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Journal of African Earth Sciences 137 (2018) 22e31

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Journal of African Earth Sciences

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Estimation of static parameters based on dynamical and physicalproperties in limestone rocks

Mohammad Ghafoori*, Ahmad Rastegarnia, Gholam Reza LashkaripourDepartment of Geology, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran

a r t i c l e i n f o

Article history:Received 25 April 2017Received in revised form1 June 2017Accepted 6 September 2017Available online 7 September 2017

Keywords:Limestone rocksStatic and dynamic propertiesPhysical propertiesEmpirical relations

* Corresponding author.E-mail address: ghafoori@um.ac.ir (M. Ghafoori).

https://doi.org/10.1016/j.jafrearsci.2017.09.0081464-343X/© 2017 Elsevier Ltd. All rights reserved.

a b s t r a c t

Due to the importance of uniaxial compressive strength (UCS), static Young's modulus (ES) and shearwave velocity, it is always worth to predict these parameters from empirical relations that suggested forother formations with same lithology. This paper studies the physical, mechanical and dynamicalproperties of limestone rocks using the results of laboratory tests which carried out on 60 the Jahrum andthe Asmari formations core specimens. The core specimens were obtained from the Bazoft dam site,hydroelectric supply and double-curvature arch dam in Iran. The Dynamic Young's modulus (Ed) anddynamic Poisson ratio were calculated using the existing relations. Some empirical relations were pre-sented to estimate uniaxial compressive strength, as well as static Young's modulus and shear wavevelocity (Vs). Results showed the static parameters such as uniaxial compressive strength and staticYoung's modulus represented low correlation with water absorption. It is also found that the uniaxialcompressive strength and static Young's modulus had high correlation with compressional wave velocityand dynamic Young's modulus, respectively. Dynamic Young's modulus was 5 times larger than staticYoung's modulus. Further, the dynamic Poisson ratio was 1.3 times larger than static Poisson ratio. Therelationship between shear wave velocity (Vs) and compressional wave velocity (Vp) was power andpositive with high correlation coefficient. Prediction of uniaxial compressive strength based on Vp wasbetter than that based on Vs. Generally, both UCS and static Young's modulus (ES) had good correlationwith Ed.

© 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Most engineering projects related to the rocks such as tunnels,foundations and slopes, petroleum reservoir geomechanics (wellbore stability analysis, reservoir compaction survey, and predictionof optimum drilling mud pressure), as well as modeling thebehavior of rocks and estimation of in situ stresses are required thestatic and dynamic properties of the rocks (Chang et al., 2006;Abdulraheem et al., 2009; Alemdag et al., 2015).

Measuring static and dynamic properties of the rocks, especiallyUCS and ES are time consuming processes, tedious, expensive andrequire well prepared rock cores. In addition, obtaining these pa-rameters of rocks are difficult and not accessible, especially deepdrilling and geomechanical purposes. Therefore, indirect methodssuch as ultrasonic and physical tests are often used to predict theUCS and ES.

Indirect tests, especially none destructive tests (ultrasonic tests),are easier to carry out because they necessitate less or no samplepreparation and testing equipment is simple. Also they can be usedin the field. As a result, in comparison to the uniaxial compressiontest, indirect tests are simpler, faster and more economical.

Some researchers have investigated the dynamical, mechanicaland physical properties of carbonate rocks. Some of these studieswere listed at below.

Najibi et al. (2015) established some empirical relations be-tween strength and static and dynamic properties of limestonerocks. The relationship of compressional wave velocity (Vp) withYoung's modulus, density and UCS of carbonate rocks were inves-tigated. Results showed that there were strong relationships be-tween wave velocities and properties of limestone rocks(Kahraman and Yeken, 2008; Yasar and Erdogan, 2004; Concu et al.,2014). The relationship between the petrographic and geo-mechanical properties of pyroclastic rocks was studied by Korkançand Solak (2016).

Stan-Kłeczek (2016) investigated the relationship of bulk, shear

Fig. 1. A view of the Jahrum formation.

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e31 23

and elastic modulus as well as Poisson's ratio with compressionalwave velocity in limestone rocks. Castagna and Backus (1993) pre-sented empirical polynomial relations for estimating shear wavevelocity (Vs) from Vp depending on data derived from sonic log.

The relationship of the compressional wave velocity (Vs) andstress of the different rock types was investigated by Chen and Xu(2016). Also, the relationship of uniaxial compressive strength andpoint load was investigated by Ozturk and Altinpinar (2017).

