechanical and petrophysical properties
	Statistical results
	Non-cemented Navajo Sandstone at the footwall of the fault in the Cache Valley
	Cemented Navajo Sandstone at the damage zone of the fault in San Rafael Swell
	Discussion
	Conclusions
	Acknowledgments
	References