Pappalardo (2015) presented some linear relationships of thecompressional wave velocity with UCS and physical properties inlimestone rocks. Likewise, the relationship of compressional wavevelocity with physical and mechanical properties of different rockswas investigated by Khandelwal (2013). Tamrakar et al. (2007)studied the relations between mechanical and lithological proper-ties of different rocks. _Ince and Fener (2016) and Ceryan (2014)presented a model for estimation of the uniaxial compressivestrength.

The effect of porosity on the tensile and compressive strength ofthe porous gypsumwas investigated by Palchik and Hatzor (2004).In addition, Palchik (2011) found the relationship of the UCS andstatic Young's modulus of carbonate rocks.

The association of the UCS and point load index of the 38different rock types was examined by Kahraman et al. (2005).Vasarhelyi (2005) also studied the influence of water content onthe strength of the limestone rocks.

Palchik (2006) presented a model to predict stressestrain re-lationships for weak to strong carbonate rocks.

Chang et al. (2006) suggested 31 empirical equations betweenp-wave velocity, Young's modulus, specific gravity and frictionangle with UCS for limestone, shale, dolomite and sandstone.

Table 1 lists some empirical relations between UCS, ES, density,water absorption (Wa) and Vs with dynamic and static data.

The main objective of this study was to predict UCS and ES oflimestone rocks. To achieve this goal, the uniaxial compression test,ultrasonic tests, physical tests such as water absorption, porosityand density, carried out on 60 limestone core specimens of theJahrum and the Asmari formations. The core specimens were ob-tained from the Bazoft dam site. The dynamic young's modulus (Ed)and Poisson's ratio were calculated based on related equations.Some empirical correlations between UCS and ES with Ed, porosity,density, water absorption (Wa), Vp and Vs for the Jahrum and theAsmari limestone were established. Also, the correlation of Vs andVp as well as UCS and ES were investigated. In addition, somesuggested empirical equations about the literatures of this paperwere adjusted with using the present data (measured values).

2. Bazoft dam site

Bazoft dam is a hydroelectric supply and double-curvature arch

Table 1Some empirical relations between UCS, Vs and ES with dynamic data (for carbonate rock

Equations Descriptions R

ES ¼ 74*LnðVpÞ � 572 Vp in m/s, ES in MPa 0UCS ¼ 31:5*Vp� 63:7 UCS in MPa, Vp in Km/s 0ES ¼ 10:67*Vp � 18:71 ES in GPa 0Vp ¼ 4:3183*r� 7:5071 Vp in Km/s, r in gr=cm3 0UCS ¼ 11:05*ES UCS in MPa, ES in GPa 0UCS ¼ 3:67*Vp Vp in Km/s 0

UCS ¼ 12:8*�

Ed10

�1:32 Ed in GPa 0

ES ¼ 0:169*Vp 0ES ¼ 0:014*Ed 0UCS ¼ 25:1*ES ES in GPa, UCS in MPa e

VS ¼ �0:055*Vp þ 1:017*Vp � 1:031 Vs and Vp in Km/s e

Wa ¼ �2:248*Vp þ 13:76 Vp in Km/s 0

dam with a height of 211 m located in Chaharmahal and Bakhtiariprovince of Iran. The bedrock of the dam site consists of the Ase-mari formation (limestone), and the Jahrum formation (limestone).Figs. 1 and 2 show pictures of the Jahrum and the Asmari forma-tions in dam site.

3. Thin section investigations

The Asmari formation age is related to Oligo-Miocene periodwhich is the main formation at the south west of Iran. The Asmariformation was studied at the Bazoft dam site.

According to the results of the petrographic examinations, thelimestone samples were dominantly calcite. Limestone of theAsmari formation includes benthic Foraminifera microfossils. Inaddition, the frequency of these microfossils showed that theAsmari formation precipitated in lagoon environment (Fig. 3).

More than 56 thin sections of the Jahrum formation wereanalyzed under the petrographic microscope (Fig. 4). The Jahrumformation consists of limestone, which includes bioclast wacke-stone to packstone. These microfossils showed that the Jahrumformation deposited in lagoon environment. Due to the great di-versity and abundance of large benthic foraminifera (includingmiliolides and textularids), the age of the Jahrum formation isrelated to the Paleocene-Eocene period.

The particles size and fossils of the microscopic sections showedthat the Jahrum formation was more fine-grained limestone ascompared to the Asmari formation. As shown in Tables 2 and 3, theaverage values of static properties (UCS and ES) of the Jahrum

s).

2 Lithology References

.74 carbonate rocks Stan-Kłeczek, 2016

.80 carbonate rocks Yasar and Erdogan, 2004

.86 carbonate rocks Yasar and Erdogan, 2004

.81 carbonate rocks Yasar and Erdogan, 2004

.79 limestone Najibi et al., 2015

.81 limestone Najibi et al., 2015

.88 limestone Najibi et al., 2015

.90 limestone Najibi et al., 2015

.87 limestone Najibi et al., 2015dolomite Chang, 2004Limestone and Dolomite Castagna et al., 1993

.90 carbonate rocks Kahraman and Yeken, 2008

Fig. 2. A view of the Asmari formation.

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e3124

formation (UCS¼ 73MPa and ES ¼ 15.53 GPa) specimens are higherthan those obtained for the Asmari formation (UCS ¼ 53.83 MPaand ES ¼ 9.34 GPa). In contrast, the physical properties of theAsmari formation are higher than Jahrum formation. Moreover,UCS and ES values were related to the carbonate percent. Carbonatecontent of samples of the Asmari and Jahrum formations are 52%and 63%, respectively.

4. Experimental procedure and results

In this study, 60 limestone core specimens of the Jahrom and theAsmari formations were obtained. Ultrasonic testing for measure-ment of Vs and Vp were performed according to ASTM D2845

Fig. 3. The thin sections of

standard (ASTM D2845, 1983). Fig. 5 shows the apparatus fordetermining of Vp and Vs. The velocities waves are calculated fromthemeasured travel time and the distance between transmitter andreceiver. Before testing the ends of the core specimens were pol-ished and covered with grease. Transducers having a frequency of0.5 MHz were used.

Uniaxial compressive strength test was performed according toASTMD2938 standard (ASTMD2938, 2002) with the loading rate of0:7Mpa=s. Fig. 6 shows a view of cores before and after test forAsmari and Jahrum formation.

The deformationwas determined using respective strain gauges.Then, stress-strain curve in order to determination of UCS and ESwas recorded. The modulus of elasticity was derived from the slopof the stress-strain curves by tangent modulus (Et). Et is the slope oftangent line of one point in stress-strain curve. Average modulus(E) is the slope of part of stress-strain curve that is almost straightline. Secant modulus (ES) is the ratio of stress to strain of one pointin stress estrain curve (Chen et al., 2007). Figs. 7 and 8 show thestress-strain curves of the samples 18 and 40, respectively.

The physical tests, such as density (r), porosity (n), water con-tent and water absorption by weight (Wa) were performed ac-cording to ISRM standard (ISRM, 1981). The porosity and waterabsorption by weight of rock samples were determined by satu-ration and buoyancy techniques. All samples were saturated bywater immersion for a period of 48 h with periodic shocks toremove trapped air. The density values were obtained from theratio of the sample mass to the sample volume. The results ofphysical, ultrasonic and uniaxial compressive strength tests on thestudied specimens are shown in Tables 2 and 3 Also, the histogramof the investigated parameters are shown in Figs. 9 and 10. Notethat, the outlier data (six data) were removed from the data list.

Table 2 shows that, the rock samples of the Jahrum limestoneexhibiting wide range of UCS (UCS ¼ 170-28 MPa). This Table alsoshows that the Jahrum limestone involves higher ES than the

the Asmari formation.

Fig. 4. The thin sections of the Jahrum formation.

Table 2Properties of the Jahrum limestone formation.

Statistics Parameters

r( grcm3) n (%) Water

content(%)

UCS(MPa)

Es(GPa)

Ed(GPa)

Wa (%) Vs(Km/s)

Vp(Km/s)

Static Poisson's Ratio Dynamic Poisson's Ratio

Mean 2.17 3.8 2.14 72.90 15.53 39.42 1.57 2.50 4.28 0.25 0.28Std. Error of Mean 0.05 0.4 0.21 6.74 3.01 2.73 0.16 0.11 0.16 0.015 0.019Std. Deviation 0.28 2.05 1.2 35.03 15.66 14.17 0.83 0.55 0.81 0.077 0.097Variance 0.08 4.2 1.45 1226.9 245.14 201 0.68 0.30 0.66 0.006 0.009Range 1 8 4.51 142 78 62 3 2 3 0.25 0.354Minimum 2 1 0.15 28 5 23 0.35 2 3 0.11 0.15Maximum 3 9 4.66 170 84 84 3 4 6 0.353 0.50

Table 3Properties of the Asmari limestone formation.

Statistics Parameters

r

( grcm3)

n (%) Water content (%) UCS(MPa)

Es(GPa)

Ed(GPa)

Wa(%)

Vs(Km/s)

Vp(Km/s)

Static Poisson's Ratio Dynamic Poisson's Ratio

Mean 2.4 9.5 3.92 53.83 9.34 24.1 4.2 1.86 3.43 0.21 0.29Std. Error of Mean 0.02 0.73 0.22 5.27 1.59 2.5 0.32 0.10 0.18 0.003 0.004Std. Deviation 0.12 4.2 1.2 30.27 9.12 14.2 1.83 0.580 1.01 0.015 0.022Variance 0.014 17.7 1.36 916.34 83.22 199.4 3.6 0.34 1.03 0.000 0.000Range 0.44 15.85 4.55 103.55 29.86 48.28 7.60 2.22 3.74 0.08 0.11Minimum 2.13 3 0.96 5.48 0.04 1.69 0.08 0.54 1.22 0.19 0.27Maximum 2.57 18.85 5.51 109.03 29.89 49.97 7.68 2.76 4.96 0.27 0.38

Fig. 5. Ultrasonic testing apparatus for determining of Vp and Vs. Fig. 6. A view of cores before and after uniaxial compressive test.

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e31 25

Fig. 7. Stress-strain curve of the sample number 18 (from Jahrum formation).

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e3126

Asmari limestone. Results demonstrated the Jahrum limestonerocks are stronger in coMParison the Asmari ones. Moreover, thewater absorption, water content and porosity (n) of the Asmarilimestone were higher than the Jahrum one.

Dynamic modulus (Ed) and Poisson coefficient (v) were calcu-lated by using Eqs. (1) and (2) for each specimen (Keary and Brooks,1991; Burger, 1992).

Ed ¼ rVS�3Vp � 4VS

�Vp � VS

(1)

v ¼ Vp � 2VS

2�Vp � VS

� (2)

Where r is the density ( grcm3 ), Vs and Vp are in Km=s, and Ed is in Gpa.

5. Statistical analysis

Several factors were analyzed such as the best-fit line, the 95%confidence limits, adjusted R square, standard error of the estimate(is a measure of the accuracy of predictions), ANOVA results and thecorrelation coefficient (R2) were determined for each regression(Table 4). Results of ANOVA test showed that therewere statisticallysignificant relationships between the independent variables (n, r,Wa, Es, Ed, Vs, Vp) and the dependent variables (UCS, Es, Ed, Vp, Vs)(Table 4). There were also power, linear and exponential relationsbetween dependent variables and independent variables. The cor-relation between water absorption and porosity with dynamic and

mechanical properties was exponential. There was linear relation-ship between density with Vs and Vp. Moreover, the relationshipbetween the static and dynamic parameters was power (Table 4).

As shown in Table 4, the correlation of UCS and Es with waterabsorption by weight (%) are lower than other studied parameters.These conclusions were expecTable because of low water absorp-tion of limestone rocks. Sonmez et al. (2006) and Ocak (2008) haveshown that the static Young's modulus could be estimated fromuniaxial compressive strength and unit weight of material. In thisstudy, correlation between UCS and density (r) with Es wereR2 ¼ 0:851 and R2 ¼ 0:70 , respectively. In addition, the best cor-relation of UCS and Es were related to the Vp and Ed, respectively.

Several researchers (e.g. Vernik et al., 1993; Lashkaripour, 2002)reported that porosity appears to be the best single predictor ofstrength in sedimentary rocks, where the porosity was known, Eqs.(3), (10) and (12) could be used for predicting the UCS, Es and Ed,respectively.

6. Static versus dynamic properties

Static rock properties are measured from cores. Deformation ismeasured on core samples as pressure is applied and dynamicproperties are calculated using sonic wave velocities and densityvalues from well logs.

Dynamic moduli are usually 2 - 10 times larger than staticmoduli (Plona et al., 1995). In this paper, dynamic Young's moduluswas 5 times larger than static Young's modulus and dynamicPoisson's ratio was 1.3 times larger than static Poisson's ratio.

Fig. 8. Stress-strain curve of the sample number 40 (from Asmari formation).

Fig. 9. Histogram of the physical properties and the static and dynamic Poisson ratio.

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e31 27

Because rock properties are both frequency and amplitudedependent, values measured at higher amplitudes in the laboratorycan differ significantly from low amplitude log measurements.

Other suggested possible reasons such as cracks and void space,time effects, stress magnitude, temperature effects, fluid saturationand differences in frequencies used to measure the static and

Fig. 10. Histogram of the static and dynamic parameters.

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e3128

dynamic properties (Fjar et al., 2008; Lama and Vutukuri, 1978).Therefore, the standard industry procedure was used empiricalcorrelations to derive static properties from dynamic properties.

7. Vp e Vs relationships

A good Vs values can be predicted form the empirical relation-ships in similar formations, if all measurement are error free.

In carbonate rocks, prediction of Vs using Vp is most reliableaccording to the laboratory and logging measurements.

Pickett (1963), demonstrated the potential of Vp=Vs as lithologyindicator. They showed that measurements corresponding tolimestone and dolomite were found along lines of constant withdifferent ratios of 1.9 for limestone and 1.8 for dolomite. In currentstudy, this ratio assessed 1.85.

8. Evaluation of previous suggested empirical relations

Fig. 11 shows the plot of predicted Vs, using the relation pro-posed by Castagna and Backus (1993) versusmeasured Vs data fromthis study. Notice that the Vp data for Castagna and Backus (1993)relation were derived from sonic log. As shown, the correlationwas polynomial with high coefficient of determination. Thisempirical relationship shows that there was good relation betweenpredicted Vs and measured Vs. This investigation shows thatCastagna and Backus (1993) equation could be used for predictingthe shear wave velocity based on Vp in limestone rocks of theJahrum and the Asmari formations. The root mean square error(RMSE) and R2 of the Castagna and Backus (1993) equation and theother studied equations were presented in Table 5.

Fig. 12 displays the relationship of the measured and calculatedUCS based on Yasar and Erdogan (2004), and Chang (2004), whichhave been fitted to linear and power regression, respectively. Theaccuracy of Chang (2004) relation was lower than Yasar andErdogan (2004). These empirical relationships showed that therewere good relations between Es and Vp with UCS.

As seen in Table 1, Yasar and Erdogan (2004), Najibi et al. (2015)and Stan-Kłeczek (2016) have presented some empirical relationsfor calculating of the static Young's modulus(Es). This parameterwas calculated based on these empirical relations and correlated

with measured static Young's modulus of this paper. Figs. 13 and 14show the correlations have high coefficients of determination. Thecomparison of suggested correlations showed that the Najibi et al.(2015) relation had the highest accuracy for predicting the staticYoung's modulus. Yasar and Erdogan (2004) and Stan-Kleczek(2016) relations were in the next orders of accuracy, respectivily.Furthermore, Najibi et al. (2015) found that the best correlation ofEs was related to the Ed. This result has confirmed by the result ofpresent paper (see Table 4).

As can be seen in Figs. 11e14 the value of predicted Vs, UCS andEs (based on other researcher's relations) were compared with themeasured data. The following Table shows the root mean squareerror (RMSE) and R-square for each study (Table 5).

As shown in Table 5, the predicted UCS from Yasar and Erdogan(2004) equation is better study and RMSE is 12.13 MPa for eachspecimen. Also, the accuracy of UCS predicted from Chang (2004)equation was lower (RMSE is 17.6 MPa) than Yasar and Erdogan(2004) equation. Yasar and Erdogan (2004) and Chang (2004)equations, predicted the UCS based on the Vp and Es, respectively.Therefore, prediction of UCS from Vp was better than Es.

Table 5 also shows that Es predicted based on Ed had higheraccuracy (RMSE is 3.6 MPa). Similar results were observed in thispaper (see Table 4, equation (9)). Hence, Edwas the best parameterfor predicting of the Es.

9. Conclusion

By performing this study some empirical relationships betweenUCS, Es with water absorption, Ed, Vp and Vs for the Jahrum and theAsmari limestone rocks were established. The correlation of UCSwith ES was also cheeked.

The statistical analysis reveals that the best correlation of UCSand Es was related to the Vp and Ed, respectively.

Regression analysis showed a reliable power correlation be-tween wave velocities, static and dynamic modulus with uniaxialcompressive strength (UCS), which allows a reasonable estimationof the limestone rocks strength. Low correlation of water absorp-tion with UCS and Es was found. The relation between Vs and Vp

showed the high correlation coefficient. There were exponentialrelations and relatively high correlation values between porosity

Table 4Empirical relations for the Jahrum and the Asmari limestone rocks.

EQUATION STD. ERROR OF THE ESTIMATE R SQUARE(R2)

ADJUSTEDR SQUARE

RESULT of ANOVA TEST

F Sig.

UCS ¼ 3:18*Ed (3)0.12 0.97 0.96 1348.62 0

UCS ¼ 108*eð�0:22*WaÞ (4)

0.471 0.47 0.46 46.4 0

UCS ¼ 110:51*eð�0:2*nÞ (5)

0.43 0.55 0.54 70 0

UCS ¼ 0:005*rð10:3Þ (6)

0.34 0.70 0.69 130 0

UCS ¼ 3:73*Vp2:1 (7)

0.091 0.984 0.973 2378.15 0

UCS ¼ 15:41*Vs1:82 (8)

0.131 0.96 0.95 1184 0

ES ¼ 0:022*Ed1:774 (9)

0.39 0.912 0.91 601 0

Es ¼ 4:3*10�8*rð21:2Þ (10)

0.71 0.71 0.70 140 0

Ed ¼ 55:51*eð�0:253*waÞ (11)

0.5 0.514 0.51 59 0

Ed ¼ 64:4*eð�0:134*nÞ (12)

0.35 0.74 0.73 164 0

ES ¼ 27:43*eð�0:45*WaÞ (13)

0.96 0.46 0.451 49.44 0

Es ¼ 38*eð�0:24*nÞ (14)

0.74 0.68 0.675 123 0

ES ¼ 0:070*Vp (15)0.45 0.862 0.85 312 0

ES ¼ 0:82*VS (16)0.48 0.841 0.84 270.1 0

VS ¼ 0:4741*Vp (17)0.056 0.975 0.974 2247 0

VS ¼ 4:99*r� 10:071 (18)0.17 0.931 0.930 780 0

Vp ¼ 7:956*r� 15:642 (19)0.21 0.96 0.96 1364 0

UCS ¼ 20:11*Es (20)0.25 0.853 0.85 301 0

Fig. 11. Correlation between predicted Vs from Castagna and Backus (1993) relationand measured Vs .

Table 5RMSE and R-square of the predicted values.

Predicted UCS (MPa) R2 RMSE

Yasar and Erdogan (2004) 0.94 12.13Chang (2004) 0.92 17.6

Predicted Vs (Km/s)

Castagna and Backus (1993) 0.97 0.21

Predicted Es (GPa)

Yasar and Erdogan (2004) 0.82 12.45Stan-Kłeczek (2016) 0.71 27Najibi et al. (2015) based on Vp 0.94 7.4Najibi et al. (2015) based on Ed 0.96 3.6

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e31 29

Fig. 12. Relationship between measured and predicted UCS based on previous sug-gested relations.

Fig. 13. Correlation between predicted Es based on empirical equations and measuredEs.

Fig. 14. Correlation between measured and calculated Es based on Najibi et al. (2015)relations.

M. Ghafoori et al. / Journal of African Earth Sciences 137 (2018) 22e3130

with static and dynamic properties.The compression between static and dynamic properties of

limestone rocks showed that the dynamic Young's modulus was 5times larger than static Young's modulus and dynamic Poisson'sratio is 1.3 times larger than static one.

Calibration of previous suggested empirical relations of otherresearchers showed that they had acceptable accuracy for theJahrum and the Asmari limestones.

The accuracy of predicted UCS based on previous suggestedrelations were compared using r-square (R2) and RMSE. As, UCSpredicted based on Vp had high accuracy. In this, UCS had the bestcorrelationwith Vp. Hence, the ultrasonic tests were recommendedfor estimation of UCS.

Acknowledgments

The authors would like to acknowledge the support receivedfrom the staffs of “Qods Niru Engineering Company” (QNEC) forproviding necessary data. The authors also wish to thank theanonymous referees for comments and suggestions that improvedthis paper. This research has been supported by a grant number 2/42623 from Faculty of Science, Ferdowsi University of Mashhad, forwhich we express our sincere thanks.

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